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dissertation entitled

ENTERPRISE MODELS FOR THE DESIGN AND MANAGEMENT
OF MANUFACTURING SYSTEMS

presented by
Bruce E. Koenig
has been accepted towards fulfillment

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ENTERPRISE MODELS FOR THE DESIGN AND MANAGEMENT
OF MANUFACTURING SYSTEMS

By

Bruce E. Koenig

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1992

ABSTRACT .

, ENTERPRISE MODELS FOR THE DESIGN AND MANAGEMENT
OF MANUFACTURING SYSTEMS I

By

Bruce E. Koenig

All engineered systems and their products (hereafter, collectively referred to as .
manufacturing systems) are called upon to perform particular technical functions in an
economic system. Economic systems are in reality networks of enterprises (corporate
and/or individual) each of which is engaged in two generic classes of processes: a) the
“real ” physical/biological processes that use energy to transform matter from one
technicallyspecific form to another through the application of human knowledge and the
dissipation of physical energy and skill-specific human time, and b) human-based
cybernetic (information and decision) control processes for which the “real” physical and
biological processes are objects of development and control. This dissertation reports a
theoretical framework and a set of logically consistent models for quantitatively
evaluating the underlying material and energy requirements of manufacturing enterprises
and the products which they produce as a physical system. This framework can be used
to compare trade-offs between monetary performance measures and loads placed on the
natural environment. These methods integrate engineering and economic information
necessary for design and management decisions at various levels of organization of the

enterprise. Because they can provide analysis at multiple levels of enterprise and

economic organization, the models are also ideally suited to environmental “Life-Cycle
Assessment” of the material and energetic loads imposed on the natural environment by
networks of enterprises producing products. Quantitative analysis using these methods
may be readily implemented using computer software. A life-cycle assessment of two
alternative packaging materials is presented, paper and polystyrene. Four alternatives
for disposal are examined; landfill, incineration, electrical power generation and
recycling. For the technologies modeled, a number of surprising results are obtained.
Recycling paper requires similar amounts of petroleum energy as the manufacture of
virgin paper. The lowest petroleum requirements are obtained when waste paper is
burned to generate electrical power, with a higher requirement of forest resources.
Recycling of polystyrene plastics results in substantially lower petroleum requirements
than the other polystyrene disposal alternatives, and lower than that of recycling paper.
Water effluents and air missions, including C02, are lower for recycling polystyrene than

any of the alternatives for products or disposal.

Copyright by
BRUCE EDWARD KOENIG
1992

Dedicated To My Beloved Father And Mother

Herman and Janet Koenig

ACKNOWLEDGEMENTS

This work begins with equations describing material transformations and energetic
costs in physical and biological systems which were developed by my father, Herman
Koenig, and his colleague, R. Lal Tummala, in 1972. Their profound development forms
the basis for this work and provides the opportunity for exciting and vital future work by
many in engineering, economics, agriculture and ecology. I am deeply indebted to my
father for his insight, wisdom and support, and to Lal Tummala for his direction, interest
and assistance in beginning my research career.

I am also grateful for the advice and guidance of my committee members, Hassan
Khalil, Erik Goodman and Lindon Robison. Their interest, criticism and approval

provided valued contributions to the work presented here.

iii

 

9.9mm

TABLE OF CONTENTS

LIST OF TABLES vi
LIST OF FIGURES viii
INTRODUCTION 1
1 ELEMENTAL PHYSICAL AND BIOLOGICAL PROCESSES 6
1.1 Material Processing and the Technical Coefficients of Transformation 6
1.2 The Energetic Costs of Material Processing 8
1 .3 The Processing Environment 11

2 NETWORKS OF ELEMENTAL PHYSICAL AND BIOLOGICAL
PROCESSFS 14
2.1 Continuity and Compatibility Equations 14
2.2 Representation of Open Networks and Multiple Levels of Organization 17
2.3 The Network Processing Environment 21
2.4 Energy Efficiency of the Network 22
2.5 Key Features of the Process Network Model 24
2.6 Comparison with Leontief Representations 26
2.7 Comparison with Economic Production Functions 26

3 ISOMORPIIIC MANAGEMENT INFORMATION AND MANAGEMENT

ACCOUNTING SYSTEMS 28

3.1 Material and Energetic Exchanges of the Enterprise Processing
Network 28
3.2 Monetary Prices and Cash Flow 29
3.3 Value Added and Amortization 30

3.4 Allocation of Processing Environment Costs Between Multiple
Products 32
3.5 Enterprise Performance Measures 34
3.6 Opportunity Sets for Exchange Within an Economy 35
3.7 Design Control 38

3.8 Operations Control 40

iv

4 A LIFE-CYCLE ASSESSMENT IN MANUFACTURING -
PAPER VS. POLYSTYRENE PACKAGING MATERIALS
4.1 Life-Cycle Assessment
4.2 Computation of Process Network Models
4.3 Paper Packaging vs. Polystyrene Packaging As An Example
4.4 Data for Parameters and Variables

5 LIFE-CYCLE ASSESSMENT OF PAPER MANUFACTURING,
USE AND DISPOSAL

5.1 Network Diagram of Paper Manufacturing
5.2 Network Model of Paper Manufacturing
5.3 Enterprise Level Results of Paper Manufacturing
5.4 Network Diagram of Paper Use and Disposal
5.5 Network Model of Paper Manufacturing, Use and Disposal
5.6 Life-cycle Level Results of Paper Manufacturing, Use and Disposal

6 LIFE-CYCLE ASSFSSMENT OF POLYSTYRENE MANUFACTURING,
USE AND DISPOSAL
6.1 Network Diagram of Polystyrene Manufacturing
6.2 Network Model of Polystyrene Manufacturing
6.3 Enterprise Level Results of Polystyrene Manufacturing
6.4 Diagram of Polystyrene Manufacturing, Use and Disposal
6.5 Network Model of Polystyrene Manufacturing, Use and Disposal
6.6 Life-cycle Level Results of Polystyrene Manufacturing, Use and

Disposal

7 LIFE-CYCLE COMPARISON OF PAPER AND POLYSTYRENE
7.1 Disposal and Recycling Alternatives
7.2 Comparison of Resource Requirements
7.3 Comparison of Energy Requirements
7.4 Comparison of Crude Oil Equivalent Energy Use
7.5 Comparison of Carbon Dioxide Emissions
7.6 Comparison of Economic Results

8 CONCLUSIONS AND POLICY IMPLICATIONS FOR THE USE OF
PAPER AND POLYSTYRENE PACKAGING MATERIALS

9 SUGGESTIONS FOR FURTHER RESEARCH
APPENDIX

LIST OF REFERENCES

42
44
50
54
58

61
61
66
75
81
34
93

98
98
101
108
113
115

122
127
127
134
136
139
142
145
147
151
153

165

LIST OF TABLES

Table 1 Paper Manufacturing Coefficients

Table 2 Paper Manufacturing Continuity Matrix

Table 3 Paper Manufacturing Variables

Table 4 Paper Manufacturing Energetic Matrix Fb F0

Table 5 Paper Manufacturing Matrix Xr

Table 6 Paper Manufacturing Prices

Table 7 Paper Manufacturing System Matrices

Table 8 Paper Manufacturing Material Flows

Table 9 Paper Manufacturing System Energetics

Table 10 Paper Manufacturing, Use and Disposal Coefficients
Table 11 Paper Manufacturing, Use, Disposal Continuity Matrix
Table 12 Paper Manufacturing, Use Disposal Variables

Table 13 Paper Manufacturing, Use, Disposal Energetic Matrix Fb F0
Table 14 Paper Manufacturing, Use, Disposal Matrix Xr

Table 15 Paper Manufacturing, Use, Disposal System Matrices
Table 16 Paper Manufacturing, Use, Disposal Material Flows
Table 17 Paper Manufacturing, Use, Disposal System Energetics

Table 18 Polystyrene Manufacturing Coefficients

67

8 $

$

73

78
79
85
88
88
88
92
95
96
97

102

Table 19
Table 20
Table 21
Table 22
Table 23
Table 24
Table 25
Table 26
Table 27
Table 28
Table 29
Table 30
Table 31
Table 32
Table 33
Table 34
Table 35
Table 36
Table 37
Table 38
Table 39

Table 40

Polystyrene Manufacturing Continuity Matrix

Polystyrene Manufacturing Variables

Polystyrene Manufacturing Energetic Matrix Fb F0
Polystyrene Manufacturing Matrix X1.

Polystyrene Manufacturing Prices

Polystyrene Manufacturing System Matrices

Polystyrene Manufacturing Material Flows

Polystyrene Manufacturing System Energetics

Polystyrene Manufacturing, Use and Disposal Coefficients
Polystyrene Manufacturing, Use, Disposal Continuity Matrix
Polystyrene Manufacturing, Use Disposal Variables
Polystyrene Manufacturing, Use, Disposal Energetic Matrix Fb F0
Polystyrene Manufacturing, Use, Disposal Matrix Xr
Polystyrene Manufacturing, Use, Disposal System Matrices
Polystyrene Manufacturing, Use, Disposal Material Flows
Polystyrene Manufacturing, Use, Disposal System Energetics
Resource and Energetic Comparisons on an Equal Mass Basis
Crude Oil Equivalent Comparison on an Equal Mass Basis
Resource and Energetic Comparisons on the Basis of Servings
Crude Oil Equivalent Comparisons on the Basis of Servings
Resource and Energetic Comparisons for Mixed Disposal Options

Crude Oil Equivalent Comparison for Mixed Disposal Options

104
104
104
106
107
110
111
112
116
118
118
118
119
124
125
126
128
129
130
131
132

133

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10

Figure 11

LIST OF FIGURES

Manufacturing Enterprise Processes

Elemental Processes

Life-Cycle Inventory

Network Diagram of Paper Manufacturing

Consolidated Network Diagram of Paper Manufacturing

Network Diagram of Paper Use and Disposal

Consolidated Diagram of Paper Manufacturing, Use and Disposal
Network Diagram of Polystyrene Manufacturing

Consolidated Network Diagram of Polystyrene Manufacturing
Network Diagram of Polystyrene Use and Disposal

Consolidated Diagram of Polystyrene Manufacturing,
Use and Disposal

viii

47
62
76

82

f

109
114

123

INTRODUCTION

The relationships between engineered systems and their performance in the economies
and natural environments within which they function is incompletely or poorly
understood both in theory and practice. Contemporary business and economic sciences
focus primarily on the information and decision processes of the economy (the human
behavioral aspects) with very limited reference to the underlying physical and biological
processes and the material and energy loads they impose on the natural environment. .
Engineering sciences, in general, have not as yet been quantitatively linked to the
economic and ecological levels of organization. The theoretical structure and analytical
tools presented in the following development provide the basis for integrated design,
management and analysis of tradeoffs between economic factors, technical performance
and environmental loads.

In general engineered systems of production can be dichotomized into physical and
biological processes and human cybernetic control processes as shown in Figure 1.
Physical and Biological Processes Models of the engineered system are represented by
networks of physical and biological transformations on the technical state of materials
which take place through specific means of transformation, called the processing
environment, and are driven by physical energy and skill-specific human time.
Technologies appear as parameters in the functional form of the model and the flow rates

of materials, energy, and human time appear as variables.

Enterprise

  

Cybernetic Control Model

  
 

Product
Opportunity Set

Resource
Opportunity Set

 

   

Design Controls:

   

Selection of Exchanges

Selection of
Processing Environment

 
   
 

v

 

4i

  
  
 

--.----‘

  

Operations Controls:

Natural Exchanges Flow Rates

Resources 7 l'

    

 

 

 

 

 

 

 

Residuals 7r

 

  

 

 

 

Resource 7 y Enterprise
Products r 0 Products
Processing Physical
Environment ye F5 (yo ) Energy
Physical - Human Time
["0797 95 Physical and Biological

   

Process Model

 
 

Human Time

Figure 1 Manufacturing Enterprise Processes

3

The processing environment may include specific combinations of automated equipment,
tools, physieal structures, chemical eatalysts, biological organisms, humans with specific
skills, etc. Models of these types were initially reported by Koenig and Tummala [1],
and Tummala and Connor [2].

The Cybernetic Control Model of the manufacturing system, which represent the
human decision and management aspects, can be divided into two parts; Design Control
and Operational Control as discussed by Koenig [3], Koenig and Tummala [4], and
Tummala and Koenig [5].

Design Control (the design phase of the control process) involves two generic control
activities. They are l) the selection of exchanges; i. e. the identification and selection
between alternative opportunities for the physical exchange of materials, energy and
human time with other enterprises and with the natural environment, and 2) the selection
of the processing environment; i. e. the identification, selection and engineering or
implementation of the requisite transformation process and the processing environment.
Design Control utilizes information including but not limited to, market research, basic
research and product development, process engineering, and technological innovation.

Operational Control (the operation phase of the control process) involves the
fulfillment of the objectives of the design control through temporal and/or spatial
distributions of the physical and biological processes. It consists of two generic control
activities; 1) the control of flow rates of material and energy through the selected
transformation processes, and 2) the control of exchanges and the associated relative rates
of exchange (prices) with other enterprises and with the natural environment. Operations

Control utilizes information including but not limited to, purchasing, materials and

4

logistic management, marketing, production level and pricing decisions, and finance,
taxation, employee contracts, personnel relations, environmental regulation and public
relations.

Together the cybernetic control model and the physical and biological process models
provide the framework for an integrated managerial/engineering information, analysis,
and accounting system which is truly isomorphic with the physical material, energy,
equipment and human time factors involved in the production processes, and the design
and operational control decisions of manufacturing enterprises. Furthermore this linkage
provides a basis for evaluating altemative designs and management decisions such as;
0 choices between alternative technologies for production processes,

0 selection of the type and the level of automation, diversity and configurations of
automated equipment and physical facilities,

0 evaluation of the physical material and net energy costs of alternative products and
production processes,

0 evaluation of the skill-specific human time costs of alternative products and
processes,

0 analysis of costs as a function of production rates and scale,

0 analysis of the by—products and environmental residuals produced by alternative
processes,

0 alternative policies for the allocation or amortization of the “fixed” costs of the
processing environment to products and alternative processes-including selection of

appropriate time scales and time horizons.

5
Chapter 1 discusses the general mathematieal description of elemental physical and

biologieal processes upon which the process network is based. Chapter 2 provides the
methods and theory for organizing these elemental process into networks and hierarchical
levels of network organization. Models of the processing environment, that is the
infrastructure or plant where processing takes place, are developed. A number of
measures of energy efficiency of the network are presented, and key features of process
network models and comparisons with other representations are discussed. Chapter 3
extends the physical and biological models of Chapter 2 into monetary and economic
contexts by mapping the process network models into economic variables. These
mappings are isomorphic to the physics and biology of the processes, and thus provide
a unique solution to contemporary issues in business management and engineering design.
The basic classes of decisions which enterprises perform in the context of the models are
discussed.

Chapter 4 introduces an application of the theory to life-cycle assessment and
discusses computation and data for such models. Chapter 5 presents first a process
network model of a paper manufacturing enterprise producing paper from both virgin
materials and recycled materials. Next, analysis at the higher level of organization, the
use and disposal / recycling of used paper, completes the life-cycle assessments for paper
packaging. Chapter 6 repeats the same stages of analysis for polystyrene packaging
materials and their life—cycle. Chapter 7 provides an extensive discussion of the results
of these life-cycle assessments, comparing the two products and four disposal alternatives
for each product; landfill burial, incineration, electric power generation and recycling.

Conclusions and policy implications are presented in Chapter 8.

1 ELEMENTAL PHYSICAL AND BIOLOGICAL PROCESSES

We begin with mathematical representations of the material transformation processes
of the enterprise, beginning initially with a material transformation at the lowest or most

basic level of the processing system, called an elemental process.

1.1 Material Processing and the Technical Coefficients of Transformation

By definition, an elemental process 3 involves a column vector of technically-specific
material resources yrs = {yl, yz, . . . }1.8 and exactly one technieally—specific material yos
which represents the object of the material transformation. As illustrated in the graphical

representation of Figure 2, a closed line is used to represent the boundary of process 3.

boundary

   
   

Primary Resources
1-
2s

Object of Transformation

its 0. 90.

TTTT

Secondary Resources
(a) Production Proceee

Primary Resources
1"8::
23

Secondary Resources

Object of Transformation

ire °' you

(b) Reduction Process

Figure 2 Elemental Processes

A set of directed line segments, called edges {os, 1s, 28, } are used to establish a

directional reference frame relative to the boundary of the process for the flow rates (in

7

units of material per unit time) of the technically-specific object of transformation yos and
the set of technically-specific material resources yrs = bi], yz, }rs .

The flow rates yrs of the technical-specific resources are linearly related to the flow

rate of the object of transformation yos

yrs = rs yos (1'1)
where hrs is a column vector with positive constants km = {1:1, k2, }rs called the
technical coefiicients of transformation.

The bold-face edge in Figure 2 is used to identify the variable which represents the
object of the transformation and which appears as the stimulus (independent) variable in
Eq. (1.1). Thus, the bold-faced edge is said to define stimulus-response orientation for
the mathematical representation of the material transformation process. The orientation
of the line segments in the reference frame of the mapping in Figure 2 are selected to
correspond to the direction of the respective physieal material flows relative to the
boundary of the process. This confines all material flow rates yos and yrs, to the positive
range of the real number system and the stimulus variable (object of the transformation)
yos may be either an output or an input flow rate to the process as shown in Figure 2(a)
and 2(b), respectively.

Reference frame Figure 2(a) is said to correspond to a production process in which
the input resources are called the primary resources since they represent the materials
from which the product is actually structured. The resource outputs, on the other hand,
are called secondary resources or by-products since they represent technically specific
residuals of the process.

Reference frame Figure 2(b) is said to correspond to a reduction process in which the

8

output resources are called the primary resources because they are the consequences of
the reduction of the object material yos in some technically-specific sense. The input
resources on the other hand are called secondary resources or co-resources since they are

essential to decomposition of the object material yes.

1 .2 The Energetic Costs of Material Processing

Any and all material transformations involve energetic resources in the form of skill-
specific human time and! or thennodynamically—speafic physical energy to effect the
transformation. They are endoenergetic if they are be driven by physical energy and/or
skill-specific human time. They are exoenergetic if they generate physical energy and/or
human time in the sense of sustaining human populations biologically and intellectually.

The first step in establishing a minimal mathematical representation of the energetic
properties of the material transformation process s of Figure 2 is to impute an energetic
cost £08 to the object of transformation yos according to the following relation

x0; = - k; X" - no...) (12)

where
1’80“) = {[10, f2(.), }OS is a row vector representing the energetic cost of
transformation,
xrs = {x1, x2, }1.8 is a row vector representing the accumulated energetic costs of
making each technically-specific resource yrs available to the boundary of the process,
er is a matrix composed of row vectors xrs ,
x0s = {x1, x2, }08 is a row vector representing the accumulated energetic costs of

the object of transformation yos,

9

kTrs is the transpose of the vector Itrs given in Eq. (1.1), and represents the weightings
applied to the energetic costs of the resources yrs in imputing an accumulated energetic
cost to the object of transformation.

The components of the energetic cost variables [8005) and x08 have the dimensions
of skill-specific time (person hours) and physical energy (measured in kW hours, units
of fuel, etc.) per unit of technically specific material yrs. A mathematical representation
of the energetic properties of the material transformation process s of Figure 2 is
completed by defining a generalized energy rate variable for each technically-specific

material rate according to the relation

‘0: a yos ’0: (1.3)
an = y” x" rs = rsl, rs2,

which has the dimensions person hours, and physical energy per unit time (hour, day,
month, etc.)

The rate at which generalized energy is produced (or consumed) by process s is
obtained by summing the energy rate em and cos in Eq. (1.3) over the boundary of the

process, thus

é's = éos 4' § érs = yos xos + y: er “-4)
where xos and yrs are given by Eqs. (1.2) and (1.1), respectively. When these
expressions are substituted into Eq. (1.4), all terms vanish except for the term
representing the energy produced or consumed within the boundary of the process.
Thus, the generalized energy produced or consumed by the transformation itself is

e: = ”Yo: 1.30,“) (1'5)
The components of the row vector es in Eq. (1.5) represent the weekly or monthly

10

work force and energy requirements for the process 8 measured in real terms and broken
down by skill categories (engineers, technicians, etc.) and the thermodynamic properties
(heating gas, motor fuel, electrical, etc.), respectively.

Negative values in the energy rate vector represent energy consumption
(endoenergetic process) while positive values represent energy generation (exoenergetic
processes). For example, an electrieal power generating plant as a material (fuel)
decomposition process will be exoenergetic in electrical energy, but endoenergetic in all
other thermodynamically-specific forms of energy, and in skill-specific human time. On
the other hand, a household or urban population center as a materials (food and
household items) decomposition process will be exoenergetic in some skill-specific human
time (labor) but endoenergetic in other skill-specific human time such as medical and
education services and in thermodynamically-specific forms of energy.

It must be emphasized that the energetic cost function [$005) in Eqs. (1.2) and (1.5)
is actually a set of functions all of which, in general, may be nonlinear and often
discontinuous with respect to the processing rate yes and are applicable only for a given
technically specific environment. If the technical features or organizational structures of
the processing environment change significantly, the component of 1;.0’03) will change
accordingly. And this is exactly the purpose of many analyses; to explore the
generalized energy requirements of alternate processing environments, all evaluated in

relationship to variable processing rates, yes.

ll

1 .3 The Processing Environment

Any and all material transformations take place within the context of a technically
specific processing environment, which may also be thought of in industry and agriculture
as the technical means of production or transformation.

Numerical values of the technical coefficients of material transformation in the
column vector kl.8 of Eq. (1.1), and the rate dependent energetic costs of transformation
in the row vector fsoios) of Eq. (1.2), are referred to collectively as the technical
parameters of process 3. Their specific values depend ultimately upon technical features
of the object of transformation (product) and upon the structural and organizational
features of the processing environment (means of production). For this reason the
vectors kl.s and 1’30“) are said to define the technology of the process 3.

Let ycs represent the technically-specific environment of a technically-specific
transformation process yes as represented in Eqs. (1.1) and (1.2). The environment yes
of this process is in itself the object of yet another material transformation process on
another set of technically-specific resources over another time frame. Since the
processing environment ycs must be completed as an object of transformation before it
can serve as a processing environment, it is convenient to refer to the materials, energetic
costs, and energy required to produce the completed processing environment.

Specifically, let ycs represent the technically-specific processing environments
required to produce a given flow rate of a technically-specific objects of transformation
yes per unit time. The material resources required to construct the technically-specific

environment ycs is

yrs " kc: yes (1'6)

12

where 1:08 is a column vector representing the technical material composition of the
processing environment. It follows that energetic resources required to engineer and
construct the processing environment are given by
x“ ' 'ka xrs 'fcso'cs) (1'7)
where [68068) is a row vector representing the skill-specific labor time and
thermodynamically-specific energy required to engineer and construct the processing
environment, and xcs represents their accumulated energetic costs, all measured in real
terms.
The generalized energy dissipated in the engineering and construction of the
processing environment, measured in real terms is
‘cs ' " yes feso'cs) (1'8)
where the components of the row vector ecs represent the skill-specific human time

(person hours) and technically specific physical energy (kWh), measured in real terms,

required to construct (reconstruct) the processing environment yes.
Note that:

a) the accounting time frames for the material resources yrs and the technical cost x0s
of the object of transformation yes are based on rates of materials and energy per
unit time,

b) the accounting time frame for the materials yrs and technical cost xcs of the
processing environment, yes, is based on the engineering and construction time,

c) construction must be completed before the time frame for transformation of yes can
begin.

Thus, there is no physical basis or principle for reconciling these differences in time

13

frames. The choice of how to allocate or amortize the accumulated technical cost cos of
constructing the processing environment ycs to the transformation yes is strictly a human
cybernetic control decision of the enterprise, and the rules of the social/political system
that the enterprise functions in.

If the technical features of the object of transformation (product) and/or the primary
resources are changed significantly, the components of kl.s will change accordingly. The
components of [8008) may or may not change, depending upon the degree of flexibility
designed into the processing environment (the means of production). However, in
general there may be many specific processing environments that might be engineered
to support a given transformation process. The technical features and organizational

structure of the process environment determine the specific components of £9909)-

2 NETWORKS OF ELEMENTAL PHYSICAL AND BIOLOGICAL PROCESSES

We turn now to mathematical representations of networks of transformation
processes, focusing on a mathematical representation of the physical interconnections
between the elemental processes as discussed above. This discussion follows that in

Koenig and Tummala [4]. For additional discussion the reader is referred to [l], [2] and

[3].

2.1 Continuity and Compatibility Equations

By definition, a process network S consists of two or more processes that are
interconnected such that the objective yo, of one material transformation process serves
as a resource to one or more other processes or vice-versa. A directional reference
frame for the flow of technically-specific materials between processes is obtained
operationally by interconnecting the edges in the reference frames of the elemental
processes in Figure 2 above. The set of interconnected edges is ealled a graph of the
network 8.

The bold-faced edges of a graph are called branches because each edge is associated
with a unique elemental subprocess or branch process os in the overall network S. The
remaining edges of are called links because they show how the process identified by
branch os is connected (linked) to the resources of other processes in the network. An
edge in the graph that does not share its end-point with at least one other edge is called

a boundary edge. The set of all boundary edges is called the boundary of the network S.

14

15
In general, the continuity equation at vertex s refers to a technieally—specific material

rate yes and can be written in the general form
yos = a, y I (2.1)
where yos is a scalar representing the technically specific material flow rate of branch
os, y, is a column vector representing the material flow rates of the links in the network,
and where as = {028,1} is a row vector with entries
1 if link I is incident to vertex 3 with orientation opposite to branch os
as, I = -1 if link I is incident to vertex 3 with orientation the same as that of branch cs
0 if link I is not incident to vertex 8.
The row vector as is referred to as the material continuity vector for vertex s. The
matrix A = {as} contains a row for each vertex 3 and is called the material continuity
matrix for the network S of elemental processes. In contrast to the mathematical
representation of the material transformation process given in Eq. (1.1), yos appears as
the dependent variable in the continuity equation Eq. (2.1).
The continuity equation for the entire network is
9b = A it (2.2)
where yb is a column vector representing the branches in the network S and y, is a
column vector representing the links in S.

By definition, a path in network S of elemental process is a subset of edges that: a)
connect the boundaries of two processes, and b) contains exactly one branch and one
link. Each of the links incident to the vertex 3 of branch yos defines a path in the
network. The orientation of a path is defined by the orientation of the branch 08

included in it. The energetic costs associated with a path of edges in a network S of

16

elemental processes are said to be compatible, if and only if, their oriented sum vanishes.
The compatibility equations can be written in the general form
x, = B, X o (23)
where x l is a row vector representing the energetic costs of link I of the network, X0 is
a matrix whose rows represent the energetic costs of the branches in the network, and
BI = {31,3} is a row vector with entries
1 if branch 03 is in the path defined by link I with orientation opposite to 1
31’s = -1 if branch os is in the path defined by link I with the same orientation as l
0 ifbranch os is not in the path defined by link I

The row vector 3, is referred to as the energetic cost compatibility vector, for link
I. The matrix B = {5,} contains a row for each link I and is called the compatibility
matrix for a network S of elemental processes. In contrast to the mathematical
representation of the energetic costs given in Eq. (1.2), x08 appears as the independent
variable in the energetic cost compatibility equation Eq. (2.3).

The compatibility equation for the entire network is

X l = B X b (2.4)

where the Xb represent the energetic costs of the branches in the network S, and where
rows of X I represent the energetic costs of the resource links.

One of the fundamental properties of linear graphs of central interest in processing
networks is that material continuity matrix A and the energetic costs compatibility matrix
B are orthogonal, i. e.

A+BT=0 or A=-BT or 3:.AT (2.5)
The implication of Eq. (2.5) is that the inner product 13 of the material rates and

l7

energetic costs vanish identically at each vertex 3 in the network. Indeed, consider

7, = r} x. + y,’ x, (2.6)
Substituting Eqs. (2. 1) and (2.3) into Eq. (2.6) gives

7,=y,TATXb+y,TBXb=o forB=-—AT (2-7)

Since Eq. (2.2) is isomorphic to the graph of the network it is appropriately referred

to as a mathematical representation of the technical structure of the processing network
and the matrix A as the interconnection matrix of the network. The graphs then are
expedients or tools for establishing the interconnection matrix A and identifying and
coordinating the choice of dependent and independent variables in the mathematical

representation of the network S.

2.2 Representation of Open Networks and Multiple Levels of Organization

A network S of elemental processes is said to be materially open (to its material
environment), if and only if, the boundary of S includes a non-empty set of technically
specific resources y, and a non-empty set of technically-specific objects of transformation
yo. The objective here is to determine the boundary and the processes included in the
system.

In the case of an individual enterprise the boundary can be viewed as circumscribing
all branch processes over which management has direct control both with regard to their
technical design and their technical operation. In this context, the boundary flow rates
represent material exchanges with other enterprises and/or the physical and biological
processes of the material environment. Alternatively, the boundary can be viewed as

circumscribing only a sub-network of processes over which management has direct

18

control; in which case some of the boundary flow rates might represent material
exchanges between operating divisions of the enterprise. In the case of Product Life-
Cycle Assessment [5] the boundary of the system might represent exchanges with the
natural environment of both raw materials and the disposal of residuals or wastes.

The objective of the following development is to derive the representation of a
network of transformation processes from the representation of the component elemental
processes of the network and the specific manner in which they are technically
interconnected, so that the technical parameters of the former can be evaluated from the
technical parameters of the latter. This procedure may be continued throughout levels
of organization, thereby aggregating lower level networks into higher level networks for
the purposes of analysis and design.

The continuity and compatibility equations for the network of processes internal to the
boundary of S were given as Eqs. (2.2) and (2.4), where the components of vector yb
and the matrix Xb are isomorphic to the branches internal to the boundary of S, and the
components vector y, and matrix X l are isomorphic to the links internal to the boundary
of S.

Let the elemental transformation processes in the network S as given in Eqs. (1 . 1)

and (1.2) be compiled into partitioned matrix forms

it = K11: ‘10 Yr (2.8)
yr Krb Km .90

19
and

p -

T T
X T T X F
a 3,0 Km‘ , .0.)
where the components of vector yo and the matrix X0 are isomorphic to branches on the

 

 

boundary of the network S, and the components of vector y, and the matrix Xr are
isomorphic to links on the boundary of S. Coefficient matrices [Klb K10] represent the
technical coefficients of transformation between the objects of transformation yb and yo
and the resources y, within the boundary. Matrix FbG‘b) and F000) represent,
respectively, the energetic costs 1;on for elementary branch processes within and, on
the boundary of S, as compiled from Eq. (1.2).

The minimal representation of a network S at its boundary is obtained from the
simultaneous solution of Eqs. (2.2) and (2.8), and Eqs. (2.4) and (2.9). Specifically,
substituting the expression for y, in Eq. (2.8) into Eq. (2.2) and solving for the internal
processing rates gives

where

Kb = (I - A Rap-1A K10 (2-11)
is called the process schedule matrix because it gives the transformation (production)
schedules yb of the internal branch processes, as an explicit function of the
transformation schedule yo on the boundary of the network, i.e. the branch rate schedules
as a function of the “master” schedule. The external resources required to support the

processing network is obtained by substituting Eq. (2.10) into Eq. (2.8). The result is

20
y, = KS yo (2.12)
where
KS = Kr), K, + Km (2.13)
represents the technical coefficients of transformation for the network, (from resources
to object of transformation) as computed from the technical coefficients of transformation
of the branch processes of the network S and the interconnection matrix A.
Substituting X l in Eq. (2.4) into Eq. (2.9) and solving for Xb gives
X1, = - (I - KgAT)"l K; X, - (I - Kgxrfl 150,) (2.14)
Substituting Eq. (2.14) into Eq. (2.9) gives the energetic cost Xo of delivering the final
objects of transformation (products) yo to the boundary of the network. The result is

r
x, = -KS x, - F300) (2.15)
where

F30.) = K,’ Fm) + Foo.) (116)
is a matrix whose rows represent the unit energetic costs of transformation for the
boundary objects of transformation yo as computed from the technical parameters of the
branch processes of the network S and the interconnection matrix A. Since the argument
yb of FbUb) is a parametric function of yo as given by Eq. (2.10), the unit energetic
costs of transformation are computable as an explicit function of the boundary flow rates
yo. Further, the unit energetic costs of transformation F500) for the network S is a
weighted combination of the energetic costs of the elemental branch processes FbO‘b);
the weighting matrix being the transpose of the process schedule matrix in Eq. (2. 10).

The generalized energy es produced or consumed per unit of time by the network

itself is easily shown to be

21

T
is = ‘30 1’50») (2'17)
The vectors K S and F500) define the technology of the network S .

It has been established that;
(a) the minimal mathematical representation of a network S of elemental processes at its
boundary is invariant in analytical form from the component elemental processes 3,
(b) the technology of the network S as represented by the transformation matrix K5 in
Eq. (2.11) and F500) in Eq. (3.16) are computable as linear combinations of the
technologies of the component elemental processes 8, as represented by Itrs in Eq.
(1.1) and £006) in Eq. (1.5), and their technical mode of interaction as represented

by the connection matrix A.

2.3 The Network Processing Environment

We now consider the processing environment for the network S of elemental
processes 8. In section 1.3 above, Eqs. (1.6) and (1.7) describe the material resources
and energetic costs required to construct the processing environment yes for an elemental
transformation process yos. The processing environment for the network as a whole is
composed of the collection of these processing environments yes, such as machines,
materials handling equipment, reaction vessels, etc. for all processes within the boundary
of the network. In addition there will normally be some components of the network
processing environment which cannot be identified with an individual elemental
processes, but are essential for the operation of the processing network as a whole.
Examples might include buildings, lighting, heating, etc. By definition all components

of the network processing environment are constructed external to the boundary of the

22

network, and construction must be completed before processing can begin. Compiling
Eqs. (1.6) and (1.8) for each and all of the components of the network processing
environment into matrices gives the representation of the material resources yr and

energetic costs Xc required to provide the processing environment yc
y ,. = Kc y c (2.18)

x, = -ch x, - Fem) (2.19)
The inclusion of the material requirements for the processing environment and

energetic costs in the model of the processing network is fundamental to the analysis of
alternative product and process designs. For many types of technologically advanced

products and/or automated production environments, the material requirements and I
energetic costs of the processing environment may greatly exceed the materials and
energetic costs of the processing itself. And in cases such as electrical power generation,
the physical endoenergetic costs of the processing environment may total 25 96 or more

of the exoenergetic energy generated over the life of the facility.

2.4 Energy Efficiency of the Network

The process network model provides variables and a number of useful definitions and
mechanisms for comparing the energy efficiency of alternative networks of processes and
the production of products.

The elements of the matrix F300) have dimensions of units of physical energy / unit
of material, e. g. kWh/kg material, labor hours/kg material, etc. Thus, efficiency as
energetic costs of transformation per unit material are given by F300) for each object

of transformation yo.

23

The elements of the matrix Xo also have dimensions of units of physical energy / unit
of material. Xo includes both the energetic costs of transformation within the boundary
of the network and the energetic costs of bringing materials yr to the boundary of the
system. So X0 represents efficiency as total energetic costs per unit material, such as
may be used in a life-cycle assessment.

Another measure of energy efficiency may be defined as the energetic costs per unit
time. The transformation energy per unit time is given by Eq. (2.17)

is 3 "jar F300) (2'17)
where rs is a row vector with elements representing each energetic form. The total

energy per unit time for each of the energetic forms is similarly given by

éo 3 jar X0 (2.20)

The energy required for production of a given vector of materials yo is given for the
network of processes by
_ T (2.21)
‘S ’ 1’0 F S (5'0)
and the total energy including the energy costs brought to the boundary of the network
is given by

T
e0 3 yo X0 (2.22)

The energy required for operation of the network over a given time period to s t s tf

is

24

es s [g 40’ F500) dr (2.23)

and the total energy for operation over a time period is

co = L’f y} x, .11 (2.24)
0

The life span of the processing environment, ye may be defined by the number of
units of product(s) produced yo or by a given time interval to s t S tf. The energy
required to produce the processing environment is given as X6 in Eq. (2.19). So the total
energy soc required to produce a given number of products during the life of the
processing environment may be defined as

e“ = y: X0 4» ycT Xe 035}
And the energy required to operate the processing environment over a temporal life span

of the processing environment may be defined as

ex = jt’f jar X0 d1 + y! Xe (2.26)
0

2.5 Key Features of the Process Network Model
The key features of the process network model of physical and biological processes

are:

0 All variables can be measured in physical and biological units and the process
network model is dimensionally consistent in these real units as well as in monetary
units if and when prices are associated with the real units.

0 The observables of the system are of two distinct classes; a) the technically-specific

25
materials .71- and yo which are physically conserved through transformations and b)

the thermodynamically-specific physical energy and skill-specific human time eS
which are physically dissipated in the transformation processes. This is an essential
distinction first noted by Koenig and Tummala [l].

The technically-specific materials are of three distinct subclasses; y, which are
components of the objects of transformation (products) yo, and ye which constitute
the technically-specific processing environment utilized to produce or reduce objects
of transformation, Koenig [3] and Koenig and Tummala [4]. The processing
environment may include specific combinations of automated equipment, tools,
physical structures, chemical catalysts, animals and other biological organisms,
humans with specific skills, etc.

The technologies employed in the transformation processes (the production
technologies) appear as the parameters KS, Kb and F5 in the equations of
transformation.

The system variables and the mathematical structure of the model are invariant and
are conceptually and analytically consistent across boundaries of exchange, and across
boundaries of partitionings and levels of aggregation within the enterprise and the
economy. The technological parameters Ks, Kb and F8 at any given level of
organization are computable from lower level parameters. These properties are
necessary and sufficient for projecting the technical and economic analysis of
alternative product designs and alternative product production processes into higher
levels of organization both within the enterprise and within an economy, and they

provide an analytical basis for product Life-Cycle Assessments.

26

0 All exchanges of materials, physical energy, and human time are accounted for in the
model, whether or not they have monetary values associated with them. This feature
provides the capability to analyze the flows of environmental residuals and the effects
of regulatory restrictions on the material flows of enterprises and networks of

enterprises in an economy.

2.6 Comparison with Leontief Representations

It is essential to note that the process network models presented here are distinctly
different from the mathematical representations of production processes employed in
economic analysis. Input-Output models of the Leontief type [6] and [‘7] are in some
respects mathematically similar to Eq. (2.12). However they make no distinction in the
definition of observable variables between the fundamental physical properties of material
flows (which are inherently conserved in the network of physical and biological
transformations) and physical energy and human time (which are inherently dissipated
or generated) in the transformation processes. This distinction is essential for both the
integrity of the physical representation of the processes and the isomorphism of
management information and accounting systems to the underlying technology and

physical and biological processes.

2.7 Comparison with Economic Production Functions
Contemporary economic theory and econometric modeling rely heavily on the
Generalized Cobb-Douglas production function, yj = II Yij exp(kij), i=1,2,..., as a

representation of the material and labor requirements of transformation processes, Varian

27
[8]. In fact, these families of production functions are equivalent to optimized Leontief

coefficients, El-Hodiri and F. Nourzad [9].

A wide variety of production functions have been developed around the general
representation given by Wicksteed in 1894, yo = f ( ya, ya, . . . ). Like the Cobb-
Douglas production function, these representations choose the resources as independent
variables, with the product as the dependent variable, Henderson [10]. This is exactly
opposite to the choice of variables in process network theory. Coneeptually it seems far
more logical from both an engineering and an economic perspective to choose the
product yo as the independent variable -- the decisions and objectives of the
manufacturing enterprise are oriented towards choosing and producing products, rather
than arbitrarily combining resources.

Most variants of these production functions are taken by construction to be twice
differentiable so that optimization can be performed with straightforward calculus. In
fact, the physical based energy functions fsoios) in process network theory will in general
be discontinuous and only locally differentiable at best. This is not a matter of
construction, but rather the nature of the physical and biological processes they
represent. Most importantly, in contemporary economic production functions, the
essential distinction between the conservative nature of material flows and the dissipative
nature of physical energy and human time is lost and the representation is not isomorphic

to the underlying physical and biological processes.

3 ISOMORPHIC MANAGEMENT INFORMATION AND MANAGEMENT
ACCOUNTING SYSTEMS

The description variables, technologies, network structure and multiple levels of
organization presented in Chapter 2 provide physical and biological models of the
material flows and energetic costs of the manufacturing system. These models can in
turn be mapped into monetary variables which may be used in design, management and
evaluation of the enterprise’s performance. This combination of process models and
mapping into monetary variables provides an isomorphic management information and

accounting system.

3.1 Material and Energetic Exchanges of the Enterprise Processing Network
In this physical and biological model of the process network, any and all enterprises

engage in four classes of exchanges of technically-specific materials, physical energy and

human time with the process networks of other enterprises in the economy and with

natural systems of the environment.

1) Exchanges of resources yr with other enterprises and the environment.

2) Exchanges of objects of transformation (products) yo with other enterprises and the
environment.

3) Exchanges of physical energy and skill-specific human time f0 with other enterprises
and/or utilization of the natural environment.

4) Acquisition of the processing environment yc from other enterprises.

These exchanges take place for all material flows and energetic costs across the boundary

of the network, whether or not there are monetary prices associated with the exchanges.

28

29
Some enterprise exchanges may take place as battered transactions, some may be

constrained by regulation, such as air emissions or water effluents, some may have prices

in the form of taxation, and of course some may be market exchanges with monetary

prices.

3.2 Monetary Prices and Cash Flow

Consider now a set of price vectors associated with the materials and energetic costs
at the boundary of the process network. These prices may be defined in monetary units,
or they may be defined as ratios of exchange between physical quantities of materials,
energy, and/or human time as the purposes of analysis dictate. The process network.
model is mapped into economic performance by assigning price vectors to the material
resources, products, byproducts, and the various forms of energy at the boundary of the
network as follows:

pr - a price vector for the resource materials and byproducts yr crossing the boundary

p0 - a price vector for the object(s) of transformation (products) yo crossing the

boundary

pe - a price vector for the energetic costs of transformation F5 and X0 - the

technically-specific physical energy and skill-specific human time utilized by the

network

pc - a price vector for the processing environment yc

With reference to monetary prices, if in Eq. (2.15) the energetic costs X, of the
materials y, brought to the boundary of the system are known, cash flow (exclusive of

processing environment costs) for the enterprise can be defined as a scalar vs

30
. T 1'
vs = r. p. + r. m. <11)
If the energetic costs X, are not lmown in real terms at the boundary of the system, i. e.
if only the energetic costs of transformation F's are known, the cash flow (exclusive of
the processing environment costs) for the enterprise can be defined as

. T T 1'
VS = yo p0 - yr pr - ’0 F800) pg (3.2)
which is equivalent to

is = r." p. - r,’ K! p, - r,’ 1750,) p, (3.3)

3.3 Value Added and Amortization

As discussed in section 1.3 above, there is no physical basis for assigning the
material requirements and energetic costs of engineering and constructing the processing
environment to the objects of transformation yo. This allocation or amortization is a
control decision of the enterprise and the social/ political rules of the economy in which
the enterprise functions. Let gs be a scalar valued function in monetary units, which
incorporates these enterprise management control decisions and the economy’s rules for
the amortization of the costs of the processing environment

as - gs(rc.pc.Xc,pe,ro.Fs(ro)no.tf) (3.4)

where the arguments of gs represent the processing environment yo, the price of the
processing environment pc, the energetic costs of engineering and constructing the
processing environment Xc, the price of energetic resources pe, the rate of production
yo, the energetic costs of the transformation FS( - ), and the beginning and ending time
of the amortization to, If.

There are three special cases of the general amortization function gs:

1)

2)

3)

31
gS(Xc, pe, yo) and gsoc, pc, yo) corresponding to the case where the cost of the

processing environment is allocated as a linear or nonlinear function of the processing
rate yo, as may sometimes be the case for manufacturing equipment.

gs(Xc, pe, 17300)) and gso'c, pc, F300» corresponding to the case where the cost
of the processing environment is allocated as a linear or nonlinear function of the
energetic costs of processing F300), as may be the case in electrical power plant
operations where the costs of the processing environment are amortized over the
production of exoenergetic energy.

gs(Xc, pe, to, tf) and gso'c, pc, to, tf) correspond to the case where the cost of the
processing environment is allocated as a linear or nonlinear function of the time
interval t0 to tf. An example might be the amortization of the costs of a building
over time, or amortization according to discount rate.

With the amortization function gs, a value added (profit) function for the enterprise

may now be defined as

r r r
vs = r, pa - r, p, - y, 175(90):), - 85 (35)

The price vectors in the value added function may be taken as functions of time p,(to,tf),

po(to,tf), pe(to,tf), pc(to,tf). They may also be taken as expectational or stochastic

variables with stationary or non-stationary probability distribution functions.

The choice of the function gs is a complex matter, but crucial to the economic

performance and technical design of the enterprise. The process network model with the

general amortization function gs can in principle incorporate any and all economic,

accounting and management rules for the allocation of fixed or indirect costs.

32

3.4 Allocation of Processing Environment Costs Between Multiple Products

An important contemporary controversy surrounding amortization of capital
(processing environment) costs is discussed by Kaplan in a 1989 article in Science,
”Management Accounting for Advanced Technological Environments“ [11]. “Flexible
manufacturing“ refers to a production plant producing a variety of products with a variety
of equipment, which may be arranged in a network of ”work cells”, Sethi [12]. In [11]
Kaplan discusses a representative example of a manufacturing plant engineered and
operated by the Siemens company, which produces a variety of electrical motors, some
of which are quite specialized and many of which are high volume standard items. The
problem becomes how to allocate the fixed and indirect costs of capital (the processing
environment) to individual products in pricing and management decisions. Previously
there has not been a systematic or scientific way to perform these allocations, often
resulting in unprofitable cross subsidies between products.

Process network theory provides a straightforward and scientific way to allocate the
amortized costs of individual processes to end products. Suppose that an amortization
function, scalar valued in monetary units, gs has been chosen for each individual
elemental process in the network where the general arguments of gs are as above

8, - s,(yc.pc.Xe.p¢.yo.f,(yo).to.tf) (3-6)
As in the case of the energetic cost functions, fsoios), the functions gs(°) may be
compiled into column vectors, 8b of the amortization functions, with one element for
each branch processes within the boundary of the network. And let g0 be a column
vector of the amortization functions for the processes on the boundary of the network.

Recall that the material flow rates within the boundary of the network yb are related

33
to the flow rates crossing the boundary yo by the schedule matrix Kb.

yb = Kb yo (2.10)
Also recall that the energetic costs for the network are related to the energetic costs of
the internal and boundary processes by the relation
T .
F50.) = K, not) + no.) (246)
In a like manner, the amortization functions 3b and g0 can be logically related to allocate
the individual process to the final products yo,
T
83 = Kb gb + go (3-7)
where gs now has dimensions of units money/ unit product for each of the products of
yo. Now the value added function in Eq. (3.5), (which is again scalar valued) takes the
form
T T T t
vs = y, en - y, p, - y, F500) p, - y, 83 (3'8)
To complete the analysis and to solve the dilemma posed by Kaplan, consider the
cash flow and value added for each individual product in the (column) vector of products
yo. Let is be a row vector, in monetary units, whose components represent the cash
flow for each of the products. Also, let * designate the outer product of vector

multiplication. The cash flow vector for the vector of individual products is then

. T T T .
vs = Yo *pa -yr *pr -y0 FS(yo)*p¢

The value added for the individual products is represented by the vector ’8 where

(3.9)

T T 1' ,
vs = ’0 amp.) " y, *p, - yo 17500)”), - yoegs (3.10)
The ability to scientifically allocate both the variable material and energy costs, and the

fixed processing environment costs between multiple products is an extremely important

development. Such a theory for allocation of fixed costs between multiple products does

34
not seem to be available in the literature, Kaplan [11] and [13], Fogarty [14], Orlicky

[15], Browne [16].

3.5 Enterprise Performance Measures
From the derivation of cash flow and value added performance measures in the
sections above, other enterprise performance measures follow directly. If return on

assets (ROA) is defined as cash flow / net asset value then

is
ROA = r (3.11)

yc pc -88

 

If return on investment (R01) is defined as net value added (profit) / initial investment

then

VS
ye pc

ROI =

 

(3.12)

These cash flow, value added, amortization, RCA and ROI functions provide
consistent and scientifically based mappings of the technical performance of the
manufacturing enterprise into economic performance. Unlike the problems arising from
contemporary management and financial accounting systems described by Johnson and
Kaplan [17], these mappings are isomorphic to the underlying resource and product flows
and energetic costs of physical energy and human time. In addition they provide a

systematic and logical method for allocating fixed and indirect costs between multiple

products.

35

3.6 Opportunity Sets for Exchange Within an Economy

Within an economy let the collection of technically-specific materials and energy be

the identified as the naturally feasible opportunity set, N 0,3,, ,yc,es} , for exchanges

between enterprises and between enterprises and the environment. Six subsets of the

feasible opportunity set N may be defined:

1)

2)

3)

4)

Information (knowledge) of the exchange opportunities in the feasible set may be
limited or bounded. The opportunity set of which a given enterprise j has
information is the information opportunity set, I- Uri-90,3238}: I,- E N, and may in
general be unique to the enterprise or may be common to a group or collection of
enterprises. The information opportunity set for the social/political processes is
I E N.

Social/political processes may bound or constrain the exchange opportunities available
to enterprises. The permissible (legal) opportunity set for the economy is defined as
L U,JoJc,eS}, L E I. The permissible opportunity set for a enterprise j,
Lj 0,303,335}, LJ- 9 L, may in general be unique to the enterprise or may be
common to a group or collection of enterprises.

Enterprises may bound or constrain the opportunities for exchange they offer to other
enterprises. The tendered opportunity set of exchanges offered by enterprise j to
enterprise k, Tjk U,,j’o,yc,és}, le, S lj, k = 1,2,...,n, k¢j, specifies the
enterprise to which the exchanges are offered and may in general be unique to the
enterprise or may be common to a group or collection of enterprises.

The available opportunity set offered to enterprise j by a enterprise k is

Ajk 0,3030%} = Tkj- The available opportunity set offered to enterprise j by all

36

enterprises k is Aj {9,3030%} =T 1] U sz U U Tkj’ kaéj.

5) The exchange opportunity set for an enterprise j with a enterprise k is
Ojk U,JOJc,eS} = Li n Ajk- Similarly, the exchange opportunity set for
enterprise j with all enterprises k is Oj {$303633} = L, n Aj.

Permissible and tendered opportunity sets for exchange either explicitly or implicitly
include utilization rights that may take on a wide variety of forms. Some natural
materials and products may be inherently indivisible by the nature of the specific
technical characteristics. The atmosphere is an example. In principle both the divisible
and indivisible utilization rights associated with a particular resource, product, or
technical form of energy become part of the bounds or constraints imposed by.
social/political processes in the case of permissible opportunity sets and by enterprises
in the case of tendered opportunity sets.

6) Exchanges between enterprises k in an economy are represented at a strictly physical
level by the selected exchanges between an enterprise j and an enterprise k,
Ejk 0,3030%} 9 Ojk n %, and the selected exchanges between an enterprise
j and all enterprises, Ej {9,3030%} = Ejl U Ejz U U E11,, k¢j.

Key features of this definition of opportunity sets and exchanges are:

0 All exchanges of materials and energy are accounted for in the representation,
whether or not monetary prices are associated with them.

0 The exchanges in the economy are dimensionally consistent, units and rates of
materials, energy, time, and prices are compatible throughout the representation.

0 The selection of the opportunity sets for permissible exchanges L, tendered exchanges

Tjk’ and exchanges E,- are independent, reflecting group and individual preferences

37

and control behavior.

Exchange opportunity set Ojk gives an explicit representation of how the
opportunities for an enterprise j are dependent on the information and behavior of
social/political processes I and L, other enterprises 1!: and Tjkr and its own
information Ij.

All preferences and control behaviors of enterprises and social/political processes
ultimately effect the system through selected real exchanges Fj of technically-specific
materials and energy between enterprises.

It explicitly shows how the structure of the economy is determined by the exchanges
Ej selected by enterprises, including the selection of the means of transformation

(technology) yc.

38
3.7 Design Control

The application of the enterprise’s cybernetic control activities to the enterprise’s
physical and biological process network model forms the basis for the design and
management of the overall enterprise. The enterprise’s cybernetic control process is
divided into two subclasses as illustrated in Figure 1 above. They are; Design Control
(the design phase of the control process) and Operational Control (the operation phase
of the control process). The objective of this paradigm is to illustrate how physical and
biological process network models can be used to meet the overall objectives of the
enterprise - be they economic competition, energy efficiency, environmental
compatibility, etc.

Design Control at the enterprise level involves two generic control activities:

1) Selection of Exchanges; the identification and selection between alternative
opportunities for the physical exchange of materials, energy and human time with other
enterprises and with the natural environment. As shown in Figure l, the enterprise’s
initial and fundamental design activity is to identify the resources y,, physical energy and
skill-specific human time as that are available to it, and the opportunities to transform
those into products yo (or physical energy es in the case of exoenergetic energy
generation, and skill-specific human time es in the case of an enterprise producing
“services”).

This phase includes analysis of; what products are technologically feasible, the
material and energy requirements of those products, the prices and quantities (exchange
rates) associated with resources, energy and products during a selected time horizon, and

any regulatory constraints that may be placed on the utilization of materials and energy.

39

Using the multi-level analysis of the process network described above, the enterprise may
evaluate the exchange opportunities for divisions of the enterprise, for the enterprise as
a whole, or for the enterprise’s activities as part of an industry. By applying process
network models to Life-cycle Analysis as illustrated in the following section, the
enterprise may analyze its role and opportunities in the context of the network model of
the entire cycle of products from raw materials and energy, through disposal or discharge
of materials to the natural environment.

2) Selection of Processing Environment; the identification, selection and engineering
or implementation of the requisite transformation process and the processing
environment. The selection of the processing environment yc typically may involve the
evaluation of known technologies, basic and applied research into new technologies,
engineering of elemental processes, the engineering of the processing network, analysis
of prices of alternative processing environments, decisions about amortization of the
processing environment costs, and evaluation of the material and energy efficiency of
producing products with the alternative processing environments. In process network
models the production environment technologies are described by the parameters of Ks
and F3. Thus alternative processing technologies may be evaluated through the modeling
and comparison of their process networks.

Normally the selection of the exchanges and selection of the processing environment
may be simultaneous activities. As discussed by Kaplan [l 1], financial accounting and
management accounting systems currently in use do not incorporate a representation of
production processes for purposes of design and engineering decisions. Utilizing models

of the process network during the design control activities provide a management

40

information and management accounting system which is isomorphic to the underlying
physical and biological transformation processes and exchange opportunities of the
enterprise and incorporates complete information about the parameters of the technology
Ks and F3 and the variables y,, yo, es and ye. Bacon and Butler [18] discuss several

aspects of the design control activities.

3.8 Operations Control

Operations Control activities of the enterprise involve the fulfillment of the objectives
of the design control through temporal and/or spatial distributions of the physical and
biological processes and consist of two generic control activities:
1) Control of Flow Rates, the control of material and energy flow rates through the
selected transformation processes. There are four general classes of control of flow rates
that can arise in the context of the process network model.
Control of production rates yo with;

a) prices po, 1),, and/or pe serving as control signals,

b) stocks (inventories) of yo and/or y, serving as control signals,

c) exchange opportunities serving as control signals,

d) the flow rate yo itself serving as a control signal.
2) Control of Exchanges, the control of exchanges and the associated relative rates of
exchange (prices) with other enterprises and with the natural environment. There are
four general classes of control of prices that can arise in the context of the process
network model.

Control of prices p0, p,, and/or pe with;

41

a) flow rates yo, y,, and/or t, serving as control signals,

b) stocks (inventories) of yo and/or y, serving as control signals,

c) exchange opportunities serving as control signals,

(1) prices p0, p,, and/or pe themselves serving as control signals.
Numerous other controls may be described as combinations of the above cases.

Operations Control utilizes information including but not limited to, purchasing,
materials and logistic management, marketing, production level and pricing decisions,
and finance, taxation, employee contracts, personnel relations and public relations.
Neoclassical economic theories of firm behavior are cases of controls 1 a) and 2 a).
Komai and Martos [20] have developed twenty one models of l a) and l b) as “non-
price” controls for Leontief type economies. Control 1 b) has been used historically by
the U.S. automobile industry and by enterprises in planned econonries. Controls 1 c) and
l d) are analogous to “management by objectives” and “market share” acquisition.
Control 2 d) is analogous to “technical trading” and “cost plus” pricing of yo.

Accounting systems and economic theory in general do not make a distinction
between the technically-specific materials y, and yo which are conserved and the
dissipated variables ep, (thermodynamically-specific physical energy and skill-specific
human time) which are actually dissipated in the transformation (production) processes.
Utilizing models of the process network for operational control activities provides a
management information and management accounting system which is isomorphic to the
underlying physical and biological transformation processes and exchange opportunities

of the enterprise in its control of flow rates and prices.

4 A LIFE-CYCLE ASSESSMENT IN MANUFACTURING -
PAPER VS. POLYSTYRENE PACKAGING MATERIALS

There are many potential applications of the paradigm of process network theory and
the economic mapping outlined above. Some applications of process network theory in
agriculture are given in references [20] through [25] . Koenig and Tummala [1] presented
the initial representation of the theory in the context of ecological systems. At the time
these analysis were done, the particulars of the economic mappings developed in Section
4 of this dissertation were not available. Obviously there are many other applications
that may be imagined, in manufacturing, micro and macroeconomic analysis, and
ecology. Some of these potential applications are described briefly as follows:

At the level of the global human economy, the system boundary may be defined as
exchanges with the natural environment, the resource vector 3%, representing the exchange
rates of natural resources and byproducts between the natural environment and the global
economy, and the technical state vector yo representing the accumulation of net products
from the global economy in the natural environment. At the level of a national or
regional economy y, may defined as imports from other economies, and yo as exports
to other economies. At a corporate level of organization 5», and yo may represent the
exchange of inputs and outputs. At an intra-firm level, the boundaries 9, and yo may
represent exchanges between subprocesses or divisions of the firm itself. And y, and yo
may be defined as exchanges at the household or individual level.

Useful definitions of the system boundaries y, and yo may be defined on a purely

physical basis for particular analysis or purposes, including:

42

43
Technically-specific types of materials and energy, net products and byproducts

exchanged with the natural environment.

Exchanges of materials and energy between ecological zones.

The material and energy requirements, products and byproducts of alternative
transformation processes (technologies).

The thermodynamic “net energy” returns of alternative (physical) exoenergetic
technologies.

The reachobility and stability of alternative technical states as bounded by net energy

and material requirements.

System boundaries may be defined on the basis of cybernetic control processes at the

enterprise level for analysis of:

O

O

0

Management “control” strategies and managerial accounting.

Engineering design and cost analysis.

Opportunities for technological and marketing innovation by enterprises in the context
of a technically-specific economic environment.

Competition between firms in industries or nations.

Vertical relationships between enterprises within industries.

The material (real) income and living standards of individuals.

System boundaries may be defined on the basis of cybernetic control processes at the

economy level for analysis of:

O

O

The “distributed control” structures of alternate political/economic systems and their
functioning and performance.

Competition/cooperation between geographic regions or national economies.

44

0 The role of structural and technological innovation in econonric evolution.

0 Definitions of “economic sectors” as employed in macroeconomic modeling.
0 The role of non-priced exchanges in economics.

0 Relative “real” price comparisons and monetary price level inflation.

0 Material vs. monetary exchange rates between “currency zones”.

4.1 Life-Cycle Assessment
A life-cycle assessment was chosen as an example of the theory and practice for this
dissertation for a variety of reasons:

0 It provides an example for the analysis and comparison of manufacturing systems,
including systems with feedback or recycling loops.

0 It provides an opportunity to illustrate economic mapping and how the paradigm
may be used to provide an isomorphic management information and accounting
system for both enterprise level and for policy decision making.

0 It provides an example where ecological-environmental loadings are an integral
part of the analysis.

0 It illustrates the application of the paradigm within the broader context of an
economic system or subsystem composed of a number of enterprises.

o It provides an opportunity to examine the material and energy requirements of
alternative manufactured products, their distribution systems, utilization, and disposal
or recycling alternatives.

0 Life-cycle assessment has become an important and controversial contemporary

issue, of great interest to policy makers, manufacturers, and the public in general.

45
What is referred to here as life-cycle assessment has roots extending back to the late

1960‘s when the need for calculation of the energy requirements of extended production
systems was recognized. During the 1970’s “fuel cycle” studies were performed to
estimate the monetary wsts and environmental implications associated with alternative
energy sources, including estimates of gaseous, solid, and liquid emissions. Such work
included the construction of “mass balances” accompanying the energy calculations, and
thus provided data on raw material requirements and on the mass of solid waste
emissions. During the 1980‘s the focus of attention in the U.S. and Europe shifted to
the solid waste disposal aspects of product life cycles as well as air and waterborne
emissions [26].

A contemporary survey of the state of the art of life-cycle assessment and
methodologies was published in January 1991 under the title A Technical Framework For
Life—cycle Assessments by the Society of Environmental Toxicology and Chemistry and
the SETAC Foundation for Environmental Education, Inc. [26]. This publication was
the result of a workshop sponsored by 15 industry and public interest groups and
organizations, research institutions and major industrial manufacturers, and the U.S.
Environmental Protection Agency.

A succinct definition of life-cycle assessment is provided in [26] and quoted here.

“The life-cycle assessment is an objective process to evaluate the environmental
burdens associated with a product, processes, or activity by identifying and
quantifying energy and materials used and wastes released to the environment, to
assess the impact of those energy and materials uses and releases on the environment,

and to evaluate and implement opportunities to affect environmental improvements.

45

The assessment includes the entire life cycle of the product, processes, or activity,
encompassing extraction and processing of raw materials, manufacturing,

transportation and distribution, use/re-use/ maintenance, recycling and final disposal. ”

SETAC defines three components of life-cycle assessments;

0 Life- Cycle Inventory - An objective data-based process of quantifying
energy and raw material requirements, air emissions, waterborne
effluents, solid waste, and other environmental releases throughout the life
cycle of a product, process, or activity.

0 Life- cycle Impact Analysis - A technical, quantitative, and/or qualitative
process to characterize and assess the effects of environmental loadings
identified in the inventory component.

0 Life- cycle Improvement Analysis - A systematic evaluation of the needs
and opportunities to reduce the environmental burden associated with
energy and raw materials use and environmental releases throughout the
whole life cycle of the product, process, or activity.

Life-cycle inventory forms the basic information, or model, for subsequent impact
analysis at ecological and human health levels. Similarly, the inventory provides for
identification of opportunities for improvement and the analysis of improvements. A
diagrammatic representation of life-cycle inventory is presented in Figure 3, reproduced

from [26].

47

Lite-(Nels inventory

—Dl Raw Materials Acquisition l--H
'29!!! Manufacturing, Processing. _
and Formulation

Enotsv —-e

 

 

 

 

Outputs

 

 

_ s Water Elituents
—O[ Distribution Md Tflmmmfl b—e Airborne Emissions

——> Solid Wastes

—.|7 Ugdfl..U.d“.|n(.n.na H—O Other Environmental Releases
Raw 7 —-D Usable Products

_.| «...... I—+
4 mm...“ 1..

System Boundary

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3 Life Cycle Inventory From SETAC Report, pp. 10

48

In this context, SETAC [26] lists four major research needs for the life-cycle
inventory component which are fulfilled by the process network models described in the
proceeding sections of this dissertation and are illustrated in the following life-cycle
assessment examples;

0 Development of generic models

0 Development of approaches to allocate inputs and outputs among
coproducts

0 Development of approaches to allocate energy and environmental releases
among incoming waste streams and to all environmental media

0 Development of approaches to take into account sensitivity analysis in life-
cycle inventory methodology

That process network theory is a generic model has already been established. The
allocation of inputs and outputs (including environmental releases) among coproducts is
performed explicitly by the parameters of the matrices K relating variables y. Likewise,
the allocation of energy is described in the matrices X and F of the model. Obviously,
since the model is a complete representation of the system, changes in parameters and
variables can be utilized for sensitivity analysis.

Chemical engineering literature from the 19603 [27] through the 1980s [28] and the
SETAC framework [26] discuss straightforward algebraic methods for calculating “steady
state” material flows and energy requirements for “cascaded sequences” or “linear
sequences” of processes in material-energy balance computations. However networks

or processes and processes involving recycling do not have closed form solutions using

49
these methods. Again quoting SETAC [26]:

“The only satisfactory way of dealing with such networks is iteration; that is,
initial values are assigned to the operators and the system is calculated. The
calculated values are now substituted for the initial values and the system is
recalculated. The new values are now substituted and the recalculation performed
again. This procedure is repeated until the changes in the recalculated values are
equal in accuracy to the input data”.

And in a discussion of “Evaluation of Recycling Systems” [26]:

“There is no scientifically valid way of separating this system into individual
product components; any method is purely arbitrary. Two methods commonly used
follow.

1. Equally divide impacts added to the system because of recycling. . .

2. Allocate the disposal credits to the product that gets recycled. . . ”

Processes network theory provides an analytical framework for closed form solutions
of networks of processes in steady state, including solutions for networks with recycling
loops not otherwise available in the literature. As discussed previously, Leontief
representations provide this description for the linear material relationships, but do not
permit nonlinear energy costs. The innovation of processes network theory that makes
this possible is simply the recognition that the energy costs .x,s of the materials brought
to the boundary of a process are linearly related to the material flow rates, and that the
normally nonlinear costs of transformation [8005) are additive. Additionally, these

features, along with the continuity and compatibility relations, make multiple levels of

50
analysis of networks, including recycling loops, possible. This enables the problem to

be decomposed and aggregated through levels of organization, with lower level detail
incorporated in the reduced-order, higher-level representation. Thus, processes network
theory provides a unique and heretofore unavailable analytical tool for life-cycle

assessment.

4.2 Computation of Process Network Models
With reference to Chapter 2, the computation of closed form solutions for process
network models requires a schematic diagram, called a network diagram, which
characterizes the system as a network of materially interconnected processes, and the.
following information about parameters and variables:
1) Coefficients of material transformation, Klb’ Kw, K10, Km. These coefficients
specify a unique product(s) y0 produced from a unique set of resources y,, with a
unique set of material flows within the network, yb, y, and a unique set of
technologies.
2) Stimulus variable(s) yo.
3) Matrix X, specifying the energy costs of bringing materials y, to the boundary of
the network.
4) Functions specifying energetic costs of transformation Fbi) and F000). These
functions normally are nonlinear, and may be discontinuous over a range of values
of variables yb and yo. In some cases they may be taken as linear functions over a
relevant range of yb and yo.

5) The continuity matrix A describing the material flow interconnections between the

51

processes of the network.
If the process network computations are to include an economic mapping and
amortization of processing environment costs as discussed in Chapter 3, the following
variables are required.

6) Economic prices p,, p,,, and p,, for materials and energy.

7) Amortization functions gb and go for the economic costs of the processing

environment for the processes within and on the boundary of the network

respectively.

Given the specification of these parameters and variables, the mathematical sequence

of computation proceeds as follows.

Kb = (I - A Kap'l A K10 (2.11)
y, = Kb yo , (2.10)

it
= K K (2.8)

.91 [ a to] [in]
r", = K5 in (2.12)

r - r r -
Xb=-(r-K,,AT)1K,,X,-(r-K,,AT)1rb(yb) (2.14)

x, = _ A T Xb (2.4) and (2.5)

Faro) = K,’ F101,) + r,(y',) . (2.16)
X0 = "KST xr " FSG’a) (2'15)

42, = 407 F500) (2.17)

Cash flow and value added may tiren be calculated as

52

vs = r.’ p. - 9? pr - r.’ Fm.) p. (33)
85 = K: x» + to (3'7)
vs = for p,, - y: p,- - tor F500) p, - tar 35 (3'3)
An ideal working environment for the modeling and computation of process networks
would be a graphically based engineering work station or personal computer software
environment that would simultaneously;
1) enable construction or “drawing” of the process network diagram,
2) provide for the entry of coefficients Itm and the function 1,005) and g8 for each
component processes in the network diagram location corresponding to that
processes,
3) provide for the entry of boundary energy information x,8 for materials y,s,

4) compile matrices and/or iteratively perform the calculations outlined above

directly from the information entered into the network diagram.

Earlier in this dissertation research, a commercial software package “Simulab” by
the Mathworks was purchased in an attempt to create such an ideal working environment.
Simulab provides the general working environment described above for modeling linear
and nonlinear systems, including extensive control libraries and the ability to write
extended functions in either the Matlab programming language or in such languages as
C and Fortran. Unfortunately the “signal flow” orientation that makes Simulab (and
programs like it) suited to graphical representations also prohibits its use in this

application. Referring to Eq. (2.12) the “signal flow” where y, is the dependent variable

53
is opposite the direction of signal flow in Eq. (2.15) where the associated energetic costs

X, are the independent variable. An object of future work is to identify or develop a
software environment with the four characteristics listed above and the ability to manage
the paired independent-dependent variable problem associated with the modeling of
process networks with a graphical block diagram user interface.

For the modeling and computation of the life-cycle assessment example presented
here a combination of three personal computer software packages were utilized
sequentially. Block diagrams giving a graphical representation of the network(s) and the
specification and labeling of variables were constructed using a word processing
program, Wordperfect 5.1, although any “draw” program for constructing and labeling
block diagrams could have been used. Tables for data entry and the representation of
results were constructed using a spreadsheet program, Framework III, which permits
individual spreadsheets to be linked--that is, to exchange data. This is important in this
application since as many as twenty linked spreadsheet “frames” were required for data
entry and for exporting data in each model. Data was exported and imported from
Framework as ASCII text files. By importing and exporting these text files, the matrix
oriented program “PC Matlab” was used to perform all mathematical calculations except
for the energy functions FbG’b) and F000) which were calculated within the spreadsheet
environment. If necessary or desired, more complex energy functions could readily be
implemented in the Matlab programnring language.

The hardware operating environment was an 80286 PC with 640 kB of RAM and
math coprocessor. This was sufficient for the required Matlab matrix operations, which

included 34 x 13 matrices, inversions, etc. as indicated. For development of the models

54
and twelve cases described below, approximately 8 megabytes of hard disk space was

required for data files of various types.

This implementation illustrates that process networks can be modeled in a very basic
and readily available software and hardware environment. However the use of three
different programs and the laborious data transfer procedure between the linked
spreadsheets and Matlab make the process of adding or deleting variables, changing
parameters, the examination of alternative cases and sensitivity studies very tedious at
best. Development of a truly interactive environment will greatly enhance the modeling
and analysis processes. The Matlab program code utilized for these models is given in

an Appendix.

4.3 Paper Packaging vs. Polystyrene Packaging As An Example

The two examples chosen for the application of processes network theory to life-cycle
assessment are the cases of paper packaging materials and plastic packaging materials.
This choice was motivated by the contemporary international debate and controversy
surrounding the comparative advantages and disadvantages of these two packaging
materials from the perspective of manufacturers, packagers, end users, disposal, public
interest and policy. During 1990 and 1991 these cases of life-cycle assessment came to
the forefront of public and analytic attention, [29] , [30].

During the late 1980s the problems of disposal of solid wastes by landfill, ocean
dumping and incineration became subjects of public and political controversy in the U.S.
Existing landfill sites in many states were full and unable to accept more waste from

major urban centers. The regulations to limit ground water contamination surrounding

55
the citing and licensing of new landfill sites in many cases prohibited expansion of
existing sites or the construction of new ones. Many suitable sites could not be
constructed because local citizens simply did not want landfills in the proximity of their
cities, towns, and residences. This resulted in widespread interstate and intrastate
transport of solid wastes to remaining sites, sometimes for distances as far as 1000 km.

On the east coast, ocean dumping of wastes became more restricted and controversial
when wastes began drifting onto beaches, despoiling recreation and scenic areas and
raising public health concerns. Incineration also became controversial and more
restricted. Air emissions from incineration plants in many cases were not complying
with Environmental Protection Agency standards, and even when standards were met,
there was public anxiety about odors, accidents, corrosive air emissions, and the safety
of permitted levels carcinogenic furan and dioxin emissions.

McDonald’s Inc. , the world‘s largest chain of restaurants, became a symbol of
packaging disposal problems. McDonald’s for several decades had utilized a variety of
expanded polystyrene containers (cups, boxes, serving trays) for serving food and
beverages. In response to public and political pressure from citizen and environmental
advocacy groups, McDonald‘s engaged in a program to study and reduce the landfill
waste produced by its restaurants [31]. In 1991 the decision was made to convert to the
use of paper containers in McDonald’s restaurants. This decision was based on the
prevailing notions that paper containers were always preferable because they were
constructed from a renewable resource (trees), could be recycled back into paper
products, and were biologically degradable if disposed of in landfills.

Whether or not this decision by McDonald‘s had a significant impact on either the

56
mass or volume of waste disposal problems, it became a very visible decision that was

widely followed by other firms in the food service industry, and users of packaging in
general. The change from plastic to paper containers was perceived by customers,
regulatory agencies, and the public in general as being “friendly to the environment” and
as a positive step in reducing the waste disposal problem [29]. During this time period
packaging of all types began appearing with coding systems reporting on its recycled
content, and in the case of plastics, coding reporting its type and suitability for recycling
[32]. Many thousands of municipalities in the U.S. and Canada began a variety of
collection and sorting programs to collect paper, plastic and glass household wastes for
recycling into new products [32]. Within two years, the volume of materials collected
had significantly exceeded the capacity of existing reprocessing facilities to reutilize the
collected materials, resulting in storage of surpluses, and in many cases the carefully
collected and sorted materials were buried in landfills, [33], [34].

The first widely publicized challenge to the wisdom of these decisions was published
in Science in February 1991 by Martin B. Hocking under the title, “Paper Vs.
Polystyrene: A Complex Choice” [35]. This “Policy Forum” article offered a basic
inventory of the material and energy requirements for paper and plastic container
manufacture and an assessment of the disposal options for each. As a standardized
example, 8 oz. paper beverage cups vs. 8 oz. polystyrene beverage cups were chosen for
the comparison of packaging alternatives. This analysis was performed in the general
framework of a life-cycle assessment (although Hocking does not refer to it as such) and

reported some surprising and controversial results.

57
o The petroleum requirements, on a per cup basis, of producing paper and plastic

cups were almost the same, despite the fact that the precursor material of the paper
cup is wood, and that of the polystyrene cup is entirely petroleum. And, of course,
the polystyrene cup consumed no wood in its manufacture.

o The mass of other chemicals required in the production process was almost 40
times more for paper than for polystyrene.

0 Air and water emissions were dramatically lower for polystyrene than for paper.
0 On a mass basis, polystyrene was less demanding of landfill disposal. On a

volume basis, the two utilized about the same landfill resources.

This counter-intuitive report received wide coverage in the national press and
television media. The debate over the results and the underlying data continued in four
letters published in Science the following June [36], [37], [38], [39], and correspondence
which Hocking received personally [40]. A full paper was published by Hocking [41]
in November 1991 with a more extensive inventory based on improved data and personal
communication with industry sources.

While Hocking‘s full paper does provide a more extensive inventory and calculations
in a life-cycle framework, it does not provide complete models of the paper and
polystyrene manufacturing processes, their distribution, use and disposal options,
including recycling. Process network theory provides a formal tool for constructing such
a “full system” model, and for comparing results with less complete and inclusive life-

cycle assessments.

58

4.4 Data for Parameters and Variables

The controversy and correspondence surrounding Hocking’s experience with the data
for his assessment and the extensive discussions surrounding data collection problems
presented in the SETAC report [26] illustrate the problems of finding accurate, consistent
data for life-cycle assessments. Data sources fall into the following general categories.

0 Theoretical calculations based on chemical stoichiometric and thermodynamic
relationships and material-energy balances. For material transformations in chemical
reactions mass is always conserved, but the actual distribution of yields of products
and byproducts may vary due to incomplete reactions or variations in reaction
conditions. Theoretical energetic calculations are even more subject to variation from
practice because of the difficulty in determining waste heat losses and variations in
reaction temperatures and temperatures of incoming and outgoing materials. In
cases of some complex reactions, envolving polymers for example, there is no
theoretical basis available for energetic calculations.

0 Reference material from books and encyclopedias describing process industries.
These sources can provide useful representative information, but in process industries
where technologies are changing, which is frequently the case, even current
references may be outdated compared with contemporary practice. In addition, there
may normally be significant variations in the design and operation of plants producing
the same or similar products.

0 Empirical data fi'om the actual operation of processes. For life-cycle assessment this
is in some respects the most appealing source, but it is also subject to limitations.

Because of plant to plant variations in design, operation, and technologies, the most

59
consistent process data could be expected by obtaining all data from a single plant.

It is then necessary to determine how representative the particular plant(s) are of the
industry practice as a whole. Normally such data are not published, but must be
obtained in cooperation with a particular enterprise, or in some cases industry groups
or consulting firms that compile such information. Such data are often considered
propriety for competitive reasons, and may not be made available to scientific
investigators. Additional problems arise because some process data may simply not
be known - not measured or not available in a tabulated form.

0 In the case of regulated air and water emissions the permitted levels may be used to
provide data. This of course assumes that the plant or processes is in compliance,
which may not be true, even at an industry wide level. And of course in many cases
actual emissions may be below the permitted levels. However the regulated level
may commonly be the only available source of information for many assessments.

In the data reflected in Hocking‘s work and references, as well as discussions in the

SETAC framework, agreement between data sources closer than 10% is considered

fortunate.

Hocking’s work began within a framework of published data which for his full paper
[41] was supplemented by direct personal contact with three spokespersons from each
industry in the U.S. and Canada in an attempt to make his assembled data as close to
current experience as possible. Thus, his full paper is an invaluable starting point for
data for use in a process network model. Hocking‘s conversions were checked again
other reference sources where available. Process data for paper manufacturing in

particular has changed substantially from the 19603 to 1980s in published reference

material, [41], [42].

However, since Hocking‘s inventory is not a full system model and is not broken
down into a network of component processes, there are a number of important
deficiencies in the data presented in his paper. In the models below, the missing
information was obtained from reference materials and in a few cases from theoretical
calculation. In a few cases where the necessary information was simply not available,
informed judgements were employed in approximation.

Conversion between units of mass, energy and fuel types was performed using
standard chemical engineering references [28], [42], [43], [44]. Petroleum fuels and
feedstocks were all converted to and expressed in kilograms (kg), and electric power in
kiloWatt-hours (kWh). All material units are converted to and expressed in kilograms

except for water, for which the units are cubic meters (m3).

5 LIFE-CYCLE ASSESSMENT OF PAPER MANUFACTURING.
USE AND DISPOSAL

5.1 Network Diagram of Paper Manufacturing

A network diagram of paper manufacturing including resource materials y, and
products yo is given in Figure 4. There are at least three major classes of paper
manufacture processes in use. The process diagramed here is the bleached Kraft process,
which is predominant in the manufacture of packaging materials because of the high
strength of the fiber structure of the paper product (others are sulfite and NSSC).

Paper manufacturing is a complex network of processes. Each of the processes
numbered 1 thru 11 in this diagram is in fact composed of anywhere from two to a dozen ‘
subprocesses. The diagram shown here is constructed to represent a minimum level of
detail necessary for the purpose of this analysis-that is, the life-cycle assessment of the
paper product and the manufacturing enterprise producing it. For purposes of other
analysis such as the evaluation of specific technological changes of subprocesses, a more
detailed model of each process 1 thru 11 shown here could be constructed in greater
detail and then incorporated in the level of this process model. Obviously the choice of
level of detail is a key modeling decision, and must be chosen to incorporate the
information necessary for the purposes of the analysis while ignoring unnecessary lower
level detail. More detailed diagrams of the subprocesses of paper manufacture may be

found in Austin [42] or many other references on paper manufacture.

 

 

Stimulus material flows are represented by dual lines > with an arrow

 

 

to indicate the orientation of material flow, and labeled 01 thru 01 1.

61

62

 

Air Emissions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C02 r14
8 wood Bark 9 CO r15
Wood Logs and Waste Waste Neod NO r16
r1 C} > Processing r >— and 802 r17
9-8 09 Black Particulates
, : Liquor r18
"bod Chips 010 Black Liquor Combustioni————
oS -———————- 10 '
Chemicals 11-10
r3 Chlorine 8-5 011 Sme1t(ash)
r4 Sodium hydroxide 10-5 later lffluent m3 H o) r22
r5 Sodium chlorate T A I Suspended soli P,/323
r6 Sulfuric acid 800 K ’ r24
r7 Sulfur dioxide Organochlorides r25
r8 Calcium oxide , Cellulosic Fiber r26
> 5 11 Inorganic salts r27
Water Pulp
r2 0 > Air Emissions
06 6-5 Manufacturing Chlorine r19
6 Sodium ._< — Chlorine dioxide r20
Sulfate Reduced sulfides r21
Recycling #- >— > 0
7-6 7-5 7
Pulp
I 07 I
Sodium ,
sulfate 7 cs Pulp 1
r9 >——-Replacement 5-1 Paper
Sodium Sulf : — ol
Paper
A 5—2
Coatings E Fillers Recycled Pulp
r10 Pigments Manufacturing 1113 820 r22
rll Coatings -——-
r12 Filler Solids r23
Its-pulping Chemicals Water Bffluent: m3 H 0 r22
r3 Chlorine 2 Suspended solids r23
r4 Sodium hydroxide BOD r24
r5 Sodium chlorate Waste Organochlorides r25
r7 Sulfur dioxide Cellulosic fiber r26
r13 Sodium phosphate Inorganic salts r27
>7 Paper >
Air Emissions
Water Chlorine r19
r2 OL > Chlorine dioxide r20
Waste paper Re-pulping Reduced sulfides r21
02 Ce. : E
Natural gas 03 Steam and
03 C? : Power -—->
Generation Air Emissions C02 r14
CO r15
NOx r16
Fuel oil 04 Steam and $02 r17
04 Ce. : Power r->
Generation Particulates r18

Figure 4

 

 

 

Network Diagram of Paper Hanufacturing

63

 

Response variables are represented by single lines > and labeled rl thru
r27 for resources and byproducts and 5-1 thru 11-10 for links between processes. The
general direction of material flow is from resources on the left to products and
byproducts, including emissions and effluents on the right.

The system boundary chosen here is the paper manufacturing enterprise. Resource
chemicals r3 through r13 are taken as the boundary resources for the network. As in
Hocking’s analysis the manufacture of these resources with their accompanying material
and energy requirements is not modeled here, but could be added through the inclusion
of models for their manufacture at the next level of analysis. Since these chemicals
collectively total about 20% of the weight of the paper produced, the role of their
manufacture may be expected to affect the life-cycle analysis, but as will be seen, is not
expected to change the conclusions presented. Models for the manufacture of these
chemicals as well as the process of wood growth and harvesting can be systematically
added as refinements to the life-cycle process network here as required to address other
classes of questions.

Wood processing 8, involves the removal of bark and waste, and chipping. The bark
and waste are burned in process 9 to generate process steam for pulp manufacturing 5
and 11, and paper manufacturing 1. In pulp manufacturing the wood chips go through
a series of cooking and digestion stages to rembve lignins from the cellulose, and then
chemical washing and bleaching to produce the finished dense liquid pulp. Chemicals
r3-r8 are used on a once through basis, but sodium sulfate is recycled, with makeup r9
being required to replace losses. In the pulp manufacturing process a byproduct liquid

called black liquor containing lignins is produced. This black liquor is burned for steam

64

generation along with the bark and waste wood in process 10. The chemically rich ash
remaining afier combustion is recycled back into the pulp manufacturing processes.

Waste paper repulping is represented in process 2. Repulping may or may not take
place at the same plant site as virgin pulp manufacture. Some plants are devoted solely
to virgin pulp and paper manufacture, some solely to repulping and paper manufacture,
and some to both functions. The model presented here is generic to all these cases since
setting the coefficients in K associated with virgin pulp manufacture to zero gives a
representation of a 100% repulping plant and vis a versa. Plants producing both virgin
wood and recycled paper pulp may be modeled by the selection of stimulus variables 01
and 02. This is very useful since any overall mix of virgin wood and recycled paper can I
be chosen to represent an industry wide pattern of production in the life-cycle
assessment.

This is an important feature to note in the network representation chosen here. The
operating decision involves the choice of levels of production ofépaper 01 and levels of
reduction of waste paper 02 at the boundary of the network. The branch stimulus
variable pulp from virgin wood 05, is a “make up” variable - which in the computation
of the model automatically calculates the level of virgin wood pulp 05 and accompanying
resources required. For this reason, the flow rate of recycled pulp at link 5-2 must be
constrained to be less than or equal to the pulp flow rate 5-1. Otherwise flow 05 would
be negative and the network would “produce” trees, clearly not a feasible condition 1

An alternative network topology for recycled paper pulp could have been chosen;
where recycled pulp would be a stimulus variable with a link to paper manufacturing as

in the case of pulp 05. In this case, the ratio of virgin wood pulp to recycled pulp would

65
be determined by the relative coefficients of K for paper manufacturing, process 1. The

choice between these two topologies at the enterprise level is an arbitrary choice of the
investigator. However the full system model to follow requires the topology shown in
Figure 4 for the network to satisfy the continuity conditions as will be seen later.

An important insight from this topological requirement is that the ratio of virgin to
recycled pulp in the paper product cannot be controlled by the paper marugfacturer in a
full system life-cycle model of the industry, but is determined by the policy or behavior
choice for paper disposal - recycling. The structure of the network requires the paper
manufacturer to behave according to the policy rule or behavior imposed at a higher level
of network organization.

Processes 3 and 4, for steam and electrical power generation illustrate the reduction
of material fuels into atmospheric emissions. This is an important and perhaps confusing
point that has not been modeled correctly in earlier process network models. While
natural gas and fuel oil are energy sources, as material fuels they are potential energy
sources. Their combustion is an exoenergetic material transformation of potential to
thermal energy. As such, both the material transformation and the energy produced must
be modeled. Note that electric power purchased in addition to the power generated on
site by the enterprise does not appear as a process since it is acquired as a kinetic energy
form from outside the boundary of the system and thus has no material transformation
character. Purchased power generation at a higher level of organization can readily be
modeled in the life-cycle analysis presented here simply by specifying that all electric

power be generated on site with the appropriate technological parameters.

66
5.2 Network Model of Paper Manufacturing

Table 1 shows the matrices Klbr K10, Kw, K,0 for the process network describing
paper manufacturing corresponding to Figure 4. Comments about the coefficient data
will be presented below by referring to processes in general by their number and to
specific elements according to their row-column labels.

In wood processing 8, 6% of the mass of wood logs is comprised of bark and waste.
Because wood chips are the independent variable, this results in a coefficient of 1.06 for
wood logs to wood chips [rl,o8] and .06 for bark and waste to wood chips [9-8,08].
This illustrates how coefficients It are inverses of the common expression of input-output
ratios cited in most discussions in process literature, i. e. wood chips to wood logs would
have a coefficient of .94. Wood chips are in turn converted to pulp with a coefficient
of 2.2. The remaining mass is the lignin content of the wood chips which appears in the
black liquor [lo-5,05] with a coefficient of 1.2 and is burned for steam generation in
process 10.

Hocking reports an aggregate total for the mass of chenricals [r3-r8,05]. The
coefficients shown here are an arbitrary division of the relative magnitudes judging from
information in Austin [42], which yield the same total chemical requirement as given in
Hocking [41]. Coefficients [66,05], [7-5,05], [7-6,o6] and [r9,o7] define the sodium
sulfate recycling loop and makeup at the replacement rate described by Hocking [41].
Air emissions rl4-r21 are based on aggregate data from Hocking. Since 56% of total
energy generation takes place in processes 9, the total emissions have been distributed
on this basis between the coefficients for processes 9 and for fuel combustion, processes

3 and 4 to result in the total emission levels given by Hocking.

67

Paper llarntfacturing Coefficients

Table 1

Fuel
Oil

Hood Haste Black Black

Sulf. Sulf. Chips Bark Liqr Liqr

0506

“0

Pulp Sod.

Irarrches

Paper Haste lat.
Paper
02

00°00

00°00

ommoo

000000000

elel “”

m .
me

see

oooooooomooooo
-

08 09 010 011

07

Lirks

5-1

Pulp

5-2
6-5

Pulp
' Sedit- sulfate

7-5

Soditm sulfate

Soditm sulfate
Hood chips

7-6
8-5

9-8

Bark I. Haste

10-5

Black timer

Smelt (ash)

11°10

Headless

r1
r2
r3
r4
r5

Chlorine
Soditm hydroxi
Soditm chlorate
Sulfuric acid

UltOl'

r6

r7

Calcitm hydroxide r8

Soditm sulfate
Pi pants
Coatings

Sulfur dioxide
Filler

r9

r10
r11

r12

r13

Soditm Phosphate

OOOOOZZEWWM3I“
“mm-e wme
CI. 0..
«cunnwmauaaaun
rrrrrrrrrrrrrr
r
«a a «a.
eel 8! it
an n ism
m mm . an
um“ um“
misao min
Riff 2 u
0500 " Isr
% 1%»11m ”ram
mm Pmmué 0C1.

68

Note that NOx and 802 coefficients are zero for natural gas combustion since these
emissions are very low. Provision is made here for inclusion of C02 coefficients for
each process. Note that in the examples that follow C02 emission rates have been set
to zero. C02 emissions are a key issue in the global warming controversy which
Hocking does not consider analytically. Carbon dioxide emissions will be discussed here
in Chapter 7 on Life-cycle Comparison. Water effluent rates r22-r27 are calculated
directly from Hocking‘s levels.

[5-1,ol] reflects the conversion of pulp to paper on a dry weight basis, which is the
common industry practice, rather than reference to wet weights which include 10-15 %
water content [42]. Thus the dry weight coefficient is 1.

In his work Hocking does not consider the process of recycling waste paper into
recycled pulp. Austin reports that the repulping of waste paper to recycled pulp operates
at a 17% loss [42], resulting in a coefficient of .83 for [5-2,02]. The chemical
requirements for recycling pulp are more difficult to ascertain. Several sources [42],
[45], provide descriptions of the repulping processes and the chemicals required, but not
the quantities. Repulping requires approximately half the total number of stages of
chemical processes that manufacture of pulp from virgin wood requires. It is assumed
here that the chemical requirements and water emissions would then also be about half
of virgin pulp manufacture. This is a useful operating assumption. Ongoing
improvements in data can help refine the model.

Table 2 shows the continuity matrix A for the network. In Table 3 various
information for variables in the model are entered. The stimulus variables 01 and 02 are

specified as described in the previous section.

69

Table 2 Paper Manufacturing Continuity Matrix

5-1 5-2 6-5 7-5 7-6 8-5 9-8 10-5 11-10
05 1 -1 O 0 O O 0 O 0
06 O 0 1 O 0 O O O 0
O7 0 O 0 1 -1 O O 0 0
08 0 0 O 0 0 1 O O 0
09 0 O 0 0 0 0 1 0 O
010 , 0 O O O 0 O O 1 O
011 0 0 O 0 O O O 0 1

Table 3 Paper Manufacturing Variables
Stimulus veriables
Paper Manufacture ol 1
Re-pulping oz 0
Gas Steam 8 Power 03
Oil Steam & Power 04

Energy use ratios

Gas In Steam Generation .00%
Oil In Steam Generation 100.00%
Cogenerated Electric .00%
Purchased Electric 100.00%
kg Natural Gas/kg Steam .047
kg Natural Gas/kWh Elect. .200
kg Fuel Oil/kg Steam .057
kg Fuel Oil/kWh Elect. .240

fable lo Paper Ilamfacturing Energetic Matrix Fb Fo

Energy type Steal Natural Fuel Elect. Diesel Direct Direct
per unit material Gas Oil Power Fuel Laber1 LaborZ
kg kg kg m: kg hours hours

Pumas
Pulp Ilamfacturing 05 I
flflhns.kumfle¢$ 0
Sodiu- S. Replace 07 0
Hood Chipping ed 0
Haste Codaustion 09 42
Haste Combustion 010 0
Pulp Manufacturing 011 0

Paper Manufacture e1
its-pulping 02
Gas Ste. I. Peter 03
Oil Ste. I. Power 0!.

70
This first example specifies 02 as zero, corresponding to the no recycling case which

Hocking discusses. Natural gas and fuel oil material rates for 03 and 04 are determined
internally in the model, since they are dependent on the energy requirements.

Energy use ratios are specified in the next section. Two options are available; the
ratio of use of natural gas to fuel oil for steam and electric power generation, and the
ratio of electric power generated on site (cogenerated power) to electric power purchased
by the enterprise. The U.S. paper industry as a whole uses about 35% oil and 65% gas
for steam generation beyond that provided by combustion of bark and waste [37]. Any
ratio ean be used in the model, but for the examples which follow 100% oil utilization
has been selected to simplify comparisons across models and comparison with petroleum
feedstocks. Comparison of oil and gas on a mass basis with natural gas is
straightforward, 1 kg of natural gas has the same energy content as 1.2 kg of fuel oil.

The final section of Table 3 gives energy conversion ratios for fuels to steam and
electricity. Fuel to steam ratios follow Hocking [41], and are aggregates of low pressure
and high pressure steam requirements. Fuel to electric power ratios assume 33 %
conversion efficiency on a Joule or kWh basis, which is a reasonable historical average
for electric power generation. In a cogeneration environment, low pressure process
steam is available downstream of the turbine driven electric generation stage. This
increases the combined thermal efficiency of steam and electrical power generation.
Cogeneration scenarios for different power generation cycles and fuels ean readily be
described through specification of the four ratios.

Table 4 reports the conversion energy functions Fb and F0. Total steam and

electrical power requirements are those reported by Hocking [41] but are divided between

dis;

 

71

processes 5 and 1. As in the case of chemical requirements, the energy requirements for
repulping are difficult to ascertain. In the absence of better information assumptions have
been made of half the energy requirement relative to the requirements for virgin pulp.

Direct labor hours are reported to be 5 hours per metric ton of finished paper by
[46]. For this illustration 4 hours were used as a basis, assuming improvement in labor
efficiency have taken place. The total labor time is distributed between the processes as
indicated.

Table 5 shows the matrix Xr for the boundary energy costs of the network resource
materials yr. As discussed in the previous section, energy costs involved in making
resources r1 through r13 available to the boundary of the network are generally unknown.
since such accounts are generally not maintained by industries. The largest energy costs
can be expected to be associated with wood growth and harvest to produce the wood logs
and the production of chlorine compounds. These costs can be systematically included
in the life-cycle assessment by extending the boundary of the network to include the
corresponding material transformation processes or they ean be determined from auxiliary
analysis of the network of precursor transformation processes involved in producing these
resources.

Table 6 provides for entry of price information for resources, products and energy
at the boundary of the network. The purpose of the economic analysis here is to
demonstrate how process network models can be mapped into economic performance,
and to illustrate how a full system model in a life-cycle analysis can be utilized by a
manufacturing enterprise to evaluate the impact of how changes in product use and

disposal effect the economic performance of the enterprise.

72
Table 5 Paper Itamfacturino Matrix Xr

Energy Type Natural Fuel Electric Diesel Direct Direct
per mit laterial Gas Oil Pouer Fuel Labor 1 tabor 2
R! to Id! to hours hours

Droanochlorides r25
Cel lulostic Fiber r26
lnoroenic salts r27

Resort-ca
Hood Loos r1 0 D D D D D
Hater r2 0 0 D 0 D 0
Chlorine . r3 0 D 0 0 D D
Sodit- hydroxide r4 0 D D D D 0
Sodiu- ehlorate r5 0 0 0 0 D D
Sulfuric acid r6 0 D D 0 D 0
Sulfur dioxide r7 0 D D 0 D 0
Calcium hydroxide r8 0 D D D D 0
South- sulfate r9 0 0 0 D D 0
Pipents r10 0 0 0 D D 0
Coatings r11 0 D D D D 0
Filler r12 0 D 0 0 D D
Soditn phosuiate r13 0 0 D D D D
(:02 r14 0 D D D 0 D
co r15 0 D D D D 0
aox r16 0 D D D D D
r17 0 D 0 0 D 0
Particulates r18 0 0 D 0 D 0
Chlorine r19 0 D D D D 0
Chlorine dioxide r20 0 D D D D 0
Iterated sulfides r21 0 0 D 0 0 0
H20 r22 0 D 0 D 0 0
Supended solids r23 0 D D D 0 0
am r24 0 0 D D D D
0 0 D 0 D 0
D D 0 D 0 D
0 0 D D 0 D

73

Table 6 Paper Manufacturing Prices
Price/kg Price/kg
material material
Resource yr pr Products Yo po
Wood Logs r1 $.08 Paper Manufacture ol $.50
Water r2 $.00 Re-pulping oz $.00
Chlorine r3 $.25 Gas Steam 5 Power 03 $.00
Sodium hydroxide r4 $.25 Oil Steam 5 Power 04 $.00
Sodium chlorate r5 $.25
Sulfuric acid r6 $.25
Sulfur dioxide r7 $.25
Calcium hydroxide r8 $.25
Sodium sulfate r9 $.25
Pigments r10 $.25
Coatings r11 $.25
Filler r12 $.25
Sodium Phosphate r13 $.25
co2 r14 $.oo
CO r15 $.00
N0x r16 $.00
$02 r17 $.00
Particulates r18 $.00
Chlorine r19 $.00
Chlorine dioxide r20 $.00
Rgduced sulfides r21 $.00
m H O r22 $.00
Suspended solids r23 $.00
BOD r24 $.00
Organochlorides r25 $.00 $ / kg
Cellulostic Fiber r26 $.00 Processing Environment material
Inorganic salts r27 $.00 Amortization Gb & Go
Pulp Manufacturing 05 $.02
Sodium S. Recycle 06 $.00
Price/unit Sodium 8. Replace o7 $.00
energy Wood Chipping 08 $.02
Energy pe Waste Combustion 09 $.02
Waste Combustion 010 $.00
Natural Gas / kg $.25 Pulp Manufacturing 011 $.00
Fuel Oil / kg .25 -------------------------------
Electric Power / kWh $.05 Paper Manufacture ol $.02
Diesel Fuel / kg $.35 Re-pulping oz $.02
Direct Labor 1 / hour$12.00 Gas Steam & Power 03 $.02
Direct Labor 2 / hour $.00 Oil Steam & Power 04 $.02

74
A detailed and accurate analysis of the economic performance of a paper

manufacturing enterprise or of the industry as a whole would require current and accurate
prices for resource materials r1 through r13 and the finished paper product 01. These
prices are normally the result of negotiation and contracts between firms and information
is not generally available from published sources. Firms normally treat this information
as proprietary for competitive reasons. Large chemical manufacturers and purchasers
often utilize the services of specialized consulting firms and extensive internal marketing
and purchasing departments to determine market conditions. This information is
considered valuable property by manufacturers and consulting firms alike, and access to
is restricted. In the case of feedstock prices for polystyrene manufacture it was possible
to obtain some basic information through the efforts of a personal industry contact, but
even this limited information required nearly a month of inquiries within his firm and
with a consulting firm working under contract [47].

For the illustration here, a price for bleached kraft paper 01 in Table 6 was assumed
to be $500 per ton on the basis of personal experience within the industry [48]. This is
also about half the wholesale price per kg of finished paper cups [49]. Chemical prices
are assumed to be a uniform $250 per ton, again a “ball park” figure for many inorganic
chemicals based on personal manufacturing experience [48]. The price of wood logs
($80 / ton) was adjusted to result in an overall cash flow that would be representative of
manufacturing industries given the other price information assumptions.

Representative prices for petroleum fuels are readily determined from published
sources and distributors prices and then converted to a kg basis. Electric power prices

vary by a factor of as much as 3 to 1 depending on region. $.05 / Kwh has been chosen

75

as representative here. Direct labor costs can also be expected to vary widely, but have
been assumed to be $12 per hour. For purposes of illustration, processing environment

amortization g], and go have been set to $.02 for each component process.

5.3 Enterprise Level Results of Paper Manufacturing

Figure 5 shows the diagram of the manufacturing enterprise illustrated in Figure 4
at the next higher level of organization. All detail has now been consolidated into the
expressions for this higher level. Table 7 shows the system matrix Ks relating products
yo to resources yr and the internal schedule matrix Kb relating the flow rates or products
yo to the flow rates of internal stimulus variables yb. Flow rates of material variables
y,, y,, yb, and yo are presented in Table 8. Note that in this example the flow rate for
finished paper 01 has been set at 1.1 kg I unit time. When adjusted for units of
measurement, the flow rates given here conform quite closely to Hocking’s aggregated
figures for paper manufacturing [41].

Energy and economic results for paper manufacturing are presented in Table 9. Some
explanation of the Fsst and F3 matrices is required. Fsst represents the system energy
requirements including the steam required in addition to that generated internally by
processes 9 and 10. This additional steam must also be generated internally by either
process 3 or 4. The conversion rates of gas and oil to steam given in Table 3 are used
to calculate the fuel requirements, in this case the fuel oil required, .2540 kg fuel oil I
kg paper 01, as shown in F5. After conversion of units, Hocking‘s Table 1 [41] reports
.2168 kg fuel oil / kg paper. Hocking does not report in detail how this particular steam

to fuel oil conversion was calculated.

Wood Logs
r1 0. >

76

 

 

Nita:

 

r2 0: >:,

Chuicals
r3 Chlorine
r4 Sodium hydroxide
r5 Sodium chlorate
r6 Sulfuric acid
r7 Sulfur dioxide
r8 Calcium oxide
r9 Sodium Sulfate

0 ,

 

Coatings E Fillers
r10 Pigments
r11 Coatings
r120 Filler

\
'

Rte-pulping Chemicals
r13C Sodium phosphate

 

Waste Paper
02 Gee, :

 

Natural gas
03 C: :

 

Fuel Oil

04 C‘ -

 

Figure 5

 

Paper

Manufacturing

Air Emissions
002
00
NO
80’;
Particulates
Chlorine
Chlorine dioxide
Reduced sulfides

r14
r15
r16
r17
r18
r19
r20
r21

 

'

Paper

W

Water Iffluent
m 320 I22
Suspended solids
BOD
Organochlorides

ol

r23
r24
r25

Cellulosic fiber r26

Inorganic salts

r27
0

 

 

 

'

Consolidated Network Diagram of Paper Manufacturing

77

Table 7 Paper Manufacturing System Matrices

Paper Waste Nat. Fuel
Paper Gas Oil
Schedule Matrix Kb 01 02 03 04
Pulp Manufacturing 05 1 -.8300 0 0
Sod um S. Recycle 06 .0090 -.0075 0 0
Sodium S. Replace 07 .0010 -.0008 0 0
Wood Chipping 08 2.2000 -1.8260 0 0
Waste Combustion 09 .1320 -.1096 0 0
Waste Combustion 010 1.2000 -.9960 0 0
Pulp Manufacturing 011 .2040 -.1693 0 0
system Matrix KS
Wood Logs r1 2.3320 -1.9356 0 0
Water r2 .1000 -.0330 0 0
Chlorine r3 .0600 -.0198 O 0
Sodium hydroxide r4 .0200 -.0066 0 0
Sodium chlorate r5 .0300 -.0149 0 0
Sulfuric acid r6 .0100 —.0083 0 0
Sulfur dioxide r7 .0100 .0017 o 0
Calcium hydroxide r8 .0100 -.0083 0 0
Sodium sulfate r9 .0010 -.0008 O 0
Pigments r10 0 0 0 0
Coatings r11 0 0 0 O
Filler r12 0 0 O 0
Sodium Phosphate r13 0 0 0 0
co2 r14 0 o o 0
CO r15 .0037 -.OO31 .0001 .0001
NOx r16 .0061 -.0050 .0004 .0005
$02 r17 .0132 -.0110 0 .0044
Particulates r18 .0020 -.0016 0 .0005
Chlorine r19 .0002 -.0001 O 0
Chlorine dioxide r20 .0002 -.0001 0 0
Rgduced sulfides r21 .0015 -.0004 O 0
m H20 r22 .0800 -.0181 O 0
Suspended solids r23 .0100 -.0033 0 o
BOD r24 .0050 -.0012 0 0
Organochlorides r25 .0030 -.0005 O 0
Cellulostic Fiber r26 .0010 .0002 0 0
Inorganic salts r27 .0600 -.0198 0 0

 

Table 8
Links

Pulp

Pul

Sod um sulfate
Sodium sulfate
Sodium sulfate
Wood chips
Bark & waste
Black liquor
Smelt (ash)

Resources

Wood Logs

Water

Chlorine

Sodium hydroxide
Sodium chlorate
Sulfuric acid
Sulfur dioxide

78

Paper Manufacturing Material Flows

Y1

5-1
5-2
6-5
7-5
7-6
8-5
9-8

10-5
11-10

r7

Calcium hydroxidere

Sodium sulfate
Pigments
Coatings

Filler

Sodium Phosphate

Particulates
Chlorine
Chlorine dioxide
Rgduced sulfides
Suspended solids
BOD
Organochlorides

r9

r10
r11
r12
r13
r14
r15
r16
r17
r18
r19
r20
r21
r22
r23
r24
r25

Cellulostic Fiberr26

Inorganic salts

r27

1.1000

0
.0099
.0110
.0099

2.4200

.1452

1.3200

.2244

2.5652

.1100
.0660
.0220
.0330
.0110
.0110
.0110
.0011

Branches

Pul Manufacture

Sod um S. Recycle
Sodium S. Replace

Wood Chipping

Waste Combustion
Waste Combustion
Pulp Manufacture

Objects

Paper Manufacture

Re-pulping

Gas Steam & Power
Oil Steam 8 Power

Yb

05 1.1000
06 .0099
o7 .0011
08 2.4200
09 .1452
010 1.3200
o11 .2244
yo

01 1.1000.
02 0
03 0
04 .2794

 

Table 9 Paper Manufacturing Systu Energetics

Energy type

per mit aaterial

Fsst Matrix

Paper Manufacture
Ila-pulping

Baa Ste. I. Power
Oil Steal I Power

F. Matrix
Paper Manufacture
lie-pulping
Gas Ste. 8 Power
Oil Ste. 8 Power

xb Matrix

Pulp Manufacture
Sodit- s. Recycle
Soditn 3. Replace
Hood Chipping

Haste Cowustion
Haste Wtion
Pulp Mamfacture

X0 Matrix

Paper Manufacture
Ila-pulping

Gas Steam 8 Power
Oil Stem 8 Power

Energy es

Energy e0
Asortiztion 0‘
Paper Manufacture
lie-pulping

Gas Steam 1. Power
Oil Steel I. Power

Value Added Vs

18.2.9.

38.2.9.

9.8.8.2.

18.2.9.

Ste.

ks

4.4560
.9615

3.09
(8.04)
8.02
3.02

Matural Fuel

Gas Oil
he to
0 0
0 0
0 0
0 D
0 .2540
0 .0540
0 0
0 0
0 0
0 0
0 0
O 0
0 0
0 0
0 0
0 -.2540
0 -.0548
0 ,0
0 0
0 .2794
0 -.2794

79

Elect. Diesel Direct Direct
Fuel Labori LaborZ
hours hours

Power
ktlr

1.0978

4.0978

ks

0900000 0609

.0041
-.0016

-.0031

-.0010
-.0076

-.0041
.0016

.0045

-.0045

0000

0000000 000°

000°

0

80

For consistency, the conversion rate used in the model here is the same conversion rate
used by Hocking in a later section of his paper. Since all electric power is purchased in
the examples shown, electric power requirements are .9980 kWh / kg paper 01. This
is in agreement with Hocking [41].

The energy requirements for waste paper repulping 02 are at first surprising, and
demonstrate an important feature of the network structure. Notice that the electrical
power figure for repulping in F3 is -.2963 kWh, which would at first glance seem that
repulping paper is generating electric power. This is not the case. The network
structure in Figure 4 shows that recycled pulp reduces the virgin pulp requirement for
the final paper manufacturing process 1. Thus, the energy requirements in F3 reflect the
reduction in energy requirements for each kg of waste paper 02 utilized in the production
of paper 01 , that is .2963 fewer kWh of electrical power are required for each kg of
waste paper 02 which is recycled. Notice that the steam and fuel oil requirements
actually increase by .9615 and .0548 kg respectively for each kg of waste paper that is
recycled despite the fact that process 2, waste paper repulping has lower steam/ fuel oil
requirements than] process 5, virgin pulp manufacturing. This occurs because when
virgin pulp is manufactured, 56% of the total steam energy is generated by the
combustion of bark and waste wood from the incoming wood logs. This is an
extraordinarily important result which has not been revealed in other analyses. As will
be discussed in the section Life-Cycle Comparison of Paper and Plastic, this will result
in petroleum consumption for recycling paper almost identical to petroleum consumption

for virgin paper manufacture, a result that is directly contrary to current assumptions.

81

5.4 Network Diagram of Paper Use and Disposal

Figure 6 presents a diagram of paper use and disposal. The boundary stimulus
variables for use and disposal are the flow of beverages 012, and diesel fuel for
transportation 013. Notice that links 1-16, paper, and links 2-18 and 2-17 used cups and
waste paper, are interconnected to the higher level network model of paper
manufacturing shown in Figure 5 at 01 and 02 respectively. This illustrates a particular
choice of modeling topology where the graph in Figure 6 is “added” to the graph of
Figure 5.

Alternatively, paper use and disposal could have been modeled as an independent
network and then the two models, one for paper manufacture, and the other for use and
disposal, could have been combined. Either approach yields the same result for the
entire system, and this equivalence illustrates the flexibility in the definition of
boundaries and subnetworks available to the investigator. The approach of adding
additional processes to the higher level manufacturing model was chosen here since it
illustrates how processes can be added in series to create a higher level model. This
approach is particularly well suited to life-cycle assessment issues and contemporary
practice.

Referring to Figure 6, paper from paper manufacturing is transported to a cup
manufacturing facility 15. Adhesive r28 is employed in the manufacture and part of the
paper is lost as waste from trimmings [17-15]. Cups then require transport in process
14 and used to serve beverages in process 12. Beverages r29 flow through process 12
and are ultimately the object 012 of the network of paper manufacturing, use and

disposal.

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Paper 16 Paper
._ >—~ Transport
01 1-16
I Paper
016
16-15
Adhesive Cups
r280—>— 15 Cup ._,..0_>__, 14 Cup
Manufacturing 015 15-14 Transport
6 Waste paper I Cups
17-15 014
Y 14-12
Beverages 12 Cup Beverages
r29 >——- Use : 0012
I
Used Cups
18-12
Y 017 Y 018 Air Emissions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

17 Waste Paper 18 Used Cup C02 r14
Transport Transport CO r15
I I I I I I NOX 1'15
V V Y Y 19-18 SO r17
19-17 \, /’ 019 Particulages r18

3 >— 19 > O

Incineration
or
Fuel Cogeneration Ash r31
r30 0: >—- >

20-17 20-18 Air Emissions C02 r14
020 Methane r32
Leachate r33
Landfill Cellulosic Fiber r34
BOD r24

> 0

2-18 Used cups for recycling 02
%>—
2-17 Waste paper for recycling 02
%)a=_

013 Cs

Diesel fuel

 

 

7

 

13 Transportation
Fuel Combustion

V

 

 

Figure 6

Air Emissions

002 :14
CO r15
NOx r16

$02 r17
Particulates r18

Network Diagram of Paper Use and Disposal

 

83
That is, 012 is the independent variable that determines all other material flows and

energy costs for the full system. It is important to note that there is nothing about the
physics of the system’s functioning that causes 012 to be the independent variable. Other
f variables could have been selected as the object of transformation. For example, ash
from incineration could have been chosen as independent with corresponding changes in
the network topology to make all interconnections meet the continuity requirements.
Recalling however that this is a human designed, engineered and managed system for
packaging beverages, the objective clearly is the consumption of beverages, not the
disposal of the cup as ash, etc.

In processes 17 and 18 waste paper and used cups are separated for three disposal
options and transported to their respective destinations. Those disposal options include
processes 19, incineration or bunting to generate electrical power and/0r steam,
cogeneration. Air emissions r14 to r18 and ash r31 are byproducts of either of these
combustion options. Supplementary fuel r30, such as fuel oil or natural gas may be
required or utilized in incineration 0r cogeneration. landfill, process 20, is a second
disposal option, with air emissions r14 and r32, landfill mass of cellulosic fiber r34,
liquid leachate r33 which may contaminate ground water, and biochemical oxygen
demand, BOD r24 which may accompany decomposition. Recycling is the third disposal
option, links 2-17 and 2-18 which are connected to paper manufacturing by stimulus
variable 02 in Figure 5.

Process 13 describes the combustion of diesel fuel by truck or railroad locomotives
for the transportation processes 14, 16, 17 and 18. It is important to note that the

combustion of fuel in process 13 is a separate processes from the transport processes

84
themselves, 14, 16, 17 and 18. That is, the diesel fuel is not a component of the objects

of transformation, paper, cups, waste paper, etc. However, the quantity of diesel fuel
combusted is related to the transport distances, as will be discussed in the following

section.

5.5 Network Model of Paper Manufacturing, Use and Disposal

Table 10 shows the matrices K 10* K b, Krb» Km for the process network describing
paper manufacturing, use and disposal corresponding to the interconnected networks of
Figure 5 and Figure 6. Comments about the coefficient data will be presented below by
referring processes in general by their number and to specific elements according to their
row-column labels.

In Table 10, the network model of paper manufacturing illustrated in Figure 5 is
aggregated with the model of paper use and disposal illustrated in Figure 6. The first
feature to notice is how the system matrix for paper manufacturing Ks given in Table 7
has been incorporated into the model. The ordering of columns of Klb’ Kb has been
chosen with the stimulus variables connecting the lower level system to the higher level
system, 01 and 02, as the first two columns in Table 10. Thus the first two columns of
KS given in Table 7 become the first two columns and first 27 rows of the matrix Kb.
Similarly, columns 3 and 4 of the matrix Ks become the second and third columns of
matrix Km corresponding to 03 and 04.

Now that paper manufacturing has been incorporated into the model, what remains

in the remainder of the matrix is to describe the coefficients relating to the processes for

paper use and disposal.

 

 

Table 10 Paper Mamfacturing, Use and Disposal Coefficients

Pmer Haste Ctps tips Paper Waste Waste Haste Haste lever list. Fuel Diesel
Iranches Paper Paper Cuts Paper Paper ages Gas Oil Fuel

this 01 02 014 015 016 017 018 019 020 012 03 04 013
Paper 1-16 0 0 0 0 1 0 0 0 0 0 0 0 0
Pan 16-15 0 0 0 1.10 0 0 0 0 0 0 0 0 0
Haste Paper 17-15 0 0 0 .10 D 0 0 0 0 0 0 0 0
Caps 13-14 0 0 i 0 0 0 0 0 0 0 0 0 0
Cups 14-12 0 0 0 0 0 0 0 0 0 1 0 0 0
Used Ctms 10-12 0 0 0 0 O 0 0 0 0 1 0 0 0
lneimllesta Paper 19-17 0 0 0 0 0 O O 0 0 0 0 D 0
lncin.Used ups 19-18 0 0 O D 0 0 0 0 0 0 0 0 0
Lmrlfill waste Pap 20-17 0 0 0 0 0 1 0 0 0 0 0 0 0
Lmdfill Used Dims 20-10 0 0 D 0 0 0 1 0 0 0 0 0 0
IacleIaste Paper 2-17 0 0 0 0 0 0 0 0 0 0 0 0 0
lecyl.Used Owe 2-18 0 0 0 0 D 0 0 D 0 0 0 0 D
0000 Logs r1 2.3320 4.9356 0 0 0 0 0 0 0 0 0 0 0

Meter r2 .1000 -.0330 0 0 0 0 0 0 0 0 0 0 0 -
Chlorine r3 .0600 -.0190 0 0 0 0 0 0 0 0 0 0 O
Sedit- hydroxide r4 .0200 -.0066 0 0 0 D 0 0 0 0 0 0 D
8001:- chlorate r5 .0300 o.0149 0 0 0 0 0 0 0 0 0 0 0
Sulfuric acid r6 .0100 -.0083 0 0 0 0 0 0 0 0 0 0 0
Sulfur dioxide r7 .0100 .0017 0 D 0 D 0 0 0 0 D 0 0
Caleitm hydroxide rD .0100 won 0 0 0 0 0 0 D 0 D O 0
Sodium sulfate r9 .0010 -.0008 0 0 0 0 0 D 0 0 0 0 0
Pipenta r10 0 0 0 0 0 0 0 D 0 0 0 0 0
Coatings r11 0 0 0 D 0 0 0 0 0 0 0 0 0
Filler r12 0 0 0 0 0 0 0 0 0 0 0 0 0
Soditm Phosphate r13 0 0 0 0 0 0 0 0 0 0 0 0 0
r14 0 0 D 0 0 0 0 0 0 0 0 0 0
CO r13 .0037 -.0031 0 0 0 0 0 .03 0 0 .0001 .0001 .070
”x r16 .0061 -.0050 0 0 0 0 0 .046 0 0 .0004 .0005 .020
S02 r17 .0132 -.0110 0 0 0 0 0 .1” 0 0 0 .0044 0
Particulates r10 .0020 -.0016 0 0 0 0 0 .015 0 0 0 .0005 .001
Chlorine r19 .0002 -.0001 0 0 0 0 0 0 O O 0 D 0
chlorine dioxide r20 .0002 -.0001 0 0 0 0 0 0 0 0 0 0 0
Rammed sulfides r21 .0015 -.0004 0 0 D 0 0 0 0 O 0 0 0
I120 r22 .0800 -.0181 0 0 0 0 0 0 D D 0 O 0
Suspended solids r23 .0100 -.DO33 0 0 0 0 0 0 0 0 D 0 0
s00 r24 .0050 -.0012 0 0 0 0 0 0 0 0 0 0 0
Organochlorides r25 .0030 -.0005 0 0 0 0 0 0 0 0 O D 0
Cellulostic Fiber r26 .0010 .0002 0 0 0 0 0 0 0 0 0 0 0
Inorgmie salts r27 .0600 -.0196 0 0 0 0 0 0 0 0 0 0 0
Adresivs r28 0 0 0 0 0 0 0 O 0 0 0 O 0
leverages r29 0 0 0 0 0 0 0 0 0 1 0 O 0
Incineration Fuel r30 0 0 0 0 0 0 0 0 0 0 0 0 0
Ash r31 0 0 0 0 0 0 0 .18 0 D 0 0 0
Methane r32 0 0 0 0 0 0 0 0 0 0 0 0 0
Lsaehata r33 0 0 0 0 0 0 0 0 0 0 0 0 0
Cellulostic Fiber r34 0 0 0 0 0 0 0 0 1 0 0 0 0

 

86

In transport processes 14 and 16, and cup use, 12, there is no transformation of the
product in material form, so coefficients for these processes are 1 for [IS-14,014], [1-
16,016], [14-12,012] and [IS-12,012]. In process 15, cup manufacturing, 10% of the
paper from manufacturing the cup is lost to waste trimmings due to the cylindrical shape
of the bottom and the tapered shape of the cup body. The coefficients for [165,015]
and [17-15,015] reflect this loss. Hocking [41] does not include these losses in his
calculations, which is important since this increases the total paper requirement per
beverage serving and material and energy requirements by 10% .

In this particular example, the case of 100% landfill disposal is being examined.
Thus coefficients [20-17,017] and [20-18,018] are set to l, and coefficients for
incineration and recycling are set to zero. later cases will examine 100% incineration,
power cogeneration, and recycling disposal options, as well as mixed disposal alternatives
where disposal is distributed between the three options. The selection of the coefficients
associated with transport processes 17 and 18 determines the distribution.

The incineration of waste paper in process 19 results in residuals r14 through r18.
These coefficients are assumed to be the same as those for the combustion of waste bark
and black liquor in paper manufacturing. More specific figures could be used to reflect
differing combustion technologies available for incineration or power cogeneration. Ash,
r31, is also a byproduct.

The landfill of waste paper in process 20 may result in five types of residuals, carbon
dioxide r14, BOD (biological oxygen demand) r24, methane r32, leachate r33, and
cellulosic fiber r34. landfill disposal is performed in a wide variety of geographic and

climatic sites, with a variety of technologies. Under some conditions buried organic

87

wastes may decompose and under others may remain relative inert, Hocking [41],
Cavaney [38]. If decomposition occurs, the primary air emissions are C02 and methane
in varying concentrations depending on the availability of oxygen (BOD) within the .
landfill substrate. Some landfill technologies deliberately manage the decomposition
process to produce methane which is then captured and stored for use as a fuel.
Leachate refers to the liquid that drains from the landfill site and may contaminate
underground water supplies or surface water. The model can accommodate these
. variations in landfill conditions, but since representative data are not available for this a
widely variable processes, here the case of an inert disposal site is represented by
assuming that all landfilled waste paper results in landfill mass.

Residuals from the combustion of diesel fuel for transportation 013 consist of air
emissions r14 through r18. These coefficients are calculated from the U.S.
Environmental Protection Agency limits on air emissions for diesel trucks [50]. These
limitswent into effect in 1986 and are currently in force.

Table 11 shows the continuity interconnection matrix for the network. Note that 01
and 02 from the network diagram of paper manufacturing are connected to links l-l6 and
2-17, 2-18 respectively. In table 12 information for various variables in the model are
entered. For this aggregated model, the stimulus variable beverage servings, 012, is the
overall stimulus for the network. The weight per cup used here is the 8.3 grams used
in Hocking‘s example, which represents a typical 8 oz. paper coffee cup. For evaluation
of other package types the appropriate weight per package can be entered. The first
group of comparisons are to be on the basis of equal weights of packaging material, so

the weight of cups has been specified as 1.0 kg, which yields 120 beverage servings.

88

Table 11 Paper Manufacturing, Use, Disposal Continuity Matrix

1'16 16°15 17-15 15-14 16-12 18-12 19-17 19-18 20-17 20-18 2°17 2-18

01 1 0 0 0 0 0 0 0 0 0 0 0
O2 0 0 0 0 0 0 0 0 0 0 1 1
016 0 0 0 0 1 0 0 0 0 0 0 0
015 0 0 0 1 0 0 0 0 0 0 0 0
016 0 1 0 0 0 0 0 0 0 0 0 0
017 0 0 1 0 0 0 0 0 0 0 0 0
018 0 0 0 0 0 1 0 0 0 0 0 0
019 0 0 0 0 0 0 1 1 0 0 0 0
020 0 0 0 0 0 0 0 0 1 1 0 0

Table 12 Paper Manufacturing, Use, Disposal Variables
Stimulus variables

Number of beverage serving 012 120

Weight per cup 9 8.30

Weight of cups kg 014 1.00

Natural gas kg 03

Fuel Oil kg 04

Diesel Fuel kg 013

Disposal Policy ' Waste Used
Paper Cups

8 Incineration/Cogen. .008 .00%

8 Landfill 100.00% 100.00%

% Recycled .008 .00%

table 13 Paper Manufacturing, Use, Disposal Energetic Matrix Fb Fo

Energy type kg fuel] kg In of Stem Ilatural Fuel Elect. Diesel Direct Direct
per urit material freidit uterial/ transport Gas Oil Power Fuel Labori Laborl
mi t- kl f rei mt kg kg kg ktlr kg hours hours

Process urit
Paper Marxrfacture 01 0 0 .2540 .9980 0 .0041 0
0.Paper Repulping 02 0 0 0548 -.2963 0 -.0016 0
Cu) Transport 014 .35 10000 300 0 0 0 0 .0105 .0005 0
Cu: Manufacturing 015 0 0 0 .001 0 .0010 0
Paper Transport 016 .35 20000 1000 0 0 0 0 .0175 .0008 0
ll.Paper Transport 017 .35 20000 1000 0 0 0 0 0175 .0008 0
0.0m Irarrsport 018 .35 20000 1000 0 0 O 0 0175 .0008 0
incineration 019 0 0 0 -1.85 0 .MD 0
Landfill 020 0 0 0 0 0 .MD 0
leverage Servings 012 0 0 0 0 0 0 0
Matural Gas 03 0 0 0 0 0 0 0
Fuel Oil 04 0 0 0 0 0 0 0
Diesel Fuel 013 0 0 0 0 0 0 D

 

89
later comparisons will be made on the basis of equal numbers of beverage servings.

The material rates for natural gas, fuel oil, and diesel fuel combustion, 03, 04, and 013
are determined internally in the model from the energy requirements as discussed below.
Finally, a disposal policy can be specified for both waste paper and used cups. These
disposal policy choices are automatieally reflected in the coefficients of Table 10.

In Table 13 the energetic matrices Fb and F0 are given. The first two rows
corresponding to 01 and 02 specify coefficients from the lower level model of paper
manufacturing, that is the first two rows of the matrix F5 for the network model of paper
manufacturing given in Table 9. The rows corresponding to transport processes, 014,
016, 017, and 018 allow entry in the model of data about the transport processes. In
the first column, the specific fuel consumption of the transportation unit is entered. The
metric coefficient of .35 kg fuel/ freight unit-km corresponds to the more familiar 7 miles
per gallon fuel consumption of a typical semi-truck in English (SAE) units [48].
Alternative specific fuel consumption rates could be specified to evaluate rail or ship
transport. The second column corresponds to the weight of material carried each freight
unit, or truckload in this case. Note that the transport of paper, waste paper and used
paper, 016, 017, and 018 assumes 20000 kg. per truckload, since this corresponds to the
legal weight limit under federal trucking regulations. However the process of
transporting cups assumes only 10000 kg per truckload since the volume of finished cups
constrains the weight that can be transported per vehicle [48].

In the third column of Table 13 the distanceof transport is specified. The figures
chosen here of 1000 km for paper, waste paper, and used cup transport are thought to

be realistic in the absence of representative industry wide data. In North America, paper

 

9O

manufacture is concentrated in three geographic zones, the Pacific Northwest, Ontario
and Quebec, and the South Eastern U.S. A 1000 km radius from each of these regions
encompasses much of the industrial and population centers of the continent. A distance
of 1000 km has also been chosen as an average for waste paper and used cup transport.
Incineration and power cogeneration plants are widely spaced geographically, and
increasingly major portions of municipal wastes from population centers are being
trucked across several states due to scarcity of landfill sites [30]. Paper repulping plants,
whether combined with virgin pulp manufacture or operating solely from recycled paper
are also geographically widely spaced. The transport of finished cups is assumed to be
300 km on an average since there are many cup manufacturers distributed more densely
throughout urban regions. The eighth column, diesel fuel kg / unit material, is computed
using the data in the first three columns. Direct labor time in the ninth column is based
on an average speed of 70 mm for each truck.

Cup manufacturing, 015 is a reasonably simple process involving electrically driven
automated machinery and is assumed to have a nominal electrical requirement and labor
requirement. If electrical power cogeneration takes place in the incineration processes
there will be electric power produced. Here 1.85 kWh per kg of waste paper or used
cups is assumed based on 20 M Joules of recoverable heat per kg of paper [41] and a
typical power conversion efficiency of 33%. In the absence of better data, reasonable
assumptions have been made for direct labor requirements.

No energy has been assumed for process 12, cup use, but an extremely
comprehensive life-cycle assessment could include the energy required to warm or cool

the beverage for consumption! The processes of fuel combustion 03, 04 and 013 produce

 

 

91

energy that is utilized by other processes at conversion efficiencies that are included in
the computations for the entries in Fb, but do not themselves have energetic requirements
except for possibly indirect labor which is not an energetic transformation cost.

Table 14 shows the matrix X0 for the energetic costs of materials brought to the
boundary of the entire system. This is the same as the matrix X0 for paper
manufacturing given in Table 5 with the addition of resources and residuals 128 through

r34.

92

Table 14 Paper Manufacturing, Use, Disposal Matrix xr

Energy Type
per mit nterial

kssotrce

000d Logs

Hater

Chlorine

Soditm hydroxide
Soditm chlorate
Sulfuric acid
Sulfur dioxide

Calcitm hydroxide

Soditm sulfate
Pi'snts
Coatings

Filler

Sodirm Phosphate
“’2

co

"ox

Particulates
Chlorine
Chlorine dioxide
Retired sulfides
:3 uzo
iSuspended solids
8CD

Organochlorides

Cel lulostic Fiber

inorganic salts
Adresive
Beverages

incineration Fuel

Ash
Methane
Leachate

Cellulostic Fiber

r9

r10
r11
r12
r13
r14
r15
r16
r17
r18
r19
r20
r21
r22
r23
r24
r25
r26
r27
r28

r30
r31
r32
r33
r34

Matural

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

OOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Power
k0

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Fuel Electric Diesel Direct
Labor 1
hours

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOG

Di rect
Labor 2
hours

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

93

5.6 Life-cycle Level Results of Paper Manufacturing, Use and Disposal

Figure 7 shows a diagram for the complete network of paper manufacturing, use and
disposal combining the network of manufacturing process of Figure 5 with the use and
disposal processes of Figure 6. Table 15 shows the system matrix Ks for Figure 7
relating products yo to resources yr and the internal schedule matrix Kb relating the flow
rates or products yo to the flow rates of internal stimulus variables yb. Flow rates of
material variables y,, y,, yb, and yo are presented in Table 16. Table 17 reports the
energetic costs for the entire network. Notice that in this example the energy per unit
material F3 and X0 are the same as the total energy es and so since the analysis is based
on one unit (kg) of paper packaging material and the boundary energies at lower levels
have all been specified as zero. A more detailed discussion of the material flows and

energetic costs shown in these tables will be given in the chapter on comparisons of the

life-cycle results of paper and polystyrene packaging to follow.

 

‘1-

94

 

 

 

W00d Logs
r1 0 :
Water
r2 >

Chemicals

r3 Chlorine

r4 Sodium hydroxide
r5 Sodium chlorate
r6 Sulfuric acid

r7 Sulfur dioxide
r8 Calcium oxide

r9 Sodium Sulfate

 

0% >47

Coatings E Fillers
r10 Pigments
r11 Coatings
r12 Filler
011

\
'

Re-pulping Chemicals
r13O Sodium phosphate

 

Waste Paper

 

02 C -

Natural gas
03 C‘ :

 

Fuel Oil
04 Cr :

 

Adhesive

 

r28 Ck ,

Beverages
r29 Oi 1>

 

Fuel

 

r30 05 >

 

Paper

Manufacturing

Use

Disposal

Air Emissions
C02 1'14
CO r15
NOx r16
802 r17
Particulates r18
Chlorine r19
Chlorine dioxide r20
Reduced sulfides r21

 

'

Beverages 01

 

7

Water Effluent

m 320 r22
Suspended solids r23
BOD r24

Organochlorides r25
Cellulosic fiber r26
Inorganic salts r27

 

'

Landfill
Ash r31

Methane r32
Leachate r33
Cellulosic Fibea r34

 

 

 

’

Figure 7 Consolidated Diagram of Paper Manufacturing, Use and Disposal

95

Table 15 Paper Manufacturing, Use, Disposal System Matrices

Bever- Nat. Fuel Diesel
ages Gas Oil Fuel

Schedule Matrix Kb 012 03 04 013
Paper Manufacture 01 1.1000 0 O 0
W.Paper Repulping 02 0 O O 0
Cup Transport 014 1 O O 0
Cup Manufacturing 015 1 O O 0
Paper Transport 016 1.1000 0 O O
W.Paper Transport 017 .1000 O O O
U.Cup Transport 018 1 O 0 O
Incineration 019 O O O O
Landfill O20 1.1000 0 0 O
SYstem Matrix Kr

Wood Logs r1 2.5652 0 O 0
Water r2 .1100 O 0 0
Chlorine r3 .0660 0 O 0
Sodium hydroxide r4 .0220 O O 0
Sodium chlorate r5 .0330 O 0 O
Sulfuric acid r6 .0110 O O O
Sulfur dioxide r7 .0110 O 0 0
Calcium hydroxide r8 .0110 O O 0
Sodium sulfate r9 .0011 O o O
Pigments r10 0 O O O
Coatings r11 0 O O 0
Filler r12 0 O 0 0
Sodium Phosphate r13 0 O O 0
co2 r14 0 o o 0
CO r15 .0041 .0001 .0001 .0780
NOx r16 .0067 .0004 .0005 .0200
SO2 r17 .0145 0 .0044 0
Particulates r18 .0022 O .0005 .0010
Chlorine r19 .0002 O O 0
Chlorine dioxide r20 .0002 0 O 0
Rgduced sulfides r21 .0017 0 O 0
m H20 r22 .0880 0 o o
Suspended solids r23 .0110 O 0 0
BOD r24 .0055 0 0 0
Organochlorides r25 .0033 0 0 0
Cellulostic Fiber r26 .0011 0 0 0
Inorganic salts r27 .0660 O 0 0
Adhesive r28 0 0 0 0
Beverages r29 1 0 0 0
Incineration Fuel r30 0 0 O 0
Ash r31 0 O O 0
Methane r32 0 O O 0
Leachate r33 0 0 0 0
Cellulostic Fiber r34 1.1000 0 O 0

Table 16
Links

Paper

Paper

Waste Paper
Cups

Cups

Used Cups

Incin.Waste Paper

Incin.Used Cups
Land Used Cups
Land Used Cups

Recyl.Waste Paper

Recyl.Used Cups

Resources

Wood Logs

Water

Chlorine

Sodium hydroxide
Sodium chlorate
Sulfuric acid
Sulfur dioxide

Calcium hydroxide

Sodium sulfate
Pigments
Coatings

Filler

Sodium Phosphate

Particulates
Chlorine
Chlorine dioxide
Rgduced sulfides
m 1120

Suspended solids
BOD
Organochlorides

Cellulostic Fiber

Inorganic salts
Adhesive
Beverages

Incineration Fuel

.Ash
Methane
Leachate

Y1

96

1-16 1.1000
16-15 1.1000

17-15
15-14
14-12
18-12
19-17
19-18
20-17
20-18
2-17

2-18

Yr

r1

r2

r3

r4

r5

r6

r7

r8

r9

r10
r11
r12
r13
r14
r15
r16
r17
r18
r19
r20
r21
r22
r23
r24
r25
r26
r27
r28
r29
r30
r31
r32
r33

Cellulostic Fiber r34

.1000

.100

OOHOOOHHH

2.5652

.1100
.0660
.0220
.0330
.0110
.0110
.0110
.0011

Branches

Paper Manufacture
W.Paper Repulping

Cup Transport

Cup Manufacturing

Paper Transport

W.Paper Transport

U.Cup Transport
Incineration
Landfill

Objects

Beverage Servings
Natural Gas

Fuel Oil

Diesel Fuel

Paper Manufacturing, Use, Disposal Material Flows

Yb

01 1.1000
02 0
014 1
015 1
016 1.1000
017 .1000
018 1
019 0
020 1.1000
Y0

012 1
03 0
O4 .2794
013 .0490

 

 

97

Table 17 Paper Manufacturing, Use, Disposal Syst- Energetics

Energy Type

per urit uterial

Fsst Matrix

Beverage Servings
Mattral Gas

Fuel Oil

Diesel Fuel

F. Matrix
leverage Servings
Matural Gas

Fuel Oil

Diesel Fuel

xb Mstri x

Paper Manufacture
W.Paper Rawlping
Cw Transport

Cw Mamfacturing
Paper Transport
W.Paper Transport
U.Cup Transport
incineration
Lmrdfill

x0 Matrix

Beverage Servings
Matural Gas

Fuel Oil

Diesel Fuel

Energy e'

Energy '0

012

013

012

013

014
015
016
017
018
019
020

012

013

Ste.

k0

OOOOOOOOO

Matural Fuel

Gas Oil
kg kg
0 .2794
0 0
0 O
0 0
O .2794
O 0
O 0
0 0
0 -.2540
0 -.0548
0 -.2794
0 -.2794
0 -.2540
0 0
0 0
0 0
0 0
-.2794 4.0988
0 O
0 0
0 0
0 .2794
0 -.2794

Elect. Diesel Direct Direct
Power Fuel Lab0r1 Labor2
hours hours

kill kg

.2963 0
-1.0988 -.0315
-1.0988 -.0210

-.9980 -.0175
0 -.0175
0 -.0175
1.8500 0
0 0

1.0988 .0490

-1.0988 -.0490

0900

.0089

000000000 0°00

0°00

6 LIFE-CYCLE ASSESSMENT OF POLYSTYRENE MANUFACTURING.
USE AND DISPOSAL

6.1 Network Diagram of Polystyrene Manufacturing

A diagram of polystyrene manufacturing including resource materials yr and products
yo is given in Figure 8. The secondary feedstocks in the production of polystyrene are
ethylene manufactured in process 10 and benzene which is manufactured in process 12.
There are a number of precursor chemical options and processes for both ethylene and
benzene manufacture, Austin [42], Hocking [41]. The precursor chemicals illustrated
here are propane, r1, and ethane r2. Propane and ethane are themselves products of the
cracking of petroleum or natural gas via a number of process options. The analysis
presented here illustrates how information about the energy 2, required to bring these
primary feedstocks to the boundary of the enterprise can be utilized in both the enterprise
level analysis and life-cycle assessment without explicitly modeling the refinery cracking
process.

Benzene manufacture produces a number of marketable byproducts; toluene,
aromatics and other fractions, r8 through r10. Similarly, ethylene manufacture results
in hydrocarbon byproducts, r11, with a variety of potential uses. Since ethylene and
benzene have a wide variety of uses, they may typically be produced at one

petrochemical plant or facility, and transported via processes 9 and 11 to another location
for the manufacture of ethylbenzene and polystyrene.

Vlfrthin the petrochemical and plastic industries there are a wide variety of enterprise

Structures, Girouard [47]. large integrated manufacturers operate facilities producing

the series of products from ethylene and benzene to finished styrene beads.

98

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Feedstocks Marketed byproducts
Toluene r8
r1 Propane 12 Benzene Aromatics r9
0» > Other fractions r10
Manufacturing >
r2 Ethane 10 Ethylene I 012 Benzene
O > Hydrocarbon products r11
Manufacturing > O
Ethylene
010 Y 12-11
11 Transport
10-9 Y 7
9 Transport Benzene
011
Ethylene
09 Water Efflugnt
m H O r19
Chemicals Suspended soli s r20
r3 Sodium hydroxide 9-6 Y Y 11-6 BOD r21
r4 Anti-oxidants Inorganic salts r22
> 6 >
Pentane Bthylbenzene
r6 >
Water and Air Emissions
r7 : Styrene r12
07 7-6 Polystyrene Pentane r13
7 Aluminum-—< -—+ > O
Chloride Manufacturing
Recycling -— >——
8-7 8-6
Sodium Hydroxide A I Polystyrene
r3 >7 I 08 06 Beads
Polystyrene
Aluminum Chloride 8 6-1 Polystyrene Beads
r5 >' Replacement >————- 1
Al Chloride 1 Shipping
A 6-2 Polystyrene
Beads
Air emissions
2 Pentane r12
Pentane Polystyrene Styrene 513
r6 > >
Waste polystyrene Recycling
02 C* :
Natural gas 3 Steam, Air Emissions
03 0* : Heat and P0wer-——>
C02 r14
CO r15
Fuel oil 4 Steam,
04 C : Heat and Power ——> O
NOx r16
802 :17
Diesel fuel 5 Transportation Particulates r18
05 : Fuel Combustion > .0
Figure 8 Network Diagram of Polystyrene Manufacturing

 

 

 

100
Other manufacturers may purchase ethylene and benzene from petrochemical

manufacturers and produce ethylbenzene and polystyrene as in process 6 of Figure 8.
The enterprise model illustrated here is that of an integrated manufacturer.

Relatively small amounts of other chemicals are used in polystyrene manufacture.
Sodium hydroxide and aluminum chloride, r3 and r5 are employed, with most of the
aluminum chloride being recycled in the process 7, Hocking [41]. It is important to note
that the continuity of the network topology requires that replacement aluminum chloride
is introduced in process 8 through the stimulus variable 08. Anti-oxidants r4 can be
introduced to improve the properties of polystyrene for recycling Girouard [47]. Pentane
gas introduced into the product gives the solid polystyrene beads the ability to “foam”
or expand into the familiar cellular structure when manufacturing the finished packaging
product.

Water effluents include the cubic volume of water, suspended solids, biochemical
oxygen demand (BOD), and inorganic salts, r19 through r22. Air emissions consist of
styrene gas and pentane which may escape during the production process. The escaped
pentane is a flammable gas which can be captured and burned as a fuel. This scenario
is not modeled here.

Polystyrene recycling, process 2, is a simple processes compared with waste paper
repulping. Used polystyrene foam is shredded with grinding machinery into a granular
or powder form and then re-extruded through a tapered auger heated to 300 to 450
degrees Fahrenheit. The only energy requirement is electric power for mechanical work
and heating the auger body. Pentane is introduced as during virgin polystyrene

manufacture.

 

 

101

As in the ease of the repulping of paper, the branch stimulus variable 06, polystyrene
beads, is a “makeup” variable. For a given level of waste polystyrene 02, the model
calculates the level of virgin polystyrene beads 06 and accompanying resources required.
Polystyrene shipping, 01, is simply a process which maintains the network continuity.
As in the case of paper manufacture, the flow rate of recycled polystyrene beads 62,
must be constrained to be less than or equal to the flow rate 6-1. Otherwise the flow 06
would be negative and the system would “produce” propane and ethane, clearly not a
feasible condition.

The generation of steam, heat, and power in processes 3 and 4, and the combustion
of transportation fuel in process 5 are all analogous to those processes in the discussion '

of paper manufacture.

6.2 Network Model of Polystyrene Manufacturing

Table 18 shows the matrices K lb, K ,0, Krb, Kto for the process network describing
polystyrene manufacturing as given in Figure 8. The coefficients for processes 6, 10 and
12 are derived from the information presented by Hocking [41]. Unfortunately
Hocking’s aggregated data and associated diagrams, calculations and discussions are not
in the rigorous framework required by process network theory. Considerable care taken
when utilizing data in this type of format for calculation of coefficients to be incorporated
in a process network model. References by Austin [42] and Erskine [43] were utilized
to resolve uncertainties in the derivations presented by Hocking. Ethylbenzene and
polystyrene manufacture is a series of reaction processes with unreacted components

being internally fed back, achieving high levels of conversion efficiency.

102

Table 18 Polystyrene Manufacturing Coefficients

 

Polysty Altm. Allll. Ethy- Ethy- Ben- Ben- Polyst Haste Mat. Fuel Diesel

Branches Beads Chlor Chlor lene lene zene zone Beads Polyst Gas Oil Fuel

Links 06 07 08 09 010 011 012 01 02 03 04 05
Polystyrene beads 6-1 0 0 0 0 0 0 0 1 0 0 0 0
Polystyrene beads 6-2 0 0 0 0 0 0 0 0 1 0 0 0
Altmintm chloride 7-6 .m 0 0 0 0 0 0 0 0 0 0 0
Altminrm chloride 8-6 .10 0 0 0 0 0 0 0 0 0 0 0
Alt-int.- chloride 8-7 0 1 0 0 0 0 0 0 0 0 0 0
Ethylene 9-6 .27 0 0 0 0 0 0 0 0 0 0 0
Ethylene 10-9 0 0 0 1 0 0 0 0 0 0 0 0
Benzene 11-6 .86 0 0 0 0 0 0 0 0 0 0 0
Benzene 12-11 0 0 0 0 0 1 0 0 0 0 0 0
Propane r1 0 0 0 0 0 0 5 0 0 0 0 0
Ethane r2 0 0 0 0 1.28 0 0 0 0 0 0 0
Soditm hydroxide r3 .011 .124 0 0 0 0 0 0 0 0 0 0
Anti-oxidants r4 0 O 0 0 0 O 0 0 0 0 0 0
Aluminua chloride r5 0 0 1 0 0 0 0 0 0 0 0 0
Pentane r6 .04 0 0 0 0 0 0 0 .04 0 D 0
Water r7 .14 0 0 0 0 0 0 0 0 0 0 0
Toluene r8 0 0 0 0 0 0 1.20 0 0 0 0 0
Aromtics r9 0 0 0 0 0 0 .95 0 0 0 0 0
Other fractions r10 0 0 0 0 0 0 1.45 0 0 0 0 0
Hydrocarbon prod. r11 0 0 0 0 .28 0 0 0 O 0 0 0
Styrene r12 .003 0 0 0 0 0 0 0 0 0 0 0
Pentane r13 0 0 0 0 0 0 0 0 0 0 0 0
002 r14 0 0 O 0 0 0 0 0 0 D 0 0
CO r15 0 0 0 0 0 0 0 0 0 M1 .lllli .078
1le r16 0 0 0 0 0 0 0 0 0 arms Jim .0211
r17 0 0 0 0 0 0 0 0 0 0 .lll44 0

Particulates r18 0 0 0 0 0 0 0 0 0 0 JAKE .001
1120 r19 .14 0 0 0 0 0 0 0 0 0 0 0
Suspended solids r20 .0005 0 0 0 0 0 0 0 0 0 0 0
our r21 .0002 0 0 0 0 0 0 0 D O O 0
inorganic salts r22 .02 0 0 0 0 0 0 0 0 0 0 0

 

 

103
Coefficients [9—6,06] and [l 1-6,o6] reflect the conversion of ethylene and benzene to

finished polystyrene beads. The coefficients for aluminum chloride describe the
recycling loop whereby 11% of the recycled flow rate is required for makeup.

Transport processes 9 and 11 and the polystyrene shipping process 1 all have
coefficients of one. The coefficients in column 012 reflect the proportions of resource
propane and byproducts r8-r10 of benzene production. Likewise column 010 reflects the
coefficients for ethylene production. The remaining resource and residual coefficients
for process 6 are found in column 06. Air emission rates for natural gas, fuel oil, and
diesel fuel combustion are the same as those utilized in the model of paper manufacture,
use and disposal.

Table 19 shows the interconnection matrix for the network. In Table 20 stimulus
variables 01 and 02 are specified. In this first example, recycling of waste polystyrene
is set to zero. Fuel combustion stimulus variables 03, 04 and 05 are determined
internally in the model according to the energy requirements. Energy use ratios and
conversion rates between energy forms are specified as before in the paper manufacture
model.

Table 21 reports the conversion energy functions Pb and F0 for the network. Steam,
fuel oil and electric power requirements are derived from Hocking [41]. Transportation
diesel fuel is calculated according to the same procedure as in the paper use and disposal
example. For the sake of comparison, manufacturing labor requirements are assumed
to be 4 hours per metric ton of polystyrene, as in the case of paper manufacture. The
recycling of polystyrene, 02, requires a small amount of electric power for shredding and

a larger amount for heating the polystyrene to a glass and then molten state.

104

Table 19 Polystyrene Manufacturing Continuity Matrix

6-1 6-2 7-6 8-6 8-7 9-6 10-9 11-6 12-11

06 1 -1 0 0 0 0 0 0 0
O7 0 0 1 0 0 0 0 0 0
O8 0 0 0 1 -1 0 0 0 0
O9 0 0 0 0 0 1 0 0 0
010 0 0 0 0 0 0 1 0 0
011 0 0 0 0 0 0 0 1 0
12 0 0 0 0 0 0 0 0 1

Table 20 Polystyrene Manufacturing Variables
Stimulus variables

Polystyrene Manufacture 01 1
Waste Polystyrene 02 0
Gas Steam, Heat 8 Power 03

Oil Steam, Heat 8 Power 04
Diesel Fuel - Transport 05
Energy use ratios

Gas In Steam Generation .008
Oil In Steam Generation 100.008
Cogenerated Electric .008
Purchased Electric 100.008
kg Natural Gas/kg Steam .047
kg Natural Gas/kWh Elect. .200
kg Fuel Oil/kg Steam .057
kg Fuel Oil/kWh Elect. .240

Table 21 Polystyrene Mamfacturing Energetic Matrix 'b F"

Energy Type kg fuel] kg km of Stem Matural Fuel Elect. Diesel Direct Direct
per mit ssterial freidrt ssteriall transport Gas Oil Power Fuel Labori Labor2
unit-km freight kg kg kg kUh kg hours hours

Pumas In"
Polystyrene Mfg. 06 3.8 0 0 .28 0 .III10 0
Al.Chl0rlde Recycle 07 O 0 0 0 0 0 0
Al.Chloride Replace 08 0 0 0 0 0 0 0
Ethylene Transport 09 .35 20000 1000 0 0 0 0 0175 .0008 0
Ethylene Manufacture 010 2.65 0 .17 0 0 .MO 0
Sansone Transport 011 .35 20000 1000 O O 0 0 0175 .0008 0
Iarrzerre Manufacture 012 2.66 0 .17 0 0 .III10 0
"anmmeflHmMuoi 0 0 0 0 0 0 0
Polystyrene Recycle 02 0 0 0 .14 0 .0010 0
Gas Steas,fleat8Power 03 0 0 0 0 0 O 0
Oil Sten,lleat&Power 04 0 O 0 0 0 0 0
Diesel Fuel Coabust. 05 0 0 0 0 0 0 0

105
The specific heat of polystyrene at standard reference temperature is available from

standard reference sources [51]. However the specific heat required to bring polystyrene
to melting is a far more complex matter, and illustrates how difficult it can be to use
theoretical information to derive energy requirements for processes. In fact the
energetics of phase transitions of non-cross linked plastics such as polystyrene through
glass to molten states is not understood theoretically, despite having been the subject of
research spanning decades [52]. Lacking empirical data measuring the power
consumption of an extruder in operation, an assumption has been made that polystyrene
recycling requires half the electrical energy of virgin polystyrene manufacture.

Table 22 gives the matrix Xr for the boundary energy costs of the network resource
materials 3’:- The boundary energetic costs for the minor resource materials r3 through
r6 are unknown. However estimates are available for the energies rm for the two
primary feedstocks, propane and ethane. The actual requirements are highly variable
depending on the facility and technology. The coefficients shown here follow Hocking‘s
approximation of 15 % hydrocarbon requirement for fueling the cracking processes.

Table 23 provides for the entry of price information for resources, products and
energetic resources. As discussed in the paper manufacturing example, operational price
information is difficult to obtain for propriety reasons. The assumed prices used here
are reasonable approximations of prices obtained by Girouard [47] in January 1992, and
illustrate how process network models can be mapped into economic performance of the
enterprise. It should be noted that byproducts r8 through r11 have economic value and
may be marketed by the enterprise or used in other manufacturing operations. Thus they

are assigned negative prices at the boundary of the network.

106
Table 22 Polystyrene Manufacturing Matrix XI,

Energy Type llatural Fuel Electric Diesel Direct Direct

per urit uterial Gas Oil Poser Fuel Labor 1 Labor 2
kg kg kll kg hours hours

Resource
Propane r1 0 .056 D D D D
Ethme r2 0 .056 0 0 0 0
Sedit- hydroxide r3 0 D 0 0 0 0
Anti-oxidants rb 0 0 0 0 0 0
Alt-ira- chloride r5 0 D 0 0 0 0
Pentane r6 0 0 D 0 D 0
Hater r7 0 0 0 0 0 D
Toluene r8 0 0 0 0 0 0
Aroutics r9 0 0 0 0 0 0
Other fractions r10 0 0 0 0 0 0
Hydrocarbon prod. r11 0 0 0 0 0 0
Styrene r12 0 0 0 D 0 0
Pentane r13 0 0 0 0 0 0
€02 r16 0 0 0 0 0 0
CO r15 0 0 0 0 0 0
sex r16 0 0 0 0 0 0
r17 0 0 0 0 0 0
Particulates r18 0 0 0 0 0 0
Ilzo r19 0 0 0 0 0 0
Supended solitb r20 0 0 0 0 0 0
am r21 0 0 0 0 0 0
0 0 0 0 0 0

inorganic salts r22

 

 

107

Table 23 Polystyrene Manufacturing Prices

Price/kg Price/kg
material material
Resource yr pr Products Yo po
Propane r1 $.25 Polystyrene Beads o1 $.70
Ethane r2 $.25 Waste Polystyrene oz $.00
Sodium hydroxide r3 $.25 Natural Gas 03 $.00
Anti-oxidents r4 $.00 Fuel Oil 04 $.00
Aluminum chloride r5 $.25 Diesel Fuel o5 $.00
Pentane r6 $.25
Water r7 $.00
Toluene r8 ($.25)
Aromatics r9 ($.25)
Other fractions r10 ($.25)
Nydrocarbon prod. r11 ($.25)
Styrene r12 $.00
Pentane r13 $.00
CO r15 $.00
nox r16 $.00
r17 $.00
:grticulates r18 $.00
320 r19 $.00
Suspended solids r20 $.00
BOD r21 $.00
Inorganic salts r22 $.00
Price/unit kg
energy Processin Environment mater al
Energy pe Amort zation Gb & Go
Natural Gas / kg $.25 Polystyrene Mfg. 06 .02
Fuel Oil / kg $.25 Al. Chloride Recycle 07 0
Electric Power / kWh $.05 A1. Chloride Replace 08 0
Diesel Fuel / kg S. 35 Ethylene Transport o9 .02
Direct Labor 1 / hour$12. 00 Ethylene Manufacture o10 .02
Direct Labor 2 / hour $. 00 Benzene Transport 011 .02
Benzene Manufacture 012 .02
Polystyrene Shipping 01 0
Polystyrene Recycle oz .02
Gas Steam,Heat&Power o3 .02
Oil Steam,Heat&Power 04 .02

Diesel Fuel Combust. oS .02

108
It should be noted also that fuels, natural gas, fuel oil and diesel fuel, are priced as

energies only, not as combustion materials 03, 04 and 05. To assign prices to both of
these roles in the model would result in double counting of their economic cost. For

purposes of illustration, processing environment amortization has been set to $.02.

6.3 Enterprise Level Results of Polystyrene Manufacturing
Figure 9 shows the diagram of the manufacturing enterprise illustrated in Figure 8
at the next higher level of organization. Table 24 shows the system matrix KS relating

products yo to yr and the internal schedule matrix Kb relating the flow rates of products

yo to the flow rates of internal stimulus variables yb. Flow rates of material variables.

)1, yr, yb and yo are presented in Table 25.

Energetic and economic results for polystyrene manufacturing are presented in
Table 26. The topology for the production of recycled versus virgin polystyrene heads
is the same topology as for paper manufacture. Thus recycling reduces the energy
requirements for each kg of waste polystyrene 02 utilized in the production of
polystyrene beads 01. Since no steam, natural gas, fuel oil, or diesel fuel are used in
polystyrene recycling, the reduction in these energy forms is exactly equal to the
quantities utilized in virgin polystyrene manufacture. Under the assumption that
electrical power requirements are half for the recycled material 02, the kWh of electricity
are reduced accordingly in Fsst and FS. After conversion of units, the fuel oil
(petroleum) energy requirement shown in X0 of .8053 kg / kg of polystyrene is in close
agreement with .7923 kg / kg given by Hocking. Electric power requirements of .28

kWh I kg of polystyrene are also consistent with Hocking [41].

 

i r

Feedstocks

rl Propane

V

109

 

 

r2 Ethane

V

Chemicals
r3 Sodium hydroxide
r4 Anti-oxidants

 

r5 OAluminum Chloride

'7

 

 

 

 

 

Pentane

r6 >
Water

r7 >
Waste polystyrene

02 Cr* :
Natural gas

03 C~ :
Fuel oil

04 Cr :
Diesel fuel

05 C‘ :

 

 

Polystyrene

Manufacturing

Marketed byproducts
Toluene r8
Aromatics r9

Other fractions r10

¥

 

'

 

Hydrocarbon products r11

Air Emissions

Styrene r12
Pentane r13
€02 r14
CO r15
NOx r16
80 r17

Particulate: r18

\

 

'

Water Efflugnt

H O r19
Suspended Solids r20
BOD r21
Inorganic Salts r22

 

'

Polystyrene Beads ol

 

 

 

'

Figure 9 Consolidated Network Diagram of Polystyrene Manufacturing

Table 24

Schedule Matrix Kb

Polystyrene Mfg.

A1.Chloride Recycle
A1.Chloride Replace
Ethylene Transport
Ethylene Manufacture
Benzene Transport
Benzene Manufacture

System Matrix KS

Propane

Ethane

Sodium hydroxide
Anti-oxidents

Aluminum chloride

Pentane

Water

Toluene
Aromatics

Other fractions

Hydrocarbon prod.

Styrene
Pentane

ngticulates
Suspended solids
BOD

Inorganic salts

06
07
08
09
010
011
012

r20
r21
r22

110

Polyst Waste
Beads Polyst
01 oz
1 -1
.0890 -.0890
.0110 -.0110
.2700 -.2700
.2700 -.2700
.8600 -.8600
.8600 -.8600
4.3000 -4.3000
.3456 -.3456
.0220 -.0220
0 0
.0110 -.0110
.0400 0
2.5000 -2.5000
1.0320 -1.0320
.8170 -.8170
1.2470 -1.2470
.0756 -.0756
.0030 -.0030
0 0
0 0
0 0
0 0
0 0
0 0
2.5000 -2.5000
.0005 -.0005
.0002 -.0002
.0150 -.0150

Nat.

Gas

03

0000000

00000000000000

Polystyrene Manufacturing System Matrices

Fuel Diesel
Oil Fuel
o4 05

O 0

0 0

O O

0 0

O O

0 0

0 0

O O

0 0

O O

0 O

0 0

0 0

0 0

0 0

O 0

0 O

0 0

0 O

0 0

0 0
.0001 .08
.0005 .02
.0044 0
.0005 .00
O 0

0 0

0 0

0 0

111

Table 25 Polystyrene Manufacturing Material Flows

Links yl Branches yb
Polystyrene beads 6-1 1 Polystyrene Mfg. 06 1
Polystyrene beat 6-2 0 Rl.Chloride Recycle o? .0890
Alt-int- chloride 7-6 .0890 Al.0hloride Replace ob .0110
Alt-ira- chloride 8-6 .1000 Ethylene Transport o9 .2700
Alt-ira- chloride 8-7 .0890 Ethylene Mamfacture o10 .2700
Ethylene 9-6 .2700 Benzene Transport o11 .8600
Ethylene 10-9 .2700 Benzene Manufacture o12 .8600
Benzene 11-6 .8600

Bernene 12-11 .8600

Resets-cos Yr wjects yo
Prop-re r1 4.3000 Polystyrene Shipping 01 1
Ethane r2 .3456 Polystyrene Recycle o2 0
Sedit- hydroxide r3 .0220 Gas Steal,ileat&Pouer 03 0
Anti-oxidants r4 0 Oil Stean,ileatBPouer 04 .5452
All-11M.- chloride r5 .0110 Diesel Fuel Count. 05 .0196
Pentane r6 .0400

Water r7 2.5000

Toluene r8 1.0320

Rmtics r9 .8170

Other fractions r10 1.2470
Mythocarbon prod. r11 .0756

Styrene r12 .0030
Pentane r13 0
(:02 r14 0
co r15 .0016
110" r16 .0007
$02 r17 .0024
Particulates r18 .0003

M20 r19 2.5000
Smpended solids r20 .0005
son r21 .0002

inorganic salts r22 .0150
Suspended solids r23 .0110
DO r24 .0055
Organochlorides r25 .0033
Cellulostic Fiber r26 .0011
inorganic salts r27 .0660

 

Table 26

Energy Type
per urit uterial

Fsst Matrix

Polystyrene Shipping
Polystyrene Recycle
Gas Shaman-Power
Oil SteufiieatIPouer
Diesel Fuel Codxrst.

8.28.8.9.

F. Matrix

Polystyrene Shipping
Polystyrene Recycle
Gas Steae,ileat&Pouer

Oil Steufileatvouer
Diesel Fuel Codxrst.

8.18.8.9.

ith Matrix

Polystyrene Mfg. o6
Rl.Chloride Recycle o7
Al.Chloride Replace 08
Ethylene Transport 09
Ethylene Manufacture o10
Benzene Transport 011
Benzene Manufacture o12

x0 Matrix

Polystyrene Shipping
Polystyrene Recycle
Gas Steu,lleat&Pouer
Oil Steu,lleat&Pouer
Diesel Fuel Coebust.

8.18.2.2.

Energy e’
Energy eo

Rnortiztion Gs

Polystyrene Shipping 01
Polystyrene Recycle 02
Gas Steumleatvouer 03
Oil Steu,ileat&Pouer 04
Diesel Fuel Cordust. 05

Cash Flow cf

Value Added vs

Ste.

Its

6.1945
-6.1945
0

0

0

-6.1945

-2.6500
-2.6500
-2.6500
-2.6500

8.07

(3.05)

8.02
8.02
8.02

8.12
8.04

Matural

0000009 00°06 00°00

00°00

CO

112

Fuel
0i l

R!

.1921
-.1921
0

0

0

. 5452
- .5452

- .4523

-.2417
-.2417
-.4500
-.4500

.5452
- .8053

Elect.
Pouer
kill

.2800
-.1400
0
0
0

.2800
-.1400

.1400

000

-.2800

Diesel
Fuel
ks

.0198
-.0198
0

0

0

.0198
-.0198

-.0198

-.0175

-.0175

- .0198
.0198

.0198
-.0198

Polystyrene Mamfacturing System Energetics

Direct Direct

Labor1
hours

- .0030

-.0018
-.0010
-.0018
-.0010

- .0030
.0020

. 0030
- . 0030

Labor2
hours

0000000 00000 00000

00900

O

113

6.4 Diagram of Polystyrene Manufacturing, Use and Disposal

Figure 10 is a network diagram of polystyrene use and disposal. The boundary
stimulus variables for use and disposal are the flow of beverages 013, and diesel fuel for
transportation 05. Notice that links 1-16, polystyrene, and link 2-17, used cups and
waste polystyrene, are connected to the network model for polystyrene manufacturing
shown in Figure 9 at 01 and 02 respectively. This illustrates a particular choice of
modeling topology where the network in Figure 9 is “added” to the graph of Figure 10.

Polystyrene beads from polystyrene manufacturing are transported to a cup
manufacturing facility, process 15. Cup manufacturing consists of heating the beads in
a molding machine which expands, or “foams” the polystyrene into the familiar cup
form. No polystyrene is wasted in the processes, but some pentane from the foaming
process is lost to the atmosphere. Cups must then be transported to the point of use in
process 13. Beverages, 013, are the stimulus variable for the overall network of
manufacture, use and disposal. In processes 17 used cups are separated for three
disposal options and transported to their respective destinations, incineration or
cogeneration 18, landfill 19, or the recycling link 2-17. Transportation fuel combustion

takes place in process 5.

 

 

 

 

 

 

114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polystyrene
Beads 16 Polystyrene
olO—>—O—>—- Transport
1-16
o16
Polystyrene Beads
Y 16-15 Air Emissions
Pentane r13
15 Cup >
Manufacturing
Cups
o15
Y 15-14
14 Cup
Transport
Cups
014
Y 14-13
Beverages 13 Cup Beverages
r23 >— Use : 013
1
Used Cups Air Emissions 002 r14
17-13 CO rlS
NOx r16
80 r17
Particula es r18
017 18 > 0
Fuel Incineration
r24 0 > or
, 18-17 Cogeneration Ash r25
Used Cup 018
Transport 19-17
F" >= 19 Land fill mass r26
019 Land fill > O

 

 

 

05

Diesel fuel

 

 

 

 

 

 

 

 

Figure 10

 

5 Transportation
- Fuel Combustion

 

 

2-17 Waste polystyrene used cups for recycling

V

02
Air Emissions

C02 r14
CO r15
NOx r16
802 r17
Particulates r18

Network Diagram of Polystyrene Use and Disposal

115
6.5 Network Model of Polystyrene Manufacturing, Use and Disposal

Table 27 shows the matrices K for K10, Krb’ Km for the process network describing
polystyrene manufacturing corresponding to Figure 10. Comments about the coefficient
data will be presented below by referring processes in general by their number and to
specific elements according to their row-column labels.

In this table, the network model of polystyrene manufacturing illustrated in Figure
9 is aggregated with the model of paper use and disposal illustrated in Figure 10. The
first feature to notice is how the system matrix for polystyrene manufacturing Ks given
in Table 24 has been incorporated into the model. The ordering of columns of Klb’ K10
has been chosen with the stimulus variables connecting the lower level system to the
higher level system, 01 and 02, as the first two columns. Thus the first two columns of
Ks given in Table 24 become the first two columns and 22 rows of the matrix K10.
Similarly, columns 3, 4 and 5 of the matrix Ks become the second, third and fourth
columns of matrix Km corresponding to 03, 04 and '05.

Now that polystyrene manufacturing has been incorporated into the model, what
remains in the remainder of the matrix is to describe the coefficients relating to the
processes for polystyrene use and disposal. In transport processes 14 and 16, and cup
use, 13, there is no transformation of the product in material form, so coefficients for
these processes are l, [15-14,ol4], [1-16,ol6], [14-13,ol3] and [l7-13,ol3]. In process
15, cup manufacturing, none of the polystyrene from manufacturing the cup is lost so
[1645,015] is one. In this particular example, the case of 100% landfill disposal is
being examined. Thus coefficients [19-17,ol7] is set to 1, and coefficients for

incineration and recycling are set to zero.

 

116

Tfile 27 Polystyrene Manufacturing, Use, Disposal Coefficients
Polyst lleste Owe Owe Polyst Used Used Used Bever- Mat. Fuel Diesel
Branches Beads Polyst leads two time cw. ages Gas Di 1 Fuel
Links o1 02 M4 o15 o16 o17 018 019 o13 03 04 05
Owe 14-13 D 0 0 D D D 0 0 1 O 0 0
Glass 15-14 0 0 1 0 D 0 0 D 0 D 0 0
Polystyrene beads 16-15 0 0 0 1 0 O 0 0 D 0 D 0
Polystyrene beat 1-16 0 D D D 1 0 0 O 0 0 0 0
Used ewe 17-13 0 D D 0 D D 0 D 1 0 D D
lncln. used ewe 18-17 0 0 D D D 0 O 0 0 0 D D
Lmrdflll med ups 19-17 0 D D D D 1 0 D 0 0 0 0
Recycle tmed ctps 2-17 0 D 0 0 0 0 0 0 0 O 0 0
Properm r1 4.3000 -4.3000 0 0 D 0 0 0 0 0 0 0
Ethos r2 .3456 -.3456 D D 0 0 0 0 0 0 0 0.
Sodltm hyd-oxide r3 .0220 ~.0220 0 D 0 D 0 0 0 0 0 D
Anti-oxidants r4 0 0 0 D 0 0 D 0 0 0 D D
thmlram chloride r5 .0110 -.0110 0 0 0 D 0 0 0 0 0 0
Pentane r6 .0400 D D 0 0 0 0 0 0 D D 0
Hater r7 2.5000 -2.5000 0 0 0 0 0 D 0 D 0 0
Toluene r8 1.0320 -1.0320 0 0 0 0 D 0 0 0 0 0
Rrutice r9 .8170 -.8170 0 0 0 D 0 0 0 0 0 D
Other fractions r10 1.2470 -1.2470 0 0 D O 0 0 0 0 0 0
Hydrocarbon prod. r11 .0756 -.0756 0 0 0 0 0 0 0 0 0 0
Styrene r12 .0030 -.0030 0 0 0 0 0 0 0 0 D 0
Pentane r13 . D D 0 .04 0 D 0 0 0 0 0 D
r14 0 0 0 0 0 0 D 0 0 0 0 D
00 r15 0 0 D 0 0 0 .028 0 0 .0001 .0001 .0780
110x r16 0 D 0 0 0 0 .046 D D .0004 .0005 .0200
r17 0 0 0 0 0 0 .100 0 0 0 .0044 0
Particulates r18 0 0 0 0 0 0 .015 0 0 0 .0005 .0010
M20 r19 2.5000 -2.5000 0 0 0 0 0 D 0 D 0 0
Suspended solids r20 .0005 -.0005 0 O 0 0 D 0 0 0 0 0
son r21 .0002 -.0002 D 0 0 D 0 D D D 0 0
Inorganic salts r22 .0150 -.0150 0 0 D O 0 0 D 0 0 0
Beverages r23 0 0 0 0 0 0 0 0 1 0 0 0
Fuel r24 0 0 0 0 D 0 D 0 0 0 0 0
Ash r25 0 D 0 0 0 0 .03 0 0 0 D 0
Landfill use r26 0 0 D 0 0 0 D 1 0 0 0 0

 

1 17
Later cases will examine 100% incineration, power cogeneration, and recycling disposal

options, as well as mixed disposal alternatives where disposal is distributed between the
three options. The selection of the coefficients associated with transport process 17
determines the distribution.

Incineration of waste polystyrene in process 18 results in residuals r14 through r18
and ash r18. These coefficients are assumed to be the same as those for the combustion
of waste bark and black liquor in paper manufacturing. More specific figures could be
used to reflect differing combustion technologies available for incineration or power
cogeneration. The landfill of waste polystyrene in process 19 is essentially chemically
and biologically inert, so the only resulting residual is the landfill mass of polystyrene.
Residuals from the combustion of diesel fuel for transportation 013 consist of air
emissions r14 through r18.

Table 28 shows the continuity interconnection matrix for the network. Note that 01
and 02 from the network model of polystyrene manufacturing are connected to links 1-16
and 2-17 respectively. In table 29 information for various variables in the model are
entered. For this aggregated model, the stimulus variable beverage servings, 012, is the
overall stimulus for the network. The weight per cup used here is the 2.4 grams used
in Hocking’s example, which represents a typical 8 oz. polystyrene coffee cup. For
evaluation of other package types the appropriate weight per package can be entered.
The first group of comparisons are to be on the basis of equal weights of packaging
material, so the weight of cups has been specified as 1.0 kg, which yields 417 beverage
servings. Later comparisons will be made on the basis of equal number of beverage

servings.

118

Table 28 Polystyrene Manufactuiing, Use, Disposal Continuity
Matr x

14-13 15-14 16-15 1-16 17-13 18-17 19-17 2-1
01
02
014
015
016
017
018
019

CO

OOOOOPOO
OOOOPO
OOOHOOOO
OOOOOOOH
OOHOOOOO
OHOOOOOO
HOOOOOOO
OOOOOOHOQ

Table 29 Polystyrene Manufacturing, Use, Disposal Variables
Stimulus variables

Number of beverage servings 417
Weight per cup 9 2.40
Weight of cups kg 013 1.00
Natural gas kg o3
Fuel Oil kg o4
Diesel Fue kg 05
Disposal Policy Used

Cups
8 Incineration/Cogen. .008
8 Landfill 100.008
8 Recycled .008

Table 30 Polystyrene Merarfacturing, Use, Disposal Energetic Matrix Fb F0

Energy Type kg fuel/ kg km of Steel Matural Fuel Elect. Diesel Direct Direct
per unit material freight aaterial/ transport Gas Oil Poser Fuel Labor1 Labor2
writ-km freidrt kg kg kg kllt kg hours hours

Pumas in“
Polystyrene shipping o1 0 0 .5452 .2800 .0190 .0030 0
Polystyrene recycle o2 0 0 -.5452 ~.1400 -.0198 -.0020 D
Ow transport o14 .35 2500 300 0 0 0 0 0420 .0018 0
upeuuhflumw ofi 0 0 0 .WD 0 .IW0 0
Polystyrene trans. o16 .35 20000 1000 0 0 0 0 0175 .0008 0
Used cup transport o17 .35 20000 1000 0 0 0 0 0175 .0000 0
lncinerationlcogen. 018 0 0 0 -3.700 0 .0010 D
Lmldfill o19 0 0 0 0 0 .MD 0
mom» on 0 0 0 0 0 0 0
assummmMuMuuwfl 0 O 0 0 0 0 0
Oil Steas,Meathouer o4 0 0 0 0 0 0 0
Diesel Fuel Count. o5 0 0 0 0 0 0 0

119
Table 31 Polystyrene Manufacturing, Use, Disposal Matrix "r

Energy Type Matural Fuel Electric Diesel Direct Direct

per mit material Gas Oil Poser Fuel Labor 1 Labor 2
kg kg kll kg hours hours

Resets-ca
Properm r1 0 .056 0 0 0 0
Ethane r2 0 .056 0 0 0 0
Soditm hydroxide r3 0 0 0 0 0 0
Anti-oxidents r4 0 0 0 0 0 0
Altmirxm chloride r5 0 0 0 0 0 0
Pentane r6 0 0 0 0 0 0
Water r7 0 0 0 0 0 0
Toluene r8 0 0 0 0 0 0
Aroutics r9 0 0 0 0 0 0
Other fractions r10 0 0 0 0 0 0
Hydrocarbon prod. r11 0 0 0 0 0 0
Styrene r12 0 0 0 0 0 0
Pentane r13 0 0 0 0 0 0
(:02 r14 0 0 0 D 0 O
00 r15 0 0 0 0 0 0
Max r16 0 O 0 0 0 0
r17 0 0 0 0 0 0
Particulates r18 0 0 0 O 0 0
M20 r19 0 0 0 0 0 0
Suspended solids r20 0 0 0 0 0 0
Bill r21 0 0 0 0 0 0
inorganic salts r22 0 0 0 0 0 0
Beverages r23 0 0 0 0 0 0
Fuel r24 0 0 0 0 0 0
Ash r25 0 0 0 0 0 0
0 0 0 0 0 0

Landfill sass r26

120

The material rates for natural gas, fuel oil, and diesel fuel combustion, 03, 04, and 05
are determined internally in the model from the energy requirements as discussed below.
Finally, a disposal pelicy can be specified for both waste polystyrene and used cups.
These disposal policy choices are automatically reflected in the coefficients of Table 27.

In Table 30 the energetic matrices Fb and I“0 are given. The first two rows
corresponding to 01 and 02, specify coefficients from the lower level model of
polystyrene manufacturing, i. e. the first two rows of the matrix F3 for the network
model of polystyrene manufacturing given in Table 26. The rows corresponding to
transport “processes, 014,016 and 017 allow entry in the model of data about the
transport processes. In the first column, the specific fuel consumption of the
transportation unit is entered. The metric coefficient of .35 kg fuel/freight unit-km
corresponds to the more familiar 7 miles per gallon fuel consumption of a typical semi-
truck in English (SAE) units [48]. Alternative specific fuel consumption rates can be
specified to evaluate rail or ship transport. The second column corresponds to the weight
of material carried by each freight unit, or truckload in this case. Notice that the
transport of polystyrene, waste polystyrene and used polystyrene, 016 and 017 assumes
20000 kg. per truckload, since this corresponds to the legal weight limit under federal
trucking regulations. For the case of waste polystyrene, this assumes that the polystyrene
foam has been shredded er compacted at the recycling collection site to increase its
shipping density before transport. However the process of transporting cups assumes
only 2500 kg per truckload since the volume of finished cups constrains the weight that
can be transported per vehicle [48].

In the third Column of Table 30 the distance of transport is spwified. The figures

121
chosen here of 1000 km for polystyrene and used cup transport are thought to be realistic

in the absence of representative industry wide data. Personal experience in the trucking
where polystyrene beads were hauled under contract indicates that these are reasonable
figures under the industries geographic structure [48]. Incineration and power
cogeneration plants are widely distributed geographically, and increasingly major portions
of municipal wastes from population centers are being trucked across several states due
to scarcity of landfill sites [48]. Polystyrene recycling plants, whether combined with
virgin polystyrene manufacture or operating solely from recycled polystyrene are also
geographically widely distributed. The transport of finished cups is assumed to be 300
km on an average since there are many cup manufacturers distributed more densely
throughout urban regions. The coefficient in the eighth column,
diesel fuel kg / unit material, is computed using the data in the first three columns.
Direct labor time in the ninth column is computed based on an average speed of
70 km / hr for each truck.

Cup manufacturing, 015 is a reasonably simple process involving electrically driven
automated machinery and is assumed to have a nominal electrical requirement and labor
requirement. If electrical power cogeneration takes place in the incineration processes
there will be electric power produced. Here 3.7 kWh per kg of waste polystyrene or
used cups is assumed based on 40 M Joules of recoverable heat per kg of polystyrene
[41] and a typical power conversion efficiency of 33 96 . In the absence of better data,
reasonable assumptions have been made for direct labor requirements.

No energy has been assumed for process 13, cup use, but an extremely

comprehensive life-cycle assessment could include the energy required to warm or cool

122
the beverage for consumption! The processes of fuel combustion 03, 04 and 05 produce

energy that is utilized by other processes at conversion efficiencies that are included in
the computations for the entries in Fb, but do not themselves have energetic requirements
except for possibly indirect labor which is not an energetic transformation cost.

Table 31 shows the matrix X0 for the energetic costs of materials brought to the
boundary of the entire system. This is the same as the matrix X0 for polystyrene
manufacturing given in Table 22 with the addition of resources and residuals 123 through

r26.

6.6 Life-cycle Level Results of Polystyrene Manufacturing, Use and Disposal
Figure 11 shows a diagram for the complete network of polystyrene manufacturing,
use and disposal combining the network of manufacturing process of Figure 9 with the
processes of Figure 10. Table 32 shows the system matrix Ks for Figure 11 relating
products yo to resources yr and the internal schedule matrix Kb relating the flow rates or
products yo to the flow rates of internal stimulus variables yb. Flow rates of material
variables y,, y,, 3,, and yo are presented in Table 33. Table 34 reports the energy costs
for the entire network. Notice that in this example the energy per unit material F5 and
X0 are the same as the total energy as and so since the analysis is based on one unit (kg)
of polystyrene packaging material and the boundary energies at lower levels have all been
specified as zero. A more detailed discussion of the material flows and energy costs

shown in these tables will be given in the chapter on life cycle comparisons to follow.

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Peedstocks Marketed byproducts
Toluene r8
r1 Propane Aromatics r9
Os > Other fractions r10
r2 Ethane
O: > Hydrocarbon products r11
> 0
Chemicals Air Emissions
r3 Sodium hydroxide Styrene r12
r4 Anti-oxidants Pentane r13
r5 Aluminum Chloride C02 r14
>7 Polystyrene CO r15
NOx r16
Pentane Cup 802 r17
r6 0 > Particulates r18
Water Manufacturing
r7 0 > Water Efflusnt
m H O r19
Use Suspended Solids r20
BOD r21
Inorganic Salts r22
Waste polystyrene Disposal >7
02 :
Natural gas Polystyrene Beads ol
03 C: : : 0
Fuel oil
04 0% :
Diesel fuel
05 C‘ :
r23 Beverages Ash r25
> 4)
r24 Fuel Land fill mass r28

 

 

 

 

 

Figure 11 Consolidated Diagram of Polystyrene Manufacturing,
Use and Disposal

124

Table 32 Polystyrene Manufacturing, Use, Disposal

Schedule Matrix Kb

Polystyrene shipping o1

Polystyrene recycle

Cup transport

Cup manufacturing

Polystyrene trans.
Used cup transport
Incineration/cogen.

Landfill
System Matrix Kr

Propane

Ethane

Sodium hydroxide
Anti-oxidents

Aluminum chloride

Pentane

Water

Toluene
Aromatics

Other fractions

Hydrocarbon prod.

Styrene
Pentane

msgrticulates

Suspended solids
BOD

Inorganic salts
Beverages

Fuel

Ash

Landfill mass

02

014
015
016
017
018
019

r1
r2
r3

r5

r6

r7

r8

r9

r10
r11
r12
r13
r14
r15
r16
r17
r18
r19
r20
r21
r22
r23
r24
r25
r26

Bever-

ages

013

OH

HOHHHH

System Matrices

Nat.
Gas

0
u

OOOOOOOO

OOOOOOOOOOOOOO

OOOOOOOOOO

Oil

0
:5

00000000

OOOOOOOOOOOOOO

O O O
GOO
0°C
#00
hU‘lH

.0005

00000000

Fuel Diesel
Fuel

0
01

00000000

OOOOOOOOOOOOOO

O O O
O OO
O Nd
H can
0000

00000000

125

Table 33 Polystyrene Manufacturing, Use, Disposal Material Flows

Links Y1 Branches Yb

Cups 14-13 1 Polystyrene ship 01 1
Cups 15-14 1 Polystyrene recycle oz 0
Po ystyrene beads 16-15 1 Cup transport 014 1
Polystyrene beads 1-16 1 Cup manufacturing 015 1
Used cups 17-13 1 Polystyrene trans. 016 1
Incin. used cups 18-17 0 Used cup transport 017 1
Landfill used cups19-17 1 Incineration/cogen. 018 0
Recycle used cups 2-17 0 Landfill o19 1
Resources yr Objects yo

Propane r1 4.3000 Beverage Servings 013 1
Ethane r2 .3456 Natural Gas 03 0
Sodium hydroxide r3 .0220 Fuel Oil o4 .5452
Anti-oxidents r4 0 Diesel Fuel 05 .0968
Aluminum chloride r5 .0110

Pentane r6 .0400

Water r7 2.5000

Toluene r8 1.0320

Aromatics r9 .8170

Other fractions r10 1.2470
Hydrocarbon prod. r11 .0756

Styrene r12 .0030
Pentane r13 .0400
€02 . r14 0
CO r15 .0076
nox r16 .0022
$02 r17 .0024
Particulates r18 .0004
m H20 r19 2.5000
Suspended solids r20 .0005
BOD r21 .0002
Inorganic salts r22 .0150
Beverages r23 1
Fuel r24 0
Ash r25 0
Landfill mass r26 1

Table 34

Energy Type

per mit uterial
Fsst Matrix

Beverage Servings

Matural Gas
Fuel Oil
Diesel Fuel

F. Matrix

Beverage Servings

Matural Gas
Fuel Oil
Diesel Fuel

11., Matrix

Polystyrene ship
Polystyrene recycle
Ctp transport

Cw mfacturing
Polystyrene trans.
Used ctp transport
lncineration/cogen.

Larflfill

x0 Matrix

Beverage Servings

Matural Gas
Fuel Oil
Diesel Fuel

Energy e‘

Energy e0

o13

05

013

05

ol

02

014
015
o16
017
018
019

013

05

00000000

Ste. Matural
Gas

0000

00000090

0000

126

Polystyrene Manufacturing, Use,

Fuel
Oil
ks

.5452
0
0
0

-.8054

COO

.5452

.8054

Disposal Syst- Energetics

Elect. Diesel Direct Direct
Fuel Labor1 Labor2

hours hours

Poser
ker

.3500

.3500

to

.0084

...i

000°

0000

00000009

OOOO

7 LIFE-CYCLE COMPARISON OF PAPER AND POLYSTYRENE
7.1 Disposal and Recycling Alternatives

Table 35 through 40 present the results of alternative cases of disposal and recycling
of paper and polystyrene packaging materials. These results are presented ”in a format
which allows direct comparison of resources, residuals and energetic requirements for
each of the cases.

Two broad classes of alternative cases are presented; 1) comparisons on a basis of
equal mass of packaging material, and 2) comparisons on a per package basis.
Examination on both of these basis is valuable. The per unit mass cases illustrate the
results where equal weights of material are required to perform the same packaging task.
The per unit package cases illustrate how the results and life-cycle assessment are
effected by the technical characteristics and merits of the material in its use for
packaging. In the case of cups for beverages, for example, the technical characteristics
of the two materials allow the same or similar packaging function to be performed by a
polystyrene cup composed of 2.4 grams of polystyrene as is performed by a paper cup
composed of 8.3 grams of paper.

A total of six disposal and recycling cases are examined for each of these two broad
classes of alternatives. Referring to Table 35 through 38, these cases are indexed in
columns as cases A, B, C, D. Tables 39 and 40 show cases E and F. Cases A through
D are “polar” cases, that is cases where all or the material is disposed of using the same
alternative. Case A examines the example most analogous to Hocking‘s analysis, the
case of 100% landfill disposal. In this case all used paper and polystyrene packaging is

disposed of by landfill, including the waste paper trimmings from cup manufacture.

127

128

Table 35 Resource and Energetic Cowarisons on an Emmi Mass Basis

qur all m, the mi Diqroeal Pelystynmm up ms", lme me! Disposal
Disposal Case: A B c D Disposal Case: A B c D

incineration disposal 08 1008 08 08 08 1008 08 08
Electric Generation dispel. 08 08 1008 08 08 08 1008 O8
Lmrdfill disposal 1008 08 08 08 1008 08 08 0!
Recycling disposal 0! 08 08 1008 08 08 OS 1008
Pram-rte y. p. m y. p0
Beverage Servirgs 120 120 120 120 Beverage Servings 417 417 417 417
Paper Owe-kg 612 i i i 1 Plastic curs-kg 613 1 i 1 1
Pmr-kg oi 8.50 1.10 1.10 1.10 1.10 Polystyrene-kg oi 8.70 1 i i i
Pmer Recycle-kg o2 O 0 O 1.10 Polyst.Recycle-kg o2 O 0 0 1
PQer “can 0‘ Flms 8.13 8.13 8.13 8.34 Poly-mum Mfg. 0‘ Flu. 8.12 8.12 8.12 8.67
Pulm’ Mfg. hlrm A“ 8.03 8.03 8.03 8.27 Polystyrmm Mfg. Valrm Arkhd 8.04 8.04 8.04 8.65
mmvo'l, a. ”wrong P.
Matte-al Gas - kg 8.8 0 D O 0 Metre-a1 Gas - kg 8.8 D O 0 0
Fuel Oil - kg 8.8 .279 .279 .279 .340 Fuel Oil - kg 8.8 .85 .85 .805 0
Electric Poser - ker 8.05 1.099 1.099 -. .773 Electric Poser - kilr 8.05 .35 .35 -3.35 .21
Diesel Fuel - kg 8.35 .049 .049 .049 .049 Diesel Fuel - kg 8.35 .097 .097 .097 .077
Direct Lfior 1 hours 812.0 .009 .009 .009 .006 Direct Labor 1 hours 812.0 .008 .006 .008 .005
Direct Labor 2 hour-s 8.00 O O 0 0 Direct Labor 2 hours 8.00 O O 0 0
net- Bsems'e- y, p, ”at. Ieems-e. 7r Pr
Hood Logs r1 8.10 2.57 2.57 2.57 .44 Propane r1 8.8 4.30 4.30 4.30 O
Hater r2 8.00 .11 .ii .11 .07 Ethane r2 8.8 .346 .346 .346 0
Chlorine r3 8.8 .066 .066 .066 .044 Sedit- hydroxide r3 8.8 .022 .022 .022 0
Soditm hydroxide r4 8.8 .022 .022 .022 .015 Anti-oxidants r4 8.!!! 0 0 O O
Sedit- chlorate r5 8.8 .033 .033 .033 .017 Altmiram chloride r5 8.8 .011 .011 .011 0
Sulfuric acid r6 8.8 .011 .011 .011 .002 Pentane r6 8.8 .040 .040 .040 .040
Sulfur dioxide r7 8.8 .011 .011 .011 .013 Meter . r7 8.00 .140 .140 .140 O
Galcirm hydroxide r8 8.8 .011 .011 .011 .002 Toluene r8 (8.25) 1.032 1.032 1.032 O
8oditm sulfate r9 8.8 .0011 .0011 .0011 .0002 Aroutics r9 (8.25) .817 .817 .817 0
Pipents r10 8.8 O O O 0 Other fractions r10 (8.25) 1.247 1.247 1.247 0
Goatims r11 8.8 0 D 0 0 Hydrocarbon prod. r11 (8.25) .076 .076 .076 0
Filler r12 8.8 0 O 0 O Styrene r12 8.00 .003 .003 .003 0
Soditm Phosflrete r13 8.25 O O 0 O Pentane r13 8.00 .040 .040 .040 .040
002 r14 8.00 O O O 0 £02 r14 8.00 0 O 0 0
co r15 8.00 .0079 .0387 .0387 .0045 cc r15 8.00 .008 .036 .036 .006
80,, r16 8.00 .0078 .0584 .0584 .0024 so), r16 8.00 .0022 .0482 .0482 .0015
802 r17 8.00 .0157 .187 .187 .0039 802 r17 8.00 .0024 .1024 .1024 O
Particulates r18 8.00 .0024 .0189 .0189 .0007 Particulates r18 8.00 .0004 .0154 .0154 .0001
Chlorine r19 3.00 .0002 .0002 .0002 .0001 .3 "2° r19 moo 2.5 2.5 2.5 o
Chlorine dioxide r20 8.00 .0002 .0002 .0002 .0001 ”pended solids r20 8.00 .0005 .0005 .0005 0
Reduced sulfides r21 8.00 .0017 .0017 .0017 .0012 am r21 8.00 .0002 .0002 .0002 0

H20 r22 8.00 .09 .09 .09 .07 inorganic salts r22 8.00 .015 .015 .015 O
”pended solia r23 8.00 .011 .011 .011 .007 Beverages r8 8.00 1 1 1 1
ear r24 8.00 .0055 .0055 .0055 .0042 Fuel r24 8.00 0 O 0 0
Organochlorides r8 8.00 .0033 .0033 .0033 .0028 Ash r8 8.00 O .03 .03 O
Cellulostic Fiber r26 8.00 .0011 .0011 .0011 .0013 Landfill sass r26 8.00 1 O 0 0
inorganic salts r27 8.00 .0660 .0660 .0660 .0442
Adresive r28 8.8 0 0 D 0
Beverages r29 8.00 1 1 i 1
incineration Fuel r30 8.00 0 O 0 0
Ash r31 8.00 0 .0330 .0330 0
Methane r32 8.00 O O O 0
Leachate r33 8.00 0 0 0 0
Cellulostic Fiber r34 8.00 1.10 0 0 0

129

Table 36 Crude Oil Emivalent Comrarison on an Equal Mass Basis

M a. m, the mi Biqroeal Pelyatyrmm up mm, lme mi Dinosal
Disposal Case: A B C D Disposal Case: A B C D
incineration disposal O8 1008 O8 08 O8 1008 O8 08
Electric Generation dispel. O8 O8 1008 08 O8 08 1008 O8
Landfill disposal 1008 O8 08 O8 1008 O8 O8 O8
Recycling disposal O8 O8 O8 1008 08 08 O8 1008
Protests yo po Prelimts yo p0
Beverage Servings 120 120 120 120 Beverage Servings 417 417 417 417
Pmrer Owe-kg 612 1 1 1 1 Plastic ewe-kg 613 1 1 i i
Pw-kg 61 8.50 1.10 1.10 1.10 1.10 Polystyreneokg 61 8.70 1 1 1 1
Pqer Recycle-kg 62 0 0 O 1.10 Polyst.Recycle-kg 62 0 O 0 1
Pqer m Cd Flmr 8.13 8.13 8.13 8.34 Palystyrmm Mfg. 0‘ Fl- 8.12 8.12 8.12 8.67
P" Mfg. rau- Admd 8.8 8.8 8.03 8.27 Palm Mfg. Baum Arkhl 8.04 8.04 8.04 8.65
”Myo'xo p. “bravo.“ p.
Hetural Gee - kg 8.8 O 0 0 0 Metrmal Gas - kg 8.8 0 O O 0
Fuel Oil - kg 8.8 .279 .279 .279 .340 Fuel Oil - kg 8.8 .85 .85 .85 0
Electric Poser - kIRr 8.05 1.099 1.099 -.936 .773 Electric Poser - kllr 8.05 .35 .35 - .35 .21
Diesel Fuel - kg 8.35 .049 .049 .049 .049 Diesel Fuel - kg 8.35 .097 .097 .097 .077
Direct Labor 1 hours 812.0 .009 .89 .009 .006 Direct Labor 1 home 812.0 .008 .008 .008 .005
Direct Lfior 2 hours 8.8 O O O 0 Direct Labor 2 hours 8.00 O 0 O 0
85st- Dame's. yr ”at. M 7r
066d Logs r1 2.57 2.57 2.57 .44 Propane r1 4.30 4.30 4.30 O
incineration Fuel r30 0 D D O Ethmre r2 .346 .346 .346 0
Methmre r32 0 O O 0 Pentmre r6 .040 .040 .040 .040
Toluene r8 1.032 1.032 1.032 0
Aromatics r9 .817 .817 .817 D
Other fractions r10 1.247 1.247 1.247 0
Hydrocarbon prod. r11 .076 .076 .076 0
incineration Fuel r24 0 0 0 0
m Mum-sin let. M 0mmm'simr Rates
kgCrrie Oil: kgCrrie Oil:
[kg Matural Gas 63 .98- [kg Matural Gas 63 .98
lkg Fuel Oil 64 1.18 [kg Fuel Oil 64 1.18
lkilr Electric .28 lker Electric .28
[kg Diesel Fuel 613 1.18 [kg Diesel Fuel 65 1.18
FeetteckmthCmrversimrlatea FestteckmiWCr-rvmsimrlates
kgCrria Oil: kngde Oil:
[kg Mood Logs r1 0 [kg Propane r1 .98
[kg incin. Fuel r30-1.18 [kg Ethane r2 .98
[kg Methmre r32 -.98 [kg Pentane r6 .98
[kg Toulene r8 -.98
[kg Aromatics r9 r.”
[kg Fractions r10 °.98
[kg HC Predicts r11 -.98
[kg incin. Fuel r24 1.18
m - kg Crash Oil .697 .697 .122 .676 Enter - kg Grub Oil 1.160 1.160 .116 .150
Feettock- kgCnlhOil O O O 0 Feettock-hMOil 1.484 1.484 1.484 .039

Total - II M0“ .697 .697 .122 .676 Total - lg Club Oil 2.645 2.645 1.600 .189

Table 37

130

Resotrce mi Energetic Comarisone on the Basis of Servings

PQII' up m, lme mi Biqeeal
Disposal Case:
incineration disposal
Electric Generation dispel.

Lmrdfill disposal

Recyclim disposal

Prmbmts y.
Beverage Servings
Per" Gee-ks
Pqer-kg

Pner Recycle-kg 62

mmo—arr-erm
qu'lfmhlrmkkmd

”Myo'

Metre-a1 Gas - kg
Fuel Oil - kg

Electric Poser - ker

Diesel Fuel - kg

Direct Labor 1 hole-s 812.0
Direct Liror 2 hots-s 8.8

”my,

Hood Logs

later

flrlorine

Soditm hydroxide
86ditm chlorate
Sulfuric acid
Sulfur dioxide

Calcitm hydroxide r8

Soditm sulfate
Pipsnts
Coatims

Filler

Soditm Phosphate
°°2

00

."x

Particulates
Chlorine
Chlorine dioxide
Retired sulfides

I‘2°
Stmpended solids
B8
Orgmrochlorides
Cellulostic Fiber
inorganic salts
Adresive
Beverages
incineration Fuel
Ash
Methmre
Leachate
Cellulostic Fiber

A
08
O8
1008
O8
’6
1000
612 8.30
61 8.50 9.13
O
8.22
x6 Pa
8.8 O
8.8 2.319
8.8 9.120
8.35 .407
.074
O
Pr
r1 8.10 21.29
r2 8.8 .91
r3 8.8 .548
r4 8.8 .183
r5 8.8 .274
r6 8.8 .091
r7 8.8 .091
8.8 .091
r9 8.8 .0091
r10 8.8 O
r11 8.8 0
r12 8.8 0
r13 8.8 O
r14 8.00 O
r15 8.8 .0656
r16 8.8 .0647
r17 8.00 .1303
r18 8.8 .0199
r19 8.00 .0017
r20 8.00 .0017
r21 8.00 .0141
r22 8.00 .73
r23 8.8 .091
r24 8.00 .0457
r8 8.8 .0274
r26 8.8 .0091
r27 8.8 .5478
r28 8.8 O
r29 8.8 8.3
r30 8.00 0
r31 8.00 O
r32 8.00 0
r33 8.8 0
r34 8.00 9.13

21.29
.91

.13
.274
.091
.091
.091

.3212
.4847
1.0433
.1569
.0017
.0017
.0141
.73
.091
.0457
.0274
.0091
.5478
0

8.3

0
.2739
0

0

0

9.13

"Ow

8.3

. 2739
0
0
0

2.820
6.“s
.407

3.62

.61
.367
.122
.138
.016
.107
.016

Pelfityrmm up ”acts-firm, Use mi Disposal
Disposal Case:

Prefimts y0
Beverage Servime
Plastic ewe-kg
Polystyreneokg
Polyet.Recycle°kg

613
61
62

8.70

Palystynmm Mfg. o-a Flme
Polyetyl'mm Mfg. him A“ 8.10

yet-Mn.“

Matural Gee - kg
Fuel Oil - kg

Electric Poser - kilr

Diesel Fuel - kg

Direct Labor 1 hours 812.0
Direct Labor 2 hours

mm”.

Propmre

Ethmre

Soditm hyrk-oxids
Anti-oxidants
Alt-1mm chloride
Pentmre

Hater

Toluene
Arontics

Other fractions
Hydrocarbon prod.
Styrene

Pentmre

“’2

8

mx

Particulates

“2°
Suspended solids
88

inorganic salts
Beverages

Fuel

Ash

Lmifill mass

.0”

pa

8.8 0
8.8 1.933
8.05 .84
8.35 .232
.020

8.8 O

I"‘r

r1 8.8 10.32
r2 8.8 .829
r3 8.8 .053
r4 8.00 0
r5 8.8 .026
r6 8.8 .096
r7 8.00 .336
r8 (8.25) 2.477
r9 (8.25) 1.961
r10 (8.8) 2.993
r11 (8.25) .181
r12 8.00 .007
r13 8.00 .096
r14 8.00 O
r15 8.00 .0182
r16 8.00 .0053
r17 8.00 .0058
r18 8.00 .0010
r19 8.00 6
r20 8.00 .0012
r21 8.00 .0005
r22 8.00 .036
r23 8.00 2.4
r24 8.00 0
r8 8.00 0
r26 8.00 2.4

1”
2.40
2.40

8.29
8.10

1.933

C 0

08 08

1008 08

08 08

08 1008
1000 1000
2.40 2.40
2.40 2.40
0 2.40
8.29 81.61
8.10 81.56
0 0
1.933 0
-8.04 .50
.232 .185
.020 .013
0 0
10.32 0
.829 0
.053 0
0 0
.026 0
.096 .096
.336 0
2.477 0
1.961 0
2.993 0
.181 0
.007 0
.096 .096
0 0
.0854 .0144
.1157 .0036
.2458 0
.0370 .0002
6 0
.0012 0
.0005 0
.036 0
2.4 2.4
0 0
.072 0
0 0

131

Table 38 Crtie Oil Equivalent Cowarisone on the Basis of Servims

P" O. meets-m, Ime mi 81.6.1 Pelyetyrmre up hrfactrrir', Use mi Disposal
Disposal Case: A B C D Disposal Case: A B C D
incineration disposal 08 1008 O8 08 O8 1008 08 08
Electric Generation dispel. O8 O8 1008 O8 O8 08 1008 O8
Lmifill disposal 1008 O8 O8 O8 1008 08 08 O8
Recyclim disposal O8 O8 O8 1008 O8 08 O8 1008
Predmte y. p. Preimts yo ’6
Beverage Servims 108 1000 1000 1000 Beverage Servings 1000 1000 1000 1000
Pmer Owe-kg 612 8.30 8.30 8.30 8.30 Plastic curs-kg 613 2.40 2.40 2.40 2.40
Poor-kg 61 8.50 9.13 9.13 9.13 9.13 Polystyrmra-kg 61 8.70 2.40 2.40 2.40 2.40
Pqer Recycle-kg 62 0 0 O 9.13 Polyet.Recycle-kg 62 0 0 0 2.40
P" metres m Fl- 81.05 81.05 81.05 82.78 Palyetyrmm Mfg. 1:. Fl- 8.29 8.29 8.29 81.61
Pym Mfg. bl- Arkhd 8.22 8.22 8.22 82.26 Palyetyrmm Mfg. Valrm A“ 8.10 8.10 8.10 81.56
Slat-Myo'xo p. "Myo'xo p.
Matte-oi Gee - kg 8.8 D O 0 0 Mental Gee - kg 8.8 0 O O 0
Fuel Oil - kg 8.8 2.319 2.319 2.319 2.820 Fuel Oil - kg 8.8 1.933 1.933 1.933 0
Electric Poser - lair 8.05 9.120 9.120 -7.770 6.415 Electric Poser - kill 8.05 .84 .84 -8.04 .50
Diesel Fuel - kg 8.35 .407 .407 .407 .407 Diesel Fuel - kg 8.35 .82 .82 .82 .185

Direct L8" 1 horre812.0 .074 .074 .074 .050 Direct Ldorihou‘a 812.0 .020 .020 .020 .013
Direct 1801' 2 hours 8.8 0 0 0 0 Direct Lfior 2 hours 8.8 0 0 0 0

”at. Base. yr ”at. Bum-e. yr
Hood Logs r1 21.33 21.33 21.33 3.65 Propmre r1 10.32 10.32 10.32 0
incineration Fuel r30 0 O 0 D Ethmre r2 .8 .8 .8 0
Methane r32 0 O O O Pentmre r6 .10 .10 .10 .10
Toluene r8 2.48 2.48 2.48 0
Aro.tics r9 1.96 1.96 1.96 0
Other fractions r10 2.99 2.99 2.99 0
Hydrocarbon prod. r11 .18 .18 .18 0
Fuel r24 0 0 0 0
Elmrgy Ommm-simr Rat. arergy Carver-slur Rates
kg Crude Oil: kg Crude Oil:
[kg Matural Gas 63 .98 [kg Matural Gas 63 .98
[kg Fuel Oil 64 1.18 [kg Fuel Oil 64 1.18
[kllr Electric .28 [kilo Electric .28
[kg Diesel Fuel 613 1.18 [kg Diesel Fuel 65 1.18
Fembteckmiwaervarsimrlates Feathtockmilypromthmrversierates
kgCrude Oil: kgCrude Oil:
[kg Mood Logs r1 0 [kg Propmre r1 .98
[kg incin. Fuel r30-1.18 [kg Ethane r2 .98
[kg Methmre r32 -.98 [kg Pentane r6 .98
[kg Toulene r8 -.98
[kg Aro.tics r9 -.98
[kg Fractions r10 -.98
[kg HC Prodrcts r11 -.98
[kg incin. Fuel r24 1.18
Elmrgy - h at. Oil 5.782 5.782 1.013 5.607 Ermrgy - kg Cash Oil 2.785 2.785 .277 .360
Femhtock - kg Cash Oil 0 O 0 O Feettock - kg Club Oil 3.562 3.562 3.562 .094

Total - h CM Oil 5.782 5.782 1.013 5.607 Total - lg Clash Oil 6.347 6.347 3.840 .454

idle 39

Pump—Mm,lhemilimm.l

Disposal Case:

lncirreration disposal

Electric Generation dispel.
Lmifill disposal
Recycling disposal

My.

Beverage Servings

PW Cult-ks
m-u

Pmrer Recycle-kg 62

*mwfl-

membrane-s

”My,“

Matte-al Gee - kg
Fuel Oil - kg

Electric Poser - kllr

Diesel Fuel - kg

Direct Lmor 1 hours 812.0
Direct Labor 2 hours 8.8

”me-my,

Hood Logs

Hater

Chlorine

Soditm hym-oxida
Soditm chlorate
Sulfuric acid
Sulfur dioxide

Calcirm hydroxide

Soditm sulfate

Pipsnts

Coatings

Filler

Sodirm Phosphate

°°z

8

MO"

Particulates

Chlorine

Chlorine dioxide

Reduced sulfides
M

Slmpmied solih
B8
Orgmrochlorides

Cellulostic Fiber

inorganic salts
Adreelve
Beverages

incineration Fuel

Ash
Methane
Leachate

Pr
8.10
8.8
8.8
8.8
8.8
8.8
8.8
8.8
r9 8.8
r10 8.8
r11 8.8
r12 8.25
r13 8.25
r14 8.8
r15 8.8
r16 8.8
r17 8.8
r18 8.8
r19 8.8
r20 8.8
r21 8.8
r22 8.8
r8 8.8
r24 8.8
r8 8.8
r26 8.8
r27 8.8
r28 8.8
r29 8.8
r30 8.8
r31 8.8
r32 8.8
r33 8.8

r1
r2

Cellulostic no» r34 :.00

I
108
108
708
108

120

1.10

8.16
8.07

8.16

.312
- .84

.87

§§§§§§§s

I
#00090?

at
as

E
108
108
708
108

1006
8.30
9.13
1.66

81.37
8.59

.5146

8.3

.0498
0

0
5.81

132

§§‘
as

108
8.30
9.13
4.”

a.”
81 .B

Resorrce mi Errergetlc Cowarisons for Mixed Disposal wtione

Pelyetyrmm Org: ”acts-17m, lme mi 01.6.1

Disposal Case: E F E F
108 O8 108 O8
108 508 108 508
708 O8 708 O8
108 508 108 508
Prat-as y. p.
Beverage Servims 417 417 180 180
Plastic ewe-kg 613 1 1 2.40 2.40
Polystyrene-kg 61 8.70 1 1 2.40 2.40
Polyst.Recycle-kg 62 .10 .50 .24 1.20
Pelystyrmm Mfg. C. Fl- 8.17 8.40 8.42 8.95
Polymtyl'mm Mfg. Belem ace-e 8.10 8.35 8.8 8.8
”at. m y. P 8. p.
Metre-a1 Gee - kg 8.8 0 O 0 0
Fuel Oil - kg 8.8 .78 .403 1.740 .966
Electric Poser - kIRr 8.05 -.O34 -1.570 -.082 -3.768
Diesel Fuel - kg 8.35 .095 .87 .228 .209
Direct Lfior 1 hows 812.0 .88 .87 .019 .017
Direct Labor 2 hours 8.8 O 0 O 0
”at. M 7r Pr
Propmre r1 8.8 3.878 2.158 9.288 5.168
Ethmre r2 8.8 .3110 .1728 .7464 .4147
Soditm hydroxide r3 8.8 .0198 .0110 .0475 .0264
Anti-oxidants r4 8.8 O 0 O O
Altmimm chloride r5 8.8 .899 .855 .088 .0132
Pentane r6 8.8 .048 .048 .0960 .0960
Meter r7 8.8 .038 .0700 .128 .180
Toluene r8 (8.25) .9288 .5160 2.2291 1.884
Arc-arm r9 '(s.zsr .7353 .4085 1.7647 .m
Other fractions r10 (8.811.128 .685 2.6935 1.4964
Mrocarbon prod. r11 (8.25) .068 .0378 .1632 .0907
Styrene r12 8.8 .827 .815 .865 .836
Pentmre r13 8.8 .048 .048 .0960 .0960
ooz r14 8.8 0 O O 0
8 r15 8.8 .0130 .0208 .0312 .0499
MOx r16 8.8 .0113 .0249 .0271 .0598
r17 8.8 .0222 .0512 .0533 .1229
Particulates r18 8.8 .833 .877 .879 .0185
1120 r19 8.8 2.258 1.88 5.408 3
Suspended solia r20 8.8 .805 .803 .812 .087
B8 r21 8.8 .802 .081 .085 .082
inorganic salts r22 8.8 .0135 .875 .0324 .0180
Beverages r23 8.8 1 1 2.408 2.408
Fuel r24 8.8 0 0 0 0
Ash r25 8.8 .0060 .0150 .0144 .0360
Landfill .ss r26 8.8 .7000 0 1.688 0

1816 40

”fluctuate-Illiqoaal

Disposal Case:
incineration disposal
Electric Generation dispel.
Landfill disposal

kecyclir' disposal

mu y. p.
Beverage Cervims

Fw Clue-kg 612
Fur-kg oi 8.50

Poor Recycle-kg 62

“mm“-
meullw

fist- B-r' y. 8 I. p

Iatwal Cas - kg 8.25
Fuel Oil - kg 8.25
Electric Fouer - kill 8.05
Diesel Fuel - kg 8.35
Direct Laor 1 how-s 812.0
Direct Léor 2 hours 8.8

”at. Buns-o. 7r
Hood Logs r1
incineration Fuel r30
lethane r32

”Cami-ulst-

kg Crude Oil:

[kg katurel Gas 63 .8
[kg Fuel Oil 64 1.18
[kill Electric .20
[kg Diesel Fuel 613 1.18

E
10!
10!
708
108

mummwm

kg Cnde Oil:

lkg ilood Logs r1 0
[kg incin. Fuel r30-1.18
[kg llethane r32 -.8

m-hmul
Fatback-hull"
letal-anlhOil

.641
0
O“‘

F E

08 101

50! 101

03 708

508 108
120 1”
1 0.30
1.10 9.13
.60 1.66
8.24 81.37
8.16 8.59
0 0
.312 2.410
-.84 7.101
.049 .407
.87 .070
0 0
1.40 10.8
0 0
0 0
.424 5.319
0 0
.424 5.319

133

§§‘
as

0.30
9.13
4.8

82.8
81.33

2.592
C“,
.81

11.65
0
0

3.519
0
3.519

Cruia Oil Emivelent Cowarison ior ilixed Disposal wtiona

Felystyrun no Wm, lbs Id Dimsal

Disposal Case:

Full-Rs y.

Beverage 8ervims
Plastic owe-kg o13
Polystyrene-kg oi
Folyst.kecycle-kg 62

P0

8.70

lelystyrn ng. u Flu

Ielystyruu IFg. Vell- A“ 8.10 8.35

”at. m y. 0 k. p.
latte-a1 Cas - kg 8.25
Fuel Oil - kg 8.25

Electric Fouer - kilI 8.05
Diesel Fuel - kg 8.35
Direct Lfior 1 hours 812.0
Direct Labor 2 hours 8.8

”st-My,

Prop-1e r1
Ethane r2
mtane r6
16luana r8
Amtics r9
Other fractions r10
Mocarbon prod. r11
Fuel r24

mean-sinuses

kg Cnde Oil:

[kg Natural Gas 63 .90
[kg Fuel Oil 64 1.10
mm Electric .28
[kg Diesel Fuel 65 1.10

E F E F
101 03 108 03
10! 508 10! 508
703 08 708 08
103 508 108 503

417 417 1” 1M

1 1 2.40 2.40

1 I 1 2.40 2.40

.10 .50 .24 1.20
8.17 8.40 8.42 8.95
8.25 8.03

0 0 0 0
.73 .403 1.740 .966
-.034 -1.570 -.002 '3.760
.095 .87 .220 .209
.M .87 .019 .017
0 0 0 0

3.078 2.158 9.2000 5.168

.3110
.048
.9200
.7353
1.1223
.068
0

.1720 .7464
.048 .0960

.4147
.0960

.5160 2.2291 1.2304

.4005 1.7647

.6235 2.6935 1.4964

.0370
0

.1632
0

FeettockudWCumimlates

kg Crude Oil:

[kg Propane r1 .8
lkg Ethane r2 .98
[kg Pentane r6 .98
[kg 1’oulane r8 -.98
[kg Arontics r9 -.98
[kg Fractions r10 -.8
[kg 11C Products r11 -.98
[kg incin. Fuel r24 1.18

m-ksCrubOil
Feattack-hCnbOil
total-hCnIhOil

.955
1.340

.133 2.291
.762 3.216

.0907
0

.310
1.020

2.294 .094 5.507 2.147

134
Case B examines 100% incineration of used packaging and waste paper trimmings. Case

C examines the option where 100% of used packaging and waste paper trimmings are
burned to generate electric power. Case D examines 100% recycling of both used
packaging and of waste paper trimmings.

Cases E and F in Tables 39 and 40 examine two scenarios for the use of mixed
disposal policies, one case approximating current practice, and another case
approximating a realistic medium term policy scenario. During the period of 1990-1992
disposal practices have been changing rapidly with the advent of widesper municipal
and volunteer recycling programs for paper, plastic and glass. It is difficult to assess
what the exact level of materials being recycled may be at the time this dissertation is
written. Many materials are accumulating in inventories for lack of reprocessing
facilities or markets for end products [33]. One estimate reports over 36% of paper in
general being recycled in 1991 [34]. Case E is based on reasonable assumptions about
what disposal policies may have looked like during the 1980’s. This case specifies 10%
incineration, 10% disposal through electric power generation, 70% disposal through
landfill, and 10% disposal through recycling. Case F examines a scenario which might
practically be attained as a policy objective; 50% use in electrical generation and 50%
recycling. In these mixed disposal cases it has been assumed that all waste paper

trimmings from paper cup manufacture are recycled.

7.2 Comparison of Resource Requirements
Referring to Tables 35, 37 and 39, resource and residual material flows y, are given

for each disposal alternative in columns A, B, C, D, E and F for both paper and

135
polystyrene. Cases A, B and C (zero recycling) all result in identical resource ,

requirements and emissions. On either a mass basis, Table 35, or a volume basis, Table
37, the inputs of inorganic chemicals rl-r8 for paper manufacture are distinctly lower in
quantity and variety than those for polystyrene manufacture, r3-r5. Air emissions, and
water effluent, r14-r27 and r32 for paper, and r12-r22 for polystyrene, are also
substantially lower for polystyrene. Notice that methane emissions from landfill disposal,
r32, and leachate r33, are not modeled here due to the great variability caused by
differing landfill sites and lack of data. As discussed earlier, C02 emissions have not
been modeled at this point of analysis, but will be discussed in a separate section below.
The landfill mass and volume after compaction are nearly the same for paper and
polystyrene on a unit mass basis, Table 35 , r34 and r26. But on a per unit package
basis, Table 37, polystyrene has an advantage of requiring about 1/4 of the landfill
resources.

The use of recycling disposal, in cases D, E and F, Tables 35, 37 and 39, reduces
or eliminates the inorganic chemical resource requirements, air emissions, water
effluents, and landfill requirements for all but a few variables, which remain similar or
unchanged. The effect of recycling is most dramatic for the 100% recycling of
polystyrene where many resources and effluents are eliminated completely.

The primary resource flow for paper production, wood logs r1, remains unchanged
for cases A, B and C, but is reduced by 83% in case D, 100% recycling, and by lesser
but important amounts in the mixed disposal cases E and F. Thus recycling ean conserve
forest resources. The primary feedstocks for polystyrene manufacture are propane and

ethane, rl and r2, with marketable byproducts r8-rll. These flows remain constant for

136
disposal eases A, B and C and are completely eliminated in case D of 100% recycling.

Mixed disposal cases E and F produce intermediate results.

Water, r2, is a primary resource in paper production for both process use and for
cooling. In polystyrene production water is used for cooling. On a mass basis water
requirements are nearly the same for both products in caSes A, B and C. Cooling water

requirements for polystyrene are eliminated for 100% recycling.

7.3 Comparison of Energy Requirements

System energy is defined as the total energy requirements of the network, yo "' X0.
In all of these example eases fuel oil has been chosen as the combustion energy source.
The fuel oil requirements for cases A, B and C are identical. Paper manufacture requires
10% more fuel oil than reported by Hocking since his analysis neglected the material loss
due to waste paper trimmings in cup manufacture. Polystyrene fuel requirements are
very close to those reported by Hocking [41]. Note that on a mass basis in Table 37,
polystyrene manufacture requires almost three times as much fuel oil, but that on a per
unit package basis (per cup) the requirement is about 15 % less for polystyrene.
Essentially, the manufacture of polystyrene cups uses less petroleum energy than paper
cups, and does not require the harvest of trees. This is the dramatic result that caused
such widespread interest and controversy in Hoclcing‘s original analysis [35]. However,
Hocking’s work did not include a full system life-cycle network assessment, including
transportation, use, disposal and recycling options which follow.

In case D 100% recycling is examined. On both a mass basis and a per cup basis,

Tables 35 and 37, no fuel oil is required for the production of recycled polystyrene

137
material. But fuel oil required for recycled paper manufacture actually increases by 21%

compared to manufacture of virgin paper. This is a most surprising and profound result
of this processes network analysis, and is directly contrary to the current beliefs of policy
makers, paper manufacturers, and the public. How this happens can be understood by
considering the material and energy cycles in the paper network. In virgin paper
manufacture, 56% of the energy is derived from the combustion of waste wood and bark
and the combustion of lignins in the byproduct “black liquor” associated with pulp
manufacturing in processes 9 and 10. These energy sources have been “stripped off"
from the remaining cellulose fiber that constitutes the paper product. Thus repulping
paper in process 2 does not contribute any energy from the combustion of waste
byproducts. Despite the lower fuel oil requirement for repulping paper in process 2 this
results in a net increase in fuel oil energy. The mixed disposal cases for paper, E and
F in Table 39, also result in net increases of fuel oil requirements compared to the
landfill, electric power generation and incineration cases. Thus from the standpoint of
fuel oil requirements, recycling is always preferred for polystyrene. 0n the other hand,
landfill, incineration or electric power generation are equally preferred for paper. With
regard to the choice between materials, on a mass basis paper is preferred to polystyrene
for eases A, B and C, but in case D polystyrene is preferred. On a per cup basis,
polystyrene is always preferred, with 100% recycling of polystyrene dominating all
alternatives.

Electric power requirements are also of great interest. For cases A and B, landfill
and incineration disposal, electric power requirements are the same; 1.099 kWh for paper

and about one third the amount, .35 kWh for polystyrene on a mass basis in Table 35.

138
On a per cup basis in Table 37, polystyrene requires less than 1/10 of the electric power

of paper. In case C, where all waste paper and polystyrene is burned to generate electric
power, there is actually a net production of electric power by the full system of
manufacture, use and disposal. On a mass basis in Table 35, case C produces .936 kWh
of electric power for paper and over three times as much, 3.35 kWh for polystyrene.
On a per cup basis in Table 37, electric power production is almost equal at 7.77 kWh
and 8.04 kWh respectively. Examining ease D, 100% recycling, reveals that electric
power consumption is reduced by about 1/ 3 compared with landfill and incineration cases
A and B. Thus from the standpoint of electric power, the optimum disposal case is
always combustion for power generation with recycling the second choice, and
polystyrene is always preferred to paper.

Diesel fuel for transportation in the full system model amounts to about 10-20% of
the quantity of fuel oil petroleum required for manufacture, depending on the ease. This
is important to note since it was supposed before beginning the analysis that
transportation fuel might dominate the fuel requirements of manufacturing. Even under
the assumptions of relatively long transportation distances in this model, and the use of
highway truck rather than more efficient rail transportation, diesel fuel still plays a
relatively minor role. On a mass basis, polystyrene uses about twice as much
transportation fuel as paper because of the assumptions for ethane and benzene and the
lower density of polystyrene. On a per cup basis, polystyrene uses about half as much
diesel fuel. Recycling reduces the diesel fuel requirements slightly by eliminating ethane
and benzene transport requirements.

Under the assumptions presented here, paper and polystyrene have about the same

139
direct labor requirements on a mass basis, but polystyrene has one third the labor

requirement on a per cup basis. Labor requirements fall by about 1/3 under the

recycling ease D.

7.4 Comparison of Crude Oil Equivalent Energy Use

It is apparent from the discussions in the previous two sections that comparison of
trade offs in material and energy resource utilization is complex. No choice of product
or disposal option dominates under all criteria. The choice depends very much on the
available resource bases.

In an economy like France, without available forest resources or petroleum and with
abundant nuclear power, polystyrene with 100% recycling would be chosen on either a
mass basis or a per cup basis. This option eliminates the forest resource requirement
with a modest electrical power and petroleum requirement. Such a choice could also
apply to an economy like Saudi Arabia, without forests, but with currently abundant
petroleum.

In an economy like Sweden, with extensive forest resources, but no petroleum and
a policy to eliminate nuclear power generation, or an economy like Canada or Russia
with extensive forests and currently abundant petroleum, or an economy like the U.S.
with limited forests and nuclear power and little remaining petroleum, the choice
becomes far more complex. The analysis is complicated further since petroleum-based
ethane and propane are fwdstocks for polystyrene manufacture and useful petroleum-
based byproducts are produced also.

One way to consolidate the analysis is to convert all energy and feedstocks to crude

140
oil equivalents and then compare the crude oil petroleum requirements and forest

resource requirements of the two products and their disposal alternatives. This has been
done in Tables 36, 38 and 40. System energy and primary resources are presented as
in Tables 35, 37 and 39, and conversion rates for natural gas, fuel oil, electric power and
diesel fuel to crude oil equivalents are shown as derived from Erskine [43] and Austin
[42]. This analysis assumes that all electric power is generated by petroleum combustion
rather than nuclear generation. This is currently a reasonable ease to explore since
nuclear power plants currently account for less than 10% of world power generation and
few new nuclear plants are being built. In the bottom three lines of each table the crude
oil equivalents for the energy requirements, the feedstock resources, and the total crude
oil equivalents are presented.

Table 36 shows this information per kg mass of packaging material. Referring first
to the paper ease, it is clear that option C, electric power generation, and option D,
100% recycling, are the preferable choices. Option C has the lowest crude oil
requirement, at .122 kg but requires 2.57 kg of wood logs. Option D has nearly the
same crude oil requirement, .676 kg, as A and B, but requires only 1/6 of the wood
resources, .44 kg. For polystyrene the 100% recycling option D clearly dominates all
others, requiring only .189 kg of petroleum. The choice between paper and polystyrene
now comes into focus also. If forest resources are constrained or not available,
polystyrene option D with its crude oil requirement of . 189 kg would be chosen.
Compared to polystyrene D, the 100% recycling of paper, option D, should never be
chosen since it requires 3.5 times the crude oil and .44 kg of wood logs in addition.

However with a resource base with abundant forests it may be desirable to choose paper

141
option C, electric power generation, over polystyrene option D. In this case the 2.57 kg

of wood logs are being utilized to reduce the crude oil requirement for the packaging
material from .189 kg to .122 kg.

This illustrates another very important result. With the technology modeled here, the
energy required for paper manufacture cannot be supplied only from the wood being
harvested for the material requirement, even if all of the waste paper is combusted for
energy retrieval - an additional .122 kg of crude oil equivalent energy is required. This
energy could be attained by harvesting more trees for steam generation or the
displacement of crude oil powered electrical power generation to provide equivalent
transportation fuel. But paper production in itself is not energetically self sufficient as
modeled here. Hocking notes that some modern paper production facilities attain as
much as 70% of their process energy from waste wood and bark, rather than the average
of 56% used here. Under these conditions, option C would come close to be
energetically self sustained through the harvest of trees alone on a life-cycle basis, but
only if the paper products are burned for combustion fuel afier use, not if they are
recycled. Recycling, option D, simply substitutes petroleum for a reduced wood
requirement. At a time when industry, policy makers and the public have assumed that
paper should always be recycled, and are engaging in large scale programs to recycle
paper, this is perhaps the most dramatic finding of this research.

Table 38 compares crude oil equivalents on a per cup basis. Paper with disposal
options A and B has nearly the same crude oil requirement as polystyrene under options
A and B, but of course polystyrene does not require the harvest of trees. As before,

paper options C and D reflect a trade off between minimizing petroleum requirements

142
and the amount of wood harvested. Because of the lower mass required per cup,

polystyrene option D uses .454 kg of crude oil, about half the 1.013 kg of crude oil
required bypaperoptionC,anddoesnotrequiretheharvestoftrees. Soonaper
package basis (per cup) 100% recycling of polystyrene is always the preferred product
and disposal option, irrespective of the resource base.

Mixed disposal cases E and F are shown in Table 40. Crude oil and wood
requirements are always lower for case F, so it is always preferred to case E for either
paper or polystyrene, on either a mass basis or a per cup basis. On a mass basis, paper
case F requires .424 kg of crude oil and 1.4 kg of wood versus .894 kg of crude oil for
polystyrene case F, resulting in a trade off between forest resources and petroleum. On
a per cup basis, polystyrene case F is always preferred since it has about 60% of the
energy requirement of paper case F, but requires no wood.

Compared with polystyrene case F, polystyrene case D, 100% recycling, is always
preferredonbothamassandpercupbasis. PapercaseFisanintermediatecase
between paper C and D, and reflects the same trade off between the use of petroleum and

wood.

7.5 Comparison of Carbon Dioxide Emissions

The role of carbon dioxide (COfl in atmospheric change and the threat of global
warming is of great contemporary importance. As reported earlier, carbon dioxide
emissions were not incorporated as coefficients in the examples presented here. C02
data for each of the individual combustion process is difficult to obtain in a consistent

fashion and was not included in Hocking‘s analysis. However, the crude oil equivalent

143
data provide a comprehensive and accurate means to compare C02 emissions for the

products and disposal options. Since petroleum products and natural gas are all
hydrocarbons, the release of energy in combustion converts these hydrocarbon chains into
carbon dioxide and water. (Carbon monoxide may also be produced, but it reacts in the
atmosphere to form C02 in a relative short time). So, in general, the carbon dioxide
released will be directly proportional to the crude oil equivalent mass of fuel undergoing
combustion, and thus to the energy produced.

For polystyrene this allows a very simple comparison. Polystyrene manufacture has
two petroleum requirements, process energy and petroleum feedstocks. All of the
process energy fuel will be converted proportionally to carbon dioxide. Part of the mass
of the feedstock may convert to C02 during process reactions, with the remainder
forming the mass of the finished product. In Table 36 the total crude oil for polystyrene
case A is 2.645 kg. Of this, a mass of 1.0 kg remains in the used cup. In the landfill
case, this 1.0 kg is buried and will not release CO} Thus the net C02 released to the
atmosphere is proportional to 1.645. In cases B and C the waste polystyrene is burned,
and C02 will be released proportionally to the total crude oil equivalent of 2.645 and 1.6
respectively. (In case C, the generation of electric power by burning the waste
polystyrene reduced the fuel oil required for power generation). In case D, 100%
recycling, the only C02 released will come from the combustion energy of . 150 kg. On
either a mass basis or a per cup basis (Table 38), 100% recycling will always be
preferred, resulting in 5-10% of the C02 emissions of the other alternatives.

In paper manufacture and use there are two C02 emission sources to consider;

combustion of petroleum for process energy, and the growth, combustion and disposal

144
of wood and paper. C02 emissions for process energy will be proportional to the crude

oil equivalent for process energy, which for paper is the same as the total kg of crude
oil equivalent. Case C, electric generation disposal is clearly the preferred option,
having about 20% of the C02 emissions of the other alternatives.

Accounting for C02 emissions related to wood is more complex. Referring to Table
36, in case A, landfill disposal, 2.57 kg of wood logs are harvested for each 1.1 kg of
paper. Ignoring the relatively minor loss of cellulose mass in water effluent, this means
thatatotalof1.47kgofwoodmasshasbeenburnedinprocesses9and lOintemalto
the manufacturing enterprise. The remaining 1.1 kg is buried in the landfill as waste
paper. If wood is being grown at the same rate as it is being harvested, the C02 uptake
by the growing trees will be proportional to 2.57. The C02 released by combustion will
be in the same proportion to 1.47. If the conditions in the landfill are such that all of
the 1.1 kg of waste paper decomposes aerobically into C02, then there will be a neutral
C02 balance for the system as a whole and no net change in atmospheric C02. If more
wood is harvested than is regrown, there will be a net increase in C02 levels since the
inventory of C02 trapped in the forest wood will be released into the atmosphere. (This
argument ignores the controversy surrounding the dynamics of C02 cycles in the
biosphere -- increased atmospheric C02 levels may cause increased rates of plant growth,
pushing the system toward a new equilibrium). Likewise, if the landfill conditions are
anaerobic such that decomposition does not take place, the C02 fixed in the 1.1 kg of
waste paper will be removed from the cycle of the biosphere, resulting in a net reduction
of atmospheric C02 levels.

Cases B and C both call for combustion of the 1.1 kg of waste paper, releasing the

145
sameamountofCOzashadoriginallybeenfixedinthegrowthofthis1.1kgofwood

mass. IncaseD,100% recycling, the.44kgofwoodmassrequired formakeupof
losses in repulping is partially combusted in processes 9 and 10 and partially lost as
water effluent in repulping. This lost effluent can be expected to decompose, so again
thenetCOZchangeintheatmospherewillbeneutralifwoodisgrownatthesarnerate
as it is harvested.

If the above scenarios for the C02 cycle for wood are taken to be neutral, then the
comparison of materials becomes a comparison of the emissions from petroleum
combustion. On a mass basis, for paper the preferred choice is C at .122 kg, and for
polystyrene the preferred choice is D at .150 kg, approximately the same. On a per cup
basis polystyrene again has clearly superior C02 emissions at .360 kg for case D, while
paper is proportional to 1.013 kg in case C.

Thus from the perspective of C02 emissions, it may be concluded that under
conditions of sustained wood regrowth and complete combustion or decomposition of
waste paper, recycling polystyrene is equivalent to or preferred to electrical power

generation with waste paper.

7.6 Comparison of Economic Results

In Tables 35 , 37 and 39 the cash flow and value added are given for each of the
disposal options. Cases A, B and C all report the same result for each product
respectively since these disposal options do not effect the material and energy flows of
the manufacturing enterprise itself. It is interesting to note the figures for case D, 100%

recycling. Under the price assumptions used here, recycling always results in a dramatic

146
increase in both cash flow and value added. This occurs primarily because the waste .

paper and polystyrene materials, 02, for recycling have a price of $.00; that is they are
free. This in fact corresponds to market conditions of the last several years for paper
and plastics. In some cases, manufacturers are being paid to take recyclable materials
in the face of rising landfill disposal costs and lack of availability of sites. As recently
as 1979, better quality used news print was purchased for $80 per ton. In 1991
manufacturers were being paid $20 per ton to take it [48]. In the case of polystyrene
cash flow and value added are further enhanced by the reduction in energy required to
produce product from recycled material. The recycling of paper does not enjoy this

advantage.

8 CONCLUSIONS AND POLICY IMPLICATIONS FOR THE USE OF
PAPER AND POLYSTYRENE PACKAGING MATERIALS

It is believed that the application of the above paradigm is essential for the future
success of manufacturing enterprises of all types and the successful functioning of the
national and global economies which encompass them. Specifically, during the decade
and century ahead economies and the enterprises of which they are composed will
fitnction in a world with ever scarcer energy and material resources and the design and
production of products will be fitrther constrained by their life cycles and disposal or
recycling within the economic system and stress-sensitive natural environments. These
challenges require the development of an integrated theory for the analysis of alternative
designs and production processes which explicitly incorporates the flows and stocks of
materials, energy, and knowledge/skill specific human time, and provides a consistent
framework for analysis of product designs, production processes, enterprise management
and life-cycle assessment.

The complexity of trading off the merits and demerits in a life-cycle assessment is
illustrated by the results and discussion presented in the preceding sections. Certainly
several conclusions are quite direct.

o On the basis of water effluents, polystyrene causes only a fraction of the loading
incurred by paper.

0 Air emissions are similar per kg of virgin packaging material produced, primarily
because of the combustion of fuels for process and transportation energy. Refinery

emissions have not been accounted for in this analysis, but since the crude oil

147

148
equivalent use of petroleum is so similar (per kg), these too should be comparable.

Polystyrene recycling, requiring relatively little energy and materials is clearly a
superior choice by this criterion.

Either landfill burial or incineration of either product is very wasteful of petroleum
and of forest resources in the case of paper. Unfortunately these disposal methods
account for the majority of past and current practice. Although generation of electric
power from municipal waste is practiced in the U.S., it seemingly deserves a far
greater role in both petroleum conservation and landfill abatement. As this is
written, it remains a mystery why coal bunting electric utilities are not firing their
boilers with the enormous supplies of free used newsprint that are being collected;
much of which is being hauled to landfills for lack of repulping capacity. Co-fueling
of coal fired power plants with paper should be straightforward and could be
expected to decrease emissions, especially of sulfur. Burning polystyrene and mixed
municipal waste cleanly can be done, but requires more specialized combustion
technology.

There is a distinct trade-off of forest resources for petroleum required for the most
favorable paper alternatives, electric power generation and recycling. This trade off
does not seem to be appreciated in the literature nor in the decisions of policy makers
and the industry.

On a per kg basis, recycling polystyrene uses 50% more petroleum than paper, but
has no wood requirement. Because of its superior mechanical properties and low
density for some types of packaging functions, recycling polystyrene will be a clear

choice for those functions where the per container weight is lower.

149

The discussion of petroleum requirements applies directly to C02 emissions. The
lower the petroleum requirement the lower will be earbon dioxide loading. This
assumes that wood is grown at the same rate it is harvested [38], [53].

Other sources of cellulose fiber such as hemp [39] may prove more efficient than the
wood varieties now employed, and should be analyzed in a life-cycle context.
Paper cups currently sell (at wholesale) for 2-3 times the price of polystyrene cups
[49]. In examining the resource requirements, it is apparent why this is so. Reeall
that the eash flow and value added calculations are on the basis of kg of product
produced.

Transportation fuels play a relatively minor role in petroleum use and emissions in.
these life-cycle assessments, lO-20% , even under the liberal assumptions for
transportation distances and the use of fuel inefficient truck transport. This is a
surprising result that is contrary to what was anticipated before the analysis.

For drinking beverages, neither product is necessary, and could be eliminated
entirely. Ceramic eating and drinking vessels have been found in the earliest known
human habitats, and were still rather popular until the 1960’s. And humans
obviously have utilized and cleaned ceramic vessels for millennia without the benefit
of petroleum or the resource chemicals required for drinking beverages from paper
or polystyrene cups. Other packaging uses of paper and polystyrene however may
be more technically unique or beneficial. The choice between the two materials for
the enormous variety of other packaging applications may depend on their merits as
substitutes as well as their relative densities, and upon other suitable materials, metal,

aluminum or solid wood containers, for example.

150

o The overriding policy implieation of this work is that it is not safe to assume that
materials should always be recycled. For some materials like polystyrene, recycling
makes sense under all conditions, but given some resource bases and package
characteristics it may make far more sense to use a paper product once and then burn
it to generate electric power. Case by case comparison of materials and disposal
methods is required to insure that manufacture, use, disposal and recycling decisions

make the wisest use of the available resource bases.

9 SUGGESTIONS FOR FURTHER RESEARCH

The most interesting opportunity to improve on the work and results presented here
will be to obtain more accurate information for the energy requirements for paper
repulping and reheating polystyrene to its molten state. The assumptions presented are
probably higher for each process than actual energy use. Lower assumptions will not
change the choices and trade-offs presented since the contrasts are in the orders of 2, 5,
and 10. Such information could be obtained through instrumented measurements on
actual processing equipment, and may be available in the engineering operating records
of some plants.

Another opportunity to improve on this work would be to model the production of
the inorganic chemicals that are used as resources for paper production. Inclusion of
these energetic costs and environmental loadings will only make paper look less favorable
than polystyrene.

Paper has been produced for at least 4000 years, long before the discovery of
petroleum, with a variety of technologies. It would be interesting to examine the life-
cycle of paper production technologies that utilized only renewable forest resources.

And, as mentioned in the Conclusions above, what is really needed for resource
utilization, product, and disposal decisions is the development of “libraries” of process
network models for products and technologies so that material flows, energetic costs, and
economic variables can be compared with resource bases and constraints. Wise decisions

require these more comprehensive and specific analyses.

151

152

Personal future research interests of the author, stemming from the work presented

in this dissertation, include:

0 Further extensions of process network models of physieal and biological
transformations and exchanges to include the functioning of ecological systems and

the interactions between human made and natural systems.

0 Investigation of the source-specific net energy efficiency, thermodynamics, and
material resource requirements of economic systems at macroeconomic levels of
structure and functioning. It is believed that such developments can provide insight

into issues surrounding “Sustainable Economics” and “Sustainable Agriculture” .

0 Investigation of the roles of finance, social and political processes, and public policy

in the macroeconomic structure, resource and energy requirements of economics.

0 Further investigation of “material-energy balance” problems of complex systems in

chemistry and chemical engineering in the context of process network theory.

APPENDIX

APPENDIX

PC Matlab Programs For Process Network Calculations

% PROGRAM TO CALCULATE PROCESS NETWORK FOR PAPER
96 MANUFACTURING '
diary testoutl

96 Program CALCPAP1.M
clear

echo on

load K1b.txt

load Klo.txt

load Krb.txt

load Kro.txt

load yo.txt

load Xr.txt

load Fb.txt

load Fo.txt

load A.txt

load go.txt
load ce.txt

load gs.txt

load ge.txt

load os.txt

load ce.txt

load pr. txt

load po.txt

load pe.txt

load gba.txt

load goa.txt

%Calculate the K matrices

[m ,n] = size(A*K1b)

Kb =inv(eye(n)-A*K1b) *A*Klo
Ks = (Krb*Kb) +Kro

Klelo= [Klb K10]

%Calculate Energies

invIKA =inv(eye(n)-Klb’*A’)
% Make Xr conformable for inclusion of steam energy in Fb F0

153

154

[P.q}=siw(Xr)
ert=[zeros(p,1) Xr]
Xb = -invIKA *Krb ’ *ert-invIKA *Fb
Xl=-A’*Xb
Fsst=(Kb’*Fb)+Fo
%Convert steam and electric to natural gas and/or fuel oil requirements for Fs
Fs=Fsst
Fs(1,2) = (Fsst(1,1)*gs*go)+ (Fsst(1,4)*ge*go*ce)
Fs(l,3)=(Fsst(l,1)*os*(1-go))+(Fsst(l,4)*oe*(l-go)*ce)
Fs(l,4)=(Fsst(l,4)*(l-ce))
Fs(2,2) = (Fsst(2, l)*gs*go) + (Fsst(2,4) *ge*go*ce)
Fs(2,3) =(Fsst(2, 1)*os*(l-go)) + (F sst(2,4) *oe*( l-go) *ce)
Fs(2,4) = (Fsst(2,4) *( l -ce))
Fs=Fs(:,2:7)
Xo=-(Ks’*Xr)-Fs
%Include calculated gas and oil in yo vector
e=yo’*Fs
y0(3.1)=e(1.1)
y0(4.1)=e(1.2)
%Calculate y variables
yr=KS*yo
yb=Kb*yo
ybyo=lyb;yo]
yl =K1bKlo*ybyo
e=yo’*Fs
exo=yo’*Xo
96 Calculate cash flow and value added
Cf= 00’“PO)-(yr"Pr)-(e*pe)
Gsa=(Kb’*gba)+goa
Vs=Cf-(yo’*Gsa)
%Output data to file
%Enter diary output file name if desired - then RETURN
diary OUTPAPlA
%keyboard
echo off
Klerb=[K1b
Krb]
KloKro=[Klo
Km]
Kb
Ks
A
go
ce

gs

155

F0

Fsst

Fs

e

exo

pr

P0

I)‘3

gba

goa

Gsa

Cf

Vs

diary off

echo on

%Enter diary Ks output file name if desired - then RETURN
diary KSPAPlA
%keyboard
echo off

Ks

diary off

echo on

%Enter diary Fs output file name if desired - then RETURN
diary FSPAPlA

%keyboard

echo off

.Fs

diary off

echo on

%Enter diary REPORT output file name if desired - then RETURN
diary REPPAPIA

%keyboard

156

echo off

yr

yo

Xo

Fsst

Fs

e

exo

Gsa

Cf

Vs

diary off

echo on

%Enter SAVE PAPERlA ouqmt file name if desired - then RETURN
save PAPERla
%keyboard

% End of ealculation file

157

% PROGRAM TO CALCULATE PROCESS NETWORK FOR PAPER

% MANUFACTURING, USE AND DISPOSAL

diary testout2

% Program CALCAPAP2.M

clear

echo on

load Klb.txt

load Klo.txt

load Krb.txt

load Kro.txt

load yo.txt

load Xr.txt

load Fb.txt

load Fo.txt

load A.txt

%Calcu1ate the K matrices

[m,n] = size(A*Klb)

Kb =inv(eye(n)-A*Klb) *A*Klo

Ks=(Krb*Kb)+Kro

Klelo==[K1b Klo]

%Calculate Energies

inva = inv(eye(n)-Klb’ *A’)

96 Make Xr conformable for inclusion of steam energy in Fb Fo

[Wt] = SW)

ert=[zeros(p,l) Xr]

Xb =-invIKA*Krb’ *ert-invIKA*Fb
=-A’*Xb

Fsst=(Kb’*Fb) +Fo

Fs=Fsst

Fs=Fs(: ,2:7)

Xo=-(Ks’*Xr)-Fs

%Include calculated gas and oil in yo vector

e=yo""Fs

yo(2.1)=e(1,1)

yo<3.1)=e(1,2)

yo(4,1)=e(1.4)

%Calculate y variables

YI=KS*YO

yb=Kb*yo

yby0=[yb;yo]

yl=Klelo*ybyo

%Calculate energy

e=yo""Fs

exo=yo’*Xo

%Output data to file

158

%Enter diary output file name if desired - then RETURN
diary OUTPAP2A
%keyboard
echo off
10me = [Klb
Krb]
KloKro= [Klo
Km]

Fo

Fsst

Fs

e

exo

diary off

echo on

%Enter diary REPORT output file name if desired - then RETURN
diary REPPAP2A

96keyboard

echo off

yr

yb

yo

Xo

Fsst

Fs

e

exo’

diary off

echo on

%Enter SAVE PAPER2A output file name if desired - then RETURN
save PAPER2A

%keyboard 96 End of calculation file

159

% PROGRAM TO CALCULATE PROCESS NETWORK FOR POLYSTYRENE
% MANUFACTURE
diary testoutl

% Program CALCSTY1.M
clear
echo on
load Klb.txt
load Klo.txt
load Krb.txt

load Kro.txt

load yo.txt

load Xr.txt

load Fb.txt

load Fo.txt

load A.txt

load go.txt

load ce.txt

load gs.txt

load ge.txt

load os.txt

load oe.txt

load pr.txt

load po.txt

load pe.txt

load gba.txt

load goa.txt

%Calculate the K matrices

[m,n] = size(A*Klb)

Kb=inv(eye(n)-A*Klb)*A*Klo

Ks=(Krb*Kb)+Kro

Klelo=[Klb Klo]

%Calcu1ate Energies

inleA =inv(eye(n)-Klb’ *A’)

96 Make Xr conformable for inclusion of steam energy in Fb Fo
[PA] = 8%)

ert=[zeros(p,l) Xr]

Xb = -invIKA *Krb’ *ert-invIKA *Fb

Xl=-A’*Xb

Fsst=(Kb’*Fb)+Fo

%Convert steam and electric to natural gas and/or fuel oil requirements for PS
Fs=Fsst
Fs(1,2)=Fsst(l,2)+(Fsst(1,1)*gs*go)+(Fsst(1,4)*ge*go*ce)
Fs(l,3)=Fsst(1,3)+(Fsst(1,1)*os*(1-go))+(Fsst(1,4)*oe*(l-go)*ce)
F8(l.4)=(Fsst(l.4)*(1-ce))
Fs(2,2) =Fsst(2,2) + (Fsst(2, l)*gs*go) + (Fsst(2,4) *ge*go*ce)

160

Fs(2,3) =Fsst(2,3) + (Fsst(2, 1)*os*(1-go)) + (Fsst(2,4) *oe*( 1 -go) *ce)
Fs(2,4) = (Fsst(2,4)*( 1 -ce))

Fs=Fs(:,2:7)

Xo=-(Ks’*Xr)—Fs

%Include calculated gas and oil in yo vector
e=yo’*Fs

y0(3.1)=e(1.l)

y0(4.1)=¢(1,2)

y0(5.1)=e(1.4)

%Calculate y variables

yr=Ks*yo

yb=Kb*yo

yby0=lyb;yol

yl =Klelo *ybyo

e=yo""Fs

exo=yo’*Xo

% Calculate cash flow and value added
Cf=<yo’rpo)-(yr’*pr)-(e*pe)
Gsa=(Kb’*gba)+goa

Vs=Cf-(yo’*Gsa)

%Output data to file

%Enter diary output file name if desired - then RETURN
diary OUTSTYIA

%keyboard

echo off

Klerb=[Klb

161

Xr
ert
Fb
Fo
Fsst
Fs
e
exo

pr
P0

P3

gba

goa

Gsa

Cf

Vs

diary off

echo on

%Enter diary Ks output file name if desired - then RETURN
diary KSSTYlA

%keyboard

echo off

Ks

diary off

echo on

%Enter diary Fs output file name if desired - then RETURN
diary FSSTYlA

%keyboard

echo off

Fs

diary off

echo on

%Enter diary REPORT output file name if desired - then RETURN
diary REPSTY 1A

%keyboard

echo off

YT

yo

Xo

Fsst

Fs

e

exo

Gsa

Cf

162

Vs

diary off

echo on

%Enter SAVE PLASTlA output file name if desired - then RETURN
save plastla

%keyboard

% End of ealculation file

163

% PROGRAM TO CALCULATE PROCESS NETWORK FOR POLYSTYRENE
% MANUFACTURING, USE AND DISPOSAL
diary testout2
% Program CALCSTY2.M
clear
echo on
load Klb.txt
load Klo.txt
load Krb.txt
load Kro.txt
load yo.txt
load Xr.txt
load Fb.txt
load Fo.txt
load A.txt
%Calculate the K matrices
[m,n] = size(A*Klb)
Kb=inv(eye(n)-A*Klb)*A*Klo
Ks=(Krb*Kb)+Kro
Klelo=[Klb Klo]
%Calculate Energies
invIKA =inv(eye(n)-Klb’*A’)
96 Make Xr conformable for inclusion of steam energy in Fb Fo
[PA] = W)
ert=[zeros(p, 1) Xr]
=-invIKA I"Krb’ *ert-invIKA*Fb
Xl=-A’*Xb
Fsst=(Kb’*Fb) +Fo
Fs=Fsst
Fs=Fs(: ,2z7)
Xo=-(Ks’*Xr)-Fs
%Include calculated gas and oil in yo vector
e=yo’*Fs
yo(2,1)=e(1.1)
yo(3.1)=e(1,2)
yo(4.1)=e(1,4)
%Ca1culatc y variables
yr=KS*y0
yb =Kb*yo
yby0=lyb;y0]
yl =Klelo“ybyo
%Calculate energy
e=yo’*Fs
exo=-yo"Xo
%Output data to file

164

%Enter diary output file name if desired - then RETURN
diary OUTSTYZA
%keyboard
echo off
Klerb = [Klb
Krb]
KloKro = [K10
Km]

Fo
Fsst
Fs
e

exo
diary off
echo on
%Enter diary REPORT output file name if desired - then RETURN
diary REPSTYZA
%keyboard
echo off
yr
yb
yo
Xo
Fsst
Fs
e
exo’
diary off
echo on
96Enter SAVE PLAST2A output file name if desired - then RETURN
Save PLAST2A
flkcyboard 96 End of calculation file

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