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Egieya et al. BMC Chemical -5(2020) 2:3RESEARCH ARTICLEBMC Chemical EngineeringOpen AccessOptimization of biogas supply networksconsidering multiple objectives and auctiontrading prices of electricityJafaru Musa Egieya1,2, Lidija Čuček3* , Klavdija Zirngast3, Adeniyi Jide Isafiade2 and Zdravko Kravanja3AbstractThis contribution presents an hourly-based optimization of a biogas supply network to generate electricity, heat andorganic fertilizer while considering multiple objectives and auction trading prices of electricity. The optimization modelis formulated as a mixed-integer linear programming (MILP) utilizing a four-layer biogas supply chain. The modelaccounts for biogas plants based on two capacity levels of methane to produce on average 1 0.1 MW and 5 0.2MW electricity. Three objectives are put forward: i) maximization of economic profit, ii) maximization of economic profitwhile considering cost/benefits from greenhouse gas (GHG) emissions (economic GHG profit) and iii) maximization ofsustainability profit. The results show that the economic profit accrued on hourly-based auction trading prices isnegative (loss), hence, four additional scenarios are put forward: i) a scenario whereby carbon prices are steadilyincreased to the prevalent eco-costs/eco-benefits of global warming; ii) a scenario whereby all the electricity auctiontrading prices are multiplied by certain factors to find the profitability breakeven factor, iii) a scenario whereby shortertime periods are applied, and investment cost of biogas storage is reduced showing a relationship between cost,volume of biogas stored and the variations in electricity production and (iv) a scenario whereby the capacity of thebiogas plant is varied from 1 MW and 5 MW as it affects economics of the process. The models are applied to anillustrative case study of agricultural biogas plants in Slovenia where a maximum of three biogas plants could beselected. The results hence present the effects of the simultaneous relationship of economic profit, economic GHGprofit and sustainability profit on the supply and its benefit to decision-making.Keywords: Biogas production, Auction trading prices of electricity, Supply network optimization, Multiple objectives,Economic profitabilityIntroductionIn December 2015, over 190 countries across the globeacceded to employing activities and technologies thatminimize the effects of global climate change [1].Among the technologies considered is to increase theutilization of biomass-derived energy sources (also calledbioenergy). Furthermore, in Yue et al. [2], utilising bioenergy has the potential to: bolster energy security ineconomies not having fossil energy sources; mitigate theeffects of variable fossil energy prices and availability;improve waste management concerning exploiting foodwastes to produce bioenergy thereby creating wealth. A* Correspondence: [email protected] of Chemistry and Chemical Engineering, University of Maribor,Smetanova ulica 17, 2000 Maribor, SloveniaFull list of author information is available at the end of the articlemore recent study in Hegnsholt et al. [3] shows that onaverage 33% of total annual worldwide food production(1.6 109 t/y) costing 1.2 1012 /y goes to waste. Thismassive loss of food is a subject of concern; it is unacceptable, and severely hampers the United Nations’Sustainable Development Goals target to cut the foodloss and waste by 50% in 2030 [4].Consequently, against this backdrop, some countries havelaid down policies to accelerate the increased integration ofbioenergy in their economy. For example, the national government of India in 2009 adopted a policy to produce about14 105 t/y of biofuels to meet 20% blending of biofuels usedin the transportation fuels by the year 2020 [5]. It is noteworthy that this policy only considers the use of non-ediblefeedstock retrieved from lands unsuitable for agriculture toprevent food versus fuel conflicts. In another case, the The Author(s). 2020 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication o/1.0/) applies to the data made available in this article, unless otherwise stated.

Egieya et al. BMC Chemical Engineering(2020) 2:3government of Ghana enacted a biofuels policy to substitute petroleum fuels with 10% biofuels by 2020 and a further increase to 20% biofuels incorporation by 2030 [6].The Ghana government included additional policies directed to exploiting energy from wastes such as municipal,industrial and agricultural wastes [6]. India and Ghana aregenerally described as developing countries but in other situations, developed countries have also instituted policies toaccelerate bioenergy exploitation. The USA, through theEnergy Independence and Security Act (EISA) of 2007, setsan annual production target of 116 106 t/y of biofuels by2022 [2]. Moreover, the EU in another case aims to substitute 10% of the transportation fuel in all EU countries withbiofuels by 2020 [7]. Alternatively, it is interesting to notethat China places bold targets to harness biomass energyfrom disparate sources implementable on five-year plans.For example, its current policy (13th five-year spanning2016–2020) indicates that on or before the year 2020, therate of utilization of energy derived from biomass shouldexceed 58 106 t/y of standard coal while biogas employedfor cooking should reach 80 106 m3 and electricity generated from the same biogas should be at least 500 MWe [8].With these policies in place, implementing them haspresented some challenges. In Hegnsholt [3], designing,modelling and effecting robust supply chains is suggested as a veritable tool required to bolster bioenergyintegration in any economy. In effect, all bioenergy production supply chains consist of several actors (farmers/waste collection and acquisition centres, production/conversion facilities and different demand zones) whichare constantly interacting [9]. These actors are usuallypresent in different geographical locations which necessitate producing bioenergy products in a timely fashionto meet certain demands. A closer examination of theseactors shows the following:i.Farmers/waste collection centres – Usuallycontain feedstocks that are described as firstgeneration (1G), second-generation (2G) and thirdgeneration (3G) [10]. The 1G feedstocks (starch-,sugar- and oil-based) are edible foods which haveled to the rise in prices of food due to competitionin accessing limited resources (like land) to producebioenergy products [1]. Today, majority of bioenergy investments are based on 1G feedstocks (suchas sugarcane, corn and palm oil) whereby mostcommercialized bioenergy production technologiesalso utilize the 1G feedstocks [11]. On the otherhand, 2G feedstocks are those which contain lignocellulosic and waste materials (like manure, municipal wastes, straw or even bagasse) and unlike the1G feedstocks, these feedstocks are not edible. Theyhave enough potential to produce bioenergy whilesimultaneously not affecting the cost and availabilityPage 2 of 23of food crops. However, the 3G feedstocks usuallyreferred to as algae, on average produce more energy per area than any other generation of feedstocks but today, 3G feedstock are only used on alaboratory scale.ii. Production/Conversion Technologies – Thereare three groups of biomass conversiontechnologies currently in use today and these arethermo-chemical conversion (direct combustion, liquefaction, gasification, pyrolysis), physico-chemicalconversion (transesterification) and biochemicalconversion (anaerobic digestion, fermentation,composting).iii. Demand centres – These centres are usually thelocations whereby the bioenergy products are eitherblended with conventional fossil fuels for onwarduse or directly consumed.As stated earlier, these bioenergy products must be delivered to meet certain demands in a timely fashion. Thedemand constraints placed on bioenergy may be set oneconomic, environmental and/or social objectives oreach of the individual objectives [2]. Hence, as a backdrop of the above context, the following section introduces some of the recent works carried out in themodelling and optimization of bioenergy or biogas production supply chains which is the focus of this work.Review of literature on biogas/bioenergy supplychain optimizationIn recent years, there has been a considerable increasein research on bioenergy supply chain optimization.These studies have generally been geared towards individually meeting economic, environmental, social objectives or a combination of the objectives on certaintimescales. For example, El-Halwagi et al. [12] simultaneously modelled the minimization of risk (as ametric of the social objective) and total annual cost(TAC) in the supply chain of biorefining system appliedto bio-hydrogen production. Zirngast et al. [13] proposed four-step methodology for flexible supply network synthesis under uncertainty applied to biogasproduction where economic, eco- and viability profitswere maximized. Emara et al. [14] developed a MILPmodel, using C#, MATLAB and Excel Solver, tominimize the TAC in the supply chain of biofuel andchemicals from waste cooking oil. Ivanov et al. [15]researched the supply chain production of bioethanolfrom 1G and 2G feedstocks whereby TAC and greenhouse gas (GHG) emissions are minimized and thenumber of jobs created maximized. The economic andenvironmental optimization of biogas supply chain(maximization of annual profit and GHG emission savings) has been performed using MILP optimization

Egieya et al. BMC Chemical Engineering(2020) 2:3approach and applied for a region in Mexico by DíazTrujillo et al. [16].Several optimization studies have been carried outover hourly, daily, monthly and yearly timeframes. Forinstance, Egieya et al. [17] modelled a multi-month andmulti-year MILP model for bioelectricity supply chainproduction in Slovenia. Mousavi Ahranjani et al. [18], ina more recent study, developed a fuzzy programmingmodel for bioethanol supply chain network design overa 10 years’ planning horizon in Iran. Čuček et al. [19]presented an optimally integrated supply chain networkto produce bioenergy from 1G, 2G, and 3G feedstocksmonthly using a MILP model. Besides, Egieya et al. [20],in another study, employed a MILP model which proposes hourly, daily, and monthly generation of bioelectricity from biogas in Slovenia.Some economic objective-based studies involve theminimization of TAC [15], others emphasize maximizingprofit [21], while a few others maximized the net presentvalue (NPV) of a supply chain [22]. Concerning environmental objectives, minimizing global warming potential, exemplified by limiting GHG emissions, is receiving the mostattention [23]. Several supply chain optimization studiesperformed optimization of economic-environmental partswhile social sustainability is less commonly addressed. It isthe least understood sustainability pillar, thus also called“missing pillar” [24]. Social pillar is often qualitative by nature and it is challenging to build a single metric for socialsustainability and to incorporate it into mathematicalmodels. Some work has been done recently, e.g. by Youet al. [25] who maximized the number of jobs created in abioenergy production supply chain, El-Halwagi et al. [12]who modelled safety as a metric of the social objective andZore et al. [26] who optimized social profit from variousmicro- and macroeconomic perspectives [27].From the previous studies, it is found that only afew researchers considered shorter time-periods, suchas hourly time periods, while the bulk of bioenergysupply chain optimization studies have concentratedon bioethanol and biodiesel production, with a limitedfew on biogas supply chains. In this work, beyondwhat has previously been done to the best of ourknowledge, two biogas plant capacities (on average ofabout 1 MW and 5 MW capacity of electricity production) are considered, and an optimization is performed based on different economic and sustainabilityobjectives simultaneously accommodating hourly, dailyand monthly optimization basis and auction tradingprices of electricity. An additional input to this studyis the integration of biogas storage to enable simultaneous electricity production at higher prices withbiogas storage at low electricity prices. Moreover,model size reduction techniques are implemented toshorten the computational time of each model.Page 3 of 23Problem statementA holistic supply network management comprising severalagricultural feedstocks (with different harvesting periods,availability and prices), transport modes, conversion technologies, and products with various prices includinghourly-based electricity prices, was considered. Egieyaet al. [28] introduced the single objective function of economic profit maximization which has been opined in several quarters to be unsuitable for realistic completeanalysis and synthesis of bioenergy supply chains/networks. In this respect, for the optimal design of biogassupply networks, other optimization criteria such as maximizing unburdening from GHG emissions (maximizingthe profit from GHG emission unburdening) and including the sustainability profit maximization are therefore addressed, see Fig. 1.Hence, the design problem entails the problemstatement given in Egieya et al. [28] and the followingadditions: eco-costs [29] of feedstocks during harvesting andcollection; eco-benefits [30] of feedstocks use; eco-costs/eco-benefits of intermediate and finalproducts; eco-costs of transport modes; GHG emissions of feedstocks during harvesting andcollection; GHG emissions of intermediate and final productsgeneration; GHG emissions due to transport; avoided GHG emissions due to harmful feedstocksuse and substitution of products [30]; social costs and profits [26].The objectives of the upgraded model are tomaximize economic profit, maximize economic profitwhile including costs and benefits due to releasedand avoided GHG emissions in the biogas supplynetwork on the other hand, and to maximize thesustainability profit. Four scenarios are performed toimprove the applicability of the biogas supply network, such as: Increasing the price for GHG emissions fromapproximately 20 /t (as of 24 February 2019 [31])or 26.6 /t by using the conversion rate of 1.33 / (as used in [17, 20, 28] to the value of eco-costs /benefits of global warming which is 116 /t [32] or154.28 /t (based on considered conversion); Multiplying the values of auction trading prices bycertain factors to obtain the prices where biogasproduction becomes economically profitable. Thisscenario could provide answers to how much

Egieya et al. BMC Chemical Engineering(2020) 2:3Page 4 of 23Fig. 1 Biogas supply network considering multiple objectives (modified from [28])subsidies may be needed to make the biogasproduction plant profitable in a case where GHGemission unburdening is not considered; Shortening the length of the time period which willenable higher differences in electricity prices.Additionally, this scenario shows the relationbetween the investment cost of biogas storage, thevolume of biogas stored and electricity production. Varying the capacity of the biogas plant capacityfrom 1 MW to 5 MW while observing its effects oneconomic profits.It follows that the variables to be optimized are: quantity, geographical location and total acquisitioncost of feedstocks and/or raw materials; cost incurred in the supply chain and types oftransport modes selected; other supply network management costs(depreciation, maintenance, operating, storage ); primary and secondary conversion facilities locationand capacities; the sustainability profits effect on the supplynetwork; global warming (GHG emissions) effect on thesupply network; impact of the solution on the profit maximization; trade-offs when choosing different objectives; subsidies required to obtain economic break-evenpoint for biogas production.The general model (MILP problem) discussed inEgieya et al. [28] is also applicable to this study which isslightly extended to include new economic, environmental and social sustainability objectives.MethodologyThis work follows the concept put forward by Egieyaet al. [28] while considering the following additions andextensions: The model is formulated on an hourly basis(previously on monthly basis in Egieya et al. [28]),where the year is divided into monthly (mp), daily(dp) and hourly (hp) time periods. Consequently, allthe equations which were based on monthly periods,are now delineated to monthly, daily and hourlyperiods. To implement this, certain model reductiontechniques are therefore introduced to reducecomputational time. Instead of subsidized prices of electricity (fixed),hourly-based auction trading prices of electricity areconsidered based on 2017 prices, ranging from 42.93 to 199.00 /MWh (between 57.1 and 264.67 /MWh) [33]. The highest electricity price was inAugust, while the lowest price was in December2017. The hourly-based electricity price variationsare illustrated in Figs. 2 and 3 for the months ofAugust and December 2017. All the data relatedto electricity prices (in /MWh) as obtained fromBSP South Pool Energy Exchange [33] arepresented in Additional file 1: Tables S1-S12).Furthermore, the average electricity prices (in /MWh) for each of the considered period basedon model reduction techniques and implemented

Egieya et al. BMC Chemical Engineering(2020) 2:3Page 5 of 23Fig. 2 Hourly-based electricity prices for August 2017 (data obtained from [33])in the model are also given in the Additional file1: Tables S13-S24). Biogas storage is incorporated to account forpossible variations in electricity production, i.e. toenable storing biogas instead of electricityproduction at low electricity prices. However, insuch situations, heat is also not produced, and thusa backup is required to generate heat from othersources. Instead of considering only one agricultural biogasproduction plant as the optimal plant and with thecapacity of up to 999 kW, a maximum of threebiogas plants could be selected. Despite thevariations in electricity production, biogasproduction should be constant with slight variationsallowed. Thus two scenarios are performed based onthe demand for methane, i) between 1.95 106 and2.38 106 m3/y (average 0.9–1.1 MW of electricityproduced) and ii) between 9.76 106 and 11.93 106m3/y (average 4.8–5.2 MW of electricity produced). Two additional objectives are considered besides aneconomic one in the form of maximizingsustainability profit [26] and the simultaneousmaximization of profit with the costs and thebenefits attributed to GHG burdening andunburdening. Hence, the model is upgraded toinclude environmental (GHG emissions) andsustainability (eco-cost and benefit and social costand benefit) objectives.Description of biogas supply networkThe biogas supply network utilized (see Fig. 4) consistsof four layers:i) First layer (L1): harvesting and collection. Thislayer consists of a set pb of biomass feedstocks(corn, wheat and triticale grains, straw, silage, andgrass silage) and different manure types (cattle, pigand poultry manure, poultry bedding and poultryslurry). For the feedstocks, characteristics such asdry matter and methane contents and biogas yields[34] are considered in the study.ii) Second layer (L2): primary processing technologywhich is anaerobic digestion. In L2, the primaryconversion product pi (a combination of biomassand waste feedstocks pb, recycled products poutpimand purchased products pbuy) is generated. Theseare later converted to intermediate products pmFig. 3 Hourly-based electricity prices for December 2017 (data obtained from [33])

Egieya et al. BMC Chemical Engineering(2020) 2:3Page 6 of 23Fig. 4 Four-layer biogas supply network applied in this study (after [14, 28])(biogas and wet digestate) or final products pdusing given conversion factors.iii) Third layer (L3): secondary conversiontechnologies involve cogeneration (CHP) combiningheat and power production and physical dewateringas in [28]. It should be noted that there are otherpossible conversion technologies, such as biogasupgrading to biomethane [35], ammonium sulfaterecovery from digestate [36] and several other,however they have not been considered in thisstudy. The products pz (a sum of intermediateproducts pm, recycled product poutpin, andpurchased products pbuy) are converted (usingconversion factors) to the desired products pp(electricity, heat and dry digestate).iv) Fourth layer (L4): demand locations.The model considers three optional distribution modesbetween the layers to convey feedstocks, intermediate andfinal products, in the form of road, pipeline transport, andtransmission lines. Besides, the model allows heat andelectricity generated from the CHP and water from thedewatering plants to be reused within the supply network.For sustainable supply of all materials within the supplynetwork, four storage facilities are also modelled at the locations of biomass and waste collection centres and primary and secondary conversion facilities, where allfeedstocks and products could be stored. Additionally, it isassumed that water, electricity, and heat are excluded fromstorage and that the purchased materials should not bestored. Note that from the previous work of Egieya et al.[28] biogas could additionally be stored.Similarly, as in Egieya et al. [28], certain characteristicsof biomass and waste feedstocks are considered, such asdifferent dry matter contents, methane contents and biogas yields [34]. Also, other parameters as presented inEgieya et al. [28] are considered, except instead of guaranteed purchase prices which are fixed, auction tradingprices which vary hourly are considered.For more details on the biogas production supply network methodology, the reader is referred to the paper byEgieya et al. [28].

Egieya et al. BMC Chemical Engineering(2020) 2:3Page 7 of 23Description of mathematical modelThe mathematical model includes material and energybalances, primary and secondary conversion constraintsand cost correlations. However, as the model now considers hourly production, all the variables, and equationswhich were based on monthly periods, are now based onmonthly, daily and hourly periods.As the hourly-based model is computationally expensive, certain model reduction techniques have been implemented based on the work by Lam et al. [37] toreduce computational time. Hence, instead of 24 h a day,three “hourly periods” or shift periods (morning, afternoon and night) are considered and are thereby definedas H1 (7 am – 2 pm), H2 (3 pm – 10 pm) and H3 (11 pm– 6 am). Furthermore, instead of 28–31 days a month,seven “daily periods” are applied based on the days ofthe week (Monday – Sunday) and are defined as D1:{d1, d8, d15, d22, d29}, D2: {d2, d9, d16, d23, d30}, D3: {d3,d10, d17, d24, d31}, D4: {d4, d11, d18, d25}, D5: {d5, d12, d19,d26}, D6: {d6, d13, d20, d27} and D7: {d7, d14, d21, d28}, seealso Egieya et al. [20]. This is due to different electricityconsumption patterns of the weekdays and weekends.All 12 months of a calendar year are on the other handfully considered in order to preserve the variability ofthe model as much as practicable. Merging of time periods is done by defining the sets MPOM, DPOD andHPOH which convert the maximal number of time periods (mpo, dpo and hpo) to merged time periods (mp,dp and hp).All the prices except electricity prices are consideredat merged hourly basis as shown in Eq. (1):X Pp;mpompo MPP p;mp;dp;hp ¼ Xðmpo;mpÞ MPOM mpo MPðmpo;mpÞ MPOMj mpo j; p P p felectricityg; mp MP; dp DP; hp HP; ðdp; mpÞ DPMð1Þwhere stands for logical condition (dollar operator inGAMS [38]).As electricity prices are provided on hourly basis, theyare averaged in order to more properly account for theirvariations. Averaging electricity prices is illustrated inEq. (2):Pelectricity;mp;dp;hpX ¼ XXmpo MPO dpo DPO hpo HPOXmpo MPO ðmpo;mpÞ MPOM ðmpo;mpÞ MPOM;ðhpo;hpÞ HPOH;ðdpo;dpÞ DPOD;ðdpo;mpoÞ DPMXj mpo j Xdpo DPO ðdpo;mpÞ DPM mp MPO; dp DPO; hp HPO ðdpo;dpÞ DPODj dpo j P electricity;mpo;dpo;hpoXhpo HPO ðhpo;hpÞ HPOHj hpo j;ð2ÞThe hourly-based variations in the model have beenintroduced with the production rate of feedstocks pb atthe harvesting zone i, which is now defined based onmerged hourly periods hp, merged daily periods dp andmonthly periods mp (PRi, pb, mp, dp, hp in kt/period), seealso Eq. (7) in Egieya et al. [28]:X X PRi;pb;mp;dp;hpdp DP hp HPðdp;mpÞ DPM¼ HY i;pb;mp Ai;pb;mp ; i I; pb PB; mp MPð3Þwhere HYi, pb, mp is the yield of feedstocks pb in monthperiod mp at harvesting zone i (in kt/(km2 month)) andAi, pb, mp is the available area for growing biomass pb atharvesting zone i in month period mp (in km2).The equations for storages additionally consider “circular operations”. The equation for storage at the inletof primary conversion facilities is for example defined asshown in Eq. (4), see also Eq. (9) in Egieya et al. [28].AinL2m;pi;mp;dp;hp ¼ AinL2m;pi;mp 1;dp 1;hp 1 þðmpk Þk K ;k¼1 ðdpk Þk K ;k¼1 ðhpk Þk K ;k¼1AinL2þ AinL2 m;pi;mp;dp;hp 1m;pi;mp;dp 1;hp 1 þðhpk Þk K ;k 1ðdpk Þk K ;k 1 ðhpk Þk K ;k¼1L2 Ainm;pi;mp 1;dp 1;hp 1 þðmpk Þk K ;k 1 ðdpk Þk K ;k¼1 ðhpk Þk K ;k¼1X X L1;L2;netX XF i;m;pb;mp;dp;hp þF L3;L2;netn;m;poutpim;mp;dp;hp þi I pb PIn N poutpim PIX buy;L2XX X L1;L4;netF m;pbuy;mp;dp;hp F L2;TF m; j;pn;mp;dp;hp þm;pi;t;mp;dp;hp j J pn PIpbuy PIðpi;t Þ PIT t 2 TL2L2ðAinm;pi;mp;dp;hp þ Ainm;pi;mp 1;dp 1;hp 1 þðmpk Þk K ;k¼1 ðdpk Þk K ;k¼1 ðhpk Þk K ;k¼1 AinL2þ AinL2m;pi;mp;dp;hp 1m;pi;mp;dp 1;hp 1 þðhpk Þk K ;k 1ðdpk Þk K ;k 1 ðhpk Þk K ;k¼1L2 Ainm;pi;mp 1;dp 1;hp 1 þðmpk Þk K ;k 1 ðdpk Þk K ;k¼1 ðhpk Þk K ;k¼1AinL2 m;pi;mp 1;dp 1;hp 1 Þ 2 ψ pi;mp;dp;hpðmpk Þk K ;k 1 ðdpk Þk K ;k¼1 ðhpk Þk K ;k¼1 m M; pi PI pi NOSTOR; mp MP; dp DP; hp HP; ðdp; mpÞ DPMð4ÞIn Eq. (4) AinL2m;pi;mp;dp;hp represents the storage quantityof material pi in each monthly mp, daily dp and hourly timeperiod hp at the location of primary conversion facility m,AinL2m;pi;mp 1;dp 1;hp 1 refers to the quantity of material piin the storage tank at the beginning of January (first hour,first day and first month) which equals the quantity of material pi in the storage tank at the last hour of December(last hour, last day, last month) of the previous year. Similarly, AinL2m;pi;mp;dp;hp 1 refers to quantity of material pi inthe storage tank for each month and day where the hourshould not be the first hour of the day, AinL2m;pi;mp;dp 1;hp 1refers to the quantity of material pi in the storage tank foreach first hour of the day and if the day is not the first dayof the month and AinL2m;pi;mp 1;dp 1;hp 1 refers to quantityof material pi in the storage tank for each first hour in aday and for each first day in a month of any given monthexcept January (first month).Additional terms in Eq. (4) are: F L1;L2;neti;m;pb;mp;dp;hp representsthe net quantity of biomass and waste feedstocks pb shippedto the primary conversion location m from the harvestinglocation i in each considered time period (mp, dp, hp),L3;L2;netF n;m;poutpim;mp;dp;hpis the net flow of “recycled” material in

Egieya et al. BMC Chemical Engineering(2020) 2:3Page 8 of 23the supply network poutpim between the secondary n andprimary conversion location m, also for each consideredtime period. Such products are electricity, heat and water, asbuy;L2shown in Fig. 4. F m;pbuy;mp;dp;hp stands for the quantity ofpurchased resources pbuy to be used at L2 (primary conversion) on the location of m in each of the considered timeperiod. F L2;Tm;pi;t;mp;dp;hp is the flow of intermediate productpi (pb, poutpim, pbuy) from storage to technology t2 T atprimary conversion location m in each time period andF L1;L4m; j;pn;mp;dp;hp quantifies the flow of unprocessed feedstockspn PI to the demand location j. The last term of Eq. (4)represents the losses of stored intermediate materials pi during the storage. Similarly as in Egieya et al. [28], it is assumed that the amount of stored intermediate products(pi PI pi NOSTOR) available in any considered timeperiod mp, dp, hp is the average of two consecutive time periods. Parameter ψpi, mp, dp, hp represents the deteriorationrate in storage which is defined on monthly basis ψpi, mp,and is then divided by the length of the daily and hourlyperiod (cardinality of sets DP and HP), as shown in Eq. (5):ψ pi;mp;dp;hp ¼ψ pi;mp; p P; mp MP; dp DP; hp HP; ðdp; mpÞ DPMj dp‖hp jð5ÞAs it was stated above, all the potential biogas plantscould be selected. Since only slight variations in capacityof anaerobic digesters are allowed, two scenarios are performed based on the demand for methane, i) between1.95 106 and 2.38 106 m3/y (average 0.9–1.1 MW of electricity produced) and ii) between 9.76 106 and 11.93 106m3/y (average 4.8–5.2 MW of electricity produced). Thecapacities of methane between their upper and lowerbounds are shown in Eq. (6) for lower bound and in Eq.(7) for upper bound.Xpi PI ðpi;methaneÞ PIPM;ðpi;ADÞ PITF L2;Pm;pi;methane;AD;mp;dp;hp 0:9 m M; mp MP; dp DP; hp HP; ðdp; mpÞ DPMDemelectricity;mp;dp;hp;L3f conv;Tmethane;electricity;CHP yL2;Tm;AD ;ð6ÞXpi PI ðpi;methaneÞ PIPM;ðpi;ADÞ PITF L2;Pm;pi;methane;AD;mp;dp;hp 1:1 m M; mp MP; dp DP; hp HP; ðdp; mpÞ DPMDemelectricity;mp;dp;hp;L3f conv;Tmethane;electricity;CHP yL2;Tm;AD ;ð7ÞIn Eq. (6) and Eq. (7) F L2;Pm;pi;methane;AD;mp;dp;hp representsthe flowrate of methane produced from material pi usinganaerobic

about 1MW and 5MW capacity of electricity produc-tion) are considered, and an optimization is per-formed based on different economic and sustainability objectives simultaneously accommodating hourly, daily and monthly optimization basis and auction trading