Optimizing low-temperature biogas production from biomass by anaerobic digestion

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durciHew19 OKeywords:Biogas productionAnaerobic digestioneomroduproduce biogas by anaerobic digestion using model dairy wastewater sludge as substrate. The Monodroducprodubeen studied experimentally and theoretically for six decades [1].be applied to increase the protability of large-scale plants,generate signicant benets without excessive energy use orchemical demand and to scale-up laboratory installations [9,10].Mathematical model-based simulations of bioreactor runs canexplain changes in process variables e biomass, substrate andThe models found in scientic literature differ in structure andzation techniquesdigestion processoperated in batcho maximize globalIn the continuouse goal is to maxi-aratus per unit ofed hydrodynamicprocesses in laboratory-scale plug-ow UASB reactors. They stud-ied process behavior using two-compartment [18] and multiplemixed-compartmentmodels [17]. Laboratory-scale installations areoften used to study process kinetics before scaling-up to full-scaleapplications. Batstone et al. [19] demonstrated that the hydraulicsof laboratory-scale plug ow-type bioreactors may differ signi-cantly from that of full-scale digesters. They recommended thatmixed ow-type models should be used instead of plug-ow re-actors for modeling full-scale bioreactors.* Corresponding author. Tel.: 48 89 523 3413; fax: 48 89 523 4469.Contents lists availabRenewable.e lsRenewable Energy 69 (2014) 219e225E-mail address: marek@uwm.edu.pl (M. Markowski).Anaerobic digestion is used to treat and recover energy from sludgein wastewater [2], municipal solid wastes [3], agricultural residuesand food processing waste [4e6]. The anaerobic digestion tech-nology offers great potential for rapid disintegration of organicmatter to produce biogas and conserve fossil energy resources [7].There is a growing interest in biogas production, and the number ofbiogas production plants and average plant size continue to in-crease [8].Mathematical modeling and optimization techniques have tolevel of complexity [8,11e14]. Different optimican be used to improve the performance of the[15,16]. If a bioreactor (laboratory or technical) ismode (unsteady state), the optimization goal is tbiogas production at the end of each batch.mode of bioreactor operation (steady state), thmize the amount of biogas produced in the apptime.Bolle et al. [17] and Singhal et al. [18] describand different kinds of organic residues in anaerobic digesters has tion, should be controlled to guarantee the desired response [11].Continuous-ow bioreactorMathematical modelingOptimization1. IntroductionIn the absence of air, biogas is pthrough anaerobic digestion. Biogashttp://dx.doi.org/10.1016/j.renene.2014.03.0390960-1481/ 2014 Elsevier Ltd. All rights reserved.maximizes the amount of biogas produced per unit of time. Total biogas production derived from thetheoretically optimized reactor in the calculation model was 1.6 times higher than that derived for theexperimental bioreactor. The methane fraction in biogas increased from 64.5% to 71.2% after optimiza-tion, whereas the carbon dioxide fraction in biogas decreased from 34.5% to 27.8%. The optimization ofthe intermediate cylinder of the digester signicantly increased total biogas production (by up to 160%)in comparison with the output noted before optimization. 2014 Elsevier Ltd. All rights reserved.ed by micro-organismsction from wastewaterproduct concentrations e accompanied by temperature changesinside an apparatus. They can also describe the inuence of thenutrient feeding rate on substrate digestion and explain howprocess parameters, including time, concentration and composi-Available onlineapproach was used to nd the optimal diameter of the two cylinder-separated stages of the reactor thatAccepted 21 March 2014 optimal geometric parameters of the digester. A continuous-mode two-stage bioreactor was applied toOptimizing low-temperature biogas proanaerobic digestionMarek Markowski a,*, Ireneusz Bia1obrzewski a, MaMiros1aw Krzemieniewski ba Faculty of Engineering, University of Warmia and Mazury in Olsztyn, 10-718 Olsztyn,b Faculty of Environmental Sciences, University of Warmia and Mazury in Olsztyn, 10-7a r t i c l e i n f oArticle history:Received 7 November 2012a b s t r a c tThe inuence of selected glow-temperature biogas pjournal homepage: wwwction from biomass byn Zielinski b, Marcin Debowski b,eliusza 14, Polandlsztyn, Oczapowskiego 5, Polandetric bioreactor parameters on the performance of continuous-ow-typection from biomass by anaerobic digestion was studied to determine thele at ScienceDirectEnergyevier .com/locate/reneneIn the present study, a continuous-mode two-stage bioreactorwas applied to produce biogas by anaerobic digestion using modelFig. 1. Experimental design diagram: a) two-stage mixed ow reactor; 1. Chamberhydrolyzer, with full mixing, 2. Methanogenic chamber with downside ow, 3.Methanogenic chamber with upside ow, arrows indicate ow direction in the reactor;M. Markowski et al. / Renewable Energy 69 (2014) 219e225220dairy wastewater sludge as substrate. The ow rate of the liquidphase at the inlet was kept constant, therefore, liquid ow veloc-ities in each stage of the digester were constant and determined bythe cylinders internal-to-external diameter ratios in each stage ofthe reactor. As part of a mechanistic framework for investigatingmass and energy balances, a set of model equations was adapted todetermine the optimal value of the cylinders diameter with twoseparate reaction stages to maximize the amount of biogas pro-duced per unit of time. Optimization methods were also used toestimate the parameters in model equations, and simulation pa-rameters, which were elaborated by simple experiment or found inliterature, were applied. Therefore, the aim of this study was todetermine the inuence of a bioreactors geometric parameters oncontinuous-ow-type low-temperature biogas production frombiomass by anaerobic digestion and to determine the optimalvalues of the digesters selected geometric parameters. The benetsof applying the general ADM1 model for the optimization ofanaerobic digestion are obvious. The ADM1model consists of manydifferential equations and various coefcients need to be accuratelydetermined, therefore, vast efforts (laboratory and programmingwork) are required to ensure the models effectiveness [20,21].Since the main aim of the present study was to investigate thepossibility of optimizing methane production based on selectedgeometrical characteristics (radius of the internal cylinder) of thebioreactor as the decision variables, a simplied version of well-established anaerobic digestion models was used in the study.The main aim of this study was to develop a simple but effectivemathematical model of anaerobic biomass digestion and to use thatmodel to optimize biogas production efciency. A similar attemptcould be made with the application of a full ADM1 model.2. Materials and methods2.1. Raw materials and sample preparationThe studywas conducted on anaerobic sludge from an anaerobicdairy wastewater treatment plant. Anaerobic sludgewas adapted toprocess conditions over a period of 60 days. The sampled dairywastewater was produced from milk powder in the amount of 1 gof milk powder per 1 l of water. The organic compound load onreactor volume was C 1 g COD/l, and the adopted hydraulicretention time (HRT) was 1 day. The main indicators of rawwastewater pollution were determined at: COD 1000 22 mg/l,BOD5 676 14 mg/l, Ntot 65 4 mg N/l, Ptot 19 2 mg P/l.The most important and most sensitive fermenting micro-organisms include Archaea of the methanogenic phase. They areresponsible for the vast part of methane production, mainly fromacetic acid. The predominant microbial species in the testedsludge belonged to the generaMethanosarcina andMethanosaeta.2.2. Experimental setupThe study was conducted in a two-stage variable ow reactorshown in Fig. 1. The reactor consisted of concentric chambersserving as the internal hydrolyzer, and two other chambers actedas methanogenic reactors. An intermediate cylinder-separateddownow and upow suspension zones in the methanogenic partof the bioreactor. Raw sewage was pumped to the hydrolyzer(volume of 20 l). A recirculating pump was used to ensureb) diagram of liquid ow and velocity distribution inside a methanogenic chamber; c)computational model of the methanogenic part of the bioreactor.specic microbial growth rate. The model is described byablecomplete mixing in the hydrolyzer. The suction pump pipe waslocated 5 cm below liquid level in the tank. Recycled sludge andraw substrate were placed at the bottom. The inow to meth-anogenic chambers was located at the top of the hydrolyzer. Thispart of the reactor was characterized by top-down ow: substrateowed from top to bottom and from bottom to top. This part ofthe reactor relied on plug ow. Methanogenic chambers had thevolume of 40 l each. The bioreactor was operated continuously atconstant mass ow rate at the inlet of the ow meter. Thedescending and ascending parts of the hydrolyzer had differentcross-sections, and different ow rates were observed in eachsection of the reactor.2.3. InstrumentationBiogas production efciency was measured on-line using theAALBORG ow meter (USA). The qualitative composition ofbiogas was determined with the use of the 430 LXi Gas Dataanalyzer (UK). The content of methane, CH4, carbon dioxide, CO2,nitrogen N2 and oxygen, O2 was analyzed. Gas quality measure-ments were performed automatically eight times a day. Thequality of efuent owing out of the reactor was analyzed daily.COD (HacheLange tests, dichromate oxidation method accordingto AWWA standards), total suspended solids (gravimetricmethod; OX 35 moisture analyzer) and pH were determined(WTW 340 pH analyzer). The changes in biomass concentrationsinside the reactor and the depth of individual reactor chamberswere measured every 10 days. Mesophilic temperature of33 2 C was maintained in the outer chamber. The study wasconducted for 60 days after the determination of the quality ofliquid efuent produced by the bioreactor. The operating pa-rameters remained stable throughout the study, and COD valuesdid not differ by more than 5% between three consecutivemeasurements.2.4. CalculationsIn recent decades, the eld of microbial growth kinetics hasbeen dominated by the semi-empirical model proposed by Monod[22]. The Monod model introduced the concept of growth-controlling or limiting substrate. In analyses of microbial growthdynamics, the Monod model is applied to determine the lineardependency between the microbial growth rate and the concen-trations of bacteria with specic growth rates as the proportioncoefcient written in exponential form:dXdt mX (1)where:m mmaxSKM S(2)where: parameter m is the specic growth rate, mmax can be denedas the increase in biomass per unit of time under optimal feedingconditions (no limiting nutrients), and KM is the substrate con-centration at which the growth rate of organisms is substrate-limited to half the prevailing maximum value. Many differentmodels for predicting anaerobic digestion have been proposed inrecent years [23e28]. This study investigates the ability of theMonodmodel to predict bacterial growth during anaerobic biomassdigestion.The link between microbial growth and substrate consumptionM. Markowski et al. / Renewdue to mass formation can be described by formulas (3) and (4).from biomass by anaerobic digestion was derived from equa-tions (1)e(10) and formulated by accounting for Monod-typedSdt 1YX=SdXdt(3)where yield coefcient YX/S is dened as:YX=S dXdS(4)and is assumed to be constant.The end product of the analyzed process is biogas. The kineticsof product formation can be calculated based on the kinetics ofsubstrate degradation and bacterial growth, respectively. Differentbiogas production models [29,30] rely on the assumption made byGaden [31] that the product results mainly from primary energymetabolism and is generated when the substrate is degraded.Consequently, kinetic equation (5) can be used to describe productformation:dPdt YP=XdXdt(5)where yield coefcient YP/X is dened as:YP=X dPdX(6)It was also assumed that the generation of heat from microbialgrowth can be described with the use of formula (7):dEdt YE=XdXdt(7)where:YE=X dEdX(8)A macroscopic analysis of the energy balance and the terms forconduction and generation of heat from microbial growth pro-duced formula (9):rCpvTvt divl$gradT YE=XdXdt(9)It was assumed that microbial growth was an adiabatic process,therefore, the energy balance equation (9) was simplied asfollows:rCpvTvt YE=XdXdt(10)In a continuous-ow-type bioreactor, it can be assumed thatsimultaneous microbial growth, substrate consumption, productformation and the temperature inside the apparatus are deter-mined by location along the axial coordinate of a bioreactor. Ifthis is the case, the time derivatives in kinetic equations may bereplaced by the product of spatial derivatives and ow rates,which is valid if the system behaves like a plug-ow system. Themathematical model of continuous-ow-type biogas productionEnergy 69 (2014) 219e225 221formula (11):to perform computer simulations of low-temperature biogas pro-Ptotal 1LZL0Px dx (16)where L is the distance between the inlet and the outlet of themethanogenic part of the bioreactor. Total biogas production maydepend on the radius (Ri) of the intermediate cylinder. The opti-mization procedure was applied to derive the value of Ri thatguarantees the maximum value of total biogas production. Theoptimal value of Ri was derived as the solution to the followingconstrained optimization problem:maxRiPtotalRi (17)with respect to Ri, subject to the set of constraints dened inequations (12)e(15) and inequalities (18):Rlb Ri Rub (18)able Energy 69 (2014) 219e225duction from biomass by anaerobic digestion in a continuous-ow-type column.8>>>:Xz 0 XinSz 0 SinPz 0 0Tz 0 Tin(13)2.5. OptimizationAll parameters, excluding mmax and KM, in models (11)e(13)were considered as known. The values of mmax and KM were esti-mated by simulating the process of low-temperature microbialgrowth in a continuous-ow-type apparatus. The inlet values ofbiomass concentration (X), substrate concentration (S), productconcentration (P) and the temperature of the liquid mixture (T), aswell as the outlet values of X and P were known, therefore, theoptimization procedure was used to estimate mmax and KM. Theobjective function Jout was dened as the difference between theestimated (Ssim) and known (Sexp) values of S at the outlet of theapparatus, and it was written in the following form:Joutmmax;KM Sexp Ssim2 (14)The values of mmax and KM were derived as the solution to thefollowing optimization problem (15):minmmax;KMJoutmmax;KM (15)with respect to mmax and KM, subject to the constraint dened inequations (11)e(13). The optimization process was performed for abioreactor conguration identical to that applied during theexperiment, i.e. the diameter of the intermediate cylinder was themean of the external and internal diameter of the bioreactor.8>>>>>>>>>>>>>>>>>>>>>>>>>>>:dXdz mmax1uSKM SXdSdz YS=Xmmax1uSKM SXdPdz YP=Xmmax1uSKM SXdTdz YE=Xmmax1u1rCpSKM SX(11)The following empirical equations were used to describe theeffect of temperature on the specic growth rate, mmax [32]:mmax 8>>>>>>>:mopt if T Toptb Tmax ToptTmax ToptmoptTmax Tb Tmax Tif Topt T Tmax0 if T Tmax(12)where mopt is the specic growth rate at the optimal temperaturefor growth, Topt and Tmax are the maximum temperatures at whichgrowth can occur, and b is the sensitivity of growth kinetics to anincrease in temperature (K). Formula (12) is an empirical equationthat was used to describe different sensitivities to temperatureincrease by modifying a single parameter, b [32]. Kinetic equations(11) and (12) supplemented by boundary conditions (13) were usedM. Markowski et al. / Renew222Total biogas production (Ptotal) along the length of the columncan be calculated with the use of the following equation:where Rlb and Rub are known values of the lower and upper boundof changes in Ri. It was also assumed that Rlb 1.1Ra andRub 0.9Rd, where Ra is the radius of the bioreactors hydrolyzerand Rd is the radius of the external section of the digester.Total biogas production (Ptotal) was expressed in units of con-centration (kg m3). The following formulawas applied to calculatethe overall biogas production rate (Qm) in the bioreactor:Qm PtotalQV (19)where QV is the volumetric ow rate of the liquid in the meth-anogenic part of the bioreactor.The constrained nonlinear optimization procedure (fmincon)implemented in the Optimization Toolbox v. 5.0 of the Matlab2010b (MathWorks Co, USA) environment was applied to solveoptimization problems (15) and (17). The fourth-order RungeeKutta algorithm, ode45, implemented inMatlab 2010b (MathWorksCo, USA) was used to solve equations (11)e(13). All simulation runswere performed using the data shown in Table 1. The values ofcoefcients YP/X and YX/S in Table 1 were adopted from the work ofZielinski et al. [33] who measured the above coefcients underhighly similar conditions. Coefcients b and YE/Xwere adopted fromthe work of Sangsurasak and Mitchell [32]. The density (r) andTable 1Parameter values applied during simulations.Parameter Value Sourcer 1000 [kg m3] (water) Measuredb 6.275 [K] [32]Cp 4191 [J kg1 K1] (water) MeasuredL 0.653 [m] MeasuredP0 0 [kg m3] MeasuredQV 1.7 105 [m3 s1] MeasuredRa 0.225 [m] MeasuredRd 0.100 [m] MeasuredSin 15.0 [kg m3] MeasuredSout 1.2 [kg m3] MeasuredTin 25 C 298 [K] MeasuredTmax 45 C 318 [K] [32]Topt 35 C 308 [K] [32]Vt 0.100 [m3] MeasuredVh 0.015 [m3] MeasuredVm 0.085 [m3] MeasuredXin 0.018 [kg m3] MeasuredYE/x 8.366 106 [J kg1 biomass] [32]1YP/x 0.004 [kg biogas kg biomass] [33]Yx/S 0.12 [kg biomass kg1 substrate] [33]thermal capacity (Cp) of the liquid at the inlet and outlet did notdiffer signicantly from those observed for water. The remainingparameters given in Table 1 were measured.3. Results and discussionThe performance of the bioreactor was analyzed, and theexperimental results of efuent quality and wastewater treatmentefciency are shown in Table 2. The efciency of organic compoundremoval was estimated at 89% for COD and 94% for BOD. The dia-the intermediate cylinder in the methanogenic part of the digester,are presented in Table 3. The optimized diameter was equal to40.5 cm and was derived as the solution to optimization problemsTable 2Experimentally determined wastewater treatment efciency.Parameters Units Raw sewage Treated wastewater Efciency [%]COD mg l1 1000.0 22.4 110.0 25.7 89.0 3.1BOD mg l1 676.5 14.2 40.6 11.2 94.0 4.3Ntot mgN l1 65.2 4.3 62.0 1.6 4.6 1.3Ptot mgP l1 19.1 2.0 18.8 0.6 1.2 0.9M. Markowski et al. / Renewable Energy 69 (2014) 219e225 223gram of the experimental bioreactor is presented in Fig. 1. Thediameter of the intermediate cylinder inside themethanogenic partof the digester (Fig. 1) was equal to 35 cm. The aim of the experi-ment was to determine a diameter of the intermediate cylinder thatwould increase bioreactor efciency and total biogas production incomparison with that observed before the improvement of biore-actor geometry.Parameters mmax and KM were estimated as the solution to theconstrained optimization problem (15) where the constraints weredescribed with the use of the Monod approach in formulas (11) and(12). The values of mmax and KM were estimated at 3.527 s1 and0.5636 kg m3, respectively. The derived values of mmax and KMwere used to simulate the steady state behavior of a plug-owdigester. In the rst step of the process, the geometrical dimensionsof the experimental bioreactor were used to determine the valuesof mmax and KM. In the second step, optimization problems (16) and(17) were solved to derive the optimal value of the diameter of theintermediate cylinder in the methanogenic part of the digester(Fig. 1). The improved value of the diameter was applied tosimulate the behavior of an optimized bioreactor.The changes in the concentrations of biomass, substrate andbiogas production, calculated along the axis of the methanogenicpart of the digester, are shown in Figs. 2e4. Changes in temperatureinside the bioreactor are presented in Fig. 5. The curves displayed inFig. 2. Biomass concentrations before and after optimization.Figs. 2e5 were derived for the diameter of the intermediate cyl-inder before (in black) and after (in red, in the web version) opti-mization (improvement) performed according to formulas (16) and(17). Non-smooth sections of the optimized curves shown inFigs. 2e5 (corresponding to the value of 0.64 on the x-axis) resultfrom changes in the area of cross-sections (transition betweenchambers with different diameters in the methanogenic part of thereactor, Fig. 1c) and rapid changes in the velocity of pumped liquid.The above was not observed in curves representing the experi-mental setup where the applied barrier setting guaranteed equalcross-sectional areas.Substrate concentrations at the outlet of the methanogenic partof the digester were determined at 1.20 0.18 kg m3. The simu-lated value of the diameter of the intermediate cylinder beforeoptimization did not differ signicantly from that noted afteroptimization and was equal to 1.14 kg m3. The above conrms thelow level of discrepancy between measured and simulated values.Total biogas production rates and the percent distribution of gasesin the biogas, calculated for experimental and optimized values ofFig. 3. Concentrations of organic compounds in the ltrate before and afteroptimization.Fig. 4. Product (biogas) concentration before and after optimization.M. Markowski et al. / Renewable224(16) and (17). The measured rate of total biogas production wasequal to 0.125 g h1, whereas the rate predicted from themodel wasdetermined at 0.0897 g h1 (Table 3). The simulated rate of totalbiogas production was underestimated by 28% in comparison withthe measured rate. Selected model parameters were cited fromliterature (e.g. parameter b in equation (12)), which explains thediscrepancy between measured and calculated results. Those dif-ferences were regarded as acceptable, and the calculated andmeasured values were consistent. Therefore, the described modelwas positively validated. Total biogas production derived for anoptimized bioreactor was equal to 0.147 g h1 and was signicantlyhigher than that reported in the experimental conguration at0.125 g h1. Our results indicate that total biogas productionderived from formulas (11)e(13) for a hypothetic bioreactor withan optimized radius of the cylinder separating downow andupow suspension zones in the methanogenic part of the biore-actor was 1.6 times higher than that reported for the experimentalsetup. The modeling process supported the determination of anintermediate cylinder diameter that increases biogas productionabove the level reported in a non-optimized bioreactor. FurtherFig. 5. Temperature in the methanogenic part of the bioreactor before and afteroptimization.experiments are required to validate those results.The optimal radius of the cylinder, Ri, dividing themethanogenicpart of the bioreactor into descending and ascending zones wasderived by solving the optimization problem described by formulas(16) and (17). The optimal radius of the intermediate cylinder, Ri,was equal to the upper bound and was determined at 40.5 cm. Thedata shown in Fig. 1b clearly indicates that the higher the radius ofthe intermediate cylinder, Ri, the higher the cross-sectional area ofthe descending zone of the methanogenic part of the bioreactor.The above results indicate that the cross-sectional area of thedescending zone of the methanogenic part of the bioreactor shouldbe as high as possible to guarantee maximum biogas production ina laboratory-scale two-stage mixed ow reactor.Table 3Total biogas production rates and percent distribution of gases in biogas, calculatedfor experimental (Exp) and optimized (Opt) variants of the intermediate cylinder ofthe bioreactor.BioreactorgeometryQm (g h1) CH4 (%) CO2 (%) H2S NH4 O2 (%)Exp 0.0897 64.5 2.3 34.5 2.5 1.0 0.5Opt 0.147 71.2 1.6 27.8 1.5 1.0 0.3The qualitative composition of biogas derived for the experi-mental and the optimized conguration of the digester is presentedin Table 3 in terms of percent distribution of gases in the biogas. Themethane fraction of biogas for the experimental digester wasdetermined at 64.5% before optimization and 71.2% after optimi-zation. An inverse relationship was observed for the carbon dioxidefraction of biogas, which was determined at 34.5% in the experi-mental digester and 27.8% in the optimized digester. The datashown in Table 3 conrms that it is possible to nd a diameter ofthe intermediate cylinder in the methanogenic part of the biore-actor that enhances methane production in an optimized digester(higher total biogas production) and improves biogas compositionby increasing its methane content and decreasing its carbon diox-ide content.The results of a performance analysis of an upgraded digesterare not discussed in this paper. Our ndings indicate that abioreactor should be characterized by an optimal diameter of theintermediate cylinder in the methanogenic part of the digester.The main purpose of a digester is to treat wastewater andgenerate biogas, but the reduction in the COD or BOD load ofwastewater and the amount of gas produced by a commercialdigester and a scaled digester are not given in this paper. Thoseparameters were measured in the experiment, but the results arenot provided.In our opinion, the proposed optimization process can beapplied in bioreactors of any size (laboratory, semi-industrial, in-dustrial scale), but since it relies on a simplied mathematicalmodel, the values of the analyzed coefcients have to be deter-mined separately for every optimized bioreactor. The theoreticalow inside the methanogenic part of the bioreactor can bedescribed with the use of the presented model, but real ow dy-namics will be different because the hydraulic diameter of theconcentric part of the reactor differs from that of a hollow purecylinder. In future work, this problem can be addressed byanalyzing real ow dynamics inside a reactor with the use of theCFD approach.4. ConclusionsThis study presented arguments for optimizing the constructionof anaerobic bioreactors to determine the optimal geometric pa-rameters of the digester. The experiments were conducted onanaerobic sludge from an anaerobic dairy wastewater treatmentplant. The Monod model was applied to describe microbial growthin a digester during low-temperature anaerobic digestion. Our re-sults indicate that the cross-sectional area of the descending zoneof the methanogenic part of the bioreactor should be as high aspossible to maximize total biogas production and optimize thedistribution of different gas fractions in biogas. The optimization ofthe diameter of the intermediate cylinder in an upgraded digestersignicantly increased total biogas production (by up to 160%) incomparison with the output noted before optimization. The di-mensions of the digester should be optimized during bioreactorconstruction to improve total biogas production efciency.Mathematical modeling and optimization techniques havemany potential applications for the construction of continuous-ow bioreactors in the biogas industry. An in-depth knowledge ofbiochemical processes in the bioreactor is required to guaranteeoptimal biogas production and stable plant operation. Mathemat-ical models can be used to expand our knowledge of the processand describe the effect of a bioreactors parameters, including itsgeometric characteristics, on its performance. The results of thisstudy suggest that bioreactor performance can be enhanced notonly by modifying the digestion control strategy, but also by opti-Energy 69 (2014) 219e225mizing a digesters geometrical characteristics.as an example of distributed cogeneration based on local renewableb sensitivity of growth kinetics to increase inQV volumetric ow rate of liquid in a bioreactor (m3 s1)opt optimalablein bioreactor inletout bioreactor outletsim simulatedReferences[1] Buswell AM, Mueller HF. Mechanisms of methane fermentation. Ind Eng Chem1952;44:550e2.[2] Kalloum S, Bouabdessalem H, Touzi A, Iddou A, Ouali MS. Biogas productionRa radius of the bioreactors hydrolyzer part (m)Rd radius of the bioreactors external part (m)Ri radius of the intermediate cylinder (m)Rlb, Rub lower and upper bound of changes in Ri (m)S substrate (general suspensions) concentration (kg m3)t time (s)T temperature (K)Tmax maximum temperature at which bacterial growth canoccur (K)Topt optimum temperature for bacterial growth (K)u velocity of liquid in a column (m s1)Vt, Vh, Vmvolume: total, hydrolyzer, methanogenic part (m3)X biomass concentration (kg m3)YE/X metabolic heat yield coefcient (J kg1 biomass)YP/X biomass-to-product (kg biogas kg1 biomass) yieldcoefcientYX/S substrate-to-biomass (kg biomass kg1 substrate) yieldcoefcientz coordinate measured along liquid stream inside thebioreactor (m)Greek symbolsm specic growth rate (s1)mmax maximum value of the specic growth rate (s1)mopt specic growth rate at the optimal temperature (s1)r density (kg m3)l thermal conductivity (W m1 K1)Subscripts0 initialexp measuredtemperature (K)Cp thermal capacity (J kg1 k1)E thermal energy (J m3)KM saturation constantL total column length (m)P, Ptotal actual total concentration of biogas (product) (kg m3)Qm total gas production rate in a bioreactor (kg s1)energy sources as part of the Innovative Economy OperationalProgram 2007e2013, as well as from the European RegionalDevelopment Fund.NomenclatureA organic compound load on reactor volume (1 g COD/l)AcknowledgmentsThis study received support from National ProjectPOIG.01.01.02-00-016/08 entitled Model agro-energy complexesM. 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Pol J EnvironStud Ser Monogr 2009;5:83e7.Optimizing low-temperature biogas production from biomass by anaerobic digestion1 Introduction2 Materials and methods2.1 Raw materials and sample preparation2.2 Experimental setup2.3 Instrumentation2.4 Calculations2.5 Optimization3 Results and discussion4 ConclusionsAcknowledgmentsNomenclatureReferences

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