Modeling and control of the anaerobic digestion process


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Modeling and control of the anaerobic digestion process
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vi, 126 leaves : ill. ; 29 cm.
Pullammanappallil, Pratap C., 1961-
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Subjects / Keywords:
Agricultural wastes   ( lcsh )
Factory and trade waste   ( lcsh )
Anaerobic bacteria -- Industrial applications   ( lcsh )
Chemical Engineering thesis Ph. D
Dissertations, Academic -- Chemical Engineering -- UF
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1993.
Includes bibliographical references (leaves 120-125).
Statement of Responsibility:
by Pratap C. Pullammanappallil.
General Note:
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University of Florida
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All applicable rights reserved by the source institution and holding location.
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Full Text








I would like to thank my committee chairmen, Professors Spyros Svoronos,

David Chynoweth and Gerasimos Lyberatos, for providing guidance above and

beyond the call of duty. Without their encouragement and assistance it would have

been very difficult to complete this project.

I would like to thank Professors John Earle, Gerald Westermann-Clark and

Oscar Crisalle for being part of my committee.

Several graduate students have helped me out in times of need. Jonathan Ben

Rodin and John Owens deserve special mention for all the technical assistance they


Finally, I would like to thank my parents and brother for their encouragement,

love and support. If not for them, I would not have been able to overcome

frustrations and disappointments I faced during the course of my stay in Gainesville.


ACKNOWLEDGEMENTS ....................................... ii

ABSTRA CT ................................................. v

CHAPTER 1 INTRODUCTION .................................. 1

O objective ..................................... 1
Technical Perspective ............................ 1
Anaerobic digestion ........................ 1
Imbalance Problem ......................... 3
Proposed Approach ........................ 6

DIGESTERS ...................................... 8

Introduction .................................. 8
Model Development ........................... 13
Stoichiometry and Biological
rate equations ...................... 13
The Physico-Chemical Relationships ........... 25
Gas Phase equations ...................... 29
Determination of Model Parameters ................ 31
Materials and Methods .......................... 35
Model Verification ............................ 38
Conclusions ................................... 49


Introduction ............................
The Optimization Problem .................
Optimization ............................
Optimal and Easily Implementable

...... 52
...... 54
...... 55

Suboptimal Control Laws ..........

ANAEROBIC DIGESTERS ..................

Introduction .........................
Control Strategies .....................
Conventional set point control law ...
Constant yield control law ..........
Key Features of the Expert system ........
The Expert System ....................
Materials and Methods .................
Testing the Expert System ...............
Simulations .....................
Experimental Validation ...........
Conclusions ..........................

......... 63

......... 63
......... 66
......... 66
......... 67
......... 68
......... 69
......... 73
......... 76
......... 76
......... 80
......... 91


CHAPTER 6 CONCLUSIONS .................................. 104

STIRRED ANAEROBIC DIGESTER .................. 106
B FEED PREPARATION ............................ 118

REFERENCES .............................................. 120

BIOGRAPHICAL SKETCH .................................... 126

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Pratap C. Pullammanappallil

May 1993

Chairman: S. A. Svoronos
Cochairman: D. P. Chynoweth
Cochairman: G. Lyberatos
Major Department: Chemical Engineering

Anaerobic digestion is a biochemical process that is used for treatment of

industrial and agricultural wastes and sewage sludge. Its advantages over aerobic

treatment processes are that it does not require aeration, produces low amounts of

sludge and generates methane which is a fuel. A major disadvantage of this process

is its susceptibility to failure when exposed to disturbances in the form of a feed

overloading or inhibitors entering with the feed.

Anaerobic digestion process models can aid in predicting the dynamics of the

process when it is subjected to disturbances and in addition aid in designing

anaerobic digesters and assessing proper operating strategies. A dynamic model for

a glucose fed continuous anaerobic digester is presented. The model incorporates

the most recent advances made in the study of this process. The kinetics of the

important metabolic intermediate, pyruvic acid, are included in the model to enhance

its predictions when the process is subjected to a feed overload.

An inhibitor entering with the feed, would cause a depression of the maximum

specific growth rate of the bacterial populations. If the maximum specific growth

rate drops below the dilution rate then washout occurs. By using a simple model for

the anaerobic digestion process and employing Pontryagin's maximum principle, an

optimal control law that maximizes the total of methane produced over a period of

several time constants was obtained. It was shown that this control law was

approximated extremely well by a linear relationship between dilution rate and

methane rate (constant yield control law). This linear relationship can be easily

implemented on an anaerobic digester.

An expert system to prevent failure of the process when it is exposed to

disturbances was developed. The constant yield control law was built into this expert

system. The expert system uses only methane rate measurements to identify onset

of the disturbance. This expert system was implemented on a bench scale anaerobic

digester and its efficacy in preventing imbalance when the digester was exposed to

a triple overload and phenol, was tested. The expert system successfully prevented

digester imbalance.



The objective of this work is to develop an on-line automatic control strategy

to prevent and mitigate imbalance in the anaerobic digestion process.

Technical Perspective

Anaerobic Digestion

Anaerobic digestion is a natural and widely used process for the stabilization

of organic matter. It is useful for stabilization because most of the degradable

component of the organic matter is converted to methane. This conversion process

is carried out by several populations of microorganisms. Almost all natural and many

synthetic organic compounds can be stabilized by anaerobic processes. Anaerobic

treatment is applied to agricultural wastes like animal manures and crop residues,

industrial waste effluents like food processing wastes, brewery wastes and paper and

pulp mill wastes and sewage sludge. Degradation of some hazardous wastes can also

be accomplished through this process. Several investigators have studied the viability


of using the process specifically for producing energy from plant biomass (Chynoweth

and Isaacson, 1987; Smith et al., 1988).

There are several advantages of anaerobic digestion over the conventional

aerobic biological treatment processes. In aerobic treatment the waste is mixed with

air. The microorganisms obtain energy for growth through oxidation of the organic

matter in waste with oxygen. Since these organisms obtain much of their energy

from this oxidation, their growth is rapid and a large portion of the organic waste

is converted to new cells. Hence, the organic portion is just changed in form (with

very little oxidation) and this biological sludge poses a significant disposal problem.

However, in anaerobic treatment systems, since air is excluded, the microorganisms

have less energy available for growth. Hence, only a small portion is converted to

new cells. A major portion of the degradable waste is converted to methane, thus

a higher degree of waste stabilization is achieved. As much as 80 to 90 percent of

the degradable organic portion of waste is converted to methane. In addition, the

requirements of nutrients like nitrogen and phosphorous are greatly reduced enabling

the process to be applied for treatment of certain industrial wastes that are deficient

in these nutrients. In anaerobic treatment substrates like phenol and other aromatic

compounds are broken into smaller molecules, whereas in aerobic treatment these

substrates are converted chemically into polymeric adducts which resist further

degradation (Schink, 1988). Moreover, since the process does not require oxygen,

the treatment rates are not limited by oxygen transfer and no energy is expended for

purposes of aeration.

Imbalance Problem

Causes. The anaerobic digestion process is prone to imbalance when exposed

to disturbances such as feed overload where the substrate concentration in the feed

increases, feed underload where the substrate concentration in the feed decreases,

or an inhibitor entering with the feed. Stable performance is based on a symbiotic

relationship between various bacterial populations (mainly the acidogenic bacteria,

acetogenic bacteria, acetoclastic methane bacteria, and hydrogen-utilizing methane

bacteria). An inhibition of any one population can introduce an imbalance in this

symbiotic relationship.

Consequences. An imbalance of the process can lead to digester failure. Since

the methanogenic bacteria are very sensitive to disturbances, these are inhibited

easily. The acidogenic bacteria continue to produce volatile organic acids and these

are no longer consumed by the methanogens. Hence, there is an accumulation of

these organic acids leading to a "stuck" digester. At this point the digester can no

longer process any waste. It may require months to recover a stuck digester causing

lengthy shut down of the operation.

Measurements. Traditionally volatile organic acid, pH and alkalinity

measurements are used to identify an imbalance (Duarte and Anderson, 1982).

When the digester is imbalanced volatile organic acids accumulate resulting in a drop

in the pH. However, recent knowledge of the process indicates that volatile organic

acid accumulation is a result of an imbalance and not the cause of the imbalance.

Gas production rate measurements have also been used to detect imbalance


(Podruzny and van den Berg, 1984). Some researchers (Whitmore and Lloyd, 1986)

have used liquid phase hydrogen concentrations to identify the onset of imbalance.

Mosey and Fernandes (1989) used gas phase hydrogen concentrations to detect both

feed overloads and inhibitors. In this study the methane production rate

measurements are used to recognize an imbalance in the process. Most recently it

has been shown that on-line NADH fluorescence measurements can be used to

detect imbalance (Owens et al., 1991).

Corrective measures. At present very few industrial scale digesters are

equipped with automatic control systems that can recognize imbalance and are

capable of taking corrective measures immediately. The automatic control systems

that exist on industrial scale digesters rely on volatile organic acid and pH

measurements to realize the onset of an imbalance (Rusell et al., 1985). A pump is

turned on to feed a base so as to bring the pH back to normal levels. Then the

cause of the imbalance is identified. If it is a feed overload, the feed is diluted or if

it is an inhibitor in the feed then once again the feed is diluted so as to bring the

inhibitor concentration below levels that can cause inhibition.

However, several control schemes have been developed for bench and pilot

scale digesters using gas (Podruzny and van den Berg, 1984), alkalinity (Rozzi et al.,

1985), liquid phase hydrogen (Whitmore and Lloyd, 1986, Dochain et al., 1991), pH

(Denac et al., 1988) and digester substrate measurements (Renard et al., 1988). All

these schemes involve keeping the measured value at a set point by manipulating the


feed rate. The set point is the value of the measured variable during normal digester


Limitations. Accumulation of volatile organic acids and the associated pH

depression are the end results of an imbalance, not the cause. Hence by the time

these changes are detected, it might be too late to take any corrective action. Gas

production rate is not a reliable indicator of imbalance. Response of the gas

production rate to inhibitors is inconsistent because it depends on the type of

toxicant. If the toxicant inhibits the growth rate of the acidogens and methanogens

then gas production rate would drop. However, if it inhibits only methanogens then

gas production rate increases because the carbon dioxide consumption rate by the

methanogens is decreased. Measurement of liquid phase hydrogen concentrations

for purposes of digester control is an attractive concept, but hydrogen measurement

can pose problems. The concentration of hydrogen in the liquid phase tend to be

around a tenth of ppm making it extremely difficult to detect and measurement

devices for hydrogen are very expensive.

Automatic digester control schemes that have been developed so far have

aimed at preventing imbalance resulting from a feed overload. A common problem

associated with treatment of wastes the presence of toxic substances in the waste.

These inhibitors appear intermittently making it very difficult to detect before hand.

If it is a persistent problem then unit operations can be designed to remove the

inhibitor from the feed before it is fed to the digester. The pulses of inhibitor that

are fed to the digester can be very toxic to the microorganisms causing an imbalance


in the process. Hence, there is a very urgent need for a control scheme that would

prevent an imbalance to the process in the presence of inhibitors in the feed.

Proposed Approach

An expert system was developed here that would prevent imbalance to a

digester when it is exposed to either a feed overload or an inhibitor entering with the

feed. This expert system makes decisions based on methane production rate

measurements. Gas production rate is measured on-line after scrubbing the carbon

dioxide. Since a feed underload or an inhibitor entering with the feed can cause a

depression in methane production rate, the methane production data are evaluated

using statistical tools to distinguish between the two cases. Depending on the cause

for a potential imbalance the expert system chooses appropriate control scheme. The

complete control strategy can be automated hence eliminating any need for

intervention by the operator.

The anaerobic digestion process was modelled by using the most recent

knowledge available for this process. A simplified version of the model was used to

arrive at a control strategy to prevent imbalance due to inhibitors entering with feed.

Then the expert system was developed. Simulations were done using the model to

test the expert system. After ensuring that the expert system performed to the

desired expectation levels, it was implemented on a bench scale digester.

Subsequent chapters detail the development of the model, theoretical

development of a control law to prevent imbalance caused by inhibitors in feed and


the development and testing of the expert system. An important observation

regarding the reliability of using volatile organic acid accumulation to identify

imbalance is included as a chapter. The final chapter lists the conclusions and

recommendations for future work.



Anaerobic digestion process models can aid in predicting the dynamics of the

process when it is subjected to disturbances, in assessing proper operating strategies

and in designing anaerobic digesters. Such a model must adequately describe the key

microbial processes and account for the key variables of interest.

The anaerobic conversion of organic matter into methane involves the

concerted action of at least five different groups of bacteria (Zeikus, 1981; Mosey,

1983). The complex carbohydrates, fats and proteins in the waste stream are

hydrolyzed by hydrolytic enzymes into simple sugars like glucose. In this work,

glucose is used as the major feed substrate; hence the hydrolysis step is not

accounted for. The acidogenic bacteria convert glucose to volatile organic acids

(primarily acetic, propionic and butyric acids). The acetogenic bacteria utilize the

higher acids, namely propionic and butyric acids, producing acetate and hydrogen.

There are two classes of acetogenic bacteria, the propionate utilizing acetogenic

bacteria convert propionic acid to acetic acid and the butyrate-utilizing acetogenic

bacteria convert butyric acid to acetic acid. The acetoclastic methane bacteria utilize



acetic acid as a substrate for growth, producing methane and carbon dioxide as

byproducts. The hydrogen and carbon dioxide that are produced in the earlier steps

are utilized by another class of bacteria, the hydrogen utilizing methane bacteria, to

form methane. It is believed that in healthy digesters approximately 70 percent of

the methane produced is due to the acetoclastic methanogens and the rest due to the

hydrogen utilizers (Kaspar and Wuhrmann, 1978). The microbial ecology of the

process, starting with glucose as the feed substrate, is depicted in Figure 2-1.

Significant work in model development has been done by several researchers.

Andrews (1969) and Andrews and Graef (1970) assumed that the methanogenesis

from acetate is the rate-limiting step and therefore the most important one in the

process. Consequently, they modeled only this step. This effort was followed by

more complex models incorporating, most or all of the main bioconversion steps

(Heyes and Hall, 1981; Mosey, 1983; Bryers, 1985; Smith et al, 1988; Costello et al.,

1991a; 1991b; Pullammanappallil et al., 1991). An important issue is how to model

the generation of the different volatile organic acids produced in the acidogenesis

step. Smith et al. (1988) assumed that the volatile organic acids were generated at

a fixed ratio and took into consideration the kinetics of all the steps except that of

methanogenesis from hydrogen. Moreover, Smith et al. (1988) developed physico-

chemical relationships for the liquid phase and state equations, based on mass

balances, for the partial pressures of methane and carbon dioxide in the gas phase.

These physico-chemical relationships and the state equations enabled the model to

predict ion concentrations in the liquid phase, gas composition and gas production


Xa : Acidogenic Bacteria
Xb : Butyrate Utilizing Acetogenic Bacteria
Xp : Propionate Utilizing Acetogenic Bacteria
Xm : Acetoclastic Methanogenic Bacteria
Xh : Hydrogen Utilizing Methanogenic Bacteria

Figure 2-1 : Microbial ecology of the anaerobic
digestion process.


rates. It has been shown that the generation rates of volatile organic acids are

influenced by the partial pressure of hydrogen in the gas phase (lannotti et al., 1973;

Kaspar and Whurmann, 1978). When the process is "healthy", the hydrogen utilizers

convert most of the hydrogen produced in the acidogenesis step to methane and the

concentration of hydrogen in the gas phase is between 1.0 and 10.0 ppm (at

atmospheric pressure). However, when the process is imbalanced the hydrogen

utilizers are no longer able to convert hydrogen and consequently hydrogen

accumulates. Accumulation of hydrogen leads to propionate build up. To quantify

this behavior, Mosey (1983) proposed that the distribution of volatile acids produced

as acetic, propionic and butyric acids is regulated by the ratio of the concentrations

of the reduced to the oxidized forms of the coenzyme nicotinamide adenine

dinucleotide ([NADH]/[NAD']). This ratio is in turn related to the partial pressure

of hydrogen in the gas phase and the pH.

The model presented here is a modification of an earlier modeling effort

(Pullammanappallil et al., 1991) and like its predecessor is largely based on the work

of Mosey (1983). The regulatory mechanism for the formation of volatile organic

acids proposed by Mosey (1983) is integrated with physico-chemical relationships for

the liquid and gas phases to predict gas production rates and composition of the gas

phase. However, whereas Mosey (1983) assumes a pseudo-steady state for pyruvate

and acetylcoenzyme A (acetyl-CoA), which are intermediates during the metabolic

conversion of glucose to volatile organic acids, our model does not. Relaxing this


assumption delays accumulation of volatile organic acids in response to an increase

in the feed load and as a result the model fits experimental data better.

Costello et al. (1991a; 1991b) presented a very similar modeling approach.

They also coupled Mosey's distribution of volatile organic acids with equilibrium and

mass transfer relationships. However, they did not account for the accumulation of

acetyl-CoA and pyruvate while they considered lactic acid as an intermediate.

Another difference between the Costello et al. model and the model presented

here has to do with the inhibition of the different bacterial populations. Costello et

al. (1991a) assumed pH inhibition for all the major bacterial populations and in

addition hydrogen inhibition for acidogenic, acetogenic and lactic acid bacteria.

In our model, the acidogenic, acetogenic and acetoclastic methane bacteria are only

inhibited by hydrogen and the hydrogen-utilizing bacteria are pH inhibited. These

inhibitions are in better agreement with experimental data (Zehnder, 1977; Chapter

5 this dissertation).

In what follows the model equations are first derived. Parameter

determination is subsequently discussed. Next, the experimental set-up, materials and

methods used for model verification are presented. Finally, the model is verified by

comparing it against experimental data. It is shown that incorporating pyruvate

accumulation significantly improves the model performance. However, further

improvement by incorporation of acetyl Co-A accumulation is negligible.


Model Development

Development of the process model has been divided into three major sections.

The first section details the stoichiometry of the key conversion steps, stoichiometry

of the bacterial synthesis steps and the biological rate equations for the bacterial

populations. In the second section, physico-chemical relationships for the liquid

phase are developed. The third section describes the dynamics of the gas phase.

Stoichiometry and Biological Rate Equations

Bacteria are unable to take up particulate organic material. By the action of

hydrolytic enzymes particulates are broken down to soluble intermediates. In this

work, glucose is used as a representative molecule to simulate these soluble organic

substrates. An empirical formula of C5H903N is assumed for all bacterial

populations (Mosey, 1983). Bauchop and Elsden (1960) suggest that one mole of

ATP provides sufficient energy for the formation of 10 grams of biomass. However,

experimental data obtained from the digester used in this study showed that this

value substantially overpredicts the amount of biomass produced and that a value of

4.0 grams might be more appropriate. This empirical value (YB) is used to

determine biomass yield coefficients from the stoichiometric relationships. Following

Mosey (1983) all other yield coefficients where determined from the stoichiometry

of the conversion reactions.

Acidogenesis step. The acidogenic bacteria convert glucose to primarily

acetic, propionic and butyric acids according to the following reactions (Mosey, 1983)

C6HO206 + 2H,2 2CH3COOH + 2CO2 + 4H2 + 4ATP (2-1)

C6H1206 + 2H2 -, 2CH3CH2COOH + 2H20 + 2ATP (2-2)

C6H1206 CH3CH2CH2COOH + 2CO2 + 2H2 + 2ATP (2-3)

Under normal conditions most of the glucose is converted to acetic acid.

Hydrogen is also produced. This hydrogen is converted to methane by the hydrogen

utilizing methane bacteria. However, if for any reason the hydrogen utilizing bacteria

are inhibited then hydrogen accumulates. High hydrogen concentrations would favor

the formation of propionic acid as can be seen from the above stoichiometric

relationship. The butyric acid formation reaction is also favored because this

reaction produces less hydrogen than the acetic acid reaction. Hence, an imbalance

in the process results in accumulation of propionic and butyric acids.

To quantify this accumulation, it is necessary to look at the metabolic pathway

of the acidogenic bacteria. A simplified diagram of this pathway is shown in Figure

2-2. It can be seen that the regulation of the formation of the volatile organic acids

is determined by the relative availabilities of the reduced (NADH) and the oxidized

(NAD') forms of the intracellular coenzyme nicotinamide adenine dinucleotide.

High NADH concentrations would favor formation of propionic acid and butyric

acid. The NADH half reaction (Figure 2-2) shows that high H' concentrations

would favor the formation of NADH. An increase in the partial pressure of


hydrogen in the gas phase would result in an increase in the concentration of H'.

To formulate a relationship between the ratio [NADH]/[NAD+], pH and partial

pressure of hydrogen, Mosey (1983) equated the redox potential of the half reaction

NAD + H+ + 2e- NADH

to that of

2H' + 2e- H2

and made the following assumptions:

a) gaseous hydrogen diffuses both freely and rapidly into and out of the

bacterial cells, so that the concentration of hydrogen inside the bacteria is

proportional to the partial pressure of hydrogen in the digester gas,

b) redox potential of the bacteria is equal to the redox potential of the growth

medium. These result in the following expression:

[NADH] 10 (logw2 pH + 29.

where Eo is the standard redox potential of the NADH/NAD+ couple, i.e. -113 mV.

The conversion of glucose to pyruvate is also affected by the

[NADH]/[NAD'] ratio (Figure 2-2). High concentrations of NAD' would maximize

this conversion rate. Following Mosey (1983), it is assumed that the uptake of

glucose for catabolism follows Monod kinetics and is proportional to the NAD'

fraction (which is equivalent to inhibition by the [NADH]/[NAD'] ratio). The rate

of utilization of glucose for catabolism is then given by


2[glyceraldehyde phosphate]
I,- 2NAD+

2[Pyruvic acid]

4 NAD +

2[Propionic aci


1L^2[Acetyl CoA] ---2[Acetic Acid]

2 NAD+

Butyric acid


NADH NAD+ + 2e- + H+

Figure 2-2: A simplified diagram of the metabolic pathway
inside the acidogenic bacteria.

r 1 kG [G] [Xa
(G + [NADH] Ks,G + [G] (2-4)
[NAD] )

where kG is the maximum rate constant of the acidogens (mMol/mg acidogen/day)

and KS,G the Monod half-velocity constant (mMol/L).

By assuming that there is no accumulation of pyruvate or acetyl-CoA, that the

converted pyruvic acid is split between propionic acid and acetyl-CoA according to

the NAD' fraction and that the converted acetyl-CoA is also split according to the

NAD fraction, the rate equations for the formation of acetic, propionic and butyric

acids can be formulated (Mosey, 1983):

d [Propionic] 2r G
dt [N2-5)
[NADH] )

d[Butyric] r G
dt + [NADH] 1 [NAD](2-6)

d [Acetic] 2r'G
dt + [NADH 2 (2-7)


However, experimental data obtained by doubling the glucose concentration

in the feed showed that the build up of volatile organic acids started at a

considerably lower rate than the above expressions would predict. This indicates that

accumulation of at least one intermediate should be considered and leads us to

investigate relaxing the pseudo-steady state assumptions for pyruvate and acetyl-CoA.

To account for pyruvate and acetyl-CoA accumulation, it is necessary to devise

expressions for the rate of utilization of pyruvate and acetyl-CoA. These expressions

are assumed to be of the Michaelis-Menten form (Bailey and Ollis, 1985). It is also

assumed that the concentration of enzymes that convert pyruvate to propionate and

acetyl-CoA to butyrate and acetate are proportional to the concentration of the

acidogenic biomass. Hence, the utilization rate expressions are

r = a [PYR [Xa] (2-8)

r COA= [CoA] [Xa] (2-9)
CoA KB,coA + [CoA]

The net rates of formation for pyruvate and acetyl-CoA are

d [Pyruvate] = 2r r_
dt PYR


d[CoA] 1 I/ -
dt (+ [NADH]

Based on the above assumptions and rate expressions the rate of formation

of volatile organic acids then become

d[Propionic] 1 r //
dt [NAD] (2-10)

d[Butyric] 1 1 r/COA
dt 2 ( [NADH] + A (2-11)
+ [NADH]

d[Acetic] 1 r/CA
dt + [NADH] A (2-12)
1 + [NAD+] )

As will be shown later, by considering only accumulation of pyruvate and assuming

pseudo-steady state for acetyl-CoA the model predictions do not change significantly.

In that case



S1 1
+ + [NADH)
[NAD'] )

The net rates of formation of the volatile organic acids are obtained by replacing

r'c from the above expression in equations (7) through (9).

The stoichiometry for the synthesis of acidogenic biomass (Mosey 1983) is

5C6H1206 + 6NH3 6C5H903N + 12H20 (2-13)

The overall synthesis rate is due to synthesis in the acetic acid formation step,

propionic acid formation step and butyric acid formation step. The net rate of

utilization of glucose by the acidogenic biomass would then be the sum of the rate

of glucose utilized for catabolic activity and the utilization rate for synthesis of


d[Glucose] + 1 YAda/A d[Acetic]
dt G YAd, a a/A dt
yAd d [Propionic]
xa/P dt

+ yAd d[Butyric] )
x a/B dt

The parameters Y are yield coefficients which are determined from stoichiometry

along with the empirical yield of 4.0 grams of biomass per mole of ATP. The

notation is explained in Appendix A.

Acetogenesis step. In this step longer acids, namely propionic and butyric

acids, are converted to acetic acid, hydrogen and carbon dioxide. The propionate-

utilizing acetogens consume propionate and the stoichiometry for this conversion

process is (Mosey, 1983)

CH3CH2COOH + 2H20 CH3COOH + CO2 + 3H2 + 1ATP (2-14)

The stoichiometry for the butyrate utilizing organisms is (Mosey, 1983)

CH3CH2CH2COOH + 2H20 2CH3COOH + 2H, + 2ATP (2-15)

From the above stoichiometric equations, it can be seen that the conversion

processes are inhibited by high hydrogen concentrations.

The specific growth rate expressions for the acetogens are of the Monod form

with terms incorporated for inhibition by hydrogen (Mosey, 1983)

Slmax,xp [Propionic] (2-16)
x (KP + [Propionic]) (1 + KIHxpPH)

Smax,Xb [Butyric] (2
(Ks,B + [Butyric]) (1 + KIHxbH2)

The stoichiometry for synthesis of the propionate-utilizing and butyrate-

utilizing biomass (Mosey, 1983) is

3CH3CH2COOH + CO2 + 2NH3 2C5H903N + 2H20 + H2 (2-18)

CH3CH2CH2COOH + CO2 + NH3 -~ CsH903N + H20 (2-19)

respectively. The rate of utilization of propionate and butyrate can be expressed as

a product of the growth rate of the acetogens and a yield coefficient (mg of

acetogens/ mMol of propionate (or butyrate) consumed) which is determined from

the above stoichiometry.

Acetoclastic methanogenesis step. Almost 70 percent of the methane

produced is due to this step. The acetoclastic methanogens convert the acetic acid

produced in the previous steps to methane and carbon dioxide. The stoichiometry

for this step (Mosey, 1983) is

CH3COOH CH4 + CO2 + 0.25ATP (2-20)

The model presented by Smith et al. (1988) assumes that the acetoclastic

methanogens are inhibited by acetic acid, the substrate and consequently they

incorporate a inhibition factor for acetic acid inhibition in the growth rate expression.

Several investigators have studied volatile organic acid toxicity in anaerobic digestion

(Buswell, 1947; Schlenz, 1947; McCarty and Mckinney, 1961; Buswell and Morgan,

1962; Kugelman and Chin, 1971; Jarrell et al, 1987; Barredo and Evison, 1991).

Buswell (1947) and Schlenz (1947) reported that volatile organic acids are toxic to

methane bacteria at concentrations of about 2000 mg/L. McCarty and McKinney

(1962) investigated the toxicity of acetic acid to methane bacteria and found that

toxicity sets in at concentrations between 2000 and 4000 mg/L. However, they

concluded that the toxicity was caused by the sodium cation (which was added at

increased amounts as part of the buffer). Following this, Buswell and Morgan (1962)

reported that propionic rather than acetic acid was toxic to methane bacteria.


Subsequently McCarty and co-workers reported that volatile organic acids did not

adversely affect methanogenesis but high concentrations of propionate (6000 mg/L)

inhibited the acidogenic bacteria (Kugelman and Chin, 1971). Jarrell et al. (1987)

reported that propionate and butyrate can be inhibitory at concentrations above 60

g/L. However, Barredo and Evison (1991) found that concentrations of propionate

as low as 1480 mg/L can cause inhibition of the methanogens. Hence, the debate

over toxicity of the volatile organic acids still continues. But studies that were done

in our laboratory (detailed in Chapter 5) showed that the methanogens were not

inhibited even at propionate concentrations of 3500 mg/L. Therefore, inhibition of

acetoclastic methanogens by volatile organic acids is omitted in the present model

development. It is proposed instead, that the kinetics of these organisms are

regulated by hydrogen. It has been shown that most species of methanogens share

the common ability to form methane via reduction of carbon dioxide with hydrogen

(Oremland, 1988). When hydrogen accumulates in the digester, due to reasons other

than inhibition of hydrogen utilizers, it becomes thermodynamically favorable for

hydrogen to be utilized rather than acetate. This is evident when the energy yields

by the two substrates acetate and hydrogen are compared. The energy yield by

acetate is -28 kJ/mol whereas by hydrogen it is -139 kJ/mol. Incorporating

inhibition by hydrogen, the specific growth rate of the acetoclastic methanogens can

be written as follows

Smaxx [Acetic] (2
m [Acetic] + Ks,A) (1 + KIHpxm) (2

The stoichiometry for the synthesis of acetoclastic methanogenic biomass

(Mosey, 1983) is

5CH3COOH + 2NH3 2C5H,03N + 4H20 (2-22)

This is used to determine the amount of acetic acid needed for synthesis of

methanogenic biomass.

Methanogenesis from hydrogen. The hydrogen-utilizing methanogens reduce

carbon dioxide with hydrogen according to the following stoichiometry (Mosey, 1983):

CO2 + 4H2 -- CH4 + 2H20 + 1ATP (2-23)

The hydrogen utilizers are assumed to follow simple Monod kinetics, regulated by

the pH of the fermentation broth. Zehnder and Wuhrmann (1977) has shown that

maximum growth occurs at a pH of around 7.1 and that the maximum specific growth

rate drops by half at pH below 6.6 and above 7.6. The functional form of pH

inhibition taken from Bailey and Ollis (1985)

rImax,Xh ~
(1+ []+
b [H+]

fits Zehnder and Wuhrmann's data well with values K = 31.93, b = 1.273 x 108 and

c = 7.58 x 10"7. Hydrogen is the limiting substrate for this microbial conversion step.

Since hydrogen is sparingly soluble in water, the concentration of hydrogen in the


fermentation broth is assumed to be proportional to the partial pressure of hydrogen

in the gas phase. The specific growth rate then is

Imax,Xh PH2 (2
I xh = (2-24)
(Ks,xh + PH2)

The stoichiometry for synthesis of hydrogen utilizers is

5CO2 + 10H, + NH3 CsH903N + 7H20 (2-25)

The above equation is used to determine the amount of hydrogen and carbon dioxide

needed for the formation of biomass and the values are incorporated into the carbon

dioxide and hydrogen utilization rates.

The kinetic expressions for substrate utilization and biomass growth based on

the stoichiometry discussed above are presented in Appendix A.

The Physico-Chemical Relationships

Relationships based on the physico-chemical properties of the various ionic

reactions are developed so as to be able to calculate ion concentrations in the

digester fermentation broth. The ionic species commonly found are OH-, H+, C032,

HCO3-,A-,P-,B-, other cations (Cion) and other anions (A,,n). A-,P- and B- are the

ionized forms of acetic, propionic and butyric acids. To specify completely a physico-

chemical system, the overall charge balance equation is required along with a mass

balance equation and an equilibrium relationship for each component species. It is

assumed that (CO2)dissoved-HCO3" is the only buffering system present.


Dissociation of acetic, propionic and butyric acids can be written as follows

AH A- + H+ (KA:equilibrium constant)

PH P- + H+ (Kp:equilibrium constant)

BH B- + H+ (KB:equilibrium constant)

The total concentrations of each volatile organic acid are the sum of the ionized

form and the unionized form. Hence, the total concentrations of acetic, propionic

and butyric acids are

[A] = [AH] + [A-]

[P] = [PH] + [P-]

[B] = [BH] + [B-]

respectively. Assuming equilibrium, the concentration of the ionized acids can be

expressed as

[A-] = K[A] (2-26)
(KA + [H*])

K, [P]
[P-] = K (2-27)
(Kp + [H*])

[B-] = KB[B (2-28)
(KB + [H] )

The dissolution of carbon dioxide gives


(CO2)D + H20 0 HCO3- + H' (I,:equilibrium constant)

where (CO2)D represents carbon dioxide dissolved in the liquid. Since anaerobic

digesters are usually operated at pH below 8, the concentration C03-2 is neglected.

The concentration of the total inorganic carbon then is

[TC] = [(CO2)D] + [HCO3-]

From the equilibrium relationship, the concentration of HC03- is

Kbo [TC]
[HCO-] K [TC (17)
(Kbc + [H])

For pH < 8 the concentration of OH- can also be neglected and the overall charge

balance is

[Z] + [Hn] = [A-] + [P-] + [B-] + [HCO-]


[Z] = net cations = [Other cations] [Other anions]

Substituting for the ionized forms of the volatile organic acids and HC03- from

equations (14), (15), (16) and (17) into the above charge balance yields

[Z] +[H]= K, [A] K, [P] KB [B] Kbc [TC]
(KA+ [H'] ) (Kp+ [H+] ) (KB+ [H'] ) (Kbc+ [H+] )

If [Z] and [TC] are known, the above equation is a fifth order polynomial in [H+]

and it can be solved numerically. However, the values of the dissociation constants

for the volatile organic acids are close to each other. For example at 350C and ionic


strength of 0.02, KA = 1.76 x 10-5, KB = 1.54 x 10-s and Kp = 1.34 x 10-5. Hence, it

is reasonable to approximate the dissociation constants of propionic and butyric acids

by that of acetic acid and the equivalent dissociation constant is denoted by Ke. This

approximation reduces the above equation to a cubic, which can then be solved

analytically. If very low values of pH (< 5) are not of interest, then the polynomial

becomes an easy to handle quadratic by neglecting the [H'] term on the left. In this

study [H'] is not neglected and the cubic equation is solved analytically.

[Z] and [TC] can be obtained by setting up respective mass balances. Net

cations would be in the form of [NH4+] and [Na'] since NaHCO3 and NH4HPO4 are

the only buffers added to the feed. Following Smith et al. (1988), the net cations are

assumed to be consumed at a rate proportional to the growth of biomass from all

species. The mass balance for [Z] for a continuously stirred anaerobic digester is

given in Appendix A

A mass balance for [TC] yields

d TC] = D([(CO2) D] + [HC0] o- [TC] ) + rco, + T

where [(CO2)Do. = dissolved carbon dioxide concentration in the feed

[HC03-] = bicarbonate ion concentration in the feed

rco2 = net rate of carbon dioxide generation from the biological


T, = carbon dioxide transfer rate from gas phase to liquid


The rate of generation (or consumption) of carbon dioxide is proportional to the

growth rate of the bacteria that are generating (or consuming) it and an expression

is given in Appendix A. The carbon dioxide transfer rate is given by

Tg = KLa (KHLpco [(CO2) D])

where KLa is the mass transfer coefficient and KHL is the Henry's Law constant.

Gas Phase Equations

The gas phase is assumed to be completely mixed and always at a total

pressure of one atmosphere. Moisture content of the gas is neglected so that

Pco, + PH, + PCH4 = PT = 1 atm

Methane and hydrogen are assumed to be insoluble in the fermentation broth and

all three gases follow ideal gas behavior. Then the mass balances for the gas phase

can be written in terms of the partial pressures

dpco, PTQCO Pco2Qgas
dt V, V,

dt V, V,


dPcH PTQCH, PcH Qgas
dt Vg Vg

Qco2, QH2 QCH are volumetric rates of production in the liquid phase for CO2, H2

and CH4 respectively, Qgas (= Qco + H2 + QCH,) the rate of gas leaving the

digester and Vg the constant volume of the gas phase. Now

Qco, = -TgVidV

Qn = r2VidV



V = volume of the liquid phase

rH2 = net rate of formation of hydrogen from the biological reactions


(see Appendix A)

= rate of formation of methane from the methanogenesis steps

(see Appendix A)

Vid = volume of one mole of gas, in liters, assuming ideal behavior, at 35 C


The complete model for a glucose fed anaerobic digester is summarized in Appendix


Determination of Model Parameters

All the yield coefficients except YB and Yz are calculated from the

stoichiometric relationships presented in the above section. Yz was estimated such

that model pH predictions fit experimental pH data. The value of Y, was estimated

such that the total biomass concentration calculated by the model fits experimental

data. Table 2-1 lists the values and the stoichiometric equation or source, of all the

yield coefficients used in the model. The notation is explained in Appendix A. The

physico-chemical parameters were obtained from the literature and is listed in Table


The kinetic parameters, maximum growth rate (Aimax) and Monod half-velocity

constant (Ks), for all bacterial species except for that of the acetoclastic methanogens

are obtained from the literature. However, for the acetoclastic methanogens a range

of values were available in the literature. Several researchers have calculated the

values for the kinetic parameters /imax,xm and IK, (Lawrence and McCarty, 1969;

Smith and Mah, 1980; Zehnder et al., 1980; Gujer and Zehnder, 1983; Smith et al.,

1988). The values reported in these papers vary significantly. The value of /max,xm

varies from 0.11 d-1 to 0.54 d-1 and the value of K, ranges from 0.44 mMol/1 to

14.53 mMol/1. Hence, it was appropriate to estimate the values of these parameters


Table 2-1
Yield Coefficients (expressed in Mol/Mol)

Yield Value Source Yield Value Source

Y, 0.031 Expt. YAtH,/ 2 2-15

y a/A 0.062 2-1 YAt,/H 2 2-18

YAda/ 0.031 2-2 At,sb/B 1 2-19

SAdXa/B 0.062 2-3 YAtco2/ 1 2-14

y AdCO/A 1 2-1 yAt, So2/ 0.5 2-18

y Ado/B 2 2-3 yAt, CO/Xb 1 2-19

y /Ad 2 2-1 YMX/A 0.008 2-20

SAd2/ 1 2-2 yM,,sX 0.4 2-22

SAd/B 2 2-3 YMC,/A 1 2-20

yAd, a/G 1.2 2-13 yMCA 1 2-20

y At A/ 1 2-14 YHCO,2 4 2-23

y AtXp/P 0.031 2-14 YHxh/H2 0.008 2-23

yAt,sp/P 0.667 2-18 YH,sCo/x 5 2-25

yAtA/B 2 2-15 yHsXh/H, 0.1 2-25

yAtXb/ 0.062 2-15 YHCH,2 0.25 2-23

yAt 2 3 2-14 Yz 1.39 Expt.

Table 2-2
Physico-chemical Parameters

Dissociation constant of the dissolved 1 x 10-6.32
carbon dioxide-bicarbonate system, KIc
Equivalent dissociation constant of 1.76 x 10-5
volatile organic acids, K, (Mol/L)
Henry's Law constant, KHL 1 x 101-5
Overall mass transfer coefficient, KLa 100
Gas Constant, d (L/Mol) 25.27
Gas Constant, Via (L/Mol)


Table 2-3
Kinetic Parameters

Maximum Growth Rates
Acidogens, kG
(mMol glucose/mg acidogen/day)
Propionate utilizing acetogens, 4.max,Xp
Butyrate utilizing acetogens, /max,Xb
Acetoclsatic methanogens, Amax,xm

Monod Half-Velocity Constants
Acidogens, Ks,G (mMol/L)

Propionate utilizing acetogens, K,p
Butyrate utilizing acetogens, Ks,B (mMol/L)

Acetoclastic methanogens, Ks,xm (mMol/L)
Hydrogen utilizing methanogens, Ks,xh (atm)

Inhibition parameters
Propionate utilizing acetogens by hydrogen,
KIHxp (atm-1)
Butyrate utilizing acetogens by hydrogen,
KIHxb (atm-1)
Acetoclastic methanogens by hydrogen,
KIHx (atm-1)

Kinetic parameters for pyruvate utilization
Maximum rate constant, a
(mMol pyruvate/mg acidogen/day)
Michaelis constant, Ks,PYR (mMol/L)














Ghosh and Pohland
Lawrence and McCarty
Ghosh and Klass (1978)

This study

Ghosh and Pohland
Lawrence and McCarty
Lawrence and McCarty
This study
Shea et al. (1968)

This study

This study

This study

This study

This study


from an optimal fit. The estimated values for these parameters were determined to

be satisfactory since these were within the ranges mentioned above. It was also

necessary to estimate the values for the parameters a, KI,PYR, B and IK,coA since no

literature values were available. Table 2-3 lists the values of all the kinetic

parameters used in the model. For those parameters whose values were obtained

from literature then the reference paper is indicated in the table.

Experimental data obtained by doubling the feed loading rate to a

continuously stirred anaerobic digester were used to determine model parameters.

The optimal estimates were obtained by minimizing the normalized sum of squared

errors between the experimental values and model predictions. Normalization of data

was done by dividing acetate concentrations by 100, propionate concentrations by

150, butyrate concentrations by 18 and methane production rate by 1. The optimal

estimates were calculated using the Marquadt-Levenberg algorithm (Press et al.,

1989). The QuickBASIC 4.5 version of this algorithm presented in Sprott et al.

(1991) was implemented on a 50 MHz IBM 80486 personal computer to perform the


Materials and Methods

A continuously-fed continuously-stirred (CSTR) 6 L digester was instrumented

for automated data acquisition of methane production rate, temperature and pH.

The digester was fed by a computer controlled peristaltic pump and temperature


controlled by a PID temperature controller with set-point control provided by the

computer. A schematic of the set-up is detailed in Figure 2-3. The computer was

equipped with a digital I/O interface board for monitoring a float switch on a U-tube

gas meter. The gas vented from the digester was scrubbed of its carbon dioxide

content before it reached the gas meter. The methane accumulated in one limb of

the U-tube by displacing the liquid. When the liquid in the other limb rose to a

certain level, a float switch was tripped, which caused two events to happen

simultaneously. A signal was sent to the computer and also the methane from the

first limb was exhausted resetting the liquid level. By measuring the time between

two successive signals and given that the volume of methane that triggers the signal

is known, the methane production rate could be calculated. The digester was

operated at a 20 day retention time with a nominal loading rate of 2 g COD LU1 d1.

Glucose and feed media were sterilized and kept refrigerated during digester

operation. Appendix B lists the components of the feed. Digester effluent was

collected from an overflow tube.

Volatile organic acids were measured on an FID gas chromatograph. The

samples were prepared by centrifugation followed by sample acidification using 20%

phosphoric acid. The samples were injected onto a 2 m long by 2 mm id glass

column packed with 80/100 chromosorb 1200 WAW coated with 3% H3PO4. A 1

gL volume was injected at an inlet temperature of 180 oC with column temperature

ramped from 130 "C to 170 o over 5 minutes and a detector temperature of 200 C

Nitrogen was used as the carrier gas.

--..------------------------- GAS METER SNITCH


Eh pH

/-^ i r




L-- ---------
-- --- ---------------- --


Figure 2-3 : Schematic diagram of the experimental set-up

Model Verification

A dynamic test was first conducted. In this experiment the glucose

concentration in the feed was doubled by increasing it from 28.8 g/L to 57.6 g/L.

The concentration of the other components of the feed media were not changed.

Figures 2-4 through 2-11 compare the experimental results to the optimal model fits.

Certain parameters, as mentioned earlier, were estimated by fitting the model to the

experimental data.

First, it was assumed that there was no accumulation of pyruvate or acetyl-

CoA. The best fit of the model to the experimental acetic acid, propionic acid,

butyric acid concentrations as well as the methane production rate is shown in

Figures 2-4, 2-5, 2-6 and 2-7 respectively. These figures show that the model

response to the feed overload in terms of the accumulation of propionic and butyric

acids and rise in methane rate was much faster than the actual result. The acetic

acid accumulation rates calculated by the model were comparable to experimental

results, with the maximum build up of acetic acid underpredicted. The model

predicted the methane rate to increase instantaneously. It also predicted an

overshoot. This is contrary to the observations, where the methane rate increased


Figures 2-8, 2-9, 2-10 and 2-11 show the best fit of the model to experimental

acetic acid, propionic acid, butyric acid and methane production rate data, allowing

accumulation of pyruvate and acetyl-CoA. The model did reasonably well in

150 [-

100 -

2 4 6

TIME (days)

Figure 2-4:

Optimal fit of the model assuming no accumulation of pyruvic
acid or acetyl-CoA to experimental acetic acid data.



150 F-

100 1-

50 V-


TIME (days)

Figure 2-5:

Optimal fit of the model assuming no accumulation of pyruvic
acid or acetyl-CoA to experimental propionic acid data.

250 |-

200 -

25 1-


TIME (days)

Figure 2-6:

Optimal fit of the model assuming no accumulation of pyruvic
acid or acetyl-CoA to experimental butyric acid data.

0 2 4 8 8

TIME (days)

Figure 2-7:

Optimal fit of the model assuming no accumulation of pyruvic
acid or acetyl-CoA to experimental methane production rate

2 4 6 8

TIME (days)

Figure 2-8:

Optimal fit of the model assuming accumulation of pyruvic
acid (and acetyl-CoA) to experimental acetic acid data.

150 -

100 -

50 -

2 4 6

TIME (days)

Figure 2-9:

Optimal fit of the model assuming accumulation of pyruvic
acid (and acetyl-CoA) to experimental propionic acid data.




25 -


0 2 4 6 8

TIME (days)

Figure 2-10: Optimal fit of the model assuming accumulation of pyruvic
acid (and acetyl-CoA) to experimental butyric acid data.

2.0 I

K 1.5-

, 1.0 V V V

S0.5 -

0.0 I I I
0 2 4 86

TIME (days)

Figure 2-11:Optimal fit of the model assuming accumulation of pyruvic
acid (and acetyl-CoA) to experimental methane production
rate data.


predicting both the accumulation rate as well as the maximum build up of acetic acid

and propionic acid. However, experimental butyrate accumulation (Figure 2-10)

occurred later than the model indicates. The calculated methane-rates were in fairly

good agreement with the experimental data. The kinetic parameters B (maximum

rate constant) and (KI,coA) (Michaelis constant) for acetyl-CoA accumulation that

gave the optimal fit were 0.18 mMol acetyl-CoA/mg acidogen/day and 0.4 mMol/L

respectively. Comparing these values to the kinetic parameters of pyruvate

accumulation (Table 2-3) indicates that a < < B and KI,PYR > K,CoA. A higher

value of B and the corresponding lower value of Ks,CoA means that acetyl-CoA is

utilized as soon as it is produced. Hence, pyruvate accumulation should dominate

acetyl-CoA accumulation. Assuming a pseudo-steady state for acetyl-CoA and

accounting for pyruvate accumulation an optimal fit of the model to the experimental

data was obtained. As expected, neglecting acetyl-CoA accumulation did not affect

model predictions. Hence, the same figures (Figures 2-8, 2-9, 2-10 and 2-11)

represent the best fit of the model to experimental acetic acid, propionic acid, butyric

acid and methane production rate data.

Table 2-4 presents the normalized sum of the squared errors for the various

fits. Relaxing pseudo-steady state assumptions for pyruvate yields a minimum value

of 105 for the normalized sum of squared errors compared to a value of 148 allowing

pseudo-steady state for pyruvate and acetyl-CoA. However, relaxing pseudo-steady

state assumption for acetyl-CoA does not improve model performance.

Table 2-4
Comparison of the optimal normalized sum of squared errors
between the three proposed mechanisms

Pseudo-steady state assumption for 148.3
pyruvate and acetyl-CoA

Pseudo-steady state assumption only
for acetyl-CoA and allowing 105.1
accumulation of pyruvate

Relaxing pseudo-steady state 106.0
assumption for pyruvate and acetyl-CoA


The steady state model predictions are compared to experimental data in

Table 2-5. The model does well in calculating the methane production rate, methane

content of the gas phase and volatile organic acid concentrations. To determine the

experimental washout HRT, the dilution rate was stepped up from the normal value

and the digester was operated at the new value until the methane production rate

reached a steady state. Then the procedure was repeated by stepping up the dilution

rate. It was found that washout occurred between 10 and 12 days residence time

which is in agreement with the model prediction of 11.2 days.


A mathematical model for a glucose fed continuously stirred anaerobic

digester was developed. The model incorporates kinetic expressions for all the major

bacterial species involved in the anaerobic digestion process and also physico-

chemical relationships in the liquid and gas phases. The bacterial populations are

assumed to be inhibited by hydrogen which is in agreement with the current

knowledge of the process, where it is believed that hydrogen accumulation causes

build up of propionic and butyric acids. The model is capable of predicting essential

design parameters like gas production rates, gas composition and pH of liquid phase.

The performance of the model in predicting volatile organic acid build-up and rise

in methane production rate when the digester was subjected to a feed overload is

evaluated. It was found that relaxing pseudo-steady state assumptions for pyruvate


greatly improves model performance. However, no further improvement is achieved

by allowing for acetyl-CoA accumulation.

Table 2-5
Comparison of experimental results during normal
digester operations to model predictions

Methane production rate
(L/day/L reactor volume)
Methane percent (%)
Total biomass (g/L)
Acetic acid (mg COD/L)
Propionic acid (mg COD/L)
Butyric acid (mg COD/L)
Washout HRT (days)

0.67 0.7 0.68

7.1 7.2
4.0 5.0
10 50
10- 40
10 -12




Biological conversion processes can fail when exposed to compounds that are

toxic to the microorganisms. The effect of a toxicant on aerobic or anaerobic

bacteria has been shown to be equally severe (Blum and Speece, 1992). However,

in anaerobic digestion if the methane bacteria are inhibited by a toxicant, the result

is an accumulation of volatile organic acids leading to a "soured" digester. Due to

the prolonged generation times of the acetoclastic methanogens, the digester may

have to be shut down for months to repopulate it with a healthy culture. Common

inhibitors of anaerobic waste treatment processes are oxygen, heavy metals and

aromatic compounds like phenol. Some of these inhibitors imbalance the process

even when present in trace concentrations. Presence of traces of oxygen can cause

failure. The methanogenic bacteria are obligate anaerobes. It is essential that a

highly reduced environment be maintained to promote their growth. Dirasian et al.

(1963) found that optimum digestion occurred with an oxidation-reduction potential

between -520 and -530 mV. Converse et al. (1971) found that at oxidation-reduction

potentials greater than -360 mV, methane production was completely inhibited.


Heavy metal ions inhibit or kill microorganisms by inactivating a wide range of

enzymes. The heavy metal ions react with the sulfhydryl groups on the enzymes.

Toxicity due to cuprous, cupric, zinc, ferrous, nickel and cadmium ions has been

studied by several researchers. Mosey and Hughes (1975) showed that 163 mg/L of

zinc, 180 mg/L of cadmium, 170 mg/L of cupric or 1750 mg/L of ferric ions can

cause failure of digestion. Though, Jarrell et al. (1987) reported that even 10 mg/L

of zinc or cuprous ions can cause 50% inhibition of the methanogenic bacteria.

Phenol is toxic and is known to cause inhibition of the anaerobic digestion process

(Field, 1989). Phenol is a monomer of polymeric compounds like tannins, humous

and lignin. It is also present in organic bactericides, pesticides and the amino acid

tyrosine. Waste streams from paper and pulp mills, food industries and synthetic

chemical processes also contain phenol. Chou et al. (1978) reported that 2444 mg/1

of phenol causes 50% reduction in activity of unacclimated methanogens. The

examples presented above indicate that even low concentrations of the above

toxicants are potent enough to cause inhibition. The toxicants lower the maximum

specific growth rate of the methanogens. If this growth rate drops below the dilution

rate then wash-out occurs. Therefore, control measures should be taken as soon as

an inhibitor enters the digester so that it does not build up. The digester can be

saved if the dilution rate is lowered below the ultimate value of the methanogen

specific growth rate. The question is how should the dilution rate be lowered.

This chapter details the theoretical development of a control law, using a

model for the process, that prevents imbalance of digesters when it is exposed to an


inhibitor through the feed. The variable that was manipulated so as to mitigate the

severity of an inhibitor was the dilution rate. Methane rate was used as the

measured variable since it is easily measured on-line.

The Optimization Problem

Since digester failure results in cessation of methane production and since the

latter is the valuable product and can be relatively easily measured on line, a

reasonable performance measure to be maximized is

J(D(t)) = ftmethane (t) dt (3-1)

where Qmethane is the methane production rate, D(t) the dilution rate and tf the final

time (> 3 time constants). To have a tractable optimization problem the dynamics

of all reaction steps except for the rate limiting one (growth of methanogens and

associated production of methane) are neglected. Also, by assuming that the feed

substrate concentration does not vary, stoichiometry can be used to express volatile

organic acids concentration in terms of methanogen concentration. Then the state

variables are reduced to two, the methanogen concentration X and the inhibitor

concentration I. Neglecting inhibitor consumption the model equations are

dX (XI)X (3-2)
-DX + M (X,I)X (3-2)

dt= D ( I)


where the specific growth rate is

M(XI) f (I)
P (X,I) +
1+ s
SO y

The function f(I) accounts for the inhibitor effect on the growth rate; two functional

forms were considered

f (I) = e-aI

f(I) =
1 + bI



The methane production rate is proportional to the methanogen growth rate




The Hamiltonian is linear with respect to the manipulated variable, D(t), and

therefore for all t the optimal D is either on a singular arc or on a bound. Using a


brute force approach, the gradient projection method (Kirk, 1970), it was established

that the optimal D(t) starts on a bound (either zero or Dma, depending on the initial

conditions) until it hits a singular arc and stays on the singular arc until the final time

(tf). Computer memory limitations did not allow the use of this approach when tf

was large. However, a different approach was used.

A unique expression for D on the singular arc in terms of the states and

costates were obtained by setting the second time derivative of the partial of the

Hamiltonian with respect to D equal to zero. The expression for D was then

substituted into the state and costate differential equations to obtain a system of four

differential equations that describes the singular arc. Since the work with the

gradient projection method determined that at ty, D was on a singular arc and since

the optimal steady state value of D was not on a bound it was concluded that for

large tf the final values of the state variables are very close to their optimal steady

state values. Pontryagin's maximum principle (Kirk, 1970) gives the final values of

the costates as zero. With this information the state and costate differential

equations were integrated backwards in time to determine the singular arc.

Depending on the initial values of the state variables, the singular arc can be reached

by operating for a short period of time either batch or at the maximum dilution rate.

Figure 3-4 shows the singular arc trajectory. Initially the optimal operation would

be to stay batch and then move along the singular arc. In this manner the optimal

control law was determined.


Optimal and Easily Implementable Suboptimal Control Laws

Figure 3-1 depicts a typical optimal dilution rate for the case where inhibitor

enters at time zero and its effect on specific growth rate is given by equation 3-4.

The optimal response is to operate the digester in a batch mode for less than 0.006

days and subsequently change the dilution rate according to the equations of the

singular arc. Similar results are obtained with inhibitors following equation 3-5. In

practice, given that the model is not accurate and that the feed stream is not

characterized on line (e.g. Io is not known) the above "optimal" control law cannot

be implemented. For this reason a good suboptimal easy to implement control law

was sought.

An inspection of Figure 1 shows that almost for the entire time interval of

optimization the dilution rate was given by the singular arc expression. If this

dilution rate is plotted against the corresponding methane production rate, the result

is a straight line (Figure 3-2). The same straight line is obtained if the inhibitor

effects are given by equation 3-5. Thus the control law on the singular arc is to

simply change the dilution rate in proportion to the methane production rate (which

can be measured on line), i.e.,

D(t) = kQH (t) (3-7)

A value very close to the optimal value of the proportionality constant can be easily

determined experimentally since under normal operating conditions virtually all the


substrate is converted to methane carbon dioxide. Thus one can take as k the

dilution rate to methane rate ratio under normal operating conditions. Equation 3-7

is not only easily implementable but is also a very good suboptimal control law as

seen from Figure 3-3.


An optimal feed-back control law that manipulates the dilution rate so as to

prevent imbalance of the anaerobic digestion process was developed using

Pontryagin's maximum principle on a simplified version of the dynamic anaerobic

digestion model that was presented in the previous chapter. The optimal control law

is a function of the state variables methanogen and inhibitor concentration. It is

impossible to implement the control law because these variables cannot be measured.

However, it was found that if the dilution rate is varied in proportion to the methane

production rate then the performance of this sub-optimal control policy was close to

that of the optimal control policy. The sub-optimal control policy can be

implemented real-time on a anaerobic digester because methane production rate can

be easily measured on-line. The usefulness of this policy in preventing imbalance to

the process will be demonstrated in the subsequent chapter.

0.35 15

0.3- -12

W 0.25- -9


0.15- -3

0.1 2 0
0 10 20 30 40 50 60
TIME (days)

Figure 3-1 : Optimal D(t) and corresponding methane rate versus t.





< 6-



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Figure 3-2 : Methane rate versus D on the singular arc with f(I)
given by either equation 3-4 or equation 3-5.




i 200-


w 100-


0 10 20 30 40 50
TIME (days)

Figure 3-3 : Cummulative methane versus time. Suboptimal line
is calculated using equation 3-7.



Z 867.5
: Singular A
z-- 867
o 866.5-

O 866-

S 865.5-

Optimal steady s
0 0.2 0.4 0.6 0.8

Figure 3-4: The singular arc



The importance of the need for an on-line control scheme for the anaerobic

digestion process was emphasized in an earlier chapter. Several investigators have

developed approaches to control the process (Podruzny and van den Berg, 1984;

Russell et al., 1985; Rozzi et al., 1985; Whitmore and Lloyd, 1986; Renard et al.,

1988; Denac et al., 1988, Dochain et al., 1991). The existing control strategy in the

industry is to rely on pH control as a means of ensuring smooth digester operation.

Rusell et al. (1985) describes the installation of automatic controls on a UASB

treating waste from a potato starch manufacturing industry. The plant was equipped

with pH, temperature and flow control units. The pH was maintained between 6.8-

7.6. However, pH is not a reliable control variable because changes in pH occur

long after the onset of an imbalance. Automatic control schemes have been

proposed for the control of bench scale and pilot scale digesters. Podruzny and van

den Berg (1984) developed a computer controlled system for a down-flow stationary

fixed film digester. The control variable used was gas production rate. The control

scheme involved maintaining the gas production rate at a set point through a

proportional-integral controller by manipulating the feed rate. When the gas



production dropped due to inhibition and the controller was not able to maintain set-

point, then the set-point was arbitrarily dropped by 40%. There is a major drawback

in using gas production rate as a control variable because its response to inhibitors

is inconsistent. Total gas production rate is the sum of methane, carbon dioxide and

hydrogen production rates. Most of the hydrogen is utilized by the hydrogen utilizers

where one mole of carbon dioxide and four moles of hydrogen are converted to one

mole of methane. Hence, due to this reaction the gas volume decreases from five

to one. However, if the hydrogen utilizers are inhibited the above conversion

reaction does not proceed resulting in an increase in the gas production rate. If the

inhibitor were to inhibit the growth rate of all bacterial species then the result would

be a drop in gas production rate. Moreover, during inhibition dropping the set-point

by 40% may not be sufficient. Automatic control based on other variables has been

developed for laboratory scale digesters. Whitmore and Lloyd (1986) developed a

membrane inlet mass spectrometer unit to detect liquid phase hydrogen. They

propose a control scheme where the liquid phase hydrogen concentration is

maintained at a certain level. They tested the efficacy of this control scheme against

feed overloads. However, this control scheme will not work when the digester is

exposed to an inhibitor like phenol. Phenol is toxic to all populations of bacteria.

Hence phenol would inhibit even the acidogenic bacteria. This would cause

hydrogen concentrations to drop, in response to which the above control scheme

would increase loading rate, thus worsening the problem. Moreover, it may not be

economical to dedicate a mass spectrometer for on-line analysis of just hydrogen.


However, using liquid phase hydrogen concentration as a control variable is an

attractive concept. Renard et al. (1988), developed an adaptive control algorithm for

a continuously stirred tank digester using digester substrate concentration as the

control variable. This controller was tested successfully in preventing imbalance due

to feed overloads. It should be pointed out that the adaptive controller also relied

on the availability of feed COD data. This information may not be readily available

since it is not measurable on-line. The problem is worsened if there are wild

fluctuations in feed COD. The studies mentioned above did not consider the

possibility of process failure due to inhibitor entering with the feed. Such a type of

inhibition complicates considerably the control problem.

An expert system for preventing imbalance of continuous glucose fed digesters

is presented here. It addresses both the feed inhibition and overload problem. The

control scheme proposed here uses methane production rate as the principal

measured variable and dilution rate as the manipulated variable. Methane

production rate is not only a readily measured quantity, but also has the advantage

of providing an early indication of digester imbalance as compared to other

indicators like pH depression or volatile organic acid accumulation. Conventional

control schemes designed to reject a disturbance due to feed overload can fail during

feed inhibition because sign reversal in the steady-state gain. Under normal

operating conditions an increase in the dilution rate would result in an increase in

the methane production rate. Thus the sign of the steady-state gain is positive. In

case of feed inhibition, however, increasing the dilution rate would add more


inhibitor to the digester thus increasing the inhibitor concentration in the reactor,

something which could possibly drop the methane production rate further; thus the

sign of the steady-state gain becomes negative. Hence, the control algorithm should

be able to recognize gain reversal and implement appropriate control laws. An

expert system was developed to accomplish this.

The expert system switches between a conventional set-point control law and

the constant yield control law developed in the previous chapter depending on the

sign of the steady state gain. Disturbances studied were feed overload, feed

underload and an inhibitor (phenol) entering with the feed. Methane production

rate was used as the measured variable. Dilution rate was the manipulated variable.

Subsequent sections detail the development of the expert system, simulations of the

expert system using the model developed in Chapter 2 and finally experimental

validation of the expert system.

Control Strategies

In this section the two main components of the expert system are briefly


Conventional Set-point Control law

Under normal conditions the digester is under conventional set-point control.

The set point to be maintained is the methane production rate obtained when the

reactor was run at a moderate dilution rate (e.g. 0.05 days1) with normal feed


concentrations. Since overloads are accompanied by an initial increase in the

methane rate, a conventional positive-gain control law responds by lowering the feed

rate and thus lowering the volatile organic acid concentration in the reactor. This

prevents organic acid build-up and saves the digester.

Constant Yield Control Law (CYCL)

Conventional positive-gain set-point control would have adverse effects if

implemented when the process gain has been reversed due to an inhibitor entering

with the feed. In the previous chapter it was shown that a control law that changes

the dilution rate D in proportion to the methane production rate Q, i.e.

D(t) = k Qmethane(t)

closely approximates the optimal response to noncompetitive feed inhibitors of the

methanogens. If the active volume of the digester does not change, the above policy

keeps the volumetric yield (ratio of the volume of methane produced to the volume

fed) constant. A value very close to the optimal value of the proportionality

constant, k, can be easily determined, since under normal operating conditions

virtually all of the substrate is converted to methane and carbon dioxide; thus k can

be taken as the ratio of dilution rate to methane production rate under normal

operating conditions. It should be observed that the constant yield control law has

negative gain, thus it is appropriate when the process gain changes sign. Harmon et


al. (1990) first suggested the use of this strategy to prevent imbalance resulting from

temperature changes.

Key features of the Expert System

Some of the key features of the expert system are listed below

1.Methane production rate is used as the sole on-line measured


2.A statistical criterion is used to quantify whether the output increases

or decreases.

3. Automatic selection of control law.

4. Smooth transfer between control laws (bumpless transfer).

Methane production rate is the on-line measured variable. Decisions

regarding the selection of the control strategy are based on the absolute value of this

variable and also the rate of increase or decrease of the variable. A t-test is used on

past sampled methane production rate data to test whether the hypothesis, "the rate

of change of the methane production rate is negative," can be accepted with a certain

degree of confidence. The t-test is done only when the methane production rate has

dropped below a minimum bound. Depending on the acceptance or rejection of the

hypothesis an appropriate control law is chosen. Before switching from set-point

control law to CYCL the digester is operated batch and a switch from CYCL to set-

point control law is done only after the methane production rate has reached the set-

point. These two switching features result in bumpless transfer between control


policies. By operating batch, it is ensured that excess substrate in the digester is

consumed and the CYCL initially implements a low value for the dilution rate.

The Expert System

The expert system is outlined in the flow diagram of Figure 4-1. As long as

the methane production rate (CH4) remains in a "normal" range

CH4min < CH4 < CH4max the digester is operated using a conservatively tuned set-point

controller. The controller must be conservatively tuned because large increases in

the dilution rate can negatively affect the culture. A choice we have been using

successfully is internal model control (IMC; Morari and Zafiriou (1989)) with

controller tuning based on an experimental step response curve. The "normal" range

should be chosen so as to include variations due to measurement noise and due to

the initial process response to the frequently encountered mild disturbances that the

set-point controller can easily handle. We have been using as "normal" range +20%

of the methane set point. If the methane production rate rises past CH4max then the

cause is attributed to a significant feed overload. To avoid running the risk of being

too late in decreasing the dilution rate (the set-point controller is conservatively

tuned), the algorithm first sets the dilution rate to a very low value Dow (e.g., 0.001

days-'), thus ensuring that the sluggish set-point controller approaches the new

dilution rate from below.

A drop in the methane rate to below CH4min is due to a severe underload or

to feed inhibition. Gain sign reversal is a possibility. If this is not the case, the set-

point controller, by increasing the dilution rate (slowly and only up to a maximum

value below the maximum specific growth rate of the acid utilizing methanogens

(0.37 days-', according to the model of Chapter 2), will increase the methane rate and

may eventually return the system to the set point. If, however, the process gain sign

has been changed the digester will respond to increases in the dilution rate by further

lowering of the methane rate. If the methane drops below the minimum bound, then

a t-test is performed on the last 30 data points to statistically determine whether the

methane rate is indeed dropping. If it is dropping then the algorithm recognizes a

reversal in the sign of the gain and exits the set-point control loop.

The preceding digester operation at a high dilution rate might have caused

some of the biomass to wash out and/or accumulation of hydrogen which is

inhibitory. Hence, before implementing the constant yield control law (CYCL),

which is appropriate when the gain reversal has taken place, the digester is operated

batch for an interval of time. An initial batch interval is also suggested by the

optimal control law (Pullammanappallil et al., 1991, Chapter 3) while the digester is

operated in a batch mode hydrogen is generated by the conversion of propionic and

butyric acids to acetic acid and utilized by the hydrogen-utilizing methanogens. Once

the levels of propionic and butyric acids drop the hydrogen concentration will rapidly

decrease to noninhibitory levels. Thus, if propionate and butyrate measurements are

available the batch phase is terminated when the concentrations of these organic

Set D = 0 until VOAs drop.
Decision based on direct VOA measurements or on dynamics of CH 4

Set Dbase = D

Monitor methane
production rate and
predict methane
production rate.

Figure 4-1 : The Expert System.

conservative setpoint
control maintains
methane rate at normal
value -
Feedback value
D=min Dmax
Dprey + ADmax

Methane rate (CH4)
-nominal,min and max
Dil. rate (D)- low, max and
maximum increase in D (AD max )
Volatile acids (VOA)- max
Target volumetric yield


acids drop to close to their normal levels (e.g., to less than 200 mg COD/L for the

sum of the two. If propionate and butyrate measurements are not available the

duration of the batch period can be decided from the following reasoning: When the

reactor goes batch the feed inhibitor concentration stops increasing. Due to

dynamics the rate of methane production may continue to drop for a short interval

of time (e.g. 8 hrs). Subsequently, if hydrogen is at high levels its consumption will

reduce its inhibition and as a result the methane rate will start rising. Eventually, the

methane rate will start dropping due to reduced substrate levels. Thus the decision

to terminate the batch phase can be based on when a downwards trend of the

methane production rate is confirmed. The recommended procedure then is, after

a short minimum interval (8 hours), to stop the batch phase when two measurements

are obtained that are by more than two measurement noise standard deviations

below the maximum value of the methane rate in the batch interval. A statistical test

involving more data points is not used since with our experimental set-up the

frequency of methane rate readings is very low at low methane rates.

After the termination of the batch phase the algorithm enters a region in

which the primary control law is the previously described CYCL, according to which

the dilution rate changes in proportion to the methane rate so as to maintain the

nominal volumetric yield. This law is well suited for responding to feed inhibitors.

In rare instances, however, the gain sign reversal that brought the algorithm to the

CYCL might have been caused by a very severe underload that dropped the

methanogen specific growth rate to below the dilution rate. Then the nominal


volumetric yield cannot be maintained and the CYCL will keep decreasing the

dilution rate towards zero. To prevent this, if the dilution rate drops to 75% of the

value at the start of the CYCL (Dbase), it is kept at that value for five sampling

intervals. Methane production data obtained during this period are then used to

predict whether or not the methanogens are washing out. Extrapolation is carried

out with a second order polynomial fit and an exponential fit. If the predicted

minimum methane rate using either extrapolation methods is less than 10% of the

normal methane production rate, then the digester is switched back to the CYCL.

Otherwise the digester will continue being maintained at a constant dilution rate until

either washout is predicted or until the volumetric yield increases to its nominal

value. In both cases then the algorithm switches to the CYCL. In case the methane

rate is dropping, the CYCL will reduce the dilution rate until the methane rate

stabilizes. If the feed conditions return to normal then the CYCL will increase the

dilution rate in response to the increase in the methane production rate, thus moving

the digester towards the set point. When the methane rate reaches the set point, the

algorithm switches to set-point control. An earlier switch is risky because the CYCL

may be operating at a dilution rate only slightly less than the methanogen specific

growth rate.

Materials and Methods

The expert system was tested on a laboratory scale 1.7 liter digester. This set

up was different from the one described in chapter 2. This experimental setup is


shown in the schematic diagram of Figure 4-2. The digester is equipped with on-line

measurement of the methane production rate and computer control of the dilution

rate. The entire setup is interfaced to an IBM compatible personal computer. The

feed is pumped through a computer controlled peristaltic pump equipped with a

second pump head to withdraw effluent. Hence, effluent is withdrawn at the same

rate as the feed is pumped. The gas vented from the digester is scrubbed off its

carbon dioxide content by passing it through a column of soda lime. The methane

accumulated in one limb of the U-tube by displacing the liquid. When the liquid in

the other limb rose to a certain level, a float switch was tripped, which caused two

events to happen simultaneously. A signal was sent to the computer and also the

methane from the first limb was exhausted resetting the liquid level. By measuring

the time between two successive signals and given that the volume of methane that

triggers the signal is known, the methane production rate could be calculated.

Normal operating conditions are a dilution rate of 0.05 days-1 and a digestion

temperature of 35 C. The feed was a glucose medium, the nominal concentration

of glucose was 28.8 g/L. The composition of other nutrients is given in Appendix B.

While making a feed overload or an underload only the glucose concentration was

changed. Sodium propionate was added to the feed so as to always maintain a

culture of propionate degrading bacteria in the digester. During normal operating

conditions the methane production rate varies between 1.0 L/day and 1.3 L/day..


Feed/Effluent pump

Figure 4-2 : The bench scale digester.


Testing the Expert System


Computer simulations were done to test the expert system before it was

actually implemented on the laboratory scale digester. The anaerobic digester was

simulated using the model that was developed in Chapter 2. The efficacy of the

expert system in rejecting a disturbance was tested for a feed underload, feed

overload and inhibitor entering with the feed.

Underload and overload. Figure 4-3 shows the expert system response to a

feed underload and feed overload. The glucose concentration in the feed was

reduced from 28.8 g/L to 20.8 g/L and then to 15.8 g/L. In response to the

underload the methane production rate dropped, hence the controller increased the

dilution rate to maintain the set point. No adverse effects, like steady state gain

reversal were created by this, so the controller continued to operate the digester at

the higher dilution rate. The controller responded in the same manner when the

glucose concentration was dropped again. Total concentration of volatile organic

acids (VOAs) remained below 100 mg COD/L.

An overload was simulated by returning the glucose concentration in the feed

from 15.8 g/L to 28.8 g/L. The controller dropped the dilution rate so as to

maintain set point. The nominal value of 0.05 d-1 was reached from below. The

volatile organic acids plot shows that the expert system succeeded in preventing any

accumulation of volatile organic acids.


Inhibitor entering with the feed. Figure 4-4 depicts the response of the expert

system to an inhibitor entering with the feed. The inhibitor was assumed to affect

only the growth rate of acetoclastic methanogens, following the kinetics of

noncompetitive inhibition. In particular the maximum specific growth rates of the

methanogens were multiplied by 1/(1 + 1000 [I]), where [I] denotes inhibitor

concentration. Due to the inhibitor the methane production rate dropped and the

controller initially increased the dilution rate so as to maintain set point. This action

of the controller fed more inhibitor to the digester, thus worsening the problem. So

the methane production rate continued to drop. When any further increase in

dilution rate caused the methane production rate to drop, the controller recognized

that the steady-state-gain sign had reversed so it changed the control scheme from

set-point control to constant yield control law after operating the digester batch for

the minimal period of 8 hours. The inhibitor was removed from the feed after 12

hours while the digester was being operated in constant yield mode. Once the

inhibitor was removed from the feed the inhibitor in the digester began to wash out

and this increased the maximum specific growth rate of the methanogens which in

turn increased the methane production rate. Since the implemented dilution rate is

proportional to methane production rate, the dilution rate increased. It took over

1000 hours for the methane rate to approach its nominal set-point value. It should

be noted that even though it took considerable amount of time to return the digester

to its set point, this could not have been helped since the CYCL sets the dilution rate

very close to the methanogen specific growth rate. An attempt to speed up this












0 100 200 300 400 500 600

TIME (hours)

Figure 4-3: Simulation of the expert system response to an underload and an




















0 5 10 15 500 1000

Figure 4-4:

TIME (hours)
Simulation of the expert system response to an inhibitor entering with
the feed.






return by increasing the dilution rate would have started washing out the

methanogens and soon methane rate drop and VOA buildup would follow.

Experimental Validation

The expert system was implemented on the bench scale laboratory digester.

The efficacy of the expert system in preventing digester imbalance when the digester

was exposed to disturbances like a feed overload, feed underload and phenol

entering with feed was tested.

Overload. Two tests were performed with an earlier slightly different version

of the expert system. In this version the digester was operated at a constant dilution

rate 0.05 days-1, and the expert system kicked in only if the methane production rate

increased or decreased by 20% of the normal value. Figures 4-5 and 4-6 show the

response of the expert system to this disturbance. In both tests the glucose

concentration in feed was stepped up to 86.4 g/L from 28.8 g/L for approximately

140 hours. The expert system entered set point control when the methane rate went

past the maximum limit. When the glucose concentration was tripled the first

response was the methane rate to increase. Since the methane production rate went

above the upper bound, the controller decreased the dilution rate to 0.001 d"' and

the dilution rate was slowly brought up. The controller was able to maintain set

point. The total volatile organic acid levels were kept below 300 mg COD/L. After

the overload was removed the controller increased the dilution rate to maintain set

point. The response of the expert system to both tests was similar.


Underload. The performance of the expert system to feed underloads was

then studied. Three tests were carried out: a mild underload, a moderate underload

and a severe underload. For the severe underload a slightly different earlier version

of the expert system where the CYCL was implemented if the methane production

rate remains below CH4min for three consecutive sampling intervals, regardless of

whether it was increasing or decreasing. In the present version of the expert system

the constant yield policy is implemented only if the methane production rate is less

than 80% of the normal value and is monotonically decreasing for three successive

sampling intervals.

Figure 4-7 shows the expert system response to a mild underload where the

glucose concentration was dropped from a nominal value of 28.8 g/L to 20.8 g/L.

Low substrate concentration caused methane to drop. However, the controller was

able to bring the methane rate back to the set point by increasing dilution rate from

0.05 d-1 to approximately 0.06 d-1 to maintain set-point. Figure 4-8 shows the expert

system response to a moderate underload. The glucose concentration in the feed

was halved. The response was similar to that of the mild underload. The dilution

rate was increased to approximately 0.075 d-' to maintain set-point. When the

glucose concentration was brought back to normal then the dilution rate dropped

close to 0.05 d-1. Figure 4-9 shows the expert system response to a severe underload.

No glucose was added to the feed, a 100% underload. The feed still contained

casamino acids and yeast extract which could be used by the bacteria as source of

energy. The glucose concentration was dropped at 10 hours and this was sustained











50 100 150 200 250

TIME (hours)

Experimental expert system response to a triple overload.



















Figure 4-5:


TIME (hours)

Experimental expert system response to a triple overload.

A lA--

I 1

Figure 4-6:

for 68 hours. The methane production rate began to drop and the controller

increased the dilution rate but could not maintain set-point. Hence, the expert

system concluded that the disturbance had caused a reversal in the sign of the steady

state gain and implemented the CYCL after operating the digester batch for half a

day. When the feed was switched to normal the methane production rate

immediately increased above the upper limit. The expert system not only brought

the digester into the set-point control mode but also sensed the response as having

been caused by an overload, and so dropped the dilution rate to 0.001 days"1. This

drop in dilution rate caused the methane production rate to remain below CH4min

and once again the expert system went to the batch phase that precedes the CYCL.

This response was unwarranted and would have been prevented if the present

requirement of a monotonic drop had been incorporated into the expert system.

Eventually, the CYCL brought the digester back to normal operating conditions (i.e

a dilution rate of approximately 0.05 days-'). The yield during batch operation is

actually infinity. However, this phase is shown to be at a yield of 1000 L methane/L

feed in the yield plot of Figure 4-9. Volatile organic acid concentrations are not

shown for any of the underload experiments because these remained below

detectable levels of the GC (i.e. < 10 mg COD/L).

Inhibitor entering with feed. To test the expert system against an inhibitor

entering with feed, 40 g/L of phenol were added to the feed. Two tests were

conducted; in the first test phenol was added to the digester for 12 hours and in the

second test phenol was added for 36 hours.



0.0 --
.4 --------------------


o.oo I------I------i-----I-------


0 50 100 150 200

TIME (hours)
0.10 50-100-1-0-

T h

TIME (hours)

Experimental expert system response to a mild underload.

Figure 4-7:

80.0 I


0 .0 I I I

.oo I I I I

0.10 I I I I
1 1 1 1 1

o.o I-I I I I


w 0.08

0.00 I I I I

0.105 --------, ------ -------- ---------------------

0 4 8 12 18 20 24

TIME (hours)

Figure 4-8: Experimental expert system response to a moderate underload.


so A

: ~n ,

:2, wV

20 I


TIME (hours)

Figure 4-9: Experimental expert system response to a severe underload.


r r 1


Figure 4-10 depicts the expert system response to a 12 hour phenol addition.

The expert system was able to maintain set-point by increasing the dilution rate.

This action did not cause any adverse effects on the microorganisms. Volatile

organic acids began to accumulate; however they dropped after the phenol was

removed. Phenol concentration in the digester reached 900 mg/L (Figure 4-11).

This was not high enough a concentration to cause a reversal of the sign of the gain

as a result the lowering of growth rates was compensated by an increase in dilution


In the second test, after 27 hours of phenol addition the expert system sensed

the onset of gain sign reversal. At this point the methane production rate had

dropped below the lower bound and had continued to drop even after increasing the

dilution rate (Figures 4-12). Subsequently, a batch phase followed. The methane

production rate profile during batch operation is shown in Figure 4-12. When it was

confirmed that the volatile organic acid concentration levels were not high the

digester switched to the CYCL mode. This mode of operation continued until the

methane reached rate the set point after which the mode of operation was switched

to set point control. Figure 4-13 depicts the response of the expert system for the

whole duration of the experiment. pH and individual volatile organic acid and

phenol concentrations are shown in Figure 4-14.

During the constant yield operation the digester was operated at a retention

time 40 days for most of the time. This indicates that there was a 50% inhibition of

the process, because the digester could handle only half the nominal feed rate so as


TIME (hours)

Figure 4-10: Experimental expert system response to a 12 hour phenol addition.

_I A


TIME (hours)

Figure 4-11: Experimental pH and phenol concentrations in the digester.




0- 750


M fi

I I-----*----


to maintain the nominal yield. This observation is consistent with that found in

literature. Several investigators have studied phenol inhibition (Field, 1989) and

have shown that about 2000 mg/L of phenol causes 50% inhibition. The

concentration of phenol in the digester when it went batch was 1600 mg/L (Figure

4-14) which is close to the value reported in literature. Phenol was degraded into

propionate through some intermediate compounds resulting in propionate

accumulation in the digester (Figure 4-14). The presence of intermediate compounds

is indicated by the fact that there was a delay between phenol depression and

propionate accumulation (Figure 4-14). Propionate accumulated to levels of 4000

mg/L. Phenol degradation and the implications of using propionate as an indicator

of digester imbalance are discussed in detail in the next chapter.

After the methane rate reached nominal set point the control was handed to

the set point controller. Very soon after this the accumulated propionate started to

degrade to acetate and then methane, causing an increase in the methane production

rate. The controller immediately dropped the dilution rate assuming that this

increase was due to an overload. Once all the propionate was degraded the dilution

rate was brought back to 0.05 d'1. Thus the expert system successfully operated the

digester even under adverse conditions like high propionate and low pH.


An expert system to prevent digester imbalance was developed. The expert

system uses on-line methane production rate measurements to decide the operating


strategy. The expert system was first simulated against the model presented in

Chapter 2. It was successful in preventing imbalance when the process was subjected

to a feed overload, feed underload and an inhibitor entering with the feed. The

expert system was then implemented on a bench-scale digester. Disturbances in the

form of feed overloads, feed underloads and phenol were tested. These disturbances,

especially phenol, resulted in adverse growth conditions for the bacterial populations.

However, the expert system effectively operated the digester irrespective of the type

of disturbance.



TIME (hours)

Figure 4-12: Experimental expert system response, showing reversal of steady state
gain, to a 36 hour phenol addition.





0 .1
Pr 0.


- 40.0-

10 0o -
,., 1 .0



E 0.5 -0

0 400 00 1000 .

0 200 400 600 800 1000 1200