Dynamic modelling of a single-stage high-rate anaerobic reactor—II. Model verification

War. Res. Vol. 25, No. 7, pp. 859-871, 1991 Printed in Great Britain.All rights reserved

0043-1354/91 $3.00+ 0.00 Copyright © 1991 PergamonPress pie

DYNAMIC MODELLING OF A SINGLE-STAGE HIGH-RATE ANAEROBIC REACTOR--II. MODEL VERIFICTION D. J. COSTELLO,P. F. GREENFIELD@ and P. L. LEE* Department of Chemical Engineering, University of Queensland, Australia (First received March 1990; accepted in revised form January 1991) Abstract--A structured model of the anaerobic degradation process, incorporating dynamic equations for the description of a single-stage high-rate anaerobic reactor was validated by comparing its predictions with previously reported experimental data. This data came from two different laboratory-scale reactors and a pilot-scale reactor. With the manipulation of key model parameters, significant improvements in the fit of the model to the experimental data were possible. This study was able to show that the production and consumption of lactic acid, and the moderate hydrogen inhibition and regulation of the acidic products of the acidogenic bacteria, can be successfully modelled. Insufficient experimental data were available to draw conclusions as to the importance of product inhibition in anaerobic reactors, while the need to use deterministic models to account for pH inhibition highlighted the need to develop mechanistic models able to reflect the pH inhibited behaviour of the major anaerobic groups present in the ecosystem. Key words--anaerobic, modelling, lactate, hydrogen, pH, inhibition, industrial treatment, high-rate, USAB

NOMENCLATURE b = first-order bacterial decay coefficient (day -l) BeD = biological oxygen demand COD = chemical oxygen demand [ghicL = estimated influent glucose (waste) concentration (mM) HCOf = bicarbonate ions (mM) k = the maximum specific substrate uptake rate (mmol/mg/day) K~= product inhibition parameter (retool/l) Ks = the half-velocity constant (mmol/l) [NaHCO3]=influent sodium bicarbonate concentration (mM) Pa2 = the partial pressure of hydrogen (atm) SRT = solids retention time (days) T = temperature (°C) Y = the bacterial yield coefficient for the carbon substrate (mg/mmol) ~t = hydrogen inhibition parameter (atm -t)

INTRODUCTION This paper examines the dynamic response and tests the validity of the mathematical model developed for the single-stage high-rate anaerobic reactor described in Part I of this investigation (Costello et al., 1991). Independent sets of data from the literature and generated in this laboratory (Grauer, 1986; Eng et al., 1986; Denac, 1988; Denac et al., 1988) are used to examine the model response of the reactor volatile acids, physico-chemical variables, and gas phase variables to step changes in the influent organic load. Furthermore, a quantitative assessment of the general *Author to whom all correspondence should be addressed.

ability of the model to fit a set of dynamic experimental data was undertaken. Until now complex anaerobic models have only been tested against limited experimental data (Bryers, 1985; Moletta et aL, 1986; Torte and Stephanopoulos, 1986). The primary objective of this investigation was to show that the dynamic behaviour of an anaerobic treatment system can be predicted by a structured process model so that the model can be used with confidence in the testing and examination of control strategies for high-rate anaerobic reactors (Costello, 1989). Only one set of biological parameters is used in the comparison of the anaerobic model to each set of experimental data. These parameters were initially chosen from other modelling studies, and then modified as necessary to provide the best overall "qualitative fit" to each independent set of experimental data. This was done to separate any unexplained "local" effects (such as local population dynamics and experimental error) from "structural" effects (on which the mathematical model is based). It was felt that individually fitting and comparing the model to each experiment would not be able to provide information on the overall structural nature of the process as it would be impossible to differentiate between "local" and "structural" effects. It was assumed that the only common factor between each case study being verified was the general structure of the anaerobic process and that the effect of local factors would be different for independent experiments. Consequently, similarities between each of the three model-experiment comparisons were

859

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D.J. COSTELLOet al.

considered as confirmation of the correct model structure. Differences were attributed to either the choice of model parameters or to defects in the general model structure. A quantitative approach to the validation of the process model was also undertaken. The experimental results from the study of Denac in this laboratory (Denac, 1988; Denac et al., 1988) were used since these data were considered to be the most reliable and accurate of the three dynamic case studies available. Using individually weighted sums of the squared errors calculated from the difference in the simulated results and experimental data of key reactor variables, kinetic parameters were manipulated to improve the "model fit" of the experimental data. DESCRIPTION OF THE EXPERIMENTAL

CASE STUDY DATA Three case studies were used in the dynamic verification of the single-stage anaerobic process model. Each case study recorded the results of a step change in the soluble substrate loading to a laboratory-size or pilot-scale, high-rate anaerobic reactor. The experiments of Denac (Denac, 1988; Denac et al., 1988) maintained a constant neutral pH throughout the loading, while the experiments by Grauer (1986) and Eng et al. (1986) maintained a constant influent alkalinity and caustic concentration to allow the pH to vary throughout the loading experiments. One experiment was taken from each case study for verification of the mathematical model. This section briefly describes the experimental conditions for each case study, and provides a background as to the conditions surrounding the experiments. Parameters used in the model simulations are listed in Table 1.

Experimental results were available for the first 72 h of the experiment, with most of the results recorded over the first 24 h. Throughout the experiment the liquid residence time remained constant at 0.25 days, while the pH was maintained at a value of 7.0 by the automatic addition of sodium hydroxide. Details of the influent alkalinity were not available, so an influent concentration of 2 mM was assumed. To convert the influent molasses concentration to a millimolar glucose concentration for the model simulation, a conversion factor of 1 g of molasses to 0.28 g of total organic carbon was used (Denac, 1988; Denac et all, 1988). Case study 2

The second case study (Grauer, 1986) showed the dynamic response of an anaerobic fluidized-bed pilotscale reactor operating at 35°C to a combined step change in the liquid residence time and the influent substrate concentration (of molasses-yeast extract). The total liquid volume was reported as 601. A disturbance to the process was undertaken by applying a shock loading of 1 h duration to the reactor, followed by a return to the initial conditions. The initial influent substrate loading to the reactor was increased from 8590 to 11,530 mg of BOD per litre per day. A constant influent alkalinity of 20 mM was maintained throughout the experiment, thereby allowing the pH of the reactor to vary freely. The only significant quantities of acids recorded during the experiment were acetic and propionic acid. The gas flowrate, methane, and carbon dioxide partial pressures, and the pH were also recorded. Most experimental data was reported during the first 8 h of each 24 h experiment, with a final reading taken at the end of the experiment. Case study 3

Case study I

The first case study is taken from the experimental work of Denac obtained in our laboratories (Denac, 1988; Denac et al., 1988). A laboratory-scale fluidized bed reactor at 35°C, with liquid and gas volumes of 3.6 and 0.425 1. respectively, was subject to step changes in the substrate loading from 12 to 42 g of molasses per litre per day.

The third case study was taken from the experimental investigations of Eng et aL (1986). Eng investigated the effects of large sucrose shock loads on a 12.51. upflow anaerobic sludge blanket reactor operating at 20°C. Under normal conditions the reactor was loaded with diluted leachate from a landfill site reported to contain mainly volatile fatty acids at a near neutral pH. The average influent

Table 1. The experimentalsimulationparameters for each case study Case study I (Denac) Casestudy 2 (Grauer) Case study 3 (Eng) Duration of simulation(day) 3.0 1.04 10.0 Duration of load (day) 3.0 0.04 3.0 Liquid volume(litre) 3.6 60.0 12.5 Gas volume(litre) 0.425 2.0* 0.2* Temperature (°C) 35.0 35.0 20.0 Reactor pH 7.0 (constant) 7.2 (initial) 7.4 (initial) Initial Loading Initial Loading Initial Loading Influentglucose(mM) 11.67 40.83 27.95 255.18 11.30 62.5 HCOj- (raM) 2.0* 2.0* 20.0 20.0 10.0" 10.0" NaHCO3 ( r a M ) . . . . . . 23.81 Liquid residencetime (day) 0.25 0.25 0.334 2.274 0.3 0.3 Solids residence time (day)* *Estimated value.

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Model verification of an anaerobic reactor model concentration of carbon to the reactor was reported as 2170 mg of chemical oxygen demand (COD) per litre. A shock loading of sucrose of 12 g of COD per litre at a hydraulic residence time of 8 h was added to the reactor for 3 days, with results recorded for about 7 days. The pH was allowed to vary freely throughout the experiment, except for the addition of 2 g per litre of sodium bicarbonate during the shock loading. The accumulation of lactic, acetic, butyric, and propionic acid were recorded throughout the experiment. The pH of the reactor, the gas flowrate, and the partial pressures of methane, carbon dioxide, and hydrogen were also recorded. This experimental data was estimated from figures of results reported by Eng et al. (1986). MODEL PARAMETERS

The parameters used in the anaerobic process model can be classified as either experimental, physicochemicai or biological. The experimental parameters describe the influent loading conditions, reactor size and the influent alkalinity (or the reactor pH) for each simulation. The physico-chemical parameters represent all model parameters directly associated with the physical chemistry of the system (for example, acid-base equilibrium coefficients, and Henry's gas law coefficient for carbon dioxide). The biological parameters characterize the growth kinetics and the various forms of inhibition imposed upon each group of bacteria.

Experimental parameters The experimental parameters were individually set for each case study simulation. The liquid and gas reactor volumes used were taken from a description of the experimental apparatus. The liquid residence time was calculated from the reported reactor volume and influent flowrate. The solids residence time was estimated from the reported solids retention times of stirred tank anaerobic reactors used in sewage sludge digestion (10-20 days), and the solids retention time for fluidized bed reactors (12 days) (Stronach et al., 1986). Preliminary simulations found that the most appropriate solids retention time for all case studies was 10 days (Costello, 1989). The most important experimental parameters considered in the model were the influent conditions for each experiment. In each case study the influent carbon substrate entering the process was modelled entirely as glucose carbon. The influent glucose concentration was set according to the amount of organic carbon entering a reactor as specified by the COD of the influent stream. A conversion factor of 192 mg of COD per mmol of glucose was used to convert the influent COD concentration to an equivalent glucose concentration. To complete the specification of the influent stream for the model, the value of the inlet alkalinity was required. Two independent variables were set to WR 25/7--H

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determine the alkalinity of the influent stream; these were the influent inorganic carbon and sodium bicarbonate concentration. Unlike the alkalinity parameters, the influent caustic concentration was fixed by the initial pH of the reactor. For Denac's experiments (Denac, 1988; Denac et al., 1988) a constant pH was maintained during the shock loading by automatically varying the influent caustic concentration to maintain the initially specified pH. The other two case studies (Grauer, 1986; Eng et al., 1986) maintained a constant influent caustic concentration throughout, thereby allowing the pH to vary freely. For all simulations, an arbitrarily small influent concentration of 1 mg/l was set for each group of bacteria. This was to ensure that there was some seed material in the event that the concentration of any group of bacteria approached zero. This sometimes occurred as the model iterated towards the initial steady-state conditions. The inclusion of such small influent bacterial concentrations did not have any significant effect upon the results of the simulation.

The physico-chemical parameters The physico-chemical parameters were fixed by the different temperatures of each case study experiment. The parameters that varied between case studies were the equilibrium coefficients, Henry's Gas Law coefficient for carbon dioxide, the vapour pressure of water the Ideal Gas Law term (i.e. the Ideal Gas Law constant multiplied by the process temperature). The values of these parameters at the simulation temperatures are provided in Table 2. The rate coefficient for the transfer of carbon dioxide from the gas to liquid phase was set to 100 (day-l), which is the value used by Graef and Andrews (1974). This parameter remained constant throughout all case study simulations.

Specification of biological model parameters This section describes the general biological parameters used in the mathematical model. The biological parameters can be subdivided into four groups: these are the kinetic, hydrogen inhibition, pH inhiTable 2. Physico-chemieal model parameters determined at simulation temperatures Temperatures (°C) Parameters Equilibrium coefficients (raM)* Carbonic acid (as dissolved CO2) ( x 104) Acetic acid ( x 102) Propionic acid ( x 102) Butyric acid ( x 102) Lactic acid ( x 10~)

Ionization constant of water (mM) ( x 10s) Henry's Law co¢tflcient for CO: (atm/mM)* Partial pressure of water vapour (atm)f Ideal Gas Law term, R T (atm.l/mmol) *Weast and Astle (1981); fLinke (1985).

20

35

4.16 1.753 1.338 1.542 1.357

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862

D.J. COSTELLOet al. Table 3. Kineticparameters used for the case study simulations k Y KI [mM-ll Bacterial mmol Ks mg b groups mg.day mM mmol da),- Non-competitive Competitive Glucose 1.5 0.128 --* 0.02 I0.0 Lactic 0.51 0.38 --* 0.02 10.0 Propionic 0.16 0.53 5.0 0.01 3.0 30.0 Butyric 0.26 0.083 7.5 0.03 Acetic 0.18 2.57 2.5 0.02 Hydrogen 1.56 0.001t 2.5 0.09 *Overall bacterialyieldscalculatedfrom the individualproduct reactions. tUnits of atmospheres.

bition and product inhibition parameters. Mosey's model parameters (Mosey, 1983) were used as a guide in the choice of kinetic parameters because of the large variations observed in the literature. Preliminary investigations were also undertaken to determine the most appropriate set of kinetic parameters for the case studies. The methodology of these investigations is discussed in more detail in the next section. Biological kinetic parameters. The biological kinetic parameters for each group of bacteria are based on a Monod-type relationship for substrate utilization (Costello et al., 1991). There are four kinetic parameters that must be specified to simulate the uninhibited substrate uptake for any given group of bacteria (Costello et al., 1991). These are: the maximum substrate uptake rate, the half-velocity constant, the growth yield coefficient, and the death coefficient. The complete list of kinetic data for each group of bacteria is given in Table 3. The substrate uptake rates and half-velocity constants for the glucose bacteria were taken from the modelling study of Mosey (1983), while the parameters for the lactic acid bacteria were estimated from Lee et al. (1974). Yield coefficients of the mixed-product bacteria were estimated from the theoretical ATP yields for each product (Stouthamer, 1976; Sheehan, 1981; Mosey, 1983) assuming that 10g of biomass are produced per mol of ATP generated (Bauchop and Elsden, 1960). The biological rate parameters for the acetogenic and acetic acid bacterial groups have been taken from the work of Lawrence and McCarty (1969), while those for the hydrogen-utilizing bacteria were obtained from Shea et al. (1968) and Mosey (1983). The yield coefficients for these bacteria were estimated from the experimental studies of Lawrence and McCarty (1969).

Hydrogen inhibition parameter. In the mathematical model, the hydrogen inhibition coefficient was used to relate the ratio of "reduced-to-oxidized" NAD (nicotinamide adenine dinucleotide) to the partial pressure of hydrogen in the biogas using the Nernst equation (Mosey, 1983; Costello, 1989). Consequently, the hydrogen inhibition parameter is dependent upon the temperature of the simulated experiment. The value of the hydrogen inhibition parameter at various temperatures is shown in Table 4. The large differences show that it is important to consider the reactor temperature when modelling hydrogen inhibition and regulation. p H inhibition parameters. Each species of bacteria in the single-stage model was classified into one of four major groupings: the mixed-product (glucose and lactic acid) bacteria, acetogenic (propionic and butyric acid) bacteria, the acetoclastic bacteria, and the hydrogen-utilizing bacteria. Each bacterial classification was assigned a pH inhibition function of the form expressed in Part I of this investigation (Costeilo et al., 1991), with the parameters shown in Table 5. The mixed product and acetogenic bacteria were assumed to have the same pH inhibition functions. The pH inhibition ranges for these bacteria were estimated from the results of Russell et al. (1979), Zoetemeyer et al. (1982), Graham and Lund (1983), Nanda et al. (1983) and Dinopoulou et al. (1988a). The inhibition function for the acetoclastic bacteria was set to approximate the pH range of Methanothrix soehngenni (Huster et al., 1982). The pH inhibiton function for the hydrogenutilizing bacteria was less severe than that for the acetoclastic bacteria because of the need to regulate the level of hydrogen and allow the generation of methane at low pH values. However, the range of inhibition was still within the region of

Table 4. Hydrogeninhibitionparameterscalculated at variousprocess temperatures Temperature Hydrogeninhibition (°C) parameter (a) 0 680 20 1300 25 1500 35 2000 50 3000 [NADH] 1139 [NAD+]=~t*Pa2'l°g~°(~)=7 T+273"

Table5. pH inhibitionparametersusedin the anaerobicdegradation model Lower Upper Power limit limit coefficient Bacterial groups pHLL pHuL m Acid-formers(glucoseand lactic) 4.0 6.0 3.0 Acetogenic(propionicand butyric) 4.0 6.0 3.0 Acetoelastic 6.6 7.2 3.0 Hydrogen-utilizing 5.0 7.2 3.0 [- pH - pHLL "]m pH inhibitionfactor= LP'~UL------~LL]"

Model verificationof an anaerobic reactor model

863

the upper end of the pH inhibition range. There was insufficient evidence to draw conclusions as to the cause of these differences. Product inhibition parameters. Product inhibition was included in the process model to account for the behaviour of the acidogenic and acetogenic bacteria during the accumulation of organic acids in the reactor. Non-competitive inhibition models were used to model the uptake of substrate by the glucose

many of the pH inhibition ranges cited by Jones et al. (1987). Each power coefficient was set to a value of 3. The form of the pH inhibition function is such that inhibition of the bacteria increases quite rapidly as the reactor pH decreases from the upper pH limit. This is in contrast with the results of the experimental studies of Huser et al. (1982) and Russell et al. (1979) which show more moderate inhibition of bacteria at

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864

D.J. COSTELLOet al.

and lactic acid bacteria, while competitive inhibition models were used for the propionic and butyric acid bacteria. The sum of the millimolar product concentrations was used as the inhibiting component for each bacterial group. Inhibition parameters were estimated from values determined by Denac 0986) and Dinopoulou et al. (1988b) and are shown in Table 3. METHODOLOGY OF SIMULATINGAN ANAEROBIC REACTOR The general philosophy used in fitting the mathematical model to each set of experimental data was to change, or manipulate, as few model parameters as possible. This assumes that the internal structure of the anaerobic model effectively constrains the simulated ouput, and so only a few key parameters need to be adjusted to account for the local experimental conditions. The flowchart shown in Fig. 1 describes the methodology used in this paper. The first step was to set the initial values of all the model parameters. The physico-chemical parameters were based upon the temperature of the experimental run, while the experimental parameters were taken from the reported description of each experiment. Initial values of the biological parameters were chosen from other modelling and experimental studies. Simulations were then undertaken to fit the model to each set of case study data. In general, the biological parameters were used to tune the simulation because of the large variations in their reported values, and the variability that was expected between case studies. Case study 1 was initially used to tune the model since the effects of pH inhibition did not have to be considered. After several iterations the most appropriate values for the product inhibition and kinetic parameters were determined. The parameters that had the most significant effects were the maximum utilization constants (k) for the different groups of bacteria. During the first iteration of case study 1 these were the only biological parameters modified. The death coefficients (b) of specific biological groups were also changed during subsequent iterations. However, product inhibition parameters remained set at their initial values as they had little effect upon the simulation results. The constant alkalinity variable pH experiments of case studies 2 and 3 were investigated once reasonable agreement had been obtained between the model and the experimental data of case study 1. Initially, the kinetic and product inhibition parameters for the simulation of case studies 2 and 3 remained unchanged from the values determined for case study 1, as it was assumed that without pH inhibition the behaviour of the anaerobic ecosystems for each case study would be the same. Only the lower limit of the pH inhibition functions were modified to tune the variable pH simulations. It was found that a pH

inhibition coefficient of 3 was the most appropriate for these simulations. Only integer changes were made to the pH inhibition coefficients because the unstructured form of the inhibition model did not justify making smaller changes. Only the lower limit of the acetic acid bacteria pH inhibition function was modified in case study 2. This was because of the moderate loading of the experiment (resulting in accumulation of only acetic acid). However, for the simulation of a large change in the influent load (case study 3), the other pH inhibition lower limits were changed. In this simulation the most important parameters were for the glucose and the hydrogen-utilizing bacteria. Some changes were also made to the kinetic parameters during the simulations of case studies 2 and 3. In general, these were only small changes (10%) to either the maximum utilization constant for the acetoclastic bacteria (to further fine tune the accumulation of acetic acid in case study 2), or the hydrogen-utilizing bacteria (to fine tune the accumulation of hydrogen, which affected the accumulation of acids in case study 3). When such changes were made the corresponding effect on case study l was investigated. A set of model parameters evolved after several simulations of the constant pH and variable pH models. Consideration was then given to modifying the solids residence time and the influent alkalinity conditions, and the process was started all over again. Only after several iterations of this procedure was the final set of model parameters determined. Deciding when the results were acceptable could only be done by taking into account the accuracy and reliability of the experimental data.

NUMERICAL SOLUTION OF THE MODEL The numerical package used to solve the differential-algebraic system of equations was a diagonally implicit, second-order, S-stable, Runge-Kutta (DIRK) routine (Cameron, 1983; Alexander, 1977). In all simulations a "relative error" test was used by the integration routine with an error specification of 0.0001 for each process variable. The starting time was zero for all simulations. The time interval between results was sufficient to provide approx. 100 data points over the duration of the simulation. A simulation takes approx. 15 min to run on an IBM XT personal computer. RESULTS AND DISCUSSION Model verification o f the accumulation o f organic acids The varying concentration of individual organic acids in a reactor gives one of the best insights into the dynamic behaviour of the anaerobic process. These acids directly and indirectly affect the physical and biological behaviour of the reactor, while the

Model verification of an anaerobic reactor model accumulation and consumption of these acids is a clear indication of differences in the growth rates of the acid-producers and acid-consumers. For this reason a comparison between the simulated and experimental behaviour of the organic acids for each case study was very important in the verification and understanding of the model. Case study 1. The concentration of acetic, butyric, and propionic acid from Denac's experiment have been superimposed on the model results and shown in Fig. 2. The results of this simulation, while showing general agreement with the observed trends of the experimental data (except for the propionic acid), indicate that the model is unable to account completely for the observed accumulation and degradation of organic acids without resorting to further manipulation of the kinetic parameters of the model. The major difference between the simulated and experimental concentration of propionic acid indicates that the observed experimental results may have been caused by changes to the population of the different sub-species of acid-forming bacteria. The problem with including more specific sub-groups of bacteria into the ecosystem model is the need for experimental data to verify the presence of and to characterize the kinetics of such sub-groups. An alternative approach to improving the fit of the accumulating propionic acid is to further refine the hydrogen inhibition-regulation model, or include a kinetic term to account for the observed effects of the increased influent loading. Before major structural changes to the model are considered, however, more

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experimental evidence would be needed to confirm that the behaviour of propionic acid observed in Fig. 2 is a structural effect characteristic of anaerobic ecosystems and not due just to the local experimental conditions. Case study 2. Only acetic and propionic acid were found to accumulate to any significant extent in both the simulation and the experimental study undertaken by Grauer (1986) as shown in Fig. 3. Agreement at this level shows that the model appears to reflect the kinetic interactions of the mixed-product and acetogenic bacteria during this moderate shock loading. The difference of 140 mg/l between the simulated and experimental peak acetic acid concentration can be accounted for by either increasing the maximum uptake rate, or decreasing the pH inhibition of the acetoclastic bacteria. It was also observed in Fig. 3 that the degradation of acetic acid after the shock loading was much slower than that predicted by the model, pH inhibition plays a major role in this experiment and it is likely that the persistence of acetic acid in the reactor is due to the slow recovery of the aeetoelastic bacteria. A more complex model for pH inhibition and recovery of the acetic acid bacteria may be needed to account for the delay in the degradation of acetic acid noted in the experimental data. Case study 3. A comparison of the accumulating organic acid intermediates of Eng et al. (1986) with the model simulation is shown in Figs 4 and 5. The volatile acidic products acetic, propionic, and butyric acid are shown in Fig. 4, while lactic acid is shown in Fig. 5. The simulated concentrations of volatile acids do not compare very well with the experimental data.

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some local variations in the kinetic constants for the bacteria possibly caused by the unusually low temperature at which this system was operated. The successful prediction of the large concentrations of lactic acid shown in the experimental results, and results of the previous two case studies where large quantitites of lactic acid were neither found in the experiments nor predicted by the mathematical model is quite significanL This suggests that lactic acid, evident only at severe shock loading conditions, may be an important intermediate in the anaerobic process, and that the lactic acid consuming bacteria may be an important sub-species in anaerobic degradation processes treating highly degradable wastes.

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Fig. 4. Comparison between the simulated and experimental results for the accumulation of organic acids in ease study 3 (Eng et al., 1986). The primary cause of the simulated behaviour during the loading is the severe inhibition of the acid-forming bacteria. During the initial stage of the experiment the level of inhibition allows the acid-forming bacteria to continue to produce acids. As the experiment continues, the falling pH of the reactor inhibits even these bacteria. The reverse effect then occurs as the pH returns to normal after the substrate loading. The experimental data, however, show that there appears to be little inhibition of the acid-forming bacteria, and only moderate inhibition of the acidconsuming groups of bacteria. This response would not normally be expected from a reactor suffering such a fall in pH (approx. 7.5-5.0). The much lower reactor temperature for this experiment (20°C as opposed to 35°C for the other case studies) may have affected the kinetic parameters of the bacteria, contributing to the much slower volatile acid accumulation rates observed in the experimental data. It should also be noted that this experiment was the fourth in a series of experiments that exposed the anaerobic bacteria to very low pH levels. Hence, some adaptation of the bacteria to such large changes in the reactor pH may have occurred; this would then account for the slow accumulation rates of the volatile acids during the shock loading (i.e. the actual inhibition parameters were less severe than those estimated). Figure 5 shows that the large concentration of lactic acid that accumulated during the experiment (maximum concentration of 4700 rag/l) has also been predicted by the simulation (maximum concentration of 4460 mg/i). The only major differences between the simulated and reported concentrations of lactic acid are in the observed accumulation and degradation rates for lactic acid. This result again points to

Model verification of caustic consumption and p H behviour Case study 1. The consumption of caustic during the constant pH experiment of Denac shows that the model overestimated the caustic required during the experiment by up to 50%. It was also observed that the simulated consumption of caustic decreased by only 7% after about 15 h even though the concentrations of volatile acids (Fig. 2) declined considerably more (64%). Also, the partial pressure of carbon dioxide in the gas phase increased from 10 to 25% during the overloading, and then remained at this level for the duration of the experiment. This shows that the consumption of caustic is relatively independent of the levels of acids in the reactor, and much more dependent upon carbon dioxide dissolved in the liquid phase. Case study 2. The simulated pH for Grauer's experiment shows very good agreement with the experimental results during and directly after the 5000 []

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Fig. 5. Comparison between the simulated and experimental results for the accumulation of lactic acid in case study 3 (Eng et al., I986).

Model verification of an anaerobic reactor model shock loading. The error in simulating each experimental data point for the first 4.5 h was less than 1% for all but one data point. The only other major difference between the simulated pH curve and experimental data are the minimum pH reached during the loading; the experimental minimum is 0.28 pH unit lower than for the predicted minimum. There is insufficient experimental evidence to draw any conclusions about the possible reasons for this difference. Case study 3. The comparison between the simulation and the experimental results for the effluent pH reflects the behaviour of the volatile acids (Fig. 4) and highlights important differences between the two sets of data. The simulated results showed a very rapid decline in the pH at the beginning of the substrate loading with a constant minimum pH of 5.5 during the increased influent load. On the other hand, there was a much slower decline in the experimental pH to a minimum value of about 5.0 in 58 h. The experimental pH returned to a neutral pH in about the same period of time as the simulation. The slow decrease in the experimental pH is probably caused by the same factors as for the volatile acids, i.e. the anaerobic bacteria were either affected by the lower operating temperatures, or they had previously adapted to large shock loadings of sucrose.

Model verification of the biogas flowrate and partial pressures Case study 1. As shown by Fig. 6, the partial pressure of methane in the gas phase of Denac's experiment is well predicted by the simulation with an average prediction error of the order of 10%. The trajectory of the simulated data follows the 100

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Fig. 6. Comparison between the simulated and experimental results for the dynamic changes in percent methane (Denac et al., 1988).

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Fig. 7. Comparison between the simulated and experimental results for the dynamic changes in the total biogas flowrate (Denac et aL, 1988). experimental data quite closely with the only major difference being the higher initial partial pressure predicted by the simulation (0.84 atmospheres as opposed to the experimental measurement of 0.79 atmospheres). A comparison of the actual and predicted gas ttowrates (Fig. 7) shows that the simulation overpredicts the net flowrate of biogas from the reactor by up to 100%. The reason for this difference can be deduced from a carbon balance around the process. The extra carbon predicted as being disposed of in the gas phase must in reality be either accumulating in the reactor or leaving via the liquid phase. For such a short experiment it is unlikely that carbon is being converted to biomass. Therefore the simulation may have overestimated the biodegradability of the influent waste, i.e. the extra carbon predicted as leaving in the gas phase was actually leaving as neutral intermediates or as untreated waste in the effluent. Alternatively, the concentrations of biodegradable influent organic carbon used in the simulation may have been overstimated; this is possible considering the undefined nature of the influent waste. Case study 2. Similar results for the gas phase partial pressures and gas flowrate predicted for case study 1 were observed in the model predictions of Grauer's experiment. Again, the prediction of the partial pressures in the gas phase is very good, yet the model overestimated the gas flow from the reactor by over 300%. Some of this error is probably associated with "local" experimental effects such as gas leaks. This is supported by undertaking a carbon balance around the reactor (at its initial steady-state condition), which shows that at least 20% of the carbon entering the process cannot be accounted for. Despite

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this, these results lend weight to the theory that the simulation, while correctly modelling the relative behaviour of the reactor, does not correctly estimate the biodegradability of the influent organic waste. Alternatively, some of the influent carbon may have been converted to other biological products not measured in the experiment, in which case the model is not sufficiently complex to represent all the biological interactions. Certainly ethanol, formic acid, alcohols and numerous types of organic acids have been observed in high-rate anaerobic reactors and perhaps some of these products may have represented a significant sink for organic carbon in Grauer's experiments. Case study 3. As with the other experimental variables previously discussed in case study 3, the observed initial rates of change in the gas phase variables are much slower than those predicted by the model. Further conclusions could not be drawn because of the small number of experimental data points, the inaccuracies and variability of the experimental data, and the major differences between the experimental and simulated results for the other reactor variables. Perhaps the most important gas phase variable is the hydrogen partial pressure since it plays a major role in the accumulation of organic acids in the simulation. A comparison of the predicted and actual concentrations of hydrogen which occurred during the shock loading found that approx. 75,000 ppm of hydrogen gas were recorded during the experiment but that the maximum partial pressure of hydrogen predicted by the simulation was only 17,600ppm. The difference between the simulated and predicted hydrogen partial pressures shows that the simulated anaerobic reactor is much more sensitive to the hydrogen partial pressure than the real process. While the previous two case studies show that the model adequately predicts the relative accumulation of acids at moderate loadings it is clear that the mechanism for hydrogen inhibition and regulation by the N A D (nicotinamide adenine dinucleotide) couple is inappropriate at the high partial pressures of hydrogen present in this experiment. A quantitative model analysis

This section investigates a quantitative approach to eliminate some of the differences between the simulation and experimental results of case study 1 (Denac, 1988; Denac et al., 1988) caused by "local effects" that were not considered when originally fitting the model to the experimental data. To determine the "goodness of fit" the sum of the squared errors between the simulated results and the experimental data for key reactor variables was calculated over the duration of the simulation. Not all data points available (within the first l0 h) were used in the model fitting exercise. Rather, a more even distribution of experimental data was obtained by eliminating some of the early data points so that the

minimum time between each set of experimental data was at least 1 h. The key reactor variables examined were: the propionic, butyric and acetic acid concentrations; the percent methane content of the biogas; the total gas flowrate; and the rate of caustic consumption. Weights were applied to each term by dividing by an appropriate constant. The propionic acid, acetic acid, and caustic consumption terms were divided by 10,000; the butyric acid term was divided by 1000; the gas flowrate term was divided by 100; and the percent methane term was divided by 10. These weights were chosen to keep each error term of the same order of magnitude. This enabled reductions in the simulation error of any of the reactor variables to have a significant effect on the summed total of the squared errors.

A disadvantage of using these weighting factors is that large reductions in one error term may be counteracted by a similar increase in a less important error term. This problem was considered but found not to be important because the variation of individual model paremeters generally affected only specific error terms. An alternative approach to using these arbitrarily defined weighting factors was to base the weights on the relative error between each set of simulated and experimental data points. This approach was considered but found to overamplify the importance of error reductions in some of the reactor variables. The results for changes in different model parameters are shown in Table 6. The base study is calculated using the model parameters used for the verification study. Each set of results represents the "optimum" change in model parameter under consideration. Unless otherwise indicated only one parameter was varied at a time, and the "optimum" value of a given parameter was found by adjusting that parameter until the smallest value of the total sum of squared errors was found to within 1%. The biggest individual error reductions came from the percent methane squared error. Significant improvements were also obtained for the other reactor variables, except for the gas flowrate for which there was an increase in the model error. Significantly, the results show that by the manipulation of only one of a number of different parameters large improvements were obtained in the model fit. The kinetic parameters varied were the glucoseconsuming, butyric acid consuming, acetoclastic, and hydrogen-utilizing bacteria substrate uptake coefficients. Decreasing the glucose bacteria uptake rate produced significant overall improvements with a total error reduction of about 18%. But this was at the expense of the model errors associated with the propionic and butyric acid concentrations, and percent methane. Decreasing the butyric acid bacterial uptake rate decreased the errors associated with butyric and acetic acid by 62 and 35%. By increasing the acetoclastic uptake rate improvements were

M o d e l verification o f a n a n a e r o b i c r e a c t o r m o d e l

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Table 6. The summed squared error terms for the quantitative analysis of the model against the experimental data of case study 1

Model parameters"t

Standard conditions Glucose (1.5: 0.023) k Butyric acid (0.26:0.16) Acetic acid (0.18: 0.23) Hydrogen (1.56:0.93) ~t (2000:3700) SRT (10:13) [Gluc]m (11.67 : 14) [NaHCO3 L (0: 21) Acetic acid (0.18:0.20) k Hydrogen (1.56:1.0) Butyric acid (0,26:0.17) [NaHCO3]in (0:18)

Sum of squared error parameters* Acetic % Gas acid Methane flowrate

Propionic acid

Butyric acid

57 70 57 59 45 45 71 73 57

49 66 19 51 51 54 61 64 49

90 10 58 16 41 45 17 25 90

46 64 45 37 49 49 36 32 2

43

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Caustic rate

Total SSE~

48 28 45 66 36 37 69 67 65

67 54 68 55 75 75 56 56 35

357 293 292 284 298 305 310 317 297

58

36

164

*Total simulation time of 3 days with a time interval for the calculation of error terms of 0.01 days. "tEach set of numbers in parentheses represents the standard and minimum error values, respectively. ~:The total of all sum of squared error terms. Units: propiooic acid, (mg/l)~ × 104; butyric acid, (rag/l)2 × 103; percent methane (__)2 × 10; gas flowrate, (1/day) 2 × 102; and caustic consumption rate (mmol/day)2 × 104.

obtained in all error terms except the propionic acid concentration (3%) and biogas flowrate (39%). The major increase in error associated with the biogas flowrate was due to the increased removal of carbon in the gas phase, previously seen as accumulating acetic acid. The hydrogen uptake rate could also be used to improve the model fit to the experimental data. Decreasing the uptake rate of hydrogen increased the partial pressure of hydrogen in the biogas thereby moving the production of acids to more reduced end products. The 24% improvement in the gas flowrate was mainly due to an increase in the accumulation of lactic acid in the reactor. The reduction in the total model error was 17%. Significant improvements were also obtained by varying other model parameters. As would be expected, increasing the hydrogen inhibition parameter produced similar results to varying the uptake rate of hydrogen. Similar behaviour was observed for the variation of the solids retention time of the initial influent concentration of glucose since both increased the initial concentrations of bacteria in the reactor. Increasing the influent sodium bicarbonate confentration was very specific in the way it affected the model simulation. Improvements were observed only in the consumption of caustic (48 %) and the percentage of methane (96%). The increased chemical production of carbon dioxide gas associated with the addition of bicarbonate resulted in a 35% increase in the gas flowrate error. To minimize the model simulation error, three areas were addressed. These were: the volatile acids, the biogas flowrate, and the percentage of methane. By using the butyric acid, acetic acid, and hydrogenutilizing bacterial uptake rates, and the influent concentration of sodium bicarbonate, significant improvements in the model simulation errors were obtained for all parameters except the biogas flowrate. Reductions in individual simulation errors ranged from 25% for propionic acid up to a 96%

reduction for the percent methane. The increase in the biogas flowrate error was approx. 22%. While significant overall improvements in the fit of the model to the experimental data could be obtained by the manipulation of a few key model parameters the differences in the observed trends for the simulation of propionic acid and the biogas flowrate could not be eliminated. These results reinforce the conclusions made earlier. Firstly, either the ecosystem model or hydrogen-regulation model would have to be modified to account for the accumulation of propionic acid over the duration of the experiment. Secondly, to obtain significant improvements in the fit of the biogas flowrate the inability of the model to account for the degradation of the other organic products, or the possible overestimation of the biodegradability of the influent waste will have to be addressed. OVERALL COMMENTS

The general mathematical model of the anaerobic process was able to provide a reasonable comparison with the three independent sets of experimental data examined. The results of the dynamic simulation studies were excellent considering the large differences in the experimental conditions between each case study. But the inconsistencies between the simulations and the experimental data have highlighted some important shortcomings of the model and the experimental data. This investigation has found that while the hydrogen inhibition model appears to predict the behaviour of the organic acids very well at low hydrogen partial pressures (of the order of 1000 ppm) it becomes increasingly inaccurate at higher partial pressures. The effects of high hydrogen partial pressures can be ameliorated by the manipulation of the hydrogn inhibition parameter (which directly affects the sensitivity of the bacteria to hydrogen) and the various bacterial kinetic parameters

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(the most effective being the maximum substrate uptake rate for the hydrogen-utilizing bacteria). This study has justified the inclusion of lactic acid as an important acidic intermediate in the anaerobic ecosytem. The accumulation of lactic acid under severe influent loading conditions was well modelled by the simulation. To produce further significant improvements in the model's ability to simulate the accumulation and degradation of organic acids it may be necessary to include other bacterial groups into the mathematical model. Whether the inclusion of more bacterial sub-species can be applied to the general process or would be used for specific conditions is an area requiring further investigation. The question of product inhibition of the anaerobic bacteria still remains unanswered because there were only two studies which generated sufficient intermediate acids to be able to produce significant product inhibition of the bacteria. In case study 3 product inhibition of the glucose bacteria was significant, but the effect on other groups of bacteria was found to be unimportant. The experimental results also show a tendency for the anaerobic bacteria to adapt to their environment and this has not been reflected in the model simulations. Unlike the simulated results, the experimental results of case study 3 show only slow, moderate inhibition of the bacteria. The pH inhibition functions appear to be most affected by the adaptability of the anaerobic bacteria to the environment, with the apparent ability of the anaerobic bacteria of case study 3 to tolerate lower pH values for greater periods of time. There is certainly a need to look at developing structured models for pH inhibition, and the causes of bacteria adaptability (e.g. domination of sub-species of bacteria at different process conditions). In general, the model of the physical reactor represented the actual process accurately. The assumption of continuously mixed liquid and solid (bacterial) phases, each with their own respective residence times, provided the basis for the good comparisons with the experimental data. In particular, a solids residence time of 10 days was found to best represent the retention of bacteria in high-rate anaerobic reactors. A constant solids residence time was assumed for all simulations even though it was possible that biomass may have been lost during the experiments. Biomass effects were not considered in the experimental results, and due to the lack of information on the mechanisms of biomass dynamics they could not be considered in this investigation. A consistent overestimation of the biogas flowrates was observed for each dynamic simulation. This could have been caused by overestimating the biodegradability of the waste or the influent substrate concentration. Experimental errors in the measurement of the biogas flowrate from the reactor may also have been a consideration. Insufficient information was available to draw further conclusions.

A quantitative analysis of the ability of the anaerobic process model to fit the constant pH data of case study 1 found that the most useful parameters for manipulating the model output were the maximum substrate uptake rates of the butyric acid, acetoclastic, and hydrogen-utilizing bacteria, and the influent concentration of sodium bicarbonate. Through the manipulation of these parameters significant improvements (between 25 and 96%) in the prediction of individual experimental variables were obtained. An important point to note with this investigation is that while the experimental conditions reported in these case studies were sufficient to be able to simulate the experiments, there was by no means enough information provided. In general only the influent substrate concentration was given and not necessarily in units that could be easily and accurately converted to an effective glucose concentration. The influent alkalinity was only sometimes provided, yet this was an important parameter which directly affected the consumption of caustic (or the change in pH), the generation of carbon dioxide, and the percentage of methane in the biogas determined during the simulation. The recording of other variables such as the effluent concentrations of organic and inorganic carbon and bacterial solids would have made the simulation and verification of the process easier. A steady-state carbon balance around the reactor would have been useful in indicating the important carbon sinks in the process and the accuracy of the experimental data. Finally, some indication of the errors involved in the experimental data and the repeatability of a given experiment should be provided to show the significance of the experimental results. CONCLUSIONS The previously developed high-rate anaerobic reactor model (Costello et al., 1991) was compared against experimental data from independent sources. The results of this investigation have shown that a structured approach to the modelling of anaerobic reactors is necessary to be able to qualitatively predict the behaviour of intermediate organic acids, physicochemical variables and gas phase partial pressures. The development and verification of such a model has provided an important tool for the investigation of advanced control strategies that may assist in the control of high-rate anaerobic reactors. Acknowledgements--The financial assistance of the Univer-

sity of Queensland through the Alfred and Olivea Wynne Postgraduate Research Scholarship is gratefully acknowledged. Special thanks to the Department of Chemical Engineering for their continual financial support of this work. REFERENCES

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