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This is to certify that the

thesis entitled

Computer Modeling and Evaluation of a

Cometabolic Sequencing Batch Reactor

presented by

Robert A. Solak Jr.

has been accepted towards fulfillment
of the requirements for

M. S . degree in Environmental
Engineering

 

 

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Major professor

Date 3/971/78

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

LIBRARY

Michigan State
University

 

 

 

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to remove this checkout from your record.
To AVOID FINES return on or before date due.

 

MTE DUE DATE DUE DATE DUE

 

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E23132881

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

use chlfiCIDdeDmpflG—nu

 

COMPUTER MODELING AND EVALUATION OF A COMETABOLIC
SEQUENCING BATCH REACTOR
By

Robert A. Solak Jr.

A THESIS

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

MASTER OF SCIENCE

Department of Civil and Environmental Engineering

1998

ABSTRACT

COMPUTER MODELING AND EVALUATION OF A COMETABOLIC
SEQUENCING BATCH REACTOR

By

Robert A. Solak Jr.

Trichloroethylene, a common industrial solvent and pollutant, has been demonstrated to
be degradable by cometabolism using phenol as a growth substrate. Competitive
inhibition for oxygenase enzymes has created problems in implementing cometabolism
as a treatment alternative for trichloroethylene. Intermittent feeding strategies, with
separate time periods for consumption of the two substrates, have been developed to
avoid such problems. Sequencing batch reactors are one system capable of separating

periods of substrate consumption.

In this study, a model of an aerobic sequencing batch reactor is developed and modeled
by computer. Predictions of substrate concentrations, biomass concentrations, and the
mass of trichloroethylene lost to air stripping are compared to observations made from
laboratory scale reactors. Parameters used in the model are determined by independent
experiments. A sensitivity analysis is also performed on the model to determine the

relative importance of various parameters to model predictions.

Dedicated to all those graduate students
who have seen deadlines come,
and deadlines go...

ACKNOWLEDGEMENTS

I would like to offer many thanks to my advisor, Dr. Craig Criddle, who had an answer

for every question and suggestions for every problem.

I would also like to thank my committee members, Dr. David Wiggert and Dr. Robert
Hickey for their comments and suggestions as well as Wang-Kwan Chang and Stephen
Callister for their tireless efforts to maintain and care for the reactors that I merely
“borrowed” on occasion. To Stephen, I owe a special thanks for running phenol samples

and lending some data when I needed it.

To my parents I am eternally grateful for all they did to give me my opportunities in life.
To my siblings and siblings-in-law, I thank them for their unending question “Is your
thesis done yet?”. And lastly, I will always be thankful to my wife for all the love,

companionship and support she gave me as I did what I had to do.

TABLE OF CONTENTS

LIST OF

TABLES ............................................................................................................................ vii

LIST OF

FIGURES .......................................................................................................................... viii

NOMENCLATURE ........................................................................................................... ix

CHAPTER 1

INTRODUCTION ............................................................................................................... 1

CHAPTER 2

MODEL DEVELOPMENT ................................................................................................. 5
Phenol Degradation .......................................................................................................... 5
TCE Degradation .............................................................................................................. 9
Mass Balance Equations ................................................................................................. 11

CHAPTER 3

MATERIALS AND METHODS ....................................................................................... l7
Reactor Design and Maintenance ................................................................................... 17
Initial Degradation Rate Studies ..................................................................................... 18
Measurement of Volatile TCE Loss During Fill Cycle .................................................. 20
Measurement of Liquid Phase TCE ................................................................................ 20
Phenol Measurements ..................................................................................................... 21
Kinetic Parameters .......................................................................................................... 21

CHAPTER 4

PARAMETER DETERMINATION ................................................................................. 26
Yield on Phenol, Y ......................................................................................................... 26
Observed Specific Growth Rate of TCE-degrading Biomass, pap. ................................. 27
Endogenous Decay Coefficient, b .................................................................................. 29
TCE-degrading Biomass Decay Coefficient, bam ............................................................ 29
Transformation Capacity, Tcb .......................................................................................... 30
Zero-Order Phenol Degradation Coefficient, k° ............................................................. 30
TCE First-Order Rate Coefficient, k’ ............................................................................. 31

CHAPTER 5

COMPUTER MODELING AND EXPERIMENTAL VERIFICATION ......................... 32

MathCAD Modeling ....................................................................................................... 32

Experimental Results ...................................................................................................... 34
One Population Model .................................................................................................... 37
Two Population Model ................................................................................................... 44

CHAPTER 6

MODEL SENSITIVITY AND PARAMETER UNCERTAINTY .................................... 45
Relative Sensitivity ......................................................................................................... 45
Parameter Uncertainty .................................................................................................... 48

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS ............................................................ 55
Computer Modeling ........................................................................................................ 55
Parameter Determination ................................................................................................ 55
Recommendations .......................................................................................................... 5 6

REFERENCES .................................................................................................................. 58

APPENDIX A

MATHCAD PROGRAMMING ........................................................................................ 60

APPENDIX B

MASS TRANSFER COEFFICIENT DETERMINATION .............................................. 63

vi

LIST OF TABLES

Table 3-1 SBR Schedule and Activity ............................................................................... 17
Table 3-2 Reactor Conditions ............................................................................................ 18
Table 3-3 Gas Chromatograph Operating Parameters ....................................................... 19
Table 4-1 Kinetic Parameters Used in Computer Modeling .............................................. 26
Table 5-1 Solids Data ........................................................................................................ 41
Table 6-1 Relative Sensitivity ............................................................................................ 48
Table A-1 MathCAD Variable Legend .............................................................................. 62

vii

LIST OF FIGURES

Figure 1-1 Oxygenase Mediated Co-metabolism ............................................................... 2
Figure 5-1 MathCAD Programming Logic ...................................................................... 33
Figure 5-2 TCE in the Reactor .......................................................................................... 34
Figure 5-3 Phenol in the Reactor ...................................................................................... 36
Figure 5-4 Solids Concentration over Time ..................................................................... 37
Figure 5-5 One-population Model Predictions ................................................................. 38
Figure 5-6 TCE Model and Data ....................................................................................... 40
Figure 5-7 Phenol Model and Data ................................................................................... 43
Figure 6-1 Uncertainty Modeling for Yield ...................................................................... 50
Figure 6-2 Uncertainty Modeling for k’ ........................................................................... 51
Figure 6-3 Uncertainty Modeling for k° ............................................................................ 52
Figure 6-4 Uncertainty Modeling for b ............................................................................. 53
Figure A-l MathCAD Programming Worksheet .............................................................. 61
Figure A-2 MathCAD Equation Matrix ............................................................................. 62
Figure A-3 MathCAD Program ......................................................................................... 63
Figure 8-1 Mass Transfer Coefficient Relationship .......................................................... 65

viii

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NOMENCLATURE

endogenous decay rate (l/day)

Non-growth substrate concentration (mg/L)
half saturation coefficient (mg/L)

zero-order rate coefficient (1/day)

specific growth rate (l/day)

dimensionless Henry’s constant

inhibition constant

first-order TCE degradation rate (L/mg-day)
substrate utilization rate (l/day)

Mass (mg)

liquid flowrate (L/hr)

gaseous flowrate (L/hr)

Growth substrate concentration (mg/L)

time (days)

Transformation capapcity (mg TCE/mg cells)
True transformation capacity (mg TCE/mg cells)
liquid volume (L)

yield coefficient (mg TSS/mg phenol)
Biomass concentration (mg/L)

subscripts

a

act—~13

active organisms
phenol-degrading organisms
TCE-degrading organisms
liquid phase

gaseous phase

CHAPTER 1

INTRODUCTION

Co-metabolism is defined as the degradation of non-growth substrate by microorganisms
which receive no apparent benefit from the transformation. Lack of specificity of
enzymes and cofactors, typically induced by growth substrate, permits the fortuitous
degradation of non-growth substrates. Many environmentally significant compounds have
been shown to be biodegradable by co-metabolism. Methanotrophic communities have
demonstrated the ability to degrade many halogenated aliphatic compounds, alkanes and
aromatic compounds. Other compounds capable of being co-metabolized include:
polycyclic aromatic hydrocarbons, alkyl-substituted cyclic hydrocarbons,

monofluorobenzoates and polychlorinated biphenyls.

Trichloroethylene (TCE) is a chlorinated aliphatic hydrocarbon. It has been widely used
as an industrial solvent and degreaser. Spillage, dumping and improper storage have
caused TCE to be one of the most frequently found groundwater contaminants. Aerobic
co-metabolism of TCE was first noted by Wilson and Wilson (1985). Since then, a
variety of microorganisms have been shown to be capable of degrading TCE by the
production of oxygenase enzymes induced by various growth substrates such as methane,
propane, toluene, phenol and others. This study used phenol as a growth substrate and as

an oxygenase inducing compound to aerobically degrade TCE.

2

Typical oxygenase co-metabolism reactions for growth substrate are presented in Figure

1-1 (Chang and Alvarez-Cohen, 1995).

(I) on
Growth substrate 0 .. ’, Canboljc _ +
NAOMI-I 9 H0 m
A memo NADm~ NAomH . a.
L ............... J
mum
(b) 02
Comcubolic substrate 03739!!! Toxic

NADMH o H' 4
NM

 

 

Figure 1-1 Oxygenase Mediated CO-metabolism
The above figure identifies some problems inherent in co-metabolism. First, toxic
intermediates can damage the cells or the enzyme itself, reducing the cells ability to
degrade non-growth substrate. Second, many co-metabolic reactions require reducing
power in the form of NAD(P)H. In the absence of growth substrate to provide
regeneration of NAD(P)H, it is possible that co-metabolic transformation can become

limited by lack of reducing power.

Various models have been proposed to describe co-metabolism. Traditional Michelis-
Menten expressions for degradation and the Monod equation for cell growth have been
shown to inadequately describe co-metabolic reactions. Alvarez-Cohen and McCarty
(1991) reported that linearized Monod equations yielded artificially elevated kinetic
parameter estimates. These errors result from the failure of the Michelis-Menten/Monod
equations to account for loss of transformation activity, product toxicity and competitive
inhibition. Alvarez-Cohen and McCarty (1991) incorporated the effects of product

toxicity by using a microbial concentration that decays in proportion to the

3

transformation capacity. Criddle (1993) proposed a general co-metabolism model which
accounted for cell growth, endogenous decay, product toxicity, competitive inhibition,
and enhancement of degradation rates by addition of growth and energy substrates. This
model was evaluated experimentally and found to be satisfactory for methanotrophic co-
metabolism of TCE (Chang and Criddle, 1997). Chang and Alvarez-Cohen (1995a)
proposed a model that further accounted for possible loss of reducing power as a limiting
factor of non-growth substrate degradation. Due to a high growth substrate to non-growth
substrate ratio used in this study it was assumed that limitations due to loss of reducing
power would not occur. This work proposes two models based on Criddle (1993): a one-
population model in which all biomass is assumed to be capable of degrading TCE and a
two-population model in which phenol degrading microorganisms are divided into two

subsets - TCE degrading bacteria and non-TCE degrading bacteria.

Much of the research concerning aerobic, mixed-culture co-metabolism of TCE has been
concerned with in-situ groundwater applications and chemostatic reactors, in which both
growth substrate and non-growth substrate are present at the same time. However, it has
been demonstrated that phenol and TCE compete for the same oxygenase enzymes.
Chang and Alvarez-Cohen (1995b) reported that although there is some apparent benefit
to adding low concentrations of growth substrate (< 0.1 mM), degradation rates begin to
decrease as higher concentrations (> 0.1 mM) are added. In response to these indications
of competitive inhibition, intermittent feeding schemes and sequencing batch reactors

have been investigated to avoid these problems (Segar et al., 1995).

Shih (1995) numerically simulated and evaluated an aerobic sequencing batch reactor that
degraded TCE using phenol as a growth substrate. Using a recharge stage to feed phenol
and a separate fill stage to feed TCE, competitive inhibition was avoided. Computer
modeling was able to predict TCE levels in the reactor. Chang (1996) confirmed the long-
term ability of a phenol-degrading community to degrade TCE. He further reported on
various methods of measuring the stability of mixed microbial communities, and the
effects of long-term exposure on the adaptation of communities to non-growth substrates

and feeding perturbations.

In this study, a dispersed growth, aerobic sequencing batch reactor was used to co-
metabolically degrade TCE using phenol as a growth substrate. Two models - a one-
population model and a two-population model - are modeled by computer using kinetic
parameters determined experimentally. Model predictions were compared to data
gathered from the laboratory scale sequencing batch reactors. A theoretical sensitivity
analysis was also performed to gauge the importance of various kinetic parameters to the

model.

CHAPTER 2
MODEL DEVELOPMENT

Phenol Degradation

Cell growth is most commonly described by the Monod Equation

Muss
= 2-1
# Ks + s ( )

 

where S = substrate concentration (mg/L), u = specific growth rate (l/day), um =

maximum specific growth rate (1/day) and K5 is the half saturation coefficient (mg/L).

Some argument has been made that phenol is a self-inhibitory growth substrate and that it

should be modeled using the Haldane expression

_M&S_ (2-2)

S
KS+S+—K—l

y:

where Kl = inhibition constant. However, Auteinrieth et al.(l991) reported that at low
phenol concentration (100 mg/L) degradation follows zero order kinetics. Shih (1995)
also reported zero order degradation, with respect to substrate concentration, for a phenol
concentration of 150 mg/L. In this reactor, phenol concentration remained below 30
mg/L, therefore zero order kinetics were used to model phenol degradation. Zero order
kinetics are described by the equation

dS_

— _ -k°X -
dt (2 3)

6

where k° is the zero-order rate constant (mg phenol/mg biomass - day) and X is the
biomass concentration (mg/L). This expression for substrate degradation may be

combined with the following relationship:

dS
Y(- a?) = ”X (M)

where Y = yield of unit biomass per unit substrate (mg cells/mg substrate), yielding
y = Yk (2'5)
This equation, however, represents growth only. To obtain a net specific growth rate, an
endogenous decay term is added to represent cell death, cell lysis, etc.
,u = Yk° — b (2-6)
where b = endogenous decay rate (l/day). This equation represents the net specific

growth rate expression for growth on phenol used in this study.

Change in biomass concentrations is expressed by the equation
— = p X (2-7)

Where X is the concentration of active phenol-degrading biomass (mg/L). Combining
equation (2-7) with (2-6) yields

dX
E = Yk°X — bX (2-8)

which represents the growth of phenol-degrading cells.

7
Some phenol-degrading cells are known to be capable of degrading TCE by co-

metabolism, while others are not. It is possible, then, to divide the population of phenol
degrading cells into two sub-populations: TCE-degrading cells and non-TCE-degrading
cells. This division of population, however, presents experimental difficulties in the
enumeration of the subdivisions. In this study, two models were developed and tested: a
two-population model, in which microorganisms are classified as described above, and a
one-population model, which views the microbial population as completely comprised of

TCE-degrading organisms. Model development continues along these two courses.

Two Population Model
In this model, biomass capable of degrading phenol was subdivided into fractions that

can degrade TCE, X and that cannot degrade TCE, X,p where subscripts denote: a,

as)"
active organisms, p, phenol-degrading organisms, and t, TCE-degrading organisms.
These fractions, however, cannot be differentiated experimentally. It is possible, however,

to indirectly measure the specific growth rate of fraction Xam, pap, (Chapter 3). Thus, an

expression for Xap, can be created:

 

anp,
dt : ”up! xapt (2'9)

where pap, = the specific growth rate. This method of determining this rate includes
effects of endogenous decay and therefore equation 2-9 needs no further modification.
However, for periods during which no TCE is present, a corresponding endogenous decay

for the TCE degrading population b must similarly be developed.

9 app

Determined experimentally, pap, represents the increase in ability to degrade TCE. This
increase may not reflect an increase in actual cells, rather, it may only represent an
increase in the ability of each cell to degrade TCE (e.g. increase in oxygenase enzyme,
replenishing of reducing power). This model assumes that the increase is an actual
increase in cells, as to assume otherwise would demand first the determination of what
process(es) contribute to increased ability to degrade TCE and second, direct enumeration

of such process(es). These ventures are beyond the scope of this study.

Total active biomass, then, is defined as
Xa = Xap + Xapt (2'10)
Expressions for the various types of biomass and phenol concentration can be created:

dX. anp dX

 

“p‘ 2-1
dt dt + dt ( 1)
dxap 0
——dt =Yk xap—bxap (2-12)
d8
3 = .—k°xa (2-13)

It should be noted that Y, b and k° are all assumed to be the same for each division of
biomass. Equations (2-9), and (2-11) through (2-13) comprise the expressions used to
model phenol concentrations and growth of biomass in this work. Other forms of biomass
assuredly exist in the reactor: predators, heterotrophic microorganisms feeding on
decaying cells and degradation by-products, etc. Accurate differentiation of these groups,

however, was not possible and is not addressed by this study.

One Population Model

The one population model assumes that all biomass is TCE-degrading biomass.
Concerning growth on phenol and degradation of phenol, the model may be described by

equation (2-8) and a simple reform of equation (2-13):

anp, o

-—d-t- = Yk Xap, — bXalpl (2-14)

d8

3 = -k°Xap. (2-15)
TCE Degradation

Various models have been introduced to describe co-metabolic reactions. Alvarez-Cohen
and McCarty (1991) demonstrated the failure of traditional kinetics to adequately account
for significant properties of co-metabolism such as the loss of ability to degrade non-
growth substrate during exposure. They introduced the transformation capacity concept.
Transformation capacity is defined as

Tb - 51-9 (2 16)

° ' dX
where dC is the mass of contaminant transformed (mg) and dX is the mass of cells
inactivated by the transformation (mg). This equation, is linked with traditional Michelis-

Menten degradation kinetics

d—C— kc x 217
dt- KS+C (‘)

 

10

and upon integration of equation 2-16. yields the following model for substrate

concentration:

1
dc k C(Xo — idea — C»

_=_ 2-18
dt KS+C ( )

 

where X0 = initial biomass concentration, KS is the half saturation coefficient (mg/L) and
k is the maximum substrate utilization rate (mg substrate/mg cell - day). This equation
describes degradation of non-growth substrate in the absence of growth substrate for
resting cells. Criddle (1993), however, commented that the above model neglects
endogenous decay and thus transformation capacity studies were measurements of the
observed biomass transformation capacity rather than the true biomass transformation
capacity, ch'. The true biomass transformation capacity is defined as the mass of non-
growth substrate transformed by a unit mass of cells in the absence of endogenous decay.
The relationship between Tcb and Tc” is expressed:

l kC

b———_—_ :
Tc — b 1 where qc Ks + C
3““??—

 

(2-19)

for resting cells. The expression for q, assumes that TCE degradation follows traditional
Michaelis-Menten kinetics. Others have reported degradation kinetics that are first order
with respect to TCE concentration (Dabrock et al., 1992; Henry and Grbic’-Galic’ 1990;
Oldenhuis et al., 1989),

qc = k'C (2-20)
This expression can be used to augment Criddle’s general model for co-metabolic

reactions in the absence of growth substrate:

ll

1
y =—b—:I_—b-.'I('C (2'21)

which can be rewritten to describe biomass:

dxapr Xapt ,
dt = —bXap, — Wk C (2-22)

 

where the subscripts a, p and t denote active biomass, phenol degrading biomass and TCE
degrading biomass. respectively. This equation, coupled with a first order expression for
substrate degradation,

dC
E = —k'Cx,p, (2-23)

constitute a model for the degradation of non-growth substrate in the absence of growth
substrate. It should be noted that this model assumes that all cell death due to TCE
degradation occurs only among the population capable of carrying out such degradation,
Xam.
Mass Balance Equations

The sequencing batch reactor modeled in this study has five distinct stages: fill, react,
settle, decant and recharge. The recharge stage can be further divided into two stages:
recharge-fill and recharge-react. Mass balance equations for these stages must be
developed. Development of these equations is similar for both the two-population and
one-population models. Except where noted specifically, equations may be applied to

both models with the exclusion, of course, of all equations dealing with X which

ap’

pertain only to the two-population model.

Fill Stage

During the fill stage, 1.00 liter of influent containing TC E was fed to the reactor over a
time period Of 60 minutes. Dilution. degradation, air stripping and sorption to biomass
can affect the concentration of TC E. Sorption of TC E to biomass has been shown to be a
negligible removal process (Shih. 1995) for similar reactors with similar biomass
concentrations. Loss of volatile compounds to air stripping in a sequencing batch reactor
can be described by the equation

ism-p = KL.a(C _ 0") (2-34)
where KLa = overall mass transfer coefficient (l/hr). C = liquid concentration of
contaminant (mg/l.) and C* is the liquid phase concentration at equilibrium (mg/L). In a
reactor where the volume is changing, Km will change. In this study, the following

empirical relationship between KLa and reactor volume for TCE was determined

experimentally (Appendix B)
Km = 1.73 892W" 3""33) (2-25)
where V is the reactor liquid volume (L). C* is defined

0" Ci 776
_ H (--- )

 

where Cg is the gaseous phase concentration (mg/L) and H is the dimensionless Henry’s

constant for TC E. In this study. a dimensionless Henry’s constant of 0.392 was used

(Gosset. 1987).

13

An initial mass balance equation for TCE in the reactor liquid can be written

d(CV)
dt

 

_ __ _ v _ _ at: 2-
_COQ CgQg an CV KL,a(C C )v ( 27)

pt
where Co = TC E concentration in influent (mg/L), Q = Influent flowrate (L/hr), Q, = Air
flowrate through reactor and V is the reactor liquid Volume (L). The terms in the
equation represent the following: mass in influent, mass in exhaust gas, mass removed by
microbial degradation and mass removed by air stripping. Separating the left side of the

equation and noting that dV/dt = Q:

dC
at— v = COQ — CgQg — k'X,,,CV — KL,,(C — C*)V - CQ (2-28)

Dividing through by V and further manipulation yields

dC Q,
—=(Co—C)%-Cgv—

C.
dt k' Xap,C — K,«a(C - —*) (2-29)

H

TCE degrading biomass will undergo three processes during the fill period, dilution,

endogenous decay and decay due to product toxicity. A mass balance may be written:

d(Xapt V) q
dt bx apt ch

 

XamV where qc = k'C (2-30)

which, upon separation, rearrangement and substitution of dV/dt = Q, yields

dX... qc Q
dtp = —bXap, - TIN—fix”, - anm (2-31)

 

Active cells that do not degrade TCE, Xap‘ undergo only dilution and endogenous decay

axa Q
dt " = —bXap — anp (2-32)

 

Equations (2-27), (2-29) and (2-30) represent a model for the fill stage for substrate and

biomass concentrations.

React Stage

The react stage is identical to the fill stage in every respect with the exception of dilution.

Batch kinetics result, and equations (2-27), (2-29) and (2-30) reduce to the following:

 

dC Q, , Cg
dt _ _(:g V — k XamC — K,,a(C — H ) (2-33)
deI qc ,
dt = -_bXap, — -i,,—.xap, where qc = k C (2-34)
dxap bX 2 35
dt — _ 3" ( - )

Settle Stage

During the settle stage, neither growth substrate nor non-growth substrate will be present.
Only anoxic endogenous decay will occur. To avoid complex equations dealing with
sludge settling rates, equations for biomass will be based on mass rather than
concentration using the entire liquid volume as a control volume. The mass balance

equations for biomass may be written as follows:

de
dt = —bMap, (2-36)

 

___ap = —bM (2'37)

where M = mass of biomass (mg). Generally, modeling of reactor concentrations during a
settling period is not of much interest. Modeling of mass however is significant, as
reactions in later stages will depend on an accurate biomass prediction. Modeling during
the settling stage allows for a correct initial biomass concentration condition to be

calculated when the reactor returns to a completely mixed state in later stages.

Mutt—Stags

After the settling stage, liquid is decanted from the top of the reactor. This study assumes
that all biomass settles completely during the settle stage. Therefore, mass balance

equations for the decant period are the same as those used during the settle period.

Recharge Stage

During the recharge stage, phenol was added as a growth-substrate. Net cell growth and
phenol degradation during the recharge—react stage is modeled by equations (2-9), (2-11)
and (2-13) for the two-population model, and by equations (2-14) and (2-15) for the one-
population model. However, during the recharge-fill portion of the recharge stage,

dilution must also be modeled.

anp O Q
dt = Yk xap — bXap — anp (2-38)

 

dxapt Q
dt = l’laptxapt — V xapt (2-39)

 

9§--Q-(S° —S)—k°X

dt ‘ v (2'40)

a

where S° is the influent phenol concentration.

CHAPTER 3

MATERIALS AND METHODS
Reactor Design and Maintenance
Reactor Design
The sequencing batch reactors consisted of two Wheaten Mini-fermenters. Syringe
pumps were used for phenol and TCE injection. Peristaltic pumps were used for influent
and effluent pumping. A timer/controller was used to control all pumping and injecting
apparatus. Air was supplied by two variable control aquarium pumps set at a flowrate of
approximately 100 mL/rnin. Tygon tubing was used for all gas flows and teflon tubing
was used for all liquid flows. Reactor temperature was maintained at a constant 23 °C by
cycling water from a water bath through a heating/cooling element immersed in the

reactor.

Reactor Schedule and Maintenance
Table 3-1 summarizes reactor activities and volume throughout the cycle.

Table 3-1 SBR Schedule and Activity

 

 

Time Activity Reactor Volume
0:00-1:00 Influent Pump, TCE Pump, aeration, 1225 mL -) 2200 mL
mrxrng

1:00- 4:00 Aeration, mixing 2200 mL

4:00-5:00 Settling 2200 mL

5:00-6:00 Decant Pump 2200 mL —> 1200 mL
6:00-6:30 Phenol Pump, aeration, mixing 1200 mL -> 1225 mL
6:30-12:00 Aeration, mixing, manual wasting 1225 mL

 

 

 

l7

One-hundred mL of reactor cells were wasted once a day (every other cycle). After
wasting, 100 mL of reactor media was injected back into the reactor to make up for lost

volume.

Table 3-2 lists reactor conditions.

Table 3-2 Reactor Conditions

 

TCE Influent Concentration 5.0 mg/L
Mass TCE Added per Cycle 5.0 mg

TCE Influent Flowrate 1.0 L/hr

Air Flowrate 100 mL/min
Phenol Influent Concentration 7200 mg/L
Mass Phenol Added per Cycle 180 mg
Phenol Influent F lowrate 50 mL/hr
Reactor Temperature 23 °C

 

 

 

 

Reagents

Trichloroethylene was obtained from Aldrich Chemicals Co., Milwaukee, WI. Reactor
media contained the following compounds: 2.13 g/L NazHPO,” 2.04 g/L KHZPO” 0.99
g/L (NH,)2SO4, 66 mg/L CaCIZ-ZHZO, 248 mg/L MgC12-6HZO, 0.5 mg/L FeS04, 0.4 mg
ZnSO,-7HZO, 0.02 mg MnC12o4H20, 0.05 mg/L C0C12-6HZO, 0.01 mg/L NiC12.6HzO,

0.015 mg/L H3BO3 and 0.25 mg/L EDTA. pH of the media was 6.8.

Initial Degradation Rate Studies

Trichloroethylene

19

Initial degradation rate studies of trichloroethylene were conducted by spiking sequencing
batch reactor cells with trichloroethylene and measuring the decrease in trichloroethylene
concentration over time. One mL of reactor liquid was added to 4 mL of reactor media in
20 mL glass vials. Three samples of each reactor were taken. The vials were then spiked
with approximately 2 uL saturated trichloroethylene solution (approximately 1100 mg/L)
and crimp sealed with butyl seals. After shaking for approximately 3 minutes, 0.1 mL of
headspace gas was injected into a Hewlett Packard Model 5890 gas chromatograph (GC)
equipped with an electron capture detector (ECD). GC/ECD operating parameters are
shown in Table 3-3. Headspace samples were injected four times at approximately 10

minute intervals.

A dimensionless Henry’s constant of 0.392 for trichloroethylene (Gossett, 1987) was
used to determine the liquid concentration of trichloroethylene in the vials. Using

corresponding solids data, degradation rates were used to calculate k’.

Table 3-3 Gas Chromatograph Operating Parameters

 

 

 

 

 

 

Parameter GC/E CD GC/F ID
Injection Temperature (°C) 250 250
Detector Temperature (°C) 350 250
Oven Temperature (°C) 90 90
Initial Temperature (°C) 90 90

Final Temperature (°C) 90 90
Carrier Flow / Gas (mL/min) 11.2 He 12.8 N2

 

20

Standards were prepared by injecting into the chromatograph a known volume of solution
of TCE in methanol. The TCE in methanol solution was prepared by adding a weighed

amount of TCE to a known volume of methanol.

Mal Suspended Solids

The method used to determine the total suspended solids concentration is provided in
Standard Methods (1995). Filters (0.2 pm, 47 mm diameter Gelman Sciences, Ann
Arbor, Michigan) were rinsed with approximately 50 mL of deionized water, dried
ovemight and weighed. After filtering 5.00 mL of reactor fluid, the filters were dried
overnight and weighed. The difference between the two measurements when divided by

the sample volume yields the total suspended solids concentration.

Measurement of Volatile TCE Loss During Fill Cycle
TCE in the gaseous phase in the reactor was measured by injecting 0.1 mL of reactor
headspace into a GC/ECD. Operating conditions of the GC/ECD are summarized in

Table 3-3. Standards preparation was the same as for the initial degradation rate studies.

Measurement of Liquid Phase TCE
In order to measure liquid phase TCE concentrations during the fill and react stages, 4.93
mL samples of reactor liquid were placed into vials containing 0.07 mL of 2 N HCl

solution in order to stop cell activity. Vials were crimp sealed and placed on a rotary

21
shaker at 300 rpm for at least 3 minutes. 0.1 mL of vial headspace was analyzed by

GC/ECD.

Phenol Measurements

Phenol samples were analyzed using high pressure liquid chromatography (HPLC). Cell
samples were injected into sampling vials through 0.2 pm syringe filters. The water
HPLC (Perkin Elmer Series 200) was equipped with a column (Hypersil Elite C18, 4.6
mm dia., 25 cm. length, 5 um particle size, Catalog No. 76884501) and UV detector
(LC235C Photodetector) and was operated isocratically ((60% acetonitrile + 40% water)
at a total flow rate of 1.0 mL/rnin. Detector wavelength was 255 nm and injection volume

was 25 uL. Detection limit was 1 mg/L.

Phenol (obtained from IT Baker, purity 99.9) standards were prepared by weight.

Standards and samples were stored at 4 °C in absence of light until analysis.

Kinetic Parameters

Yield on Phenol Y

 

To determine the yield on phenol, 10.0 mL of cells were removed from the reactor,
placed in an Erlenmeyer flask and diluted with 90.0 mL of reactor media. The diluted
cells were then injected with a known amount of phenol. The flask was shaken at 300
rpm and remained open to air to provide oxygen for aerobic metabolism. A sponge cap

was used to prevent infiltration of airborne solids. At the time of cell removal, the total

22

suspended solids (TSS) concentration in the reactor was measured. After allowing time
for phenol degradation, TSS concentration in the flask was measured. The increase in

T88 was divided by the mass of phenol added to obtain Y.

It should be noted that the yield measured in this way is an “observed” yield rather than a

true yield coefficient (see Chapter 4).

chific Growth Rate of TCE-deggding Biomass, gm
During growth on phenol, TCE degrading bacteria repair damage caused by product

toxicity and are induced to produce more TCE-degrading enzyme. These phenomena
cause an effective increase in the biomass capable of degrading TCE, X3“. However,
since direct enumeration of this fraction of the total biomass was not possible, change in
biomass concentration was expressed using the specific growth rate. The specific growth
rate was determined by measuring the initial TCE degradation rate for a subsample of
cells, spiking those cells with phenol, and measuring the initial TCE degradation rate
after the degradation of phenol was completed. Assuming that the increase in degradation
rate is proportional to the specific growth rate, the specific growth rate of the TCE-
degrading biomass can be effectively represented by the natural logarithm of the ratio of

initial degradation rates before and after phenol consumption.

Endogenous Decay, b

23

Approximately 75 mL of reactor cells were removed to conduct endogenous decay
experiments. The cells were placed on a shaker table in an Erlenmeyer flask capped only
with a sponge to prevent airborne contaminants from entering the culture. Over a period
of seven days, five biomass concentration measurements were taken. A log-normal plot
of concentration vs. time yields a straight line with a slope equal to the endogenous decay

rate.

Endogenous Decay of TCE Degrading Population, bap,

 

As direct enumeration of the biomass fraction Xapt was not possible, the endogenous
decay rate was determined indirectly, similar to the method used for the determination of
um. Approximately 50 mL of reactor cells were removed from the reactor and placed on a
300 rpm shaker table. Periodically, sub-samples were removed and the initial degradation
rate was determined. A log normal plot of the ratio of degradation rate at any time t to the

rate at the beginning of the experiment versus time yields a line with slope bam.

Transformation Capacit_v_, T,b

Transformation capacity experiments were conducted by spiking reactor cells with a
known amount of TCE and measuring the total mass of TCE degraded. 9.75 mL of
reactor cells were placed with 10.00 mL reactor media in a 45 mL screw-top amber glass
vial fixed with a Mininert valve. 0.250 mL of saturated TCE solution was injected into
the vial and the vial was placed on a shaker table. A reactor solids measurement at the

time of cell removal provided for the calculation of mass of cells in the vial.

24
Measurements of TCE in the vial headspace were analyzed on a GC/FID. When TCE

degradation had ended, the mass of TCE degraded was divided by the mass of cells

present in the vial, yielding the observed transformation capacity.

Standards for the GC/F ID were created by injecting a known amount of TCE saturated
solution into a make-up volume of reactor media. The same size glass vials and Mininert
valves as used in the transformation capacity determination were used for the standards
preparation. The total volume of TCE solution and make-up volume was the same as that

in the transformation capacity experiments.

TCE Rate Coefficient k’

 

At the low concentrations observed in the reactor, TCE degradation is assumed to be first
order with respect to concentration

dC
a = k'CXapt (3-1)

Five mL of reactor cells were placed in glass vials, spiked with 4 uL TCE saturated water
and crimp sealed. TCE concentration was measured by headspace analysis using
GC/ECD. A plot of the natural logarithm of TCE concentration versus time yields a
straight line with a slope equal to the product of biomass concentration and k’. Dividing
this determined slope by a measured biomass concentration yields the TCE rate
coefficient. It should be noted that no experimental method was used to separate biomass
fractions. Thus, in determining k’, a total suspended solids measurement is used rather

than a true measurement of X3“.

25

Zero-order Phenol Degradation Coefficient¢°

 

Approximately 20 mL of reactor cells were removed from the reactor to determine k°.
The cells were spiked with phenol and subsamples were removed and filtered with
syringe filters. F iltrate was analyzed for phenol concentration using high pressure liquid
chromatography (HPLC). A plot of phenol concentration versus time yields a straight line
with a slope equal to the product of k° and X, Dividing this slope by a biomass
concentration measurement yields the zero-order coefficient, k°. It should be noted that
the measurements used in this study to represent biomass concentrations were total

suspended solids measurements, as enumeration of the different fractions of biomass was

not possible.

CHAPTER 4

PARAMETER DETERMINATION
Yield on Phenol, Y
To determine yield on phenol, 10 mL of cells were removed from the reactor, placed in
an Erlenmeyer flask and diluted with 90 mL of reactor media. The diluted cells were then
injected with a known amount of phenol. The flask was placed on a rotary shaker table at
300 rpm and remained open to air to provide oxygen for aerobic metabolism. A sponge
cap was used to prevent infiltration of airborne solids. At the time of cell removal, the
total suspended solids (TSS) concentration in the reactor was measured. After allowing
time for phenol degradation, TSS concentration in the flask was measured. The increase
in biomass was divided by the mass of phenol added to obtain Y. Results are presented in
Table 4-1.

Table 4-1 Kinetic Parameters Used in Computer Modeling

 

 

 

 

 

 

 

 

Parameter Control Exposed

Y (mg TSS/mg Phenol) 0.9 1.3 (1 01.3)
p.29, (l/day) 21.5 2.7
b ( 1/day) 0.06-0.3 0.05 (0.02-0.3)
bap,(1/day) 0.2-3.9 0.85 (0.4 - 1.3)

Tcb (mg TCE /mg TSS) 0.38 0.29

k’ (L/mg TSS-day) - 0.2

k° (1/day) - 2.6 i 1.1

 

 

 

 

 

’values in parentheses represent the experimental range of values

A typical yield coefficient for activated sludge is 0.6 mg/mg (Metcalf and Eddy, 1991).
Values for mixed cultures using phenol as a growth substrate range from 0.45 mg/mg
(Beltrame et al., 1980) to 0.9 mg/mg (Autenrieth et al. 1991) with most reporting near

0.55 mg/mg (Kotturi et al., 1991; Chang and Alvarez-Cohen, 1995b).

26

27

It should be noted that in this study, total suspended solids was used to represent biomass.
Under controlled conditions, when the influent flow is known to contain no suspended
solids, this assumption is valid. Other problems, however, arise from using a TSS
measurement to represent biomass in the determination of other kinetic parameters,
particularly in regard to the two-population model. Kinetic parameters such as trap, and bapt
are theoretically specific to the sub-population Xm. However, due to the inability to
differentiate or separate biomass fractions, determination of these parameters had to be
made using TSS measurements. This undoubtedly skewed these parameters, and perhaps

contributed to the failure of the two population model (Chapter 5).

It should also be noted that this method of determining the yield coefficient produces an
observed yield rather than a true yield. This method fails to discount the effects of
endogenous decay during the growth on phenol. For this reason, the models do not
include an endogenous decay term during those periods in the reactor when phenol

concentration is greater than zero.

Observed Specific Growth Rate of TCE-degrading Biomass, um

During growth on phenol, TCE-degrading bacteria repair damage caused by product
toxicity and are induce to produce more TCE-degrading enzymes. These phenomena
cause an effective increase in the biomass capable of degrading TCE, X,,. Typical

representations of changes in biomass, such as the yield coefficient, however, could not

28

be determined directly due to the inability to differentiate between fractions of biomass
(i.e. active biomass, inactive biomass, TCE-degrading biomass, non-TCE degrading

biomass, etc.). Consequently, an indirect expression of biomass change was required.

An assumption was made that the ability to degrade TCE is proportional to the
concentration of TCE-degrading biomass. Based on that assumption, a semi-log plot of
the ratio of initial TCE degradation rates before and after phenol consumption versus time
will yield a straight line with a slope which effectively represents the specific rate of
growth of TCE-degrading biomass. Expressed mathematically,

dC dC
1n(dt)'—ln(dt °
t1 - to

 

u... = (4-1)

where dC/dt represents the initial degradation rates (mg/L/hr), t is time (hours) and
subscripts t and 0 represent the time after phenol consumption and before phenol

addition, respectively. Results of palm experiments are presented in Table 4-1.

Almost an order of magnitude difference exists between the control reactor and the
exposed reactor measurements of pm. It is possible that the TCE-degrading population in
the exposed reactor must devote more energy and mass to repairing damage done to the
cells during TCE exposure, which the control reactor does not undergo. This lack of
damage may also permit the phenol-induced control reactor cells to more quickly create

oxygenase enzymes, thus increasing their ability to degrade TCE.

29

Endogenous Decay Coefficient, b

The aerobic decay coefficient for all biomass was determined by placing approximately
75 mL of reactor cells on a shaker table in an Erlenmeyer flask capped with a sponge to
prevent airborne contaminants from entering the culture while maintaining aerobic
conditions. Over a period of seven days, five biomass concentration measurements were
made. A log-normal plot of concentration versus time yielded a straight line with a slope

equal to the endogenous decay rate, b.

A large range of values ‘for b were observed. The reason for this is unknown. Experiments
were conducted during the same period of the SBR cycle. Observation of other
parameters such as solids concentration and phenol degradation rates have shown
variability in the reactors over time. It is possible that endogenous decay rates vary as

well, however there is not enough long-term data to support any conclusion.

TCE-degrading Biomass Decay Coefficient, b”,

As with the specific growth rate, the determination of b“ was limited by the inability to
directly enumerate the population of TCE-degrading microorganisms. Consequently, a
similar indirect method of measurement was employed. An aerated flask containing
approximately 50 mL of reactor cells was capped with a sponge and placed on a shaker
table at 300 rpm. Periodically, cells were removed to determine the initial rate of TCE
degradation. This rate is used as an indication of the remaining active TCE-degrading

population. A semi-log plot of the ratio of the degradation rate at any time to the

30

degradation rate at the start of the experiment was plotted versus time. The slope of this

plot was equal to the decay coefficient, bm.

Transformation Capacity, Tcb

Transformation capacity experiments were conducted by spiking reactor cells with a
known amount of TCE and measuring the total mass of TCE degraded. 9.75 mL of
reactor cells were placed with 10.00 mL reactor media in a 45 mL screw-top amber glass
vial fixed with a Mininert valve. 0.250 mL of saturated TCE solution was injected into
the vial and the vial was placed on a shaker table. A reactor solids measurement at the
time of cell removal provided for the calculation of mass of cells in the vial.
Measurements of TCE in the vial headspace were analyzed on a GC/F ID. When TCE
degradation ceased, the mass of TCE degraded is divided by the mass of cells present in

the vial, yielding the observed transformation capacity.

Zero-Order Phenol Degradation Coefficient, ko

k° was determined by spiking a known concentration of reactor cells with phenol and
observing phenol concentrations over time. Three flasks containing the same amount of
reactor liquid were spiked with varying amounts of phenol. Sub-samples from the flasks
were removed periodically and filtered to stop phenol degradation. The subsamples were
then analyzed by HPLC and the data was plotted versus time, yielding a straight line with
a slope, when divided by biomass concentration, equal to the zero-order degradation

coefficient.

31

TCE First-Order Rate Coefficient, k’

Five mL of reactor cells were placed in glass vials, spiked with 4 uL TCE saturated water
and crimp sealed. TCE concentration was measured by GC/ECD. A plot of the natural
logarithm of TCE concentration versus time yields a straight line with a slope equal to the
product of biomass concentration and k’. Dividing this determined slope by a measured
biomass concentration yields the TCE rate coefficient. It should be noted that no
experimental method was used to separate biomass fractions. Thus, in determining k’, a

total suspended solids measurement is used rather than a true measurement of X3”.

CHAPTER 5

COMPUTER MODELING AND EXPERIMENTAL VERIFICATION

MathCAD Modeling

Mathematical expressions developed in Chapter 2 to describe the sequencing batch
reactor system were modeled using MathCAD software. The MathCAD software uses a
fourth order Runge-Kutta approximation method to solve differential equations. A
flowchart of the MathCAD programming logic is presented in Figure 5-1. Appendix A
contains MathCAD worksheets and an explanation of the programming language used in

the two-population model.

32

33

Figure 5-1 MathCAD Programming Logic

 

Start

 

 

 

 

 

 

Enter Kinetic Parameters: kc. k'. Y. b. bat. muat. ch
Enter Initial Reactor Conditions: Vc, Co, Pa, Xao. Xato. Q. 09. Cid. Hc

 

 

 

Solve Differential Equations

 

 

for one cycle

 

 

 

 

 

Reset Initial Conditions except for solutions for
Xa. Xap and Xapt from previous cycle

 

 

 

 

Solve Differential Equations
for one cycle

 

 

 

 

 

Reset Initial Conditions except for solutions for
Xa and Xat from previous cycle
Waste 100 mL of cells and add replacement volume

 

 

 

 

 

No

 

Repeating Solution?

 

 

 

Yes

 

 

Stop

 

 

 

 

34

Experimental Results

TCE During Fill and React Stagg

Liquid and gaseous phase TCE concentrations were measured during the fill and react

stages on two separate occasions (Figure 5-2).

 

TCE In Fill-React Stages

 

 

0.3 -2 ,__ 222222 r____
A
A l
A
0.25 .
A
A
‘ |
0.2 ; A i
|
A ‘ i
a _ .
v 1
1 I CI 9130197
0.15. lo ( I
I I ‘ “GHQ/24197)
8 A . mats/30197);
I: -~————— .
8 g I O
A
01;
I A .
A
A A A A A
I A A ‘
A A A
A A
A
0.05 .
I A A
A
A
o 0 I A
I D 0 O D 0 a A
A D o D D A A
D . I A A
D a .
0 fl .. _. _ ___._ _.__. D D _._+_._6 ._ _...
0 20 40 60 80 100 120 140

TIme (minutes)

 

Figure 5-2 TCE in the Reactor

 

 

35

From these measured values, it is possible to estimate the mass of TCE lost to air

stripping. The rate of mass lost to air stripping is described by the equation

dM airstrip
T = Qg Cg (5-1)
where Qg is the airflow rate through the reactor (Min) and CE is the gaseous concentration

in the reactor headspace (mg/L). If airflow is constant, then total mass lost to air stripping

may be described by the equation
Mairstrip = 09 I ngt (5'2)

In this case, the integral was approximated using the trapezoidal rule. TCE loss for the
two sampling events was 0.64 mg and 0.16 mg for 9/24/97 and 9/30/97, respectively.
These losses due to air stripping account for 12.8 % and 3.1 % of TCE introduced during

the fill cycle.

Phenol During Recharge Stagg

 

Phenol was measured in the reactor on two separate occasions, 10/6/97 and 10/24/97.
Data is presented in Figure 5-3. Due to slight variations in the speed of the syringe pump
which provides phenol to the reactor, the end of phenol injections does not occur exactly

at 30 minutes. Therefore, decline in phenol values sometimes began before 30 minutes.

36

Phenol During Recharge

25

 

N
O

.A
0'

o ,. 10/24/9‘7"
, e ,0 10/6/97 ;

 

Concentration (mgIL)
8
0

 

 

 

0 10 20 30 40 50

Time (minutes)

Figure 5-3 Phenol in the Reactor
Total Suspended Solids
Total suspended solids measurements were taken over a long period of reactor operation.
These measurements were used in calculations to represent active biomass, X,, as

differentiation of biomass fractions was not possible. Data is presented in Figure 5-4.

37

Figure 5-4 Solids Concentration over Time

Total Suspended Solids vs. Time

 

 

 

 

2500
2000 '
s W _°o° .' -
E 1500 'o° _________.
8 00“ if.“ . . 0 Control Solids
'8 :00 so I o a ' .
o o ,. posed Solids
g 1000 0': o o ____ .
O
O
5
o 500 2
0 ;
3/31/97 4/20/97 5/10/97 5/30/97 6/19I97 7/9/97 7/29/97 8/18/97 9/7/97
ate
One Population Model

Using the parameters contained in Table 4-1, the one population model predicts repeating
solutions for biomass concentration, gaseous phase TCE concentration, liquid phase
concentration, phenol concentration and cumulative mass lost to air stripping (Figure 5-

5).

ICE ( ‘uncen. (mg/I.)

 

 

 

(‘nnccnlration (mg/l .)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Biomass Concentration Phenol Concentration v. Time
2500 I 35 I T I
E: 25 - —‘
2000 — — E’
2 2t) — -‘
l .5
_:_: 15 - -
1500 — é .
== 111 P —
5 — —
l l l l
i l
“”0348 354 360 t354 354.25 354.5 354.75 355
Time Time
_ Xa
TCE Concentrations During F ill-React Cumulative Mass lost to air strip vs. I
0.3 F I I 0'3 I I I
30
5
—- I A :1
02 ’ |‘ 3: 0.2 P
r , ;,
' I 3
. ‘ A
r ‘ :3
0.1 r ‘ — .5 11.1 - —
l | "5.:
I ‘ e
I \ '3
l s "
l) l l —‘L 0 1 J I
348 348.5 349 349.5 350 348 348.5 349 349.5 350
Time Time

Figure 5-5 One-population Model Predictions
k” = 0.2 L/mg-day, k° = 2.6 l/day, ch = 0.29 mg/mg,
Y = 1.3 mg/mg, b = 0.05 1/day

39

Discussion
The model predicts a repeating solution biomass concentration of approximately 2100

mg/L during the recharge stage. The measured solids concentration data is presented in

 

 

 

Table 5-1.
Table 5-1 Solids Data
Average Standard High Low Median
Reactor Concentration Deviation (mg/L) (mg/L) (mg/L)
(mg/L) (mg/L)
Control 1418 249 2030 970 1410
Exposed 1440 307 2 140 1040 1330

 

 

 

 

 

 

 

 

Comparing the model with the data, it can be seen that the model overestimated the
biomass concentration. This is possibly due to the failure of the model to account for
predator-prey interactions known to take place in the reactor (microscopic observation

verified the presence of multi-cellular organisms such as rotifers).

Figure 5-6 contains a plot of the model predictions and measured data for TCE in the
reactor. The model predicted the liquid TCE concentration to reach a maximum level of
0.22 mg/L and the measured maximum values were 0.27 mg/L and 0.14 mg/L. The
duration of degradation, however was not as well predicted. The model requires 90
minutes to degrade the TCE, whereas the measured values showed TCE present in the

reactor as long as 140 minutes.

Concentration (mg/L)

 

4o

TCE in Reactor

0.3 -~— - 7-77 77- .—__ ._-_____._ ..__ _.

0.25 #

"Ca—(92097) 1
Ca (9/30/97)
CL (9124/97)
CL (9/30/97)
CL Model
" " ' Cg Model

IDDD;

 

 

 

 

 

 

 

140

Tlme (minutes)

Figure 5-6 TCE Model and Data

41

This difference presents an interesting problem. Experimentation with the model showed
that if the first order rate coefficient for TCE, k’, is decreased in an attempt to lengthen
the time of TCE degradation, the peak concentration also increases. It is most likely then,
that a combination of changes in parameters is required. For example, a decrease in the k’
value, coupled with an increase in the mass transfer coefficient, would result in the
desired lengthening of degradation time while the increased influence of air stripping

would decrease the peak liquid concentration.

It should be noted that the method used to determine the liquid TCE concentration
provides more opportunity for error than the method used to determine gaseous TCE
concentration. This inherent error in the method may necessitate manipulation of the data
to give an improved sense of where the data may actually lie. A running-average analysis
of the data, for example, may yield data that more closely resembles theprediction of the

model.

Further, the uncertainty analyses performed over the range of parameter values (Chapter
6) indicate that with a change in kinetic parameters, large changes in model predictions
may result. Considering the variability of the experimental system as evidenced by
observed changes over time in some kinetic parameters, model predictions would also

fluctuate over a range large enough to encompass both data sets.

42

Gaseous TCE modeling was more successful. The concentration was predicted to reach
0.04 mg/L and the measured peaks were 0.03 mg/L and 0.09 mg/L. The model predicted
the disappearance of TCE in the reactor headspace very well, particularly with the data
set from 9/3 0/97. The model predicts a ratio of peak gaseous concentration to peak liquid
concentration of 0.166 whereas the measured ratios were 0.32 and 0.22. This difference
between the model and actual measurements may indicate that the mass transfer of TCE
between the two phases is not adequately described by the KL... relationship observed

experimentally (Appendix B).

The mass lost to air stripping was predicted to be 0.215 mg or 4.3% of the mass injected.
Estimates based on the measured gaseous TCE concentrations in the reactor were 0.64
mg (12.8%) and 0.16 mg (3.2%) for 9/24/97 and 9/30/97, respectively. The large range in
measurements reflects the variability of the experimental system as a whole. This

variability was also evident in other parameters.

Figure 5-7 presents phenol data along with the one-population model prediction. The
model overestimates the peak concentration however the slope of the post-fill degradation
curve ( > 30 minutes) is similar to the data sets. More disturbing than the model’s
overestimation of peak concentration is the difference in shape between model and data.
The data, while it supports a zero order rate assumption in it’s linear, post-fill stage,
appears to follow a curve similar to a first-order reaction during the fill portion. More

data however, would be needed to verify such a phenomena.

Concentration (mg/L)

43

Phenol during Recharge Stage

 

40?

35+

      
 

’...

30

25

20

15

-- -._. *.____. _.-_.-_--+-_.__-___ -*_. -_. ._..__

1oT

 

 

O 10 20 30 40
Time (mg/L)

Figure 5-7 Phenol Model and Data

 

 

 

Q 10/24197
I 1016/97
—Model

 

 

Two Population Model

Using the parameters experimentally determined (Table 4-1), the two-population model
predicts that the phenol-degrading population, Xap, becomes dominant, while the TCE-
degrading biomass, Xap” declines to zero. After experimenting with various changes to
kinetic parameters, it was found that in every case either Xap, or X,p became dominant,
with the other population declining to zero. This phenomena indicates a problem inherent
with modeling any two populations which consume the same growth substrate:
differences in net growth rate will, in time, demand that one population becomes
dominant. The fact that multi-population cultures exist indicate a problem with this two-
population model. This model contains no limiting factor that can restrain a population
from becoming dominant. A predator-prey relationship may be one method of applying

such a limit.

Certainly other modeling techniques for such a system should be explored. Possible
alternatives include modeling TCE-degrading microorganisms as a subset, rather than
separate, of the phenol-degrading population, modeling TCE-degrading capability as a
function of oxygenase enzyme level within the greater phenol-degrading population and
modeling population subsets as occupying individual “niches”, in which different
organisms’ kinetics become dominant at different substrate concentrations. These
techniques would avoid the competition for growth substrate problem of the model in this

study.

CHAPTER 6

MODEL SENSITIVITY AND PARAMETER UNCERTAINTY

Relative Sensitivity

SBR modeling presents unique problems with sensitivity assessments. Since differential
equations governing solids and contaminant concentrations vary over the cycle, and since
steady-state is never truly reached, standard sensitivity analyses are not feasible. For this
reason, the sensitivity of the model to each parameter was based on actual model
predictions over a small range (i 10%) of each parameter. Model differences were

expressed by the relative sensitivity, defined as

@v/

pm

Split,ps = @S (6'1)
[)5

where S is the relative sensitvity, pm = the parameter modeled for and ps is the parameter
changed by i10%. For example, a 10% increase in the endogenous decay coefficient
yields a 100 mg/L decrease in the biomass concentration which was originally 1500

mg/L. The corresponding relative sensitivity, wa would be

 

The normalization of 5pm and Sps by pm and ps allow a comparison to be made between
sensitivity coefficients of different parameters and predictions. Values chosen for to
represent pm were the maximum levels of each prediction made by the model for the

cycle that was determined to be the quasi-steady-state solution.

45

Model Sensitivity to Parameters: Results and Discussion

Sensitivity for each modeling parameter (Y, b, Tc”, k°, k’) was assessed for each of four

modeling predictions (Xam, CL, Cg, S, Mm”). In order to avoid sign confusion, the

absolute values of the relative sensitivities for +10% and -10% of a parameter were

averaged and presented in Table 6-1.

Table 6-1 Relative Sensitivity

 

 

 

 

 

 

 

pm —>
ps 1 x,,, CL C3 3 MW...
Y 0.98 0.90 0.89 5.42 0.93
b 0.24 0.23 0.23 0.90 0.23
T3 0.13 0.13 0.13 0.50 0.13
k° 0.007 0.006 0.006 3.57 0.005
k’ 0.13 0.81 0.80 0.47 0.84

 

 

 

 

 

 

The table provides powerful insight into the model. Investigation by row provides an

overall sense of the importance of each parameter to the entire model. By column, the

table can be used to gauge the relative importance of each parameter to a specific model

output. It is apparent that the yield coefficient is the parameter that the overall model is

most sensitive to whereas the zero order phenol degradation rate, k°, is the parameter least

 

47

important to the model predictions (with the exception of phenol concentration, S, of
course). This would seem to indicate that biomass concentration is very important to the
model, which is not surprising, as a term involving biomass is present in virtually every
differential equation used to describe the system. It is perhaps this dominance that is
reflected in the near constant sensitivity in four of the five rows. That is, a change in a
parameter affects biomass a certain way, and since biomass is so important to the system,

the sensitivity to an individual parameter is the same for nearly all model predictions.

Some other interesting trends are readily apparent in the data. For all parameters but one,
k’, it appears that one predicted value, S, is most affected by a change in the parameters.
Degradation of phenol is dependent solely on the zero. order rate coefficient, k° and
biomass concentration, X“. As the k° value is kept constant in these sensitivity analyses,
this is more evidence that the biomass concentration is the most influential factor in the
model. This importance demands a closer look at biomass.

Investigating column X it is apparent that biomass is most sensitive to the yield

apt’
coefficient, followed by the endogenous decay term. T,b and k’, being indirectly related to
Xap” have near the same, low bearing on Xap, and k° has virtually no influence on biomass
concentration. The yield coefficient, then, is perhaps the most important parameter to the

model. This is important, since future studies should pay closer attention to a solid

determination of the yield coefficient.

48

Similar investigations by column were conducted on the other model predictions. In all
cases, the yield coefficient is the most important parameter. Beyond that, columns
differed but their trends were the same: after yield, the parameters most influential on a
prediction were those that were directly related to the prediction (e.g. k’ for CL, Cg and

M k° for P). This dominance of the yield coefficient over even those parameters that

airstrip?

are directly related to predictions (i.e. in the actual differential equations) further

solidifies its importance.

Parameter Uncertainty

In a system that experiences fluctuations in kinetic parameters, it is essential to determine
how the model predictions vary over the range of experimentally determined values for
each parameter. To this end, modeling was performed over the range of determined
parameter values. For those parameters with a large enough data pool (k’ and k°)
modeling was performed over the range bounded by the calculated standard deviation.
For those parameters with only a few data (Y and b), analyses were conducted over the
actual range of values, with an average value for reference. Figures 6-1 through 6-4

present modeling predictions over the range of each parameter.

Discussion

Model predictions over the range of values for the yield coefficient are presented in
Figure 6-1. Biomass was particularly affected, with maximum concentration predictions
ranging from approximately 2100 mg/L to 1600 mg/L. Effects on TCE degradation, mass

lost to air stripping and phenol degradation were similarly affected, indicating the

49
importance of the yield coefficient to all aspects of the model. Application of the model

to engineered systems would require a well-defined, reliable range of yield

measurements.

Concentration (mgxl)

Phenol Cone. (mg/l .)

Liquid Phase TC E During F ill-React 006

 

Gaseous Phase TCE During F ill-React

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l I
I I
0.5 - -< :3 ’- -.
an / 1
511.04- ,"“ —
a I.
3
r ‘ '._'_ " S
’/ ‘— _\ g 0.02 -‘
O
o
~ 0 I I
0 l 1 348 349 350 351
348 349 350 351
T' (h ) Time (hours)
rme ours
_ -, . —' Cg(Y=l.3)
(.L (Y = 1.3) _ _ ., _ -
_ . _ Lg (Y — 1.15)
CL(Y=1.15) _ Cg(Y=10)
' ' CL (Y = 1.0) ‘ '
Phenol Concentration v. Time Biomass Concentration
100 2500
l l I I
75 F -1 3) 2000
5
E
50 — — E 1500
E
.3
C
25 — — 5 1000 w} — — — —{' —
- I l
0353 354 355 356 500 350 355 360
Time (Hours) Time (hours)
— Y = 1.3 — Y = 1.3
- Y=1.15 — Y=1.15
" Y=1.0 " Y=l.0
Cumulative Mass lost to air strip vs. I
0.3 T 1
C ————————————
I "
1': 0.2 - -
"'5
a l
3 0.1 —
:1
E
5
0 1 1
350 355 360

Time (Hours)
1.3
1.15
1.0
Figure 6-1 Uncertainty Modeling for Yield

Y = variable (mg/mg), k’ = 0.2 L/mg-day, k° = 2.6 1/day
Tcb = 0.29 mg/mg, b = 0.05 l/day

Phenol Cone. (mg-’1.)

Concentration (mg'l..)

Liquid Phase T CE During Fill-React Gaseous Phase TCE During Fill-React

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I 1
t 5 5
5
= ’-
:2: 0.05 t. I “ —‘
:5 ,’¢---\
é I '
o \
\
0 \ l
J 348 349 350 351
350 351
T' (h ) Time (hours)
. ime ours _ Cg(ll('=0.28)
‘"" CL(k=0.28) -- C ,',_
_ , g (k — 0.2)
CL (1‘ = 0'2) - Cg (k' =0.12)
' ' CL (k' =0.12)
Phenol Concentration v. Time Biomass Concentration
100 2500
I I I I
g 2000 .5
G
.2
50 - - g
.‘3
5
g 1500 —
0 I 1000 I l
353 354 355 356 350 355 360
Time (Hours) Time (hours)
— k'=0.28 — k‘=0.28
— k'=0.2 " k'=0.2
" k'=0.12 " k'=0.12
Cumulative Mass lost to air strip vs. t
0.4
I T
1;) '------------------
a r
:7 11.3 —- r _
r; r
:— I
"5 I
4 r
./
43
E 0.1 _
'3
l
0 1 1
350 355 360
Time (Hours)
—' k' = 0.28
_ k' = 0.2
' ' k' = 0.12

Figure 6-2 Uncertainty Modeling for k’
Y = 1.3 mg/mg, k’ = variable (L/mg-day), k° = 2.6 1/day
Tcb = 0.29 mg/mg, b = 0.05 l/day

Concentration (mg-l.)

Phenol Conn. (mgrl .)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . , . . Gaseous Phase TCE Dunn Fill-React
LIqUId Phase TcE During Fill-React 11.114 1 T g
I I
0.5 —- — I:
:19
5
5
=3 0.02 —
E
:J
3:
.9.
0 1 1
0 , l 1 348 349 350 351
348 349 350 351
T' (h ) Time (hours)
rme ours
_ _ Cg (k0 = 3.7)
CL (ko=3.7) _ ._ C _.7
_ 8 (ko - 46)
CL (ko=2.6) —' Cg (ko= 1.5)
‘ ‘ CL (k0 = 1.5)
Phenol Concentration v. Time Biomass Concentration
100 2500
l I I I
75 — A — ED
0 s 5 2000
l \‘ g
— I --t °
50 , ‘ E
l 0 g
'1 ‘ “ g 1500
O
25 _ a l ‘ t T U
y |
/ 1 .
1 _-..- ‘ [t l I
0353 354 355 356 ”’00 350 355 360
Time (Hours) Time (hours)
— ko=3.7 — ko=3.7
- ko=2.6 - ko=2.6
"' ko=l.5 " ko=l.5
Cumulative Mass lost to air strip vs. t
0.3 T 1
:éi
;; 0.2 — f""‘“""""—"=
29
E 0.1 1— —
D
E
.=..
U
0 1 1
350 355 360
Time (Hours)
_ k0 = 3.7
- ko = 2.6
' ' k0 = 1.5

Figure 6-3 Uncertainty Modeling for k°
Y = 1.3 mg/mg, k’ = 0.2 L/mg-day, k° = variable (l/day)
Tcb = 0.29 mg/mg, b = 0.05 l/day

~—

(‘oncentration (mull .)

Phenol Cone. (mg’l .)

LII
b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . . . . 3 ‘ ,‘ CE . . _ ‘
quUId Phase TCE Dunng Fill-React ”9‘60” Phil—:6 T Durlmg F111 React
1 I
0 5 — —l a
E o"-
2‘; 0.05 1— I I‘ p
'-‘ I
35 "' — a
.5 ’ \‘t
‘V \
\ \
0 L \“
0 , 348 349 350 351
348 349 350 351
Time (hours) Time (hours)
— CL(b=03) _ Cg<b=0'3)
- CL(b=O:l75) " Cgtb=9175>
- - CL (b = 0.05) _ Cg 0’ = 005)
Phenol Concentration v. Time Biomass Concentration
“’0 3000 1 r
75— _ 3’ ----------
g 2000 F ,e _.
g I
50 '— —1 .3 “ 'l
g L“ --_ I z’-""""'
i»; 1000 ' " " " /
25 T — 3 \\_ _ _ _ 1f
1 1
0353 —356 0 350 355 360
Time (hours)
— 19:03 — b=0.3
- - b = 0.05 - - b = 005
Cumulative Mass lost to air strip vs. t

0.6 I

 

I

 

0.4

Cumulative Mass ot’TCE (mg)

 

 

 

 

355 360
Time
_ b=0.3
— b=0.175
" b=0.05

Figure 6-4 Uncertainty Modeling for b
Y = 1.3 mg/mg, k’ = 0.2 L/mg-day, k° = 2.6 1/day
Tcb = 0.29 mg/mg, b = variable (1/day)

54

Predictions over the range of k’ values and k° values validate the conclusions drawn from
the sensitivity analyses. Predictions that are not directly related to the parameter in
question are not affected by changes. For k’, phenol degradation and biomass
concentration are essentially unchanged. The zero-order rate coefficient for phenol
degradation, k° has little effect on any prediction except phenol concentration. Worthy of
note is the prediction for a k° value of 3.7 l/day, which predicted phenol to be degraded
so rapidly that it produced a “sawtooth” shaped graph, an artifact that the model produces

when the concentration of phenol drops below zero during the recharge-fill stage.

The large differences in the predictions based on the range of b values arise from the size
of the range itself - from 0.05 to 0.3 l/day. As with the yield coefficient, b is directly
related to biomass concentrations, which has a direct influence on all model predictions.
This large variation in an influential parameter may be a factor in the differences between
the observed data of TCE in the reactor. Here again, a larger data pool is needed to
provide more reliable predictions for the model and a more satisfactory understanding of

the true variability of the endogenous decay coefficient in the system.

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

Computer Modeling

The one-population model developed in this study adequately described TCE
concentrations, both liquid and gaseous, in the reactor. Mass lost to air stripping was also
within the observed range. Phenol predictions were less accurate than those for TCE,
visually differing from the shape of observed data and overestirnating the peak
concentration of phenol in the reactor. Considering the variability of the system as
evident in the range of experimentally determined parameters and solids concentrations

over time, the model can be considered successful.

Failure of the two-population model indicated a problem inherent in this model’s
treatment of two separate populations feeding on the same substrate. Over time, one
population or the other became dominant, depending on net growth characteristics. This
suggests that other alternatives need to be explored. Possible alternatives include
modeling TCE-degradation as a function of oxygenase enzyme level in a single
population or modeling TCE degrading organisms as a subset of a larger phenol

degrading population.

Parameter Determination
The large variability in solids measurements and k° values over time may imply that other

kinetic parameters also vary over time. Therefore it is necessary to collect many
55

56

measurements of kinetic parameters. Some parameters used in this study were not based
on large pools of values, and it is possible that deficiencies in modeling were due to

inadequate assessments of those parameters.

The sensitivity analysis performed on the model was a powerful tool in determining
which parameters are most influential to model predictions. Results of this analysis can
guide future research to focus more on the most influential parameters. It was seen that in
this model, the yield coefficient played a large role in determining the outcome of all

model predictions and future work should reflect this importance.

Recommendations

0 The one-population model was shown to adequately predict TCE levels in the reactor.
Time required to degrade TCE and phenol concentrations, however were not as
accurately modeled. Better estimations of important parameters should be made and
the model reevaluated.

o Other two-population models should be explored. Models that consider TCE
degradation as a function of enzyme level rather than biomass may have more success
and avoid the problems of competition between populations utilizing the same growth
substrate.

0 Experimental methods of differentiating between forms of biomass need to be

developed. Although models can be created to account for dead and decaying cells,

57

predator populations, heterotrophic bacteria feeding on degradation by-products, etc.,

experimental verification will not be possible until differential methods are created.

58
REFERENCES

Alvarez-Cohen, L. and P. L. McCarty. 1991 . “A cometabolic biotransforrnation model for
halogenated aliphatic compounds exhibiting product toxicity.” Environ. Sci. Technol. 25:
1 3 8 1-1 3 87.

Auteinrieth, R.L., J. S. Bonner, A. Akgennan, and M. Okagun. 1991. “Biodegradation of
phenolic wastes.” Journal of Hazardous Materials 28: 29-53.

Beltrame, P., P. L. Beltrame, P. Carniti, and D. Pitea. 1980. “Kinetics of phenol
degradation by activated sludge in continuous-stirred reactors.” J. Water Pollut. Control
Ee_d, 52: 126-133.

Chang, H-L. and L. Alvarez-Cohen. 1995a. “Model for the cometabolic biodegradation of
chlorinated organics.” Environ. Sci. Technol. 29: 2357-2367.

Chang, H-L. and L. Alvarez-Cohen. 1995b. “Transformation capacities of chlorinated
organics by mixed cultures enriched on methane, propane, toluene, or phenol.”

Biotechnology and Bioengineering 45: 440-449.

Chang, W-K. 1996. “Kinetics characterization of cometabolizing communities and
adaptation to nongrowth substrate.” Ph.D. Dissertation.

Chang, W-K. And C. S. Criddle 1997. “Experimental evaluation of a model for
cometabolism: prediction of simultaneous degradation of trichloroethylene and methane
by a methanotrophic mixed culture.” Biotechnology and Bioengineering 56 (5), 492-501.

Criddle, C. S. 1993. “The kinetics of cometabolism.” Biotechnology and Bioengineering
41: 1048-1056.

Dabrock, B., J. Riedel, J. Bertram, and G. Gottschalk. 1992. “Isopropylbenze (curnene) -
a new substrate for isolation of trichloroethene-degrading bacteria.” Archives of
Microbiology 158: 9-13.

Gossett, J. M. 1987. “Measurement of Henry’s law constants for CI and C2 chlorinated
hydrocarbons.” Environ. Sci. Technol. 21: 202-208.

Henry, S. M. and D. Grbic-Galic. 1990. “Effect of mineral media on trichloroethylene
oxidation by aquifer methanotrophs.” Microb. Ecol. 10: 151-169.

Kotturi, G., C. W. Robinson, and W. E. Inniss. 1991. “Phenol degradation by a
psychrotrophic strain of Pseudomonas putida.” Appl. Microbiol. Biotechnol. 34: 539-
543.

59

Metcalf and Eddy, Inc. Tchobangoglous, G. and F. L. Burton. 1991. Wastewater
Engineering: Treatment, Disposal and Reuse. 3rd Edition. McGraw-Hill, Inc. New York.

Oldenhuis, R., R. L. J. M. Vink, D. B. Janssen, and B. Witholt. 1989. “Degradation of
chlorinated aliphatic hydrocarbons by Methylosinus trichosporium OB3b expressing
soluble methane monooxygenase.” Appl. Environ. Microbiol. 55: 2819-2826.

Segar Jr., R. L., P. Kalia, B. I. Dvorak. 1995 “Simulation of sequencing batch and biofilm
reactors for trichlroethylene (TCE) cometabolism.” Book: In Situ and On Site
Bioremediation: Volume 3.

Shih, Chien-chun. 1995. “Experimental and numerical evaluation of cometabolism in
sequencing batch reactors.” Ph.D. Dissertation.

Wilson, J. T., and B. H. Wilson. 1985. “Biotransformation of trichloroethylene in soil.”
Appl. Environ. Microbiol. 29:242-243.

APPENDIX A
MATHCAD PROGRAMNIING

60
The MathCAD model begins with a statement of variables and initial conditions (Figure

A-l). Experimentally determined parameters are converted to units of hours for use in the
subsequent program. Initial conditions are required by the software to begin the

differential equation solving process.

Once initial conditions and parameters have been entered, the next step in MathCAD
programming is to enter the differential equations. MathCAD requires these to be entered
into a matrix, each row of the matrix corresponding to a different variable. The actual
entry is the differential equation. Each variable being solved for is assigned a name based
on it’s position in the differential equation matrix: the first variable, corresponding to the
first row of the matrix is named x0, the second x,, etc. In this program, there are eight
rows, corresponding to eight variables. The names of the variables and what they

represent are summarized in Table A-1.

Table A-1 MathCAD Variable Legend
Name Variable
x0 CL - Liquid phase TCE concentration (mg/L)
xl CG - Gaseous phase TCE concentration (mg/L)
rt2 V - Reactor liquid volume
it3 X,“ - TCE-degrading biomass concentration (mg/L)
x, S - Substrate (phenol) concentration (mg/L)
x5 Mm,"-p - Cumulative mass of TCE lost to air stripping

(mg)

 

 

 

 

 

 

 

 

 

 

Each variable has different equations to describe it at different times of the cycle. To deal
with this, MathCAD allows conditional statements to be attached to differential

equations. Furthermore, conditional statements may be linked by Boolean logic.

61

Dimensionless
Henry's Constant

Airflow into SBR Qg v 6 Uhr

H - .392

Transformation Capacity ch 20.29 mgTCE/mg cell

First Order TCE Degradation Coefficient k 2:371 L/mg-hr

7
Zero-order Phenol Degradation Coefficient kp 23 1/hr

09;
24

Endogenous Decay b 1/hr

Yield on Phenol Y 1.3 mg/mg

Initial Conditions

Reactor Volume Vo 1.25 L

TCE concentration injected Co .:5 mg/L
Phenol concentration injected Po r7200 mg/L
Total Reactor Volume Vt .: 2.5 L

Initial Biomass Xato 2000 mg/L

Initial Reactor Concentration CLo 20 mg/L
Initial Gaseous Phase Concentration CGo 0
Initial Liquid Volume Vlo 71.25 L

Initial Phenol Concentration in Reactor PLo *0

A coefficient was added to the mass transfer
a 1 term to investigate the effects of a change in the
mass transfer coefficient (not used in this study)

Figure A-l MathCAD Programming Worksheet

E(t,x)

 

 

 

 

 

 

 

 

I00 CO- X 1 771 -‘ X
- - 0 173892 a- x,‘ 1‘89" - x0 - I (11le x3 1f 0t 1
v16 .-1 1.00 : ~.» . .y H
128922 " "1‘ 7 . .
l73892ax x - ~.rk-xx. 1f(1);t54
‘ 2. ‘0 H. 0 3,
0 if x0<0
0 otherwrse
. , p ,, x, x ‘1 x x 100
173892 a x,. 1289“. ..-_...--__5-;x0 - '5 -Q -51— . ~I___. 1f 0.1-5.1
"" Vt— x,“ 1 H/ (Vt—x, Vt x.,"
F 9 7 X x ~l; x 1
1.73892 8 x, "“892“. ..... 3_1x0 . l. _ Qg.__...l-.__ If 1<r~4
”‘ Vt -x.,' ‘ H; Vt- x,
0 1f xl<0
0 otherwrse
1.00 If Oitfil
(-100) 1r 5"it‘i6
0.05 if 65136.5
0 otherwise
X ‘ k X \11
1 ’ ch k x01x3/1
I , k ("01 1
‘rbx3 ———«——;--— .-x3 If l<t ‘4
L -. -_.b_,
t .ch k-xO-x3/A' I
\ bx}. If 4<t‘5
7 X3 1 -
1 bx3 -—(Al.00)| if 5<t":6
1 1 "2 J
1 ; 1
. 1 X3 1 . _
7-4 «*5 __, ,5 Ytkp-x = if (6<1:%>.5)- 'x :0
Vlo ‘ 3' > 4 .
‘ — —~ 4 (t - 6)! '
1 00
x3 ,
i . + b-x3i‘. If (6<t"6.5)- x4<40
V10 4(1- 6). - ' -
{0,05 4
1 Ykp-x3 1f (6.5<t"‘12)-:x47“0)
‘ ' '5- / z ‘.
. 'b'X} If(65<Ia12)I\X4\0/1
0 othenmse
: 0-5 —-—- 'Po-x4“; kpsg/x3\) if (6<t 7.6.5). x4 03.
Vo-.05(t 6) ‘ / \ . "
. . ~95--~——(P0)1 1r(6<1::6.5).(x4<0
V045 05-(1- 6) J \ ,1
. ,' \1 «1’ ,’
rkp \xx” 1f ((6.5<t.512))v1,\x4>0>
0 1r (6 5<t“‘12)-.;"x4'50\;
0 otherwrse
03 x]
1

Figure A-2 MathCAD Equation Matrix (One-population model)

A program is created to evaluate the differential equations repeatedly, changing the initial

conditions for biomass concentration with each iteration. Solutions are placed in a matrix.

Figure A-3 contains the program used in this work.

Resultl cycle)

 

WCLo I
CGo
Vlo
xe— Xato
PLo
0
O .
Ro—(OOOOOOOO)
for re l..cycle
Solutiono-rkfixedt 31.0, 12,999, E)
R0— stackt R . Solution)
CLo
CGo
Vlo

xo— SOIUIIOD999‘4 ,
PLo
0
Solution999' 7

Solutions—rkfixedt x,0. 12.999. E1
Ro—stackl R,Solution)

CLO

CGo

Vlo

100

its-1 Solution999‘4 ., Vlo

PLo
0
Solution999' 7

 

This step sets the initial conditions to solve the
differential equations for the first cycle

This equation for R establishes a 1 row 6 column "dummy" array
which will be stacked on top of the array generated by the
equations solver It is needed so that the stack funtion in the first
cycle of the "lei" loop can function.

"Solution" is the name I‘ve given to the array to be generated by the
differential equation solver. Mixed.

"R" is the matrix created by stadting the previous array named
RontopofthenewlyaeatedarraySolution Asthe'for'loop
progresses. R redefines itself. becoming a larger matrix
consisting of the “old” R and the new matrix named Solution.

This last step in the "for" loop creates the new initial conditions which
will be used in the next evaluations of the differential equations Note
that the only thing that chages in the initial conditions is the biomass

concentration.

The wasting step assumes injection of a makeup volume

After completion of the ”for“ loop this last line of the program tells MathCAD
that the funcuon ”Result" 18 defined as the large array “R"

Figure A-3 MathCAD Program

64

Evaluation of the program requires the input of the number of days to be modeled. Output

can be in the form of a matrix or by graphing explicit columns of the solution matrix.

APPENDIX B
MASS TRANSFER COEFFICIENT DETERMINATION

65

The mass transfer coefficient was determined by spiking a known mass of TCE into the
reactor at various volumes prior to inoculation with microorganisms and measuring the
presence of TCE in the reactor headspace over time. From this data a mass transfer
coefficient was determined at each volume. This data was plotted versus volume and a
best fit analysis was performed using Microsoft Excel software. The plot with determined

equation and r2 value is presented in Figure B-l.

Kla vs Reactor Volume for TCE and PCE

 

 

 

3.5 -
i
y = 3.7088X“-“53 E
I
3 * R2=0.9441 1
i
2.5 _. '
t 2 - . , rce
E 1 _ . “’5
g _m 1
x 1.5 . E er(PCE)
. l—Fbwer (TCE)
1 - l
0.5 2
y =1.7389215+00x-1~2°mw
R2 = 978789501
0 -___._ _. .._ _-._ .4
0 0.5 ‘I 1.5 2 2.5

Reactor Volume (L)

Figure B-l Mass Transfer Coefficient Relationship