Multi-objective optimization of methane production system from biomass through a

Weijun Li,Jakob Kjøbsted Huusom ,Zhimao Zhou ,Yi Nie ,Yajing Xu ,Xiangping Zhang ,*

1 Beijing Key Laboratory of Ionic Liquids Clean Process,State Key Laboratory of Multiphase Complex Systems,Institute of Process Engineering,Chinese Academy of Sciences,Beijing 100190,China

2 Sino-Danish Center for Education and Research,University of Chinese Academy of Sciences,Beijing 100049,China

3 Department of Chemical&Biochemical Engineering,Technical University of Denmark,DK 2800 Kgs.Lyngby,Denmark

Keywords:Biogas production system MINLP Multi-objective optimization Non-dominated sorting genetic algorithm II Green degree value

ABSTRACT This work addressed the multi-objective optimization of a biogas production system considering both environmental and economic criteria.A mixed integer non-linear programming(MINLP)model was established and solved with non-dominated sorting genetic algorithm II,from which the Pareto fronts,the optimal technology combinations and operation conditions were obtained and analyzed.It's found that the system is feasible in both environmental and economic considerations after optimization.The most expensive processing section is decarbonization;the most expensive equipment is anaerobic digester;the most power-consuming processing section is digestion,followed by decarbonization and waste management.The positive green degree value on the process is attributed to processing section of digestion and waste management.3:1 chicken feces and corn straw,solar energy,pressure swing adsorption and 3:1 chicken feces and rice straw,solar energy,pressure swing adsorption are turned out to be two robust technology combinations under different prices of methane and electricity by sensitivity analysis.The optimization results provide support for optimal design and operation of biogas production system considering environmental and economic objectives.

1.Introduction

Due to the depletion of fossil fuel and the environmental problems associated with fossil energy,considerable effort has been made to search for alternative energy[1,2].Biogas produced via anaerobic digestion of livestock and crop straw has attracted worldwide interest as it is clean and renewable energy[1,3].The produced biogas is generally utilized for the production of electricity,heat,vehicle fuel[4]and natural gas substitute after purification,and the digestate byproductcan be employed as fertilizer after treatment.Atypicalbiogas production systemincludes the processing section ofbiomass collection and transportation,pretreatment,anaerobic digestion,biogas cleaning and decarbonization,and waste management.In addition,there are a variety of options for feedstocks,digestion heat supply technologies and biogas decarbonization technologies.Thus,it's difficult to obtain the optimal flowsheet and section combination for a biogas production system only by simple calculation and empirical analysis.

Considerable efforts have been made to evaluate and optimize the individual processing sections of a biogas production system.For example,Yu et al.[5,6]improved a site selection and biomass delivery model,and make it suitable for many types of biomass and road delivery.Singh et al.[7]developed a mathematical model for collecting and transporting biomass from fields to the power plant.The model was used to calculate the unit transportation cost,and found that the unit cost decreases as the transportation distance increases.Ariunbaatar et al.[8]compared factors like efficiency,environmental sustainability,capital and operational costs of different pretreatment pathways,and found that the process with thermal pretreatment at low temperature with two stages digestion presents the best economic performance.Mendes etal.[9]used ADM1 modelto investigate the variation ofbiogas yield and biogas composition with changing digestion time.Wu et al.[10]established two-column six-step pressure swing adsorption simulation model for biogas decarbonization.It was found that the processes with MOF-508b and CMS-3K as adsorbents can decrease the energy consumption by 56%and 50%,respectively,compared with the Zeolite 13X absorbent.Rehl et al.[11]conducted Life Cycle Assessment(LCA)to compare the energy efficiency and environmental impact of different biogas digestate treatment alternatives.The belt dryer is turned out to be the option with highest primary energy demand,Global Warming Potential(GWP)and acidification potential(AP)among the compared options.The solar dryer has the lowest environmental impact.

Furthermore,for comprehensive assessment of the biogas production system,Wu et al.[12]established energy models for each processing section and evaluated the energy efficiency of the system in 32 scenarios(2 digestion technologies alternatives,4 decarbonization technology alternatives,2 heatsupply methods,and 2 waste heatrecovery options).In addition,they conducted energetic-environmentaleconomic assessment of a typical biogas production system with three utilization pathways(CPH,bio-methane and fuel cell)[13].

The literature work focused eitheron the modeling and optimization of individual processing sections,or on the assessments of the biogas production system.However,systematic optimization of the whole system considering multi indicators like economic performance and environmental impact which has a great significance to both future research and industrial applications,has not been reported.

The aim ofthis study is to establish a superstructure fora typicalbiogas production system considering nine kinds of common feedstock materials,three kinds of common heat supply technologies and four kinds of promising decarbonization technologies.Following this,the biogas production system is optimized with respect to the criteria of economic and environmental performance,and solved by employing non-dominated sorting genetic algorithm(NSGAII)[14].Sensitivity analysis of methane and electricity price as well as plant scales,are performed and discussed.

2.Methodology

2.1.System description

The benchmark data of this work is based on the Nanjing University of Technology's biogas demonstration project,which have a biogas production of 500 m3per day.The studied biogas production system is present in Fig.1,which consists of the following processing sections:Biomass collection and transportation,Pretreatment(chopping(CHO)and briquetting(BRI)),Co-digestion,Desulphurization,Dehumidification,Decarburization(PWS,ILs,PSA,MEA),Waste management(solid-liquid separation,drying,slurry concentration).

The mass flowrate of the feedstock(chicken feces mixes with crop straw and fresh water)is fixed at 13.6 ton per day.The total solid content(TS)in the feedstock is specified as 10%.The digestate slurry outlet from digester with higher temperature is used to pre-heat the biomass feedstock by a heat exchanger.The products from the whole system are 2×106Pa methane,solid fertilizer and liquid fertilizer.For PWS process,the CO2is emitted to the atmosphere directly;for other decarbonization processes,the resulting pure CO2is treated as product.The circulating water is used to prepare digestion feedstock.The detailed description of each sections are conducted in following sections,where the models of energy consumption,economic performance and biogas yield are included and explained,as part of the objective functions.

2.2.Models

2.2.1.Collection and transportation

The demonstration project is built in the livestock farm,so only the cost and energy consumption for collecting and transporting crop straw is considered.Wu et al.[12]developed an energy consumption model Eq.(1)for the process considering a circle collection area and a tortuosity factor to validate the straight line distance.

where Ec&tisthe specific thermalenergy consumption forcollection and transportation section,in MJ·m-3;FCbis the specific fuel consumption,in L·t·km-1;FHV is the lower heating value of the liquid fuel,in MJ·L-1;τ is the tortuosity factor,equal to 1.5;ρ is the distribution density of crop straw,in t·km-2;mcaris the mass of transport truck,in ton;s is the distance from livestock farm to crop straw collection site,in km;Q is the collection rate of crop straw,in t·d-1;VCH4is the volume flowrate of methane,in m3·day-1.

The cost of this section is only fuel cost from transportation by assuming no commercial value of chicken feces and crop straws.Then the cost is calculated by Eq.(2)

where Cc&tis the cost of collection and transportation section,in USD·d-1;Ptis the specific transportation cost,in USD·km·t-1.

Fig.1.Biogas production and upgrading system.

The mass flowrates of feedstock materials are calculated by Eqs.(3)-(4)

where Qchickenfecesis the mass flowrate of chicken feces in feedstock,in t·d-1;Qi,strawis the mass flowrate of i straw in feedstock,in t·d-1;n is the mass ratio of chicken feces and crop straw;TSchickenfecesand TSi,straware the solid content in chicken feces and i straw,i=wheat,corn,rice.

2.2.2.Pretreatment

Machines for chopping and briquetting are employed for the pretreatment of the crop straw to enhance its decomposition and hence the biogas yield.

Bitra et al.[15]presented the energy consumption model of the chopping process

Mani et al.[16]presented the energy consumption model of the briquetting process

Total energy consumption was calculated by using Eq.(7)

where Echop,Ebriqand Epreare the specific energy consumption of chopping,briquetting,pretreatment processes,in MJ·m-3,respectively.d is the particle size after chopping,in mm;Qstrawis the straw collection rate,in t·d-1;ηHTEis conversion efficiency of thermal energy to electric energy,0.39[17];PBis the briquetting pressure,in MPa;M is moisture content of crop straw.

The equipments involved in this section are machines of chopping and briquetting,with fixed cost of 3000 USD for each one.The variable cost is the power prices,calculated by Eq.(8).

where EPpreisthe electricity costperday,in USD·d-1;Peleisthe electricity price,in USD·kW·h-1.

2.2.3.Co-digestion

Co-digestion is the simultaneous digestion of a mixture of two or more substrates,with technological,ecological and economic advantages[18].This project applied a mixture of chicken feces,crop straw(wheatstraw,corn straw,rice straw)and fresh water as digestion feedstock.The biogas yield strongly depends on the types and composition of feedstock,the digestion temperature(T),and the residence time(t).The empirical equation of biogas yield is reported by Ou-yan et al.[19],as a function of T,t and substrate composition.

The energy consumption of an anaerobic digestion section mainly consists of four parts:heat for heating the fresh feedstock(Eheating),heat loss of the digester due to convection heat loss(Eloss),power for mechanical agitation(Eagi)and the power for pumping the feedstock(Epump).The models are presented in Eqs.(9)-(14).The power of the pump is necessary to estimate its investment cost and is calculated by Eq.(13)[20].

where Eheating,Eloss,Eagi,and Epumpare the specific energy consumption by heating substrate,compensating heat loss,agitation and pumping,in MJ·m-3,respectively;Wagiand Wpumpare the power of agitator and pump,in kW,respectively.t is the digestion time,day;T and Tambare the digestion and ambienttemperature,in°C,respectively.Cpmis the specific heatcapacity ofsubstrate in digester,assuming 4.2 kJ·kg-1·K-1,because it has similar property with water.Qfis the mass flowrate of the feedstock,in t·d-1;Stop,Sbot,Ssideare the top,bottom and side areas of the digester,in m2,respectively,which can be easily calculated by assuming that the diameter equals to height;δinsand δDare the thickness of the insulation layer and the digester,in m,respectively.λinsandλDare the coefficientofthermalconductivity ofthe insulation layerand the digester,in W·m-1·K,respectively.αis the heattransfer coefficient,in W·m-2·K;ρfis the feedstock density,in kg·m-3;P1and P2are the pressure before and after pumping,in 105Pa,respectively.ηpand ηmare the efficiencies of pump(0.5)and motor(0.9),respectively.

The equipment involved in the digestion section includes digester,pump,agitator and heat supply equipment.The equipment for heat supply includes three alternatives,i.e.,solar collector,biogas boiler and biomass boiler.The price of digester and insulation is 100 USD·m-3[13],the price of agitator is estimated according to its power,around 700 USD·kW-1[21].The prices ofbiogas boiler and biomass boiler are 4200 USD.The cost of solar collector is 150 USD·m-2[22].The investment cost(IC)of pump is estimated according to the bare module costs method reported by Biegle et al.[20],shown in Eqs.(15)-(16)

where BC is the base cost,and IC is the investment cost and UF is an update factor for current price,4.91[23];C0is the reference cost,in USD;S0is the reference characteristic values of equipment like power and heat duty;S is the characteristic values of equipment;MPF and MF are material and pressure correction factor and module cost.

The area of solar collector is calculated according to Eq.(17)

where A is the area ofsolarcollector,in m2;I is intensity ofsolarradiation per day,in kJ·m-2·d-1;ηjis the efficiency of solar collector,0.55;ηsis the heat loss rate of pipeline and water storage tank,0.1.

The power price is calculated by Eq.(18)

2.2.4.Desulfurization and Dehumidification

Biogas mainly consists of CO2and CH4and small amount of water vapor and trace amountofH2S.Generally,the H2S contentin raw biogas is in the range of 200 to 2000 μl·L-1.The desulfurization method and setup as well as plant performance and economic factors are reported by Krischan et al.[24].The water vapor in biogas ranges from 5%to 10%,depending on the temperature[25],assuming 7%in this study.Refrigeration dryer is employed for dehumidification.Its price and power is 4500 USD and 3 kW,respectively.

2.2.5.Decarburization

The technology options for decarburization section include pressured water scrubbing(PSW),ionic liquid scrubbing(ILs),monoethanolamine scrubbing(MEA)and pressure swing adsorption(PSA).The modeling of these upgrading technologies is our previous work[10,26,27].For the former three technologies,L16(43)orthogonal test is designed to obtain empirical models for key parameters,i.e.gas liquid ratios,the amount of circulating gas,diameter of columns and energy consumption.

The empirical formulas are used to determine the gas flowrate,circulating solvent flowrate,which are necessary to calculate the size and power of pump,compressor,blower, flash,and the investment of solvents.For PWS and ILs processes,the gas flowrate into the absorber is determined by Eq.(19);for MEA process,it's determined by Eq.(20).The circulating solvent flowrate in absorber is calculated by Eq.(21).For MEA process,the biogas flowrate in to the absorber is calculated by Eq.(22)

where Ffeedgasis the flowrate of gas into absorber,in m3·d-1; γ is the amount of circulating gas,in%;Vbiogasis the flowrate of biogas,in m3·d-1;L is the flowrate of solvent,in m3·d-1.

For PWS,ILs and MEA processes,their specific energy consumptions are calculated according to the empirical models.For adiabatic PSA process,the energy consumption is estimated according to Eq.(23)[28].

where F is the flowrate of gas stream,in mol·s-1;Phighand Ploware the adsorption pressure and the desorption pressure,in 105Pa,respectively.Tfeedis the temperature of gas stream,in °C;γ =Cp/Cv,which assumes a value of 1.31;η is the mechanical efficiency,0.8 in this study.

After decarbonization,a multistage pump is employed to compress the CH4to 2 MPa to meet the natural gas grid requirement.The equipment involved in each processes are summarized in Table 1.

The investment costs of pump,vacuum pump,compressor,blower,column,heat exchanger,reboiler and condenser(treated as heat exchangers),and flash are calculated by Eqs.(15),(16),(24)[20].

where L0,D0are the reference characteristic values ofequipmentlike size,power and heat duty;L,D are the characteristic values of equipment.

The purchase cost of water,MEA solvent,[Bmim][Tf2N]solvent and CMS-3 K adsorbent is 0.46 USD·t-1,1500 USD·t-1,224900 USD·t-1and 15000 USD·t-1,respectively.

2.2.6.Waste management

In this study,the digestate is firstly sent to a screw-press for solidliquid separation.Then solid fraction of digestate with 65%water contentgoes to a dryermachine to getsolid bio-fertilizer.The liquid fraction goesto hybrid membrane technology forrecovery ofliquid fertilizerand industrialwater[29].The sand filter firstly traps the suspended materialand bacterial.Then the permeate get through micro filtration membrane,ultra filtration membrane and nano filtration membrane successively to get the concentrated liquid fertilizer and circulating water.The operation pressure of MF membrane and NF is 2×105Pa and 4.8×105Pa,respectively.Hence two pumps are employed to meet the operation pressures.Assume that after concentration,permeation fluid accounts 80%of the total slurry flowrate.The energy consumption for screw-press and dryer,Esep&dry,was established by Wu et al.[12]and shown in Eq.(25)

Table 1 Equipment involved in different processes

where mslurryis the mass flowrate of the digestate slurry,in t·d-1;mdigestateis the mass flowrate of solid fraction of digestate,in t·d-1.

The energy consumption for the two pumps and the waste management section is calculated by using Eq.(26)-(28).

where Ewm,Epump1,Epump2are the specific energy consumptions ofwaste management section,in MJ·m-3.EPwmis the electricity price,in USD·d-1.

The electricity price is calculated by using Eq.(29)

The cost of sand filter,micro filtration membrane,ultra filtration membrane,nano filtration membrane and biogas slurry pool is 1274 USD,600×4 USD,577×4 USD,360×4 USD and 6000 USD,respectively.The costs of pumps are calculated by using Eqs.(15)and(16)from the previous section.

2.3.Optimization

2.3.1.Objective functions

In this study,the economic and environmental performance are evaluated using NPV method and Green degree method,respectively.The NPV of the biogas production system is calculated by Eqs.(30)and(31).The projectis economically feasible ifthe NPV is positive[30].

where CF0is the initial investment,USD;GM is the gross margin per year,a constant value by assuming stable operation,USD;r is the discount rate,which assumes a value of 0.05.

Payback period(PB)and internalrate ofreturn(IRR)are two important economic parameters for assessing economic feasibility of the process.They can be calculated according to Eqs.(32)and(33).

The initial investment(CF0)is the total facility investment(TFI),which consists of two components i.e.base plant cost(BPC)and project contingency(PC);the gross margin(GM)is defined as the revenue of product minus the operation cost.The methodology was proposed by Hussain[31]and is shown in Table 2.

Table 2 Economic and process factors for biogas project

Green degree(GD)is a composite index proposed by Zhang et al.[33]for quantitatively assessing the environmental impact of a substance,stream or process based on nine environmental categories[33].The Green degrees of substance,stream and process are calculated by Eqs.(34)-(39).A positive GD value indicates that the process is benign to environment.

Based on models established above,seven important variables were chosen for our optimization problem:digestion temperature,residence time,absorption pressure,lean liquid loading,types and compositions of biomass,decarbonization technologies and heating modes of digester.They are summarized in Table 3.

Table 3 Variables of the optimization problem and their boundaries

The presented energy and economic model are coupled with the mass balance models for each technology in formulation of the optimization problem.Gas densities of biogas,CO2and CH4are 1.276 kg·m-3,0.717 kg·m-3and 1.96 kg·m-3,respectively,which are necessary for mass balance.

Note that the local variables are activated only when relevant technologies are selected.The absorption pressure will be activated when ILsand PWS technologiesare selected.The lean liquid loading willbe activated when MEA technology is selected.

2.3.2.Multi-objective optimization formulation

Fig.2.Pareto optimal curve.

Table 4 The optimized technology combinations

With all these models,variables and objective functions,a mixedinteger nonlinear programming(MINLP)problem is formulated and solved with a real-coded non-dominated sorting genetic algorithms-II(NSGA-II)to maximize the NPV and Green degree simultaneously.The MINLP model is coded in MATLAB.All the computational studies are performed on a workstation with an intel Xeon@professor E5-2670 v3 2.30 GHz-CPU,and 64-GB(8×8GB)RAM.The population size is set as 1000,and the number of generation is set as 6000.The crossover probability of crossover(Pc)and mutation(Pm)are 0.9 and 0.1,respectively.

3.Results and Discussion

3.1.Optimization results

The program is implemented 10 runs,from which the consistent Pareto-optimal solution set is obtained.The Pareto solutions are generated with respect to two objectives,shown in Fig.2.Note that the true Pareto frontis difficultto obtain,hence in industriala reference solution set is used to represent it.The Pareto curve shows the optimal trade-off designs of the biogas production system.Each Pareto point on the three curves represents the optimal design of the biogas production system with unique tradeoff between the NPV and Green degree.As shown in Fig.2,the environmental impact is positive for all the Pareto solutions,in the range of 1.23×105gd·a-1to 1.75×105gd·a-1.The NPV is positive for all the Pareto solutions,from 0.30×105USD to 1.40×105USD.So the solutions are feasible in both environmental and economic considerations.Curve A presents highest average Green degree,but lowest average NPV.Curve C presents highestaverage NPV,but lowest average Green degree.

The technology combinations of these three curves are shown in Table 4.According to the simulation results listed in Tables 4,3:1(wt%)chicken feces and rice straw and 3:1(wt%)chicken feces and corn straw are demonstrated to be the optimal two feedstock among the feedstock candidates in this study.PSA is demonstrated to be the optimal decarbonization option.The ILs and PWS technologies have relative low energy consumption but high fixed cost.Because they are physical absorption with relative low absorption capacity,hence they have large amount of circulating solvent,resulting in large equipment sizes and high fixed cost.The advantages of lower energy consumption cannot compensate their disadvantages of higher fixed cost,so they died in the evolution.The MEA process is based on chemical absorption with high absorption capacity,so it has small equipment size and fixed cost.But it has much higher energy consumption due to higher reboiler duty.And the extra electricity cost associated with energy consumption can compensate the advantages of fixed cost.Sothe MEA process died in the evolution.The PSA technology has relative low fixed cost,low energy consumption and it doesn't emit CO2to the environment hence it's optimal in both economical and environmental considerations.By comparing curves A and B with C,solar energy has advantage regarding environmental feasibility while biomass boiler has advantage regarding to economic feasibility.Because the solar collector is expensive while the biomass boiler is cheap but it releases lf ue gases like CO2,SO2and NOx.Biogas to supply heat demand doesn't appear in the optimized profile hence it's demonstrated to be an unideal choice.

Table 5 The process configurations and performance of the selected Pareto points

Fig.3.The equipment purchase cost distribution(BRI:Briquette;CHO:Chop;DGR:Digester;BB:Biomass Boiler;AGT:Agitator;PM1:Pump1;PM2:Pump2;PM3:Pump3;DS:Desulfurization;DEH:Dehumidification;ADS:Adsorber;DES:Desorber;CP1:Compressor1;CP2:Compressor2;SCP:Screw Press;SLP:Slurry Pool;MBR:Membranes;SF:Solid Filter;DRY:Dryer).

Fig.4.The processing sections purchase cost distribution(PRE:Pretreatment;DGN:Digestion;DEH:Dehumidification;DEC:Decarbonization;WM:Waste Management;CT:Collection&Transportation).

By visualinspection,the Pareto fronts in differenttechnology combinations have similar trend.The NPV are increasing in the direction from Pareto point A1 to C3 at the expense of decreasing the Green degree value,which shows the tradeoff relations between NPV and Green degree.A1 has the highest Green degree of 174830 gd·a-1due to its lowest energy consumption and the use of solar collector.But it has the lowest NPV 30191 USD due to its lowest biogas yield resulting from the lowest digestion temperature and shortest residence time.C3 has the highest NPV 139850 USD and the lowest Green degree 123460 gd·a-1.

The goal of the optimization is to maximize these two objectives simultaneously,but along the Pareto front no objective can be improved without the expense of other objectives.The region above the Pareto front is the infeasible region.

The operation condition and systemperformance for selected Pareto points are shown in Table 5.The digestion temperature is distributed between 35 °C and 48 °C and the residence time is distributed between 18.7 day and 25.4 day.Higher digestion temperature can consume a lot of energy and decrease the biogas yield simultaneously.Longer digestion time can resultin large digestion volume and large agitation energy consumption hence higher fixed cost and energy consumption.

Fig.5.The energy distribution between processing sections.

Pareto point B1 is selected and analyzed to revealthe sections costdistribution,the cost distribution of equipment in each section,the energy distribution and the green degree distribution of the system.Fig.3 presents the equipment purchase cost distribution of Pareto point B1.The most expensive equipment is the anaerobic digester,followed by compressor1 and compressor2 in the PSA process,and the desulfurization setup.The fixed cost distribution between processing sections is shown in Fig.4.The most expensive processing section is decarbonization,followed by digestion and waste management,respectively.Fig.5 presents the energy consumption distribution among seven processing sections.As shown in Fig.5,28.40%of the total energy consumption is attributed to the digestion section,which includes the energy consumption of agitation and pumping.Within the digestion section,the agitation contributes 72.70%of the energy consumption of the digestion section.27.92% of the total energy consumption is attributed to the decarbonization section,which includes the energy consumption of compressor1,compressor2.27.79%ofthe energy consumption isattributed to waste management section,which includes the energy consumption of pump2,pump3 and screw press and dryer.Within the waste management section,the pump2 and pump3 contribute 22.82%and 64.55%of the energy consumption,respectively,and the screw press and dryer contributes 12.62%.It's hence concluded that most of the energy consumption comes from the pumps;membranes with better performance and atlower working pressure needs specialattention in the research and development.Fig.6 presents the GD distribution between processing sections.All the processing sections except decarbonization and waste management have negative Green degree.The decarbonization section has the lowest Green degree,which indicates the worst environmental performance.The Green degree of the decarbonization section is attributed to its energy consumption,and the decarbonication has very high energy consumption share as shown in Fig.5.Note that the Green degree of energy consumption is calculated based on the environmental impact associated with the energy production.For the digestion section,on one hand,it consumes a lot of energy.On the other hand,it converts biomass waste with negative GD value to crude biogas product with GD of 0 and biogas digestate with less environmental impact,which has positive Green degree.Compromise of the two effects mentioned above resulted in the positive Green degree,which indicates an environmental friendly process.This processing step is the biggest contributor in terms of numericalvalue,hence it's key to have an environmentalfriendly process.For the waste management section,although it consumes a lot of energy,it converts biogas digestate into fertilizer product with GD of 0.Compromise of these two effects resulted in the positive Green degree,which indicates an environmental friendly process.For the processing sections of collection and transportation,pretreatment,desulfurization and dehumidification,their Green degree are attributed to their energy consumption.

Fig.6.The green degree distribution between processing sections.

Table 6 The optimized technology combinations at different conditions

3.2.Sensitivity analysis

Since the prices of electricity and methane fluctuate frequently and different plant scales are required in industrial application,hence sensitivity analysis is conducted for them one by one,in order to study their effects on the optimized profiles and to study the robustness of the Pareto solutions.The optimized profile atdifferentprices of electricity and methane is shown in Table 6.

The electricity price can affect the two objective functions by affecting the energy consumption of the system hence to affect its methane yield and operating cost.The methane price can affect the objective functions by affecting the methane yield.As a result,new Pareto solutions including technology combinations and operation conditions are obtained at different electricity price and methane price,as shown in Table 6.It's interesting thatsome technology combinations are included in all the optimized profiles,i.e.3:1 chicken feces and corn straw,solar energy,PSA and 3:1 chicken feces and rice straw,solar energy,PSA,which indicates robust technology combinations.It is also found that the plantscale has no effecton the optimized technology combinations.Consequently,these technology combinations can be safely extended to other scales.

4.Conclusions

Pareto fronts and solutions were obtained and analyzed for the biogas production system.The results indicate an environmental friendly and economically feasible process and can provide strategy for design and operation of the biogas production system.It's found that the most expensive processing section is decarbonization;the most expensive equipment is anaerobic digester;the most power-consuming processing section is digestion,followed by decarbonization and waste management.The positive green degree value on the process is attributed to section of digestion and waste management.3:1 chicken feces and corn straw,solar energy,PSA and 3:1 chicken feces and rice straw,solar energy,PSA are turned out to be two robust technology combinations under different prices of methane and electricity by sensitivity analysis.