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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St. John's Road, Tyler's Green High Wycombe, Bucks, England HP10 8HR 7900725 M E K K H O F , R O N A L D LEE T H E E C O N O M I C F E A S I B I L I T Y OF U T I L I Z I N G W A S T E H E A T F R O M E L E C T R I C A L P O W E R P L A N T S IN I N T E G R A T E D A G R I C U L T U R A L AND A G U A C U L T U R A L SYSTEMS UNDER MICHIGAN CONDITIONS, MICHIGAN STATE UNIVERSITY, University Microfilms International 300 n z e e b r o a d ,a n n a r b o r ,m i *0106 PH.D., 1978 THE ECONOMIC FEASIBILITY OF UTILIZING WASTE HEAT FROM ELECTRICAL POWER PLANTS IN INTEGRATED AGRICULTURAL AND AQUACULTURAL SYSTEMS UNDER MICHIGAN CONDITIONS By Ronald L. Meekhof A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1977 ABSTRACT THE ECONOMIC FEASIBILITY OF UTILIZING WASTE HEAT FROM ELECTRICAL POWER PLANTS IN INTEGRATED AGRICULTURAL AND AQUACULTURAL SYSTEMS UNDER MICHIGAN CONDITIONS By Ronald L. Meekhof Low grade energy in the thermal discharge of steamelectric power plants is dissipated into the environment via cooling towers, reservoirs, or spray canals. Waste heat is generally not considered to be a resource that can be applied to industrial processes or urban use. It has been found, however, that in controlled circumstances, the growth rates of selected agricultural crops and fish spe­ cies have increased significantly with the use of waste heat in cultural practices. Whether recycling of the waste heat in an integrated system of agricultural and aguacultural uses is economically feasible was evaluated. Least cost systems of sizes and types of uses were determined for several economic condi­ tions. For each of the least cost system designs, a water transport system was designed. Whether a waste heat utiliza­ tion system is a least cost alternative to conventional dis­ sipation methods was then assessed. Several management and acquisition options were discussed. The impact of those Ronald L. Meekhof options on the distribution of costs, and consequently on the feasibility of a waste heat utilization system, was de­ termined. A pseudo-dynamic linear programming model was speci­ fied to solve for the optimal system design. Synthesized agricultural and aquacultural subsystems which are repre­ sentative in terms of initial capital requirements, annual costs, productivity responses, and heat dissipation capabil­ ity were the activities. Model specification stipulated that the amount of waste heat from a 1,000 megawatt electri­ cal plant be dissipated. Two cases of a purchase and leaseback option were ana­ lyzed should the utility decide not to manage the utilization system but maintain capital ownership. If ownership of fixed capital is not desired, a contractual arrangement was also evaluated. Partial budgeting analysis was used to assess the impact of each option on total monetary outlays of the utility. The research results indicate that the least cost com­ bination of subsystems is comprised of 375 acres of fish ponds, 100 acres of soil warming reservoir. (tomatoes), and a 208 acre However, when costs for the water transport sys­ tem are included, the total monetary outlays for this sys­ tem are greater than those for a system comprised of 160 acres of fish ponds, 100 acres of soil warming (tomatoes) , and a 352 acre reservoir. Both systems are, however, least cost alternatives to conventional methods of waste heat Ronald L. Meekhof dissipation. When prices for aguacultural and agricultural commodities were reduced 17 and 45 percent respectively, the waste heat utilization system was not a least cost alterna­ tive. Analyses of alternative management and acquisition op­ tions indicate that when a purchase and leaseback option is employed and no claim on system revenues is made by the utility, the waste heat utilization system is not a least cost alternative. However, if the utility obtains rents that allow the utilization system management to cover the annual operating co&ts and managerial expense, the utiliza­ tion system is a least cost alternative. When the contractual arrangement is employed, all capi tal and annual costs are borne by the utilization system management. Net monetary returns to subsystem operation are, however, negative and a monetary incentive must be paid to attract capital and management resources. However, the utility could afford to pay costs for the transport system. The primary implication of this research is that in­ tegrated agricultural and aguacultural systems which utilize waste heat should be further studied. tive gains from waste heat utilization. The study shows posi­ A small scale demon stration facility would better define operational character­ istics of full scale systems and would allow refinement of the model. The viability of an integrated system also needs to be examined under a wider range of exogenous conditions and system parameters. ACKNOWLEDGMENTS I would like to extend my sincere appreciation to Dr. Larry J. Connor for the advice and guidance he offered in his capacity as my thesis and academic advisor. I consider myself fortunate to have been associated with him on a pro­ fessional and personal basis throughout my graduate training. I am grateful to Drs. Fred Bakker-Arkema, Stephen B. Harsh, Lester V. Manderscheid, and A. Allan Schmid for their expeditious reading of the final draft of this dissertation. Their criticisms and questions regarding this research were insightful and stimulating. I would also extend my appreciation to the members of the research group at Michigan State University with whom I was affiliated in the study of waste heat utilization. With­ out the models they developed, this dissertation would not have been possible. Of particular importance in this re­ spect are Dr. Fred Bakker-Arkema, Dr. Larry J. Cpnnor, Irwin Schisler, Wilma Schultink and Larry Walker. I would also thank my father and mother for the type of guidance and encouragement which was so important. The sacrifices they made earlier in my educational training will not be forgotten. Lastly, I thank my wife, Joyce and daughter, Alison for the forbearance, support, and the sacrifices that each ii of them has made. It is to them that this dissertation is dedicated. iii I TABLE OF CONTENTS Page LIST OF T A B L E S ......................................... viii LIST OF F I G U R E S ..................................... xi Chapter I. INTRODUCTION .............................. 1 Problem Statement ...................... 2 Utilization and Dissipation Approaches . 4 The Integration Approach ............... 8 Review of Relevant Literature ......... 12 Purpose of the R e s e a r c h ............. 15 Research Objectives ................... 16 Dissertation P l a n ................... 17 II. PARAMETERS OF THE WASTE HEAT UTILIZATION PROBLEM AND ENVIRONMENTAL CONSIDERATIONS 19 Parameters of the Waste Heat Problem . . 19 Technical Factors Affecting the Waste Heat Utilization Facility ......... 20 Limited U s e ..................... 21 Low Value to Cost R a t i o ........ 22 Cost of R e t r i e v a l ............... 22 Need for Highly Controlled E n v i r o n m e n t ................... 23 Chemical Fouling ................... 24 Economic Factors Affecting the Waste Heat Utilization Facility ......... 24 Capital and Land Availability ... 24 Optimization over System Operation . 24 Sensitivity to Supply of Waste Heat. 26 Flow R a t e s ....................... 26 Management and Ownership Option . . 27 Spatial Relationships and the ............. 27 Distribution System Type of C o m m o d i t y ............... 28 Timeliness of Operation ........... 28 Technical Factors Affecting the U t i l i t y ............................ 29 Costs of R e t r o f i t t i n g .......... 29 Reliability of Supply ............. 29 iv Chapter Page Plant O u t a g e s ................. 30 Economic Factors Affecting the Utility 30 30 Salable Commodity .................... Site S e l e c t i o n .................... 31 31 Regulatory Approval .................. U n c e r t a i n t y ......................... 32 Cost of Backup F a c i l i t y ........... 32 Lead Time and Life Cycle . . . . . . 33 Environmental Costs of Thermal Discharge 34 Heated Water Discharges ............. 34 Conventional Systems ............... 38 Cooling Ponds ...................... 38 Evaporative Mechanical Draft Towers 38 Evaporative Natural Draft Towers. . 39 Dry Mechanical and Natural Draft 40 T o w e r s ........................ Conventional Cooling System Cost . . 40 Environmental Considerations of an Inte­ grated Waste Heat Utilization System. . 41 III. M E T H O D O L O G Y ........................ 46 Sources and Types of D a t a .............. 46 Subsystem Cost D a t a .................. 47 General Piping and Distribution System Cost D a t a .................. 48 S u b - m o d e l s ........................... 49 Analytical Constructs .................... 49 The Allocation Simulation Model . . . . 50 Components of the Allocation Model. . . 53 POND M o d e l ........................ 53 Soil Warming M o d e l ................ 53 Fish Growth M o d e l .................... 54 55 Crop Growth M o d e l .................... Iterative Procedure .................... 56 Optimization Procedure .................. 56 Optimization Characteristics ......... 58 Properties of the A l g o r i t h m ........... 59 The Objective Function ............... 63 Theoretical Model ........................ 64 A s s u m p t i o n s ........................... 65 The M o d e l ................. 66 Factors Limiting Allocative Efficiency . 68 The Model R e v i s i t e d .................. 70 D e s i g n ................................. 72 The M o d e l ............................. 72 Discount R a t e ........................ 73 S u m m a r y ................................. 74 v Page Chapter IV. OPTIMAL DESIGN CHARACTERISTICS FOR THE WASTE HEAT UTILIZATION SYSTEM . . . . . . 76 77 Price A s s u m p t i o n s ..................... Availability of Resource Assumptions. . 77 Base Yield and Stocking Rates 78 A s s u m p t i o n s ......................... Optimal Design with no Constraints on Subsystem Size (Model I) ............. 78 78 System D e s i g n ......................... Financial Analysis ................... 81 Cost Minimizing Flow R a t e s ........... 81 84 Shadow Prices ......................... Non-basis Activities ................. 90 Optimal Design with Constrained Fish Pond Acreage (Model I I ) ............... 93 System Design ......................... 93 Financial Analysis ................... 95 Shadow Prices . . . . . ............... 97 Optimal Design with Lower Commodity Prices (Model III) ......................102 System Design ......................... 104 Financial Analysis ................... 105 Shadow Prices ............. . . . . . . 107 V. COMPARATIVE ANALYSIS OF WASTE HEAT UTILIZA­ TION SYSTEMS WITH CONVENTIONAL DISSIPATION M E T H O D S .....................................Ill General Piping and Distribution System. . 112 Comparison Among Waste Heat Utilization S y s t e m s .................................. 114 Comparison among Conventional Mechanisms and Waste Heat Utilization Sustems . . 119 VI. MANAGEMENT AND ACQUISITION OPTIONS . . . . Other Management and Acquisition Options. ............... Fee Simple Acquisition Purchase and M a n a g e ............... 127 Purchase and Leaseback ............. Purchase and Resale on Condition . . Less than Fee Simple Acquisition . . . Easement Purchase ................... Contractual Agreements ............... Waste Heat C o o p e r a t i v e ............... Contractual Arrangement ............. Public Authority ..................... Feasible Options ....................... Partial Budget Analysis for Purchase and Leaseback and Contractual Arrangement . vi 123 124 127 128 128 129 129 129 129 130 130 131 133 Chapter Page Purchase and Leaseback ............... Contractual Arrangement ............. Bargaining Range when a Contractual Arrangement is E m p l o y e d ......... Summary ..................... 146 153 VII.SUMMARY AND C O N C L U S I O N S ..................... Problem Definition ..................... Research Objectives ................... M e t h o d o l o g y ............................ Empirical Results ..................... I m p l i c a t i o n s ............................ Limitations of the S t u d y ............... Suggestions for Further Research . . . . 155 155 156 157 158 162 165 167 A P P E N D I C E S ......................................... 169 BIBLIOGRAPHY 205 ....................................... 136 143 LIST OF TABLES Table 2-1 2-2 4-1 4-2 4-3 Page Estimated Generating Capacity, Operating Efficiency, and Waste Heat Production, 1970-2020 ..................................... 36 Comparison of Cooling Systems Cost on Dollars per Kilowatt B a s i s ........................... 41 Reservoir Utilization Rates by Month for Model I ....................................... 80 Initial Capital Requirements, Discounted Net Revenues, Reservoir Operating Costs and Replace­ ment Capital Costs, and Net Monetary Returns for the OptimalDesign Obtained from Model I 82 Shadow Prices for Waste Heat by Month for Specified Discount Rates and Planning Horizons, Model 1 ....................................... 86 Shadow Prices for Reservoir Utilization for Specified Discount Rates and Planning Horizons, Model I ....................................... 88 Shadow Prices for One Additional Acre of Fish Pond and Soil Warming (Tomatoes) for Specified Discount Rates and Planning Horizons, Model I . 89 4-6 Competitive Positions of Non-basis Activities . 92 4-7 Reservoir Utilization Rates by Month for Model I I ..................................... 94 Initial Capital Requirements, Discounted Net Revenues, Reservoir Operating Costs and Re­ placement Capital Costs, and Net Monetary Returns for the Optimal Design Obtained from Model I I ..................................... 96 Comparison of Absolute Differentials and Per­ centage Changes in Capital Outlays, Discounted Net Revenues, Reservoir Operating Costs and Capital Replacement Costs, and Net Monetary Returns at a Discount Rate of 12 Percent for 28 Years for Models I and I I ..................... 98 4-4 4-5 4-8 4-9 viii Table Page 4-10 Shadow Prices for Waste Heat by Month for Specified Discount Rates and Planning Horizons, Model I I .......................................... 100 4-11 Shadow Prices for Reservoir Utilization for Specified Discount Rates and Planning Horizons, Model I I .......................................... 101 4-12 Shadow Prices for One Additional Acre of Specified Subsystems and Cost of Explicit C o n s t r a i n t ........................................ 103 4-13 Discounted Net Revenues and Net Monetary Costs for Model III and their Comparisons with those for Model I ...................................... 106 4-14 Shadow Prices for Waste Heat by Month for Specified Discount Rates and Planning Horizons, Model I I I ........................................ 108 4-15 Shadow Prices for One Additional Acre of Fish Ponds and Soil Warming (Tomatoes) for Specified Discount Rates and Planning Horizons, Model III. 110 5-1 Net Monetary Returns, and Initial Capital Re­ quirements and Discounted Annual Costs for the General Piping and Distribution System, Model I. 115 5-2 Net Monetary Returns, and Initial Capital Re­ quirements and Discounted Annual Costs for General Piping and Distribution System, Model I I .......................................... 116 5-3 Net Monetary Returns, and Initial Capital Re­ quirements and Discounted Annual Cost for General Piping and Distribution System, Model I I I ........................................ 117 5-4 Comparison of Total Monetary Outlays for In­ tegrated Waste Heat Utilization Systems and Alternative Methods ............................ 120 Ranking in Terms of Total Monetary Outlays, of Dissipation Alternatives ................... 122 Management and Acquisition Options for Waste Heat Utilization Systems ....................... 126 5-5 6-1 ix Table 6-2 6-3 6-4 6-5 6-6 6-7 Page Initial Capital Requirements, Discounted Costs, Net Revenues and Replacement Capital Costs for Models I, II and III, and Corresponding General Piping and Distribution System for 12 Percent and 28 Y e a r s .......................... 134 Partial Budget Analysis: Purchase and Lease­ back Management Option: Case I .............. 137 Total Monetary Outlays for Alternative Systems where the Purchase and Leaseback Option is used for the Utilization S y s t e m ............. 139 Partial Budget Analysis: back Option: Case I I 141 Purchase and Lease­ Total Monetary Outlays for Alternative Systems where the Purchase and Leaseback Option is used for the Utilization System: Case II . . 142 Payments by Utility Necessary to Make Net Mone­ tary Returns of Subsystem Operation and Owner­ ship Equal to Zero: Annual and Discounted B a s i s .......................................... 145 6-8 Total Monetary Outlays for the General Piping and Distribution System when Model II is employ­ ed: Annual and Discount Dollar Basis (in Thousands of Dollars)........................ . 148 6-9 The Difference in Terms of Total Monetary Out­ lays, beteween the Mechanical Draft Cooling System and the General Piping and Distribution System for Model I I .......................... 149 Net Monetary Returns for Model II when the Utilization System Management Obtains the Maxi­ mum Amount it can Bargain for. (in Thousands of Dollars)..................................... 151 6-10 6-11 Net Monetary Returns to System Management and Total Monetary Outlays by the Utility when Fifty Percent of the Maximum Bargaining Range is Transferred from the Utility to Management of the Utilization System (in Thousands of D o l l a r s ) ......................................... 152 x LIST OF FIGURES Figure 3-1 3-2 3-3 3-4 Page Major Components and Component Interfaces of the Allocation-Simulation Model ........... 51 Schematic of the Interactive Procedure between the OPTBOX Program and Linear Programming Model to Find an Optimal Solution............. 57 Allocative Efficiency in Waste Heat Use: Mar­ ginal Factor Cost Equals Shadow Price . . . . 68 Schematic of Program OPTBOX Method of Finding the Efficient Allocation of Waste Heat Given the Dynamics of Changing Flow R a t e s ........ 71 APPENDICES Appendix Page 1 C o m m e n t s ........................................ 169 2-A The Allocation P r o g r a m ......................... 170 2-B The POND M o d e l ................................. 175 2—C The Soil Warming M o d e l ........................ 177 2-D The Pish Growth M o d e l ......................... 178 2-E The Crop Growth M o d e l ......................... 180 LIST OF APPENDICES TABLES Table 3-A Page Initial Capital Requirements for a 4-20 Acre Fish Pond S u b s y s t e m ................. 181 3-B Annual Costs for the 4-20 Acre Fish Pond S u b s y s t e m .......................................... 182 3-C Initial Capital Requirements for a 24-20 Acre Fish Pond S u b s y s t e m ............................... 184 3-D Annual Costs for the 24-20 Acre Fish Pond S u b s y s t e m .......................................... 185 3-E Initial Capital Requirements for 100 Acres of Soil Warming A r e a ..................................187 3-F Annual Costs for 100 Acres of Soil Warming for T o m a t o e s .......................................... 188 3-G Initial Capital Requirements and Annual Costs for the R e s e r v o i r ..................................189 3-H Initial Capital Requirements for a 216,000 Square Foot Greenhouse ........................ 190 3-1 Annual Costs for a 216,000 Square Foot Green­ house ............................................... 191 3-J Initial Capital Requirements for 8-20 Acre P o n d s ............................................... 193 3-K Annual Costs for the 8-20 Acre Fish Pond S u b s y s t e m .......................................... 194 4-A Initial Capital Requirements and Annual Costs for Waste Heat Dissipation Alternatives . . . . 196 4-B Initial Capital Requirements for the General Piping and Distribution System for Models I and I I I ................................................. 197 4-C Annual Costs for the General Piping and Dis­ tribution System for Models I and I I I ........... 199 xiii Page Table 4-D 4-E Initial Capital Requirements for the General Piping and Distribution System for Model II . . 200 Annual Costs for the General Piping and Dis­ tribution System for Model I I ................... 202 xiv LIST OF APPENDICES FIGURES Figures Page 2-A (1) Simulation Flow Chart A L L O C ................. . 1 7 3 2-A (2) Optimization S e q u e n c e ............. ...........174 5 -A Proposed Spatial Relationships and General Piping and Distribution System: Models I and I I ..................................... 203 5-B Proposed Spatial Relationships and General Piping and Distribution System:Model II . xv . 204 CHAPTER I INTRODUCTION Waste heat generation from steam-electric generating facilities is a significant ecological and resource use prob­ lem. For every kilowatt hour of electricity produced, the equivalent of between one and one-half and two kilowatt hours of electrical energy will appear as waste heat in the cool­ ing water of power plants. It has been estimated that the rate of waste heat discharge from these sources will increase 15 from 2.15 x 10 kilocalories per year in 1970 to 8.42 x 15 10 kilocalories per year in the year 2000 (Boersma, et al. 1972). The rather conservative estimate of waste heat pro­ duction in the year 2000 is nearly eight times greater than total generating capacity for the United States in 1970. With minor exceptions, the thermal discharge effluent is directly dissipated into the environment by cooling towers, reservoirs, or spray canals. The waste heat produced in the electrical power generation process is treated as an exter­ nality in production. The energy in the cooling water is generally not considered to be a resource that can be managed for effective use. It is treated as waste. The dispersed nature of energy in the discharged cooling water of power plants has conventionally precluded the recycling of the cooling water for productive use. 2 Problem Statement The general problem to which this study is addressed is whether the waste heat from power plants can be treated as a resource to be managed in controlled circumstances for pro­ ductive use. More specifically, the problem which this study addresses is whether integrated waste heat utilization sys­ tems comprised primarily of agricultural and aguacultural uses are economically feasible under Michigan conditions. The emphasis of this research is on the least cost design and organization of a system structure that will achieve desired goals subject to specified constraints. To that effect, the task to be accomplished is one of determining a mixture of agricultural and aguacultural uses which in total form a sys­ tem that utilizes waste heat in productive ways. Should such a system be shown to be feasible, we could expect a reduction in the use of conventional means of dis­ sipating thermal discharge effluent, the disuse of waste heat, and possible reduction in the use of other energy sources. Several researchers have studied the economic aspects of individual uses of waste heat. Economic feasibility of waste heat utilization was assessed on the basis of costs and returns of a particular individual use. This research, how­ ever, will evaluate the feasibility of an integrated^- as op­ posed to a combined system of several uses. For this problem, 1The definition of a single use system is self-evident. Boersma, et al. (1974) defines a combined system as "... one made up of various numbers of waste heat components. No at­ tempt is made to optimize the number of components or size of 3 integration can be defined as the level of economic and physi­ cal coordination among the several uses. This would involve the mobility of allocating inputs between uses according to some established criterion, the joint use of a fixed capital facility, and the common use of managerial skill. The degree of integration postulated here does not entail full utiliza­ tion of the possibilities for coordinating power plant opera­ tions with that of the integrated waste heat utilization sys­ tem. The only coordination specified, in this case, is that the integrated waste heat utilization system receives cooling water and returns it to the power plant subject to minimum water quality requirements. Whether an integrated system of agricultural and aqua­ cultural uses is economically feasible depends on satisfying two criteria. The first criterion is whether several uses can be integrated in an optimal manner to form a least cost system that utilizes a specified amount of waste heat. In this regard, we are operating in an optimization mode to satisfy a set of constraints. Economic feasibility in this context is a matter of cost effectiveness in that we are each component used, nor to consider the arrangement of the components in the total system...no interaction or feedback among the components is considered; and there is no overall philosophy to operate the system in order to maximize a par­ ticular parameter." The systems are in contrast to an in­ tegrated system which Boersma has also defined as a system in which "... the type and number of each component is care­ fully chosen and added to the system in an attempt to maxi­ mize an operational parameter such as profit. Interactions and feedback among all components are considered, and the overall system is designed and operated to maximize the above mentioned parameter..." 4 determining whether the optimal size and mix of agricultural and aquacultural uses is a least cost alternative to conven­ tional methods (cooling towers, reservoirs) that are used to dissipate thermal effluent. In order to determine whether this nonconventional ap­ proach is economically feasible, it is also necessary to ex­ amine whether basic operational criteria can be met. issue here is not one of constrained optimization. The The in­ stitutional apparatus which facilitates the transfer of waste heat from the utility to the use system and between the dif­ ferent types of uses will affect conditions necessary for an efficient allocation of waste heat, and, in some respects, the design of the system. As stated earlier, the emphasis is on design or organiza­ tion of a system structure that will achieve desired goals. The physical interdependencies between the power plant and the waste heat utilization system, formed by the common use of the water resource, necessitate an examination of how or­ ganizational arrangements between these two parties will af­ fect that performance. The types of issues of importance here are ownership of capital and land resources and manage­ ment of the individual uses and of the total system. Utilization and Dissipation Approaches Two methodological approaches have been developed for assessing the feasibility of using thermal discharge efflu­ ent from steam-electric power plants. While each is related to the effective use of waste heat, they differ greatly in 5 -terms of scope and objectives. Since the approaches differ in the nature of the objective function to be minimized or maximized, and assumptions concerning the plant discharge options and characteristics, siting the results will differ in the use of selected subsystems and optimal sizes of those subsystems. As an example of how results are influ­ enced by these two approaches, Shapiro (1975) has evaluated the design of a soil warming subsystem for the level of use associated with the utilization and dissipation approaches. Gilham (1974) states that "the principal objective under the dissipation philosophy is to dissipate heat, while the objective under the utilization philosophy is to derive some benefit from the heat which is currently being wasted ...the two approaches are not mutually exclusive, or indeed, completely separable..." With the dissipation approach, the explicit goal is to design a system which will serve as an alternative to conventional methods of dissipating waste heat. The design of this type of system, where presumably conventional methods of heat dissipation are not incorporated, is organized on the basis of maximizing dissipation at mini­ mum cost. A system organized with this approach is con­ strained by these stipulations: 1. The system is comprised of uses which will en­ sure the dissipation of most, or preferably all, of the waste heat from a power plant for all seasons of the year and expected load patterns. 6 2. For closed systems, the return water must meet minimum temperature and quality requirements so as not to adversely affect plant operating efficiency. 3. The design of the system must ensure noninter­ rupted power plant operation. Gillham states that there are two major advantages of such a system. First, plants with conventional dissipation systems (presumably closed systems) will have higher dis­ charge temperatures than plants with once-through cooling systems.1 Consequently, a greater level of energy is avail­ able for use. Secondly, the system dissipating the heat generates revenues and "less tangible social benefits" which can be used to offset capital costs and other monetary out­ lays by the utility. A comparison of the net monetary out­ lays of systems that use waste heat to those which do not can be made. The major disadvantages of systems designated under this philosophy are that large seasonal excess capacity of subsystems and associated capital land resources can occur where there is seasonal fluctuation in meteorological condi­ tions. Also, the operational capacity and efficiency of the power plant is directly associated with the dissipation and operating characteristics of the dissipation system. 1This advantage accrues primarily to the waste heat utilization system as high input temperatures to the system will correspond to higher return temperatures, which in ef­ fect reduces plant efficiency. The second approach designated by GiIlham is the utili­ zation approach. The primary objective incorporated in a utilization system design is "to maximize the economic and social benefits" of waste heat utilization rather than the minimization of costs (p. 3). This approach is primarily ap­ plicable to situations where there are no legal or regulatory pressures to refrain from one-through cooling. The primary constraints are as follows: 1. In that this approach is feasible where legal, regulatory and physical constraints permit one-through cooling, the implementation of a waste heat system is justified by economic costs, returns and social benefits of each individual use. 2. The system should not interfere with power plant operation or be catastrophically af­ fected by a plant shutdown. 3. As a closed system is not required, discharge temperatures are lower, and therefore, the year around operation of some uses is not certain. It is argued that the advantages of systems designed on this principle are: 1. The use of capital, land, and other resources are justified by economic costs and returns and not on a production basis. 2. There is no requirement that a specified amount of waste heat be utilized by the different uses. 8 3. As the system is open, there is no restriction on the temperature of the water leaving the system which would allow greater flexibility in the system. The disadvantage of such a concept for this research is that the Federal Water Quality Administration (now the Environmental Protection Agency, EPA) forbade dumping of virtually any heat into Lake Michigan in 1970. states have set similar standards. Several The more recent (1974) effluent limitation guidelines of the EPA require "essen­ tially no discharge" of thermal pollutants for many plants now in operation or being built, and for "all new sources" that will begin operation after 1983 (Belter, 1974). Hence, closed-cycle cooling options are required for all sites. Each of these approaches is useful where the scope of the research and problem definition conforms with the stipu­ lated conditions and resources available. However, the dis­ sipation approach does not guarantee an overall least cost combination of variable and capital resources. The utiliza­ tion approach does not stipulate the dissipation of a speci­ fied amount of waste heat. The Integration Approach The primary disagreement with the dissipation approach is its failure to guarantee an optimal allocation of re­ sources. It is not specified that in dissipating waste heat under this approach an attempt is made to allocate capital and land resources to uses which at the margin return the 9 greatest revenue per dollar invested in these resources, or whether some other criterion is chosen. The utilization ap­ proach allocates waste heat on the basis of economic costs and returns per use and as such does not employ the advan­ tages obtainable where optimization is carried out over the total system. Neither of these approaches is suited to deal with the design of a feasible system of waste heat uses given the technical, operational and economic factors that con­ strain the waste heat utilization problem as it has been pre­ viously stated. The problem requires that optimization be over the num­ ber or types of subsystems and the size of subsystems used. The approach used must also account for the interaction and feedback among subsystems. Furthermore, the type and size of subsystem is carefully chosen in an attempt to maximize or minimize some operational parameter such as system profit or total monetary outlays respectively. An integrated system can be achieved by economically and physically coordinating different subsystems. The higher the degree of integration within the system, the greater the ability to match waste heat energy availability with the level of energy optimal for subsystem operation, to spread fixed costs attributable to common fixed resources, ensure an optimal allocation of variable resources due to free mo­ bility of those resources and arrive at a least cost combina­ tion of land, capital and other scarce resources. 10 With an integrated system, it is possible to allocate the waste heat water on the basis of achieving the highest possible return from those resources. While the operation of the different subsystems in a combined system are inter­ dependent and coordinated to some extent, the effects of more completely integrating subsystems on a design basis has not been dealt with in previous studies of this topic. Consideration of an integration approach permits greater flexibility in subsystem selection than would exist with the utilization approach. Optimization of resource use is carried out over total system operation and not for in­ dividual subsystems. The reason for this is that agricul­ tural and aquacultural uses differ with respect to heat transfer, productivity response, cost of operation, and time period which waste heat can be used. Some generate signifi­ cant revenues above costs but utilize waste heat at a slow rate. For others the reverse is true. The economic feasi­ bility of individual subsystems is of less concern than the economic feasibility of the total system. Another aspect of this approach is that it does not foreclose the option of partial or reduced use of cooling towers or reservoirs as the dissipation approach stipulates. This aspect is not so much derived from the meaning of in­ tegration as it is based on conformance with physical facts of power generation. The constraints on a system organized under such an approach are as follows: 11 1. The total system (inclusive of conventional methods) will utilize all of the waste heat generated by a specified power plant regard­ less of season or load pattern. 2. The return water under a closed system must meet temperature and quality requirements so as not to reduce plant operating efficiency. 3. System design should ensure reliability in operation of the power plant. 4. While the above constraints will affect feasi­ bility, the actual implementation is based on a least cost comparison with conventional methods of waste heat utilization. The factors discussed above represent the basis for interest in an integrated approach and integrated system. Gillham underlines this reason for analyzing integrated sys­ tems when he states: By designing a system with several uses, the temperature requirements of individual com­ ponents may be different and the output water from one component may serve as the in­ put to another. As a result, more efficient use is made of the available heat, the system cooling function may be greater, and the eco­ nomics of the overall system may be consider­ ably more attractive than the economics of the individual components. Boersma points to a different class of reasons when he states: Society faces many problems related to its growth in numbers as well as standard of living. Not the least of these problems is the degradation of the environment 12 caused by industries, individuals, and communities. The ultimate solution must be found in the development of integrated systems in which resources are not used in a destructive manner, but are recycled. Power generating stations offer a unique opportunity to develop such systems. The waste heat represents a valuable resource to be managed for beneficial use. At the same time, water is becoming more and more a limited resource and should be subjected to multiple use. The production of food and fiber is rapidly becoming an industrial­ ized process with high production rates on small areas (Boersma, et al., 1972). Review of the Relevant Literature Agricultural and aquacultural organisms have been shown to respond in a favorable manner when controlled use is made of waste heat energy to alter the environment in which these organisms grow. The productivity response of field and spe­ cialty crops to a warmed soil environment has been studied extensively by Allred et al. (1975), Boersma et al. 1974), Decker (1975), and Skaggs and Sanders (1975). (1972, The use of thermal effluent for increasing the growth rates of aqua­ culture organisms has been studied by Walker (1975), T.V.A. (197 4), and by others (Guerra, et al. 1975) in New Jersey, New York, Texas, and California. The use of waste heat as a substitute heat source for greenhouse operation has been stud­ ied by Price and Peart (1973), Bond et al. et al. (1975), T.V.A. Boersma et al. al. (1974), Ashley (1975) and Boersma et al. (1972), Berry et al. (1974). (1974), and DeWalle et (1974) have studied the use of cooling water for irriga­ tion. Some of these uses are a commercial reality, while others are in an experimental state of development. 13 These studies dealt primarily with investigating techni­ cal parameters of utilizing waste heat for productive means. Productivity responses to waste heat were studied and in many cases growth models were developed on the basis of the experi­ mental data obtained. Economic analysis on the feasibility of utilizing waste was conducted on an individual use basis or on a combined system basis. DeWalle et al. (1974) evaluated the capital, operating and maintenance costs of a soil warming system and also costs and benefits of a single use irrigation system. A comparison was made on the total net costs of the AgroPower-Waste Water Complex relative to conventional methods of dissipating waste heat. The comparison is conducted on the basis of capitalized annual costs per kilowatt of plant capacity. As the system studied is a single use system, it was not necessary to optimally allocate the distribution of water. Rather, design parameters of field area, number of sections, ratio of field length to width and piping charac­ teristics were optimized. Boersma et al. (1974) conducted a systems analysis of the economic utilization of using waste heat and bleed-off steam in a combined system. This non-integrated system was comprised of urban uses, greenhouses, algal basins, and soil warming. Again the economic analysis was conducted on an in­ dividual subsystem basis. Costs and revenues were, discounted. For urban uses, a comparison study was conducted which evalu­ ated the cost of a steam heat system with alternative heat 14 sources. For other subsystems, the type of economic analysis varied from rough cost of production studies to present value analysis. Design optimization analysis was conducted over individual subsystems and for different sets of contingencies. The study conducted by Johns et al. (1971) deals spe­ cifically with using off-peak electrical energy and cooling water for agricultural purposes. While less specific in technical analysis than the two previously mentioned major reports, it does present well specified partial budgets and gross margins for several subsystems using waste heat. This study did not consider subsystem design optimization but eco­ nomic advantages of using waste heat were evaluated. The Tennessee Valley Authority (TVA) has also extensive­ ly studied possible beneficial uses of waste heat. A multi­ objective applied research program has been conducted to examine the feasibility of raceway production of catfish (Goss et al. 1975). The research at the Gallatin Steam Plant concentrated primarily on technical aspects of fish produc­ tion utilizing waste heat. The technical feasibility of this use was well documented. Questions remain concerning economic feasibility of raceway production methods. The utilization of waste heat as a substitute heat source in greenhouses is also being examined by TVA. emphasis of this research is The on technical capability of con­ trolling greenhouse environment, the effect of waste heat utilization on horticultural crop production and an evalua­ tion of economic aspects of greenhouse use of waste heat. 15 The study of economic factors centered on cost of production for several crops, implications of alternative production management systems and consumer acceptance of new products. A soil warming research facility has been installed at Muscle Shoals, Alabama to evaluate the potential of waste heat utilization in the production of field and vegetable crops. Economic results of various pipe spacing and water temperatures are not yet available. The TVA has also been engaged in research studying the possibility of using waste heat for warmed animal shelters and practical applications of biological nutrients from ani­ mal wastes. Economic results from these studies are also not yet available. In summary, the major economic studies on the feasibili­ ty of utilizing waste heat deal with individual uses or com­ bined systems. The general philosophy of these studies is similar to the utilization approach discussed previously. If design optimization is studied, it is conducted at the subsystem level. Purpose of the Research The purpose of this study is to investigate the feasi­ bility of utilizing waste heat in an integrated system of interdependent agricultural and aquacultural uses. As a feasibility study, it will provide insights and guidelines as to whether such an undertaking is economically reasonable. It is not the purpose of this research to reach a definitive 16 statement concerning the likelihood or necessity of construct­ ing such a system. Rather, the goal is to assess whether the topic requires further investigation. To accomplish this task it is necessary to develop an analytical system which represents the major components of such a system. The construction of an analytical system facilitates the observation of how changes in important para­ meters affect economic feasibility of a system of waste heat uses, and the range of conditions where such a system is eco­ nomically feasible. An analytical system is limited in that not all parameters can be made endogenous to the system. Hence, not all factors that affect feasibility can be repre­ sented . Research Objectives The purpose of this study is to assess the economic feasibility of utilizing waste heat energy from steam-elec­ trical generating facilities. This requires an examination of what has been termed the design problem and also the in­ stitutional context in which the goals of the utility and owner(s) of the waste heat utilization facility can be most suitably met. In accomplishing these tasks it is necessary to accomplish the following objectives: 1. Identify relevant crops and species of fish for which their biological receptivity to in­ tensive cultivation and the waste heat input is proven, and for which their growth response under controlled conditions has been estimated. 17 2. Determine the initial capital requirements, annual costs, and revenues for various types of subsystems and selected sizes. 3. Construct a model that determines an optimal system design subject to specified constraints. 4. Investigate the sensitivity of the optimal system design to changes in the value of criti­ cal parameters. 5. Identify a feasible set of institutional alter­ natives for the organization of capital, land, and managerial resources. 6. Identify information that describes important operational and economic characteristics of waste heat utilization systems. 7. Propose a system configuration for each least cost system and the pumping and piping charac­ teristics of a corresponding water transport system. 8. Determine, within a limited range, the optimal flow rates of waste heat water to agricultural and aquacultural subsystems. Dissertation Plan Chapter 2 contains relevant concepts and information regarding parameters of the waste heat utilization problem and environmental considerations. The methodology employed in this study is discussed in Chapter 3. The sources and 18 types of data, analytical and theoretical models, and the optimization procedure are presented and discussed. Chapter 4 shows the least cost system design for three alternative economic conditions. The general piping and distribution systems and comparisons of systems which use waste heat with conventional dissipation alternatives are discussed in Chap­ ter 5. Management and acquisition options are discussed in Chapter 6. These options are narrowed to a list of feasible alternatives and their impact on the monetary outlays by the utility are shown. The summary and concluding statements are shown in Chapter 7. CHAPTER II PARAMETERS OF THE WASTE HEAT UTILIZATION PROBLEM AND ENVIRONMENTAL CONSIDERATIONS Parameters of the Waste Heat Problem The utilization of waste heat energy poses technical and economic problems for the utility generating the waste heat and the facility that receives the thermal effluent. The utility faces problems that stem from the complexity of the fuel conversion cycle, legal requirements of what can or must be done with thermal effluent before its discharge into the environment is deemed safe, federal and state regulatory requirements that constrain activities within that of power generation and supply, and the operation of conventional means of dissipating waste heat. The waste heat utilization facility faces problems that arise from the entropy charac­ teristics of thermal effluent, uncertainty in input supply, the allocation of a multiple use input, external economies, and interdependencies in investment decisions. The problem has been stated such that the utility and utilization facility are the primary agents that affect a solution to the problem. Hence the discussion of parameters of the problem centers on factors that affect their opera­ tion and performance in utilizing waste heat. There is another class of factors that do not so much affect the nature of the solution to the problem as it has 19 20 been defined, as they demand a solution. Fossil fuel availa­ bility and thermal effects of power generation are concerns that presently do not directly affect feasibility of utiliz­ ing waste heat. They are, however, third party concerns which give added importance to the actions of the primary agents and whether waste heat utilization in the manner dis­ cussed here is indeed feasible. The purpose of presenting empirical information on these technical and economic problems and how they relate to the problem to which this research is addressed is to lay a basis for the formulation of research hypotheses, and insight into the nature of the problem. Outlining problem areas with related information also provides insights into the nature and necessity of assumptions that have to be made. Lastly, this exercise should show operational constraints that in­ fluence the behavior of the different parties. Technical Factors Affecting the Waste Heat Utilization Facility The factors mentioned below indicate some of the major technical problems affecting economic feasibility of the in­ tegrated waste heat utilization system. These factors have been researched by Michigan State University research groups or are peculiar in that information can be obtained on how they affect operational characteristics. Assumptions are made on other technical factors for which research evidence is not available. 21 Limited use In the process of converting fuels to work, the fuel input moves from a highly concentrated, low entropy level to a more dispersed, disorganized state of lower value. The free, low entropy energy loses the ability to produce me­ chanical work in this process. "Waste" heat refers to energy which is so degraded in temperature that its uses are limited. That energy of this nature has zero or small negative value has typically meant that it is economically practical to dis­ charge it directly into the environment. Large amounts of such energy appear in the form of cool­ ing water used for condensing steam discharged from the tur­ bine in steam-electric power plants. Depending on the ambi­ ent temperature, the quantity of that water circulated, the type and age of the power plant, climate, type of heatsink and other factors; the typical outlet temperature for such cooling water is in the range of 7°C to 40°C (50°F to 105°F) . Most industrial processes and urban uses require a much high­ er temperature range. Typical temperature requirements for processes where hot water can be used is from 71° to 204°C (160° to 400°F). As we have seen in sections regarding literature re­ view and subsystem description, the introduction of waste heat into certain biological and life cycle processes pro­ vide the most promising outlook for limited uses of waste heat. Even so, while there may be appreciable growth re­ sponse to waste heat, several technical and economic 22 questions remain. Low value to cost ratio The high entropy level of thermal discharge effluent means that the usable work per unit of volume is low. The relation of the supply cost of the input to its bulk is im­ portant. For bulky (low value-high entropy) resource inputs, unit transportation costs (which are part of supply costs) rise rapidly with the distance that the resource must be transported. If the transportation costs are absorbed by the waste heat user, the combined effect of these factors can significantly affect the optimal size of the enterprise that uses the waste heat input. Cost of retrieval Another element of supply cost is what will be termed cost of retrieval. The waste heat water enters the particu­ lar use in crude form. It is not so much the warmed water that is the resource input to be put into productive use, as it is the low grade energy in the water. In most instances the cost of extracting the usable energy is great. The fixed capital requirements for heat exchangers and control mecha­ nisms for most uses are significant. Furthermore, the use for which the different facilities can be employed is limited. The impact of high cost of retrieval on the use facil­ ity is that its ability to react to relative price changes is reduced and that new processes or technological innova­ tions are adopted at a slower rate. Given that the firm is 23 in a rather inflexible position and that capital requirements demand a large commitment of funds, its equity ownership may be initially low and thus lead to possible liquidity problems. Need for highly controlled environment The demand for waste heat by individual subsystems will vary on a daily basis. This is due to variability in meteor- oligical conditions, the effect this variability has on the performance of the heat transfer mechanisms, and the desira­ bility of maintaining the environment of the aquacultural and agricultural organisms at or near an optimal growth tempera­ ture. Failure to equate supply of waste heat with the physi­ cal demands of the organism can result in lost productivity by means of a death or retarded growth. Temperature is but one variable affecting productivity, but is an important one as the growth process of the organism is primarily tempera­ ture variant. The variety and number of other controllable inputs that affect growth will differ among uses. The reason for introducing this information is that the introduction of the waste heat resource into agricultural and aquacultural processes increases the cost of error of not maintaining the system at optimal conditions. The necessarily large fixed cost complement increases the sensitivity of the firm to adverse price movements and also productivity losses. Losses of this nature will reduce returns to fixed factors which for some uses, can be significant. 24 Chemical fouling Periodic cleaning of the condenser tubes results in the accumulation of chemical impurities (chlorine and heavy metals) and solids in the cooling water. These substances can adversely affect the productivity response of some or­ ganisms where the cooling water is a medium for growth. Similarly, the utility will require minimum water quality standards for water returned from the waste heat utilization system. Economic Factors Affecting the Waste Heat Utilization Facility As has been indicated, there are several technical factors that will affect operational characteristics of the waste heat utilization system as well as capital require­ ments. There are also economic factors that affect design and management behavior. The factors discussed are of a lesser magnitude of importance than the primary constraints affecting feasibility: a) a specified amount of waste heat must be utilized by the system, b) the system in total must generate sufficient revenues to cover costs, c) the total system, inclusive of the general piping and distribution system, must be a least cost alternative compared to conven­ tional methods of dissipating waste heat. Capital and land availability Large amounts of initial capital for construction, re­ placement capital, and operating capital for subsequent years 25 of operation are required. The interest rate at which these expenditures are financed affect desirability of investment. Control and ownership of capital facilities affect the na­ ture of decisions. Characteristics of the soil affect thermal conductivity of the soil warming mechanism. Sandy types of soil are preferred as the growth response to the waste heat input is optimized. The proximity of land with this characteristic affect capital requirements and operat­ ing expense of the water transport system. Optimization over system operation Given the costs and returns, capital investment re­ quirements, heat dissipating capability, and physical con­ straints for each individual subsystem, an optimal combina­ tion of size and type of subsystem can be found. The choice of subsystems and corresponding sizes is determined from the viewpoint of the total system. This optimization perspec­ tive is necessary as some uses contribute little to or sub­ tract from total system profit, but yet may be efficient heat transfer mechanisms. Other systems may generate large revenues but dissipate heat inefficiently. Therefore, on a subsystem basis, it may be "optimal" to have all green­ houses, or all fish culture, but designing a system on this basis would possibly cause the use of excessively large amounts of land and/or capital, or large seasonal excess capacity in capital, labor, and managerial skill. 26 Sensitivity of size to supply of waste heat The supply of waste heat is assessed to be equivalent to that supplied by a nominal one thousand megawatt, base loaded electrical generating facility. however, fluctuates on a seasonal basis. Electrical demand, Also, a specific plant may not remain on line as a base loaded facility, but rather be used for peak demand periods as its age increases. The issue of operational interest then is the extent by which optimal system design is affected by different levels of waste heat availability. Flow rates The initial step in determining optimal system design is to specify flow rates that maintain the temperature in the subsystem at or near the optimal range for growth pur­ poses. These temperatures are determined by the allocation- simulation program, which is discussed in a later chapter. The flow rates given by the allocation program determine heat dissipation rates for subsystems and thus affect opti­ mal system design. The pumping costs, and capital requirements associated with these flow rates are incorporated in the linear pro­ gramming model. allocation model. These costs are not incorporated in the In order to evaluate whether the flow rates given by the allocation program are economically opti­ mal, the costs associated with flow rates 10 percent above and 10 percent below the flow rate given by the allocation 27 model are also incorporated in the linear programming model. This is done for each activity in the linear programming model. Dissipation rates, pumping costs, and productivity responses are changed in proportion to these flow rates. Economically optimal flow rates are then determined by solv­ ing the linear programming problem. Management and ownership options The form of economic organization affects the level of economic and physical integration, the nature and distribu­ tion of externalities generated, and the distribution of costs and revenues. The type of management organization governing the use of capital and variable resources, as well as the allocation of waste heat forms the basis on which intrasystem tradeoffs ani complementarities are affected. Long term stability of system operation is also affected. Spatial relationships and the distribution system The spatial relationships of the subsystems to the power plant and to each other brings in another set of is­ sues that affect economic feasibility. Connecting subsys­ tems to the power plant is a general piping and distribution system. In finding the optimal size and mix of subsystems, the general piping and distribution has been treated as analytically separate. The costs associated with the dis­ tribution system are not directly attributable to the opera­ tion of any one subsystem. An optimal configuration for the distribution system and location of subsystems is then chosen 28 after the best mix of subsystems has been determined. The set of spatial relationships, or configuration is subject to environmental and physical constraints. Several criteria can be used to determine optimal spatial charac­ teristics. The choice of this criteria can cause signifi­ cant differences in spatial relationships. Type of commodity The decisions concerning the choice of agricultural and aquacultural products to be raised/reared are influenced by the capability of the existing food marketing system in the region to process, distribute, and sell those products in local and regional markets. Consideration must be given to existing demand, perishability, seasonality, and the im­ pact of additional volume on price. Whether existing facili­ ties exist for off-season production is also an important consideration. Factors other than marketing constraints must also be dealt with. The biological receptivity of the organism to a changed environment is critical. Within the constraints mentioned above it is desirable to produce a mixture of crops that react favorably in terms of growth to the waste heat input. Timeliness of operation The time period in which subsystems demand waste heat is critical as the total flow rate generated by the plant is fixed. Higher flow rates to each subsystem are required as 29 air and cooling water temperature falls. If one of the ob­ jectives is to minimize reservoir or cooling tower size, the period in which subsystems operate and the mix operating at any one time will affect achievement of this goal. The solu­ tion of this problem is complicated by the desirability of finding a mix of subsystems that is optimal for year around operation. Designing a system that is optimal for operation during the summer will result in large excess capacity dur­ ing colder periods. Technical Factors Affecting the Utility Cost of retrofitting The lead time for a power plant ranges from seven to ten years. Plants already in operation or in the process of being constructed would require redesigning in order to com­ plement a waste heat utilization complex. Costs of retro­ fitting for either facility would be significant {Womeldorff, 1975). Hence, there is increased importance placed on plan­ ning and coordinating both plant design and design of a waste heat utilization facility in initial stages of planning (Rochow and Hall, 1975). Reliability of supply Reliability in supply of the returned condensate is crucial for uninterrupted power plant operation. Due to the nature of heat transfer mechanisms, a waste heat utilization complex will not be able to accept the complete heat load 30 during warm, humid periods. This requires that a back-up system or supplementary cooling system be used. Failure to dissipate sufficient heat by the utilization system can re­ sult in decreased plant operating efficiency. Not only must the returned cooling water meet tempera­ ture requirements but the quality of the returned cooling water must enable its continued use in the power generating cycle. If supply requirements are not met# plant outage costs can be significant and totally outweigh profits from the utilization system (Ray, 1975), or increased fuel ef­ ficiency attributable to the waste heat utilization system. Plant outages If the utilization system is fully integrated with plant operation, a plant shutdown is of significant concern. The effect of such an outage will depend on length of the outage, type of uses affected, and the season of the year. If the use complex is associated with a multiple plant siting, then this concern is not as crucial. Where single plant sites are used, back-up heating systems may be required when feasi­ ble. Planned maintenance outages can be scheduled to comply with periods of low demand, but forced outages can cause thermal shock to the biological organism (Ray, 1975). Economic Factors Affecting the Utility Salable commodity With significantly higher fuel prices and rapidly di­ minishing oil reserves, the discussion of the value of waste 31 heat has increased. ty. The reject heat may be a salable commodi­ If so, net monetary outlays by the utility will be reduced. However, the value of the waste heat can vary greatly Fac­ tors affecting the value of the waste heat are the usable level of energy available, water loss by the user, condensate return from steam, demand and load factor, capital require­ ments for conversion, possible deoptimization of plant ef­ ficiency, firmness of heat sink, and duration of the contract (Womeldorff, 1975). System design and product price will also influence the value of the waste heat resource. Site selection Consideration of implementing a waste heat utilization facility would necessitate incorporating additional factors into the site selection process. tural land has been mentioned. The proximity of agricul­ Other factors may include nearness to urban markets and the consumptive use of the waste heat utilization facility. If the system is a closed system and makeup water requirements are minimal, the possi­ bility exists for inland siting. The land use effects of a utilization system are not as severe as with reservoirs; nor are the environmental effects as adverse as cooling towers because point source concentration of waste heat disposal is not as high as that for cooling towers. Regulatory approval The primary responsibility of investor owned utilities is the production and sale of electricity. The management 32 and ownership of agri-business ventures of any nature is not perceived as compatible with their primary concern or within the scope of existing capabilities (Rochow and Hall, 1975). There are also serious questions or objections, as perceived by the utility, that can be asked by State and Federal Regu­ latory Commissions regarding this type of activity and the utilization of required funds and resources. Communications with two major utility companies of this type reveal that their responsibility in an activity of this nature should be one of supplying the waste heat to an independent organi­ zation. Their involvement would cease at that point. Uncertainty The seeking of regulatory approval, commitment or hir­ ing of required management skills, and establishing a new department, division, or subsidiary to manage the utiliza­ tion system require a fixed commitment of resources. The implementation of waste heat utilization in plant engineer­ ing and planning is approached with caution. This hesitancy is related to the commitment of the above resources and also scarce capital resources to projects that involve a high de­ gree of technical and economic uncertainty (Lam, 1975). Cost of backup facility It has been previously mentioned that reliability in the supply of cooling water is the first priority for power plant operation and that the waste heat utilization system will not always demand or dissipate heat at a rate in harmony 33 with which it is produced. These factors necessitate a back­ up system preferably along conventional lines. The cost for such a system will vary and depend on whether an open or closed system is implemented and site characteristics. If the system (waste heat utilization system plus back­ up) is designed for once through use of the cooling water (open system) and regulatory permission is obtained, the capi­ tal costs can be relatively low (Ray, 1975). hand, the cooling water is recirculated If on the other (closed system) and the utility desires to optimize fuel conversion efficiency and reduce risk, the costs for possible underdesign of the backup system can be significant. (Higher temperatures of plant input water means less steam can be extracted to drive the turbines). The backup system should be designed to dis­ sipate a high proportion of the thermal discharge. Lead time and life cycle The life of a power plant is between twenty-five and forty years with an average of about thirty years without major refitting. Its life as a base loaded facility is less than its qperational life. The planning and operating de­ cisions of the utility are made on this basis. As mentioned, the lead time for implementing a particular design is from 7 to 10 years (Womeldorff, 1975) . If the implementation of a waste heat utilization system is a joint venture, a dif­ ference in planning horizons and the expected life of major capital components can lead to operational and/or financial I 34 differences between parties with investment interests. Environmental Costs of Thermal Discharge The purpose of this section is to present a general evaluation of the impact of thermal discharge into the envi­ ronment. By giving such information the additional heat load discharged into the environment from power plants can be put in perspective. Emphasis is also placed on the ecological costs, advantages and disadvantages of conventional methods of waste heat dissipation and a waste heat utilization sys­ tem. 1 Heated water discharges The increase in steam-electric power generation has led to increasing concern for the impact of waste heat on the environment and water resources. The Committee on Water Resources Research in the Executive Office of Science and Technology has concluded that the problem of "satisfactory control of heated water discharges" 2 has emerged as one of the ten most critical areas in the water resources field (Belter, 1974). The effect on aquatic life and reproduction of thermal effluent discharged into natural bodies of water 1The once-through cooling alternative is not fully evaluated. Because of possible adverse effects on aquatic life, this alternative is being increasingly foreclosed. 2 While it is not explicit, this statement refers to discharges into rivers, lakes and streams. It does not refer to discharge of waste heat into the atmosphere via towers or reservoirs. 35 is a major concern. Warren, in 1969, found that electric power generation accounted for three-fourths of total cool­ ing water use and one-third of total water use. It has also been estimated that at 1980 "approximately one-fifth of the total runoff in the United States will pass through power plant condensers at one time or another" (Boersma et al. 1972) . The control of heated water discharge from power plants is not only a water use problem. Rather, the rate at which heat is produced and the method of dissipation give added importance. In 1970, electric power generation accounted 15 for 22 percent (14 x 10 Btu's) of total energy consumption. As approximately two-thirds of the energy input is rejected as waste heat in this process,^ the amount of energy input 5 rejected into the atmosphere is 13 percent (8 x 10 Btu's) of total United States energy consumption. Christianson and Cannon project that by the year 2000, electrical power genera­ tion will account for 50 percent of total United States ener­ gy requirements. Based on this projection, waste heat re­ jection from this source alone would nearly equal total An efficiency of 33 percent to 40 percent is not low. Given the second low of thermodynamics which states: "It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding ob­ jects," 100 percent efficiency can be achieved if the sur­ rounding temperature is 459.4°F below zero. The maximum theoretical ideal thermal efficiency limit of 60 percent is considered to be the upper limit for thermal steam cycle (Rankine cycle) (Kolflat, 1971). Therefore, thermal effi­ ciency of 40 percent is in actual terms, 67 percent thermal efficient. 36 United States energy consumption in 1970 (Christianson and Cannon, 1975). Table 2-1 shows the estimated growth of U. S. electri­ cal generating capacity to the year 2020, and for projected operating efficiencies, the rate of waste heat production. It should be noted that for the later years in this period, the estimated rates of waste heat production are based on the implementation of MHD converters, fusion, and other high temperature conversion processes in power generation. As Table 2-1 illustrates, increasing the efficiency of energyto-work conversion process reduces the amount of waste heat while also extending energy resources. TABLE 2-1 ESTIMATED GENERATING CAPACITY, OPERATING EFFICIENCY AND WASTE HEAT PRODUCTION, 1970-2020 (BOERSMA, ET AL. 1972) Year Projected Generating Capacity 10^8 cal/yr 1970 1980 1990 2000 2010 2020 1.11 2.27 4.24 7.20 10.99 16.28 Projected Operating Efficiency^% 34 37 41 46 53 61 Rate of Waste Heat Production 1018 cal/yr 2.15 3.86 6.11 8.42 9.78 10.42 Projected operating efficiencies are in all probability over estimated as the technology required to meet these ef­ ficiencies (Breeder reactors, metal MHD and plasma MHD cycles, and fusion) are in varying stages of research and basic de­ velopment. 37 Presently, the thermal discharge from steam-electric plants is dissipated by mechanical and natural draft cooling towers, man-made reservoirs; or spray canals. One-through cooling (open cycle), which was at one time the predominant method being used is being increasingly foreclosed. et al. Boersma, (1972) states that the "recent history of power plant development indicates that utilities will be forced to use cooling towers even at locations where one-through cooling is technically feasible." The Federal Water Quality Admini­ stration (now the Environmental Protection Agency) in the spring of 1970 forbade the dumping of virtually any heat into Lake Michigan. standards. Since then several states have set similar The more recent (1974) effluent limitation guide­ lines of the Federal Environmental Protection Agency require "essentially no discharge" of thermal pollutants for many plants now in operation or being built and for "all new sources" that will begin operation after 1983 (Belter, 1974). Without the granting of variances, the guidelines would eventually require construction of cooling towers or other closed cycle cooling options at all sites. The rates of waste heat production shown in Table 2-1 are exceedingly large numbers but can be put in perspective. Approximately 150 cal/cm through solar radiation. 2 day is received by the earth In 1972, 0.063 additional cal/cm day was generated by electrical generation. 2 This rate of waste heat rejected into the atmosphere is about 0.04 per­ cent of the total radiation received. Waste heat rejection 38 in the year 2000 will represent 0.163 percent of the total heat load received by the earth. Conventional systems*For purposes of comparison, it would be advantageous to present general information on land use and possible en­ vironmental effects of alternative cooling methods. Cooling ponds Cooling ponds require approximately three-fourths of an acre per megawatt of electrical generation. A medium size plant of 1000 MW can then require a significant area to be withdrawn from agricultural production or some other use. Depending on soil type and pond construction, consumptive water losses can be significant. Plant capacity is not as adversely affected as by other alternatives where pumping requirements are significantly greater. required. Fans are also not The outlet temperature approaches wet-bulb tem­ perature under favorable conditions. Evaporative-mechanical draft towers Evaporative-mechanical draft cooling towers require from two to three acres for a 1000 MW plant. Maximum con­ tact of air with water surface is achieved. Disadvantages of this method are that significant power is required to operate fans and pumps for water distribution. ^Discussion of these systems is taken primarily from Kline, 1971. 39 Cold water temperature is limited by wet bulb temperature. Evaporative losses and drift losses can amount to two percent and one percent of water circulation flow respectively (Kolflat, 1971). Electrical power for pumpscan require .5 and .8 percent of plant capacity, whereas fans may require one percent of plant output. Due to evaporation, salts, chromium and zinc will accumulate in the blowdown. Water treatment is required as these elements can be toxic. The location of these apparatus is limited due to fogging, noise, and aesthetics. Kolflat (1971) estimates that this type of dissipation will constitute 50 to 70 percent of all types by 1980. Evaporative-natural draft towers Approximately five acres are required for this type of tower for the same 1000 MW plant. A significant advantage is that fans are eliminated which reduce plant capacity. Fogging is not seen as a major problem. Furthermore, the efficiency of natural draft towers improves as relative hu­ midity increases for a given wet bulb temperature. The disadvantages of such a system are that water loss can be significant. ficiency. Also, siting is important for full ef­ Under certain conditions cooler air plumes from towers can result in plume lowering. Hence, plume disper­ sion and direction are important factors given possible ef­ fects of the vapor plume on the local environment. 40 Dry mechanical and natural draft towers Where availability of water limits evaporative types of towers, dry mechanical and natural draft cooling towers are most often used. While these types of systems minimize water loss through evaporation and drift, there are several major disadvantages. The amount of cooling is limited by ambient dry bulb air temperature. As this temperature is higher than wet bulb temperatures the temperature of the heat sink is higher. This leads to reduced efficiency of the steam cycle which af­ fects fuel waste and greater waste heat generation. As the heat transfer mechanism is indirect, both apparatus are ex­ tremely costly. The life of such systems is less than evap­ orative methods as the finned tubes are subject to corrosion and deposits which also reduce heat transfer. Kline (1971) states that because of the water temperature limitation and resulting high back pressure, dry towers cannot be used with the types of turbines presently in service or manufactured. Conventional cooling system cost Kolflat in 1971 summarized several studies on the ini­ tial capital costs for various types of conventional systems (Table 2-2). While these figures range significantly for each type and are somewhat dated, they do give an indication of relative capital requirements. While a comparative analysis of operating expenses for the various types of systems has not been compiled, the in­ creased energy requirements for pumps and fans has been 41 TABLE 2-2 COMPARISON OF COOLING SYSTEMS COST ON A DOLLAR PER KILOWATT BASIS1 Cooling System $/KW Once-through 2 - 10 Cooling Lakes 2 - 13 Evaporative Mechanical Draft Tower 4 - 14 Evaporative Natural Draft Tower 6 - 20 Dry Mechanical Draft Tower 15 - 37 Dry Natural Draft Tower 25 - 65 Costs include towers, lakes, pumps, structures, pip­ ing, and miscellaneous costs. Costs of the power plant con­ denser is excluded as are maintenance, operating and capa­ bility (capacity), costs. estimated (Kline, 1971). If wet cooling towers were used for all steam-electric plants in Michigan, an additional 500 MW would be needed or the equivalent of 1.5 million tons of coal ($137.5 million at 1977 prices). If dry mechanical towers were used, an additional 1500 MW capacity would be required or the equivalent of 4 million tons of coal at a cost of $340.0 million. Environmental Considerations of an Integrated Waste Heat Utilization System It should be understood that a system which utilizes waste heat does not reduce the amount of thermal effluent eventually discharged into the environment. However, the 42 the method of heat transfer, as we have seen, can affect en­ vironmental conditions.^ The heat transfer mechanisms which agricultural and aguacultural uses employ disperse waste heat effluent over a larger geographical area. Hence the first advantage of this type of system is that the power plants' point source concentration level of thermal discharge is re­ duced. Fogging and blowdown problems are not present as they would be for evaporative-mechanical and natural draft cool­ ing towers. The second advantage is that the types of heat transfer mechanisms postulated for use in a waste heat utilization system do not rely on water dispersion (spraying or splash­ ing) to cause heat transfer. This reduces evaporative and drift losses that exist with wet towers. are not entirely eliminated. 2 Consumptive losses Whether a net benefit exists depends on siting characteristics and other factors. 3 A third advantage which Faucher (1972) mentions is that this type of system can provide improved efficiency in ^As an example, cooling ponds do not affect a vapor plume that can alter or have an adverse impact on the microclimatological conditions and wildlife. Most towers, how­ ever, do not require the large amount of land. 2 Evaporative loss will occur when water surface is in contact with air. Furthermore, consumptive loss can occur where ponds are used due to drainage losses. 3 No study has been found which compares consumptive losses for alternative systems for a specific site. 43 the use of energy resources. 1 . While "first law efficiency" 2 is an important technical standard upon which an evaluation of system performance can be made, it is not the only per­ formance parameter. A low first law efficiency rating means that energy is being lost or wasted in conversion to work. This parameter is useful in comparing systems with like or equal grade inputs and outputs. A perhaps more useful measure of performance is "second law efficiency." This performance parameter is defined as the ratio of heat or work usefully transferred to maximum possible heat or work transferable^ (Physics Today, 1975). This parameter measures the effectiveness of a use or system and as such indicates true thermodynamic performance of a system. Reistad (1975) states that this parameter measures how well a device or system performs with respect to the op­ timum possible performance. A low effectiveness rating means The definition of energy efficiency can be stated as the ratio of energy output in desired product to energy in­ put required (Reistad, 1975). When Faucher states that an improved efficiency in energy resource use can be realized with a waste heat utilization system, it is my belief he bases this statement on reduced losses in power generation due to used plant capacity for pumps, fans, and other mechan­ isms which reduce energy output or size of the numerator in above definition. Whether this is in fact true will depend on the pumping requirements and other losses in plant capac­ ity found in a waste heat utilization system. Hopefully, re­ sults of this analysis provide the basis for a comparison of whether a waste heat utilization system is more energy ef­ ficient as defined above. First law efficiency is defined in the immediately preceding footnote. 3 Second law efficiency is defined as the ratio of in­ crease in availability of desired output to decrease in availability required (Reistad, 1975). 44 that energy is being wasted while it is being used. Commoner (1976) states that a low thermal effective system is one where work is poorly directed and that there is a faulty re­ lationship between energy source and energy requiring task."** Hence, this is a task related performance parameter not a devide related performance parameter. The reason for introducing these parameters is for dis­ cussing the potential a waste heat utilization system has for improved effectiveness in the use of energy resources. If energy efficiency of the system is the discriminating criterion, the decision as to whether resources were con­ served would depend on whether, in gross terms, more work was obtained per unit of energy consumed by the plant and utilization system. No indication would be given as to whether energy sources had been more effectively used or whether the type of energy available had been best suited to the task for which it was used. A waste heat utilization system, by supplying low grade energy to uses or tasks that effectively transfer that energy to desired output, has the potential for energy conservation. Research conducted on waste heat utilization 2 ^Commoner explains this concept via two examples. Given this definition of effectiveness, a diesel engine is an effective way to convert fuel energy into electricity but effectiveness is wasted if electricity is in turn used to produce hot water. Similarly, the effectiveness of corn as a solar energy trap is reduced if inorganic nitrogen is used. 2 Reference to this research is made in the sections. Review of Literature, and will not be further mentioned here. 45 indicates that the productivity response to this input is significant for many biological (agricultural and aquacultural) processes. The implication then is that additional productivity (desired output) or work can be obtained from the low grade energy input for specific tasks and that the low grade energy can serve as a substitute for inorganic fertilizers which represent high energy sources and other cultural practices which require petroleum based products.^ ^The extent of that saving will not be examined here. CHAPTER III METHODOLOGY Sources and Types of Data Several researchers have conducted studies on the costs and technical coefficients relating to the subsystems in this study. These studies, while indicating the physical operat­ ing and capital requirements, were specific to conventional fish cultivation techniques, greenhouse operation methods, or crop cultivation requirements. Where individual and/or combined systems were studied, the plant size, design, and operating characteristics, and environmental conditions dif­ fered significantly from those employed or found in an in­ tegrated waste heat utilization system and subsystems stud­ ied herein. The design of the general piping and distribution systen is specific to a given mixture of types and sizes of subsystems with corresponding flow rates. Hence, much of this data is generated internally. In order to allocate waste heat efficiently, heat transfer models, growth models, a weather model, and a water transport model were developed.^" General models to deal with ^These models were developed by other members of the research group at Michigan State University. Description and citation of those models are mentioned in a later sec­ tion of this chapter. 47 these problems were modified for Michigan conditions or were completely developed within the Michigan State University re­ search group studying waste heat utilization. Subsystem Cost Data The economic feasibility of beneficial uses of waste heat has been evaluated on an experimental basis where pilot studies have been conducted. reality. Other uses are a commercial Data on costs and technical coefficients have been obtained from these studies and also from studies on conven­ tional methods (where waste heat is not used) of fish cul­ ture, greenhouse operation, or cultural practices for field crops. Modifications are necessary, however, as these data are specific to subsystems where the utilization approach was applied, the scale of operation was not appropriate for use in this study, or the subsystems did not meet the physi­ cal characteristics or suitable design properties to serve as a heat dissipation device for a power plant. That these subsystems are used in conjunction with power plants will necessitate design changes to insure reliability. As some uses will employ intensive methods of cultivation, complex control and monitoring devices, or non-conventional technol­ ogies; a reassessment of managerial and labor skill require­ ments must also be made. After the necessary modifications are made, each sub­ system is synthetically constructed according to the purposes 48 for which it is used. As it is an integral part of a complex heat transfer mechanism, capital and operating costs for water transport within the subsystem are estimated. Data on the various costs associated with non-conventional requirements of the subsystems were obtained from con­ struction costs manuals, and mechanical engineers. Construc­ tion supply firms and utility companies were also a useful source. Construction and costs of major components were vali­ dated by reliable experts. General Piping and Distribution System Cost Data Costs for the water transport system are obtained in a similar fashion as those for subsystems. Technical coeffi­ cients relating to the water transport system were evaluated by an engineering graduate student specializing in hydrology. After flow rates, friction losses, pressure requirements, and piping distances were determined, appropriate sized pumps, motors, pipes and auxiliary requirements could be specified to meet these and utility requirements. Flow rates and pressure requirements determine pump sizes. Major operating expenses accrue to pumping. Electri­ cal expense was estimated by calculating power replacement costs and capacity replacement costs per kilowatt hour of electrical consumption. 49 Sub-models Data on the productivity response of fish and heat dis­ sipation rates for fish ponds and cooling reservoir are taken from models developed by Walker and Bakker-Arkema (1975).^ Subsoil heat dissipation rates and field crop productivity responses to waste heat were obtained from models developed by Schisler and Bakker-Arkema (1975). Optimal flow rates and corresponding dissipation rates were determined by a multivariate, nonlinear optimization routine modified and adapted by VanKuiken and Tummala (1975). Pump size specifi­ cations, pipe diameters and piping distances were determined by Schultink (1975). Productivity response of the organisms is important in determining gross revenues for the subsystems. The flow rates determine pumping and design characteristics internal to the subsystems. The dissipation rates of the subsystems and cooling reservoir are technical coefficients used in d e ­ sign optimization. The physical characteristics of the water transport system significantly affect capital requirements. Analytical Constructs The research presented here interfaces with component models and techniques developed by others on the Michigan State University research group studying waste heat utiliza­ tion. These models and simulation techniques are difficult ^"L. P. Walker, I. Schisler, J. VanKuiken, and W. Schultink were also members of this group. 50 to describe as the construction is unique and interaction multifaceted. To assist in the understanding of these models, a general description is given of the allocation simulation model and followed by a general description of the component models. Appropriate appendices are indicated which give a better description of these models. The Allocation Simulation Model^ In order to find an optimal allocation of waste heat from the power plant to subsystems, given subsystem sizes, a simulation model comprised of mathematical models which describe important parameters of those subsystems was con­ structed. Models of the subsystems are comprised of growth rate equations, and heat and mass transfer equations. As an important factor affecting heat dissipation at any one time is meteorological conditions, a weather model is incorporated as a component. Figure 3-1 illustrates major components for a system comprised of two subsystems plus a reservoir, the inputs af­ fecting modelled subsystem behavior, and outputs of those subsystems. This figure illustrates in gross form that weather parameters, input heat rates and initial subsystem sizes in combination with fish and crop growth characteris­ tics and heat dissipation rates for each subsystem determine output temperatures to the power plant and final amounts of agricultural and aquacultural products. ^For a complete description see Appendix 2-A. WEATHER PARAMETERS v INPUT SIZES INPUT HEAT RATES FISH GROWTH v 1 t 1 1 SOIL WARMING >— >OUTPUT TO >POWER PLANT 1 1 I 1 CROP GROWTH 1 1 1 1 RESERVOIR Figure 3-1 Major components and component interfaces of the Allocation-Simulation Model. (VanKuiken and Tummala, 1975) AGRICULTURAL OUTPUTS 52 The flow of operations in program ALLOC begins with in­ itialization of subsystem sizes, optimization parameters, initial estimated flow rates, and length of simulation run. The WEATHER model is then called to give appropriate average monthly values for wind speed, drybulb temperature, dewpoint, and solar radiation. With this and initial heat input, the subsystem temperatures are found.1 As the primary variable affecting incremental growth rates for the agricultural and aquacultural crops is temperature, the incremental growth and hence subsystem revenue for those surface and soil tempera­ tures is found with established models. The remaining heat is then allocated to the reservoir and POND is called to determine necessary reservoir size to meet system constraints. Simulation then returns to WEATHER and continues until the objective function shown in the pre­ ceding section is minimized. The outputs given the allocation simulation model are surface temperatures of the fish ponds and reservoirs, the soil temperature at the root zone, and temperature of the cooling water to the plant. Heat dissipation rates of the subsystems and reservoir are determined as are corresponding flow rates. Area of the reservoir is found. Other impor­ tant outputs are monthly incremental profits and fish growth, expected yields at harvest, final fish size and population. 1The relevant temperatures are pond surface tempera­ ture, subsoil temperature at the lateral, and greenhouse temperature. 53 Components of the Allocation Model POND model1 The POND model is used to determine the equilibrium temperature, or temperature at which the heat input and amount of heat dissipated are balanced, for both the fish ponds and reservoir. Once the equilibrium and thermal ex­ change coefficient are determined, water temperature at the surface can be found. Strong dependence on local meteoro­ logical conditions for several of the coefficients in the model requires interaction with the WEATHER model. The output of this model is fish pond and reservoir surface temperature. Interaction with WEATHER determines heat dissipation rates which are readily converted into flow rates. The interface with the linear programming model is that flow rates and thus temperatures of fish ponds affect revenue by affecting incremental productivity and quantity of fish harvested. The optimal flow rates affect physical requirements for ponds and the reservoir and hence capital and annual costs. Soil warming model 2 The premise on which this model is based is that the flow rates and physical aspects of the underground grid of pipes are designed to give optimal temperatures to maximize ^"For a more detailed description, see Appendix 2-B. 2For a more detailed discussion, see Appendix 2-C. 54 the objective function found in the upcoming sections. Stated simply, the computational scheme begins with finding a root zone temperature that will maximize the objective function. A heat dissipation rate is found which is then assigned to a surface balance equation. A surface temperature is found which is then evaluated on the basis of being feasible given the necessary pipe temperature needed to attain that tempera­ ture. If the solution is feasible, the corresponding flow rate is used to calculate capital and annual costs. Incre­ mental rates of production and final production are tempera­ ture dependent, hence, revenues will be determined. Fish growth1 Population density and temperature are the primary fac­ tors affecting the growth rate of fish (Andrew and Stickney, 1972; Brett, et al. 1969; Swift, 1964). While it is known that the growth rate for fish follows an exponentially de­ creasing function that can be characterized by a set of dif­ ferential equations (Laird, et al. 1965) , data were not available to estimate coefficients in these equations for the species chosen. As necessary data for estimating the growth response was not available for a broad temperature range, a constant growth rate was assumed. As temperature will change, a linear approximation of the growth rate at different temperatures was used 1975). (Walker and Bakker-Arkema, While this is a gross approximation, significant ^For a further discussion of the fish growth model, see Appendix 2-D. 55 results were obtained in employing this method. Monthly incremental yields are obtained given the aver­ age monthly temperatures from the POND model. As final popu­ lation and average fish weight can be found on an annual basis, annual revenues can also be determined. Crop growth model^ In many of the models based on experimental data, in­ cremental crop growth was observed under conditions where the root zone temperature was maintained at close to a fixed temperature (Mack and Ivarson, 1972; Rykbost, et al. 1974). For integrated systems where two or more subsystems may oper­ ate coincidentally and compete for waste heat, the occurance of this is unlikely. Because of this, Schisler and Bakker- Arkema (1975) suggest that a switched growth model developed by Paltrige and Denholm (1974) be used. The parameters and the switch time in the set of differential equations are hypothesized to depend on a set of climatic factors discus­ sed by Gross and Ruse (1972). The shape of the growth func­ tion, assuming constant parameters, gives a reasonable ap­ proximation for the crops considered. The results from this model are in a similar form as those from the fish growth model and are used in the analy­ sis of optimal design for similar purposes. "''For a further discussion of the crop growth model see Appendix 2-G. 56 Iterative Procedure The above models and a statement of constraints comprise subroutine OPTBOX. Its primary function is to determine an optimal combination of flow rates and corresponding heat dis­ sipation rates for subsystems operating during any monthly period, given a set of subsystem sizes. The heat dissipation rates then become a new set of constraints to determine a new set of subsystem sizes. Figure 3-2 shows the iterative pro­ cedure between the linear programming model (which will be discussed) which optimizes design and the OPTBOX program which determines waste heat allocation. It should be noted that both programs optimize the same objective function for reasons of converging combinations of monthly flow rates, constant subsystem sizes, and monthly reservoir sizes. Optimization Procedure As was stated in the "Problem Statement," the problem addressed by this research is whether a waste heat utiliza­ tion system comprised of agricultural and aquacultural uses is economically feasible. One of the major questions is whether the optimal design is a least cost system compared to conventional cooling methods. The procedure chosen to deal with this question is least cost or cost effectiveness analysis. This type of analysis, as opposed to benefit-cost analysis, can be used to determine a least cost combination or resources that will achieve a specified goal. It is also WEATHER v > OPTBOX PROGRAM INITIAL HEAT DISSIPATION RATES A OBJECTIVE FUNCTIONS v INITIAL SUB- < SYSTEM SIZES LP PROGRAM < Figure 3-2 Schematic of the Iterative Procedure between the OPTBOX Program and Linear Programming Model to find an Optimal Solution (VanKuiken and Tummala, 1975) 58 effective in comparative analysis of different investment alternatives. With the use of present value discounting tech­ niques, this method is especially useful in analyzing the cost of long-range planning alternatives. With this pro­ cedure then as the general format there are other charac­ teristics specific to optimization that must be dealt with by the procedure. Optimization Characteristics 1. The utilization of an agricultural and aquacultural system is one investment alternative out of several that is faced by a utility or firm. Each investment alternative will affect the cash flow or total monetary outlay by the firm over the planning horizon. In order to make decisions con­ cerning future expenditures or revenues, these sums must be converted into current dollars. Hence the time value of money is a decision variable. 2. The cost per unit of output changes with the scale of the plant. Diseconomies of size is related to several operational characteristics of the subsystems and limited variable resources. The objective function then is non­ linear. 3. The allocation routine specifies optimal flows for productivity and thus revenue purposes. Whether these flows are optimal, given pumping costs and corresponding capital requirements, is an important economic question. 4. Power plant operation is contingent on the system utilizing a specified amount of waste heat. For each month, 59 however, there will be a residual amount of waste heat that will not be utilized by agricultural or aquacultural uses and must be diverted to a cooling reservoir. One of the de­ sign objectives is to minimize reservoir size and examine which monthly periods are surplus periods for the beneficial uses. 5. There are a finite number of processes or activi­ ties by which the objective of utilizing a specified amount of waste heat can be obtained. Among these alternatives we want to find those activities which are least costly in uti­ lizing resources to meet that objective. Properties of the Algorithm Problems, which require as a solution a course of ac­ tion to be taken, for which some parameter is to be maximized or minimized, for which a limited amount of resources are available, and that can be resolved in a finite number of ways; can be suitably treated with linear programming methods. Given the optimization characteristics listed above, the fol­ lowing properties are incorporated into the algorithm. 1. To deal with the long term planning problem, pseud dynamic properties are incorporated which will allow the sum­ mation of net revenues and capital costs over the planning horizon. The pseudo-dynamic aspect of incorporating the time value of money to find the net present value of future net returns reduces to multiplication within the algorithm when the net revenues to be discounted are constant over the planning horizon. The multiplicative constant is the discounting factor which is determined by the discount rate and length of the planning horizon. As objective function values are sensitive to the discounting factor, it is desira­ ble that the discounting be handled internally. This can be accomplished by grouping discounted and non-discounted annualized cost coefficients as separate rows in the activity matrix. A diagonal submatrix is then used to weight and transfer the sum of discounted and non-discounted values for activities in solution to a cost coefficient col­ umn that is nonzero only in the entries above this submatrix (Schisler, Meekhof, et al. 1976). The discounting factor is the weight in the submatrix and can be conveniently changed when the effect of a different discount rate and time hori­ zon on the objective function value needs analysis. 2. The characteristic of a non-linear objective func­ tion can be dealt with by separable programming techniques (Charnes and Lemke, 1954). The non-linear relationship is linearized by dividing the curve into linear segments. This technique solves non-linear problems where (a) the objective function separates into a sum consisting of functions of single variables, (b) each function in the sum is concave. This can be shown as: 1) Max Z = EC .X . + Ef. (X.) j 3 subject to: 3 j 3 3 61 3) 0 where: Z - net monetary returns Cj = net returns per unitarea Xj = size of subsystem j EC.X. j ^ ^ = total net returns forsubsystem j,where cost size relationships are linear Ef.X. j 3 3 = total net returns for subsystem j, where cost size relationships are non-linear ofsubsystem j a.. = heat dissipation rates per subsystem j for month i b = total amount of waste heat to be dissipated by agricultural and aguacultural uses, and reservoir The non-linear formulation is converted to an appro­ priate linear programming problem (Schisler, Meekhof et al. 1976): 4) Max Z = EC .X . + E S. Y. j j 3 with the additional convexity condition 5) V (m) j - E Yj = 1 V (k) where: V (k) = a vector of column indicators which in­ dicate the start of convexity controlled activities V- » - a vector of column indicators which indicate the end of convexity controlled activities Sj = areas of convexity controlled j activities 62 While the activities denoted by size for each subsystem are mutually exclusive to the extent permitted by the constraints, this condition also implies 6) 0 = R ±1 < Y. < R iN where R ^ and denote the smallest and largest areas of a subsystem respectively in the linear approximation scheme. The objective function and properties of the algorithm show that separable characteristics are employed to deal with the non-linear cost-size relationship for the utilization sub­ systems. This non-linear relationship indicates a non-linear objective function. It will also be shown that in the fish pond subsystem as additional amounts of waste heat are sup­ plied the productivity response of fish will decline. This situation implies diminishing marginal returns to the waste heat input and that the algorithm is non-linear in constraints. 3. The flow rates to each subsystem impose costs and create revenues. Whether the flow rates given by the alloca­ tion subroutine are indeed optimal or whether "non-optimal" flow rates are desirable can be analyzed with minor changes to the above formulation. The consequent changes will also permit analysis of non-optimal flows or shortages and sur­ pluses in available supply on monetary outlays for individu­ al subsystems and the system in total. With this added con­ dition, the linear programming problem then becomes 7) Max Z = C j X j + Z Z S jw Y jw 3 w 63 with the convexity condition that o* V (m) j = V (n) w = z Z V (k) Y . DW V {1) = 1. where: V (l) V (n) “ a vector of column indicators which indicate the start of convexity controlled activities with less than optimal, optimal, and greater than optimal flow rates. - a vector of column indicators which indicate the end of convexity controlled activities with less than optimal, optimal, and greater than optimal flow rates. The Objective Function The above mathematical formulation is the basis for the objective function. The objective function chosen for analy­ zing the integrated system is consistent with the planning and investment decision making criteria of the utilities with whom this research was conducted. This function will determine optimal subsystem sizes and flow rates subject to dissipating a specified amount of waste heat. 9) ^ ^ Max Z = Z Z A. j=i w=i 3 |R— C ) ^ Jjw _ K j 1 (l+r)n jw [Z where; Z = Net monetary returns current dollars S = Subsystems A. ]" = Area of subsystem j with flow rate w, acres K. =* Initial capital outlay of subsystem j with flow rate w, $/acre n = Life of project or planning horizon,years 64 R = Annual gross revenue for subsystem j with flow rate w, $/acre C = Annual operating cost of subsystem j with flow rate w, $/acre r = Discount rate or opportunity cost While this objective function is useful for determin­ ing the optimal combination of subsystem sizes and flow rates,it does not give the total monetary outlay as the costs for the general piping and distribution system are excluded. In order to make comparisons with conventional methods, the capital and operating costs of the distribution system must be accounted for. The preceding objective function was modified outside the optimization model to reflect 10) Max Z = E j=l the additional [E Cjjw - K . - E Ft , - K 1 (1+r)n 3 1 (1+rP costs associated with the general piping and distribution systems. P E A. w=l 3W They are defined as follows: = Make-up power and other annual costs of the general piping and distribution system in year t K gp = Capital outlays for the general piping and distribution system. Theoretical Model The allocative efficiency in waste heat distribution is an important theoretical concern and a major factor af­ fecting feasibility. The problem to be dealt with is the allocation of a variable input which initially has zero or small negative value. The input to be allocated between competing uses is the high entropy, waste heat effluent. 1 65 While the allocation of zero-prices inputs with seemingly un­ limited supply can be perceived to be a trivial problem, there are cost constraints which necessitate efficient allo­ cation. Economic theory is explicit with regard to conditions which satisfy the optimal allocation of inputs. Inputs are allocated between uses in an optimal manner when the ratio of marginal value products to marginal factor costs is the same for all uses of the input. (A shadow price of a linear programming model is a specialized marginal value product. This definition is useful for further discussion). Theorems of this nature are often used for insight into and interpre­ tation of applied problems. The characteristics of the op­ timization models developed for analyzing the waste heat problem and the manner in which this problem is defined per­ mits a modified application of marginal analysis or the model provided by economic theory. It should be interpreted as a construct by which optimal allocation of the waste heat re­ source can be discussed. The strict conditions defining the optimal allocation of a resource were not employed. The following discussion should be interpreted as a theoretical discussion concerning the allocation of a zero or possibly negatively priced input. Assumptions Several assumptions must be made before directly pro­ ceeding with this discussion. The time period for which the 66 decision affecting an efficient allocation is one month. This is necessary to assure constancy in several parameters and particularly for the plant, general piping and distribu­ tion system, and number and level of subsystems. Secondly, within this time period heat dissipation rates per subsystem are constant as meteorological conditions are assumed con­ stant . Growth rates for the organisms being grown for this time period are also constant. This is necessary as the ana­ lytical models are discretized for this same time period. Prices for all agricultural products and input costs are constant. Lastly, for matters of convenience the waste heat is sold at a zero price to the waste heat utilization system. The Model With these facilitating conditions, a model can be specified. The marginal factor cost (MFC) of the waste heat input per subsystem is determined by the cost of supplying the input. The supply cost is constant within a set of spa­ tial relationships, and for the number and type of subsys­ tems operating for any one month. The value of the intermediate product, waste heat, is determined by its value to the subsystem. The value of the waste heat over a monthly period is imputed. The increase in the revenues of the subsystem due to an increase in sup­ ply or capacity to utilize waste heat is the measure of the value of an additional unit of waste heat. Let the increased 67 revenues for a use due to the supply of waste heat indicate the shadow price (SP) of waste heat for that use. The problem of finding the optimal allocation of waste heat per subsystem becomes one of finding an allocai.U tion between uses where MFC of the j subsystem equals the shadow price in subsystem j, for all subsystems. Hence, the revenue function to be maximized can be stated as: 11) Max H = Z SP. X. j Subject to: 12) C = EMFC.X. j J 3 Finding the optimal allocation for waste heat in the i month/ given costs and revenues, is an exercise for which the Lagrange technique for constrained optima can be used. This is shown as: 13) H = £ SP .X. - \ j (ZMFC.X. - C) 3 j J By taking the first partial derivatives and setting them equal to zero: 14’ SP1 - “TC. = 0 • • • * • » • • • * • • • * • • H.= SPj - = 0 it can be shown by first order conditions that allocating waste heat on the basis of 15) SP1 SP2 = ... _ SPj MFC1 “ MFC2 MFC^ 68 will give an optimal allocation. Factors Limiting Allocative Efficiency The preceding model postulates a constant marginal fac­ tor cost for a specified month, design, and spatial re­ lationship. For the same conditions a declining relation­ ship is postulated for the dollars per unit and quantity of waste heat allocated. These relationships are shown in the following graphical illustration. $/unit+ Shadow Price Marginal Factor Cost Units of Waste Heat Figure 3-3 Allocative Efficiency in Waste Heat Use: Marginal' Factor Cost Equals Shadow Price 69 That the marginal factor cost of waste heat is deter­ mined by the constant cost of supply and is assumed to be priced at zero by the seller leads to an improper conclusion of an unlimited supply of the variable resource. In actuality, the total amount is physically limited such t h a t : 16) S I q* <_ Q * i=l 1 where S is the number of subsystems operating, q* is the quantity allocated to the ith subsystem and Q* is a fixed amount of discharged thermal effluent. For months where the total amount Q* is an insufficient supply, the allocative efficiency criterion as shown in equation 15 will not be met for one and possibly all subsystems.1 A second factor limiting allocative efficiency is that in some monthly periods Q* does not fulfill subsystem demand. Where supply is limited one subsystem is not allowed to transfer its usage to another. The waste heat resource is not perfectly mobile. Figure 3-3 is drawn to allow for instances where the shadow price for waste heat is negative. The theoretical model developed above will still apply with negative shadow prices for waste heat. In order to obtain conditions of ^As system profits are to be maximized and there are physical constraints on the reduction of waste below levels desirable for the organism, the standard principle of reduc­ ing input usage to less productive subsystems first is not employed. 70 allocative efficiency with negative shadow prices, a nega­ tive marginal factor cost is incurred. The negative margin­ al factor cost that equals the negative shadow prices is the payment to the utilization system for dissipating waste heat. The Model Revisited Figure 3-4 gives a simplified graphical interpretation of the allocation problem. This analysis is more suggestive than indicative as these demand and supply relationships are not empirically estimated. While the explanation of the supply curve (MFC) facing the firm is reasonably straight forward and plausible, what is represented as a demand curve (SP) is not as intuitively clear. The shadow price or imputed value of waste heat can­ not, in fact, be represented as a schedule of quantities and prices. In reality the shadow price of the input is represented by a point given those factors fixed in the monthly period (e. g., climatological conditions, design, spatial relationships, growth rates, dissipation rates, etc.). If this is so then the graphical illustration of allocative efficiency is shown as: 71 $/unit+ MFC MFC MFC MFC MFC Figure 3-4 Schematic of Program OPTBOX Method for Finding the Efficient Allocation of Waste Heat Given the Dynamics of Changing Flow Rates 72 where point A indicates the imputed negative value of waste heat to the firm at the negative MFC^. Should the general piping and distribution system change so as to decrease sup­ ply price to the subsystem, the imputed value of waste heat will correspondingly increase. Points A, B, C, D, and E represent shadow prices for waste heat with different plants. A curve connecting these points is not analogous to the mar­ ginal curve of a single variable input for the firm. Design The Model The decision making process of determining optimal de­ sign is a problem of making decisions in the present that will affect the attainment of other goals or the ability to undertake alternative investments over a multi-period time horizon. With the growth models, dissipation models and cost coefficients known, the decision maker is assumed to have perfect knowledge. Risk and uncertainty can be incorpo­ rated into each investment alternative by weighing each al­ ternative by an appropriate discounting factor. The ideal model would be built on the maximization of a payoff function where the current and future actions are incorporated. As not all future actions are known, the mone­ tary outlay, or conversely cash flows, will not be known. A fully dynamic model where all input usage and generated reve­ nues are dated cannot be employed. 73 A pseudo-dynamic model is then employed. The decision criteria becomes one where the profitability of alternative investments are reduced to present dollar terms instead of basing present decisions on all possible investment paths over the specified future time period. Alternatives avail­ able at the current time period constrain the range of choice. A capital budgeting approach is used to formulate a basis on which decisions concerning the optimal design^" can be made. In using the net present value method, all future net revenues are converted to present value terms using a discounting factor. The decision criteria on which optimal design is found is to maximize the net present value of monetary flows (Z) where: ® Z = E j=1 ^ E A. w=l ^ (d * n \ 2 [E H ;.jy_ - K . ] 1 (1+r)“ Hence, for j agricultural and aquacultural activities w flow rates for each activity, and monthly sizes for the reservoir, the linear programming algorithm, will find the optimal so­ lution. Discount Rate The discount rate is a measure of what is lost by re­ ceiving money later rather than now. Interest rates have ^ i v e n the preceding discussion, the choice of "opti­ mal" design refers to alternatives available at the present. 2 This statement is unchanged from equation 9, page 63. A description of terms is listed there and will not be repeat­ ed here. 74 a broader meaning as it covers all costs which accrue auto­ matically with the passage of time.1 The two concepts are related by the formula D= l/(l+i) if the capital market is at least approximately perfect. 2 Different firms will discount investment and construc­ tion projects at different rates. In an effort to compare investment in a waste heat utilization system by a utility with other possible investments, some comparability is de­ sired in the discount rate. One utility participating in this research uses a weighted average of the cost of seven different sources of funds. As the amount of funds derived from each source will vary on an annual basis, the discount rate may differ over the life of the investment. It should also be noted that the discount rate will differ depending on the nature of the investment. For this reason and lack of certainty on the exact procedures used by utilities, sensitivity analysis is conducted on the effeet of several discount rates on present value. 3 Summary This chapter presented the methodology that is employ­ ed in assessing whether utilizing waste heat in an integrated agricultural-aquacultural system is economically feasible. ■^William J. Baumol, Economic Theory and Operations Analysis, Englewood Cliffs, Prentice Hall, Inc., 1972. 2Ibid., p. 451. 3 While the exact procedure has not been given, a gen­ eral indication of the appropriate rate has been indicated. 75 The data employed are derived from several sources. system costs developed from synthetic data. The sub­ The mathematical models in the allocation-simulation model were used to find productivity responses and heat dissipation characteristics of the subsystems. Those models are also discussed. The linear programming model is developed and its interaction with the allocation program is shown. A theoretical model is also developed to illustrate the basis for the optimal allocation of the waste heat input. CHAPTER IV OPTIMAL DESIGN CHARACTERISTICS FOR THE WASTE HEAT UTILIZATION SYSTEM This chapter presents the results of the linear pro­ gramming model under three alternative situations. The pri­ mary characteristic of the first alternative situation (Model I) is that subsystem sizes are not explicitly con­ strained. Model II determines the optimal design when the fish pond enterprise is constrained at the eight-20 acre pond level. Model III shows the optimal combination of sub­ systems and subsystem sizes when prices are reduced below levels assumed in the previous models. While these three models do not incorporate all alternative constraints and probable economic conditions, they do show the sensitivity of important subsystem parameters to the alternative sets of constraints. They also provide a basis for which com­ parisons of the waste heat utilization system to convention­ al heat dissipation systems can be made. The figures reported represent the net monetary re­ turns for the optimal combination of subsystem size and types given 1974 input and product prices. Net monetary returns for subsystem operation do not include initial capi­ tal cost or discounted annual expenditures for the general ^Constraints for each subsystem, except the reservoir, ■are implicitly provided by the separability constraints. 76 77 piping and distribution system. Price Assumptions Product price for corn was assumed to be $2.75 per bushel. The per bushel price for tomatoes and soybeans is $5.50. The price received for sweet corn is $.75 per dozen, and field beans are priced at $15.00 per hundredweight. The price per pound for undressed channel catfish is $.30 per pound.^ The wholesale prices for a standard ornamen­ tal flower rotation are as follows: $2.60 for 6-inch Chrysanthemums, $3.25 for 6-inch Poinsettias, $2.60 for 6inch Lilies, and $.65 for 4-inch Geraniums. Availability of Resources Assumptions Land and initial capital are stipulated to be readily available at market prices in optimal system design.^ 2 and are not a limiting factor Skilled and unskilled labor is also assumed to be available at market prices as are man­ agers with skills required for intensive aquaculture and an ornamental greenhouse operation. ^The price is representative of what would be re­ ceived for fish reared for commercial and fresh market use. 2 Initial capital requirements are discussed in sec­ tions dealing with each particular model. 3 The exception to this is the availability of 2-inch PVC piping. Price per unit for this material is not con­ stant throughout. This is reflected in the statements for initial capital requirements as shown in Appendix 4-E. 78 Base Yields and Stocking Rates Assumptions The allocation program determines the productivity response for optimal flow rates of waste heat water and for initial yields for the soil warming enterprises. A base stocking rate of 24,000 fingerlings per acre was assumed for the fish pond enterprise. cial rearing facilities. This rate is low for commer­ The per acre rates for corn and tomatoes are 125 bushels and 500 bushels respectively. The base yield for sweet corn is 750 dozen, while the assumed rate for field beans is 17.5 hundredweight per acre. bean yield is assumed to be 42 bushels per acre. Soy­ While the growth rates of ornamental flowers are not affected by the waste heat input,1 it was assumed that Chrysanthemums, Poinsettias, and Lilies use one square foot of available space while Geraniums use one-quarter square foot of avail­ able bench space. Optimal Design with no Constraints on Subsystem Size (Model 1)^ System Design Model I represents a set of circumstances where there are no constraints on the allocation of fixed resources. 1The waste heat serves as a substitute heat source in the greenhouse with no affect on yields. While there were no explicit constraints on subsystem sizes, the solution is implicitly constrained by the largest of the separable parts. Fish ponds are implicitly constrain­ ed at 24-20 acre ponds. Soil warming for field crops is 79 The results under these conditions show that 375.44 total acres of fish ponds and 100 acres of soil warming acreage where tomatoes are grown comprise the optimal combination of waste heat utilization enterprises. The utilization of reservoir acreage, which will vary with the availability of waste heat not dissipated by the activities listed above, is shown in Table 4-1. These waste heat utilization activities and reservoir utilization rates are similar for all discount rates and time horizons studied. The total fish pond acreage is comprised of .2639 of the first separable part (4-20 acre ponds) and for a flow rate 10 percent greater than that indicated to be optimal by the allocation program. The remainder of the total fish pond acreage is accounted for by .7361 of the fourth separable part of the fish pond subsystem (24-20 acre ponds). Again, a flow rate 10 percent greater than that indicated by the allocation program was found to be economically optimal. The initial capital requirements and annual costs for 4-20 acre ponds are shown in Appendix Tables 4-A and 4-B respec­ tively. The same information for 24-20 acre ponds is shown in Appendix Tables 4-C and 4-D. Those for the soil warming (tomato) subsystem are shown in Appendix Tables 4-E and 4-F. The initial capital requirement and annual costs for the reservoir are jointly shown in Appendix Table 4-G. constrained as 400 acres. Soil warming for specialty crops is constrained at 100 acres. Greenhouse size is constrained at 216,000 square feet. 80 TABLE 4-1 RESERVOIR UTILIZATION RATES BY MONTH FOR MODEL I Month Acreage Required to Dissipate Waste Heat Not Utilized by Subsystems J anuary 101.56 February 101.41 March .0 April .0 May 207.41 June 207.04 July 206.89 August 206.89 September 207.91 October .0 November .0 December 101.31 81 Financial Analysis Table 4-2 shows the inital capital costs, discounted net revenues, discounted annual costs for the reservoir, dis­ counted capital replacement costs for capital replaced at the tenth and twentieth years and net monetary returns. Dis­ count rates of 8, 10, 12, and 15 percent were used in com­ bination with 25, 28, and 30-year time horizons. These re­ sults show that the greater the opportunity cost of capital and funds used in the investment decision, the less desira­ ble is the investment of resources in a waste heat utiliza­ tion system. As expected, however, the results also show that the greater the time period over which these expendi tures are made, the greater will be the net monetary returns.^ This table also shows that net monetary returns are sensi­ tive to what the investor determines as his appropriate dis­ count rate for such an investment. Cost Minimizing Flow Rates The linear programming results also show that for the separable parts of the fish pond subsystem that came into solution, flow rates 10 percent higher than those in the allocation program were found to be the cost minimizing rates ^Net monetary returns are the difference between dis­ counted net revenues and initial capital outlays, discount­ ed reservoir operating costs, and discounted capital re­ placement costs. TABLE 4-2 INITIAL CAPITAL REQUIREMENTS, DISCOUNTED NET REVENUES, RESERVOIR OPERATING COSTS, REPLACEMENT CAPITAL COSTS, AND NET MONETARY RETURNS FOR THE OPTIMAL DESIGN OBTAINED FROM MODEL I (IN THOUSANDS OF DOLLARS) Discounted rate and Time Horizon In itia l Capital Outlays (a) Discounted Net Revenues Discounted Reservoir Opera t i ^ Costs (b) Discounted Capital Replacement Costs at the 10th Year (d) Discounted Capital Replacement Costs at the 20th Year (e) Net1 Monetary Returns (f) 8 percent-25 years 7269.7416 19718.5439 3336.2230 1346.4955 1970.1810 5795.9028 10 percent-25 years 7269.7416 16731.2654 2830.7985 1233-0141 1708.3993 3689.3115 12 percent-25 years 7269.7416 14456.9765 2446.0071 1133.8137 ■1498.8787 2108.5355 15 percent-25 years -7269.7416 11915.0741 2015.9371 1035.9032 1256.0442 337.4480 8 percent-28 years 7269.7416 20369.8197 3446.4239 1346.4955 1970.1810 6337.0377 10 percent-28 years 7269.7416 15693.7791 2655.2644' 1233.0141 1108.3993 2827.3597 12 percent-28 years 7269.7416 14717.3698 2490.0669 1133.8137 1498.8787 2324.8889 15 percent-28 years 7269.7416 12042.8994 2037.6973 1035.9032 1256.0442 433.5131 8 percent-3 0 years 7269.7416 20567.8552 3479.9198 1346.4955 1970.1810 6501.5173 10 percent-30 years 7269.7416 17376.2012 2939.9170 1233.0141 1708.3993 4225.1292 12 percent-30 years .7269.7416 14847.7969 2512.1308 1133.8137 1498.8787 2433.2321 15 percent-30 years 7269.7416 12102.7580 2047.6918 1035.9032 1256.0442 493.3773 *Net monetary returns (f) are the difference of column b and columns a, c, d, and e. 83 in the design formulation.* It was found from the allocation program that by increasing flow rates by 10 percent, the aver­ age weight per fish for the two harvesting periods increased from .682 pounds and .6418 pounds to 1.1768 pounds and .4785 pounds. The final fish population remained the same for the first harvesting period while increasing eight-tenths of one percent for the second population. Total pounds per pond at the end of a year was 26.55 percent higher where flow rates were increased by 10 percent. Where flow rates were decreased by 10 percent from the optimal (as determined by the alloca­ tion program) it was indicated by the allocation program that total pounds of fish per pond increased by only one-half of one percent.* The linear programming results also show that the flow rates to the soilwarming subsystem which minimized total monetary outlays were 10 percent below that determined to be While this discrepancy is difficult to account for, discussions with the systems analyst and person with the most intimate knowledge of the allocation program indicate that it is probably due to the linear programmings ability to better incorporate changes in flow rates with changes in pumping costs and feed costs. The changes in flow rates were assumed to have no impact on initial capital require­ ments (e.g., pumps, motors, pipes) of the subsystem. A marketable size fish is larger than this and is ap­ proximately the size fish harvested in the first crop in August. This small size is the size of fish at year's end. 3 That total poundage for the year increased at all with reduced flows goes against model construction should be attributed to an inability to control all interactions and is treated as insignificant. 84 optimal by the allocation program. This can be explained again by looking at the productivity response and associated costs due to changed flow rates. When flow rates are in­ creased by 10 percent, yield per acre for tomatoes increased by only 7.6 percent from the base yield. This would indi­ cate that the corresponding increased root zone temperature was too high. For a 10 percent reduction in flow rates, yields increased by 52.27 percent. This productivity increase is the same as that obtained with the flow rate i determined by the allocation program as optimal. It is ob­ tained, however, at correspondingly reduced pumping costs. Shadow Prices Positive shadow prices can be used to indicate the amount by which income can be increased if one more unit of a limiting resource is available. They can also be used to indicate increased income if a unit of a constrained activi­ ty is brought into solution. The value of this information is also illustrated in that they indicate pressure to ex­ pand the use of particular resources or eliminate bottle­ necks that reduce the level of constrained activities. Nega­ tive shadow prices will indicate the amount by which income can be increased if one less unit of the constraint is speci­ fied. They are also interpreted as the increase in costs due to the use of the last unit of that resource. The limiting resource in the linear programming formu­ lation is waste heat. Shadow prices can be used to estimate 85 the value of the last unit of thermal discharge used in the waste heat utilization system.^ Positive values will show what entrepreneurs will pay for an additional unit of the waste heat input. Negative values indicate what they will pay for receiving one less unit of waste heat. Negative shadow prices would also indicate when it would be profitable to add or increase a waste heat utilization subsystem. Table 4-3 shows the shadow prices for the waste heat resource for the specified interest rate and time horizons. The figures in Table 4-4 indicate that more units of waste heat could be effectively utilized during March, April, October and November. 2 It is also consistently shown that an excess supply of waste heat exists in September. Generally speak­ ing, the shadow prices for waste heat would indicate that the soil warming enterprise, which presently operates from May through August, could be expanded to operate later in the fall. This would be subject to maintaining soil surface temperature at a level conducive to plant growth. Shadow prices should not be confused with marginal value products (MVPs) derived from continuous functions. MVP by definition is the addition to total value product attributable to the addition of one unit of the variable to the production process, given a fixed schedule of fixed resources. MVPs will differ from shadow prices due to the assumed perfect complementary relationship among all inputs in the model. Hence other resources will not remain con­ stant. 2 The absolute values of shadow prices should not be given as much attention as should their relation to each other. Shadow prices will often exhibit instability due to factors mentioned earlier. TABLE 4-3 SHADOW PRICES FOR WASTE HEAT BY MONTH FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL I (in dollars per thousand Btu's) 8* 25 Yrs. 10* 25 Yrs. 12* 25 Yrs. 15* 25 Yrs. 8* 28 Yrs. 10* 28 Yrs. 12* 28 Yrs. 15* 28 Yrs. 6* 30 Yrs. 10* 30 Yrs. 12* 30 Yrs. 15* 30 Yrs. January - - - - - - - - - - - - February - - - - - - - - - - - - - - - - - - - - - - - Month March A pril 2.2019 - 1.5111 1.1788 2.2991 1.6532 1.5694 1.2068 - - - - - June - - - - - - - - - - - - July - - - - - - - - - - - - August - - - - - - - - - - - - -1.7992 -1.6305 -1.5021 -1.3585 -1.81(72 -1.5719 -1.5168 -1.3658 -1.8412 -1.6669 -1.5241 -1.3691 October - - - - - - 1.5499 1.1979 - - November - - - - - - - - - - December - - - - - - - - - - May September 1.8079 - - 2.3286 - 1.9041 87 The shadow prices for waste heat are in agreement with conclusions drawn from Table 4-1. March, April, October, and November are months where reservoir utilization rates are zero. Waste heat utilization subsystems are fully utilizing the thermal discharge. The maximum reservoir utilization rate occurs during September. An excess supply condition exists and an expansion of subsystems will reduce reservoir size. Shadow prices are also available for reservoir utiliza­ tion activity. Table 4-4 presents those values. Non-zero shadow prices exist only for the month of September. These positive values indicate the amount by which costs can be re­ duced or income increased if one more acre of reservoir is available. Constraints on separable parts of a subsystem limit activity sizes by restricting the sum of the fractions of the separable parts that come into solution to be less than or equal to one. Hence subsystems that come into solution are implicitly restricted to the maximum acreage of the sepa­ rable parts. Table 4-5 indicates the amount by which income will be increased if another acre of fish ponds or soil warm­ ing (tomatoes) were available. The figures indicate that constraints of 480 acres on the fish pond enterprise and 100 acres on tomatoes grown for fresh market on the soil warming acreage are relatively se­ vere. While total fish pond acreage in the basis solution is not 48 0 acres, the shortage of waste heat in March, April, TABLE 4-4 SHADOW PRICES FOR RESERVOIR UTILIZATION FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL I (IN THOUSANDS OF DOLLARS PER ACRE) Month 8)1 25 Yrs. 10* 25 Yrs. 1236 25 Yrs. 156 25 Yrs. 86 28 Yrs. 106 28 Yrs. 28 Yrs. 126 156 28 Yrs. 86 30 Yrs. 106 30 Yrs. 126 30 Yrs. 156 30 Yrs. September 25.9266 23.4956 21.6448 19.5762 26.4566 27.6513 21.8567 19.6809 26.6177 24.0204 21.9628 19.7290 TABLE 4-5 SHADOW PRICES FOR ONE ADDITIONAL ACRE OF FISH POND AND SOIL WARMING (TOMATOES) FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL I (IN THOUSANDS OF DOLLARS PER ACRE) 8? 25 Yrs. 10* 25 Yrs. 12* 25 Yrs. 15* 25 Yrs. 8* 28 Yrs. 10* 28 Yrs. 12* 28 Yrs. 15* 28 Yrs. 8* 30 Yrs. 10* 30 Yrs. 12* 30 Yrs. 15* 30 Yrs. Fish Ponds 1124.7 933.6 789.3 627.7 1170.2 861.2 807.5 636.7 1184.0 978.7 616.6 640.8 Soli Warming (Tomatoes) 2013.2 158^1.7 1259.6 896.0 2110.6 1429.6 1298.5 915.1 2140.2 1681.1 1318.0 924.1 90 October, and November does act to constrain this activity. The separability constraint on the soil warming enterprise does, however, restrict that activity. The value of the shadow prices and inclusion of all 100 potential acres of soil warming (tomatoes) in the optimal design verify the severity of that constraint. Non-Basis Activities The cost of forcing in activities which are non-optimal indicate the income penalties of bringing in one unit of non­ basis activities into the solution. positive. These values are always If non-optimal activities were forced in, with the given income constraint, they would replace an activity already in solution which contributes more to system profits. In this respect they act as shadow prices for non-basis ac­ tivities. Their value in the analysis of this problem is that they indicate the relative profitability of non-basis activities. The cost of forcing in non-optimal activities shows relative competitive positions of those activities. As such they indicate the order in which those activities would come into the optimal design were there more of the limiting resource available. The cost of the preferences of system management is also indicated should they desire a non-optimal subsystem to be a part of the total waste heat utilization system. Table 4-6 indicates the competitive position for the first 20 of the non-basis activities.1 1As it would be redundant and time-consuming to report the cost of forcing in non-optimal activities for all discount 91 The greenhouse subsystem did not enter as a basis ac­ tivity in the optimal design. As has been indicated, its competitive position with non-basis activities was not high either. Despite its capacity for generating significant revenues and system profit, the heat transfer mechanism is not efficient. The ability of the finned tube heat exchang­ ers to dissipate heat during the middle six months of the year is rated as poor. Capital costs for initial and re­ placement capital are high on a dollars per Btu dissipated basis. The types of crops grown provide better returns than most specialty crops; however, greater revenues could be generated should foliage plants (house plants) be raised. The greenhouse activity was specified to use waste heat on a year-around basis. That it uses waste heat on a year-around basis placed it in direct competition with fish ponds which are efficient dissipation mechanisms and have relatively high net returns. What could have been done, given the results obtained, would be to set up an activity whereby the greenhouse would be allocated waste heat when there existed conditions of excess supply of waste heat in the other subsystems. Greenhouses may be used as a supple­ mentary system that would utilize waste heat when shadow prices for other systems are negative. subsystem in non-integrated systems. It may be a feasible But as its cost per rates and time horizons, only those for 12% at 28 years is reported. Relative positions would not change greatly from one discount rate-planning horizon to another. 92 TABLE 4-6 COMPETITIVE POSITIONS OF NON-BASIS ACTIVITIES (IN THOUSANDS OF DOLLARS PER ACRE) Activity Order Cost 1. 2. S.W. ^ Tomatoes, 100 A ,2 Optimal^ S.W. Sweet Corn, 25 A, 1055+ and Optimal 120.0223 3. it. S.W. Sweet Corn, 25 A, 1056 + 157.7330 S.W. Sweet Corn, 50 A, 1056+ and Optimal 271.4899 5* 6. S.W. Tomatoes, 75 A, 1056 + 282.4247 S.W. Tomatoes, 75 A, Optimal 294.9523 7. 8. F.P. 16-20 A Ponds, 1056 + 386.5396 S.W. Sweet Corn, 75 A, 1056+ and Optimal 440.9042 9. 10 . F.P. 8-20 A Ponds, 481.6776 S.W. Sweet Corn, 75 A, 10J6 + 554.0203 11 . 12 . S.W. Tomatoes, 50 A, 1056 + 574.4493 S.W. Tomatoes, 582.8010 G.H. 54000 ft2 , 1056 + G.H. 54000 f t 2 , Optimal 592.4543 621.5047 15. 16 . G.H. 54000 ft2 , 102+ 678.1750 S.W. Sweet Corn, 100 A, 10$+ and Optimal 691.8187 17. 18 , S.W. Corn, 100 A, 10$+ and Optimal 780.8696 S.W. Soybeans, 856.1792 19. 20 . S.W. Field Beans, S.W. Corn, 100 A, 10$+ 13. 14. 1056 + 50 A, Optimal 100 A, 10$+ and Optimal 100 A, 10$+ and Optimal 16.7355 856.2032 865.5769 ^S. W. indicates soil warming, F.P. indicates fish ponds, G. H. indicates greenhouse. 2 A number followed by "A" indicates size in acres (e.g., 100 acres). ^"Optimal" indicates flow rate determined to be optimal by the allocation program, 10%+ indicates flow rates 10% above that optimal, 10%+ indicates flow rates 10% below that optimal. 93 unit of waste heat dissipated per time remains low relative to other subsystems, it is not feasible in an integrated system. Appendix Tables 4-H and 4-1 show the estimated ini­ tial investment requirements and annual costs for a 216,000 square foot greenhouse. Optimal Design with Constrained Fish Pond Acreage (Model II) Model I indicated that a 37 5 acre fish pond subsystem is one of the major components in the optimal system design. The amount of channel catfish produced from this subsystem would strain existing marketing and distribution channels. Unless input supply contracts could be obtained, there is also some possibility of not obtaining fingerlings of spe­ cified size and quality. Given these marketing constraints. Model II was developed. System Design In Model II, the acreage available for fish ponds is restricted to 8-20 acre ponds. In that a fixed amount of waste heat must be dissipated, this will lead to changes in the optimal design given by Model I . The results, with this added constraint, show that the fish pond enterprise is 160 acres and the soil warming plot on which tomatoes are grown is 100 acres in size. The utilization of reser­ voir acreage by month is shown in Table 4-7. The utiliza­ tion rate is determined by the availability of waste heat not dissipated by the waste heat utilization system and is unchanged by discount rate and planning horizon. 94 TABLE 4-7 RESERVOIR UTILIZATION RATES BY MONTH FOR MODEL II Month Acreage Required to Dissipate Waste Heat Not Utilized by Subsystems J anuary 348.47 February 347.96 March 351.64 April 350.36 May 351.64 June 350.87 July 350.63 August 350.63 September 351.14 October 331.74 November 351.00 December 347.63 95 The 160 acres of fish ponds is comprised of .5775 of the second separable part (8-20 acre ponds), and .1450 of the fourth separable part (24-20 acre ponds). All flow rates were indicated to be 10 percent above the optimal de­ termined by the allocation program. (tomatoes) subsystem is 100 10 percent below optimal. The soil warming acres in size with a flow rate The initial capital requirements for 8-20 acre ponds are shown in Appendix Table 4-J. Cor­ responding annual costs are presented in Appendix Table 4-K. Similar cost information for the first and fourth separable parts of the fish pond subsystem, the soil warming area, and reservoir are cited in the discussion of optimal design for Model I in the previous section. Financial Analysis The capital requirements, discounted net revenues and replacement capital, and subsequent net monetary returns are shown in Table 4-8. Comparison of these figures with those in Table 4-2 for Model I indicates that the cost of the ex­ plicit constraint that the fish ponds in total can be no greater than 160 acres is substantial. For all specified discount rates and planning horizons, net monetary returns are negative. For a planning horizon of 28 years where costs and returns are discounted at a rate of 12 percent, the loss in net monetary returns is $6,233,426.50 from that indicated for Model I. The difference in discounted net revenues amounts to a combined loss of $7,070,068.00 to ownership of TABLE 4-8 INITIAL CAPITAL REQUIREMENTS, DISCOUNTED NET REVENUES, RESERVOIR OPERATING COSTS AND REPLACEMENT CAPITAL COSTS, AND NET MONETARY RETURNS FOR THE OPTIMAL DESIGN OBTAINED FROM MODEL I I (IN THOUSANDS OF DOLLARS) Discount Hate and Time Horizon In itia l Capital Outlays Discounted Net Rev^njies Discounted Reservoir Opera tip ^ Costs Discounted Capital Replacement Costs at the^J.j)th Year Discounted Capital Replacement Costs at the^ 2j)th Year Netl Monetary R e^ns 8 percent-25 years 6146.51 10245.9779 5642.6465 612.6324 896.3987 3052.2098 10 percent-25 years 6146.51 8693.7543 4187.8087 561.0003 777.2925 3578.8573 12 percent-25 years 6146.51 7512.0081 4136.9996 515.8658 681.9642 3969.3315 15 percent-25 years 6146.51 6187.5201 3429.1516 471.3182 57 ] ,4786 4430.9383 8 percent-28 years 6146.51 10584.4193 5829.0324 612.6324 896.3987 2900.1542 10 percent-28 years 6146.51 8154.6647 4490.9223 561.0003 777.2925 3821.0605 12 percent-28 years 6146.51 7647.3218 4211.5193 515.6656 681.9642 3908.5376 15 percent-28 years 6146.51 6257.6264 3446.4139 471.3182 •571.4786 4318.0945 8 percent-30 years 6146.51 10687.2896 5885.6849 612.6324 896,3987 2853.9365 10 percent-30 years 6146.51 9028.8702 4972.3632 561.0003 777.2925 3428.2958 12 percent-30 years i 15 percent-30 years 6146.51 7751.0828 4248.8365 515.8658 681.9642 3878.0938 6146.51 6288.7296 3463.3179 471.3182 571.4786 4363.8952 *For d e fin itio n of net monetary return see Table 4-2. 97 the system. Due to increased reservoir size, discounted operating costs are $1,721,452.40 higher over 28 years for a percentage increase of 69.13 percent. Initial capital re­ quirements for this design are reduced from $7,269,741.60 to $6,146,510.00. Table 4-9 summarizes this information by showing absolute and percentage differentials for the spe­ cified items for a 28-year planning horizon ^fcnd discount rate of 12 percent. Shadow Prices A change in the design of the waste heat utilization system will alter the value of the waste heat resource. As less utilization capacity is available because of the acreage constraint on the aquacultural enterprise, a larger propor­ tion of the thermal effluent is dissipated by the reservoir. A comparison of Tables 4-1 and 4-7 indicates that the size of the reservoir under Model I is 208 acres, whereas under Model II maximum reservoir utilization is 352 acres. At no time under Model II is the rate of reservoir utilization zero acres per month. As a result of these conditions, at no time do waste heat utilization systems compete for the waste heat input, nor is there a shortage of waste heat available for use in the system. This contrasts with re­ sults of Model I where during the months of March, April, October and November reservoir acreage requirements were at the zero level. Hence, instead of temporary conditions of excess demand for waste heat, conditions of excess supply exist given the constraints and design of the system with TABLE 4-9 COMPARISON OF ABSOLUTE DIFFERENTIALS AND PERCENTAGE CHANGES IN CAPITAL OUTLAYS, DISCOUNTED NET REVENUES, RESERVOIR OPERATING COSTS AND CAPITAL REPLACEMENT COSTS, AND NET MONETARY RETURNS AT A DISCOUNT RATE OF 12 PERCENT FOR 28 YEARS FOR MODELS I AND I I (IN THOUSANDS OF DOLLARS) Discounted Capital Replacement Costs at the 20th Year In itia l Capital Requirement Discounted Net Revenues Discounted Reservoir Oper­ ating Costs Model I 7269.7416 14717.3898 2490.0669 1133.8137 1498.8787 2324.8889 Model I I 6146.51 7647.3218 ' 4211.5193 515.8658 681.9642 3908.5376 Absolute Difference 1123.2316 7070.0680 1721.4524 617.9479 816.9145 6233.4265 15.45 48.04 69.13 54.44 54.47 Percentage Change Discounted Capital Replacement Costs a t the 10th Year Net Monetary Returns 268.2 99 Model II. An examination of the shadow prices for the waste heat input indicates the amount by which system income will be increased if one less unit of waste heat is available. The incidence of negative shadow prices also indicates when there is pressure to contract utilization capacity. The ab­ solute value of the negative shadow price indicates what system ownership would pay for one less available unit of waste heat. Table 4-10 shows the shadow prices for waste heat by month and for specified discount rates and planning horizons. The only months with non-zero shadow prices are March and May. The results show that for the months of March and May waste heat is in excess supply for the mix of subsystems. Another conclusion is that there may be some pressure to re­ duce system size during those months with the incentive to reduce size being greater in May. The maximum reservoir utilization rates occur for the months of March and May. The minimum utilization rate occurs during October and is only 20 acres less than the maximum 352 acres. Positive shadow prices exist for reservoir utili­ zation during the months where there is no excess capacity. Table 4-11 indicates the increase in system income if another acre of reservoir were available. Along with the implicit constraints resulting from re­ stricting the separable parts, Model II restricts acreage for aguacultural production. The cost of these constraints is stated in terms of income that would be obtained if one TABLE 4-10 SHADOW PRICES FOR WASTE HEAT BY MONTH FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL I I (IN DOLLARS PER THOUSAND BTU'S) 82 25 Yrs. 25 Yrs. 152 25 Yrs. 82 28 Yrs. 28 Yrs. 28 Yrs. 152 25 Yrs. 28 Yrs. 82 30 Yrs. 30 Yrs. 122 30 Yrs. 152 30 Yrs. March -.7549 -.6405 -.5535 -.4587 -.7798 -.6 0 0 8 -.5634 -.4610 -.7874 -.6652 -.5684 -.4633 -1.2315 -1.1495 -1.0871 - 1.0180 -1.2494 - 1.1211 -1.0943 -1.0209 -1.2584 -1.1672 -1.0979 -1.0225 May 102 122 102 122 102 100 Month TABLE 4-11 SHADOW PRICES FOR RESERVOIR UTILIZATION FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL II (IN THOUSANDS OF DOLLARS PER ACRE) Month 8* 25 Yrs. 10* 25 Yrs. 12* 25 Yrs. 15* 25 Yrs. 8* 28 Yrs. 10* 28 Yrs. 12* 28 Yrs. 15* 28 Yrs. 8* 30 Yrs. 10* 30 Yrs. 12* 30 Yrs. 15* 30 Yrs. 8.30 7.04 6.08 5.04 8.57 6.61 6,20 5.07 8.66 7.32 6.25 5.10 April 17.62 16.45 15.56 14.00 17.88 16.04 15.66 14.61 17.95 16.70 15.71 14.63 101 March I 102 more acre were available for each of the different subsystems in the basis solution. The per acre cost of the explicit constraint limiting fish ponds to 160 acres is also shown in Table 4-12. For a discount rate of 12 percent for 28 years, it is shown that an additional acre of each subsystem will result in $84,510.00 increased income to fish ponds and that addi­ tional income in the amount of $943,720.00 will accrue to the soil warming enterprise. The cost of the explicit con­ straint on aquacultural production is $35,110.00. Optimal Design with Lower Commodity Prices (Model III) The assumed price for tomatoes in the previous two models reflect what could be obtained were they sold for consumption in the fresh market. There are market conditions which may prevent the price of $5.50 per bushel from being obtained. First, the quantity available from 100 acres (76,000 bushels) would in all likelihood have a dampening effect on price. Secondly, in many states and local areas existing supply and demand conditions would not warrant this price. Lastly, for the production practices specified in the models presented here, this is no allowance for double cropping of 50 acres or for marketing a portion of the crop other than during the traditional August-September period. The price assumed for undressed channel catfish at $.30 per pound would be in a reasonable range for most uses. Greenfield (1970) indicates that the prices paid by TABLE 4-12 SHADOW PRICES FOR ONE ADDITIONAL ACRE OF SPECIFIED SUBSYSTEMS AND COST OF EXPLICIT CONSTRAINT (IN THOUSANDS OF DOLLARS PER ACRE) 10* 25 Yrs. 12* 25 Yrs. 15* 25 Yrs. 8* 28 Yrs. 10* 28 Yrs. 12* 28 Yrs. 15* 28 Yrs. 8* 30 Yrs. 10* 30 Yrs. 12* 30 Yrs. 15* 30 Yrs. 113.82 96.58 83.45 69.17 117.84 90.59 84.95 69.51 118.73 100.30 85.71 69.86 Soil Warming (Tomatoes) 2047.72 1616.91 1290.04 936.69 2145.60 1461.00 1329.16 943.72 2175.35 1713.84 1348.78 952.72 Explicit Constraint on Fish Pond Acreage 49.35 40.76 34.28 27.23 51.43 37.45 35.11 27.43 52.06 42.82 35.53 27.63 Fish Ponds 103 8* 25 Yrs. 104 processors in 1969 for cultured catfish averaged $.41. Given a 25 cent per pound charge for dressing (gills and viscera removed) and packing, the resulting price would correspond to that presently being received for processed channel cat­ fish by commercial catfish farming enterprises. Should, how­ ever, the catfish be used for feed and as a source of protein for livestock, we would expect a lower price to be received. Questions concerning changing market conditions, their effect on price, and consequently the profitability of the waste heat utilization are important. To deal with these questions we will assume that lower prices will be received for these two commodities. In this model (Model III) a price of $3.00 per bushel is assumed for tomatoes while a price of $.25 per pound is assumed for channel catfish. These lower prices are used to reflect the probable influ­ ences of increased supply on local and regional markets. A lower price for catfish makes its increased use as a source of protein in feeds more appealing. System Design Model III represents a set of circumstances where lower prices are assumed as stated above and where there are no constraints on the allocation of fixed resources (system de­ sign) . The size and types of subsystems determined as opti­ mal under these conditions are identical to those in Model I. The results show that 375.44 acres of fish ponds and 100 acres of soil warming (tomatoes) comprise the optimal waste 105 heat utilization system. The total fish pond acreage is com­ prised of .2639 of 4-20 acre ponds and .7361 of 24-20 acre ponds. Both separable parts have flow rates 10 percent above the optimal level determined by the allocation program. The linear programming model also indicates that 100 acres of soil warming (tomatoes) have a flow rate 10 percent below that optimal rate indicated by the allocation program. The monthly utilization rates for reservoir activity are consequently identical to those indicated in Model I. The maximum acreage used occurs during September and is 207.91 acres for that month. The reservoir acreage required to dissipate the waste heat not utilized by the above sub­ systems can be reviewed in Table 4-1. Financial Analysis The similar design characteristics under different as­ sumed prices indicate that the design is stable for different market conditions. Table 4-13, however, indicates that there will be significant differences in net monetary returns for specified interest rates and time horizons. As initial capi­ tal requirements, discounted replacement costs for the tenth and twentieth y e a r s , and discounted reservoir operating costs are identical to those in Model I, they will not be presented here.^ Discounted net revenues and net monetary returns for Model III will be presented. For comparison the net monetary returns of Model I will also be shown. 1For review purposes, these figures are available in Table 4-2. TABLE 4-13 DISCOUNTED NET REVENUES AND NET MONETARY COSTS FOR MODEL III AND THEIR COMPARISONS WITH THOSE FOR MODEL I (IN THOUSANDS OF DOLLARS) Model III Model I Difference in Net Monetary Net Monetary Returns Returns Net Monetary Returns 8 percent-25 years 7779.7416 -6143.5912 5795.9028 11939.4940 10 percent-25 years 6600.5558 -6441.3982 3689.3115 10130.7097 12 percent-25 years 5703.3391 -6645.1019 2108.5355 8753.6374 15 percent-25 years 4421.3758 -6850.4739 337.4480 7187.9519 8 percent-28 years 8036.0047 -5996.8374 6337.0377 12333.8751 10 percent-28 years 6191.2630 -6675.1564 2827.3597 9502.5161 12 percent-28 years 5806.0732 -6586.4277 2524.8889 8911.3166 15 percent-28 years 4468.8085 -6824.8014 433.5131 7258.3145 8 percent-30 years 8114,1068 -5952.2311 6501.5173 6452.7484 10 percent-30 years 6854.9857 -6296.0863 4225.1292 10521.2155 12 percent-30 years 5851.5194 -6557.0454 2433.2321 8990.2775 15 percent-30 years 4515.0015 -6798.9969 493.3773 7292.3742 106 Discounted Net Revenues 107 While the optimal design is not changed with a differ­ ent regime of prices, the net monetary returns show signifi­ cant modification. For a discount rate of 12 percent over a 28-year time period, the discounted net monetary returns are -$6,586,427.70 given the prices assumed for Model III. corresponding amount for Model I is $2,324,888.90. The The dif­ ference for these two models amounts to $8,911,316.60 over 28 years. Shadow Prices A relevant question to be asked for this particular model is whether the lower prices for the agricultural and aquacultural products, and consequently reduced discounted net monetary returns, will significantly affect shadow prices for the waste heat resource for monthly time periods. Table 4-14 indicates the amount by which system income will increase if another unit of waste heat is available tive shadow prices) (posi­ and also the amount by which system costs will increase if another unit of waste heat is used. A comparison of Table 4-14 with Table 4-3^ indicates the negative shadow prices during September) (which occur almost exclusively are either identical or nearly so for the specified discount rates and time periods. This would indi­ cate that the effect of excess supply of waste heat for this ^Table 4-3 presents the corresponding shadow prices for Model I. TABLE Jj-14 SHADOW PRICES FOR WASTE HEAT BY MONTH FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL III (IN DOLLARS PER THOUSAND) 8* 25 Yrs. 10? 25 Yrs. 12? 25 Yrs. 15* 25 Yrs. 8? 28 Yrs. 10? 28 Yrs. 12? 28 Yrs. 15* 28 Yrs. 8? 30 Yrs. 10? 30 Yrs. 12? 30 Yrs. 15* 30 Yrs. January - - - - - - - - - - - - February - - - - - - - - - - - - - -.3902 - - Month March .6746 - .3914 - .7213 .4377 .4194 .5149 April - - - - - - - - - - - - May - - - -.7181 - - - - - - - - June - - - - - - - - - - - - July - - - - - - - - - - - - August - - - - - - - - - - -1.7992 -1.6305 -1.5021 -.6454 -1.8360 -1.5719 -1.5168 -.9783 -1.8472 -1.6669 October -■ - - - - .4100 .2665 November - December - September .5120 - .2585 - - - - - - - - - - - - •7355 - -1.5241 -1.3691 - - - - - - - - .5582 109 time period has close to an identical impact on the cost of operation of the system for both models. The average shadow price during September for Model I is -1.5833. III, the corresponding amount is -1.4906. For Model The implicit value of the marginal unit of the variable resource where shadow prices are positive differs significantly between Models I and III. The average shadow price for March is 1.6611 for Model I and .3956 for Model III. The corresponding shadow prices for October and November are 1.7539 for Model I and .4568 for Model III. The conclusion to be drawn from these results should be no surprise. The demand price for a vari­ able resource will be greater the higher the selling price of the commodity it is used to produce (1). The shadow prices for additional acreage of the two subsystems in Models I and II indicate that the soil warming (tomatoes) subsystem is a greater bottleneck to increased system income than is the aquacultural subsystem. Given the prices assumed in Model III, system income can be increased more by expanding the aquacultural subsystem than by the soil warming (tomatoes) subsystem.^ Table 4-15 indicates the amounts by which system income will be increased should ad­ ditional acreage of each subsystem be forced into solution. ■'‘This is true except where a discount rate of 8 per­ cent is applied. TABLE 4-15 SHADOW PRICES FOR ONE ADDITIONAL ACRE OF FISH PONDS AND SOIL WARMING (TOMATOES) FOR SPECIFIED DISCOUNT RATES AND PLANNING HORIZONS, MODEL III (IN THOUSANDS OF DOLLARS PER ACRE) 8* 28 Yrs. 10* 28 Yrs. 28 Yrs. 15' 28 Yrs. 8* 30 Yrs. 10* 30 Yrs. 12* 30 Yrs, 15? 30 Yrs. 313.09 630.8 445.6 417.7 318.2 639.3 518.5 423.4 325.3 129.5 729.2 365.3 300.4 130.1 745.3 502.7 311.1 130.8 12* 25 Yrs. 15* 25 Yrs. 490.6 406.45 450.0 279.1 8JE 25 Yrs. 10* 25 Yrs. Fish Ponds 602.5 Soil Warming (Tomatoes) 675-9 12% CHAPTER V COMPARATIVE ANALYSIS OF WASTE HEAT UTILIZATION SYSTEMS WITH CONVENTIONAL DISSIPATION METHODS The previous chapter dealt with important operational and financial characteristics of waste heat utilization sys­ tems. Certain exogenous variables were changed so that the effect of different economic situations could be measured as to their effect on these characteristics. The utiliza­ tion systems were analyzed as sets of economic activities or­ ganized to accomplish a specific goal. Least cost criteria determined the optimal design of those systems given the spe­ cified constraints. Ignored in this previous analysis are the overhead ac­ tivities, the costs of which cannot be directly attributed to the operation of a single subsystem. The determination of the least cost combination of activities which satisfy specified constraints could not be conducted with the tech­ niques available if overhead costs were specified as a func­ tion of subsystem size. However, whether a waste heat utili­ zation system is a least cost alternative to conventional methods of waste heat dissipation necessitates the inclusion of overhead costs. Chapter 5 assesses whether a waste heat utilization system specified in the previous chapter and its consequent 111 112 overhead costs is a least cost alternative to conventional methods that power plants presently use to dissipate waste heat. Capital and annual costs were obtained for natural and mechanical draft cooling towers, cooling pond (reser­ voir) , and spray canal type heat dissipation alternatives. These costs are found in Appendix Table 5-A.^ General Piping and Distribution System Overhead capital and operating costs are incurred by the operation of a general piping and distribution system. 2 Several alternative types of distribution systems were stud­ ied. These included open flow channel, surface pipe, buried pipe, and combinations of the above. From these, a buried pipe system was chosen. As the waste heat utilization system is not site spe­ cific, assumptions were made regarding topology and spatial relationships between the subsystems and between subsystems and the power plant. For simplicity, it was assumed that The comparability of the cost studies compiled by this researcher and those obtained from one of the participating utilities cannot be insured. As the investment criteria and objective functions utilized by utilities differ from those used herein, the presentation of secondary data will not be in a form immediately usable. Hence the secondary data found in Appendix Table 5-A underwent slight modification for use in this analysis. The modifications made did not in any instance make those alternative methods more costly. 2 For a detailed study of this system, see V. M. Schultink, "Feasibility Study of the Utilization of Waste Heat in Agriculture," Unpublished Masters Thesis, Michigan State University, Department of Agricultural Engineering, October, 1975. 113 the plant and subsystems are located on a plane field. As­ sumptions regarding spatial relationshipswere not so easily made. The obvious cost minimizing general piping and distribu­ tion system is that for which all subsystems are located at a point immediately adjacent to the power plant. The next best alternative would be to locate them in a vertical rela­ tionship immediately adjacent to the plant. While both al­ ternatives would minimize transport and capital costs, they would in all likelihood not meet legal sanctions. A more reasonable approach was taken in locating subsystems. Sche­ matics for the proposed layout of subsystems for Models I and III, and Model II are shown in and 5-B Appendix Figures 5-A It is not known whether these layouts minimized capital costs or operating costs for the general piping and distribution system. Legal questions were also not consider­ ed. The purpose of the general piping and distribution system is to convey the heated water from the power plant to the subsystems and then return the cooled water from the subsystems to the power plant. It does not include the pump­ ing of the water through the condenser or subsystems. It does regulate flows to subsystems and insure return of cool­ ing water to the power plant. 114 Comparisons Among Waste Heat Utilxzatxon Systems The comparison of the three waste heat utilization sys­ tems with conventional alternative methods is conducted in two steps. The first step is comprised of assessing net monetary returns for each utilization system, and initial capital requirements and discounted annual costs for the general piping and distribution system for each of the three models studied in the previous chapter. It indicates the least cost system among systems that use waste heat when general piping and distribution costs are included. second step compares each of the three designs The (general pip­ ing and distribution costs included) with conventional heat dissipation methods. It is then determined which alternative is the least cost alternative for dissipating the specified amount of waste heat. Table 5-1 shows the initial net monetary returns for Model I as they have been derived in Table 4-2, initial capi­ tal requirements, the discounted annual operating costs of the general piping and distribution system and total sys­ tem costs. Model II. Table 5-2 shows a corresponding analysis for The derivation of net monetary returns is shown in Table 4-8. The corresponding figures for Model III are shown in Table 5-3. Net monetary returns for this model have been derived in Table 4-13. The initial capital re­ quirements and discounted annual costs for the general pip­ ing and distribution system for Models I and III are shown TABLE 5-1 NET MONETARY RETURNS AND INITIAL CAPITAL REQUIREMENTS AND DISCOUNTED ANNUAL COSTS FOR GENERAL PIPING AND DISTRIBUTION SYSTEM: MODEL I (IH THOUSANDS OF DOLLARS) Total Monetary Outlays (d) 8 percent for 25 years 5795.9028 9727.235 Discounted Annual Operating Costs GP & DSl (c) 51713.481 10 percent for 25 years 3689.3115 9727.235 43973.027 50010.950 12 percent for 25 years 2108.5355 9727.235 37995.466 45614.165 15 percent for 25 years 337.4480 9727.235 31314.976 40704.763 8 percent for 28 years 6337.0377 9727.235 53536.446 56932.174 10 percent for 28 years 2827.3597 9727.235 43390.510 50290.385 12 percent for 28 years 2324.8889 9727.235 38679.986 46082.332 15 percent for 28 years 433.5131 9727.235 31651.181 40994.902 8 percent for 30 years 6501.5173 9727.235 54537.792 57763.509 10 percent for 30 years 4225.1292 9727.235 45668.098 51170.203 12 percent for 30 years 2433.2321 9727.235 39022.973 46316.975 15 percent for 30 years 493.3773 9727.235 31808.528 41042.385 Discount Rate and Time Horizon Net Monetary Returns (a) Initial Capital Requirements GP & DSl (b) ■^General Piping and Distribution System. p Total monetary outlays (d) are equal to (a), (b), (c) 55644.813 TABLE -5-2 NET MONETARY RETURNS AND INITIAL CAPITAL REQUIREMENTS AND DISCOUNTED ANNUAL COSTS FOR GENERAL PIPING AND DISTRIBUTION SYSTEM: MODEL II (IN THOUSANDS OF DOLLARS) Total2 Monetary Outlays (d) Discount Rate and Time Horizon Net Monetary Returns (a) Initial Capital Requirements GP & DS1 (b) . Discounted Annual Operating Costs GP & DS1 (c) 8 percent for 25 years -3052.2098 5180.726 39391.367 47624.302 10 percent for 25 years -3578.8573 5180.726 35495.282 42254.856 12 percent for 25 years -3969.3315 5180.726 28942.035 38092.092 15 percent for 25 years -4430,9383 5180.726 23853.349 33465.013 8 percent for 28 years -2900.1542 5180.726 40719.962 48800.842 10 percent for 28 years -3821.0605 5180.726 34575.013 43576.893 12 percent for 28 years -3908.5376 5180.726 29463.450 38552.713 15 percent for 28 years -4378.0945 5180.726 24109.444 33668.264 8 percent for 30 years -2853.9345 5180.726 •41542.711 49577.371 10 percent for 30 years -3428.2958 5180.726 34786.458 43395.479 12 percent for 30 years -3878.0938 5180.726 29724.711 38783.530 15 percent for 30 years -4363.8952 5180.726 24243.396 33788.017 ^"General Piping and Distribution System. p Total monetary outlays (d) are equal to (a), (b), (c). TABLE 5-3 NET MONETARY RETURNS AND INITIAL CAPITAL REQUIREMENTS AND DISCOUNTED ANNUAL COSTS FOR GENERAL PIPING AND DISTRIBUTION SYSTEM: MODEL III (IN THOUSANDS OF DOLLARS) it Discount Rate and Time Horizon Net Monetary Returns Initial Capital Requirements GP & DS1 (a) (b) Discounted Annual Operating Costs GP & DSl (c) Total2 Monetary Outlays (d) - 8 percent for 25 years -6143.5912 9727.235 51713.481 67584.307 10 percent for 25 years -6441.3982 9727.235 43973.027 60141.660 12 percent for 25 years -6645.1019 9727.235 37995.466 54367.802 15 percent for 25 years -6850.4739 9727.235 31374.976 47952.684 8 percent for 28 years -5996.8374 9727.235 53536.446 69260.518 10 percent for 28 years -6675.1564 9727.235 43390.511 59797.902 12 percent for 28 years -6786.4277 9727.235 38679.986 55193.646 15 percent for 28 years -6824.8014 9727.235 31651.181 •48203.217 8 percent for 30 years -5952.2311 9727.235 54537.792 70217.258 10 percent for 30 years -6296.0863 9727.235 •45668.098 61691.419 12 percent for 30 years -6557.0454 9727.235 39022.973 55307.253 15 percent for 30 years -6798.9969 9727.235 31803.528 -48329.759 ^"General Piping and Distribution System. 2 Total monetary outlays (d) are equal to (a), (b), (c). 118 in Appendix Tables 5-B and 5-C respectively. Initial capital requirements for the distribution system of Model II are shown in Appendix Table 5-D, while annual costs are shown in Appendix Table 5-E. When capital and operating costs for the general pip­ ing and distribution system are included, it is shown that Model II is the least cost waste heat utilization system. Model II, where fish pond acreage is constrained, was not, however, a least cost combination of sizes and types of sub­ systems. Tables 5-1 through 5-3 show that the initial capi­ tal requirements for the distribution system are $5,180,726.00 for Model II as opposed to $9,727,235.00 for Models I and II. This significant difference can be accounted for by the dif­ ferences in design. The fish pond acreage for Model II is 160 total acres versus 375 total acres for Models I and III. Reservoir size for Model I is 352 acres, whereas the maximum size for Models I and III is 2 08 acres. The capital requir­ ed for pipes and pumps for 375 acres as compared to 160 acres of fish ponds is significantly greater than reduction in these costs in going from 352 acres of reservoir to 208 acres. Discounted annual costs for the general piping and distribution system for Model II are $29,463,450.00 for 28 years at 12 percent. $38,679,986.00. Those for Models I and III are The difference in these costs is attribut­ able to the increased flow rates and distances that the waste heat water must be pumped for the aquaculturalsubsystem. 119 The higher initial capital requirements and discounted annual operating costs for the general piping and distribu­ tion system for Model I are not offset by the higher dis­ counted net returns for this model. Hence, as Tables 5-1 and 5-3 show, the least cost system of waste heat uses is not the least cost alternative between waste heat utiliza­ tion systems when costs for the general piping and distribu­ tion system are included. The total costs for the system design under Model I are $46,082,332.00 whereas the total cost for the system configuration in Model II is $38,552,713.00 for a 28-year planning horizon at a discount rate of 12 per­ cent. Comparison Among Conventional Mechanisms and Waste Heat Utilization Systems Table 5-4 indicates the total monetary outlays for the three integrated waste heat utilization systems, natural and mechanical draft cooling towers, cooling pond, and spray canal type heat dissipation systems. These figures show that Model III will, over the planning horizons and for discount rates specified, generate approximately the same total monetary outlays as cooling ponds and natural draft cooling towers. It is also shown that utilization of an agricultural-aquacultural system such as that specified in Model I will for all discount rates and time horizons cost slightly less than mechanical draft cooling towers and spray canals. Model II, where the fish pond subsystem is constrained to 160 acres in size, is indicated as the least cost method for dissipating TABLE 5-4 COMPARISON OF TOTAL MONETARY OUTLAY FOR INTEGRATED WASTE HEAT UTILIZATION SYSTEMS AND ALTERNATIVE METHODS {IN THOUSANDS OF DOLLARS) Waste Heat Utilization System Model I Waste Keat Utilization System Model II Waste Keat Utilization System Model III Natural Draft 8 percent for 25 years 55644.613 47624.302 67584.307 68973.806 10 percent for 25 years 50010.950 42254.856 60141.660 12 percent for 25 years 45614.164 38092.092 15 percent for 25 years 40804.763 8 percent for 28 years Cooling Ponds Spray Canals 61268.320 67547.297 62382.997 63045.924 55690.012 62398.423 57027.011 54367.802 58423.229 51382.167 58422.209 52890.855 33465.013 47952.684 53351.991 46567.743 53978.413 48268.309 56932.740 48800.842 69260.518 70369.890 62582.075 68759.915 63644.392 10 percent for 28 years 50290.385 43576.893 59792.902 64131.478 56711.550 63341.320 58077.836 12 percent for 28 years 46082.332 38552.713 55193.646 58992.347 51875-480 58877.545 53364.507 15 percent for 28 years 40994.902 33668.264 48203-217 53609.467 48810.480 54202.053 48500.945 8 percent for 30 years 57763.509 49577.371 70217.258 71136.753 63303.715 69426.001 64337.271 10 percent for 30 years 51170.203 43395.479 61691.419 64344.062 56911.598 63475.968 58199.991 12 percent for 30 years 46316.975 38783.510 55307.253 59255.017 52122.660 59105.696 53601.835 15 percent for 30 years 41042.385 33708.017 48329.759 53729.969 46923.431 54306.715 48609.821 Mechanical Draft 121 waste heat for the size plant previously specified. Table 5-5 indicates the relative order in terms of to­ tal monetary outlays for each of the alternatives considered. It also indicates the percentage in terms of total monetary outlays that less costly alternatives are of the most costly. * It should be noted that the ranking of the different alternatives in some instances will change with the discount rate and planning horizon. 5-5. Two instances are shown in Table For a discount rate of 8 percent for 25 years, the sys­ tem design for Model III becomes relatively more costly than the cooling pond. For 30 years at 15 percent, cooling ponds become the most expensive alternative. The change in order of costliness is due to the varying proportions between dis­ counted annual costs or returns and initial capital require­ ments for each alternative. In all cases, however, Table 5-4 indicates that Model II is the least cost alternative given the conditions spe­ cified. Table 5-5 shows that the cost savings over a 28- year time period at a discount rate of 12 percent is approxi­ mately 20 million dollars if the waste heat utilization sys­ tem specified in Model II is used rather than a natural draft cooling tower. TABLE 5-5 RANKING, IN TERMS OF TOTAL MONETARY OUTLAYS, OF DISSIPATION ALTERNATIVES (IN THOUSANDS OF DOLLARS) Percentage of Most Costly (1555, 30 Yrs.) Total Monetary Outlay (12J5, 28 Yrs.) Percentage of Most Costly (1255, 28 Yrs.) Percentage of Most Costly (855, 25 Yrs.) Natural Draft Cooling Tower 58992.3^7 100.00 100.00 98.94 2. Cooling Ponds 58877.5^5 99.80 97.93 100.00 3. Model III 55193.646 93.60 97.985 88.99 4. Spray Canals 53364.507 90.50 90.40 89.51 5. Mechanical Draft Cooling Tower 51875.480 87.90 88.85 86.40 6. Model I 46082.332 78.10 80.67 75.57 7. Model II 38552.713 65.50 69.05 62.22 Dissipation Alternative 1. CHAPTER VI MANAGEMENT AND ACQUISITION OPTIONS In this chapter, a variety of management and capital acquisition options are discussed. Based on the institu­ tional and operational constraints mentioned in the first chapter, the possible options are narrowed to ones which ap­ pear to be feasible. Where there is a divergence from the management and ownership options underlying the analysis of the preceding two chapters, a partial budgeting approach is used to indicate how the distribution of investment costs, operating costs, and costs of providing operating capital change. Correspondingly, if the distribution of monetary benefits is altered, those changes are also distinguished. The net result is reformulated budgets which indicate net changes in costs and/or benefits. As this chapter is written to assess the impact of management and acquisition options, the emphasis is on the final empirical results of changes in those options. More can be said about the relative bargaining positions and al­ ternative pricing arrangements that could possibly be em­ ployed by the utility and firm(s) that manage or own the waste heat utilization subsystems. Bargaining and pricing of waste heat are, however, treated as intermediate steps in arriving at a feasible set of management, ownership and 123 124 pricing agreements. Areas where the price of waste heat can be bargained are indicated. That alternative bargaining posi­ tions and prices for waste heat, other than the zero price assumed here, are not evaluated as to their impact on the total monetary outlays of the utility or net monetary returns of the utilization system is a limitation of the study. The preceding discussion of the financial and operat­ ing characteristics of waste heat utilization systems employ­ ed assumptions regarding the management of the waste heat utilization system, general piping and distribution system, and the acquisition of land and capital resources. The fi­ nancial results of Chapters 4 and 5 were predicated on man­ agement of the agricultural and aquacultural subsystems and general piping and distribution system by the utility company. All capital requirements and operating costs were borne by the utility. This set of assumptions facilitated the compari­ son of waste heat utilization systems with conventional al­ ternatives for waste heat disposal. That a single firm sup­ plies all necessary resources, inputs, and managerial skills implies that the results of the two preceding chapters apply to cases where the utility company is investor owned or where the utility is publicly owned and managed, such as the case with electrical generating plants of the Tennessee Valley Authority. Other Management and Acquisition Options Several options exist which lie between the extremes of full private or public ownership and management. Several 125 institutional and technical questions were raised in Chapter 1 of this analysis which suggest that other management and ownership options should be assessed.1 In this section, institutional alternatives are discussed and evaluated with regard to their appropriateness as a framework for organiz­ ing subsystem operation and as an interface with the utility company. The management and acquisition options shown in Table 6-1 can be evaluated from several viewpoints. As this analy­ sis deals primarily with the effect of feasible options on the cost of operation and economic feasibility; the viewpoint of the utility and organization taking control of the use rights of the land, or provision of capital or managerial re­ sources, or some combination of these activities are given primary consideration. 2 Diverse criteria can be used to The two management and acquisition options assumed in the previous analysis are conditional upon the utility provid­ ing the managerial expertise for intensive aquaculture and cultivation of specialty crops. Marketing and organizational expertise would also be required. Specialized capital for these subsystems is also stipulated. The utility companies with which this research was conducted have stated that en­ tering agribusiness and aquacultural ventures is not consis­ tent with the firm's goals or the state regulatory agency's restrictions. These conditions were, however, ignored to facilitate the comparison of waste heat utilization systems with alternative mechanisms. 2 This is not to say that the viewpoint of present own­ ers of the land in question, or local community are unimpor­ tant. However, given the questions being considered and the non-existence of necessary information, the breadth of the analysis of institutional alternatives is necessarily limited. 126 TABLE 6-1 MANAGEMENT AND ACQUISITION OPTIONS FOR WASTE HEAT UTILIZATION SYSTEMS Management and Capital Acquisition Option Fee Simple Acquisition^" Purchase and Manage Purchase and Leaseback Purchase and Resale on Condition Less than Fee Simple Acquisition Purchase Easements Contractual Agreements - No Real Property Interest Waste Heat Water Cooperative Contractual Arrangement 2 Public Authority^ Costs incurred by a body seeking fee simple acquisi­ tion include payment of interest and principal on bonds raised to finance purchase of the land, administrative costs, possible cost of compensating the affected communities for property taxes foregone where land is purchased by a tax ex­ empt body and leased back for agriculture-aquaculture. 2 Should the utility company decide not to fully control the total integrated system and not raise the capital for one or all the separate subsystems, it can enter a contractual agreement with private entrepreneur(s) to supply waste heat water. 3 Publicly owned and managed, per examples provided by Tennessee Valley Authority. 127 evaluate these options. Among those that are of potential importance are economic and social impacts on the local com­ munity.^ The viewpoint from which these options are evalu­ ated will, however, narrow these criteria. The criteria utilized are the financial characteristics that the option implies as well as stability of system operation and degree of control exercised by the utility and/or organization oper­ ating the subsystems. Fee Simple Acquisition Fee simple acquisition of land confers absolute owner­ ship by the purchaser. The owner can sell all rights to the land on a voluntary basis, or if a public agency is involved, the power of eminent domain can be employed. The land can be leased, resold on condition, or managed by the purchaser. Purchase and manage This option represents the most highly integrated form of operation of the waste heat utilization system. purchased by fee simple acquisition. Land is Capital for the general piping and distribution system and individual subsystems is provided by the utility. Operating capital as well as man­ agerial expertise would also be procured by the utility. Sub­ system distribution system and management becomes an accessory ^"Of primary importance here would be the impact on local or regional employment for both construction and con­ tinuing operation, the impact of increased local and region­ al income on other industries and secondary services, shifts in the supply and demand of inputs and other resources, as well as indirect monetary and non-monetary costs and benefits. 128 to utility operation. Purchase and leaseback Again fee simple title to the land is obtained. ment capital is provided by the utility. Invest­ Instead of manag­ ing the individual subsystems, the utility can lease the land to farmers for use of the soil warming plots or to aquaculturists for operation of fish ponds. The integrated nature of the system would be maintained if the physical facilities were leased to a single management firm which would maintain the operation of all subsystems. A cash rent or crop shar­ ing contract are the most common types of leasing arrange­ ments. All or a major share of operating costs are borne by the lessee. Whether there is a fee for the waste heat re­ source and/or services of the general piping and distribu­ tion system is a further consideration. Where net monetary returns are negative for the sys­ tem operation, the instance of offering an incentive to private entrepreneurs to manage the individual subsystems must be studied. In all cases, a long term leasing agreement would be necessary for stability and continuous operation of the plant. Purchase and resale on condition Another management option available following fee simple acquisitions of land and provision of investment capital is to resell the land and facilities on condition that they can be used in conformance with continuous and stable power plant 129 operation. This type of arrangement is frequently used in urban renewal projects. It insures that the subsequent use of the land conforms to land use objectives and development plans. Less than Fee Simple Acquisition Easement purchase An easement is a right or advantage in the use of land that is purchased from the total bundle of rights that land ownership confers. Easement purchase refers to the transfer of partial property rights from private individuals to an­ other individual or governmental unit. It should be noted that easement purchase and resale on condition will in all probability apply only to the soil warming subsystem. Easements are most easily used when the original uses of the land are not disturbed. Contractual Agreements Waste heat cooperative The goals of an integrated system can be accomplished by cooperative ownership of subsystem investment capital and the provision of managerial services. Under such an arrange­ ment, a cooperative group of firms would agree to use the waste heat from the power plant and bear necessary expenses of subsystem operation. It is assumed that initial capital expenses and annual operating costs of the distribution sys­ tem are incurred by the utility. This option along with the 130 purchase and resale option would minimize the financial and managerial responsibility of the utility. However, control over the heat dissipation mechanism is also substantially re­ duced. Contractual arrangement Should the utility decide not to fully control the to­ tal system and not raise the capital for one or all of the separate subsystems, it can enter into contractual arrange­ ments with private firms to supply waste heat water. Bar­ gaining will occur between the utility and the individual users with regard to the distribution of costs and benefits associated with the supply and utilization of waste heat water. With this type of institutional arrangement, the utility would likely supply the capital for the general pip­ ing and distribution system, and conceivably be involved in cost sharing for other items associated with individual sub­ systems such as initial capital outlays. The contracts would necessarily be long term in nature with specific and binding stipulations on both parties. The contract would conceivably be open for periodic negotiation. The degree of control exercised by the utility in such an arrangement would depend upon the nature of specific conditions in the contract. Public Authority This option would be quite similar to the fee simple acquisition option of purchase and management. The system would be fully integrated in terms of ownership and operation. 131 The primary difference would be that public capital versus private capital would be involved. An example of such a system would be the Tennessee Valley Authority owned and operated power stations. Feasible Options^ Not all of the capital acquisition and management op­ tions previously discussed are feasible. The discussion of feasible uses of waste heat was not meant to be constructed around redesigning institutions and their normal operating procedures so that such a system would be affected. Rather the analysis presented here presumes that the salient and relevant operating procedures of existing arrangements will remain relatively unchanged. Discussions with planning and engineering personnel of two investor owned utilities in Michigan indicate that reliability in the operation of the heat transfer mechanism is essential in power plant operation as the cost of plant shutdown or operating at reduced capacity is significant. They also indicate that direct management of agribusiness or aquacultural enterprises is not a goal or objective of the utility regardless of financial incentives. These two prerequisites are sufficient to limit several acquisition and management options. ^"Feasibility often describes the technical or economic workability of something. The concern here is workability of an option within existing institutional constraints. 132 The purchase and management option can be excluded if the utility does not desire direct involvement in the manage­ ment of agricultural and aquacultural enterprises. While purchase and resale is an option for which these enterprises are no longer an adjunct to utility operation, the reliabil­ ity of system operation is diminished. That the utility can sue for damages or injunctive relief, if conditions specified in the sales contract are not suitably performed, is insuf­ ficient compensation for inefficient plant operations or possible shutdown. Easement purchase can be eliminated as a feasible op­ tion in that total and exclusive use of the rights accruing to land ownership is necessary. As such, this option would cost equally as much as fee simple ownership. This option can also be excluded in that significant alteration of the land would be required for installation of soil warming pipes, fish ponds and the general piping and distribution system. The waste water cooperative is attractive in that no real property interest is necessary by the utility. For this reason, however, the degree of control exercised over the system is significantly reduced. Such an option would have desirable characteristics if waste heat water were sold to or obtained without charge by the cooperative. Transporting the waste heat water beyond the immediate perimeter of the plant location would represent significantly increased capi­ tal and operating costs beyond those stipulated in Chapter 3. As the utility would have little control over the 133 cooperative's actions it is doubtful they would supply this capital or bear a larger proportion of pumping costs. As these costs are significant, it is doubtful that sufficient investment capital could be obtained by the cooperative. The Tennessee Valley Authority is an example of the public authority option. It has conducted experimental re­ search and funded pilot projects studying waste heat utili­ zation. While no discussions have been held with them con­ cerning implementation of an integrated waste heat utiliza­ tion system, there is no reason to suspect a commitment of managerial expertise for aquacultural and agricultural en­ terprises of the required scale, or the commitment of large amounts of capital expenditure financed through public funds. Partial Budget Analysis for Purchase and Leaseback Purchase and leaseback, and some form of contractual arrangement remain as possible institutional alternatives if the utility does not wish to become involved in the manage­ ment of subsystems. These two alternatives are evaluated with the design and general piping and distribution system found in Model II. The optimal design and general piping and distribution system found in Model I was not chosen as the capital requirements for the distribution system are sub­ stantially greater than that for Model II, as shown in Table 6-2. While this would not be a critical factor if the sys­ tem and general piping and distribution system were owned by a single firm, it is when the two systems are owned by TABLE 6-2 INITIAL CAPITAL REQUIREMENTS, DISCOUNTED NET REVENUE AND REPLACEMENT CAPITAL COSTS FOR MODELS I, II, AND III AND CORRESPONDING GENERAL PIPING AND DISTRIBUTION SYSTEM FOR 12 PERCENT AND 28 YEARS.* (IN THOUSAND DOLLARS) Model, Discount Rate and Time Horizon -K 1? (R"C> 1 _ N + 1 points form the The program evaluates the objective func­ tion at each point and replaces the point of smallest value with a new point located at a distance a times as far from the centroid of the remaining points as the distance of the rejected point along the line connecting the rejected point and the centroid. The coordinates of the centroid of the remaining points are given by: xi ^ 1 /c 1 JvA k z x i -i “ x i j= l *J n (old)], j i = 1,2, ..., N The coordinates of the new point are specified by: X. n (new) = lffl a (X. .(old) 1 / J +X. 1 ic , i = 1,2, ...,N and a = 1.3 is recommended. The remaining set of points together with the new one become a new complex and the process is repeated until con­ vergence, as specified by the user, is acquired. Convergence 172 occurs when the objective function values at each point of the complex are within 0 units for y consecutive iterations. Each point of the complex must satisfy constraint limits. If explicit constraints are violated, the point is moved a distance Mize use 6 inside the violated limit. 6 = .0001. Kuester and If implicit constraints are violated the point is moved one-half of the distance to the centroid of the remaining points: x. .(new) = (x. x rj If] .(old) + X. x,C ) /2 i = 1,2, ..., N It a point repeats in giving the lowest function value, that point is moved one-half the distance to the centroid. Program ALLOC is the simulation package that controls the order of operations, provides storage of information, and calculates additional simulation variables (other than independent variables) at optimums. A flow chart of pro* gram ALLOC is shown in Figures 1 and 2. Inputs to ALLOC are subsystem sizes and optimation para­ meters. OPTBOX then selects various heat dissipation values for the fish pond and soil warming plots. POND and TSOIL determine pond surface temperature and root zone temperature with the use of weather inputs. FISH and CROP find asso­ ciated productivity responses on a monthly basis. 173 C Initialize Variables ------- Input Convergence Criterion Length of Run, etc. Call WEATHER (to retrieve monthly average weather conditions) Call OPTBOX (to optimize distribution of heat to FISH and CROPS) K Figure 2 Allocate remaining heat to reservoir : & :z. Call POND (determine necessary size of reservoir to meet system constraints) Store monthly values of temperatures, heat dissipation rates, profits, reservoir size, etc. Increment time counter (Month * Month + 1 ) 3Z END Simulation? YES ) I NO Figure 1 Simulation Flow Chart of ALLOC + Output Stores Results c STOP 174 Subroutine OPTBOX Call FUNC (objective function to be maximized— Q, and Q_ the . independent variables) Call CONST (constraints) ■ Return Subroutine FUNC Call POND (to find surface temp., given heat input and weather) Call FISH (to find incremental growth and profit at given temp.) Call SOIL (to find soil temp, given heat input and weather) Call CROP (to find incremental growth and profit at given temp.) F = profit fish + profit crops (objective function) Return Subroutine CONST 0 < Qi5Qp oi Q2i °p o< Qi+Q2iQp Return Figure 2 Optimization Sequence 175 APPENDIX 2-B THE POND MODEL 1 The POND model is used in both the FUNC subroutine and in the reservoir component. The POND model is based on in­ vestigations by Edinger, et al. (1968) and Littleton (1970). The principle on which this model operates is that the tem­ perature of a shallow natural pond (e.g. fish pond or reser­ voir) when subject to constant climatic conditions will ap­ proach a steady state or equilibrium temperature. The equi­ librium temperature is defined as that temperature a body of water reaches when the heat input and heat dissipated are balanced. The importance of this model is that if climatic condi­ tions, physical characteristics of the pond, and rate of heat input are known; the pond temperature can be found. This will then determine growth rates of fish and consequently revenues for the fish ponds. As Figure 1 of Appendix 2-A shows, once the input heat rates to subsystems are known the amount of waste heat that must be dissipated by the reservoir can be determined and hence reservoir size. It should be noted that a well mixed pond (one with no vertical temperature gradient) was assumed in finding pond surface temperature and the size 1For further reference as to the development and charac­ teristics of the POND model. Walker and Bakker-Arkema (1975), can be reviewed. b 176 of the reservoir. 177 APPENDIX 2-C THE SOIL WARMING MODEL1 A differential equation model was used to calculate soil temperature for a given heat input into a system of sub-surface piping. The soil warming model is based on work by Kendrick and Havens (1973) where soil temperature is stated as a major indicator for crop growth. The flow of operations for this model starts with the maximization of net revenues. From this operation heat dis­ sipation rate can be found and assigned to the surface bal­ ance equation. The surface temperature is then found. The Hendrick-Havens equation used for calculating surface tem­ perature can also be used to assess whether the pipe tem­ perature is physically feasible. If so, the flow rate which corresponds to the surface temperature is used to calculate pumping costs and fixed capital requirements. 1The mathematical model and the method by which it is solved is found in Schisler, and Bakker-Arkema (1975). 178 APPENDIX 2-D THE FISH GROWTH MODEL1 The fish growth model is also a mathematical model used in predicting biological productivity. The variables affecting fish growth rates are temperature (as derived from the POND model) and population density (given in initial conditions). Investigations by Brown, 1957; Swift, 1964; Brett, et al., 1969; and Andrew and Stickney, 1972; support the model. While it is desirable to express growth rates as exponentially related to temperature and density, impor­ tant parameters which represent the proportional growth rate for the specie of fish used in the model was not known. The lack of appropriate data and known relationships between temperature population density, and growth rates forced the use of a constant growth rate. The constant growth rate was estimated using linear ap­ proximation methods using data available in Andrew and Stickney, 1972. While a nonlinear function would have been desirable, given the possible range of plant output tempera­ tures, the linear approximation used made it possible to assess the impact of different temperature on fish growth. This mathematical model forms the core of the FISH component. 1A complete description of this model and its limita­ tions is found in Walker and Bakker-Arkema, 1975. 179 As can be observed in Figure 2 of Appendix 2-A, FISH is part of the FUNC subroutine. The flow chart indicates that given simulated weather conditions and flow rates which maximize the objective function, surface temperature is found for the fish ponds. This is then used in the FISH model to find incremental growth rates. I 180 APPENDIX 2-E THE CROP GROWTH MODEL1 The crop growth model or CROP is also a mathematical model formulated to describe a biological growth process. Many models for crop response had been predicated on a fixed root zone temperature. Given the impact of weather, variable flow rates, and physical constraints, a model was developed to accommodate non-constant soil temperatures. Furthermore, for economic evaluation, the model must relate the effect of improved emergence and vegetative growth on grain yield or fruit yield. Given the nature of the problem and desired information a switched growth model in the form suggested by Partridge and Denholm (1974) was used. While the coefficients of the model depend on climatic factors and hence should change with time, constant coefficients were used as a reasonable approxi­ mation to model the growth of the crops used in the study. The placement of the crop growth model in the compila­ tion sequence and use in the economic analysis is similar to that for the fish growth model. For a further discussion of this model and the proce­ dures used in its development, see Schisler and BakkerArkema, 1975. A description of crop data is also discussed. APPENDIX 181 APPENDIX TABLE 3-A INITIAL CAPITAL REQUIREMENTS FOR A 4-20 ACRE FISH POND SUBSYSTEM Dollars Item 57,000 400,000 1,000 1,000 4,300 6,000 2,500 7,500 174,000 174,000 Land Pond Construction Feeding Equipment Disease and Parasite Control Equipment Harvesting Equipment Storage Barn Offices Miscellaneous Pumps (8) Installation Motors (8) Fluid Drive Couplings (8) Belts, Splines, Circuit Breakers, Starters 24,000 45,000 3,000 Filtration and Aeration 50,000 TOTAL 9*18,800 182 A PPENDIX TABLE 3-B ANNUAL COSTS FOR THE 4-20 ACRE FISH POND SUBSYSTEMl Item 2 Annual ownership costs Interest on land Investment Dollars 4,560 ■5 Depreciation Pond construction Feeding Disease and parasite control Harvesting equipment Filtration and aeration Storage Pumps Motors Fluid drive coupling Belts, splines, circuit breakers and starters Miscellaneous Interest on investment Pond construction Feeding Disease and parasite control Harvesting equipment Filtration and aeration Storage barn Office Miscellaneous Pumps Motors Fluid drive coupling Belts, splines, circuit breakers and starters SUBTOTAL Annual operating costs Repairs and maintenance Feeding equipment Disease and parasite control Harvesting equipment Pumps, motors, accessories Miscellaneous equipment Pumping costs Chemicals Fingerlings 13,333 100 100 540 1,667 100 5,800 1,600 1,600 375 750 16,000 40 40 172 200 120 100 300 6,960 960 1,970 120 57,507 65 32 200 1,250 400 137,200 3,550 307,200 183 APPENDIX TABLE 3-B (continued) Item Feed Manager Labor Taxes, insurance, bookkeeping and general office overhead ^ Filtration and aeration SUBTOTAL Interest on operating capital TOTAL ANNUAL OPERATING COSTS TOTAL COSTS Dollars 310,680 15,000 10,000 5,000 5,000 795,577 30,203 825,780 883,287 Thomas H. Forster, John E. Waldrop, Cost Size Relation­ ships In the Production of Pond Raised Catfish for F oo d , Mississippi State University Agricultural and Forestry Experi­ ment Station, State College, Mississippi, January, 1972. Costs are modified to reflect Michigan conditions, 1976 prices and other costs Incurred due to the non-conventional nature of the pond construction and operation. Interest at a rate of 8 percent was charged on onehalf of the original investment in depreciable Items and at 9 percent on one-half of the estimated operating costs. Non­ depreciable Items, land, and land improvements were charged at a rate of 8 percent of full inventory value. These charges will remain the same throughout for other subsystems, general piping and distribution system and alternative systems. JA straight-line depreciation method was used where the first, fifth, sixth, seventh, eighth and ninth items were depreciated over a thirty-year period. The second, third, and fourth items were depreciated over a ten-year time period. The tenth item was depreciated for a six-year time period, and the eleventh item for an average of twenty-one years. A straight-line depreciation system will be applied to other subsystems and the general piping and distribution system. As the exact needs of the filtration system have yet to be determined, the inclusion of the Initial capital ex­ pense and annual operating cost for this component is more a matter of completeness than accuracy. 184 APPENDIX TABLE 3-C INITIAL CAPITAL REQUIREMENTS FOR 24-20 ACRE PONDS Dollars Item Land Pond Construction Feeding Equipment Disease and Parasite Control Equipment Harvesting Equipment Storage Barn Offices Miscellaneous Pumps (2*1) Installation Motors (2*1) Fluid Drive Couplings (2**) Belts, Splines, Circuit Breakers, Starters Filtration and Aeration TOTAL 342,000 2 ,**00 ,000 6,000 6,000 22,800 18,000 15,000 45,000 1,044,000 1,044,000 144,000 288,000 18,000 300,000 5 ,692,800 185 A P PEN DIX TABLE 3“D A NNUAL COSTS FOR THE 24-20 ACRE FISH POND SUBSYSTEMl Dollars Item 2 Annual ownership costs Interest on land investment 27,360 D ep reciation Pond construction Fe eding Disease and parasite control H arvest i ng equipment Filtra t io n and aerat i on Storage Pumps Motors Fluid drive coupling Belts, splines, circuit breakers and starters Misc ellaneous 80,000 600 600 3,225 10,000 600 34,800 9 ,600 9,000 2,250 4,500 Interest on investment Pond con struction Feeding Disease and parasite control Harvesting equipment F il t ra t io n and ae ration Storage barn Office Miscellaneous Pumps Motors Fluid drive coupling Belts, splines, circuit breakers and starters 96,000 240 240 1,032 1,200 240 600 1,800 41,760 5,760 11,520 720 SUBTOTAL Annual operating costs Repairs and m aintenance Fe eding equipment Di sease and parasite control H arvesting equipment Pumps, motors, accessories Miscell aneous equipment Pumping costs 339,327 390 275 1,350 7,500 2,400 823,200 186 APPENDIX TABLE 3-D (continued Item Dollars Chemicals Fingerlings Feed Manager Labor Taxes, Insurance, bookkeeping and general office overhead ^ Filtration and aeration SUBTOTAL Interest on operating capital 21,333 1,946,983 1,864,080 60,000 118,125 30,000 50,000 4,925,636 208,542 TOTAL ANNUAL OPERATING COSTS 5,264,963 TOTAL COSTS 5,473,505 Refer to Appendix Table 3-B for Footnotes 1-4. 187 APPENDIX TABLE 3-E INITIAL CAPITAL REQUIREMENTS FOR 100 ACRES OF SOIL WARMING AREA Dollars Item Land Lateral Piping 2-lnch PVC 6 .24 ft. 63,000 523,224 Installation @ .015/ft. Headers 32,701 1.25 diameter 6 4.20/ft. Installation Pumps - 2 X 9,000 Installation - 2 X 9,000 Valves - 4 X 2,200 Installation - 4 X 1,375 Motors - 2 X 4,050 Belts and Splines - 2 X 600 Circuit Ereakers and Starters - 2 X 200 16,380 16,380 18,000 18,000 8,800 5,500 8,100 1,200 400 TOTAL 774,685 188 A P P E N D I X T A B L E 3-F ANNUAL COSTS FOR 100 ACRES OF SOIL WARMING FOR TOMATOES ~1 Dollars Item 5,040 Annual ownership costs Depreciation Lateral Piping Headers Pumps Valves Motors Belts, etc. 17,440 585 643 314 289 57 Interest on Investment Laterals Headers Fumps Valves Motors Belts, etc. 22,237 1,310 1,440 572 324 64 SUBTOTAL Annual operating costs Materials Labor Custom hire Pumping costs Manager 50,315 70,800 54,400 9,837 9,870 10,000 SUBTOTAL Interest on operating capital 164,907 3,630 TOTAL ANNUAL OPERATING COSTS 158,667 TOTAL COSTS 208,982 I 189 APPENDIX TABLE 3-G INITIAL CAPITAL REQUIREMENTS AND ANNUAL COSTS FOR THE RESERVOIR Dollars Item Initial capital requirements Land Reservoir construction 225,000 3,450,000 TOTAL Annual costs Annual ownership cost Depreciation Interest on investment 3,675,000 1,800 115,000 138,000 SUBTOTAL Annual operating costs Manager and labor Chemicals Filtration Repairs Miscellaneous 254,800 20,000 91,388 100,000 50,000 37,700 SUBTOTAL Interest on operating capital 299,088 8,612 TOTAL ANNUAL OPERATING COSTS 307,700 TOTAL COSTS 562,500 190 APPENDIX TABLE 3-H INITIAL CAPITAL REQUIREMENTS FOR A 216,000 SQUARE FOOT GREENHOUSE Item Dollars Land Structure Covering (T-20 tedlar acrylic) Forced air finned tube heat exchangers (15) Finned tubing Boiler (hot water - fuel oil) Controls Single speed ventilator fans (14 X 48") Dual speed ventilator fans (14 X 48") Installation, wiring and lighting 4,800 139,700 Benches (80JiS space utilization) Head house, storage, office, work area, loading facility and lavatories Climate controls Pumps and installation Motors Circuit breakers, belts, splines and starters TOTAL 124,800 60,000 148,000 72,000 12,000 22,400 28,000 301,600 18C,000 120,000 4,800 24,000 60,000 2,400 1,291,300 191 APPENDIX TABLE 3-1 ANNUAL COSTS FOR A 216,000 SQUARE FOOT GREENHOUSE Item Dollars Annual ownership costs Interest on land investment 384 Interest on investment Structure and covering Forced air finned tube heat exchanger Finned tubing Boiler Controls Fans Installation Benches Head house, etc. Climate controls Pumps Motor Belts, e tc. Depreciation Structure and covering Heating system and controls Ventilator fans Installation, wiring and lighting Benches Head house, etc. Pump Motors Belts, etc. _ SUBTOTAL Annual operating costs Labor Materials Heating Maintenance Office supplies Management Office workers Selling costs 9,312 2, 400 5,920 2,880 480 504 12,064 7,200 6,400 192 960 240 128 7,760 11,064 5,040 30,160 6,000 5,332 800 200 108 29,260 120,000 454,284 100,000 230,000 2,400 88,000 12,000 20,000 192 APPENDIX TABLE 3-1 (continued) Dollars Item SUBTOTAL 87,400 20,000 1,134,112 TOTAL 22,572 1,185,944 Pumping costs Miscellaneous Interest on operating capital 193 APPENDIX TABLE 3-J INITIAL CAPITAL REQUIREMENTS FOR 8-20 ACRE PONDS Dollars Item 11*1,000 Land (190 acres) Pond construction (earth moving, drainage structures, rip-wrap armored) Feeding equipment Disease and parasite control 800,000 2,000 2,000 Harvesting equipment Storage barn Offices Miscellaneous Pumps (8) Installation Motors (8) Fluid drive couplings (8) Belts, splines, circuit breakers and starters Filtration and aeration TOTAL 8,600 6,000 5,000 15,000 3**8,000 3 *1 8 , 0 0 0 *1 8 , 0 0 0 96,000 6,000 100,000 1 ,897,600 APPENDIX TABLE 3-K ANNUAL COSTS FOR THE 8-20 ACRE FISH POND SUBSYSTEM! Item Dollars 2 Annual ownership costs Interest on land investment 9 ,120 Depreciation Pond construction Feeding Disease and parasite control Harvesting equipment Filtration and aeration Storage Pumps . . Motors Fluid drive coupling B e l t s , s p l i n e s , c i r c u i t b r e a k e r s and starters Miscellaneous Interest on investment Pond construction Feeding Disease and parasite control Harvesting equipment Filtration and aeration Storage barn Office Miscellaneous Pumps Motors Fluid drive coupling Belts, splines, circuit breakers starters 3,333 200 11,600 3,200 3,200 750 1,500 32,000 80 80 344 400 240 200 600 13,920 1,920 3,840 and SUBTOTAL Annual operating costs Repairs and maintenance Feeding equipment Disease and parasite control Harvesting equipment Pumps, m o t o r s , a c c e s s o r i e s Miscellaneous equipment 26,667 200 200 1,080 240 114,914 130 66 432 2,500 800 195 AP P E N D I X T A B L E 3-K (continued) Item Dollars Pumping costs Chemicals Fingerlings Feed Manager Labor Taxes, Insurance, bookkeeping and general office overhead ^ Filtration and aeration SUBTOTAL 274,400 7,110 643,911 621,360 1,633,209 Interest on operating capital TOTAL ANNUAL OPERATING COSTS TOTAL COSTS 69,285 1,702,494 1,817,408 25,000 37,500 10,000 10 ,000 Refer to Appendix Table 3-B for Footnotes 1-4. APPENDIX APPENDIX TABLE 4-A INITIAL CAPITAL REQUIREMENTS AND ANNUAL COSTS FOR WASTE HEAT DISSIPATION ALTERNATIVES! Initial Capital Requirements Cooling System Net Unit Output - MW (1) Annual Heat Rate Diff - Btu/kWh Cooling Water Flow - GPM Cooling Water Power Reqmt - kW Make-up Water Power Reqmt - kW Fan Power Reqmt - kW Spray Power Reqmt - kW 1975 Capital Cost for 2 Units Annual Cost (2 Units) Fixed Charges on Investment Circ Water - Power Consumpt Make-up Water Power Consumpt Fan Power Reqmt Spray Power Reqmt Annual Heat Rate Cost Water Treatment Costs/Yr Maintenance Cost/Yr Fixed Charges on Net Capability Once Through 1,336 Base 1,100,000 15,385 Base Base $1,190,800 Base Base Base Base $1,190,800 Cooling Pond :rs)---------- Spray Canal 1,329.4 +71 750,000 6,279 76 1,334.6 +71 750,000 6,279 76 $29,370,000 $24,000,000 $33,148,000 11,190 $26,600,000 Natural Draft 1,329.4 +71 750,000 15,700 76 kW $4,467,000 $1,217,500 $7,000 $757,800 $236,600 $33,100 $175,700 $6,894,700 $1,190,800 $5,703,900 Mechanical Draft 1,334.6 +85 750,000 15,700 76 4,642 $3,650,000 $1,217,500 $7,000 $293,900 $907,200 $236,600 $53,100 $42,600 $6,407,900 $1,190,800 $5,217,100 $5,042,000 $487,000 $7,000 $4,046,000 $487,000 $7,000 $757,800 $118,300 (2) $10,000 $175,700 $6,597,800 $1,190,800 $5,407,000 $708,500 $757,800 $118,300 (2) $40,000 $42,600 $6,207,200 $1,190,800 $5,016,400 ^■These costs were used as a basis for computing the values used in Chapter IV. were made to make the data comparable for this study. Minor modifications 197 A P P E N D I X T A B L E 4-B I NIT IAL CA P I T A L R E Q U I R E M E N T S FOR T HE G E N E R A L PIPING AND D I S T R I B U T I O N S Y S T E M FO R MOD ELS I AND III Item Pumps1 1. At 2. At 3. At 4. At power plant to subsystems fish pond to reservoir soil warming plot to reservoir reservoir to plant^ TOTAL PUMP COSTS Piping costs 1. To soil warming plot from plant 1,100* at 1.75' diameter Materials Installation 1 ,1 7 5 * at 1 .2 5 ' diameter Materials Installation 2. From soil warming to reservoir 2 X 200* at 1.25’ diameter Materials Installation 3. From plant to reservoir 2 X 200' at 11* diameter Materials Installation 4. From reservoir to plant 3 X 200* at 1 0 ’ diameter' Materials Installation 5. Supply and return lines for fish ponds 2 X 450* at 11* diameter Materials Installation 4,200* at 11* diameter Materials Installation 4 X 350* at 8.5' diameter Materials Installation 4 X 650* at 8.0* diameter Materials Installation 4 X 650* at 7 .0 ' diameter Materials Installation Dollars 1,925,000 706,275 30,000 1,612,500 4,273,775 7,865 7,685 4,725 4,725 1,680 1,680 80,540 38,000 101,340 48,000 183,150 85,500 856,170 400,000 199,570 85,400 300,300 143,000 234,570 114,400 198 APPENDIX TABLE 4-B (continued) Item 4 X 650' at 6.0* diameter Materials Installation 5 X 650’ at 5.0’ diameter Materials Installation 4 X 500’ at 3.5’ diameter Materials Installation 650' at 7 -51 diameter Materials Installation 6 5 0 ' at 10’ diameter Materials Installation 650' at 11.0' diameter Materials Installation 350’ at 11.0’ diameter Materials Installation 650' at 8.5' diameter Materials Installation 6 5 0 ' at 4.5' diameter Materials Installation 100’ at 2.5* diameter . Materials Installation 1,650’ at 10.0’ diameter Materials Installation 2 X 1,650' at 9' diameter Materials Installation TOTAL PIPING COSTS Total Initial Capital Investment Dollars 171,600 102,960 150,150 104,979 48,400 40,000 62,205 31,850 120,185 58,500 132,275 61,750 71,347 33,250 92,657 39,650 24,310 19,500 1,320 1,320 278,685 136,950 536,250 227,700 5,453,460 9,727,235 ^"Cost for pumps is Inclusive of motor, belts, splines, circuit breakers, and starter. 2 pump. It Is assumed that power plant will contain condenser 199 A P P E N D I X T A B L E 4-C A N N U A L CO STS F O R T H E G E N E R A L PIP ING AN D D I S T R I B U T I O N S Y S T E M F O R M O D E L S I AND III Dollars Item 347,401 Depreciation1 Interest on Investment 2 389,089 SUBTOTAL Annual operating costs Repairs and maintenance^ Pumping costs Manager Labor Miscellaneous h Interest on operating capital TOTAL ANNUAL OPERATING COSTS 736,490 486,362 3,379,515 - 3 0 ,000 30,000 30,000 152,078 4, 8 4 4,445 Depreciation is calculated by the straight-line method. For simplicity, the expected life of capital items is assumed to be 28 years with zero salvage value for those assets at that time. p Interest on investment is equal to 8 percent of onehalf of initial capital costs. ■3 Repairs and maintenance are estimated to be 5 percent of initial capital investments. 4 Interest on o p e r a t i n g costs Is e q ua l to 9 percent on o ne - h a l f of m a j o r a n nual o p e r a t i n g costs (pumping costs). 200 APPENDIX TABLE 4-D INITIAL CAPITAL REQUIREMENTS FOR THE GENERAL P I P I N G A N D D I S T R I B U T I O N S Y S T E M F O R M O D E L II Item Pumps 1. 2. 3. 4. 1 At At At At power plant to subsystems fish pond to reservoir soil warming plot to reservoir reservoir to plant2 TOTAL PUMP COSTS Piping costs To soil warming plot from plant 1. (1,675* of 1.75* diameter) Materials Installation From soil warming to reservoir 2. (2,250T of 1 .2 5 * diameter)'' Materials Installation 3- 4. Dollars 1,612,500 470,850 58,650 1,612,600 3,754,500 11,900 11,900 9,450 9,450 Supply and return lines for plant to plant 2 X 200' at 11' diameter 81,540 Materials 38,000 Installation 2 X 200' at 11* diameter ^ * 81,540 Materials Installation 38,000 1 X 2 0 0 ’ at 10' diameter Materials 33,780 Installation 19,000 Pipes to fish ponds 5 5 0 * at 9*5* diameter Materials 91,163 Installation 41,800 3,300' at 6.5* diameter Materials 257,730 Installation 141,735 350' at 6.5* diameter Materials 27,335 Installation 15,033 1,300' at 5.5* diameter Materials 71,500 Installation 47,950 1,300' at 4.5' diameter Materials 48,625 39,000 Installation 201 AP PEN DIX TABLE 4-D (continued) Item 1,300' at 3.0' diameter Materials Installation 5. Out of fish pond to reservoir 650' at 4' diameter Materials Installation 650' at 5 f diameter Materials Installation 650* at 7* diameter Materials Installation 400* at 7.5' diameter Materials Installation TOTAL PIPING COST Total Initial Capital Investment- Costs Dollars 24,310 24,310 20,020 20,020 30,030 25,995 58,630 38,600 38,280 29,600 1,426,226 5,180,726 Cost for pumps is inclusive of motor, belts and splines, circuit breaker, and starter, if appropriate, and installation. p It is assumed the power plant will contain the con­ denser pumps. 202 A P P E N D I X T A B L E 4-E A N N U A L COSTS FO R TH E G E N E R A L PIP ING D I S T R I B U T I O N S Y S T E M F OR M O D E L II Item Do llars Depreciation1 185,026 Interest on invest m en t ^ 207,329 S UB T OT A L Annual o p e r a t i n g costs ^ Repa irs and m a i n t e n a n c e P um p i n g costs Manager Labo r Miscellaneous Interest on o p e r a t i n g capital** T O T A L A N N U A L O P E R A T I N G COSTS 392,355 259,036 2,793,049 30,000 30,000 30,000 125,087 3,690,127 F or the sake C a l c u l a t e d by the s t r a i g h t - l i n e method. of simplicity, life of ca p it a l items is a ssumed to be 28 years w i t h zero salv age value. 2 Interest on investm en t is a cash cost and equal to 8 percent of o n e- h a l f of the in itial ca pital costs. 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