a monod-based model of attached-growth anaerobic fermenters

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Biological Wastes 31 (1990) 275-289 A Monod-Based Model of Attached-Growth Anaerobic Fermenters J. P. Bolte* & D. T. Hill Department of Agricultural Engineering and Alabama Agricultural Experiment Station, Auburn University, Auburn, Alabama, USA (Received 17 June 1988; revised version received 10 July 1989; accepted 12 July 1989) A BS TRA C T A simple mathematical model of steady-state attached-growth anaerobic fermenter kinetics is described. The model considers a single methanogenic culture foUowing Monod growth kinetics. The model accounts for effects of &fluent biodegradabilio, and volatile solids" concentration, temperature and hydraulic retention time, and predicts volumetric methane productivity and volatile solids reduction. It is distinguished from conventional suspended- growth reactor models by its explicit consideration of bacterial concentration in the reactor system, based on hydraulic .flow and &fluent volatile solids" concentration. The model was validated using data from both porous- and solid-media attached-growth .fermenters. INTRODUCTION Anaerobic fermentation of animal wastes using attached-growth reactor designs has received considerable attention recently as a means of effectively converting dilute waste streams to methane at short hydraulic retention times (HRT). A number of attached-growth reactor configurations have been developed, based on the concept of fixing and concentrating bacterial cells on surfaces placed within the reactor environment. Anaerobic bacteria readily colonize these surfaces, forming a biofilm layer consisting of active * Present address: Department of Agricultural Engineering, Oregon State University, Corvallis, Oregon 97331, USA. 275 Biological Wastes 0269-7483/90/$03.50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

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Page 1: A Monod-based model of attached-growth anaerobic fermenters

Biological Wastes 31 (1990) 275-289

A Monod-Based Model of Attached-Growth Anaerobic Fermenters

J. P. Bolte* & D. T. Hill

Department of Agricultural Engineering and Alabama Agricultural Experiment Station, Auburn University, Auburn, Alabama, USA

(Received 17 June 1988; revised version received 10 July 1989; accepted 12 July 1989)

A BS TRA C T

A simple mathematical model of steady-state attached-growth anaerobic fermenter kinetics is described. The model considers a single methanogenic culture foUowing Monod growth kinetics. The model accounts for effects of &fluent biodegradabilio, and volatile solids" concentration, temperature and hydraulic retention time, and predicts volumetric methane productivity and volatile solids reduction. It is distinguished from conventional suspended- growth reactor models by its explicit consideration of bacterial concentration in the reactor system, based on hydraulic .flow and &fluent volatile solids" concentration. The model was validated using data from both porous- and solid-media attached-growth .fermenters.

INTRODUCTION

Anaerobic fermentation of animal wastes using attached-growth reactor designs has received considerable attention recently as a means of effectively converting dilute waste streams to methane at short hydraulic retention times (HRT). A number of attached-growth reactor configurations have been developed, based on the concept of fixing and concentrating bacterial cells on surfaces placed within the reactor environment. Anaerobic bacteria readily colonize these surfaces, forming a biofilm layer consisting of active

* Present address: Department of Agricultural Engineering, Oregon State University, Corvallis, Oregon 97331, USA.

275 Biological Wastes 0269-7483/90/$03.50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

Page 2: A Monod-based model of attached-growth anaerobic fermenters

276 J. P. Bolte, D. T. Hill

and inactive bacterial cells embedded in a secreted gelatinous polysac- charide matrix. The retention of active bacteria in the attached biofilm and interstitial pore spaces provides these reactors with several advantages over conventional suspended-growth reactor systems, including (1) faster substrate conversion rates due to higher concentrations of active bacterial mass in the reactor, (2) reduced bacterial 'washout' at short HRT, (3) rapid reactor response to varying operating conditions, and (4) enhanced reactor stability under adverse operating conditions.

Young and McCarty (1968) developed the first effective attached-growth anaerobic system, termed an 'anaerobic filter'. This reactor employed a rigid, inert solid support system consisting of smooth quartzite stone. Two synthetic soluble wastes were used in these reactors (protein-carbohydrate and volatile organic acids mixtures) at influent concentrations ranging from 0.375 to 10.0 g chemical oxygen demand (COD)/liter. HRT for their study ranged from 2"25 to 72 h, resulting in COD loadings of 0.425-3-4 g COD/liter day. COD conversion rates ranged from 38"8 to 98-6%. They concluded that the anaerobic filter was ideally suited to convert dilute, largely soluble waste where plugging of the interstitial void spaces by influent solids and biological growth would be less likely.

Subsequent studies (Brumm & Nye, 1982; Kennedy & van den Berg, 1982; Hasheider & Sievers, 1983; Norstedt & Thomas, 1983) showed the anaerobic filter to be suitable for conversion of a variety of largely soluble agricultural wastes. Removal efficiencies have been improved using high void volume (0-80-0"90) support surface configurations providing large surface area-volume ratios, with solids blockage minimized by controlling packing geometry. Using these improved designs, loading rates of 10-20 g COD/liter day at reasonable removal efficiencies (>70%) have been reported (Callander & Barford, 1983).

To overcome problems associated with filter blockage while retaining the advantages of attached growth, Fynn and Whitmore (1984) and Blanchard and Gill (1984) developed porous-media reactors based on earlier work by Atkinson et al. (1980) on anaerobic treatment of municipal wastewater. Lightweight, highly porous polyurethane foams or reticulated nylon cuboids were used as surfaces for bacterial attachment. The high porosity (>95%) and tightly knit matrix of these particles provided substantial surface area for biofilm formation and protected the biofilm from losses due to hydraulic shear. The support particles were suspended in a semi-fluidized state in the reactor by mechanical mixing. Because of the lightweight character of the support particle and extensive biofilm development within the matrix, low energy inputs were required to maintain a semi-fluidized bed. Blanchard and Gill (1984) used these reactors to treat high-strength (45 g volatile solids (VS)/liter)+dairy waste. Similar reactors, with reticulated

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Model of attached-growth anaerobic fermenters 277

polyurethane foam media, were used by Poels et al. (1984) to treat concentrated (60-70g VS/liter) swine waste. Effective fermentation was accomplished at HRT as short as 2.5 days at mesophilic temperatures.

Subsequent to these studies, Bolte et al. (1986) evaluated the potential fermentation of dilute (15 g VS/liter) screened swine waste liquids using synthetic porous biomass support particles at mesophilic (35°C) and thermophilic (55°C) temperatures. Their media consisted of a mixture of heat-bonded matted nylon and open-cell polyurethane foam at a fill ratio (media volume-total reactor volume) of 50%. Completely mixed conditions were maintained by fluid recirculation. Successful fermentation operation was obtained at HRT as low as 2 and 1 day for mesophilic and thermophilic reactors, respectively.

Results from these and other studies (Hill et al., 1985; Hill & Bolte, 1986) indicate that both solid- and porous-media anaerobic reactors are capable of retaining high concentrations of active bacterial mass and providing stable reactor operation at HRT shorter than can be achieved using conventional stirred tank reactors.

This study was initiated to provide predictive tools for operating and designing attached-growth anaerobic reactor systems. A number of mathematical models have been developed to predict performance of conventional anaerobic reactor designs (Hill & Barth, 1977; Chen & Hashimoto, 1980; Hill, 1982; Feilden, 1983). These models have generally employed Monod (1949) or Contois (1959) kinetic descriptions of single- culture bacterial growth operating at steady-state (Chen & Hashimoto, 1980; Feilden, 1983) or multiple-culture systems in a dynamic environment (Hill & Barth, 1977; Hill, 1982).

In contrast, attached-growth anaerobic systems have received relatively little modeling effort. Young and McCarty (1968) presented a simple empirical equation predicting ultimate soluble biological oxygen demand (BOD) removal as a function of HRT and a media-based 'proportionality' constant. This simple relationship did not consider influent characteristics, temperature, explicit media factors such as surface area and packing density, and was limited to predicting BOD removal only. Mueller and Mancini (1976) developed an anaerobic filter model incorporating two-phase digestion, Monod-based bacterial growth kinetics, pH, alkalinity, ammonia and gas production. This model excluded explicit media considerations, biofilm response and solids transport, and relied heavily on empirically derived parameter values. Bolte et al. (1984) applied diffusion-reaction biofilm kinetics developed by Rittmann et al. (1982) to simulation of anaerobic filters and developed a dynamic model employing a two-culture description of bacterial growth based on kinetics developed by Hill and Barth (1977).

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278 J. P. Bolte, D. T. Hill

Because of their complexity, these models are cumbersome to use and require significant computer resources to run. To provide an alternative to these large and complex models, Bolte and Hill (1985) developed a simplified single-culture, single-substrate description of steady-state attached-growth fermenters using Contois kinetics. This model predicted volumetric methane production and VS reduction based on influent VS concentration, HRT, a waste-specific 'ultimate methane yield' factor and an empirical inhibition coefficient. This model was validated with data from both conventional anaerobic filters and porous-media reactors treating screened swine waste. The model presented here was developed as an alternative to the Bolte and Hill (1985) model, using Monod-based growth kinetics to provide a more theoretical description of the fermentation process while maintaining a simple model structure.

METHODS

Model development

In the development of the model presented here, a number of assumptions concerning the reactor kinetics were made. First, the reactor contents were assumed to be spatially homogeneous and completely mixed; no distinction was made between the biofilm and bulk liquid regions, and a single- substrate, single-culture bacterial system was assumed. Secondly, biode- gradable volatile solids (BVS) were considered as the lumped substrate for bacterial growth. Third, reaction kinetics were assumed to apply uniformly throughout the reactor contents, and the kinetic parameters used were considered independent of the waste type or influent composition. Microbial growth rates were assumed to follow Monod growth kinetics, and were derived for the steady-state only. Substrate transformation was assumed to result from microbial metabolism only. Employing these assumptions in developing steady-state mass balances on bacteria and substrate resulted in a model capable of predicting volumetric methane productivity and VS reduction.

The model requires five input parameters to be specified. These include (1) total influent VS, (2) hydraulic flow-rate through the reactor, (3) the reactor fill ratio (support medium volume-total reactor volume), (4) operating temperature and (5) a waste-specific biodegradability constant. These inputs are summarized in Table 1.

Influent VS is partitioned into biodegradable (BVS) and non- biodegradable (NBVS) fractions, using the biodegradability constant. Upon introduction into the reactor, BVS are utilized by a single methanogenic

Page 5: A Monod-based model of attached-growth anaerobic fermenters

Model of attached-growth anaerobic fermenters

TABLE 1 Summary of Model Inputs

279

Parameter Symbol Units

Total influent VS STo g VS/liter Hydraulic flow rate F liter/day Fill ratio e, liter/liter Temperature T °C Waste biodegradability /3 g BVS/g VS

culture and converted into methane according to Monod kinetics, based on reactor BVS and bacterial concentrations, temperature and a Monod 'half velocity' kinetic parameter. It is the treatment of the bacterial concentration term which distinguishes this model from conventional suspended-growth models. Rather than considering bacteria to be freely suspended in the reactor liquid and subject to hydraulic flow, the bacterial concentration term is calculated independently of the reaction kinetics, based on influent VS loading and retentive capabilities of the support medium. This approach reflects real characteristics of attached-growth fermenters, which typically operate at bacterial concentrations substantially greater than those achieved in suspended-growth reactors, and allowed good prediction of performance of real attached-growth fermenters.

For a completely mixed continuous-flow system, transient variation of the concentration of rate-limiting substrate can be described by the following differential equation:

dSB_ SRo-- SB /tX (1) dt 0 n Y

where SB = rate-limiting substrate concentration in the reactor (g/liter), SBO = rate-limiting substrate concentrat ion in the influent (g/liter), X = effective bacterial concentration (g/liter), t = time (days), p = specific bacterial growth rate (per day), 0. = actual HRT based on hydraulic (void) volume (days), and Y = bacterial yield coefficient (gX/gSB). The actual HRT (0.) is based on the void volume of the reactor, and can be determined by

F 0n - V × (1 - e) ( 2 )

where V= total reactor volume (liters). Influent substrate concentration is determined by partitioning the influent

VS into biodegradable and non-biodegradable fractions using a waste- specific biodegradability constant (fl). Values for fl for various animal wastes

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280 J. P. Bolte, D. T. Hill

TABLE 2 Parameter Values Used in the Simplified Model

Parameter Symbol Value

Waste biodegradability fl Swine 0'90 g BVS/g VS Screened swine waste liquids 0-95 g BVS/g VS Beef (confined) 0'70 g BVS/g VS Beef (dirt) 0-60 g BVS/g VS Dairy 0.36 g BVS/g VS Poultry (broilers) 0.70 g BVS/g VS Poultry (layers) 0"90 g BVS/g VS

Monod half-velocity coefficient Ks 9.00g BVS/liter Bacterial yield coefficient Y 0-20 g X/g BVS Maximum bacterial concentration XM 8.94 g X/liter Bacterial coefficient Kxs 1.50 g BVS/liter day Bacterial inhibition coefficient Kx~ 51.9 g BVS/liter day Specific methane productivity ns 0'52 liters CHJg VS

were taken from Hill (1982), and are given in Table 2. This constant reflects the por t ion of the influent VS which are susceptible to biological metabolism. Influent BVS is calculated by

S~o = Stuff (3)

Under steady-state conditions, eqn (1) reduces to

SBo - SB # X = (4)

O H Y

According to M o n o d kinetics, bacterial growth on a single rate-limiting substrate can be described by

/~MSB -- - - (5)

K s + SB

where /~M=maximum specific bacterial growth rate (per day) and Ks = M o n o d half-velocity coefficient (gSB/liter). K s is defined as the substrate concentrat ion at which p-/~M/2.

Combin ing eqns (4) and (5) results in the following dimensionless relationships:

f6) SBo--2 YS.o O,o YS, o SBo ] Sao ] J

Equat ion (6) has two solutions, only one of which (the additive solution) can be usefully interpreted. U p o n inspection of eqn (6), three dimensionless

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Model of attached-growth anaerobic fermenters 281

terms are apparent. The first term (Sa/SBo) is the ratio of concentrat ions of substra te in the reactor to substrate in the influent. The second dimensionless term (#MXOn/YSBo) is the ratio of the max imum substrate utilization rate to the substrate loading rate. The final dimensionless term (Ks/Sao) is the ratio of the half-velocity substrate concentrat ion to the influent substrate concentrat ion. Equat ion (6) predicts that substrate conversion increases with increasing #~, X and 0 w

VS reduct ion across a fermenter is a measure of the conversion efficiency of the reactor and is defined as

VSR = [1 - (S B + SRo)/Svo ] × 100 (7)

where V S R = V S reduct ion (%), and S R o = r e f r a c t o r y VS influent concentrat ion (g/liter), SRO is calculated using the biodegradabili ty constant (//):

SRO = STO -- SBo ----- (1 --//)STo (8)

Substi tuting eqns (3) and (8) into eqn (6) results in the following expression for calculating VS reduction:

VSR =/1(1 - SB/S,o) (9)

where SB/SBo is calculated from eqn (6). It is apparent f rom eqn (9) that under identical operating conditions, VSR will be directly propor t ional to the biodegradabil i ty of the waste.

Specific methane productivi ty (rts) is defined as liters methane produced/g VS destroyed, and has been found to be relatively constant between various waste types, varying between 0"5 (McCarty, 1964) and 0-83 (Bolte et al., 1986). Volumetr ic methane productivity (r~v), defined as liters methane produced/l i ter reactor volume per day, can be calculated at steady state as

7rv = ns(SBo -- SB)/On = (~sSTo VSR)/O. (10)

Parameter determination

Implementat ion of the model involves evaluating the kinetic parameters #M and K s, biomass yield coefficient Y, biomass concentrat ion X and specific methane productivi ty rt s. Appropr ia te values of K s, Y and n s were determined by searching the literature for previously reported values f rom fermenters t reat ing animal wastes. Actual values used represented intermediate values f rom the range reported in the literature, and were selected based on model fit to real ns. These values are given in Table 2.

M a x i m u m bacterial growth rate (/~ra) was assumed to be temperature- dependent (Hill & Barth, 1977; Chen & Hashimoto, 1980), and was

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282 J. P. BoRe, D. T. Hill

estimated using criteria of best fit with real volumetric methane productivity data at 24, 35 and 55°C. Best fit values were fitted to a second-order polynomial relation:

ItM = 0"3677 - 0"0101 48 x T + 0"000301 x T 2 (11)

This expression produced values slightly higher than those suggested by Chen and Hashimoto (1980) for suspended-growth anaerobic fermenters treating animal wastes, but are near the values used by Bolte and Hill (1985) to describe attached-growth fermenter kinetics. The enhanced capability for selection and retention of more efficient bacterial strains lends credibility to the use of slightly higher/~M values for attached-growth systems.

Determination of effective bacterial concentration in the reactor is a key consideration in modeling attached-growth systems. It is the retention of high bacterial concentrations that distinguishes these systems from conventional suspended-growth systems and accounts for their improved performance in utilizing dilute wastes and/or high hydraulic loads. Bacterial concentrations in attached-growth fermenters treating animal wastes have been modeled (Bolte, 1987) and measured experimentally (Hill et al., 1985; Hill & Bolte, 1986), with reported values ranging from 8 to 16g bacterial mass/liter total reactor volume. For this study, effective bacterial concentration in the reactor was estimated to be a function of BVS loading rate (Sao/On), incorporating the effect of both VS and hydraulic loading. The desired response function would approach zero as VS loading approaches zero, rise to a maximum value at intermediate loading rates, and decrease as VS loading becomes large, subjecting the bacteria to hydraulic and inhibitory stress. Plots of calculated values of X versus BVS loading rates, based on real rc v values and estimated parameter values, confirmed this relationship. A function similar to the Monod inhibition equation (Hill & Nordstedt, 1980) provided good fit to the data and possessed the desired response relationships. This relationship had the form

x - - xM (12) 1 + Kxs/Lvs + Lvs/K,,,

where Kxs = BVS loading rate at which bacterial concentration is one-half the maximum concentration the medium is able to support in an uninhibited state, Kx~ = BVS loading rate inhibition coefficient, and Lvs = BVS loading rate, S~o/On.

'Best fit' values of X M, Kxs and Kxl are given in Table 2. A plot of X versus VS loading rate is given in Fig. 1. This equation produced values consistent with those reported by Hill et al. (1985) and Hill and Bolte (1986) for porous- media reactors.

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Model of attached-growth anaerobic fermenters 283

o o

o ,t-

o

Fig. 1.

0 I I I i 0 10 20 30 40 50

BVS Looding Rote ( g / L - d o y )

Bacterial concentration (X) versus BVS Loading Rate.

The final parameter needed for predicting volumetric methane productiv- ity is the specific methane productivity (TZs). Hill (1982) reported this value to be relatively constant for different waste types and independent of temperature. A value of 0'52 liters CH4/g VS destroyed was used here for model validation; this value allowed good simultaneous estimation of both VSR and ~z v.

RESULTS

The simplified model was validated with results reported in the literature from both solid- and porous-media attached growth fermenters. The literature was searched for studies reporting both zc v and VSR for fermenters in controlled environments with well-defined operating con- ditions. For porous-media reactors, 12 studies were found using screened swine waste liquids at two temperatures (Bolte et al., 1986; Hill & Bolte, 1986). A larger number of studies (31) were found using solid-media reactors; however, five of these did not report effluent VS concentration, allowing only 26 to be used for validation of VSR prediction. Twenty-seven of these studies used screened swine waste liquids as influent material (Brumm & Nye, 1982; Kennedy & van den Berg, 1982; Hasheider & Sievers, 1983). The study of Liao & Lo (1985) used screened dairy waste influent. All solid media reactors were operated at 35°C, with the exception of those used by Brumm & Nye (1982), which operated at 24°C. Data reported for each of these studies are summarized in Table 3.

Summaries of observed and predicted values of rc v and VSR are given in Table 4, and are shown graphically in Figs 2 and 3. In general, 7Zv prediction was very good for both porous- and solid-media reactors, with an overall coefficient of determination (R 2) value of 0-96. VSR prediction was less effective, with R 2 values of 0"64 and 0"61 for the porous- and solid-media

Page 10: A Monod-based model of attached-growth anaerobic fermenters

TABLE 3 Summary of Studies Used for Model Validation

Reference S o On" T (g/liter) (day) (°C)

~V a

(liter/liter day)

VSR (%)

Bolte et al. (1986)

Hill & Bolte (1986)

Brumm & Nye (1982)

Kennedy & van den Berg (1982)

Hasheider & Sievers (1983)

Liao & Lo (1985)

9.83, 5.0 35 0-84 64"3 9'29 2.5 35 1.38 50-7

10.32 1.5 35 2.06 46'5 11-34 1.0 35 2.42 36-0 10.38 2'5 55 1.84 66"9 9.57 1"5 55 2.68 60-8

10.02 1.0 55 3-29 48.9 11.34 0"5 55 4.86 40'6 18.7 3.75 35 1.71 50"3 15.2 2.25 35 2.56 47-2 15.6 1.5 35 2.87 42.9 16.0 0.75 35 2-88 36.2 3.92 6'0 24 0.315 58"5 3.34 3'0 24 0.443 54.3 3-82 2.0 24 0.658 54"9 3"90 1-0 24 0-839 46-2

20.00 8"0 35 1.41 - - 17.02 3"7 35 2"10 - - 17.82 2"7 35 2"20 - - 17-34 1-7 35 2"60 - - 18"70 1'0 35 3'80 - - 36"0 6'0 35 3.225 64-7

6"0 6"0 35 1"903 41"9 36"0 4"0 35 1"419 67.0 24-0 4"0 35 1"502 73.7 12-0 4-0 35 1"250 55"0 4"0 4"0 35 0"978 53"5

18"0 2"0 35 0"797 73-0 12'0 2"0 35 0.706 76-2 6"0 2"0 35 0-660 68'3 2-0 2"0 35 0"548 52.9 9"0 l'0 35 0"379 84"4 6-0 1-0 35 0"368 83"8 3"0 1'0 35 0'345 68.7 1'0 1"0 35 0'285 59'7 4'5 0"5 35 0-185 78.4 3-0 0-5 35 0.172 77.7 1"5 0"5 35 0"156 75.3 0"5 0"5 35 0.126 56.8

35'0 8"0 35 0"88 25-7 34'0 6-0 35 0"89 27.4 34'0 4"0 35 1.42 24.6 37"0 3"0 35 1"50 23"0

a Based on hydraulic (void) volume.

Page 11: A Monod-based model of attached-growth anaerobic fermenters

TABLE 4 Comparison of Real and Predicted Model Outputs

Reference Observed Predicted Observed Predicted ltv nv VSR VSR

(liter/liter (liter~liter (%) (%) day) day)

Bolte et al. (1986)

Hill & Bolte (1986)

Brum & Nye (1982)

Kennedy & van den Berg (1982)

Hasheider & Sievers (1983)

Liao & Lo (1985)

0"84 0"79 64"3 77"1 1"38 1"31 50"7 67"6 2"06 2-01 46"5 56"2 2"42 2"53 36"0 43'8 1.84 1'72 66-9 79"8 2'68 2'40 60-8 72"2 3"29 3"28 48"9 62"9 4"86 4"65 40-6 39"4 1"71 1"92 50"3 73-9 2-56 2"25 47"2 65-9 2"87 2'82 42'9 52"1 2"88 3-26 36'2 29"4 0.315 0"23 58"5 66"2 0"443 0"34 54"3 58"5 0"658 0"54 54-9 54"7 0"839 0"87 46-2 42"7 1"41 1"08 - - - - 2"10 1"77 2.20 2'31 - - - - 2.60 2.89 - - - - 3"80 3"44 3.225 2.48 64.7 79.4 1-903 1"52 41.9 48.8 1.419 1"76 67"0 84"7 1.502 1-68 73.7 80"6 1'250 1'47 55'0 70.8 0.978 1.02 53.5 49.1 0.797 0.87 73-0 84.0 0.706 0"83 76-2 79.6 0"660 0"72 68"3 69.0 0"548 0.48 52.9 45"9 0.379 0"42 84"4 80-9 0'368 0.39 83"8 75"5 0.345 0.33 68.7 63.1 0-285 0.20 59.7 38.7 0-185 0"19 78.4 74.9 0-172 0-18 77.7 67.9 0.156 0-14 75.3 53.2 0.126 0"08 56-8 29.0 0-88 0'83 25.7 36"5 0.89 1.05 27.4 35.5 1.42 1.47 24.6 33.3 1.50 1.99 23.0 31-0

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286 J. P. Bolte, D. T. Hill

5

! , f 0 I I J I

0 I 2 3 4 S Observed 'a" v ( L / L - d a y )

Fig. 2. Predicted versus observed methane productivities (nv) for porous- and solid-media reactors.

reactors, respectively. However, VSR is difficult to measure in attached- growth systems, since VS accumulation tends to occur within the reactor considerably after the reactor reaches an apparent steady state. Given this phenomenon and inherent variability in measuring VSR, the model fit to the experimental data was considered acceptable, particularly in predicting nv.

D I S C U S S I O N

The model presented here provides a simple approach to modeling steady-

100

8 0 - ¢w

"v 6 0

4 0 ft..

Fig. 3.

20 '

0 - I~¢~ml M~ l l~

- ~ d l d JA~lla

I I I

A

0 20 4-0 60 80 1 O0

Observed VSR

Predicted versus observed VSR for porous- and solid-media reactors.

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Model of attached-growth anaerobic fermenters 287

state methane production from attached-growth systems treating animal wastes. By utilizing Monod growth kinetics coupled with an explicit representation of bacterial concentration, the model accurately predicted volumetric methane productivity and VSR for a variety of attached-growth anaerobic fermenter configurations. The model was validated with data from fermenters treating swine and dairy waste liquids. A number of assumptions were made in the development of the model, and should be considered when applying the model to predict performance of real fermentation systems. First, the assumption of completely mixed conditions in the reactor environment was made in the interest of simplifying the model as much as possible while maintaining a broad view of the process kinetics. This assumption clearly violates the basic operating principle of most attached-growth systems where distinct biofilm and bulk liquid regions are maintained. However, the 'lumped parameter' approach used in describing effective biomass concentrations provides a rationale for making this assumption where quasi-homogenous conditions are maintained. Most fermenters are operated using either mechanical mixing or fluid recircu- latlon. Under these conditions, the completely mixed assumption should be reasonably valid. However, in columnar reactors with no recirculation or sludge blanket reactors, this assumption is violated and the model cannot be legitimately applied.

The second assumption relating to model application involves the use of waste-specific coefficients describing BVS fractions (fl) for various waste types. The values used here for validation for swine and dairy wastes were taken from Hill (1982) and provided good results when compared to data reported in the literature. Validation data were not found for other waste types; therefore, the model must be used carefully when applied to treatment of wastes other than swine and dairy liquids.

The simplified model does not directly allow determination of the effects of different media materials or configuration geometries. However, by modifying the coefficients of the bacterial concentration eqn (11), particularly the maximum bacterial concentration )i'M, effects of different media configurations might be introduced into the model. Bolte et al. (1984), using a complex model describing multiculture anaerobic biofilm dynamics and substrate conversion, found that simulated biofilm thickness varied inversely to surface area for a given substrate loading, resulting in only small net effects of media geometry on overall bacterial concentration and reactor performance. Biofilm concentrations in that study were primarily a function of VS loading rates rather than media configuration. This observation is borne out here in the analysis of the validation data sets, where similar conversion rates for similar VS loadings were observed, regardless of the specific reactor media configuration. This adds credibility

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288 J. P. Bolte, D. T. Hill

to the model assumption of negligible effects of media variation and suggests that at tached-growth reactor design should focus on providing good operational characteristics (such as media durability, blockage control, etc.) rather than strictly maximizing available surface area.

CONCLUSIONS

The model presented here allows a simple, rational basis for predicting the performance of at tached-growth anaerobic fermenters using substrate mass balances and Monod growth kinetics. The model predicts that methane product ion will be primarily a function of waste biodegradability, temperature and VS loading rate, and that similar performance can be expected for porous- and solid-media reactors as long as a reasonable level of bacterial solids retention is maintained. The model has been validated for treatment of swine and dairy waste liquids.

A C K N O W L E D G E M ENTS

This research was conducted under Southern Regional Research Project S-202 with funds provided by the Alabama Agricultural Experiment Station. Manuscript approved as Journal Series No. 2-881581P of the Alabama Agricultural Experimental Station.

R E F E R E N C E S

Atkinson, B., Blackard, G. M. & Pinches, A. (1980). Process intensification using cell support systems. Process Biochemistry, 15(3), 24-32.

Blanchard, J. P. & Gill, T. A. (1984). Suspended particle fixed biomass anaerobic digesters for livestock waste. Transactions of the ASAE, 27(2), 535-40.

Bolte, J. P. (1987). A comprehensive mathematical model of attached growth anaerobic fermenters. PhD dissertation, Agricultural Engineering Depart- ment, Auburn University, AL.

Bolte, J. P. & Hill, D. T. (1985). Modeling suspended particle attached growth reactors. In Agricultural Waste Utilization and Management (ASAE Pub. No. 13-85). ASAE, St. Joseph, MI, pp. 104-15.

Bolte, J. P., Nordstedt, R. A. & Thomas, M. V. (1984). Mathematical simulation of upflow anaerobic fixed bed reactors. Transactions of the ASAE, 27(5), 1483-90.

Bolte, J. P., Hill, D. T. & Wood, T. H. (1986). Anaerobic digestion of screened swine waste liquids in suspended particle attached growth reactors. Transactions of the ASAE, 29(2), 543-9.

Brumm, T. J. & Nye, J. C. (1982). Dilute swine waste treatment in an anaerobic filter. In Proceedings of the 36th Industrial Waste Conference, ed. J. M. Bell. Ann Arbor Science Publishers, Ann Arbor, MI, USA.

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Model of attached-growth anaerobic fermenters 289

Callander, I. J. & Barford, J. P. (1983). Recent advances in anaerobic digestion technology. Process Biochemistry, 18(4), 24-37.

Chen, Y. R. & Hashimoto, A. G. (1980). Substrate utilization kinetic model for biological treatment processes. Biotechnology and Bioengineering, 22, 2081-95.

Contois, D. E. (1958). Kinetics of bacterial growth relationships between population density and specific growth rates of continuous cultures. J. General Microbiology, 21(7), 40-50.

Feilden, N. E. H. (1983). The theory and practice of anaerobic digestion reactor design. Process Biochemistry, 18(5), 34-7.

Fynn, G. H. & Whitmore, T. N. (1984). Retention of methanogens in colonized reticulated polyurethane foam biomass support particles. Biotechnology Letters, 6(2), 81 6.

Hashieder, R. J. & Sievers, D. M. (1983). Limestone bed anaerobic filters for swine manure. ASAE Paper No. 83-40053. ASAE, St. Joseph, MI.

Hill, D. T. (1982). A comprehensive dynamic model for animal waste meth- anogenesis. Transactions of the ASAE, 25(5), 1374-80.

Hill, D. T. & Barth, C. L. (1977). A dynamic model for simulation of animal waste digestion. J. Water Pollution Control Federation, 49, 212943.

Hill, D. T. & Bolte, J. P. (1986). Evaluation of suspended particle attached growth fermenters treating liquid swine waste. Transactions of the ASAE, 29(6), 1733 8.

Hill, D. T. & Nordstedt, R. A. (1980). Modeling techniques and computer simulation of agricultural waste treatment processes. Agricultural Wastes, 2, 135-6.

Hill, D. T., Bolte, J. P., Prince, T. J. & McCaskey, T. A. (1985). Operating and performance characteristics of suspended particle attached growth anaerobic fermenters treating screened swine waste. In Agricultural Waste Utilization and Management (ASAE Pub. No. 13-85). ASAE, St. Joseph, MI,

Kennedy, K. J. & van den Berg, L. (1982). Anaerobic digestion of piggery waste using a stationary fixed film reactor. Agricultural Wastes, 4, 151 8.

Liao, P. H. & Lo, K. V. (1985). Methane production using whole and screened dairy manure in conventional and fixed film reactors. Biotechnology and Bioengineer- ing, 27, 266-72.

McCarty, P. k. (1964). Anaerobic waste treatment fundamentals, II. Environmental requirements and control. Public Works, 95, 123.

Monod, J. (1949). The growth of bacterial cultures. Annual Review of Microbiology, 3, 371.

Mueller, J. A. & Mancini, J. L. (1976). Anaerobic filter--kinetics and application. In Proceedings of the 30th Industrial Waste Treatment Conference, ed. J. M. Bell. Ann Arbor Science Publishers, Ann Arbor, MI.

Nordstedt, R. A. & Thomas, M. V. (1983). Wood media for fixed bed reactors. ASAE Paper No. 83 4015. ASAE, St. Joseph, MI.

Poels, J., Van Assche, P. & Verstraete, W. (1984). High rate anaerobic digestion of piggery manure with polyurethene sponges as support material. Biotechnology Letters, 6(11), 747-52,

Rittmann, B. E., Strubler, U E. & Ruzicka, T. (1982). Anaerobic filter pretreatment kinetics. J. Environmental Engineering Division, A SCE, 108 (EE5), 900-12.

Young, J. C. & McCarty, P. L. (1968). The anaerobic filter for waste treatment. Technical Report No. 87, Department of Civil Engineering, Stanford University, Stanford, CA.