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CONVERSION EFFICIENCY OF ORGANIC MATERIAL TO METHANE HELENICE O. FLORENTINO, ADRIANA F. V. BISCARO, JORGE DE LUCAS JÚNIOR Depto de Bioestatística IB, PG FCA, Depto de Engenharia Rural FCAV UNESP Depto de Bioestatística do Instituto de Biociências da Unesp, Botucatu SP Brazil Abstract: - The conversion of organic material to methane and carbon dioxide by microbiological activity consists of consecutive, parallel, and independent reactions which make up a very complex biological process. Microbial ecology studies of this digestion process have shown that the conversion to biogas has six stages (polymer hydrolysis, fermentation of amino acids and sugars, oxidation of acid and alcohol products from the previous phase, oxidation of intermediary volatile acids, conversion of both acetate and hydrogen to methane). From this it is possible to simulate the anaerobic process and predict biomass variation, and biogas production and composition. This work studies mathematical models using Monod techniques and predicting the efficiency of converting organic material to methane and carbon dioxide in relation to retention time. We also propose a method to calculate optimum digestion efficiency for total solids and volatiles. These techniques are proposed to help study methane production efficiency in biodigesters. Keywords: - Mathematical models, anaerobic digestion, treatment efficiency, biodigester. 1 Introduction From this, there is a growing There is worldwide concern need to understand techniques that about renewable energy generation and allow the rational use of available environmental protection. These issues energy, and to look for alternative have much in common, because they sources to oil in both energy production deal with the increasing energy demand from raw material and raw-material use from several primary sources, favoring in industries. In this way, biodigesters the easiest extraction methods. In this could have a very important role [1], way oil, coal, and natural gas have [2], [3], [7], [8], [9] and [11]. assumed the predominant role. They Anaerobic digestion stands out cause the highest environmental impact from other microbiological sources of when burnt or transformed. energy; it is a fermentation process where several bacteria species transform and methane (CH4) in an anaerobic organic material into a gaseous mixture, biodigester. biogas. The conversion of organic There are studies in literature material to methane and carbon dioxide with mathematic techniques to help by microbiological activity consists of understand which consecutive, parallel, and independent organic reactions with a very large number of material to methane and carbon dioxide microorganisms involved in a very which make use of mathematic models. complex biological process. Microbial These models can be used to predict ecology studies of the digestion process various parameters in the anaerobic have shown that conversion to biogas digestion could processes microbiologically convert process (retention time, be in six stages (polymer temperature, etc), which could help hydrolysis, fermentation of amino acids biodigester and sugars, oxidation of acid and efficiency in methane production. alcohol products from the previous According to [13], anaerobic phase, oxidation of intermediary biodigester mathematical models are volatile acids, conversion of both formulated acetate and hydrogen to methane). species by and observing bacteria environments and Based on this, it is possible to simulate extracting the main variables which the anaerobic process and predict, influence their growth or reduction. biomass These production and composition. Some models describe substrate variation, and variation in a biodigester, in which it is mathematical assumed that bacteria growth depends developed to simulate this conversion on substrate quantity, and that substrate process, but many use extensive and consumption is viable. complex experimental data making the Merkel, approximate [12], theoretical estimated values models have biogas been models complex and difficult to use. to More simple models have been calculate mass transfer by analyzing found that can help in biodigestion experimental data from a mathematical projects, model which described the anaerobic optimization tool and helping in the digestion process. The author discussed analysis of experimental data. For this, the controlling factors that influenced the microorganisms can be divided into mass transfer of carbon dioxide (CO2) smaller groups, according to certain serving as a process characteristics. Monad’s model has often been used; it groups all the anaerobic digestion processes into two conversion processes, first, the biomass 2 The Anaerobic Digestion Process The conversion of organic components are converted into volatile material to methane and carbon dioxide acids by a group of acetogenic bacteria, by microbiological activities consists of second, the acids produced by the first consecutive, parallel, and independent group are converted to methane and reactions and involves a very large carbon dioxide by another group of group of microorganisms performing a methanogenic bacteria, and the kinetics very complex biological process. This of anaerobic digestion are applied conversion could be in six stages to separately to each of these groups. arrive at biogas (polymer hydrolysis, Observing these kinetic parameters, fermentation of amino acids and sugars, mathematical modeling can be applied oxidation of acid and alcohol products to from the previous phase, oxidation of anaerobic system operation [4], [5] and [6]. design and intermediary volatile acids, conversion of both acetate and hydrogen to methane) as illustrated in Figure 1. Complex organic (carbohydrates, proteins, lipids) Fermentative bacteria (hydrolysis) Simple organic (sugars, amino acids, peptides) Fermentative bacteria (Acidogenesis) Organic acids (acetic, propionic and butyric) Acetogenous bacteria (Acetogenesis) Acetogenous bacteria hydrogen producers H2 + CO2 acetate Acetogenous bacteria hydrogen consumers Methanogenous bacteria (Methanogenesis) CH4 + CO2 Hydrogentrophic methanogenic bacteria Acetoclastic methanogenic bacteria Fig. 1 Metabolic sequence and microbial groups involved in anaerobic digestion substrate concentration where = m/2 2.1 Kinetics of Digestion This section aims to determine the equations microorganism for The combination of (1) and (2), effluent concentration and gives us an equation relating bacterial growth with substrate use. substrate concentration. Bacterial (g m-3). growth can dX S μm . .X dt ks S be expressed as a function of actual (3) bacteria concentration in the reactor at a Considering the reduction in particular moment in time. The gross microorganisms due to the endogenous growth rate of a bacteria population is a metabolism, net microorganism growth function of this number, mass or rate can be expressed as: concentration and a particular moment in time. This rate could be expressed in dX S μm . .X k d X dt ks S where the form of an equation (1). kd is the coefficient (4) of endogenous respiration, d-1. dX μX dt (1) On the other hand, we remember where, X is the concentration of that the bacterial mass equilibrium microorganisms in the reactor, SS or equation is: SSV g m-3; is the specific growth rate, dX S V Q X0 QX V μ m X k d X dt ks S d; t is the time, d. The growth rate (1), is used for growth without substrate limitation. [10], confirmed that the effect of a limiting substrate or nutrient could be adequately expression, defined as in using Monad’s the following where, V is reactor volume, m3; Q is the rate of in or outflow, m3 d-1; X0 and the concentration of influent suspended solids, mg L-1 or g m-3. According to Tchobanoglous, [10], ignoring influent microorganism concentration and considering that there equation: S μ μm . ks S (5) was no accumulation in the steady state (2) where, is the specific growth rate, d-1; condition (dX/dt = 0, X0 = 0), equation (5) could be written as: Q S μm . kd V ks S m is the maximum specific growth rate, d-1; S is the concentration of Using hydraulic retention time, growth-limiting substrate, g m-3; ks is the constant of saturation, defined as the (6) θ V 1 S , we have: μ m . k d (7) Q θ ks S Using the maximum utilization rate 2.2 Anaerobic Digestion Efficiency of substrate per unit of microorganism mass In this section is presented the (k), k μm , where Y is the coefficient of Y cellular production, in gSSV (g(DQO))-1 in equations (6) and (7) we have: (8) model to predict the efficiency of conversion for organic material to biogas by anaerobic that the anaerobic digestion is two conversion processes, first the biomass From (8) we have: components are converted into volatile (1 θ k d) ks S θ(Yk k d) 1 is mathematical digestion, [4]. This author considered 1 kYS kd θ ks S Which Jeyaseelan the (9) equation to acids by a group of acetogenic bacteria, second, these acids are converted to methane and carbon dioxide by another determine substrate concentration. In function of substrate use, one part is converted by new cells and the other is oxidized into final inorganic and organic products. The equation which describes the solids balance is: group of methanogenic bacteria. To apply the model, the residue is considered as a mixture of carbohydrate (C), protein (P), lipids (L) and a very small proportion of other materials, and are known the percentages of each of dS V Q S0 QS Vμ dt (10) these components. These components where, S0 is influent concentration of biodegrade independently, without any growth-limiting substrate, g m-3. interactions within the intermediate substrate compounds, except in the second stage concentration, as it does not accumulate in where the combined volatile acids are the steady state condition (dS/dt = 0), from degraded to produce biogas. Figure 2 Ignoring influent kYS ks S (10) we have: So S θ illustrates this conversion. (11) incorporating the new concepts to From (7) and (11) we have: 1 So S θkX kd θμ m μ m consider carbohydrates, lipids, proteins, (12) From (12) we therefore have the equation for effluent microorganism (S0 S)Y 1 kd θ and the organic substances substituted i (13) other separately, equations (9) and (13) are X1 concentration: X In the first phase of conversion, by: Yi (Soi S1i ) i C, L, P, O (14) (1 θk di ) and S1 S1i i i C, L, P, O (15) k si (1 θk di ) θ(Yi k i k di ) 1 Where S1i other organic compounds, the initial concentrations can be expressed as parts and the sub-index 1 indicates phase 1 of of the conversion process. concentration. The substrate in solution in the the total influent The substrate individual concentrations are represented by: S oi c o a o a Si 100 , i C, L, P, O acid formation phase, represented by S1, (18) is the feed substrate for the methane where, c0 is the influent residue formation phase, and therefore, the final concentration, %; a0 is the volatile concentration of substrate in solution solids concentration, %; asi is the ratio and microorganism mass which forms of component i/volatile solids; the methane are given by the following equations: X2 and arrive at the mathematical model for Y2 (S1 S 2 ) (1 θk d2 ) S2 With these parameters, we can (16) digestion efficiency, or the percentage of biogas produced based on total solids k s2 (1 θk d2 ) θ(Y2 k 2 k d2 ) 1 (E) and volatile solids (EV). (17) E where sub-index 2 indicates phase 2 of (c o a o 100 S2 X1 X 2 ) 100 (19) c o 10000 and the process. As the waste is composed of EV carbohydrates, lipids, proteins, and (c o a o 100 S2 X1 X 2 ) 100 100 c o a o 10000 (20) Organic Material Carbohydrates (C) Lipids (L) Proteins (P) Other Organics (O) Phase 1 Bacteria (X1) Organic Acid Others Phase 2 Microorganisms (X2) Biogas Fig. 2 The Conversion process using the Jeyaseelan mathematical model. volatile solids can be estimated by k si (1 θk di ) θ θ i i i k di ) 1 k / θ k di k si lim si θ i (Yi k i k di ) 1/θ equations (19) and (20). The object of 3 Digestion Efficiency Optimization According to Jeyaseelan , [4], digestion efficiency based on total and lim S1 lim i this section is to find the optimum value of E and EV in function of retention time θ , or to determine the retention time that efficiency, maximizes k di k si (Yi k i k di ) Then: lim S1 θ i digestion E E( ) . For this the θ Maximize E (θ) (21) subject to : {S1 0, S 2 0, X 1 0, X 2 0, θ 0} Efficiency E in terms of retention time has the following curve: k si k di i C, L, P, O. (22) (Yi k i k di ) In the same way with S2 we have: lim S2 following model is proposed: θ(Y k k s2 k d2 (Y2 k 2 k d2 ) (23) For X1 and X2 we have: lim X1 lim θ θ i Yi (S 0i S1i ) 0 (24) (1 θk di ) and Y2 (S1 S 2 ) 0 (25) θ (1 θk ) d2 lim X 2 lim θ From (22), (23), (24) and (25) we have: (d) k d2 k s2 Y2 k 2 k d2 (26) c o 100 c o a o 100 Fig. 3 Curve for digestion efficiency in E max lim E(θ) terms of hydraulic retention time (). θ In the same way, for the As can be seen in Figure 3, digestion efficiency increases according digestion efficiency of volatile solids, the maximum is given by: to a horizontal asymptote, or tending to a value Emax, which could be k d2 k s2 Y2 k 2 k d2 100 c o a o 100 c o a o 100 E v max lim E v () θ determined solving the limit: E max lim E(θ) θ Thus maximum an upper anaerobic limit (27) for digestion To analytically determine the efficiency was determined. However limit of E, we calculated the following this needs a very high retention time limits: which is not viable in practice; this value can be used as an analysis parameter of efficiency and retention time control. References: [1] Chanakya, H.N.; Venkatsubramaniyam, R.; Modak, J. Fermentation and methanogenic 4 Acknowledgements The authors are grateful to characteristics of leafy biomass (grant feed stocks in a solid phase numbers 557-01-DCP, 250/04-DFP and biogas fermentor, Bioresearch 030/2004-PROINTER/PROPP) for their Technology, v. 62, 1997, p.71- support. 78. FUNDUNESP and PROPP [2] Groscurt, H.M.; Almeida, A.; Bauen, A.; Costa, F.B. Total 5 Conclusions Mathematical anaerobic system modeling projects in and operations is a valuable prediction tool. It contributes to the understanding inherent phenomena in the process and The model proposed by [4] to estimate the efficiency of anaerobic digestion in the conversion of organic material to biogas is simple and easy to influence of hydraulic retention time on anaerobic digestion efficiency is a limiting factor, because depending on treatment and residue type, a long retention time is not viable. The optimization model proposed here is a good tool to help in the analysis of confidence Union, Energy, v. 25, 2000, p.1081-1095. [3] Hall, D.O. Biomass energy in of the future, Forest Ecology and Management, v. 91, 1997, p.17-45. [4] Jeyaseelan, S., Mathematical calculate. efficiency, selected regions of the European industrialized countries-a view helps in the practical limitations. The costs and benefits of biomass in giving to the establish hydraulic retention time. operator the best A Simple Model for Anaerobic Digestion Process. Wat. Sci. Tech. V 35(8), 1997, pp. 185-191. 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