structured modeling of the anaerobic digestion of biomass particulates

Structured Modeling of the Anaerobic Digestion of Biomass Particulates

J. D. Bryers* Swiss Federal Institute for Water Resources and Water Pollution Control (EA WAG), Swiss Federal Institutes of Technology, CH-8600 Diibendorf. Switzerland

Accepted for Publication September 7, 1984

Anaerobic digestion of biological organic particulates to methane has been described by a structured mathematical model based on multiple-reaction stoichiometry, con- ventional material balances, and liquid phase equilibrium chemistry. A general stoichiometric treatment for any set of multiple biological reactions is derived based on a unit mass of oxygen equivalents of the reactions limiting substrate. The model agrees well with two existing experimental studies of anaerobic digestion of biomass particulates. Hypothetical computer simulations are presented to illustrate possible instabilities of the anaerobic process under various operating scenarios.

INTRODUCTION

Anaerobic digestion of biopolymeric particulates to methane is considered to proceed according to the reaction scheme illustrated in Figure 1. 1-3 Complex particulate organics are first hydrolyzed to simpler polymers (e.g., lipids, carbohydrates, and proteins) which are further hydrolyzed to amino acids, simple sugars, and high-molecular-weight fatty acids. This portion of the digestion process is called the particulate hydrolysis phase and has been r n ~ d e l e d , ~ - ~ for lack of information, as a single reaction step. Research on the mechanism, stoichiometry, and kinetics of bio- polymer hydrolysis by bacteria is sorely lacking.

Amino acids and simple sugars are then converted into either intermediate by-products (e.g., propionic, butyric, and other volatile acids) or directly fermented to acetic acid (reaction 2, Fig. 1). High-molecular- weight fatty acids are anaerobically oxidized to either the same collective intermediate by-product pool or directly to hydrogen (reaction 3). Intermediate by- products are converted to acetic acid and hydrogen (reaction 4). Collectively, reactions 2-4 are called aci- dogenesis or the acid phase of the digestion process. In the past, reactions 2-4 have been considered to be mediated by a group of chemoheterotrophic bacteria collectively named “acid formers. ” Recently research&’ has distinguished separate bacterial groups mediating

* Present address: Department of Civil and Environmental En- gineering, Duke University, Durham, North Carolina 27706.

Biotechnology and Bioengineering, Vol. XXVII, Pp. 638-649 (1985) 0 1985 John WiIey & Sons, Inc.

the conversion of intermediate by-products in reaction 4.

Methane is formed in anaerobic digestion from the reaction of acetic acid and the conversion of hydrogen and carbon dioxide (reaction 5 and 6, respectively). These final two reactions are together called methanogenesis. Recent microbiological research’3638v9 has focused on reactions 4-6, but partial information exists for all six processes. Further details of the sequence above can be found in reviews by Gujer and Zehnder,” Hobsen,’ and Zehnder et al.” The reaction sequence in Figure 1 has been determined at mesophilic temperatures but is considered valid for the thermophilic situations dealt with later in this paper. The stoichiometric distribution of substrate flow in the above sequence can be estimated,” but changes in the relative contributions of each reaction to the overall process, under changing operating conditions, has not yet re- ceived significant attention.

This paper will first develop a general stoichiometric protocol applicable to any system of multiple biological reactions, based on a unit mass of limiting substrate theoretical COD (chemical oxygen demand). Second, a structured model based on the specific anaerobic digestion sequence above is derived. The resultant model is then calibrated to existing laboratory studies of mesophilic (35°C) acid phase and thermophilic (50- 60°C) anaerobic digestion of waste-activated sludge. Finally, several scenarios are presented to determine the stability of the anaerobic process.

MATHEMATICAL MODELING

Models ’ that either describe growth merely as an increase in biomass or consider only simplistic microbial conversion reactions are called “unstructured” models. Such approaches can ignore, for example, species dynamics in mixed cultures or changes in cellular composition in response to changes in environmental conditions. Consequently, such models can only be legitimately applied to systems of “balanced growth.”

Conversely, “structured” models do consider the

CCC 0006-3592/85/050638-t 2$04.00

COMPLEX BlOD EGR AD A B L E PARTICULATES

PA RTICUL AT€ HYDROLYSIS

PROTEINS AND

FATTY ACIDS A M I N O A C I D S S I M P L E S U G A R S

3 A INTERMEDIATES

e t t

n I 0

* 7 ACETIC ACID t---?---j H Y D R O G E N e,TcJ" METHANE

M E r n ~ N O G E N E S I S

Figure 1. degradable organic particulates.'

Proposed reactions in the anaerobic digestion of bio-

additional detail of mixed-culture population dynamics, microorganism composition, and/or multiple-reaction schemes as a function of environmental conditions. A complete structured model would consist of the following items:

I . A list of components (reactants, intermediates, and products) pertinent to the reaction scheme math- ematically expressed as a component vector.

2 . A stoichiometric coefficient matrix with each component in each reaction.

3. A list of reaction rate expressions for each reaction also expressed as a vector quantity.

4. Material balances for each component in the reaction system.

Stoichiometry of Biological Reactions

ficients, can be written as, A general multiple-reaction scheme, in molar coef-

U , , ~ S , + v1,2S2 + ... + vl,nSn = 0

v , , ,S , + v2,2S2 + ... + v2,nSn = 0

r ,

r2 (1) . . . . . .

v, , ,S, + V , , ~ S ~ + ... + v , , ~ S , , = 0 rm

where v,,, is the stoichiometric coefficient for t he j th component in the ith reaction, m is the total number of reactions, and n is the total number of components.

Equation (1) is transformed to a unit mass COD basis by normalizing each reaction by the mass COD equivalent of the reaction's limiting reactant. Each reaction is treated separately and normalized to its own limiting reactant. Rewriting equation (1) on a unit mass COD basis results in

( - 1)Sl + ( - Y,,2)S2 + ... + (+ Y,, , )S, = 0 TI

( - Y2, , )S1 + (- l)Sz + ... + (+ Y2,n)S, = 0 r2

(- Y,,,,)S, + (- Y,,,2)S2 + ... + ( - 1)S, = 0 r,

. . (2) . . . .

where Y,,, = (v,,,MW,a,)/[v,,,]MW,a,; Y,,, is the yield coefficient of component S, in reaction i (mass COD of component S, consumed or formed in the ith reaction per unit COD mass of component S, consumed in the ith reaction); a is component S , , normally the limiting reactant in the ith reaction; MW, is the molecular weight of component S,; 0; is the mass COD equivalence of component S, (mass COD per mass component). Equation ( 2 ) can also be written, in matix notation, as

Y . S = O (3)

where Y is an m x n yield coefficient matrix and S is an n-dimensional vector. Details of the above stoichiometric framework, the unit mass COD basis, and the matrix notation are provided e l~ewhere . '~ , ' ~

A reaction rate vector r can be easily written as

r = r, y T (4)

where r, is an n-dimensional reaction vector and YT is the inverse transpose of the matrix Y.

Applying the above stoichiometric approach to the anaerobic reaction scheme in Figure 1; where S , is the hydrolyzable particulates, S2 the amino acids and simple sugars, S3 the volatile fatty acids, S, the intermediate by-products, S5 the total acetic acid, S6 the hydrogen, S7 the methane, and S8 the biomass, results in equation (5):

- 1 0.66 0.34 0 0 0 0 0 -1 0 0.29 0.50 0.16 0 0.05

' 0 0 -1 0 0.65 0.31 0

0 . j

0 0 0 - 1 0.59 0.39 0 0.02 0 0 0 0 - 1 0 0.96 0.04 0 0 0 0 0 - 1 0.96 0.04

( 5 )

which represents six chemical reactions, with reaction rate expressions r l + t-6, involving eight components. Stoichiometric values used in equation (5) were obtained directly from existing literature" and are assumed constant over the range of residence times (7) employed in the experimental studies considered below. Reaction rate expressions for the above six equations are r e p ~ r t e d ' ~ . ' ~ - ' ~ to follow simple saturation kinetics of the form

BRYERS: STRUCTURED MODEL OF PARTICULATE DIGESTION 639

where i = 2 + 6; p* is the maximum growth rate constant, K is the saturation coefficient for the limiting reactant, and X is the concentration of the specific bacteria mediating the reaction.

Material Balances

For a constant-volume system with no concentration gradients, a general material balance, in vector notation, can be written as

S = r + B (7)

where S is the vector of component S, accumulation terms (dS,/dt) and @ is the vector of the net rates of substrate transport to the system. For the anaerobic reaction system of equation (3, the resulting material balances are summarized in the Appendix. Reaction rate expressions used in the substrate material balances incorporate the concentrations of three bacterial groups necessitating three additional material balances for the acid-forming (X,), propionic acid-degrading (X,), and methanogenic (X,) bacteria (also given in the Appendix).

Rate Expression Details

Literature indicates that methanogenic bacteria are very pH sensitive, having an optimum pH at 7.4-7.8 and zero activity at pH extremes of 6.0 and 8.0. Pre- viously, to simulate observed system failures at si- multaneous pH changes and acetic acid surges, Andrews and co-workers'*-*" used a Monod-like rate expression for acetic acid conversion that was modified for growth rate inhibition by the limiting substrate, which in their work was assumed to be the un-ionized form of acetic acid. Their approach simulated a depressed methane production rate as a function of both pH and acetic acid. Although biochemical justification exists for the preferential uptake of un-ionized acetic acid by methanogens,21 in this work a slightly different approach is employed which models the acetic acid degradation rate, r s , with a standard saturation expression (see equation6 for i = 5) where p: exhibits the pH de- pendency reported by Gujer and Zehnder."

Estimation of digester pH requires simulation of the carbonate equilibrium chemistry within the digester liquid. Here bicarbonate alkalinity, [HCO;], is calculated from

[HCOTl = [zl + "H :I - [S4I - [Ssl (8) where [ ] indicates molar concentration units. Here 2 is the net concentration of miscellaneous cations and anions other than CO:+, H', HCO,, OH-, NH:, acetic acid S4, and propionic acid S,; NH: is the ammonium ion concentration. The accumulation rate of ammonia in the digester is due to the net ammonia input rate, the rate of ammonia used in biomass synthesis, and the rate of ammonia production from particulate hydrolysis, i.e.,

- (yn/x . YR) + ( f 3 . v,) (9)

where Y,+ is the stoichiometric ammonia nitrogen re- quirement for biomass synthesis (moles NH; - N/g COD biomass), vn is the summation of all individual bacterial growth rates, and f 3 is the fraction of ammonia nitrogen available upon hydrolysis of biodegradable particulates. Hydrogen ion concentration, [H'], can be calculated using equation (8) and the relationship

where [Coi l is the dissolved carbon dioxide concentration calculated as [C,] - [HCO;] with [C,] the total carbonic acid species concentration in the digester.

Very little is known about the governing mechanisms, much less the kinetics, of biological particulate hydrolysis in microbial systems. Traditionally, biodegradable particulate utilization has been empirically modeled using simple kinetics that are first order in the remaining particulate c~ncen t r a t ion .~ .~ Conse- quently, the particulate hydrolysis rate, v I , is written, based on experimental evidence below, as

Y1 = khSl (1 1)

where kh is the first-order hydrolysis rate constant

The role of hydrogen in the anaerobic sequence of Figure 1 is not accurately portrayed in the above mathematical model. An obligate symbiotic relationship exists between acetic acid-forming and hydrogen-utilizing bacterial groups. For example, the free energy change for the reaction of propionic acid to acetic acid is negative only if hydrogen concentrations are below lo-' mol/L atm H2 partial pressure). Otherwise, should hydrogen exceed this concentration, intermediate volatile acids will accumulate. Thus, hydrogen- utilizing bacteria can indirectly regulate acid bacteria metabolism by shifting electron transfer from anaerobic oxidation to anaerobic fermentation products.

This hydrogen effect is classically based on thev- modynamic arguments. However, such an argument does not directly translate into a kinetic rate expression, which is required in digester material balances. One approach in modeling hydrogen effects on acetic acid- forming bacteria would be to simply incorporate hydrogen inhibition terms directly into the kinetic expressions. It is questionable whether a thermodynamic limitation can be directly simulated in the kinetic rate expression. Perhaps a more accurate approach would be to relate the change in free energy of the reactions in question to hydrogen concentration and then directly relate the free energy change to the bacterial yield coefficient for each reaction. Thus, hydrogen would inhibit the turnover rate of bacteria, reducing

(t-I).

640 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 27, MAY 1985

their concentration with increasing hydrogen concentration, thus causing intermediate acids to accumulate.

Experimental justification for either approach is nonexistent; consequently, hydrogen inhibition effects are ignored in the model above. Thus, the model only relates to systems where hydrogen is low. Once the appropriate approach is selected, modification of the kinetic expressions and material balances would be simple. This lack of process information concerning hydrogen effects illustrates another advantage (i.e., collection of known and unknown data) of using a structured model approach.

EXPERIMENTAL SYSTEMS CONSIDERED

Results of two different experimental studies that considered the anaerobic digestion of biomass particulates are used here to calibrate the structured model above.

Eastman and Ferguson' reports on the solubilization of particulate organic carbon during only the acid phase of anaerobic digestion. Methanogenesis in their experiments was suppressed by operating digesters at dilution rates greater than maximum methanogenic bacterial growth rates (minimum D = 0.33 day-') thus creating an acid condition (pH S 6.6) which is also inhibitory to methanogens. A particulate biomass slurry collected from a municipal aerobic waste treatment process served as the sole substrate. Acid phase digestion in their study' was carried out at the mesophilic temperature range (i.e., 35°C).

Hamer et al.23 summarizes a 2-year study on thermophilic (i.e., 55°C) anaerobic digestion to methane and carbon dioxide of waste-activated sludge biomass. Methanogenesis was not suppressed in this second study until experimental protocol dictated digester dilution rates of 20.2 day-'. Although not controlled, pH in their study remained constant at 7.78.

Analytical methods and experimental parameters in both studies were quite similar. Salient features of experimental protocol for each study are given in Table I with further details provided in the original

In calibrating the model above, based on mass of COD, to these experimental studies, it was necessary to convert many reported parameters to a common

COD basis. Conversion factors and supporting as- sumptions used are given in Table 11.

RESULTS

Comparison to Existing Data

Table I11 provides the numerical values of the kinetic and thermodynamic constants used in model simulations of both experimental studies. Values for all such constants were taken directly from the literature" (after appropriate temperature adjustments) except for certain system-specific parameters (e.g., kh , particulate hydrolysis rate constant) that were estimated directly from the experiments. Correlations used for temperature adjustments are given elsewhere.*'

Acid Phase Digestion

Eastman and Ferguson' operated four anaerobic digesters in parallel, each at a different dilution rate but fed the same influent slurry. All reactors were initially filled with anaerobic sludge from a municipal digester that was actively producing methane at a neutral pH. Each reactor required a certain start-up time at its selected dilution rate before the pH dropped and methane production ceased. Figure 2 exemplifies the start-up period for a reactor operating at a dilution rate of 0.07 day- ' (7 = 1.5 days). Superimposed on the data are computer simulations based on the model above. Predictions agree well with reported decreases in both gas production rate and pH. Experimental and model predicted total volatile acid COD concentrations and the concentrations of the individual volatile acids as a function of dilution rate are given in Figure 3 . The model overestimates the total volatile acid concentrations and presents an incomplete description of the volatile acid composition at each steady state. Both these latter discrepancies are due to the model's simplistic assumption that propionic acid is the only intermediate volatile acid formed besides acetic acid. Additional stoichiometric equations would be required to estimate accurately the volatile acid composition. Note the above comparisons were the results of a trial- and-error estimation of the initial bacterial concentra-

Table I. Details of experimental studies used in model calibration.

Inlet substrate Temperature Dilution rate concentration

Study PH ("C) range (day-') (g/O Reference

Solubilization of 5.55-6.70 35 0.661-2.67 36.2 TSS 5 particulate organics in acid 26.6 VSS phase anaerobic digestion 52.0 COD

digestion of biomass 15-25 VSS particulates COD not measured

Therrnophilic anaerobic 1.78 55 0.067-0.133 20-40 TSS 23


Table 11. Conversion factors used in computer comparisons to experiments.

Parameter Conversion factor Basis

Biomass COD Carbohydrate COD Methane COD Hydrogen COD Acetic acid COD Acetic acid TOC Propionic acid COD

Propionic acid TOC VFA COD Cell nitrogen DOC total

POC (particulate organic carbon)

TOC

1.3 g COD/g biomass 1.067 g COD/g glucose 2.86 g COD/L CH, 0.714 g COD/L Hz 1.066 g COD/g acetic acid 0.399 g C/g acetic acid 1.512 g COD/g propionic

0.486 g C/g propionic acid 2.88 g COD/g VFA 0.124g N/g biomass Sum of DOC equivalence of

Sum of organic carbon

acid

S,, S,, S4, and S,

equivalence of P, X,, X,, and X,

POC + DOC

C,H,NOZ C&id& STP STP MW MW MW

MW Palmitic acid

Definition

Definition

C,H,NOz

Definition

tions since no such information was provided in the original work. Except for these “guestimates,” no other modifications to the literature parameters in Table 111 were made.

Thermophilic Digestion Batch Experiments

Data from a thermophilic anaerobic batch experiment, as reported by Hamer et al.,23 are shown in Figure 4a. Data indicate a portion of the VSS is readily hydrolyzed while a residual fraction (-60-70%) is either not hydrolyzed or hydrolyzes at an extremely slow rate. The hydrolyzable volatile particulate concentration at any time in the batch experiment, P(r), is defined here operationally as P(t) = VSS(r) - V S S ( t = m ) .

r = 1.5 days , T = 35 O C 4 GAS PRODUCTION RATE

(!/day)

2 4 6 8 10 12 14

PH 6.0

5.0 0 2 4 6 8 1 0 1 2 1 4

TIME ( d a y s )

Gas production rate and pH history during start-up phase Figure 2. of a mesophilic, acid-phase digester.’ Model predictions (---).

Assuming an overall first-order rate expression, one can plot the data as In[P(t)/P(t=O)] versus time (Fig. 4b), which results in a straight line of slope 1.14 days-’.

Model predictions are superimposed on batch data in Figure 5. Predictions and experiments agree well for the parameters TSS, VSS, TOC, and DOC. Pre- dicted acetic and propionic acid concentrations only agree qualitatively to observation. Once again, the predictions in Figure 5 were generated using kinetic and stoichiometric constants (see Table 111) either taken directly from the literature or assumed. Only initial bacterial compositions were determined by trial and error. No further parameter optimization of assumed constants was considered necessary.

Table 111. Kinetic constants used in computer simulations.

Substrate Y turnover rates p* K (g Biomass/g d

(g COD/L day) (day-’) (g COD/L) COD . substrate) (day-’) References

r2 (amino acids 6.0 0.022 0.036 0.025 10,14 and simple sugars)

acids) r3 (volatile fatty 0.23 0.50 0.029 0.010 15.19

r, (propionic acid) 0.08 0.80 0.014 0.010 7,16

r, (hydrogen) 1.4 6.0 x 0.029 0.010 17 r, (acetic acid) 0.34 0.50 0.029 3 x 10-3 10

Parameter Temperature

35°C 55°C

0.0556 0.0268

16.80 3.0

0.156 0.0173

1.14 17.4


(rnode1)y’ P

(MODEL)

10 20 30 DlGE STER RESl DE N CE

T I M E ( d a y s )

Figure 3. Propionic and acetic acid concentrations at steady-state digester residence times for a mesophilic, acid phase digeste?. Model predictions (- - -).

Thermophilic Digestion Continuous Experiments

Figure 6a-d chronicles influent conditions imposed on the digester during 70 days of continuous-flow operation. Four separate 10-day time periods (designated A-D) are chosen for model simulation because volumetric flow rate remained constant during these periods. Variations in influent feed composition within each test period are simulated using simple, linear, time-dependent functions illustrated as heavy lines in Figure 6a-d.

Model predictions for periods A-D of all performance

20.

18.

16.

14.

12. - A.

parameters are superimposed on experimental values in Figures 7 and 8. Predicted values of three bacterial groups during Periods A-D are also shown in Figures 7c and 8c.

Predicted suspended solids (TSS and VSS) and organic carbon (TOC and DOC) concentrations agree extremely well with observation; only in period C did the model overestimate digester TSS concentration in response to the step increase in feed TSS. Both model predictions and experiments indicate that while traditional performance indicators, these four parameters, are insensitive to changes in reactor conditions and thus are poor choices as control parameters.

Model TOC and DOC effluent concentrations are virtually identical to experimental values in all four periods. Predictions indicate DOC concentrations consist predominantly of residual acetic and propionic acids since predicted effluent amino acids and simple sugars plus volatile fatty acids concentrations are negligible. However, experimental values of acetic and propionic acids account for less than 30% of the total DOC leaving the digester during any simulated period. Apparently, the model overestimates the effluent concentrations of the two volatile acids while either not accounting for other sources of dissolved organics (i.e., butyric acids, intermediate alcohols, etc.) or under- estimating the contribution of the amino acids, simple sugars, and higher fatty acids. Since these latter components were not analytically measured, one can only speculate as to the source of the above discrepancy. Negligible predicted concentrations of amino acids,

I I I I I I I 1 0 1. 2. 3. 4. 5. 6. 7. 10. I

BATCH R E A C T I O N T I M E (days) Figure 4. (B) Semilogarithmic plot of batch solids data based on equation (11).

(A) Volatile suspended solids data from a batch thermophilic anaerobic digester.z3


PROPIONIC

U rACETIC

U

4 8

BATCH REACTION TIME (DAYS)

Figure 5. Prediction versus observation of batch, thermophilic anaerobic digestion of activated-sludge bi~rnass.’~ Model prediction (-4.

simple sugars, and volatile fatty acids suggest that these components are not limiting the overall digestion process.

Model acetic and propionic acid values do not compare quantitatively to the sporadic concentrations observed; they do, however, qualitatively model steady- state concentrations reasonably well but generally overestimate observation. Model predictions do simulate observed trends in propionic acid somewhat better than for acetic acid.

TIME PERIODS SIMULATED BY COMPUTER MODEL

. , . . 2 0

1.0

FLOW RATE ( ( I d )

50. 4 0. 26.

SUSPENDED SOLIDS CONCENTR.

20. ( g m l l I

14.

ORGANIC 2o CARBON CONCEN TR

10. ( g m i l )

0.

30.

A C I D 20.

(mMol l l1 10

CONCENTR

‘0. 10. 20 30 40. 50. 60. 70. 80. CONTINUOUS OPERATING TIME ( d a y s )

Figure 6. Influent conditions to a continuous, thermophilic anaerobic digester.*’ (A) Volumetric flowrate; (B) suspended solids, TSS, and VSS; (C) organic carbon, TOC, and DOC; and (D) intermediate acid concentration histories of influent slurry. Heavy lines represent computer-simulated influent conditions.

Figure 9 summarizes both predicted and measured total gas production rates for the continuous experiment in the thermophilic digestion study. Observed gas composition remained constant at 66% methane/33% carbon dioxide (v/v) throughout the experiment. The model does not predict the random nature of the measured total gas production rates but does simulate, reasonably well, a “time-smoothed’’ version of all transient periods. Generally, the model overestimates the initial total gas production rate in response to loading changes, which could be due to the simplified estimation RcOz used in the model.

Both predicted and measured pH remain constant throughout the simulated periods at 7.7-7.8, indicating an extremely high alkalinity that provides sufficient buffering capacity to maintain constant pH despite the surges in volatile acids seen following loading changes.

Hypothetical Simulations

Above, computer solutions compare reasonably well to both experimental studies, thus circumstantially verifying the structured model. However, certain experimental nuances limit conclusions about the more fundamental aspects of anaerobic digestion. The two major constraints were:

1. Influent slurry to the digester was allowed to become anaerobic, developing significant concentrations of anaerobic acid-forming bacteria and reaction by- products. Thus, the influent slurry maintained a steady supply of both bacteria and acetic and propionic acids to the digester. Conclusions about which reaction step(s) limits overall digestion to methane in the above experiments would be conjecture since digester concentrations of bacteria and volatile acids were maintained at levels artificially higher than if the digester were fed particulates only.

2. Due to a high alkalinity, pH in the continuous thermophilic experiments remained constant at 7.78 in- dependent of digester residence time. Consequently, modeling equilibrium chemistry, its buffering effect in digester, and resultant pH effects on methanogenic bacteria was superfluous and provided no useful information about the pH sensitivity of thermophilic anaerobic digestion.

Therefore, consider a thermophilic digester (55°C) treating an ideal slurry of only biomass particulates (VSS = TSS = 23.0 g biomass/L = 30.0 g COD/L) which contains neither volatile acid intermediates nor any compounds that may serve to buffer the digester (i.e., NH3, HC03). Figure 10a illustrates operation of such a hypothetical digester over a series of step increases in slurry feed rate (residence time step decreases). In this scenario ammonia release in the digester liquid is assumed proportional to the biomass hydrolysis rate (i.e., -0.Olr-J. This ammonia release is considered the


PERIOD A P E R I O D B

20. 30-L

''.C A

0 . PROPION:

5 1010 5 10 6. r

Figure 7. predictions for simuated periods A and B .

Effluent from continuous thermophilic dige~ter.'~ (-) indicates model

0 V

/? PROPIONIC

0 . / > o o : : - O O 5

2.0 .-. -. - .-. -. -.-.

2 1.0 - 1010 0 -- -

T I M E (DAYS) T I M E (DAYS)

Figure 8. predictions for simulated periods C and D.

Effluent from continuous thermophilic digester.23 (-) indicates model


7

P 0 1 I I I I I I I 0 10. 20. 30. 40. 50. 60. 70.

CONTINUOUS OPERATING TIME ( d a y s )

Figure 9. a thermophilic digester."

Predicted versus observed total gas production rates in

only source of buffering in the digester aside from C02 gas dissolution. Initial bacterial composition at T = 15 days was the same as used in the thermophilic digester simulations above.

Figure 10a shows the increasing dominance of acid bacteria over both propionic acid-degrading and

methanogenic bacteria as the system approaches a 5- day residence time. Digester pH remains stable at all residence times 7 2 6 days, but at 7 G 5 days pH drops sufficiently to curtail methane production. Si- multaneously, effluent DOC increases markedly, re- flecting the increase in components S2 + S 5 , predominantly acetic and propionic acids. Effluent biodegradable particulates, P , also increased at T = 5 days, but solids removal was still 90%. Figure 10a shows that the particular NH, release rate simulated was inadequate to maintain a constant pH.

Figure 10b illustrates an alternative 7 = 5 day scenario where ammonia release from the hydrolysis of particles is augmented by a steady supply of NH, (influent concentration = 0.12 mol NH,/L day; ammonialoading = 0.43 g NH3/L day). This additional supply of ammonia acts indirectly as a source of alkalinity, trapping CO, from the digester gas-space. This serves to maintain pH z- 7.7 at T = 5 days. However, methane production still decreases but is not completely suppressed as in Figure 10a. This drop in CH, production can be at- tributed simply to wash-out of the methanogenic bacteria at T = 5 days.

Figure 11 summarizes, from a series of such scenarios, the amount of continuous ammonia loading required to maintain a stable pH in a thermophilic digester at various digester residence times. Figure 11 is calculated assuming NH, release from the hydrolyzed cells is zero and, consequently, is a "worse case" situation. As ammonia is added to the digester, C02

- . " . .A 5 d 15io i Ib 140 5 io 14 .A

I I

I" [-pH -

5 K) 15 days

SIMULATED TIME ELAPSED' SINCE SPEP CHANGE IN INFLUENT RATE '

Figure 10. Predicted response of a thermophilic anaerobic digester receiving a hypothetical feed slurry of biomass particulates. (A) Ammonia influent concentration is zero and ammonia release rate is 1.0% of particulate hydrolysis rate. (B) Ammonia release rate same as in (A) but inlet ammonia concentration is 0.12 mol NHJL.


STEADY - STATE 4.0 AMMONIA LOADING RATE (D.No)

rlWb11 -day)

3.0 I \

RESIDENCE TIME ~ T ( d a y s )

Figure 11. Hypothetical ammonia loading required to maintain indicated pH in a thermophilic digester vs. digester residence time. Ammonia release from particulate hydrolysis is assumed zero.

must dissolve into the fluid to reequilibrate the solution. However, this equilibration requires time. Conse- quently, either pH adjustment or control in a digester by pulse additions of ammonia is not a practical control option. Addition of a direct alkalinity source (i.e., NaHCO,) versus an alkalinity “trap” is suggested.

CONCLUDING REMARKS

Structured modeling provides details concerning microorganism composition, mixed-culture population dynamics, and/or multiple reaction mechanisms as a function of prevailing conditions in a biological system. Evidence exists indicating that structured models describe in more detail the dynamic response of microbial systems than do more traditional unstructured model^.*^-'^ The application of similar structured con- cepts for understanding the physiology of biological waste treatment processes (processes that experience a high degree of transience) proffers significant promise. ’’

Illustrated in this article is a structured model of the anaerobic digestion of biomass particulates; a system consisting of multiple biological reactions and mixed- culture population interactions. Previous unstructured models of anaerobic digestion have considered only one reaction (i.e., acetic acid and ammonia to cells, CH4, and CO,) mediated by a nondescript collection of microbial Particulate hydrolysis effects, population dynamics, and chemical intermediate involvement in equilibrium chemistry are ignored in such models.

Applying any model requires information on applicable kinetics and stoichiometry. Structured models merely shift the debate from deciding on the most applicable of complex kinetic expressions to defining the appropriate reaction scheme and its stoichiometry. Kinetic expressions need not be more complex than Monod functions. Roels proposes a unit molar carbon basis for structured models of industrial fermentations.” Proposed here is an alternative stoichiometry based on the unit mass of theoretical COD which is more applicable to biological waste treatment processes due to the complexity and variability of substrate compositions.

Based on the microbiological reaction scheme proposed by Kaspar’, a structured model with unit mass COD stoichiometry is derived which, with minimal parameter optimization, predicted observations in two different experimental systems anaerobically digesting biomass particulates. Simulations of a thermophilic, methanogenic digester, for example, indicated that biomass particulate removal can be carried out at >90% efficiencies at 7 5 days, but the digester would be predominated by acid bacteria at a pH of 6.6 with a significant DOC effluent concentration attributable to volatile acid intermediates. Predicted methane production in the thermophilic process is curtailed at T d 5 days irrespective of whether digester pH is controlled at neutrality or allowed to “go sour.” The rate of ammonia release via particulate hydrolysis, which could be a function of particulate composition (i.e., activated sludge versus a cellulytic straw), can have a pronounced effect on digester pH and subsequent pH control. Digester pH dynamics are a complex interaction of liquid phase chemistry, gas transfer, and biological reaction. In this latter respect a structured model is capable of accounting for the various intermediates that exert direct influence on pH equilibrium while an unstructured model is not.

This study was supported by a grant from the Swiss National Research Program No. 7B.

APPENDIX*

Material Balances Hydrolyzable particulates, S,:

Amino acids and simple sugars, S,:

ds, = D(S,U - S 2 ) + 0.66r, - r, dt

(A2)

Volatife fatty acids, S,:

(A3)

* Equations in this appendix required numerical solution using

_ - dS3 - D(S,O - S,) + 0.34r, - r3 dt

the computer package MIMIC.”


Propionic acid, S4:

dS4 - = D(S,O - S,) + 0.29r2 - r, d f

Acetic acid, S,:

- D(S,” - S,) + OSOr, + 0.65r3 + o.59r4 - r, d s , _ - df

Hydrogen, s6:

_ - ds6 - D ( S ~ - s6) + 0.16r2 + 0.31r3 + 0.39r4 - r6, dt

Inert particulates, I:

Liquid Phase Equilibrium Chemistry

Hydrogen Ion Concentration, [H’]:

Bicarbonate alkalinity, [HCO;]:

[HCO;] Z + [NH:] - [Ssl - [S,l

Dissolved carbon dioxide, [COfl

[CO:] = C7 - [HCO;]

Dissolved carbon dioxide at equilibrium, [COT]:

Acid-forming bacteria, X, :

_ - dxa - D(X,” - X,) + Y2r, + Y3r3 - (d2 + d3)X,

_ - dxp - D(X,O - X,) + Y4r, - d.&

dr

Propionic acid-utilizing bacteria, X,:

d f

Methanogenic bacteria, X,

dx, - = D(X2 - X,) + Y,r, + Y6r6 - (d5 + d6)X, d f

Gas Phase Equations

Carbon dioxide partial pressure, Pco2 :

Rate Expressions NOMENCLATURE

[CO:] [COT]

concentration of dissolved carbon dioxide (mol/L) concentration of dissolved carbon dioxide at equilib-

Total biomass decay rate, rd:

rd = ( d , + d,)X. + d4Xp + (d, + d6)Xm

Methane generation rate, RCH,:

RCH, = f, x 0.96(r5 + r.5)

Total gas generation rate, R,:

RK = 1.5RCH4

Carbon dioxide gas transfer rate, Rco,:

Rco2 = KLa(CO: - CO:)

Particulate hydrolysis, rl:

rl = khSl

Amino acids and simple sugars utilization rate, r,:

rium (mol/L) concentration of total carbonic acid species, [CO;] + [HCO;] (mol/L) reactor dilution rate (day-’) microbial decay rate constants for reactions i, i = 2 + 6 (day-’) conversion factor (g COD/L day to L/day) gas volume conversion factor (17.9 L/ mol at 55°C and 1.5 atm) Henry’s gas law constant for CO,/water (mol/L atm) hydrogen ion concentration (mol/L) dissolved hydrogen gas concentration (mol/L) concentration of inert, nonvolatile particulates

saturation constants in reaction i, i = 2 --* 6

first dissociation constant for carbonic acid system,

concentration of ammonium ion (mol/L) partial pressure of C02 in gas phase (atm) partial pressure of water in gas phase (aim) total pressure in digester (atm) turnover rate of component i, where i = 1 + 6

total biomass decay rate (g COD/L day) methane production rate (day-’) total gas production rate (day-’) rate of COz transfer from liquid to gas (mol COz/L

component i, where i = 1 + 6 (g COD/L) digester liquid volume (L) digester gas volume (L)

(g COWL)

(g COD/L)

(mol/L)

(g COWL day)

day)

c7

D d,

f’ h

f h

H’ H2 I

K,

KPH

Pco,

p7 r,

NH

p H 2 0

rd

R C H ~ RG Rco2

S, V VK

Volatile fatty acid utilization, r3 :

Propionic acid utilization, r,:

Acetic acid utilization, r s :

Hydrogen conversion, r,:


Z CL:

7

0

concentration of acid-forming bacteria (g biomass/L) concentration of propionic acid degrading bacteria (g biomass/L) concentration of methanogenic bacteria (g biomass/L) yield for bacterial growth on substrate i, i = 2 -+ 6 (g biomass/g COD substrate) net concentration of cation-anion (mol/L) maximum biological growth rate constant for substrate i, i = 2 + 6 (days-‘) stoichiometric coefficient for j t h component in ith reaction digester residence time, D-’ (days) indicates inlet condition

ABBREVIATIONS

P VFA AAS PR propionic acid, S, A acetic acid, S, H, hydrogen gas, S, CH, methane gas, S,

biodegradable, hydrolyzable particulates, substrate S , volatile fatty acids, substrate S, amino acids and simple sugars, S,

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structured modeling of the anaerobic digestion of biomass particulates

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