ARTICLE IN PRESS WAT E R R E S E A R C H 41 (2007) 323 – 332 Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/watres Anaerobic fermentation of cattle manure: Modeling of hydrolysis and acidogenesis M. Myinta, N. Nirmalakhandanb,, R.E. Speecec a Civil Engineering Department, MSC 3CE, New Mexico State University, Las Cruces, NM 88003, USA Civil Engineering Department, MSC 3CE, New Mexico State University, Las Cruces, NM 88003, USA c Civil Engineering Department, Vanderbilt University, Nashville, TN 37235, USA b art i cle info A B S T R A C T Article history: A mathematical model for the hydrolysis and acidogenesis reactions in anaerobic digestion Received 1 April 2005 of cattle manure is presented. This model is based on the premise that particulate Received in revised form hydrolysable fraction of cattle manure is composed of cellulose and hemicellulose that are 14 September 2006 hydrolyzed at different rates according to a surface-limiting reaction; and, that the Accepted 12 October 2006 respective soluble products of hydrolysis are utilized by acidogens at different rates, Available online 4 December 2006 according to a two-substrate, single-biomass model. Batch experimental results were used Keywords: to identify the sensitive parameters and to calibrate and validate the model. Results Anaerobic hydrolysis predicted by the model agreed well with the experimentally measured data not used in the Acidogenesis calibration process, with correlation coefficient exceeding 0.91. These results indicate that Cattle manure the most significant parameter in the hydrolysis–acidogenesis phase is the hydrolysis rate Process model constant for the cellulose fraction. & 2006 Elsevier Ltd. All rights reserved. Cellulose Hemicellulose 1. Introduction Manure residues from livestock industries have been identified as a major source of environmental pollution. Traditionally, these wastes have been disposed of, directly or after composting, as soil amendments in the agricultural industry (van Horn et al., 1994; USDA, 1995). Since this practice has resulted in the degradation of air, soil, and water resources, new regulations for protecting the environment have been promulgated to control land application of animal manure (US EPA, 1995). As such, livestock industries and regulatory agencies are seeking alternate technologies to manage manure residues in environment-friendly manner (Sims, 1995; van Horn et al., 1994; USDA, 1995). Biotechnologies have the potential to manage this problem in a cost-effective and sustainable manner. Even though cattle manure residues are complex and naturally polymeric Corresponding author. Tel.: +1 505 646 5378; fax: +1 505 646 6049. E-mail address: nkhandan@nmsu.edu (N. Nirmalakhandan). 0043-1354/$ - see front matter & 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2006.10.026 (Palmisano and Barlaz, 1996; Ong et al., 2000), anaerobic digestion has been recognized as a preferred process for stabilizing such complex wastes and at the same time regenerating useful chemicals, generating energy, and reducing the volume for disposal (Ghosh, 1987; Speece, 1996; Lettinga, 2001). 1.1. Anaerobic technology Anaerobic digestion of complex wastes in the liquid form (o5% total solids) is a mature technology that has been well studied and successfully implemented at full-scale (Speece, 1996; Munch et al., 1999). Several studies have adapted this technology to digest particulate wastes in slurry form (5–15% total solids). More recently, feasibility of anaerobic digestion of high-solid substrates (420% total solids content), referred to as ‘‘dry digestion’’, has been demonstrated (Mata-Alvarez, ARTICLE IN PRESS 324 WA T E R R E S E A R C H 1989; Kayhanian et al., 1996; Vavilin et al., 2002). Examples of dry digestion studies include: municipal solid wastes in a leach-bed reactor (Ghosh, 1987); fruit and vegetable wastes in a plug flow reactor (Negri et al., 1993); organic fraction of municipal solid wastes in a solid phase reactor (Veeken et al., 2000) and with leachate recycling (Vavilin et al., 2002); and food wastes by a hybrid solid–liquid reactor (Hai-Lou et al., 2002). In the case of animal wastes, anaerobic digestion in slurry form has been reported previously (Hill and Barth, 1977; Eastman and Ferguson, 1981; Hashimoto et al., 1981; Bryers, 1985; Munch et al., 1999; Masse and Droste, 2000; Miron et al., 2000; Ruel et al., 2002; Noykova et al., 2002; Sung and Santha, 2003; Mahmoud et al., 2004). However, dry-digestion of animal wastes has not been investigated. The anaerobic conversion of particulate substrates to biogases has been regarded as taking place in two distinct phases—an acid-production phase and an acid-consumption phase (Munch et al., 1999). The conversion process involves at least six independent, parallel, and sequential reactions, mediated by different groups of biomass under different environments (Gujer and Zehnder, 1983; Mata-Alvarez, 1987; Noykova et al., 2002). These reactions include: (1) anaerobic hydrolysis where, hydrolysable complex particulate organics such as insoluble cellulose and hemicellulose, are converted into monomers such as amino acids, sugars, and long-chain fatty acids; (2) fermentation where, amino acids and sugars are converted to volatile fatty acids; (3) acetogenesis where, longchained fatty acids are converted to acetate and hydrogen; (4) anaerobic oxidation where, intermediate products such as volatile fatty acids are converted to acetate and hydrogen; (5) aceticlastic methanogenesis where, acetate is converted to methane by acid-utilizing methanogens ; and (6) hydrogenotrophic methanogenesis where, hydrogen is converted to methane by hydrogen-utilizing methanogens. Most of the studies on anaerobic digestion of organic particulates in slurry form have concluded that hydrolysis is the rate-controlling step in the overall process (Eastman and Ferguson, 1981; Gossett and Belser, 1982; Pavlostathis and Giraldo-Gomez, 1991; Veeken et al., 2000; Vavilin et al., 2002). Therefore, attempts to improve the overall process have to focus on the hydrolysis reaction. 1.2. Anaerobic hydrolysis Even though Bryers (1985) and Mata-Alvarez (1989), among others, had pointed out that the mechanisms, stoichiometry, kinetics, and modeling of biological particulate hydrolysis had not been adequately studied, recent reports have addressed many of those areas. Most of the early studies, including the first anaerobic digestion model (ADM1) proposed by IWA, had focused mainly on fermentation and methane production (Ruel et al., 2002; Batstone et al., 2002). In one of the early studies of anaerobic hydrolysis of animal waste slurries, the kinetics of the process was assumed firstorder in acidogenic biomass (Hill and Barth, 1977). In a study of digestion of primary sludge, Eastman and Ferguson (1981) assumed first-order hydrolysis kinetics in the remaining particulate concentration. Recognizing the limited knowledge about the mechanisms and kinetics of this phase, Bryers 41 (2007) 323– 332 (1985) followed the same assumption as Eastman and Ferguson (1981). Mahmoud et al. (2004) have used a similar approach in their study of anaerobic stabilization of primary sludge. Noykova et al. (2002) assumed second-order kinetics in acidogenic biomass concentration and volatile solids concentration. Munch et al. (1999) have proposed a kinetic expression based on the observation from the Contois kinetic model that the hydrolysis rate is reduced when the biomass concentration is high, probably due to limited surface area causing mass transfer limitations. Their work proposed the hydrolysis rate to be proportional to the ratio of (particulate concentration  hydrolytic enzymes concentration) to acidogenic biomass concentration. This model is similar to that proposed in the IWA Activated sludge Model No. 2. Ruel et al. (2002) followed a similar approach, incorporating the concept of surface-limited reaction, with a maximum rate for anaerobic hydrolysis and a saturation coefficient, limited by the ratio of particulate concentration to acidogenic biomass concentration. In a review of the relevant literature up to 1990, Pavlostathis and Giraldo-Gomez (1991) found that most studies had used the first-order model to describe anaerobic hydrolysis of particulate wastes. Subsequent studies have affirmed this conclusion, but using different models for the hydrolysis process (Munch et al., 1999; Veeken et al., 2000; Ruel et al., 2002; and Mahmoud et al., 2004). We have evaluated three of the more common hydrolysis models—the first-order model; the second-order model; and the surface-limiting reaction model, for their suitability in describing hydrolysis-acidogenesis of cattle manure residues. We found that the twoparameter, surface-limiting reaction model followed the trend of the measured data more closely and fitted the measured data slightly better than the other two models (Myint and Nirmalakhandan, 2006). 1.3. Objectives of this study Our ongoing study builds upon the literature reports to develop a 2-phase leach-bed reactor system for dry digestion of cattle manure residues. One of the goals of our study is to optimize chemical oxygen demand (COD) generation by enhancing hydrolysis and acidogenesis and minimizing methanogenic activity by maintaining pH below 5.5 (Eastman and Ferguson, 1981; Yu et al., 2003) and heat treatment of seed sludge (Oh et al., 2003). The objectives of this paper are to develop a two-substrate, single-biomass model for the hydrolysis/acidogenesis phase and to validate it using batch experimental data. Also included in this paper are a sensitivity analysis of the model parameters, and a comparison of the parameters with values from the literature. 2. Modeling approach In our preliminary studies of dry digestion of cattle manure residues in a leach-bed reactor, substrate degradation curves typically exhibited two distinct segments. Based on the reports by Frigon et al. (2002), Ong et al. (2000), Orhon et al. (1999), Chandler and Jewell (1980) and Robbins et al. (1979), we ARTICLE IN PRESS WAT E R R E S E A R C H 325 41 (20 07) 32 3 – 332 propose that the observed 2-segment profile is due to two components of cattle manure, a readily degradable fraction (e.g. hemicellulose), and a slowly degradable fraction (e.g. cellulose). Accordingly, our model presumes different hydrolysis parameters and biokinetic parameters for the two components. A similar 2-segment profile can be observed in the data presented in a study of landfills (Fig. 2, Vavilin et al., 2002) where, the substrate was considered composed of cellulose and hemicellulose. The study by Vavilin et al. (2002), however, considered cellulose and hemicellulose together as a single substrate. 9 8 7 pH Reactor 3 6 Reactor 2 5 Reactor 1 4 3 0 2.1. Modeling hydrolysis Our model for hydrolysis incorporates two possible enzymatic mechanisms—one mediated by native organisms found in manure residues; and the other mediated either by external enzymes or by seed cultures, added to the reactor to augment the hydrolysis process. In the first mechanism, native organisms are assumed to grow as colonies attached to particles in the solid matrix. The rate of hydrolysis by these organisms is considered dependent on the surface area of the particles occupied by the organisms. When the surfaces of the particles are fully saturated with the organisms, the rate will be first-order with respect to particulate concentration; at low biomass concentrations when the surfaces are not fully occupied, the rate will be first-order with respect to biomass concentration. In the two-substrate, single-biomass model that we propose, hydrolysis step is modeled as surfacelimiting reaction as suggested by Munch et al. (1999) and Ruel et al. (2002). The second mechanism is modeled by an initial concentration-dependent conversion factor. A family of enzymes that act to hydrolyze cellulose has been identified as cellulase. Huang (1975) reported that cellulase secreted by Trichoderma viride served best in degrading insoluble cellulose to soluble sugars. According to Gaudy and Gaudy (1988), various strains of fungi produce cellulase that hydrolyzes cellulose to glucose, which in turn can be metabolized by fungi and many other microorganisms as well. Poulsen and Peterson (1985) have used crude cellulase from cellulolytic bacterium to hydrolyze carboxymethylcellulose. Heukelekian and Mueller (1958) used lipase enzyme to increase the hydrolysis rate of unsaturated lipid. In this study, we have used seed cultures to augment hydrolysis, with the express purpose of validating the proposed model. The hydrolysis process had been thought to be dependent upon pH, temperature, and concentration of total volatile fatty acids (VFA) or undissociated VFA (Veeken and Hamelers, 1999). In a recent report, Veeken et al. (2000) concluded that the hydrolysis rate of organic solid wastes of municipal origin was dependent on pH but not on total VFA or undissociated VFA. The dependence on pH was investigated in pH range of 5–7, and the following model for the hydrolysis rate constant k (day1) was reported based on linear regression analysis of eight data points (2 points at pH ¼ 5; 3 points at pH ¼ 6; and 3 points at pH ¼ 7 (Veeken et al., 2000)): k ¼ 0:048pH  0:172. (1) 10 20 30 40 Elapsed time [days] 50 60 Fig. 1 – Average pH in the liquid phase of Reactors 1–3. However, the goodness of fit of this model was weak, with r2 ¼ 0:471 and significance of p ¼ 0:06. Further, in the pH range of 5–6, an analysis of their data did not yield any statistically significant dependence (r2 ¼ 0:24, p ¼ 0:4). Since the pH in this study (Fig. 1) remained below 6.0, we did not consider the effect of pH on the hydrolysis rate. Based on the above suppositions, the rate of anaerobic hydrolysis of component, i, (i ¼ h for hemicellulose and i ¼ c for cellulose) can be expressed for a batch reactor as     Pi;0 dPi Pi =X ¼ K1i X  ai . (2) dt K1si þ ðPi =XÞ Ph;0 þ Pc;0 The parameters are defined in Appendix A. The first term on the right-hand side of Eq. (2) represents the first mechanism of hydrolysis discussed earlier. The second one is an optional term, which represents the second mechanism of augmentation of hydrolysis by a supplement (such as external enzymes or seed organisms). Here, ai is the solubilization rate of component i by the supplement, given by ai ¼ Ci SMR, where Ci is the specific COD conversion rate of the supplement (g COD/g supplement-day) and SMR is the supplement-to-manure ratio (g/g). The contribution by this term in the model can be turned off by setting SMR to zero if no supplement is added. In this study, we have used heattreated anaerobic sludge as supplement. The heat treatment was done following the procedure of Oh et al. (2003) to suppress only methanogenic activity. Thus, it is assumed that the dominant processes occurring in the reactor are hydrolysis and acidogenesis. 2.2. Modeling acidogenesis The acidogenic biomass is assumed to grow on the soluble products of hydrolysis consisting of a readily degradable component, hemicellulose; and a slowly degradable component, cellulose. The growth of acidogenic biomass is modeled as a single biomass (acidogens) feeding on two non-inhibitory substrates (soluble hemicellulose and soluble cellulose) with different biokinetic constants. According to this model (derived in Appendix B), the uptake rate of soluble cellulose, ARTICLE IN PRESS 326 WA T E R R E S E A R C H 41 (2007) 323– 332 Table 1 – Reactor contents Reactors Amount of cattle manure, wet (g) Moisture content of cattle manure (%) Amount of seed added, dry (g) Seed-to-manure ratio, SMR (g/g) Total water (L) Dry manure-to-liquid ratio, MLR (g/L) Initial concentration of biomass (g COD/g manure) Initial concentration of hemicellulose (g COD/g manure) Initial concentration of cellulose (g COD/g manure) Initial COD concentration hydrolyzed from hemicellulose (g COD/L) Initial COD concentration which hydrolyzed from cellulose (g COD/L) for example, would be given by !   dSc Sc X
¼ kc MLR: dt uptake Ksc 1 þ ðSh =Ksh Þ þ Sc (3) The rate of change of dissolved component i in the reactor (i ¼ h for hemicellulose and i ¼ c for cellulose) can be expressed for a batch reactor as   dSi dP dSi ¼  i MLR þ . (4) dt dt dt uptake Combining the uptake equations for the two components with the respective yield coefficients, and introducing the death rate, the net growth rate of acidogenic biomass can be expressed for a batch reactor as !   i¼h dX X dS ¼ (5) Yi  i  kd X. dt uptake dt i¼c 1 2 3 120 77.5 0.00 0.00 0.523 51.68 0.035 0.42 0.41 0.83 0.82 120 77.5 4.85 0.18 0.528 51.15 0.035 0.42 0.41 0.87 0.84 120 77.5 7.28 0.27 0.532 50.90 0.035 0.42 0.41 0.88 0.85 Treatment Plant. The heat treatment was done according to Oh et al. (2003), to suppress the growth of methanogens. The initial concentrations of acidogens, particulate hemicellulose, and particulate cellulose per gram of manure are summarized in Table 1. Initial concentration of acidogenic biomass was estimated following data reported in the literature (El-Mashad et al., 2005; Anderson et al., 2003; and Vavilin et al., 2002). Initial concentrations of dissolved COD, which resulted from hemicellulose and cellulose after adding water (measured following the procedure described by Miron et al. (2000) and Standard Method 5220D (APHA, AWWA, WEF, 1998) are also shown in Table 1. All the reactors were placed in a water bath maintained at 3772 1C. Samples from the liquid phase were withdrawn to measure pH and COD over the test period of 52 days. pH was measured using Cole-Parmer pH electrode probe, and COD was measured following the Standard Method 5220D (APHA, AWWA, WEF, 1998). All the state variables in the above equations, Pi, Si, and X are expressed in terms of COD and are defined in Appendix A. The model formulation involves four hydrolysis process parameters (K1c, K1h, K1sc, and K1sh) and four biokinetic parameters (kc, kh, Ksc, and Ksh). These eight parameters were established following a curve-fitting process using experimental data from one batch reactor run without any supplement. Experimental data from two batch reactors run with various doses of heated anaerobic sludge as supplement were then used to validate the model using the parameters estimated from another reactor. The pH in all the six reactors remained below 6.0 throughout the tests as shown in Fig. 1. Since methanogens have negligible activity at pH less than 6.0 (Eastman and Ferguson, 1981; Bryers, 1985), our results uphold the modeling assumption that the dominant processes occurring in the test reactors are hydrolysis and acidogenesis. 3. 4.1. Experimental approach Batch experiments were conducted in three 600 mL glass bottles (reactors), each in duplicate. Manure samples were collected at a nearby dairy farm from a pile under the separator that is used to separate the manure from manure slurry resulting from the cleaning of the farmhouses with running water. Average age of the samples in the pile was 2 days. Equal amounts of manure sample were placed in each of the six reactors and filled with the equal volumes of water. While Reactor 1 did not receive any external supplements, Reactors 2 and 3 were seeded with different amounts of heattreated anaerobic sludge from the Las Cruces Waste Water 4. Results and discussions Model parameters Yield coefficients for acidogenic growth on soluble hemicellulose and cellulose were established based on literature studies on similar substrates. Simeonov et al. (1996) reported 0.026 g COD of VSS/g COD for growth on cattle manure wastewater as substrate; Bryers, (1985) has reported 0.047 g COD of VSS/g COD with amino acids and sugars; Ruel et al. (2002) have reported 0.1 g COD of VSS/g COD with amino acid, sugars, and fatty acid. Based on a sensitivity analysis, we found that even when the yield was changed by a factor of two, the variation in the COD values predicted was less than 10% of the measured value. Based on these observations, the ARTICLE IN PRESS WAT E R R E S E A R C H 327 41 (20 07) 32 3 – 332 Table 2 – Model parameter output Model parameters Value at 37 1C Maximum rate of hydrolysis, K1i (1/day) Saturation constant for hydrolysis, K1si (–) Saturation constant for fermentation, Ksi (g COD/L) Maximum substrate utilization rate, ki (1/day) yield values were set at 0.084 and 0.042 g COD of VSS/g COD, respectively. Specific COD conversion rates, Ci, were determined by fitting predicted COD data to experimentally measured COD data from Reactor 2. Correlation coefficient 40.93 and po0.005 were used as criteria to establish the goodness of fit. This process yielded specific COD conversion rates to be 0.15 g COD/g sludge for hemicellulose, and 0.001 g COD/g sludge for cellulose. The four hydrolysis parameters (K1h, K1c, K1sh, and K1sc) and the four biokinetic parameters (kh, kc, Ksh, and Ksc), determined through curve fitting using measured COD data from Reactor 1, and validated with the laboratory data from Reactors 2 and 3, are listed in Table 2. The maximum hydrolysis rates, K1 established in our study for the surface-limiting model (1.4 day1 for hemicellulose and 0.09 day1 for cellulose) are lower than the value reported by Vavilin et al. (1996) for cattle manure (3.0 day1) and for cellulose (1.25 day1). Values recommended by Ruel et al. (2002) and Munch et al. (1999) for complex wastewaters (2.50 and 0.75 day1, respectively) are also comparable to our values. However, the hydrolysis saturation constants, K1s established by us (28 g COD/g COD for hemicellulose; and 1.5 g COD/g COD for cellulose) differ significantly from the values reported by Vavilin et al. (1996): 0.3 and 7.5 g COD/g COD for cattle manure and cellulose, respectively. Values reported by Ruel et al. (2002) (0.5 g COD/g COD) for proteins, carbohydrates, and lipids are lower as expected since these substrates are more readily degradable compared to hemicellulose or cellulose. Nonetheless, as shown later, K1sh and K1sc are the least sensitive of the eight parameters; even with an error of 750%, the error in cumulative dissolved COD predicted by the model was under 75%. Since a new biokinetic model (Eq. (3)) was used in this study, corresponding model parameters could not be found in the literature. The maximum growth rate of acidogens, found in our study was 0.151 day1 for soluble hemicellulose and 0.034 day1 for soluble cellulose. The literature on anaerobic processes in landfills considers the substrate to be primarily a mixture of cellulose and hemicellulose (63% of refuse weight, Vavilin et al., 2002). Our results are comparable to typical maximum growth rate of 0.12 day1 reported in that area (White et al., 2003). Ghaly et al. (2000) reported a slightly higher value of 0.319 day1 for dairy manure slurries. Other values reported in the literature for wastewaters containing fatty acids, sugars, and amino acids range from 0.27 to 0.7 day1 (from animal wastewater by Hill and Barth (1977); Hemicellulose Cellulose 1.470.13 28.072.52 15.071.35 1.870.16 0.0970.008 1.570.14 10079.0 0.8070.07 from cattle manure wastewater by Simeonov et al. (1996); from biomass by Bryers (1985); and from municipal wastewater by Ruel et al. (2002)). The values for the saturation constant Ks established in this study (15 and 100 g COD/L for hemicellulose and cellulose) are not within the range reported by Ghaly et al. (2000). Their study evaluated cattle manure slurries, assuming single substrate. Values in the range of 0.0022 to 2.0 g/L have been reported for amino acids and long chain fatty acids in soluble form (Munch et al., 1999). The wide variations in Ks may be attributed to the form of the substrate used in the respective studies; Ks values for substrates in particulate form may be expected to be higher than those for substrates in slurry or dissolved form. A summary of kinetic parameters found in the literature for complex organic wastes is presented in Table 3. Due to the differences in nature and form of the waste sources; reactor and test conditions; analytical procedures and models used; and, the methods of interpretation, it is difficult to rationalize and reconcile inter-laboratory results of process parameters. 4.2. Model validation COD values predicted by the model were compared against the measured data to validate the model. As shown in Fig. 2, model predictions using the parameters established in this study closely followed the temporal trend in the measured COD data from Reactor 1, which did not receive any supplement. Measured data from Reactors 2 and 3 that received seed supplement were used to further validate the model. The two variables that distinguish Reactors 2 and 3 from each other and from Reactor 1 are the seed-to-manure ratio and the manure-to-water ratio as shown in Table 1. Fig. 3 shows the agreement between the COD values predicted by the model and the measured COD values from the three reactors. The agreement between the predicted and measured COD values was statistically significant (po0.005), individually for the three reactors (with r2 ¼ 0.980, 0.933, and 0.872, respectively) as well as for the three reactors together (with overall r2 ¼ 0.91 at po0.002). This agreement validates the modeling approach as well as the eight model parameters established in the previous study. 4.3. Sensitivity analysis A sensitivity analysis exercise was conducted to identify the most sensitive parameters in the hydrolysis–acidogenesis ARTICLE IN PRESS 328 WA T E R R E S E A R C H 41 (2007) 323– 332 Table 3 – Summary of model parameters: this study vs. literature values Parameter This study at 37 1C Literature values Maximum rate of hydrolysis For hemicellulose, K1h (1/day) 1.4 0.0008–0.0016 for food and paper waste (Borzacconi et al., 1997); 0.04 from polysaccharides or crude cellulose (Ghosh et al., 1980); 0.06–0.24 for biowaste and 0.07–0.26 for food waste (Veeken and Hamelers, 1999). For cellulose, K1c (1/day) 0.09 0.13 for cellulose with seeded fungi at 34 1C (Woods and Malina, 1965) 0.54 for hemicellulose at 35 1C xylans, petosans (Ghosh et al., 1980) 2.50 for proteins, carbohydrates, lipid at 20 1C (Ruel et al., 2002); 0.75 for complex wastewaters (Munch et al., 1999). Saturation constant for hydrolysis, COD basis For hemicellulose, K1sh (g/g) For cellulose, K1sc (g/g) 28 1.5 0.50 for proteins, carbohydrates, and lipid (Ruel et al., 2002). 0.75 for cellulose 0.3 for manure (Vavilin et al., 1996). For hemicellulose, Ksh (g/L) 15 0.0085 for fatty acids, sugar, amino acid (Ruel et al., 2002); 0.02 for particulate biomass (Bryers, 1985); For cellulose, Ksc (g/L) 100 0.20 for particulate biomass (Siegrist et al., 1993); 2.00 for long chain fatty acids at 5 1C (Noykova et al., 2002). 24 (25 1C) and 25 (35 1C) for manure (Ghaly et al., 2000) Specific maximum growth rate for acidogens For hemicellulose, h (1/day) 0.151 0.4 with animal waste (Hill and Barth, 1977); 0.4 for sugar from cattle manure wastewater (Simeonov et al., 1996); For cellulose, c (1/day) 0.034 0.6 with particulate biomass (Bryers, 1985); 0.7 with fatty acid, sugar, amino acid (Ruel et al., 2002). Saturation constant for fermentation, COD basis 12 10 Measured COD [gm/L] Dissolved COD [gm/L] 10 8 6 4 8 6 4 Reactor 1a 2 2 Reactor 1b 0 0 0 10 20 30 40 Elapsed time [days] 50 0 60 Fig. 2 – Comparison of measured COD and fitted COD for Reactor 1. Data markers represent measured data (duplicates); curve represents fitted values. step, with the augmentation term switched off (i.e. SMR ¼ 0 in Eq. (2)). For each of the eight parameters, nine values were selected over a typical range, and nine simulations were run at each of those values to generate nine COD profiles. The nine profiles were combined to generate a mean profile with a spread of one standard deviation. A compilation of these mean profiles for each of the eight parameters is presented in Fig. 4, along with the measured COD data from Reactor 1. These plots indicate that the maximum hydrolysis rate 2 4 6 8 Fitted/predicted COD [gm/L] 10 12 Fig. 3 – Comparison between measured COD and predicted COD for Reactors 1–3. Data markers represent average of duplicate reactors. constant K1c for cellulose to be highly sensitive, followed by the biokinetic coefficients kh and Ksh for hemicellulose, to a lesser extent. A sensitivity coefficient, sp, for the parameter, p, defined as follows (Bernard et al., 2001) was calculated to quantify the average spread for each of the parameters. sp ¼ 1 tf Z tf 0 ðCODpþDp  CODp Þ dt, CODp (6) ARTICLE IN PRESS WAT E R R E S E A R C H 10 10 K 1c = 0.05 (0.01) 0.13 K 1h = 0.78 (0.16) 2.02 8 8 6 6 4 4 σ = 0.140 2 σ = 0.059 2 0 0 10 10 K 1sc = 0.83 (0.16) 2.17 K 1sh = 15.6 (3.0) 40.4 8 8 6 6 4 Dissolved COD in Reactor 1 [g/L] 329 41 (20 07) 32 3 – 332 4 σ = 0.022 2 σ = 0.031 2 0 0 10 10 k c = 0.44 (0.09) 1.16 8 8 6 6 4 k h = 1.0 (0.2) 2.6 4 σ = 0.042 2 σ = 0.061 2 0 0 10 10 K sc = 55 (11.0) 144 K sh = 8.3 (1.7) 21.7 8 8 6 6 4 4 σ = 0.034 2 σ = 0.063 2 0 0 0 10 20 30 40 50 0 60 Elapsed time [days] 10 20 30 40 50 60 Elapsed time [days] Fig. 4 – Sensitivity of dissolved COD in Reactor 1 to model parameters. Data markers represent average of measured COD from two duplicate reactors. where, tf is the test duration; CODp+Dp is the COD predicted by the model when the value of the parameter p is changed from the base value by an amount Dp; and CODp is the COD predicted by the model with the base value for the parameter p. Based on the sp values calculated (included in Fig. 4), the maximum hydrolysis rate constant for cellulose, K1c, can be seen to be the most sensitive parameter, with s ¼ 0.140. This is in agreement with the previous reports that hydrolysis is the rate-limiting step in the digestion of particulate substrates (Eastman and Ferguson, 1981; Veeken et al., 2000; Vavilin et al., 2002; Higuchi et al., 2005). As pointed out earlier, the least sensitive parameters are the hydrolysis saturation coefficients, K1sh and K1sc with s ¼ 0.031 and 0.022, respectively. 5. Conclusions A two-substrate, single biomass model-integrating hydrolysis and acidogenesis in anaerobic digestion of cattle manure was validated using batch experimental data. The model was based on the following premises: (a) cattle manure is composed of two distinct fractions—a readily degradable fraction (hemicellulose) and a slowly degradable fraction (cellulose); (b) the hydrolysis process is according to a surface-limiting reaction; and (c) the acidogenesis process is according to a two-substrate, single biomass system. The model parameters included two yield coefficients, four hydrolysis rate constants and four biokinetic coefficients. Predictions by the model using the parameters ARTICLE IN PRESS 330 WA T E R R E S E A R C H established in this study agreed well with the data measured under different conditions, with overall r2 of 0.91, with po0.002. Sensitivity analysis procedures indicated that the hydrolysis rate constant for cellulose fraction is the most sensitive parameter in the hydrolysis–acidogenesis of cattle manure. Since hydrolysis has been recognized as the rate-limiting step in the anaerobic digestion of complex particulate substrates, the findings of this study regarding readily degradable and slowly degradable fractions can be of value in designing, monitoring, analyzing, and optimizing the anaerobic gasification process. Acknowledgments Funding for this study was provided, in part, by US Environmental Protection Agency, Grant No. SU832485, and by the National Science Foundation, Contract No. BES-0607175. 41 (2007) 323– 332 k3 k1 E þ Sc 2 ESc ! E þ P k2 and k6 k4 E þ Sh 2 ESh ! E þ P. k5 Assuming that the reactions proceed under equilibrium concentrations of substrate-enzyme complex dðESc Þ ¼ 0 ¼ k1 ESc  k2 ESc  k3 ESc , dt dðESh Þ ¼ 0 ¼ k4 ESh  k5 ESh  k6 ESh . dt Hence, ESc ESc ¼ ½ðk2 þ k3 Þ=k1  Ksc ESc ¼ and Appendix A. Nomenclature Ci specific COD conversion rate of supplement (g COD/ g supplement) i component of manure, i ¼ h for hemicellulose; i ¼ c for cellulose kd ki decay rate of acidogens (1/day) maximum utilization rate of component i by acidogens (1/day) ESh ES ¼ h. ½ðk5 þ k6 Þ=k4  Ksh ESh ¼ From conservation of E, Eo ¼ E þ ESc þ ESh or E¼ E0 . 1 þ ðSc =Ksc Þ þ ðSh =Ksh Þ K1i K1si maximum rate of hydrolysis of component i (1/day) saturation coefficient for hydrolysis of component i (g COD/g COD) Hence, Ksi saturation coefficient for fermentation of dissolved component i (g COD/L) ESc ¼ MLR Pc,0 manure to liquid ratio (g manure/L) and Ph,0 Pi Pi,0 initial concentration of biodegradable particulates of cellulose i (g COD/g manure) initial concentration of biodegradable particulates of hemicellulose i (g COD/g manure) concentration of biodegradable particulates of component i (g COD/g manure) initial concentration of biodegradable particulates of component i (g COD/g manure) Si SMR concentration of dissolved component i (g COD/L) tf X Yi test duration (day) ai solubilization rate of component i by supplement (g COD/g manure-day) sp sensitivity coefficient for parameter p supplement (seed sludge) to manure ratio (g supplement/g manure) concentration of acidogenic biomass (g COD/g manure) growth yield of acidogens with dissolved component i as substrate (g COD/g COD) Appendix B. E0 Sh . Ksh ð1 þ ðSc =Ksc ÞÞ þ Sh ESh ¼ Now, the rate of uptake of Sc can be found from:  dSc dt  ¼  k1 ESc þ k2 ðESc Þ ¼ k3 ðESc Þ uptake ¼  k3 E0 Sc , Ksc ð1 þ ðSh =Ksh ÞÞ þ Sc which can be expressed as  dSc dt  ¼ uptake  m Sc X . Y c Ksc ð1 þ ðSh =Ksh ÞÞ þ Sc  Similarly  dSh dt  uptake   m Sh X ¼ . Y h Ksh ð1 þ ðSc =Ksc ÞÞ þ Sh Therefore, Derivation of Eq. (5) Consider single biomass utilizing two substrates, Sc and Sh with enzymatic interaction: E0 Sc Ksc ð1 þ ðSh =Ksh ÞÞ þ Sc  dX dt  growth ¼ Yc  dSc dt  þ Yh uptake   dSh , dt uptake ARTICLE IN PRESS WAT E R R E S E A R C H     dX dX ¼  kd X, dt dt growth !   i¼h dX X dS ¼ Yi  i  kd X. dt dt uptake i¼c R E F E R E N C E S APHA, AWWA, WEF, 1998. Standard Methods for the Examination of Water and Wastewater. American Public Health Association, Washington, DC, pp. 5–17. Anderson, K., Sallis, P., Uyanik, S., 2003. Anaerobic treatment processes. In: Mara, D., Horan, N. (Eds.), Handbook of Water and Wastewater Microbiology. 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