# Effectiveness Factors in Anaerobic Biofilms A Pseudoanalytical Equation for Parallel and Consecutive Reactions.

код для вставкиСкачатьEffectiveness Factors in Anaerobic Biofilms: A Pseudoanalytical Equation for Parallel and Consecutive Reactions C.R. Escalera', A. Maezawa', S. Uchida'. and M. Kuroda3 'Department of Chemical Engineering, 2Graduate of Electronics Science and Technology, Shizuoka University, 3-5- I Johoku, Hamamatsu, 432, Japan Department of Civil Engineering, Gunma University, 1-5- I Tenjincho, Kiryu, Gunma, 376, Japan The effectiveness factors for an anaerobic biofilm in which a parallel-consecutive reaction occurs were studied theoretically. A pseudo-analytical equation to represent the effectiveness factors (Efi)was developed as a function of a dimensionless parameter called the overall biofilm property value (Moj), and dimensionless concentrations at the surface of the biofilm (Bj). The parameter MOj is a combination of the individual biofilm property values (Mj) which represent biofilm characteristics. The applicability of these approximation equations is demonstrated experimentally for the degradation of a mixture of volatile fatty acids in which acetic acid is predominant. As the decompositions of these acids are considered to be rate-limiting in anaerobic biofilm processes, this approximation equation may be used for the design and/or performance evaluation of biofilm reactors. Introduction The decomposition of the soluble organic fraction of industrial and domestic wastewaters can be accomplished successfully by the use of anaerobic biofilm treatment systems such as packed, expanded and fluidised beds. In these systems, the immobilisation of purifying bacteria on the surface of solid-supports permits loading rates that are several times higher than those possible in conventional suspended systems,' and better stability records are observed in biofilm reactors when stressed by shock loadings. In attempts to predict or evaluate the performance of such processes, several mathematical biofilm models have been proposed. They basically consider intrabiofilm diffusion and decomposition of substrates, liquid layer resistance to substrate diffusion, and biofilm growth and decay. Several models24 assumed a single rate-limiting substrate under steady-state conditions, and pseudo-analytical overall rate equations were developed in terms of dimensionless concentrations at the surface of the biofilm, and parameters which were usually some form of a modified Thiele modulus. 'To whom correspondence should be addressed. Developments in Chemical Engineering and Mineral Processing, Vol. 1, No 2/3,page 158 Eflectiveness Factors in Anaerobic Biofilms I59 Recently, biofilm modelling has been improved by considering the existence of mixed bacterial populations, and two limiting substrates which are degraded et d 7proposed simplified equations consecutively within the b i ~ f i l m . ~Kuroda -~ for the effectiveness factors for two-step consecutive reactions systems in biofilm reactors operated under a complete-mixed flow regime, and their applicability was demonstrated for butyrate and propionate degradations. They used a biofilm model6 which considers the liquid layer resistance to be negligibly small for large Reynolds numbers. However, differences larger than 20% occurred between the experimental data and the numerical solution of the basic differential equations, especially in the case of large bulk concentrations and large values of biomass concentrations in biofilm. Furthermore, two-step consecutive systems like propionate and butyrate degradations are only part of the more complex parallel and consecutive reaction system of the anaerobic decomposition of organic wastewaters, e.g. those containing carbohydrates. This paper includes a theoretical study of the effectiveness factors for a biofilm in which a mixed bacterial population degrades a mixture of rate-limiting substrates, in a combination of parallel and consecutive reactions. The liquid-layer diffusional resistance is also taken into consideration. Analytical solutions for the effectiveness factors for a first-order reaction approximation are presented, and a pseudo-analytical general equation is developed. This represents approximately t h e effectiveness factors for one-step reaction, and the combined parallel-consecutive reaction system for a large range of biofilm surface concentrations. Reactor Model The reactor model (Figure 1) proposed by Sakakibara’ was the conceptual basis used in this study. The model considers a complete-mixed biofilm reactor with a planar biofilm of uniform density (p) and uniform thickness (LF), where the mixture of primary substrates is degraded by the attached micro-organisms according to the following equation: P 1 B - A - G where P and B = primary substrates; A = intermediate product; G = final product. As discussed above, this type of reaction represents the rate-limiting decomposition steps of the general bio-reaction pathway occurring in the anaerobic degradation of soluble organics contained in wastewaters, e.g. sugar wastes. It is assumed that both the substrates and the intermediate are transported by molecular diffusion within the biofilm and the laminar liquid layer, and that their degradation rates can be represented by Monod-type relations. Furthermore, considering that biofilm growth and decay are very slow compared with concentration changes, quasi-steady-state mass balances for the substrates and the intermediate in the biofilm yield the following equations. For the substrates B and P: 160 C.R. Escalera, A. Maezawa, S. Uchida and M.Kuroda Solid support CAb CPb Figure 1 Biofilm Reactor Model as proposed by Sakakib~zra.~ For the intermediate A: The boundary conditions for the system of equations (2) and (3) are: EfSectiveness Factors in Anaerobic Bioflms 161 Mass balances for the substrate and intermediates in the bulk liquid lead to the following equations: The mass fluxes for primary substrate and intermediate products are: In the absence of any diffusional resistance within the biofilm, or when the diffusion rates are much larger than the decomposition rates, the concentrations of substrate and intermediates throughout the film are everywhere equal to the surface concentrations. Therefore, the corresponding fluxes are given by: The effectiveness factors are then defined as: Equations (2)-(5) can be represented in terms of dimensionless parameters as follows: I62 C.R. Escalera, A. Maezawa, S. Uchida and M. Kuroda From equation (6), in dimensionless variables: In the foregoing equations, M, values are biofilm property values for the substrates (B) and the intermediate (A), and represent the corresponding ratios of utilisation rates to diffusion rates in the biofilm. Parameters Pe, are operational parameters for substrates (B) and intermediate (A), and represent the corresponding ratios of loading rates per unit area to diffusion rates. Parameters Bi, are the corresponding Biot numbers which represent the ratios of diffusion rates in the liquid layer to those in the biofilm. Numerical Rates The effectiveness factors (Efi) were calculated for values of M, varying from 0.1 to 10, and values of the biofilm surface concentrations B, varying from 0.01 to 100. Kuroda el d7calculated the effectiveness factors for two-step consecutive reaction systems within these ranges. These ranges of the parameter values were chosen by taking into account typical values of the specific growth rates, diffusivities, half-velocity coefficients and biofilm thicknesses occurring in anaerobic processes." As an example, Figure 2 shows the relation between EfA and BA, for M B = MA = 4 and M p = 0 . 7 M ~and Bjj = 10, taking the distribution of the concentrations of A , B and P in the feed as a parameter. The figure shows clearly that when the concentration of the intermediate (A) in the feed is predominant, the effectiveness factors are smaller than those corresponding to lower concentrations of A. This is because the intermediate A produced by the degradation of the substrates B and P is subsequently rapidly decomposed, and does not accumulate within the biofilm. However, when larger relative amounts of B or P are present in the feed, the intermediate A accumulates within the biofilm yielding larger effectiveness factors. First Order Approximation When the concentrations are much larger than the half-velocity coefficients (E, > l), the reaction rates in equations (2) and (3) can be approximated to zero-order reaction rate and the effectiveness factor is near to 1 (see Figure 2). When the concentrations are much smaller than the half-velocity coefficients (Cj < K,, i.e. E, < l), the rate terms in equations (2) and (3) can be approximated to first-order reaction rates. The following analytical solutions for the effectiveness factors can then be obtained: EfSectiveness Factors in Anaerobic Biofilms I63 BA Figure 2 Relation between effectivenessfactor Ef, and dimensionless concentration at biofilm suvace (B,) for intermediate decomposition. EJs = tanh M s / M s (S = E , P ) EJA = where the parameter Op, is defined as: When Pe, is much smaller than 1 (small loading rates), the values of the parameter Op, approximate to Pej For these cases and for M, values larger than 3, the analytical solution of the effectiveness factors for the substrates and the final intermediate approximate to the following equations: 164 C.R. Escalera, A. Maezawa, S. Uchida and M. Kuroda where: By following the same procedure, it can be shown that the expressions MA + ~ / M Band ) MA + 1 / M p ) are the effectiveness factors for a first order approximation which correspond to the B-A-G consecutive reaction and P-A-G consecutive reaction, respectively. The parameters MOB-A and MOP-A are defined as the pathway biofilm property values, and correspond to the individual two-step consecutive reactions as defined by equation (1) (B-A-G and P-A-G reactions). The overall biofilm property (MoA) is a combination of the biofilm property values corresponding to the individual consecutive reaction pathways, arranged in the same way as a parallel-series diffusion resistance configuration. This configuration suggests that an overall biofilm property value (Mo,)can be defined for any system of consecutive and/or parallel reactions, as a combination of the individual pathway biofilm property values. Bj Figure 3 Relation between parameters a and p and dimensionless concentrations at bioflm surface Bs and B, for primary substrates and intermediate uptakes. Eflectiveness Factors in Anaerobic Biofilms 0.1 1.0 10 0.1 1.0 10 .- 165 100 loo BA Figure 4 Error obtained by using equations (26) and (27) in calculation of effectivenessfactors with respect to numerical solutions. Development of Approximation Equations Equations (1 8) and (23) can be utilised to represent the effectiveness factors when the values of the biofilm surface concentrations are very small. However, when these concentrations become larger (for example B, > l), the Monod-type relationships in equations (2) and (3) cannot be simplified to first-order rate equations. Numerical solutions for the system of differential equations are then needed to obtain the effectiveness factors. In order to avoid the numerical work, the following development of a general approximation equation was performed. The effectiveness factor for the primary substrates B and P (or first steps of the corresponding consecutive reactions) and the intermediate A can be represented approximately by the empirical function: Ef,= tanh(aMo,8) ( j = A, B , P) C.R. Escalera, A. Maezawa, S. Uchida and M.Kuroda I66 - I I 1 I I I I I I MS Figure 5 Comparison of experimental and calculated values of effectiveness factors for propionate and butyrate decompositions in a packed bed reactor. which can be rearranged in the following form: Plotting equation (25) by using data from the numerical solution for different values of the surface concentration (B,), the relationships can be obtained for a and p. Figure 3 shows the relationship for the primary substrate. These parameters can be approximated by the following equations as functions of the concentration Bj: + 0.6573B,+ 0.0228; (26) - 0.0448, + 0.000828: (27) a = 1.059 /9 = -1.0 for the range of 0.01 < B, < 100. The errors resulting from the use of the approximation equations relative to the numerical solution are presented in Figure 4. The errors ES for the first steps are consistently less than 10% for all the values of Ms and Bs considered. The errors &A for the parallel-consecutive reaction system are consistently less than 10% for Eflectiveness Factors in Anaerobic BioJilms 10-2 lo-’ 167 100 10’ loo 10‘ PeA 1o-2 PeA Figure 6 Comparison of experimental and calculated results of the removal eficiency and bulk concentrations for decomposition of a mixture of acetic, propionic and butyric acids (Ace:Pro:Bru = 0.56:0.32:0.12). I68 C.R. Escalera, A. Maezawa, S. Uchida and M.Kuroda all the values of M A and BA considered, when the proportion of A in the feed is larger than one third of the total. It can also be observed that errors less than 5% occur for larger proportions of A. Data have been reported11912for anaerobic reactors treating agricultural wastewaters that are not stressed by shock-loadings, e.g. molasses, beet sugar, and fruit-processing waste liquors. It was observed that among the acids produced in the acid-forming decomposition step, the intermediate acetic acid was produced in large proportions compared to propionic and butyric acids. Considering these data, equations (24) and (27) can be applied to evaluate or design anaerobic biofilm reactors that treat such wastewaters, and other wastewaters in which the decompositions of the mixture of acids become the rate-limiting steps. Applicability of the Proposed Equations In order to illustrate the application of the approximation equations, Figure 5 shows a comparison of the effectiveness factors obtained experimentally and the values calculated by using the pseudo-analytical equation, for the first steps of the consecutive proprionate and butyrate decompositions. The experimental procedures and the experimental data are given by Sakakibara et al. l 3 They used packed-bed anaerobic reactors operated under high wastewater-recycle conditions. Therefore, the liquid-layer mass transfer resistance was minimised and represented less than about 20% of the intrabiofilm diffusion resistance. As shown in Figure 5 , there was good agreement between the experimental and calculated results obtained for a wide range of biofilm surface concentrations. Figures 6(a) and (b) show a comparison of the experimental and calculated values (obtained by using the pseudo-analytical equations) of the removal efficiency and effluent concentrations (bulk concentrations) for the anaerobic decomposition of a mixture of acetic, propionic and butyric acids i n a laboratory-scale packed bed reactor. Experimental details and data are a ~ a i l a b l e . ~ Good agreement is obtained between the experimental and calculated results. Conclusions The effectiveness factors for the decomposition of a mixture of primary substrates and the final intermediate occurring in an anaerobic biofilm were studied. The theoretical basis was a biofilm model that considered a system of parallel and consecutive anaerobic reactions and diffusion rates in the liquid layer and biofilm. The following results were obtained: (i) The effectiveness factor of the intermediate depends on the composition of substrates and intermediate in the feed. (ii) The effectiveness factors of the primary substrates and the intermediate (Ed) can be approximately represented by a pseudo-analytical equation expressed in terms of the overall biofilm properties (Moj). These are defined by equations (21) and (22) and their corresponding concentrations at the biofilm surface (Bj). (iii) These approximation equations can be applied to the design and/or performance evaluation of anaerobic biofilm reactors, in which the degradations of a mixture of organic volatile fatty acids (i.e. acetic, propionic and butyric acids) are the rate-limiting steps. Effectiveness Factors in Anaerobic Biofilms 169 Nomenclature a >j C dfF CTF D, specific surface area of biofilm, (In) concentration of component j in biofilm, (M/L3) concentration of componentj at biofilm surface, (M/L3) concentration of componentj in bulk liquid, (ML3) primary substrate concentration in feed, (M/L3) overall substrate concentration in feed, (M/L3) effective diffusivity of component j in biofilm, (L2/r> removal rate of componentj , (M/(L~T>> removal rate of component j without biofilm diffusion resistance, (h4/(L2T)) half-velocity coefficient for component j uptake, (M/L3) mass transfer coefficient of component j in liquid layer, (YT) biofilm thickness (L) distance from the solid support surface (L) .%, % kLj LF x Dimensionless variables and parameters normalised concentration of component j in biofilm, CJCTF J* normalised concentration of component j in biofilm surface, CyCTF jb normalised concentration of component j in bulk liquid, C’JCTF jF normalised concentration of component j in feed, C.,JCTF B. dimensionless concentration of component j at biodlm surface, BTFKA//j* dj Biot number for componentj , L$L/D, BTF dimensionless substrate feed concentration, CT,JKA ratio of effective diffusivities, D/DA effectiveness factor for componentj , J p * K,,, ratio of half-velocity coefficient, KJKi M . biofilm property value for componentj , LF(u,ajp/KjDj)ln d o j overall biofilm property value for component j Opj operational parameter for component j defined by equation (20) Pej operational parameter for componentj , L/a8Dj X normalised distance from solid support surface, x/LF Urn yield coefficient for final intermediate formation from substrate S YGIA yield coefficient for final product formation @ Greek Symbols a parameter defined in equation (26) mass fraction of component j in biofilm aj parameter defined in equation (27) p error committed in calculation of effectiveness factor of componentj , (%) E~ maximum specific decomposition rate of componentj , (1/T) uj p biofilm density (h4/L3) 8 hydraulic retention time (T) Subscripts intermediate A B substrate B P substrate P A I70 C.R. 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