Optimal Design and Planning of Biofuel Supply Chain with Reduced Greenhouse Gas Emission

Bulgarian Chemical Communications, Volume 46, Number 2 (pp. 294 – 305) 2014

Optimal design and planning of biodiesel supply chain considering crop rotation model Part 1. Mathematical model formulation of the problem

B. Ivanov1*, B. Dimitrova1, D. Dobrudzhaliev2 1Institute of Chemical Engineering-BAS,Acad. G. Bonchev Str., Bl. 103, Sofia 1113-Bulgaria E-mail: bivanov @ bas .bg, systmeng @ bas .bg 2 Prof. Dr. Assen Zlatarov University, Bourgas 8000-Bulgaria

Received June 3, 2013; revised January 3, 2014 This paper addresses the optimal design and location facility of biodiesel supply chains (BSC) under economic and environmental criteria. The economical aspect scale is assessed by the total annualized cost. The environmental objective is evaluated by the total GHG (Green House Gases) emissions for a whole life cycle. A mathematical model that can be used to design the supply chain (SC) and manage the logistics of a biodiesel is proposed. The model determines the number, size and location of biorefineries needed to produce biodiesel using the available biomass. Mixed-integer linear programming model is proposed that takes into account infrastructure compatibility, demand distribution, as male as the size and location of biorefineries needed to produce biodiesel using the available biomass and carbon tax. An important feature of the model proposed is the account requirement of crop rotation important from agronomic perspective. In second part of this study Bulgaria is examined as the testing ground of the model. KEYWORDS: Biodiesel supply chains, Energy crops, Production cost, Carbon tax, Crop rotation, MILP

INTRODUCTION targets. In order to explicitly stimulate a shift to renewables in transportation, thes European Aimed at mitigating emissions, diversifying the Commission has, in addition to the overall 20% energy supply and reducing dependence on renewable energy target, set a mandatory target of imported fossil fuels, the European Union (EU) has 10% renewable energy in transport by 2020 [8], set ambitious targets for a transition to renewable with a transitional target of 5.75% for 2010 [4]. energy. The integrated energy and climate change A number of policy instruments that directly or policy adopted in 2008 defines general targets of indirectly affect the production and use of biofuels 20% greenhouse gas reduction, 20% reduced are today in place in the EU. Targeted biofuel energy use through increased energy efficiency and policies such as exemption from or reduction of a 20% share of renewable energy by 2020 [8]. transport fuel taxes, quotas and blend obligations Among the available alternative energy sources effect directly the competitiveness and market that would help to respond to such challenges, shares of biofuels. biomass crops have many advantages over This paper presents development and use of a conventional energy and over some other optimisation model suitable for extensive analysis renewable energy sources (e.g. wind, photovoltaic, of biofuel production scenarios aimed at etc.). In particular, this is due to reduced determiniation and investigation of advantageous dependence on short-term weather changes, locations for biodiesel production. The main focus promotion of regional economic structures and is on assessing how different parameters affect provision of alternative sources of employment in biodiesel production regarding costs, plant rural areas. locations, production volumes and the possibility of Becouse biomass can replace fossil fuels in the reducing global fossil emissions. Key parameters to transport sector increased production and use of be studied are economic policy instruments bioenergy is promoted as a key to facher the affecting biodiesel production, such as targeted biofuel support and the cost for emitting, energy * To whom all correspondence should be sent: prices, feedstock costs and availability, and capital E-mail: : [email protected]. © 2014 Bulgarian Academy of Sciences, Union of Chemists in Bulgaria

38 Boyan Ivanov et all., Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model ……

B. Ivanov et al., Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model …… costs. The above mentioned 5.75% share of plants, biomass and bioethanol flows between biofuels for meeting the 2010 target is used as a regions, and the number of transport units required starting point, with the analysis focusing on for the transfer of these products between regions boundary conditions that affect the possibility of as well as for local delivery. The model also meeting this goal. determines the optimal bioethanol production and The paper is focused on the creation of biomass cultivation rates. conditions for stable operation of BSC by providing You and Wang (2011) [16] recently addressed a stable supply of feedstock. According to recent the life cycle optimisation of biomass-to-liquids SC research in agricultural activities [21,17,12,18] crop under the economic and environmental criteria. rotation is the basis for sustainable yields. The Their work shows that distributed biomass model proposed includes conditions for crop processing followed by centralized upgrading of rotation as realistic ones. intermediates may lead to economically viable and environmentally sustainable biofuels supply chains. LITERATURE REVIEW Akgul, O., et al. (2012) [18] presents a multi- The papers most relevant to the problem objective, static modeling framework for the addressed in this work are on the optimal design optimisation of hybrid ﬁrst/second generation and operations of the process (SC). A general biofuel supply chains. Using the proposed review of this area is presented by Shah (2005) [5] modelling framework, different aspects are and Papageorgiou (2009) [9]. Some recent work analysed including the potential GHG savings, the specifically focused on BSCs is reviewed below. impact of carbon tax on the economic and Zamboni et al. (2009) [10] presented a MILP environmental performance of a BSC, the trade-off model for the strategic design of biofuel supply between the economic and environmental networks. The model takes into account the issues objectives and the maximum bioethanol throughput affecting a general BSC simultaneously, such as that can be achieved at different cap levels on the agricultural practice, biomass supplier allocation, total SC cost. The trade-off between the conﬂicting production site locations and capacity assignment, objectives is analysed by solving the proposed logistics distribution, and transport system multi-objective model using the  -constraint optimisation. method. Eksioglu et al. (2009) [11] proposed a MILP Bioenergy represent a sustainable solution for model for the design and operations of a biomass to energy generation. To achieve these goals, one biorefinery SC. The model determines the optimal must create the conditions for sustainable yields of number, size, and location of biorefineries and energy crops. According to research conducted in feedstock collection as well as the amount of recent years [17,18] this can be achieved by biomass to be processed and shipped and biomass rotation of crops. Further studies [12,21] in this inventory levels through a multi period formulation. direction indicate that crop rotation has a beneficial Recently, Kim et al. (2011) [13] proposed a impact on reducing greenhouse gases generated in MILP model for the optimal design of biorefinery the cultivation of energy crops. supply chains. The model aims to maximize the Crop rotation has been long recognized as a overall profit and takes into account different types system that can reduce soil erosion, improve soil of biomass, conversion technologies, and several structure, enhance permeability, increase the soil feedstock and plant locations. microbial activity, enhance soil water storage Another recent contribution in this area is the capacity, and increase soil organic matter [1,2]. work by Aksoy et al. (2011) [14]. The authors Moreover, crop rotation can reduce the use of investigated four biorefinery technologies for external inputs through internal nutrient recycling, feedstock allocation, optimal facility location, maintenance of the long-term productivity of the economic feasibility, and their economic impacts in land, avoidance of accumulation of pests associated Alabama, through a MILP based facility location with monoculture, and consequently increase crop model that minimizes the total transportation cost yields [2]. The aforementioned beneficial effects on and takes into account county-level information. soil physical, chemical and biological properties Akgul et al. (2011) [15] presented recently a can further be improved by combining crop MILP model based on the one proposed by Zaboni rotations with cover crops and reduced or no tillage et al. (2009) [10] for the optimal design of a practices bioethanol SC with the objective of minimizing the An additional novelty of our work is that the total SC cost. Their model aims to optimize the proposed model takes into account most of the locations and scales of the bioethanol production major characteristics of the BSC and is integrated

39 B. Ivanov et al., Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model …… with LCA. From the literature available in this area For each transportation link, the transportation it can be concluded that the models of BSC biofuels capacity (in both volume and weight), available used account for the basic characteristics but no transportation modes, unit transportation cost of works go into details to account for the rational use each mode, transportation distance, and emissions of the available land. The models do not include of each transportation type are known. also agronomic conditions for long-term cultivation of crops for biofuel production such as the ones the General formulation of the problem needed for different bio cultures. Finally, the overall problem can be summarized AIM as: Given are: The main objective this sudy is to propose an  potential locations of biofuel demand centers and optimisation model hat could predic determine their biofuel demand, location and size of biodiesel production plants, given the locations of feedstock and energy  demand for liquid fuels (diesel) for each of the demand. The model comed minimise the costs of demand centers for fuel, the complete BSC of the studied system, including  the minimum required ratio between classical biomass harvest, biomass transportation, and proportions fuels and biofuels for blending, conversion to biodiesel, transportation and delivery  biomass feedstock types and their geographical of biodiesel. Economic performances can be availability, evaluated in terms of Net Present Value (NPV).  unit biomass cultivation cost for each feedstock Environmental impact based on GHG emissions type, reduction, calculated through LCA, is important in  unit production cost of biodiesel based on the order to ensure proper or wise criteria approach to technology and feedstock type, sustainability and to allow distinguishing the  transport logistics characteristics (cost, modes), differences between various feedstock as. Fossil  capital investment cost for the biodiesel emissions meet be also considered, by including production facilities, costs for emisions, such as tax or tradable emission  specific GHG emission factors of the biodiesel permits. Sustainability of the work of BSC can be life cycle stages, ensured through sustainable supply of bio-  carbon tax, resources, that in turnis guaranteed by annual  government incentives for biodiesel production rotation areas for different bio cultures. and use. PROBLEM STATEMENT The problem addressed in this work can be MATHEMATICAL FORMULATION OF THE stated formally, as follows. A set of biofuel crops PROBLEM that can be converted to biodiesel. These includes Given the scenario, the role of the optimization agricultural e.g. sunflower, energy crops and a.s.o. model is to identify what combination of options is A planning horizon of one year government most efficient to supply the facility. A very regulations including manufacturing, construction important efficiency measure is to minimize the and carbon tax is considered. A BSC network facility supply cost taken as a present value. superstructure, including a set of harvesting sites The problem for optimal location of biodiesel and a set of demand zones, as well as the potential (B100) production plants and efficient use of the locations of a number of collection facilities and available land is formulated as a mixed integer bio refineries is descanted. Feed stocks can be linear programming (MILP) model with the shipped to the bio refineries directly. notations, given in Tables 1-3. Unit cost and emission data for biofuel crops As noted in item 3, the assessment work of production and harvesting are also given. For each BSC production and distribution of biodiesel potential collection facility, we the fixed and (B100) will be carried out based on two variable cost of facility construction are given. For criteria, namely, economically and each potential biorefinery given the cost of production for different levels and capacity. environmentally. The optimal solution would For each demand zone, the biofuel demand is be a compromise between these two criteria. given, and the environmental burden associated with biofuel distribution in local region is known.

40 B. Ivanov et al.: Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model ……

Table 1. Input Sets used in the model Sets Description of Sets/Indices I Set of biomass types indexed by i ; L Set of transport modes for biomass indexed by l ; B Set of transport modes for biodiesel is a subset of L ( B  L ) indexed by b ; S Set of life cycle stages of a BSC indexed by s ; P Set of plant size intervals indexed by p ; G Set of regions of the territorial division indexed by g F Set of candidate regions for biodiesel plants established, which is a subset of G indexed by f ; C Set of biodiesel customer zones, which is a subset of G ( C  G ) indexed by c .

Table 2 Input variables for the problem Symbol Description Emission factor for cultivation of biomass type i in region g , EFBCig kg CO2  eq / ton biomass Emission factor for biodiesel(B100) production from biomass type , EFBPi i  I

kg CO2  eq / ton biofuel Emission factor for transport of biomass per unit of type with transport type , EFTRAil i  I l kg CO2  eq / ton km Emission factor for transport of biodiesel(B100) with transport type , EFTRBb b  B kg CO2  eq / ton km

EFTM l Transportation emission factor of for mode l  L , kg CO2  eq / ton km

GHGB GHG emission from BSC, kg CO2  eq / ton Actual delivery distance between regions producing biomass and regions producing ADDgfl biodiesel(B100) via model l , km Actual delivery distance between regions producing biodiesel(B100) and demand regions ADFfcb c  C via model b  B , km Biomass to biodiesel(B100) conversion factor for biomass type to biodiesel(B100)  i i  I ton biodiesel/ton biomass, Dimensionless

C Carbon tax per unit of carbon emitted from the operation of the BSC, $ / kg CO2  eq CO2

YOc Years demands of petroleum diesel in the customer zones, ton / year ENO Energy equivalent unit of petroleum diesel , GJ / ton ENB Energy equivalent unit of biodiesel(B100), GJ / ton PO Price of petroleum diesel, $ / ton PB Price of biodiesel(B100) produced from biomass, $ / ton

Cost p Capital cost of plant size p  P for biodiesel(B100) production, $ MIN / MAX Minimum/Maximum annual capacity of the plant of size p  P for biodiesel(B100) PBp production, ton / year MAX The annual demand for biodiesel(B100) in the customer zones, ton / year ZBc MAX Maximum flow rate of biomass from region g  G , QI ig i  I ton / d MAX Maximum flow rate of biodiesel(B100) from region f  F , QB f ton / d MIN / MAX Minimum/Maximum biomass of type which can be produced in the region g  G per PBIig i  I year, ton / year

41 B. Ivanov et al., Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model ……

 g Operating period for the region g  G in a year, d / year

f f Operating period for biodiesel(B100) production plants in region f  F in a year, d / year

cc Operating period for the region c  C in a year, d / year

INS f The government incentive includes construction incentive and volumetric, $ / ton

ECB Emissions emitted during the combustion of CO2 unit biodiesel(B100),

kg CO2  eq / ton biofuel

ECG Emissions emitted during the combustion of CO2 unit petroleum diesel,

kg CO2  eq / ton biofuel CCF Capital charge factor, year 1 g UCCig Unit biomass cultivation cost of biomass type i in region , $ / ton Unit biodiesel production cost from biomass type i at a biorefinery of scale p installed in UPCipf region f  F , $ / ton

UTCigfl Unit transport cost of biomass i  I via mode l  L between region g  G and biorefinery f  F , $ / ton

UTB fcb Unit transport cost of biodiesel(B100) via mode b  B between biorefinery f  F and demand regions c  C , $ / ton S Set-aside area available in region g  G , Ag ha Food Set-aside area available in region for food g  G , Ag ha TEIF MAX Maximum permissible values for the total environmental impact of biodiesel(B100) network of SC and fossil fuel in the regions, kg CO2  eq / d TDC MAX Maximum total cost of a biodiesel(B100) SC network, $

 ig The yield per hectare of type i  I biomass in the region g  G , ton / ha Food The total amount of bio-resources of type i  I , which must be provided for all regions QB i g  G for food security, ton MIN Optimal capacity of transport l  L used for transportation of biomass i  I , ton QTil MIN Optimal capacity of transport b  B used for transportation of biodiesel(B100), ton QTBb K mix Proportion of biodiesel(B100) and petroleum-diesel subject of mixing for each of the c customer zones. The ratio of biodiesel(B100) and petroleum diesel is more energy equivalent

ENB QEBc mix cC between the two fuels. K c  , Dimensionless ENOYOc cC const Factor to the change of the base price, depending on the region f  F where the plant is M f const installed M f  1, Dimensionless

Table 3. Decision variables for the problem Positive Continuous Variables

PBBig Production rate of biomass i  I in region g  G , ton /d

QIigfl Flow rate of biomass i  I via mode l  L from region g  G to f  F , ton /d

QBipfcb Flow rate of biodiesel produced from biomass i  I via mode b  B from region f  F to c  C at a plant of scale p located in region f  F , ton /d

42 B. Ivanov et al:, Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model …… Quantity of petroleum diesel to be supplied to meet the energy needs of the region , QEOc c  C ton / year Quantity of biodiesel(B100) produced from biomass to be supplied to meet the energy needs of the QEBc region c  C , ton / year Land occupied by first generation crop in region g , Aig i ha F Land by crops needed for food security of the population in the region g  G , Aig i  I ha Binary variables

X igfl 0-1 binary variable, equal to 1 if a biomass type i  I is transported from region g  G to f  F using transport l  L and 0 otherwise

Yfcb 0-1 binary variable, equal to 1 if a biodiesel is transported from region f  F to c  C using transport b  B and 0 otherwise

Z pf 0-1 binary variable, equal to 1 if a plant size p  P is installed in f  F and 0 otherwise

Basic relationships  biomass transportation from source Total environmental impact at work on BSC. The locations to processing facilities, environmental impact of the BSC is measured in  emissions from biodiesel production,  transportation of biodiesel(B100) facilities terms of total GHG emissions ( kgCO  eq ) 2 to the demand zones, stemming from SC activities and the total emissions  emissions from biodiesel(B100) usage in are converted to carbon credits by multiplying them vehicle operations. with the carbon price (per kgCO2  eq ) in the Ecological assessment criteria will represent the market. total environmental impact at work on BSC through The three main greenhouse gases emitted the resulting greenhouse gas emissions. These emissions are equal to the sum of the impact that from the SC are methane ( CH 4 ), nitrous oxide each of the stages of the life cycle has on the N O CO ( 2 ) and carbon dioxide ( 2 ). The values environment and are expressed by the dependence: of these parameters for life cycle inventory are obtained. Life Cycle Inventory after grouping TEI  ELBC  ELBP  ELTR  EBCAR (1) the GHGs (i.e., CO2 , CH 4 and N 2O ) into a where single indicator in terms of carbon dioxide TEI Total environmental impact at work on equivalent emissions (CO  eq / year ) by 1 2 BSC ( kg CO  eq d ); using their respective global warming 2 potentials (GWPs) based on the ELBC  recommendation of Intergovernmental Panel  ELBP  Environmental impact of life cycle on Climate Change (IPCC, 2007) [6] for the  ELTR 100 year time horizon is, as follows: 1 for CO2  stages ( kg CO  eq d 1 ); , 25 for CH 4 , and 298 for N 2O . 2 The environmental objective is to minimize EB Emissions from biodiesel usage in the total annual GHG emission (te) resulting CAR 1 from the operations of the biodiesel supply vehicle operations ( kg CO2  eq d ); chains. The formulation of this objective is The environmental impact is evaluated at based on the field-to wheel life cycle analysis every stage s  S of the life cycle as: that takes into account the following life cycle A. Growing biomass (including drying, stages of biomass-based liquid transportation storage); fuels: B. Production of biodiesel(B100);  biomass cultivation, growth, and acquisition, C. Transportation resources (biomass and biodiesel(B100)).

43 B. Ivanov et al: Optimal design and planning of biodiesel supply chain…..Part1.diesel) Mathematical to provide model the …… energy balance of 1 Greenhouse gases to grow biomass is: the region ( kg CO2  eq d ); TEI Environmental impact at work on BSC (   ig Aig  1 EL   EFBC  kg CO2  eq d ); BC  ig  (2) iI gG  g   EGCAR Emissions from petroleum diesel usage in vehicle operations ( kg CO  eq d 1 where, ELBC denotes the total environmental 2 impact of biomass cultivation, which in general ); represents the production rate of resource i  I in Emissions from petroleum diesel usage in vehicle region g G , refers in this equation to the to supplement the energy balance: cultivation rate of biomass i  I in that region.  ECG QEOc  EG    (7) Total emissions from biodiesel(B100) production is CAR  c  determined by the equation: cC  c  Total cost of a BSC network. The annual ELBP   EFBPi iQIigfl  (3) gG iI f F lL operational cost includes the biomass feedstock acquisition cost, the local distribution cost of final where ELBP is total environmental impact of biodiesel(B100) production through given fuel product, the production costs of final products, and the transportation costs of biomass, and final technology ( kg CO eq d 1 ). 2  products. In the production cost, we consider both The environmental impact of transportation is the fixed annual operating cost, which is given as a calculated by: percentage of the corresponding total capital investment, and the net variable cost, which is ELTR   EFTRAil ADDgfl QI igfl  proportional to the processing amount. In the iI gG f F lL transportation cost, both distance-fixed cost and (4) distance-variable cost are considered. The  EFTRBb ADFfcbQBipfcb  iI pP f F cC bB economic criterion will be the cost of living expenses to include total investment cost of where is environmental impact of ELTR biodiesel(B100) production facilities and operation 1 transportation of resources ( kg CO2  eq d ); of the BSC for the operating period. This price is expressed through the dependence: Emissions from biodiesel (B100) usage in vehicle TDC  TIC  TPC  TTC  TTAXB  TL (8) operations: where TDC Total cost of a BSC network for year ( EBCAR   ECB QBipfcb  (5) iI pP f F cC bB $ year 1 ); where EBCAR is emissions from biodiesel(B100) TIC Investment costs of production capacity of 1 biodiesel(B100) relative to the operational usage in vehicle operations ( kg CO2  eq d ). period of redemption and up time of the Total environmental impact of the used fuels plant per year ( $ year 1 ); (biodiesel(B100) and diesel) to provide the energy 1 balance of the region. Environmental goal is to TPC Production cost ($ year ); reduce the annual equivalent of greenhouse gases, TTC Transportation cost ($ year 1 ); resulting from the operations of SC of TTAXB A carbon tax levied according to the total biodiesel(B100) and diesel to meet the energy needs of the regions. amount of CO2 generated in the work of Annual equivalent of greenhouse gases of the the whole BSC for year ($ year 1 ); B. Ivanov et al: Optimal design and planning of biodiesel supply chain…..Part1. Mathematical model …… used fuels is determined by the equation: TL Government incentives for biodiesel 1 TEIF  TEI  EGCAR (6) production and use ( $ year ). where TEIF Total environmental impact of the used a/ Total investment costs model: fuels (biodiesel (B100) and petroleum The components TIC of (8) shall be determined under the following relationships:

44 TICB. IvanovCCF et al: OptimalCost designF Z and planning of biodiesel supplya variable chain…..Part1. cost Mathematical ( IB ,OB model). Fixed …… costs include  pf pf  (9) il b f F pP loading and unloading costs. They do not depend The refinery capital cost consists of fixed and on the distance of transport. Variable costs include variable capital cost. The fixed capital cost varies fuel cost, driver cost, maintenance cost etc. They by the refinery locations. The variable capital cost are dependent on the distance of transport. of biomass-to-biodiesel(B100) plants, is mainly d/ Government incentives for biodiesel (B100) influenced by the plant size, since the technology is production cost model considered mature. Government incentives for biodiesel(B100) Variable capital cost are scaled using the general production and use is determined by the equation: relationship [20].   R   TL   INS f   i Aig ig  (12) Cost p  Sizep      f F gG iI     ,   Cost base  Size base  e/ A carbon tax levied cost model A carbon tax levied is determined by the where Cost p is variable capital cost and Sizep equation: represents the investment cost and plant capacity YELBC  YELBP  respectively for the new plant, Costbase indicates TTAXB    C (13)   CO2 the known investment cost for a certain plant YELTR  FEBCAR  capacity Sizebase , and R is the scaling factor where, YELBC is the total GHG emissions for usually between 0.6 and 0.8. biomass cultivation, YELTR is the environmental Capital cost of biorefinery for each region is impact of transportation of resources within the determined by the equation: network and YEL is the environmental impact of Cost F  M cost Cost ,p, f , BP pf f p biodiesel (B100) production a year working in the cos t where M f is a correction factor in the price of BSC and determined by the following equations: bio-refineries in the region f  F according to its YEL  EFBC A  cos t BC  ig ig ig , installed M f 1. iI gG b/ Total production cost model YELBP     g i EFBPiQIigfl , TPC  UCCig Aig  ig  gG iI f F lL iI gG , (10) YELTR    g EFTRAil ADDgfl QI igfl    iI gG f F lL  f f UPC pf QBipfcb  iI pP f F  cC bB   f f EFTRBb ADFfcbQBipfcb  c/ Total transportation cost model iI pP f F cC bB FEB  ECBQEB  TTC    gUTCigflQIigfl TI (11) CAR  c , gG lL iI f F cC where, QEBc    f f QBipfcb .  iI pP f F bB UTC  IA  IB ADD igfl il  il gfl   Total cost of fuel used by the regions. The annual  UTB fcb  OAb  OBb ADFfcb   , cost of providing the energy balance in the region  includes the cost of diesel and the production and TI   f f UTB fcbQBipfcb  transportation cost in the stores for blending iI pP f F bB cC  biodiesel (B100). In manufacturing costs, we

IAil and IBil are fixed and variable cost for consider both fixed annual operating costs, which is given as a percentage by the total amount of transportation biomass type i  I and (OA ,OB ) b b investment capital and net variable cost that is are fixed and variable cost for transportation proportional to the amount of processing. In biodiesel (B100). transport costs, distance fixed price and distance The biomass transportation cost UTCigfl is variable costs are considered. The economic described by Börjesson and Gustavsson, 1996 [3]. criterion will be the total cost of year’s base, They are composed of a fixed cost ( IA ,OA ) and including investment costs for biodiesel (B100) il b production and use of the BSC for the lifetime and

45 cost of the used classic fuel supplement on the  X igfl   Z pf , i, f (20) energy balance of the region. This price is given by gG lL pP the equation: g TBGB. Ivanov TDC et al:, TG Optimal design and planning of(14) biodiesel supplyC/ chain…..Part1.Limit guarantee Mathematical that each model region …… will where provide only one plant of biomass type i  I TBG Total cost of fuel used (conventional and  X igfl  1, i, g (21) biofuels(B100)) to ensure region's energy f F lL balance ($ year 1 ); D/ Limitation of assurance is provided that at TDC Total cost of a BSC network for year ( least one region g  G produces biomass that $ year 1 ); is connected in a plant located in a region TG Total cost of petroleum diesel used from f  F 1 the regions ($ year ); Y fcb   Z pf , f (22) cC bB pP The component TG of (14) shall be determined under the following relationships: Y fcb  1, f ,c (23) bB TG  PO QEO  c (15) Y  X , i, f cC  fcb  igfl (24) cC bB gG lL 5.6. Restrictions Transport links. Plants capacity limited by upper and lower bounds A/ The quantity transported between different constrains. Plants capacity is limited by upper and regions is limited by upper and lower bounds, lower bounds, as indicated by Eqs. (16), where the as indicate by Eq. (25) minimal production level in each region is obtained MIN affecting the capacity installed. PBIig MIN  PB p Z pf  f f QBipfcb   g iI cC bB (16) (25) AS  AFood  PB MAX Z , p, f  g g  ig p pf  QI igfl  , i, g f F g lL 2 g Balance of biodiesel(B100) to be produced from B/ Restrictions on transportation of biomass biomass available in the regions. are MAX  QEBc    i PBIig  cC iI gG  QI   , (17)  igfl QEB    AS lL  c   i ig g   S Food (26) cC iI gG  0.5Ag  Ag  ig  X igfl , i, g, f   QI  lL  i g igfl  C/ Limitation that ensures the admissibility of iI gG lL , (18) flow rate for biomass and biofuel f f QBipfcb , f iI pP bB cC Productivity of biomass in the region restriction MAX QIig X igfl  QIigfl  Logical constraints. (27) QT MIN X , i, g, f ,l A/ Restriction guarantees that a given region g il igfl installed power plant with p for Flow rate of biomass restricting biodiesel(B100) production MAX QB f Y fcb  QBipfcl  Constraint (19) determined that only one size of iI pP (28) the plant can be installed in a given region: MIN QTBb Y fcb , f ,c,b  Z pf  1 , f (19) pP Supply chain design constraints. These constraints B/ Limitation of assurance is provided that the are material balances among the different nodes in the SC. The following are constraints between biomass plant installed in a region g G of at different SC nodes: least one different region g G

46 A/ Productivity of biomass in the region Crop rotation can be applied if the quantity of restriction energy crops in a given year can be produced in the S Food next one but in other areas of the region. This can Ag  Ag  ig (29) F PBBig  ,i, g A A 2 be achieved if land ig and ig such that B. Ivanov et al: Optimal design and planning of biodiesel inequalitiessupply chain…..Part1. are implemented. Mathematical model …… Restriction for total environmental impact of all F S Food regions. Aig  Aig 2.0  Ag  Ag , i, g (35) TEIF  TEIF MAX (30) Energy restriction. A/ Limitation ensuring that the overall energy MAX where TEIF is maximum permissible values balance in the region is provided for the total environmental impact of Limitation of enforceability of the energy biodiesel(B100) network of SC and fossil fuel in balance: the regions ( kg CO  eq d 1 ) EGD  EB  EO . (36) 2 Energy equivalent diesel, which is necessary to Mass balances between biodiesel(B100) plants and meet the energy needs of the all customer zones biomass regions. The connections between where no use biodiesel(B100) is determined by the biodiesel (B100) plants and biomass regions are equation: determined by the equation: EO  ENO YOc MAX  , (36a) cC  iQI igfl   PB p Z pf ,f (31) lL gG iI pP where EO is annual requirement of energy 1 Mass balances between biodiesel(B100) plants and (petroleum diesel) of all regions ( GJ year ). biofuel customer zones. The energy equivalent of petroleum diesel that MAX must be added, in order to balance the energy  f f QBipfcb   ZBc ,c (32) iI pP bB f F required for all customer zones is determined by the equation: Land constraints. EGD  ENOQEOc , (36b) A/ The constraints explained in this section mainly cC aim to avoid the negative impacts on food where EGD is annual energy added to petroleum production to avoid competition with other sectors diesel fuel to balance the required energy for all for biomass use and to maintain the sustainable use regions (GJ year 1 ). of land. The following constraint is introduced to The Energy equivalent of biodiesel (B100) the model to avoid the competition between received per year of work BSC is determined “biomass for food” and “biomass for fuel”: according to the dependence:  A   PBB , i  ig ig   g ig  (33) EB  ENB QEB gG gG  c , (36c) cC The land used for raw materials cultivation and where EB is annual energy received from the for food security must not exceed the available land extracted biofuel (biodiesel(B100)) of BSC for all for each region: customer zone (GJ year 1 ). F S Food Aig  Aig   Ag  Ag ,g , (34) B/ Limitation ensuring that the overall energy iI balance in each customer zones is provided B/ Limitation guaranteeing crop rotation Limitation of enforceability of the energy The crop rotation allows to ensure control of balance for each region: pests, improve soil fertility, maintenance of the ENO QEO  ENB QEB  ENO YO ,c (37) long-term productivity of the land, and c c c consequently increase the yields and profitability of C/ Limitation ensuring that each region will be the rotation. Other criteria to take in consideration provided in the desired proportions fuels when planning crop rotation with energy crops are ENBf f QBipfcb   the environmental and economic conditions in a iI pP f F bB (38) given region. Moreover, the combination of crop mix Kc ENO QEOc , c rotation and fallowing is a common practice that is gaining momentum again due to environmental Total cost of a BSC network restriction benefits and promoted reduction in the dependence MAX on external inputs. TDC  TDC (39)

47 where TDC MAX is maximum total cost of a BSC CONCLUSIONS network ($ ). This study considers the optimal location of biodiesel (B100) production plants and the Optimisation problem formulation operation of the BSC. MILP approach for the The problem for the optimal design of a BSC is design and planning of BSC under economic and formulatedB. Ivanov as et aal: mixed Optimal integer design and linear planning programming of biodiesel supplyenvironmental chain…..Part1. Mathematical criteria model is …… developed. The (MILP) model for different target functions as significance of the problem has been expressed by follows: the extensive investigation of the biofuels sector that has been taking place during the recent years Minimizing GHG emissions. As discussed in for particular fatal replacement of the highly section 4.5.2 environmental objective is to polluting conventional fuels. An optimisation minimize the total annual CO2 -equivalent model was developed that enables decision making greenhouse gas emissions resulting from the for the infrastructure of biofuel conversion operations of the BSC and petroleum diesel used to processing including processing locations, volumes, provide the energy balance of the regions. The supply networks, and logistics of transportation formulation of this objective is based on total GHG from regions of biomass to bio-refineries and from emissions in the SC and other fuels are estimated bio-refineries to markets. The development of a based on life cycle assessment (LCA) approach, flexible optimisation model may solve a wide where emissions are added every life stage. spectrum of biofuel problems since this area is very The task of determining the optimal location of rapidly changing (not only in economic but also in facilities in the regions and their parameters is other dimensions, such as strategic decisions formulated as follows: concerning the development and progress in the T field, i.e. land dedicated to biofuels). All these can Find : X Decision variables    very easily be accommodated in the optimisation MINIMIZE TEIFX  (Eq.6) (40) model, resulting in significant benefits from the s.t.: Eq.16  Eq.39  optimisation approach. One of the valuable features   of the approach is the capability to identify and solve a wide range of different scale and level Minimizing annualized total cost. The economic problems, such as facility location, raw materials objective is to minimize the annualized total cost, selection, conversion facilities location and design including the total annualized capital cost, the and operational characteristics. Furthermore, the annual operation cost, the annual governmental model itself could be easily extended to incentive, and the cost for emitting CO2 . The task accommodate strategic planning issues, such as of determining the optimal location of facilities in investing or not on new production facilities, their the regions and their parameters is formulated as siting, and the introduction of environmental and (41) other externalities in the calculation of the total The problem 5.7.1 and 5.7.2 is an ordinary cost. The model that has been developed includes Mixed Integer Linear Program (MILP) and can thus technical constraints as well as constraints be solved using standard MILP techniques. The originating from the limits in various problem model was developed in the commercial software parameters. The optimisation criteria of the model GAMS [7] using the solver CPLEX. The model will in any case express the goals of the stakeholder will choose the less costly pathways from one set of and may include maximum economic efficiency, biomass supply points to a specific plant and best environmental behavior, minimum land further to a set of biodiesel(B100) demand points. occupation, minimum total cost, etc. Another The final result of the optimisation problem would characteristic of the proposed approach is that the then be a set of plants together with their model is rather simple and can easily be solved corresponding biomass and biodiesel(B100) with the available solvers, without needing to demand points. develop new codes or optimisation methods. This characteristic is important in the potential future Find : X Decision variablesT    exploitation of the approach and the development MINIMIZE TDCX  (Eq.8) (41) of a Decision Support System. However, the main s.t.: Eq.16  Eq.39  critical point in the implementation of this approach   is the difficulty to identify reliable quantitative information of the various problem parameters.

48 Therefore, significant progress in other fields or 9. L.G. Papageorgiou, Computers & Chem.Eng., 32, research in order to provide reliable quantitative 1931 (2009). information and data (such as the agricultural 10. A. Zamboni, N. Shah, F. Bezzo,. Energy & Fuels, 23, materials properties, the conversion process 5121 (2009). efficiency, various costs, land availability etc.) are 11. S.D. Eksioglu, A. Acharya, L.E. Leightley, S. Arora, B. Ivanov et al: Optimal design and planning of biodiesel supply chain…..Part1.Computers Mathematical & Ind. Eng., model 57, 1342 …… (2009). critical factors in the performance and the 12. A. Iriarte, J. Rieradevall, X. Gabarrell, J. of Cleaner contribution of the present work. Prodctn, 18, 336 (2010). A final conclusion is that in order to reach the 13. J. Kim, M.J. Realff, J.H. Lee, C. Whittaker, L. EU targets particularly in Bulgaria a more Furtner, Biomass& Bioenergy, 35, 853 (2011). improved interdisciplinary and improved cross- 14. B. Aksoy, H. Cullinan, D. Webster, K. Gue, S. sectoral in the energy system will be needed. Sukumaran, M. Eden, N.S. Jrd, Environ. Prog. Correspondingly the model developed and used Sustain. Energy,30,.720 ( 2011). within this study, may constitute a key component 15. O. Akgul, A. Zambon, F. Bezzo, N. Shah, L.G. for this kind of studies. Consequently, it is which Papageorgiou, Ind. Eng. Chem. Res., 50, 4927 makes it highly relevant for policy makers. (2011). 16. You F, Wang B., Ind. Eng. Chem. Res., 50, 10102 REFERENCES (2011). 17. M.M. Moreno, C. Lacasta, R. Meco, C. Moreno, Soil 1. D.G. Bullock, Crit Rev Plant Sci. 11, 309 (1992). & Tillage Research, 114, 18 (2011). 2. D.L. Karlen, G.E. Varvel, D.G. Bullock, R.M. Cruse, 18. W. Zegada-Lizarazu, A. Monti, Biomass and Adv. Agron. 53, 1 (1994). Bioenergy, 35, 12, (2011). 3. P. Börjesson, L. Gustavsson, Energy, 21, 747 (1996). 19. O. Akgul, N. Shah, L.G. Papageorgiou, Computers 4. http://europa.eu.int & Chem. Eng., 42, 101 (2012). 5. N. Shah, Computers & Chem.Eng., 29, 1225 (2005). 20. E. Wetterlund, S. Leduc, E. Dotzauer, G. 6. www.ipcc.ch/publications_and_data Kindermann, Energy, 41, 462 (2012). 7. B.A. McCarl, A. Meeraus, P. Eijk, M. Bussieck, S. 21. P.B. Parajuli, P. Jayakodya, G.F. Sassenrathb, Y. Dirkse, P. Steacy, McCarl Expanded GAMS user Ouyangc, J.W. Potea, Agric. Water Management, Guide , 2008. 119, 32 (2013). 8. Dir 2009/28/EC. Directive 2009/28/EC of the European Parliament and of the Council of 23 April 2009 Directives 2001/77/EC and 2003/30/EC.

ОПТИМАЛНО ПРОЕКТИРАНЕ И ПЛАНИРАНЕ НА РЕСУРСНО ОСИГУРИТЕЛНАТА ВЕРИГА ЗА ПРОИЗВОДСТВО И ДОСТАВКИ НА БИОДИЗЕЛ С ОТЧИТАНЕ НА СЕИТБООБРАЩЕНИЕТО. ЧАСТ 1. ФОРМУЛИРОВКА НА МАТЕМАТИЧНИЯ МОДЕЛ Б.Иванов1*, Б.Димитрова1, Д.Добруджалиев2 1) Институт по инженерна химия, Българска академия на науките, 1113 София 2)Университет “Проф. Асен Златаров”, 8000 Бургас

Постъпила на 3 юни, 2013 г.; коригирана на януари, 2014 г. (Резюме) Тази статия е насочена към решаване на проблема за оптимално проектиране на ресурсно осигурителни вериги за производство и разпространение на биодизел. Използувани са два критерия за оценка на оптималността на веригата (икономически и екологичен). Икономическият критерий оценява общите годишни разходите, докато екологичният критерий оценява общите емисии на парникови газове в атмосверата за целия жизнен цикъл на продукта. Предложен е математически модел, който може да се използва за проектиране на веригата за доставки (SC) и управление на логистиката на биодизел. Моделът определя броя, размера и местоположението на биорафинериите необходими за производството на биодизел като се използва наличната биомаса. Моделът се формулира в термините на смесеното линеино програмиране. Важна особеност на този модел е че отчита влиянието на ротацията на биокултурите.