Mathematical Modeling of an Anaerobic Butyrate Degrading Consortia: Predicting Their Response to Organic Overloads Foroozan Labib,+ John F. Ferguson,'J Mark M. Benjamin,? Mohamed Merigh,* and N. L. Ricker* Departments of Civil Engineering and Chemical Engineering, University of Washington, Seattle, Washington 98195
The steady-state and dynamic response of a butyrateusing methanogenic consortia has been modeled as three sequential bacterial growth reactions. The model simulates the concentration of fermentation intermediates (acetate and hydrogen), incorporating their inhibition of butyrate oxidation and stimulation of methanogenesis. The h ydrogen-producingacetogenicconversionof butyrate is modeled as a product-inhibited or reversible, modified Monod reaction, while hydrogen-using and acetoclastic methanogenesis are simple Monod reactions. The growth yield coefficient for each growth reaction is variable and dependent on the Gibbs free energy of the energyreaction, which in turn depends on the time-varying concentrations of reactants and products. These substrate utilization and growth reactions are incorporated into mass balances for a completely mixed, fluidized bed reactor, resulting in a series of coupled ordinary differential equations that were solved with numerical integration software. The model was calibrated with experimental data from a highrate laboratory reactor; a single set of biological kinetic parameters was found to successfully reproduce steadystate, step-loading, and pulse-loading results involving butyrate, acetate, and hydrogen or formate substrates. The response for the consortia was also simulated for a wide range of steady-state and step-loading conditions to better understand the interactions in this microbial consortia that lead to process stability or instability.
by conversion of fatty acids ( I ) , and these conversions may indicate impending problems with the overall microbial system. In an earlier publication (2), we showed the influence of Hz and acetate on the degradation of butyrate in a continuous flow, anaerobic fluidized-bed reactor. Fluidization was achieved by using a high recycle rate, which essentially created a completely mixed environment for the liquid in the reactor. The first step in butyrate degradation is an Hz-producing acetogenic reaction. Both H2 and acetate partially inhibited utilization of butyrate while the free energy change for the butyrate oxidation was still negative, and butyrate oxidation was completely inhibited when the Ha and acetate concentrations became so large that the calculated free energy change was positive. This paper presents a model of an anaerobic butyratedegrading culture based on our understanding of the culture described previously. Experiments and model simulations are presented showing the effects of long-term changes in the butyrate, acetate, and hydrogen loadings to an anaerobic reactor. The simulations provide insights into the response of a part of the anaerobic microbial community (the Haproducing acetogens and the methanogens) involved in treatment of complex wastes. The changes in the acetate and hydrogen loadings that are investigated represent realistic changes that might occur in a complex wastewater being treated by an anaerobic reactor.
Introduction
Model Development
Studies of anaerobic degradation have shown that waste stabilization requires interactions among several microbial groups. While fermentations of soluble organics, in general, are usually not believed to be rate limiting and are carried out by many anaerobic and facultative bacteria, the hydrogen-producing, acetogenic fermentations of substrates such as long-chain fatty acids are particularly sensitive to concentrations of fermentation intermediates. These fermentations typically involve formation of acetic acid and hydrogen by one group of bacteria and concomitant methanogenesis by hydrogen users and acetoclasts. The overall digestion of complex materials may be limited
The model of the butyrate-degrading reactor considers kinetics of sequential reactions involving three distinct microbial groups carrying out Ha-producing acetogenesis, methanogenesis from Ha, and methanogenesis from acetate (Table I). The hydraulic characteristics of the model reactor are those of a continuous stirred tank reactor (CSTR) with attached biofilm growth, so that the solids retention time (SRT) is, to a first approximation, independent of the hydraulic flow rate. The model assumes the same SRT for all the three groups of bacteria in the reactor. Growth of the groups is tightly linked by the sequential metabolism. McCarty and Smith ( 4 ) have suggested that the H2-producing acetogens and the HZ consumers must be in close physical proximity, so the assumption of closely linked SRTs appears reasonable. Based on the applied loadings of butyrate, acetate, or
* Correspondingauthor.
+ Department of Civil Engineering. 4
Department of Chemical Engineering.
0013-936X/93/0927-2673$04.00/0
0 1993 American Chemlcal Society
Envlron. Sci. Technol., Vol. 27, No. 13, 1993 2673
Table I. Reactions and Energetics of Anaerobic Degradation of Butyrate [Standard Free Energy Changes at 37 OC, Using Values from Thauer (3) and Typical Free Energy Changes at Concentration during the Reactor Study free energy changes (KJ/mol of butvrate)
AG, = -k,AAG, (3) where A is the ratio of electron equivalents of substrate utilized for energy to electron equivalents of substrate utilized for cell synthesis, AGr and AG, are expressed as energy per electron mole of catabolic and synthetic reactions, respectively, and kt is the energy transfer efficiency. Only AGr differs from McCarty's model, and in our modification it depends on the time-varying concentrations in the reactor. The growth yield coefficient, Y, is defined as the ratio of grams of cell synthesis per mole of substrate used. Using the cell formula, C ~ H ~ O Z N , and letting n equal the electron equivalents per mole of substrate, the yield is given by
reaction acetogenesis (1) CH3(CH2),COO-+ 2H,O
2CH,COOmethanogenesis (2) 2CH,COO(3) 2H,
+ 2Ht
+ 0.5C0,
-
-15
-159.1
-45
-63.0
-10
-136.1
-70
+ 2H2+ Ht
-
2CH4 + 2C0,
-
86.0
0.5CH4+ H,O overall butyrate degradation
-
(4) CH3(CH,),COO- + H,O + Ht 2.5CH4 + 1.5C0,
the energy obtained from catabolic reactions involving different substrate concentrations (7-10). The energetic model relates the free energy change associated with the biosynthetic reactions (AG,) to the free energy change from catabolic reactions (AG,), using the following equation
hydrogen and acids and bases, the model calculates the concentrations of butyrate and acetate in solution; the gas flow rate and the partial pressures of CHI, COZ,and H2 in the gas phase (assuming gas-liquid equilibrium); the solution pH; and the bacterial concentration for each metabolic group. Mass transfer effects in the biofilm have not been incorporated in the model.
Y = 5.65n/(1+ A ) (4) A and n are determined for each specific growth reaction. Y could easily be converted into conventional units of g of cells/g of substrate by dividing by the molecular weight of the substrate. Steps in determining the yield coefficient follow McCarty (5, 6) except that AGr is calculated for each of the metabolic reactions (Table I) for the reactant and product concentrations in the reactor at each time increment. Hz utilizers are assumed to grow heterotrophically using acetate as a carbon source. "3-N is the nitrogen source. AG, values for the catabolic reactions are calculated using the following equations:
Microbial Kinetics
butyrate utilizers (n = 20)
Typical AGra, observedin the reactor study using concentrations measured in the bulk gas and liquid phases. (I
Monod kinetics have been used for bacterial growth and substrate utilization for separate bacterial populations carrying out butyrate oxidation (reaction 1 , Table I), methanogenesis from Hz (reaction 3), and methanogenesis from acetate (reaction 2 ) . The typical Monod expressions (eqs 1 and 2 ) for substrate utilization and bacterial growth were modified in two significant ways presented in the sections that follow. -rs = k S X / ( K s + S)
(1)
rg = -Yr, - b
(2)
Determination of Microbial Growth Yield Using the Energetic Approach. The biomass yield and the concentration for each bacterial group are calculated for heterotrophic growth on butyrate and acetate using the energetics model developed by McCarty (5,6). The model is modified to incorporate changes in the bacterial growth yield as the free energy change for utilization of each substrate changes. This approach results in a variable growth yield for each bacterial group, influenced by the substrate and product concentrations. In effect, the total available energy from the conversion of butyrate to CHI and COz is partitioned among the three bacterial groups. The partitioning is based on the AG, from each catabolic reaction for the predicted concentrations of substrate and product. Typical steady-state values of AGr for the three reactions involved are shown in Table I. Although no experiment was performed to validate this approach, there is some evidence that bacterial growth yield is related to 2674
Environ. Sci. Technol.,Vol. 27, No. 13, 1993
AG,, = 4.3 + 1/20RT In
acetate^^[^^^^ [H+I [butyrate]
(5)
acetate utilizers ( n = 8 ) AGrA = -9.94
IPCH4] [pC02] + 1/8RT In [acetate] [H'I
(6)
hydrogen utilizers ( n = 2 )
Substrate Kinetics with Inhibition. Based on our experimental results (2)demonstrating inhibitory effects of acetate and HZon the butyrate oxidation reaction, the Monod rate expression for substrate (butyrate) use was modified to incorporate two additional terms. One term incorporates product concentrations. The second accounts for the reduction in the available free energy for butyrate oxidation which accompanies the accumulation of Hz and acetate. These have been adopted by their close analogy to the Michaelis-Menten equation (eq 8) and the related rate expression for a reversible enzyme-catalyzed reaction (eq 9) (11):
where [SI is the substrate concentration, [SI,, is the
Table 11. Sequential Substrate Utilization Rates Expressions. Methanogenesis acetoclastic
Hz utilization (7)
Acetogenesis
a r is the reaction rate, Ks is the half-saturation constant; k is the maximum substrate utilization rate; X is the biomass concentration; S is the substrate concentration; subscripts A, H, and B refer to acetate, Hz,and butyrate, respectively; and KA, K H ,and Kp are inhibition coefficients.
equilibrium substrate concentration, [PI is the product concentration, Vnet is the net reaction rate, Vm=,f is the maximum forward reaction rate, and Ks and Kp are the kinetic constants for substrate and product. The replacement of the substrate concentration, [SI, by ([SI - [SI,,) in the numerator of eq 9 accounts for the reversibility of the reaction; the term (1+ [P]/Kp)in the denominator increases the effective half-saturation constant for substrate, incorporating product inhibition. With an enzyme reaction, the constants are functions of the microscopic rate constants for the reaction. In the extension to bacterial substrate utilization, the constants become empirical parameters and may reflect a variety of effects in addition to the forward and reverse reaction rates of a reversible reaction displaced from equilibrium. Since [SI,, = [SI exp(AGr/RT)
where AGr is the Gibb's free energy change for butyrate oxidation (eq 4), R is the ideal gas law constant, and T i s the temperature. In the current case, two inhibitory products (acetate and H2) were considered. These inhibitors could potentially operate independently in an additive manner or in a more complex,synergistic manner. During development of the model, these possibilities were investigated by defining the term [PI/Kp in the following two ways:
[SAIKA + [SHIKH 2. (synergistic, multiplicative): [PI/Kp [SA][SHlKp KAand KHare the individual inhibition coefficients for acetate (SA)and hydrogen (SH), respectively, and Kp is a "mixed- inhibition coefficient for acetate and hydrogen operating in concert. The forms of all the rate expressions used in the model are shown in Table 11. Monod kinetics were used for acetate and H2 utilization rates because their 1. (independent, additive):
[PIIK,
reaction products were not observed to affect their utilization rates. Both expressions for butyrate (eqs 8a and ab, Table 11)were tested and were reasonably able to predict the effect of hydrogen and acetate concentrations on the butyrate oxidation reaction. In the simulations that follow throughout this work, expression 8a is used for butyrate utilization. The AGr term in the numerator ensured that the reaction rate becomes zero when the reaction becomes energetically unfavorable. The rate was set to zero when AG, was positive, which is consistent with our experimental observation that butyrate or other volatile acids were not formed in significant amounts when the free energy became positive. There have been several approaches to modifying the basic Monod rate expression for substrate degradation in anaerobic processes (12,13) to account for the overall stoichiometry and kinetics of anaerobic treatment, as well as toxicity and inhibition effects. For instance, Mosey (13) presented a model for degradation of glucose in an anaerobic process. His model attempted to explain the complexpatterns of production and degradation of volatile acids in terms of relative availabilities of reduced NADH and oxidized NAD+. He showed that if these molecules are in equilibrium with Hz, then P H 2 indirectly controls both the overall rate of glucose conversion and the decomposition of the acids formed. Costello et al. (14,15) described a mathematical model of a high-rate anaerobic reactor in which H2 regulated product formation as modeled by Mosey, and in addition, they included pH inhibition factors and considered product inhibition terms for fatty acids. Smith and McCarty (16) presented their energetic/kinetic model of a methanogenic culture receiving ethanol and propionate, which includes reversible formation of propionate. While our proposed model does not have all these features and it is not uniquely able to describe the data set, it has the desirable characteristics of separating the principal microbially mediated reactions and of addressing inhibitions that were observed in the experiments. As discussed later, in the simulation of the experimental reactor under transient loadings, simpler models would not be able to simulate the experimental data. Material Balance and Calculations of p H and Gas Flow Rate Materials balances for butyrate, acetate, hydrogen, methane, and carbonate were written, as were balances for butyrate-, acetate-, and hydrogen-utilizing biomass (Table 111). A charge balance was used to calculate pH, and materials balances were combined to compute the methane and carbon dioxide gas flow rates. Equilibrium is assumed between the liquid phase and a minimal gas holdup volume (VG)in the reactor. Simplifications are made to limit the pH range of applicability to about 5.7-9. In most calculations, solids retention time, SRT, and the partial pressures of methane and CO2, P C H and ~ Pc02, are treated as parameters in the calculations. The differential equations are integrated numerically, with respect to time, using a numerical integration software package (EPISODE)available at the Department of Chemical Engineering, University of Washington. The computer programming is in Fortran. The concentrations of reactants and products, biomass, pH, and gas and liquid mass flows are computed for steady-state and transient Envlron. Sci. Technol., Vol. 27, No. 13, 1993 2675
Table 111. Materials Balance Equations.
[H+l + [cations] defining Z [H+l butyrate acetate hydrogen
Table IV. Kinetic Parameters and Reactor Constants Used in the Model specific substrate utilization rate kg, g of COD (g of bacteria)-1 d-1 kH, g of COD (g of bacteria)-1 d-1 kA, g of COD (g of bacteria)-' d-1 half-saturation constants Ksg, mg of COD L-1 KSH,mM H2 L-1 KSA,mg of COD L-1 product inhibition constants K Ain eq 8a KHin eq 8a Kp in eq Bb, L mol-' solids retention time (SRT), d energy transfer efficiencies for cell synthesis
Charge Balance = [OH-] + [HCOa-] + SB + SA+ 2[COaZl + [anions] = [cations] - [anions], neglecting [C032-], and assuming Sg and SAto be completely ionized = -[Z] + IHCOs-] + Sg + SA Reactor Biomass AXg/dt = -Ygr,g - (KDB l/SRT)Xg AXA/dt = -YArsA - (KDA+ ~/SRT)XA m H / d t = -YHrsH - (KDH+ ~/SRT)XH
S is the substrate in the reactor (mol L-l); Sois the substrate in the feed (mol L-9; r, is the substrate reaction rate (after subtracting the biomass formation rate; (mol reactor' min-1); VL is the reactor's liquid volume; QL is the hydraulic flow rate; PHZ is the H2 partial pressure (atrn); PCH4 is the partial pressure of CHI (atrn); K H , His~ the Henry's constant for Hz in water (0.000743mol L-l atm-1);KH,CH.I is the Henry's constant for CH4 in water (0.001136 mol L-1 atm-1); KCOZis the Henry's law constant for C02 in water (0.0246 mol L-1 atm-l); KAis the first dissociation constant for carbonic acid (5.012 X lo-'); [HC03-l0 is the bicarbonate in feed (mol L-1); 10-pHo is the (H+)ions concentration in feed (mol L-l); VQis the gas volume (i.e., gas holdup volume in reactor liquid) (0.01 L); QQis the gas production rate (L min-l); R is the ideal gas law constant (0.082 L atm mol-' K-l); Tis the reactor temperature (310 K). The subscripts B, A, H2, CH4, and C02 represent butyrate, acetate, hydrogen, methane, and carbon dioxide, respectively. Equilibrium is assumed between the gas and liquid phases. [cations] is the total cation concentration, excluding H+(mol L-l); [anions] is the total anions concentration, excludingthose identified explicitly on the RHS (mol-l);and [Cos2-] is the carbonate concentration (mol L-l). X is the biomass in the reactor (g); Y is the growth yield, (g of bacteria (mol of substrate)-'); KD is the specific biomass decay rate (time-'); SRT is the solids retention time, (a of biomass in reactorhate of biomass wash out).
0.7,0.5
140
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Hydrogen>0.00, 2.5
Model Parameters and Steady-State Predictions
Envlron. Scl. Technol., Vol. 27, No. 13, 1993
0.02 1500 6 X lofi 5.6
ktH, kpH ktA, kpA hydraulic flow rate, L d-l reactor liquid volume, L reactor gas volume, L
conditions. Reduced reactants and products are reported in chemical oxygen demand (COD) concentration units.
2676
0.8 0.8 38.4
ktB, kpB
a
Estimates of kinetic parameters were made based on the experimental results and on comparisons with the literature values. Table IV shows the kinetic parameters used. They were obtained by comparing the simulation results and the experimental data from 15transient loading experiments and from the steady-state operation of the reactor. The values of Ks for hydrogen found in literature are quite variable (In,and the value in Table IV is at the lower end of the range (1-10 mM). The bacterial decay rate of 0.01/d is used for all the bacteria. Since the biomass of the individual bacterial groups could not be determined experimentally, the specific substrate utilization rate was estimated using the experimentally determined maximum substrate utilization rate and the model prediction of biomass concentration for each bacterial group. Based on the energetics model, growth of the acetateutilizing population accounts for the highest proportion (about 60%) of the total bacterial yield. Figure 1shows
63.4 85.6 10.3
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Table V. Variations of Steady-State S/Ks with SRT
Fraction of each biomass
-
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SRT (d) 5.6 10 20
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30 40 SO 60 70 80 Solids Retention Time SRT (days)
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butyrate apparent S/apparent KSB KSB
21.1 11.8 7.7
0.73 0.23 0.09
acetate
hydrogen
s/KsA
s/KsH
3.59 1.05 0.42
0.068 0.046 0.025 1
-I
20 10
-
'0
Flgure 2. Model prediction of the fraction of each biomass with increaslng SRT.
concentration is close to the estimated value for the experimental reactor (2). This SRT of 5.6 d was used in the model simulations. At this SRT, the maximum substrate utilization rates (IZX)for butyrate, acetate, and hydrogen are 22,10, and 29 g of COD L-l d-l, respectively, in accordance with experimental observations. As would be expected, the model predicts increasing biomass and decreasing substrate concentrations with the increasing SRT (Figure 1). Also, the yield coefficientsfor the acetate and hydrogen bacteria decrease, while that for the butyrate bacteria increases with increasing SRT. This occurs because the decreases in P H 2 and acetate concentrations reduce the free energy obtained by the methanogens utilizing these substrates. Although the butyrate concentration is decreased at higher SRTs, the lower P H 2 and acetate concentrations result in a net increase in the free energy for the butyrate oxidation. Thus, unlike H2 and acetate, the butyrate yield coefficient increases with increasing SRT, while the net total bacterial yield is predicted to decrease slightly. In Figure 2, the modelpredicted proportions of the different bacterial groups in the reactor show a considerable change as the SRT is increased to 100 d. The ratios of S / K s (substrate concentration at steadystatelhalf-saturation constant) give an indication of the degree to which the substrate utilization rate is limited by the population of each bacterial group. When this ratio is less than 1, the bacteria are metabolizing substrate at less than 50% of the maximum rate they are capable of maintaining. If substrate concentration is increased under such conditions, their metabolic rate will increase quickly, and the extra substrate will be processed efficiently. On the other hand, if [SIIKs is substantially greater than 1, the bacteria are processing substrate at close to their maximum rate. In such a case, an increase in substrate concentration will lead to the accumulation of substrate in the reactor. Since individual organisms cannot process the additional substrate efficiently, the only way for it to be metabolized is for the population of these bacteria to increase, which may take many hydraulic residence times (HRTs). The [SIIKs ratios have been calculated for each substrate at different SRTs and are shown in Table V. It can be seen that at low SRT the acetate utilizers are substratesaturated, while the Hz utilizersare greatly undersaturated. At higher SRTs, the unutilized capacities of all bacterial groups at steady state increase, leading to a greater reactor stability to organic overloadings. In eq 8a, the KSBfor butyrate is constant (0.8 mg of COD L-1). However the apparent half-saturation constant (including the inhibi-
300
500 , Acetate
"
Flgure 3. Model simulation of a series of butyrate loading changes and the reactor data.
tion terms) is a function of acetate and hydrogen concentrations and varies with the SRT. The [s]/&B ratio for butyrate decreases at higher SRTs, indicating excess capability for butyrate oxidation at higher SRTs. In the following section, the model is used to simulate the experimental results involving transient loadings to the butyrate reactor and to test hypotheses regarding the effects of Hz and acetate on the oxidation rate of the butyrate. The simulationsuse the set of kinetic parameters shown in Table IV. The simulations show the success of the calibration and also show the model sensitivity to certain parameters.
Simulation 1: Reactor Response to Butyrate Loading Changes In this section, the reactor response to changes in butyrate loading is compared with the model predictions for concentrations of butyrate and acetate and for PHZ. Figure 3 shows the applied loading and the experimental and predicted results for acetate, butyrate, and hydrogen. The initial biomass concentrations for acetate and butyrate utilizers were decreased and increased by lo%,respecEnvlron. Sci. Technol., Vol. 27, No. 13, 1993 2677
tively, from their predicted steady-state concentrations to reflect the higher butyrate and lower acetate concentrations at the beginning of the experiment. Thirty minutes into the experiment, the butyrate loading was halted, and the concentrations of all three substrates started decreasing. Increasing the loading rate to 25 g of COD L-l d-1 at 60 min increased the butyrate concentration in the reactor. Oxidation of butyrate produces acetate and Hz, so these products increased as well. However the increase in Hz partial pressure was very effectively damped by the Ha-utilizing methanogens both in the reactor and in the simulation. This is due to the low KSfor Hz and a relatively high maximum hydrogen utilization rate. Although both butyrate and acetate concentrations rose continuously during the period of high loading, the H2 concentration increased for only 10 min, after which it stabilized. The continued increases in the butyrate and acetate concentrations indicate that the reactor capacity to utilize these substrates was saturated. After 180 min, the loading was stopped again, and the concentration of butyrate decreased abruptly. Butyrate oxidation continued in the reactor, so the acetate concentration did not decrease as rapidly. As the concentration of butyrate continued to decrease, its reaction rate was reduced. Acetate was not formed as rapidly, and continued utilization lowered the acetate concentration in the reactor. The experimental PHZin Figure 3 was obtained from measurements made in the reactor gas phase and appears damped when compared with the model prediction, in which hydrogen mass transfer resistances (in biofilm and the gas-liquid interface) were neglected. Methane partial pressure stayed rather constant (data not shown), and the methane production rate increased as a result of high COD loading. The model predicted the total methane production rate, which is a measure of COD conversion efficiency. However,the model predicted a higher total gas production rate due to the higher rate of carbon dioxide leaving in the gas than was observed experimentally. Since the model pH was 7 and the reactor pH was close to neutral, the discrepancy in Pco2 prediction is thought to be due to neglecting the COz transfer resistance at the gas-liquid interface. This example showed that the model could predict the reactor response to a series of butyrate-loading changes rather well. Slight adjustments were made to the biomass concentrations to reflect the initial reactor conditions. The simulations that follow show the model's ability to predict reactor responses to acetate and hydrogen loadings using the same set of kinetic parameters without adjustment of the biomass concentrations. Simulation 2: Reactor Response to an Acetate Loading While the reactor received a continuous butyrate loading of 10g of COD L-l d-l, a pulse acetate loading was imposed on it. The experimental data and the model simulation results for the volatile fatty acids and hydrogen partial pressure in the reactor subsequent to the pulse loading are shown in Figure 4. The acetate loading increased the acetate concentration in the reactor to around 7000 mg of COD L-1, after which it decreased, both as a result of biological uptake and also because of hydraulic washout. In response to the acetate loading,the butyrate oxidation reaction was inhibited, and the butyrate concentration in 2878
Environ. Sci. Technol., Vol. 27, No. 13, 1993
-T
3
n
10
Butyrate Loadmg 8.92 g C0DL.d
B
E
I
q i
300
e
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Butyrate
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200
8
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300
400 500 600 700 800 T i e (min) Figure 4. Comparison of the model simulations of an acetate loading and the reactor data. 0
the reactor increased as butyrate loading continued. The use of simple Monod kinetics for the butyrate oxidation cannot predict any increase in butyrate concentration in response to acetate loading. The predicted butyrate concentration profile (model in Figure 4) was obtained using the kinetic model for reversible enzyme kinetics (expression 8a in Table 11). The free energy term in the numerator of the butyrate rate expression allows the oxidation rate of the butyrate to vary with the thermodynamic driving force (AG,B). An increase in the acetate concentration reduces this driving force and reduces the butyrate oxidation rate. The acetate term in the denominator of the expression accounts for possible product inhibition caused by acetate. In order to determine the relative influence of the AG,B term and the acetate product inhibition term in the butyrate rate expression,the simulation was repeated using only one of these terms at a time. The result, shown in Figure 4, indicates that the terms were about equally important in influencing the butyrate concentration profile. The lines in Figure 4 are for simulations using only one of the inhibition terms with the same parameter values as in the earlier simulation including both terms. Not surprisingly, the simulations using only one term did not fit the data very well, when the data were modeled using only one inhibition term. When the value of the inhibition term was adjusted to give the best correspondence between the experimental and simulation results, a reasonable fit could be obtained. However, the simulations of experiments involving Hz loading using those same parameters did not fit the experimental results. The
H2 consumed
Butyrate Loading 1OgCODiLd
10 U m i n I
l . , , l , , . , , , , I
.
50
40 30
inhibitiontmns only
a
20 10
0 170 Acetate
Experiment
160
130
a"
. 0
200 250 300 350 400 Timc (min) Flgure 5. Comparison of the model simulations of a H2 loading and the reactor data. 50
100
150
only consistent set of parameters that was able to model all the experiments reasonably well included terms for both product inhibition and rate reduction in proportion to changes in free energy. This simulation demonstrated the ability of the model to predict the reactor response under transient acetate loading. A similar approach used to model the reactor response to a transient Hz loading is presented in the following simulation.
Simulation 3: Reactor Response to Hydrogen Loading H2 gas was injected to the reactor under a constant butyrate loading (Figure 5) for approximately 100 min. In such an experiment where Hz gas was sparged into the reactor, the Hz transfer rate from the gas into the liquid was found to be limiting, and the PHZin the gas was not at equilibrium with the liquid H2 concentration, which was much lower than expected at equilibrium. Furthermore, the concentration at or near the cells may be different from that of the bulk liquid, Based on mass balance on the H2 inputs and outputs, the rate of Ha consumption by the Hz-utilizing methanogens was found to be approximately 10 mL min-', which could be confirmed by an increase in the measured CH4 production rate of 2-2.5 mL min-l. The simulation is thus carried out for a H2 loading of 10 mL min-l (Le., 10.4 g of COD L-l d-I), all of which is available for methanogenesis. The experimental data and the model prediction results are shown in Figure 5. Only the predicted PHZis shown in Figure 5, since the high PHZ(about 10% ) leaving in the reactor gas was far from the equilibrium HZconcentration in the liquid. Dissolved PHZduring this period was
approximately 0.2 % (2000 ppm), based on measurements from liquid samples. The decrease in butyrate oxidation rate, during the transient H2 loading, increased its concentration in the reactor. The kinetics of the butyrate oxidation, as expressed by eq Ba, enables the model to predict such a decrease in the butyrate removal rate as a result of an increase in the hydrogen partial pressure. The decrease in the acetate concentration is due to a lower acetate formation rate from butyrate, following the Hz loading. When the Hz loading ends, the inhibition of the butyrate reaction is relieved,and its removal rate increases, reducing the butyrate concentration back to its value prior to the H2 loading. After the end of Hz loading, a higher butyrate oxidation rate produces acetate and increases its concentration in the reactor. To investigate the relative significanceof the free energy and H2 product inhibition terms in expression Ba, the simulation was repeated using these terms, one at a time. The predicted butyrate concentrations are also shown in Figure 5, labeled "inhibition term only" and "AG term only". In this case, the free energy term by itself has very little effect, while the Hz inhibition term accounts for nearly all the model response. It should be pointed out that the inhibition of the butyrate use is stillvery small, from about 99.7 % initial butyrate use to 99.4 % followingthe hydrogen loading. I t should also be emphasized that the model parameters were calibrated against the measurements made in the reactor gas and liquid phases. As a consequence of concentration gradients near and within biofilm, the microbial population is exposed to somewhat different concentrations than those measured in the reactor liquid or gas phases. Thus, the available free energies from the reactions carried out by the microbial population within the biofilm are probably different. It was possible to simulate the experimental results for the H2 loading or the acetate loading by changing the value used for standard free energy for the butyrate oxidation ( A G o , ~ ) . This change is equivalent to assuming fixed concentration gradients for H2, acetate, and butyrate within the biofilm. The standard free energy had to change by 7.15 K J in Hz simulation compared to 1.8 KJ in the acetate simulation, suggesting rather different mass transfer effects in the two tests. These results emphasize that the model selected is not uniquely capable of simulating the results, nor are the parameters used unambiguously determined by an experiment. However the ability to use the same kinetic parameters and inhibition constants to simulate all the experiments, including 11not reported in this paper, is a better validation of the model.
Simulation 4: Reactor Response to a Hydrogen-Step Loading A simulation for a Hz-step loading experiment is carried out, using a similar approach to that described in simulation 3. Figure 6 shows the experimental data and the predicted results for butyrate, acetate, and hydrogen. Only the predicted PHZis plotted, since the H2 in the gas was not in equilibrium with the liquid H2. As can be seen, in response to the H2 loading the predicted increase in butyrate concentration is similar to the experimental results, although the concentrations are somewhat lower. The initial reactor concentrations are higher than in the Environ. Sci. Technol., VoI. 27, No. 13, 1993 2670
I
H2 Pulse 10 W m i n consumed
50 Butyrate Experiment/
-
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Butyrate concentration
2x
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previous experiment, indicating that the reactor was not at steady state. However, the measured parameters, such as gas flow rate and composition, pH, ORP, and VFA concentrations were steady with the COD removal rate close to 94 % . In response to the H2 loading, the butyrate oxidation rate was reduced. Thus acetate production decreased, and its concentration in the reactor dropped. As in simulation 3, the Hz inhibition term in the butyrate rate expression of 8a was eliminated to determine the effect of the free energy change by itself (Figure 6). The results agree with the conclusion reached in the previous section that a H2 inhibition term in expression 8a is necessary to predict the reactor behavior under transient H2 loadings. In the following sections, the butyrate model is utilized to obtain some understanding of the response of a butyratedegrading microbial consortium to loading changes in an anaerobic reactor and its consequence on the reactor stability.
Model Application One important potential application of the model is to investigate loading scenarios that might have drastic and/ or long-term effects on the reactor and that are therefore not readily amenable to experimental testing. The response of the butyrate-degrading consortium to several such changes in butyrate, acetate, and hydrogen loadings was simulated with the model. Simulated loading was varied by changing the feed concentration and keeping the hydraulic detention time and SRT constant at 1 2 h and 10 d, respectively. The simulations were carried out assuming a fully neutralized feed with 13 mequiv L-l of 2880
Environ. Sci. Technol., Vol. 27, No. 13, lQQ3
5
10
15.
20 25 30 Time (days)
35
40
45
50
Flgure 7. Predicted reactor response to increasesIn butyrate loadlng at day 5. SRT is 10 d and pH is 7.
excess bicarbonate alkalinity, so the reactor pH would stay near 7. The model runs started from steady-state loadings of 10 g of COD L-l d-l as butyrate. The following simulations were conducted: Step increases in the butyrate loading to 20, 30, 50, or 100 g of COD L-l d-1 A step increase in the butyrate loading to 30 g of COD L-1 d-1 for SRTs of 5.6,10,15, and 20 d Step increases in the acetate or hydrogen loading to 20 g of COD L-l d-l, while the butyrate loading remained at its initial value (10 g of COD L-l d-l). Given the model assumptions and constraints and without validation, the following simulations serve only to provide insight into important factors that shape and influence the behavior of such a microbial community in an anaerobic reactor.
Simulations of Reactor Response to Different Butyrate Loadings and Different SRT Values Simulation results carried out for butyrate loadings 2, 3,5, and 10 times the steady-state loading of 10 g of COD L-1 d-1 are shown in Figure 7. The transient responses lasted from 2 to 10 d before returning to essentially the initial effluent concentrations. At high butyrate loadings, the butyrate utilizers became saturated, allowing a rapid buildup of butyrate in the reactor. This buildup continues until the butyrate-utilizing biomass in the reactor increases sufficiently to metabolize the butyrate at the same rate it is entering the system (Figure 8). The reactor response to the butyrate loading is very significantly affected by the reactor SRT (Figure 9).
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Figure 0, Predicted reactor response to the butyrate loading increase of 20 g of COD L-I d-' at different SRTs. pH is 7.
Time (d)
Figure 8. Predlcted reactor biomass changes in responseto increases in butyrate loading at day 5. SRT is 10 day and pH Is 7.
Investigation of Interaction between Butyric Acid Loadings, SRT, and Alkalinity Addition
Doubling the SRT from 10 to 20 days reduced the peaks in the butyrate and acetate concentrations by about 40and 10-fold, respectively, and the time to return to the steady-state concentrations was correspondingly shorter. The predicted changes in biomass concentrations are shown in Figure 10. In both simulations, the return to steady-state concentrations in the time period shown is only possible if the reactor is capable of maintaining the specified SRT with a relatively high steady-state biomass concentration. A reactor design that can accommodate high biomass concentrations is essential for resilient performance when organic loadings increase. The fluidized sand bed reactors used in this research did not maintain large biomass concentrations (2),although other researchers have maintained much higher biomass on media in fluidized beds [Jeris and Owen (18) in a denitrifying reactor; Switzenbaum and Jewel1 (19) and Hickey and Owen (20) in anaerobic reactors]. Use of a smaller sand size, and correspondingly lower fluidization velocity with less turbulence, could increase the biomass concentration in the reactor, as would use of rough or porous media such as granular activated carbon, sintered glass, or ceramic beads. The higher turbulence and low biomass concentration in our reactors resulted in thin biofilms. These reactors had high mass transfer rates and very high specific substrate utilization rates. Much higher biomass concentration would probably be associated with some mass transfer limitations and in lower specific substrate utilization rates.
The predicted pH response to the COD overloads in the simulations described above was significantly affected by the reactor SRT. In this section, the predicted reactor response to doubling the COD loading for various SRTs is described, and the significance of higher SRTs in preventing a significant drop in the reactor pH during organic overloads is demonstrated. When anaerobic conversion of butyric acid to methane is stoichiometric, an anaerobic reactor will maintain nearneutral pH if alkalinity is added in proportion to the COz content of the biogas. The alkalinity needed may range from 20 to 100 mequiv L-1, which may be substantially less than that needed for neutralization of a volatile acid feed (21). However,the first step in butyric acid conversion produces 2 mol of acetic acid, which consumes alkalinity. If acetic acid builds up during a transient episode (Le., if butyrate oxidation temporarily outpaces acetate destruction), alkalinity considerably in excess of that needed to neutralize the volatile acid feed may be necessary to maintain a pH suitable for methanogenesis. While the model does not consider inhibition of methanogens due to pH change, it can compute the pH response of the reactor to transient changes in loading for various initial (feed) alkalinities. Several simulations were conducted to elucidate the effect of step loading changes in butyric acid on reactors at constant alkalinity addition rates (50mequiv L-l at pH 7). The lowest pH resulting from each organic overloading is shown in Table VI. If the pH dropped below about 6.8 in any simulation, the simulation was repeated, with higher influent alkalinities. The minimum pH computed with each influent alkalinity was noted. The Envlron. Scl. Technol., Vol. 27, No. 13, 1993 2681
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Figure 10. Predicted reactor biomass changes in response to the butyrate loading increase of 20 g of COD L-I d-i at different SRTs. pH is 7.
Table VI. Minimum pH in Reactor after Step Increases in COD Loadings at Various SRTsa
SRT (d) 5.6 5.6 10 10 10
20 20 20 20 20 20 30 30 30
loading increase (g of COD L-l d-1)
alkalinity (HCOs) (mequiv L-l)
minimum pH
20 20 20 30 30 20 30 40 40 50 50 40 50 50
50 80 50 50 90 50 50 50 70 50 120 50 50 60
6.47 6.85 6.95 6.20 6.81 no drop, 7.05 7.00 6.62 6.83 5.05 6.78 7.00 6.67 6.78
Bicarbonate alkalinity is added at the feed flow rate. At the steady-state baseline loading of 10 g of COD L-l d-1, 50 mequiv L-' alkalinity is added and the reactor pH is 7.05. The alkalinity needed to neutralize butyric acid at 10 g of COD L-l d-l is aboue 31 mequiv L-1. a
influent alkalinity needed to prevent the pH from dropping below about 6.8 in each simulation is also shown in Table VI. At a 5.6-d SRT, doubling the loading from 10 to 20 g of COD L-l d-' caused the reactor pH to drop to 6.47, and an increase in the influent bicarbonate concentration from 50 to 80 mequiv L-l was needed to keep the pH above 6.8. In contrast, with a 10-d SRT, the same increase in the feed butyric acid concentration decreased the pH only 2682
Environ. Scl. Technol., Vol. 27, No. 13, 1993
5
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Flgure 11. Predicted reactor response to an acetate step loading of 20 g of COD L-' d-i at day 5. SRT is 10 d and pH is 7.
to 6.95. A 3-fold increase in the loading dropped the pH to 6.2 (10-d SRT), requiring an increase in bicarbonate to 90 mequiv L-l. Higher SRTs increased the reactor's capacity to maintain pH at higher COD loading. For example, at a 30-d SRT the reactor could withstand a 4-fold loading increase without any increase in the influent alkalinity; a 5-fold increase in COD loading under those conditions dropped the pH to 6.67 and required a modest increase in the feed alkalinity, from 50 to 60 mequiv L-I. Thus, the stability of the process to withstand an organic overload is significantly enhanced at higher SRTs. Under these conditions, the reactor supports more biomass,which is able to respond more quickly to transient increases in acetic and butyric acid concentrations and damp pH excursions. The base requirement needed to maintain neutral pH is significantly reduced to values well below , that needed to neutralize the feed butyric acid.
Effects of Acetate and Hydrogen Loadings on Reactor The effects of adding an acetate or a Hz loading of 20 g of COD L-l d-l to the butyrate reactor were also simulated and are shown in Figures 11 and 12. Both the butyrate and acetate in the feed were assumed to be fully neutralized, so the reactor pH was 7. The hydraulic retention time and the SRT were held constant at 1 2 h and 10 d, respectively. At steady state, the acetate and HZ production rates from the butyrate oxidation were 8 and 2 g of COD L-l d-l, respectively. The acetate loading causes the acetate concentration in the reactor to increase over the first day and inhibits butyrate oxidation. Thus, butyrate in the reactor increases from 2.7 mg of COD L-l to about 140 mg of COD L-l. As
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a result of the higher acetate loading, there was an initial decrease of about 30% in the butyrate-utilizing biomass, which eventually recovered, and a large increase in the acetate-utilizing biomass. This suggests that there is a potential for biomass washout with higher acetate loadings and/or lower reactor SRT. A simulation of the reactor response to a higher acetate loading of 80 g of COD L-' d-1 with a 5.6-d SRT showed that about 85% of the butyrate oxidizers were washed out. Thus, an acetate overload has the potential to create instability and process failure by inhibiting growth on butyrate, thereby allowing dilution and washout of the butyrate utilizers. The situation could be worse in a reactor if a higher hydraulic flow accompanied the acetate overload and more biomass was lost in the effluent. In this simulation, the acetate biomass constituted about 80% of the total biomass at steady state. A high acetateutilizing biomass fraction may be representative of anaerobic reactors treating complex organics,since most organics in the waste are converted to acetate in methanogenic reactors. The changes in PHZ are relatively insignificant; however, their explanation helps elucidate some characteristics of the model. The inhibition of butyrate oxidation reduced by a small amount Hz production and decreased PHZ initially. In response to the buildup of butyrate, the butyrate oxidation rate began increasing, the Hz production rate increased, and t h e P ~ began 2 to rise by yet another significant amount until about day 8. However, the increasing biomass of Hz-utilizingorganisms acted to lower in the reactor, reducing PHZto 47 ppm after 40 d. the PHZ The reason for a small predicted increase in the Hz-utilizing biomass is related to the thermodynamics of methano-
genesis from Hz and COz. The imposed acetate loading increases the total acetate splitting reaction rate, producing more HC03- and, at constant pH of 7, causing more COZ to be released to the gas. The higher COz production increases PCOZ, thus increasing the available free energy for methanogenesis from the HdC02 reaction (Table I, reaction 3). There is no experimental evidence suggesting that this effect occurred in our tests. Figure 12 shows the predicted reactor response to the Hz loading increase at t = 5 d. The initial response of the reactor to the HZloading is to increase the PHZ by about 18-fold,from 49 to about 900 ppm. As a result of highPH2, butyrate oxidation is inhibited, and its concentration increases in the reactor. Inhibition of the butyrate oxidation reduces the acetate production, thus the acetate concentration is decreased. The simulated Hz loading (20 g of COD L-l d-l) leads to a 10-fold increase in the rate of H2use in the reactor under steady-state butyrate loading. However, due to the high methanogenic capacity of the Hz utilizers at steady state, the model predicts significant removal of the Hz during the loading increase and, compared to the acetate loading, a much smaller impact on the butyrate utilizers (Figure 12). The butyrateutilizing biomass decreased by about 5 %, compared to a 30% decrease under acetate loading (Figure 11). A small increase in the acetate-utilizing biomass is predicted due to a higher acetate biomass yield. As more COZis used to convert Hz into CH4, the thermodynamics of the acetate splitting reaction becomes more favorable. In fact the high HZloading increased the demand for COZbeyond the COZinputs from the feed bicarbonate alkalinity and from the acetate splitting reaction. Therefore, following the HZloading, the bicarbonate concentration in the feed had to be increased by about 7.5-fold to support HZutilization. In a reactor treating a complex organic waste, the loss of the butyrate oxidizers is analogous to the loss of the lipid-degrading capability of the reactor. It would take extraordinary HZloads to seriously reduce the butyrate user biomass, while very high loadings or production of acetate could result in significant loss of a critical part of the methanogenic consortia. Of course, high acetate concentration is likely to have similar (if not worse) effects on the propionate-oxidizing population in the reactor treating a complex waste (22). Significant loss of both butyrate and propionate-oxidizing populations would almost certainly lead to reactor failure.
Discussion There is increasing interest in the development of control strategies for anaerobic wastewater treatment processes. The search has been focused on determining and monitoring key process parameters which could predict impending process failure and be used as advance warning signals. The model simulations presented here of various organic overloads showed that a major cause for reactor instability was the pH drop due to volatile fatty acid (VFA) accumulation following an organic overload. Changes in the waste characteristics, resulting in higher acetate production, may readily saturate the acetoclastic methanogens, consequently increasing the acetate concentration. The increased acetate concentration has the potential to inhibit and cause the washout of the Hz-producing acetogens (in this case, the butyrate utilizers). The potential for the biomass washout was less when Hz was Envlron. Scl. Technol., Vol. 27, No. 13, 1993 2883
produced. The Hz-utilizing methanogens responded to the reactor overloads effectively, lowering p H 2 in a relatively shorter time, and the reactor recovery was fast. This result may be different for the other major group of Hz-producing acetogens, the propionate oxidizers. In the anaerobic process, propionate oxidation produces 1 mol of acetate, instead of 2 mol from the butyrate oxidation, but produces 3 mol of Hz instead of 2 mol from the butyrate oxidation. The free energy from propionate oxidation is more sensitive to increases in the PHZand less sensitive to the acetate concentration than is butyrate oxidation. Therefore, the energetics of substrate use would predict that increased Hz loadings may inhibit the propionate oxidizers and cause their more rapid washout compared to the butyrate oxidizers. The reactor stability in response to the butyrate step loadingssignificantlyimproved at higher SRTs. In general there was a significant initial reactor response following the step increase in loading. For example, the increase in the butyrate loading caused an initial accumulation of the acids (butyric and acetic acids) in the reactor. The high acid concentrations would increase the amount of alkalinity or other buffering agents required to prevent excessive reactor pH drop, which can cause reactor souring. The rise in acids concentration was considerably smaller at higher SRTs. Therefore, the reactor capacity to absorb higher organic overloads increased with higher SRTs, and the alkalinity requirement was reduced. Depending on the magnitude of the butyrate loading increase (from 2 to 10 times the initial loading), the butyrate concentrations in the reactor decreased by more than 90% from the highest concentration in 3 d to 1 week. The reactor achieved a new steady state in 3-6 weeks (at the 10 times loading increase). However, the new steady state at the higher loadings can only be achieved if the reactor can support higher biomass concentrations and if metabolism can continue without significant mass transport effects. Conclusions
A model of anaerobic butyrate-degrading consortia was developed using Monod kinetics for HdC02 and acetate as substrates. The Monod model was modified for butyrate oxidation to incorporate inhibition by acetate and hydrogen and the effect of a thermodynamic driving force. The model parameters were calibrated with our experimental reactor data, and the model was validated against data obtained from various other reactor perturbations. The bacterial growth yield was made dependent on the concentrations of reactants and products. The dependence of bacterial yield on the energy obtained from their substrate was not verified in our experiments. This theoretical approach had very little influence on predictions of short-term perturbations, since net organism growth and decay are insignificant in such circumstances. However their marginal effects would be seen when changes in organic loadings occur over long periods of time. The stability of a butyrate-degrading consortia was more sensitive to acetate loadings than to hydrogen. High acetate concentrations could cause loss of butyrateoxidizing biomass and acids accumulation, leading to a
2684
Envlron. Scl. Technol., Vol. 27, No. 13, IQQ3
pH drop and subsequent process failure. Solids retention time had significant influence on the stability of the consortia. High solids retention time substantially improved stability of the consortia to various organic overloads and reduced alkalinity requirements for control of pH. Hydrogen did not have much influence on the stability of the consortia, because hydrogen partial pressures resulting from loading perturbations were effectively damped by hydrogen utilizers. Acknowledgments This research was supported by the National Science Foundation (Grant ECE-841650). Literature Cited (1) Eastman, J. A,; Ferguson, J. F. J . Water Pollut. Control Fed. 1981,53, 352-366. (2) Labib, F.; Ferguson, J. F.; Benjamin, M. M.; Merigh, M.; Ricker, N. L. Enuiron. Sci. Technol. 1992, 26, 369-376. (3) Thauer, R. F.; Jungermann, K.; Decker, K. Bacteriol. Rev. 1977,41, 100-180. (4) McCarty, P. L.; Smith, D. P. Environ. Sci. Technol. 1986, 20, 1200-1206. (5) McCarty, P. L. Energetics and bacterial growth in organic compounds in aquatic environments; Faust, S. D., Hunter, J. V., Eds.; Marcel Dekker Inc.: New York, 1971; Chapter
21. (6) McCarty, P. L. ACS Adv. Chem. 1971,105,91. ( 7 ) DeMoss, R. D.; Bard, R. C.; Gunsalus, I. C. J . Bacteriol. 1951,62, 499-510. (8) Gunsalus, I. C.; Gibbs, M. J . Biol. Chem. 1952, 194, 871880. (9) Chung, K. T. Appl. Environ. Microbiol. 1976,31,342-348. (10) Traore, A. S.; Gaudin, C.; Hatchikian, C. E.; Le Gall, J.; Belaich, J. P. J . Bacteriol. 1983, 155, 1260-1264. (11) Segel, I. H. Enzyme Kinetics; Wiley-Interscience: New York, 1975. (12) Ozturk, S. S.;Palsson, B. O.;Thiele, J.; Zeikus, J. G. Modeling of the interspecies Hz transfer in microbial flocs;Ho, C. S., Oldshue, J. Y., Eds.; American Institute of Chemical Engineers: New York, 1988. (13) Mosey, F. E. Water Sci. Technol. 1983, 15, 209-232. (14) Costello, D. J.; Greenfield, P. F.; Lee, P. L. Water Res. 1991, 25 ( 7 ) , 847-858. (15) Costello, D. J.; Greenfield, P. F.; Lee, P. L. WaterRes. 1991, 25 (7), 859-871. (16) Smith, D. P.; McCarty, P. L. Res. J . Water Pollut. Control Fed. 1990,62, 58-64. (17) Ahring, B. K.; Westermann, P. Appl. Environ. Microbiol. 1987, 53, 434-439. (18) Jeris, J. S.; Owen, R. W. J . Water Pollut. Control Fed. 1975, 47, 2043-2057. (19) Switzenbaum, M. S.; Jewell, W. J. J . WaterPollut. Control Fed. 1980,52, 1953-1965. (20) Hickey, R. F.; Owen, R. W. Biotechnol. Bioeng. 1981, 11, 399-413. (21) Ferguson, J. F.; Eis, B. J.; Benjamin, M. M. Water Res. 1984,18, 573-580. (22) Kaspar, H. F.; Wuhrmann, K. Microb. Ecol. 1978,4, 241248.
Received for review June 1, 1993. Accepted July 27, 1993.' Abstract published in Advance ACS Abstracts, September 15, 1993.
