Ind. Eng. Chem. Res. 2008, 47, 5337–5345
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Volatile Fatty Acid Anaerobic Degradation: Kinetic Modeling with an Inoculum under Controlled Conditions Karina Boltes,* Pedro Leton, and Eloy Garcia-Calvo Departamento de Ingenierı´a Quı´mica, UniVersidad de Alcala´, Edificio de Ciencias, Campus UniVersitario, 28871 Alcala´ de Henares, Spain
Due to the multiple reactions that are involved, the mathematical description of anaerobic degradation of organic matter is normally complicated. Several efforts have been made for the development of the ADM1 model, that cover the major processes involved in complex organic substrate conversion. This model application requires a large number of constants and coefficients, which were proposed, reviewed the information available at the time of their publication. The more recent published papers about ADM1 model application report a necessary revision of the kinetic parameters used for volatile fatty acid (VFA) degradation. This work presents a kinetic study of VFA anaerobic degradation performed in batch and continuous stirred tank reactor. Acetic, propionic, and butyric acids (mixed in a ratio 2:1:1 COD basis) and acetic acid only were used as substrate. The biomass for kinetics assays was previously produced in a codigestion process using pig manure mixed with sewage sludge obtained from anaerobic municipal digester. The inoculum build-up and maintenance were conducted in a laboratory stirred tank digester, under controlled conditions to avoid any variability of the resulting parameters obtained. Moreover, the black box approximation was applied in order to reduce the number of parameters for a complete description. A set of lineal relations was obtained to estimate methane, carbon dioxide, and mixed biomass production rates, from VFA degradation rates only. Finally, a good simulation of experimental data was obtained for VFAs, biomass, methane, and carbon dioxide both in continuous and batch operation modes. 1. Introduction The anaerobic degradation of organic matter to methane is a highly complex process. On the microbial level, the process requires the combined and coordinated action of a variety of distinct bacteria. The reaction scheme proposed by Gujer and Zhender1 includes the following processes: hydrolysis of degradable particulate organic matter, fermentation of amino acids and sugars, oxidation of long chain fatty acids, oxidation of volatile fatty acids (VFAs), and methanogenesis. The more relevant characteristic of this biological system is that the metabolism of each group of bacteria is dependent on the others, and consequently, the degradation involves multiple reactions in series and/or in parallel catalyzed by different groups of microorganisms. The volatile fatty acid (VFA) conversion is assumed to be the most important step of the global process for degradation of organic matter to methane.2 Since 70% of the methane produced comes from acetic acid degradation, long chain fatty acids need to be converted to acetic acid before they can be converted to methane. The microbial groups that degraded fatty acids, acetate and propionate, are slowly growing bacteria and are therefore important for digester stability.3 In this way, the inhibition processes that are involved in acetogenesis and methanogenesis are very recognized. There are several studies published about mathematical modeling of organic matter anaerobic degradation.4–7 Even a standardized reference model, namely, ADM1, has been established by the IWA Task Group to provide a unified basis for anaerobic digestion modeling.8 The ADM1 model is the more accepted and valued one because of its possible applicability for different types of bioreactors and operational conditions. In general, the application of this model requires a great number of kinetics parameters to describe the conversion rates of * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +34-918856422. Fax: +34-918855088.
different substrates; the growth and endogenous decay of each trophic group of bacteria as well as the corresponding yield coefficient for each microorganism on the substrate are needed. All of these parameters were obtained from an extensive bibliography revision of the experimental data available at that time. The use of the ADM1 model to describe an anaerobic degradation process with accuracy is normally complicated, and only a few studies exist in implementing the ADM1 model for experimental data simulation.9–11 The most recent published works in which the ADM1 model was applied report a necessary revision of the kinetic parameters used for volatile fatty acid (VFA) degradation. It would appear that the inhibition functions associated with low pH values tend to overestimate the impact of pH on biokinetic rates for acid-consuming bacteria.9 In addition, the kinetic parameters proposed in the ADM1 model for propionate and acetate utilization, identified as the most sensitive, were optimized manually for better data simulation;10 therefore, it is evident that these kinetic constants must be revised. In other cases, the decay rate initially set for mesophilic UASB reactors was increased by a factor of 5, resulting in more realistic data like those reported by Batstone et al.11 The objective of this study is to contribute with a set of kinetic constants for the anaerobic digestion modeling and simulation. We present a kinetic study of VFA degradation to methane using an inoculum developed and maintained in a laboratory reactor under controlled conditions. A mixture of acetic acid (HAc), propionic acid (HPr), and butyric acid (HBut) was used in a ratio of 2:1:1 (chemical oxygen demand (COD) basis) as the carbon source. In addition, only acetic acid was used in another set of assays as the carbon source for methane production. The inoculum build-up was performed in a previous stage using a stirred tank reactor. Pig manure and sludge were collected from a municipal sludge anaerobic digester. Manure contains a high content of proteins and urea, which upon degradation release ammonia, a potent inhibitor of aceticlastic
10.1021/ie071583p CCC: $40.75 2008 American Chemical Society Published on Web 07/02/2008
5338 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008
methanogens.12 Moreover, excessive VFA accumulation can inhibit methanogenesis, as high hydrogen levels can inhibit propionate and butyrate degrading acetogens.13 The original manure and sludge mix was prepared to adjust the solids, acids, and soluble chemical oxygen demand (COD) levels in order to avoid high inhibition processes. For several months, this bioreactor was followed by means of a methanogenic activity test, VFA concentration, suspended solids, and biogas production. The black box approximation was applied as a tool to reduce the number of parameters for a complete system description. From the black box application, it was found that it is necessary to define only four rate conversion equations for the estimation of the others. Principally, the most important is the methane formation rate. The kinetic constants for butyrate, propionate, and acetate degradation under mesophilic conditions were obtained in continuous and batch assays. Moreover, the decay constant of the mixed biomass was then calculated. Finally, the experimental data of VFA and methane were simulated for the different operation modes, using the kinetic constant presented and the lineal relation obtained from the black box description. 2. Black Box Aproximation The most important aspect of microbial systems is that they are open systems because microorganisms exchange mass and energy with their environment. In microbial processes, we are faced with an enormous complexity which could lead to countless model parameters. Therefore, there is a need for approximation to obtain a mathematical model with minimal complexity. The main approximation applied in engineering is the macroscopic approximation. Here, the system can be considered to contain many so-called elementary volumes, which in the case of a bioreactor could be 1 L of culture volume. This elementary volume can be described by their average value, which is a system property or the so-called macroscopic properties. The properties denominated as intensive ones (pressure, temperature) cannot be added up, but the extensive properties (like mass and energy) are related to the system quantities and can be added or can make balances. For the full system definition in a constant volume system, the establishment of the kinetics of all chemical compounds as well as the transfer over the system boundary are necessary. However, in the case of a microbial system, in which there are almost 800 chemical compounds (intra- and extracellular) involved, a mathematical model containing a large number of parameters (about 1600) can result. Considering the extremely large complexity described, the need of minimization of model parameters can be satisfied by the following:14 -The assumption of the pseudostationary state of intracellular compounds. Because there is no mass transfer over the cell membrane, their concentration is generally very low and almost constant due to the fact that microorganisms tend to maintain a constant internal environment. This is the so-called black box approach. -The definition of the relevant compounds only. This means that one can limit the chemical compounds to those which cross the cellular membrane, at least: N-source, C-source, water, and biomass. -Application of conservation principles: conservation of mass, elements, electric charge, and energy (1st law of thermodynamics). -Definition of a reaction scheme. If knowledge of metabolic pathways exists, it is possible to specify some reactions like anabolism, polymerization, oxidation of electron donor, and ATP
Table 1. Black Box Description of VFAs Anaerobic Degradation
relevant compound biomass acetic acid (electron donor) propionic acid (electron donor) butyric acid (electron donor) methane (product) ammonium (nitrogen source) water protons bicarbonate (electron acceptor)
elemental composition
net conversion rate
CH1.4O0.4N0.2 CH2O CH3O2/3 CH4O1/2 CH4 NH4+ H2O H+ HCO3-
rAx rAAc rAPr rABu rAm rAn rAw rAp rAc
Scheme 1. General Form of System Matrices
production by electron transfer. In this paper, the system was modeling using the black box approximation, defining a set of relevant compounds, and applying conservation principles for each one. The use of metabolic information is difficult because biomass is a mixed culture, formed by different strains of methanogens. The most important simplification that was introduced is the consideration of the mixed anaerobic biomass as another relevant component of the reaction system with a fixed elemental composition. Due to this, the cells can be considered as a black box, exchanging only heat and compounds such as substrate and products with the environments and dissipating Gibbs energy, in the so-called black box thermodynamic approximation. Here, the pseudostationary state of intracellular compounds was adopted and only the exchangeable ones are considered.15 These exchangeable compounds are the relevant denominated ones, and the first step is the identification of them. 2.1. System Definition. In the anaerobic VFA mixture degradation, we consider that there are three carbon sources in a fixed proportion; methane is the only final product of catabolism, because carbon dioxide is considered as the final electron acceptor. The nitrogen source was NH4+ added in the form of NH4Cl. The elemental composition of anaerobic biomass can be represented by C5H7O2N.16 A detailed black box definition of the anaerobic VFA consumption system is summarized in Table 1. 2.2. Derivation of the Lineal Relations. A set of lineal relations between the net conversion rates of relevant compounds was obtained from elements, electrical charge, and Gibbs energy balances.17,18 These equations allow estimation of dependent rates, i.e., methane or biomass formation, as a function of those selected as independent (VFA conversion and dissipated Gibbs energy). Calculation of the lineal conservation relations is simplified remarkably by use of lineal algebra from the definition of a system of matrices and vectors. All of the information for the black box description is contained in the elemental composition matrix E. In addition, matrix M contains electrical charge and Gibbs energy balances. Hence, matrix E is a submatrix of M, as shown in Scheme 1. The advantage of matrix M is evident because it contains the Gibbs energy dissipation rate (Ds01) that can be estimated by a simple correlation proposed by Heijnen and van Dijken.18
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The lineal relations were obtained from matrix M and the net conversion rate column vector r, applying the following conservation equation. The vector r includes the net conversion rates of all relevant compounds and the Gibbs energy dissipation rate too. M×r)0 (1) The right definition of system matrices and a correct choice of measured rate vector are essential for the successful use of lineal relations. For this reason, we use a systematic procedure proposed by Noorman et al.15 that involves the application of three tests: the independency, consistency, and observability tests. For the Gibbs energy balances, the values given by Roels17 for the free energy of formation of relevant compounds were used. See Table 1 for elemental composition and rate definition. r ) [rAAc, rAPr, rABu, rAx, rAn, rAc, rAp, rAw, rAm, Ds01] C H O M) N electrical charge λ
rAAc rAPr
rABu
rAx rAn rAc
rAp rAw
1 2 1 0 0
1 2 1 /2 0 0
1 1.4 0.4 0.2 0
0 1 0 0 1
1 2 2 /3 0 0
0 4 0 1 1
1 1 3 0 -1
0 2 1 0 0
rAm Ds01 1 0 4 0 0 0 0 0 0 0
-186 -120.33 -94.5 -67 -80 -588 -40 -238 -51 1
The system results in four degrees of freedom, so four independent rates are necessary to estimate the others. If individual VFA conversions and Gibbs energy dissipation (Ds01) were chosen as independent, the next lineal relations (in C-mol · L-1 h-1) result: rAx ) -1.845rAAc - 1.725rAPr - 1.290rABu - (1/18.7)Ds01 rAn ) 0.369rAAc + 0.345rAPr + 0.25rABu + (1/93.5)Ds01 rAc ) 0.422rAAc + 0.446rAPr + 0.27rABu + (1/37.4)Ds01 rAp ) 0.053rAAc + 0.101rAPr + 0.012rABu + (1/62.3)Ds01 rAw ) -1.529rAAc - 1.314rAPr - 0.794rABu - (1/17)Ds01 rAm ) 0.422rAAc + 0.279rAPr + 0.020rABu + (1/37.4)Ds01
(2)
Ds01 is the dissipated Gibbs energy and can be estimated (per C-mol of biomass produced) using the next correlation.18 Ds01/rAx ) 200 + 18(6 - C)1.8 + exp[{(3.8 - γs)2}0.16(3.6 + 0.4C)] (3) where C is the number of carbon atoms and γs is the degree of reduction of carbon source. For the application of eq 3, we used average values for C and γs based on the proportion of each volatile acid present in the mixture and their number of carbon atoms. For an acid distribution of HAc/HPr/HBut (2:1:1 COD basis), the result is C ) 2.67, γs ) 4.376, and Ds01/rAx ) 406.96 kJ/C-mol. Using the calculated value of Ds01/rAx, a major simplification was obtained for the lineal relations (eq 2), as can be seen next: rAx ) -0.081rAAc - 0.076rAPr - 0.057rABu rAn ) 0.369rAAc + 0.345rAPr + 0.25rABu + 4.352rAx rAc ) 0.422rAAc + 0.446rAPr + 0.27rABu + 10.881rAx rAp ) 0.053rAAc + 0.101rAPr + 0.012rABu + 6.532rAx rAw ) -1.529rAAc - 1.314rAPr - 0.794rABu - 23.939rAx rAm ) 0.422rAAc + 0.279rAPr + 0.020rABu + 10.881rAx
(4)
With these lineal relations, it is possible to estimate biomass, methane, and carbon dioxide production rates, and some not
usually measured as nitrogen source consumption, from VFA net conversion rates only. The required kinetic parameters to define VFA conversion rates (acetic, propionic, and butyric acids) were obtained in a kinetic study in continuous and batch modes. 3. Experimental Procedure 3.1. Inoculum Build-up. Pig manure collected in a pig farm next to the city of Alcala de Henares and sludge from an anaerobic digester of a wastewater municipal plant placed in the same city was used to produce the anaerobic mixed biomass that was later inoculated in reactors for kinetic assays. A high concentration of long chain fatty acids (LCFAs) and ammonia can be generated in hydrolysis of lipids and protein fermentation steps, respectively. It is recognized that both of them produce inhibition of acetogens and methanogens.12,13 For this reason, the pig manure was pretreated prior to the codigestion. First, the manure was diluted with distilled water in 1:4 volume proportions and agitated vigorously; then, it was filtrated with 1 mm pore size metallic mesh in order to remove the major solid contents for hydrolysis enhancement.19,20 To reduce the long chain fatty acids and ammonia concentration, the reaction volume of 5 L was prepared as follows: 20% v/v of the pig manure filtrate fraction, 10% v/v of the anaerobic sludge, and water. The anaerobic codigestion was conducted, as previously indicated, in a 5 L stirred tank reactor placed in a room with temperature controlled at 37 °C. pH was adjusted daily (6.8-7.2) by adding 0.5 M HCl or NaOH. For four months, the reactor was followed by measuring the total and volatile solids, COD, VFA concentrations, and gas production. Once the digester showed a decrease in methane generation along with constant values of methanogenic activity, a small fraction of reactor content was separated and fresh media with 5 g/L of glucose and nutrients were added. This procedure was repeated for several months, measuring methanogenic activity, VFA, COD, and solid contents in each new step of fresh synthetic media addition. The culture medium used was an Evans minimal medium modification21 that includes chlorine salts of Fe2+, Co2+, and Ni2+. Methanogenic Activity. The anaerobic biomass evolution was followed by a methanogenic activity test using a VFA mixture (HAc, HPr, and HBut) as substrate, according to the method proposed by Soto et al.22 The medium contains 2 g of COD/L, 6 g of VSS/L, Na2S · 9H2O (0.1 mg/L), and NaHCO3 (1000 mg/L). Tests were conducted by triplicate using 100 mL sealed Erlenmeyer flasks in an orbital shaker at 200 rpm. A blank test with no carbon source addition completes the series. Temperature was maintained at 37 °C, and pH was adjusted to 7 initially. The methanogenic activity was evaluated by measuring the methane generation rate in the free volume of the T-flask. Methane accumulated was expressed as grams of COD generated per grams of VSS (biomass) and per day. The gas was sampling manually, and the methane content was determined by gas chromatography coupled by a flame ionization detector according to the method described in part 3.3. Once the activity test has shown acceptable and constant values, the biomass maintained was transferred to the reactor for kinetic assays. 3.2. Substrate and Reactor for Kinetic Studies. The kinetic studies were conducted in batch and continuous operation modes at a controlled temperature of 37 °C. For continuous feeding, a 2 L stirred tank reactor equipped with a sedimentation vessel for biomass recirculation was used. The reactor, operated at a
5340 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 Scheme 2. Experimental Apparatusa
a A, feed vessel; B, pump; C, pH controller; E, feed; F, refrigeration system; G, gas exit; H, acid vessel; K, reactor; L, liquid exit; M, stirrer motor; OH, basic vessel; P, gas measurement device; R, biomass recirculation; S, mixed liquor exit; T, gas sampling port.
constant hydraulic retention time (HRT) of 9.12 days, was fed with increasing organic loading rate from 0.087 to 0.634 g of COD/g of VSS · d. The anaerobic bioreactor was connected to a gas measurement device that permits sampling, according to Scheme 2. Batch assays was performed in a 2 L stirred tank reactor, with a gas measurement device similar to that used in continuous operation. As substrate, a mixture of HAc/HPr/HBut at an initial concentration varying from 1 to 4.2 g of total COD/L was used. The initial biomass concentration was always adjusted to around 5 g of VSS/L. In all of the kinetic assays performed at reactor scale, the pH was automatically controlled in the range previously indicated. 3.3. Analytical Methods. The analysis of VFAs was carried out by gas chromatography (GC) equipped with a flame ionization detector (FID). A 1 µL portion of a filtered sample was injected onto a 30 m NUKOL capillary column (ID 0.25 mm, film 0.25 µm) with nitrogen as the carrier gas. The temperature program includes a hold at 60 °C for 2 min followed by an initial ramp rate of 8 °C · min-1 up to 80 °C, a next ramp at a rate of 21 °C · min-1 up to 160 °C, and a final warming up to 180 °C at a rate of 5 °C · min-1. The final temperature was maintained by 4 min for purge. Both injector and detector worked at 200 °C. In the same way, the gas composition was analyzed by GC with a thermal conductivity detector (TCD). A packed column PORAPAK-N 80/100 (1/8 in. × 4.5 m) was used with helium as the carrier gas. The column temperature was programmed as follows: initial temperature 40 °C (2 min) and a ramp up to 150 °C at a rate of 20 °C · min-1. The TCD temperature was maintained at 120 °C (filament 180 °C). A sample volume of 0.4 mL was manually injected. The mixed liquor volatile suspended solid (VSS) was used as biomass concentrations, which was measured according to section 2540 E in Standard Methods. In addition, total solids and total volatile solids were obtained as the solid remaining after warming at 105 or 550 °C. The soluble chemical oxygen demand (COD) was also measured according to section 5220 D in Standard Methods.
4. Results and Discussion 4.1. Inoculum Build-up. The manure and sludge codigestion was initiated with 10 g /L of soluble COD, 24 g/L of total solid, and 17 g/L of volatile solid concentration in the culture broth. pH was adjusted to near neutral by addition of sodium bicarbonate in the reactor media. Figure 1 shows the evolution of these variables over a period of 2 months as well as the gas production. The results indicate a reduction of the total and volatile solid content with methane production at almost neutral pH. Acetate was the major acid component of the reactor content in this first stage, followed by valeric and propionic acids, both at low levels. Results obtained from the methanogenic activity tests show an increment of activity over the time during the first 2 months, followed by maintenance of the methanogenic activity value near 0.30 g of CH4-COD/g of VSS · d from the third month of digestion (see Figure 1). The methanogenic activity measured over the VFA mixture indicated that the biomass is an active consortium that can be used for kinetic assays. The microscopic examination of the biomass was conducted by electronic microscopy. A sample of the liquid content of the reactor was filtered and fixed for dehydration. Figure 2 shows the morphologic forms found in the bioreactor prior to the use of this biomass as inoculum. Here, it is evident that there are two types of cocci and two types of rods. The biomass produced was maintained as previously indicated during a period of six months; during this time, the inoculum was used both for batch test assays and for the start-up of the continuous feeding reactor. 4.2. Kinetic Study. For a bioreactor with biomass recycling in continuous operation, a difference exists for the retention time of the liquid and solid biomass. In these systems, the specific substrate consumption rate can be expressed by q)
SF - SE X·HRT
(5)
where SF and SE are the substrate concentration in the feed and effluent of the system as total soluble COD, X is the mixed biomass concentration in the reactor at steady state, and HRT is the hydraulic retention time. The sludge age (θ), which is defined as the ratio of the biomass content of the reactor to the net growth, can be calculated by the next expression θ)
X·V XE·QE
(6)
Here, V is the reaction volume, QE is the exit flow rate, and X and XE are the biomass concentration in the reactor and liquid exit (L in Scheme 2), respectively. Equation 6 was used for sludge age estimation due to fact that the residence time of the sludge in the settle is very short compared with the reactor residence time. In addition, for steady state conditions, the net growth of biomass was assumed to be equal to the biomass exit from the system, because there is no biomass inlet in feed flow and purge was not done. On the other hand, the substrate consumption and the biomass production are related through the biomass yield on substrate (YXS). q)
Kd 1 1 + YXS θ YXS
(7)
For the experimental system with biomass recycling, the previous equation was used to obtain the mixed biomass decay
Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5341
Figure 1. Evolution of parameters during the inoculum production step.
Figure 2. Photographs taken of the biomass in the 5 L stirred tank (inoculum reactor).
constant (Kd) and the yield YXS, considering that, in the steady state, the sludge age is equal to the inverse of the biomass specific growth rate (µ). Figure 3 shows the experimental data of methane production, effluent COD, and biomass concentration during continuous feeding at a hydraulic retention time (HRT) of 9.12 days and at a feed substrate concentration varying from 2.2 to 18 g of COD/L. In each run and after the increment of the organic loading, the digester was operated until the stationary state was reached. Analysis of Figure 3 shows that an increment of organic loading at 0.634 g of COD/g of VSS · d produces a reduction of methane generation rate and an accumulation of effluent COD, principally due to acetic and propionic acids (data not shown). Although the HAc, HPr, and HBut contents in the feeding were
in a ratio of 2:1:1, respectively, the ratio of these acids in the effluents was different at high organic loading. High acetic acid levels produce results in inhibition processes usually detected in anaerobic reactors, like product inhibition for acetogenesis from propionic acid and substrate inhibition for methanogenesis from acetic acid. We did not detect process inhibition in continuous operation until reactor failure, so from this data series, the Monod kinetics parameters, maximum specific rate of consumption, and saturation constant were obtained for individual VFA consumption and total COD elimination. In addition, mixed biomass yield on substrate expressed as the sum of VFA, YX/S, was calculated. The obtained kinetic parameters for each volatile acid are summarized in Table 2.
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Moreover, the acetic acid consumption is inhibited by high substrate concentration. This process was usually described by the Haldane equation.24,25 Here, the specific rate of HAc consumption (qa) can be calculated by eq 9. In this work, the inhibition constant, Kia, was obtained by nonlineal fitting of the experimental data from batch assays, considering that the Monod parameters previously obtained in continuous reactor operation (qma and KMa) correspond to the values when no inhibition was detected. qa ) qma
Figure 3. Effluent COD (SE), biomass concentration (X), and methane production (CH4) with specific organic loading, q, (mg of COD/mg of VSS · d).
Moreover, the kinetic parameters for mixed biomass were obtained by fitting the steady state values for specific substrate consumption rate (q) and sludge age (θ) according to eq 7. The resulting biomass yield over the mixed substrate, expressed as the sum of VFA concentration in COD basis, was 0.116 g of VSS/g of COD, with a decay constant, Kd, of 0.0054 d-1. Due to the fact that there was not inhibition detected in continuous feeding, the more relevant inhibition processes mentioned above were studied in batch assays. A modification of the generalized form of Monod kinetics proposed by Han and Levenspield23 to account for all kinds of product inhibition was used to analyze the propionic and butyric acid degradation. This model assumes that there exists a critical inhibitor concentration above which the processes stop, and that the constants of the Monod equation are functions of this limiting inhibitor concentration. The next expression is proposed for both HPr and HBut consumption:
(
qi ) qmi 1 -
HAc HAc*
S
n
) S+K
(8) HAc m HAc* Here, the specific rate of substrate consumption (qi) depends on the inhibitor concentration (HAc). HAc* represents the critical inhibitor concentration above which reaction stops, qmi is the maximum specific rate of substrate consumption, and KMi is the Monod saturation constant. In addition, n and m are other kinetic parameters to calculate. This equation can account for several common patterns of inhibition processes. From analysis of the data obtained in batch assays with different initial HAc concentrations, we found that the maximum specific rate of HPr consumption (qmp) was almost constant and similar to that obtained from reactor continuous operation, whereas the saturation constant obtained (KMp) increased with the acetic acid concentration. This means that acetic acid acts as a competitive inhibitor, parameter n ) 0 in eq 8. Using the kinetic parameters for the Monod equation from continuous operation (where no inhibition was detected), the kinetic parameters m and HAc* for propionic acid degradation were estimated. On the other hand, the analysis of the data for HBut degradation obtained in batch assays confirms the kinetics parameters resulting from continuous operation, where the Monod equation is valid.
(
Mi
1-
)
HAc
( )
HAc2 KMa + HAc + Kia
(9)
Table 2 contains all of the kinetic parameters obtained for both inhibition processes studied. The kinetics parameters reported in the literature are quite different. These differences are probably due to the inoculum, system configurations, and operation modes employed. The biomass used as inoculum affects the kinetic parameters obtained from the type of microorganism that predominates in a mixed culture. The influence of the retention time of the solids as well as organic loading on the population is well-known for the anaerobic systems. These operation parameters can determine the type of methanogens that is dominant in the culture: Methanotrix at long SRT and low substrate loading or Methanosarcina at short SRT and high substrate loading, like it was shown by Vasiliev and Vavilin.26 Pavlostathis and Giraldo-Gomez27 reviewed the Monod kinetic parameters for the anaerobic process; from this paper, it is easy to note the great variability of the same parameter. For acetate degradation: KM ) 11-421 mg of COD/L, µmax ) 0.08-0.7 1/days, and YXS ) 0.01-0.045 g of VSS/g of COD. For other VFA: KM ) 12-500 mg of COD/L, µmax ) 0.13-1.2 1/days, and YXS ) 0.025-0.047 g of VSS/g of COD. Anyway, the yield on substrate for the mixed biomass (YX/S) obtained in this study as well the Monod parameters are in the range previously indicated. With respect to the inhibition modeling, we found much more variability considering the type of inhibition as well as the form in which the inhibitor concentration was considered. For example, for HAc degradation, in the majority of published works, the total acetate (ionized and unionized forms) was considered as substrate,28,29 while, in others, only the unionized acetate was assumed as the substrate.30,31 In the ADM1 model, all of the anaerobic oxidation processes are subject to inhibition by hydrogen or free ammonia accumulations, as well as due to extreme pH. These effects on the conversion rate were implemented by introducing in the Monod type rate velocity equation several multiplier terms that reflect noncompetitive inhibition. In general, the model tends to overpredict VFA concentrations maybe due to the form in which the inhibition is treated. In this work, the product inhibition was treated in a similar way, but the substrate inhibition was best accounted for using a Haldane type expression, considering total acid concentration (ionized and unionized forms). Simulations of the experimental data of VFA consumption are obtained using the kinetic parameters resulting in the kinetic study presented. Also, the next stoichiometric coefficients for acetic acid production were assumed: 0.802 g of COD HAc/g of COD HBut and 0.575 g of COD HAc/g of COD HPr. Figure 4 shows the experimental (as symbols) and predicted values (as lines) of each acid in two batch assays with 2682 and 5351 mg of COD/L as initial VFA total concentration. In these cases,
Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008 5343 Table 2. Kinetic Parameters Obtained for Acetic, Propionic, and Butyric Acids continuous feeding
batch assays
substrate
qm (g of COD/g of VSS · d)
KM (g of COD/L)
Kia (g of COD/L)
HAc HPr HBut soluble COD
0.682 0.082 0.239 0.751
0.892 0.426 0.055 2.077
0.667
a
nb (g of COD/g of VSS · d)
mb (g of COD/L)
I*c (g of COD/L)
0 0
-6.405 0
4.633
Haldane model. b Monod modified. c Acetic acid concentration.
Figure 4. Experimental and predicted values for acetic (9), propionic (∆), and butyric (1) acids in two batch assays with the next total initial concentration: (A) 2682 mg of COD/L; (B) 5351 mg of COD/L.
Figure 5. Experimental and predicted values for acetic (9), propionic (∆), and butyric (1) acids in two continuous feedings with the next organic loading rate: (A) 0.151 mg of COD/mg of VSS · L; (B) 0.634 mg of COD/mg of VSS · L.
the biomass concentration (VSS concentration) was measured only at the initial and final time of reaction due to the high volumes that are necessary for their determination. Experimentally, we probed that the VSS content was almost constant in batch assays, probably due to the short time of reaction; for this reason, the profiles of VFA were predicted using the kinetic expressions 8 and 9. From Figure 4, it is verified that all of the VFAs measured can be simulated acceptably. In addition, propionic acid is the most resistant to degradation, remaining in fermentation broth at low levels starting off with lower concentration of the inhibitor (HAc). On the other hand, Figure 5 presents the experimental and predicted values for individual VFA in two continuous feedings
with an organic loading rate of 0.151 and 0.634 mg of COD/ mg of VSS · L. Here, the deviations from predicted values at the initial time of organic loading changes are greater, but the steady state concentration can be predicted accurately. 4.3. Application of Lineal Relations. According to the described methodology, we can estimate biomass growth rates in all experiments conducted in continuous operation mode, using the correspondent lineal relation (set of eq 4) and the kinetic parameters obtained (Table 2). The net growth rate was calculated as the growth on the mixed substrate minus the decay rate. In the same way, methane production was simulated, with the correspondent linear relation obtained, as a function of each
5344 Ind. Eng. Chem. Res., Vol. 47, No. 15, 2008
Figure 6. Experimental and predicted values for acetic acid (0), biomass (O), and methane ([) in two continuous feedings with the next organic loading rate: (A) 0.087 mg of COD/mg of VSS · d; (B) 0.151 mg of COD/mg of VSS · d.
fatty acid conversion rate and biomass production as well. Here, we suppose that all of the hydrogen produced from oxidation of propionic and butyric acids was converted for methane. Figure 6 shows the experimental and predicted values obtained in continuous operation for biomass and methane production. The main differences in methane estimation are observed at an organic loading rate of 0.151 mg of COD/mg of VSS · L and at the first moments of organic loading change, but this is probably due to errors in gas collection. In a general way, in accordance with Figure 4B, we observed that the acetic acid tends to be accumulated preferably to propionic and butyric acids. This situation indicates that the higher VFAs continue producing acetic acids, although the methanogenic step was inhibited. A similar behavior was reported by Lin et al.32 Finally, the estimation of dependent velocities in the anaerobic VFA degrading system could be down using the lineal relationships derived by the black box description. This is especially useful to estimate methane generation and biomass production, but it is also possible to calculate some rates not usually measured, namely, N-source consumption. 5. Conclusions The methodology applied to approach the modeling of the anaerobic degradation of VFAs in a more simplified manner was successfully used for the modeling of many aerobic microbial processes, but it always was used for pure cultures of microorganisms growing on a pure substrate. The more relevant results presented in this work can be summarized as follows: -The application of the black box description permits simplifying the kinetic study for the system, because it is necessary to provide only four kinetic expressions to describe the VFA comsumption, biomass production, and methane generation. The lineal relations obtained in this study are suitable for VFA degradation only, due to the fact that it is based on an important parameter, namely, Gibbs energy dissipation per C-mol of biomass produced (Ds01/rAX), that
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ReceiVed for reView November 21, 2007 ReVised manuscript receiVed May 7, 2008 Accepted May 8, 2008 IE071583P
