Hardwood Biomass to Gasoline, Diesel, and Jet Fuel - ACS Publications

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Hardwood Biomass to Gasoline, Diesel, and Jet Fuel: 2. Supply Chain Optimization Framework for a Network of Thermochemical Refineries Josephine A. Elia,† Richard C. Baliban,† Christodoulos A. Floudas,*,† Barri Gurau,‡ Michael B. Weingarten,‡ and Stephen D. Klotz‡ †

Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States Lockheed Martin Mission Systems and Sensors (MS2), 199 Borton Landing Road, Moorestown, New Jersey 08057, United States

‡

S Supporting Information *

ABSTRACT: Biomass-based energy processes pose logistical challenges because of the dispersed nature of biomass resources. A nationwide supply chain optimization framework is applied to a biomass-to-liquid (BTL) system that uses hardwood biomass resources in the United States to produce gasoline, diesel, and jet fuel. Using optimized BTL refineries of differing capacities (i.e., 0.8, 1, 2.5, and 10 thousand barrels per day) and fuel product ratios (i.e., commensurate with the United States demand, maximization of diesel, and maximization of jet fuel), the supply chain case studies that correspond to the three product ratios are addressed via a large-scale mixed-integer linear programming (MILP) optimization model. The mathematical formulation includes the locations of hardwood biomass in the United States, the delivery locations of fuel products, the transportation costs of every input and output of the refinery, the material balances of each BTL refinery, water resources, and electricity requirement of the supply chain. The framework is also adapted to generate a rank order list of the top 5 locations for each BTL refinery. Solutions of the proposed MILP optimization model provide useful information for the strategic locations of BTL refineries to produce a total of 40 thousand barrels per day of fuels, the allocations of feedstocks and products in the supply chain, and a quantitative basis in evaluating each cost-contributing factor.

1. INTRODUCTION Biomass has been vied as an energy source that will continue to grow in significance in the future. A growing demand for fuels in the United States transportation sector as well as the effort to reduce reliance of petroleum imports will naturally put pressure on the development of domestic energy sources. As part of the energy sources portfolio, biomass not only provides nonpetroleum alternatives for fuel generation but also acts as a mitigating agent to greenhouse gas (GHG) emissions because of the CO2 intake from the atmosphere during cultivation. Thus, the combined benefits of increasing energy independence and improving environmental performance in the energy sector can be achieved through the use of biomass as feedstock. Various studies have emerged that investigate bio-based process designs and synthesis in recent years, either as a single feedstock stream or in combination with one or two fossil-based sources, such as coal and natural gas.1−26 The large number of studies based on bio-based feedstocks is highlighted in a recent review,2 and the advantages of applying a systems perspective to biomass conversion processes, ranging from process chemistry, design, synthesis, and supply chain of biomass-based systems, are outlined by Kokossis and Yang27 and Daoutidis et al.28 To gain the aforementioned environmental benefits, biomass must be harvested sustainably and must not adversely affect the food chain. Many biomass-based processes rely on corn or soybean supplies for ethanol and diesel, respectively, which lead to concerns surrounding how prices and availabilities of these commodities will be affected.29 In contrast, lignocellulosic biomass, such as agricultural residues, forest residues, or perennial grasses © XXXX American Chemical Society

grown on uncultivated land would not compete with the food chain and are regarded as viable sources of energy.26,30 In particular, forest residues are a major biomass source available across the United States. In the Billion Ton Study, the U.S. Department of Energy (DOE) estimated that approximately 129 million dry tons/year (MDTY) of forest residues may be harvested sustainably and a total of 226 MDTY may be available by 2030.30 Sustainable harvesting includes a holistic approach that considers the effects of expanding production on the ecosystem and surrounding natural habitats, soil carbon management, erosion mitigation, nutrient management, water/ air quality, and global fiber production.26 The total production amounts of forest residues are a combination of (1) fuelwood harvested for current residential/commercial heating, (2) primary and secondary mill residues, (3) pulping liquors from paper manufacturing, and (4) municipal solid waste sources. In comparison to agricultural residues or perennial grasses, forest residues can be obtained at a lower cost on a dry basis, although they may require additional investments in the conversion processes to remove the high moisture content (i.e., up to 50%) of woody biomass.30 On the logistical front, there are advantages to using forest residues as opposed to agricultural residues or perennial Special Issue: Accelerating Fossil Energy Technology Development through Integrated Computation and Experiment Received: March 11, 2013 Revised: May 7, 2013

A

dx.doi.org/10.1021/ef400430x | Energy Fuels XXXX, XXX, XXX−XXX

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and the feedstock supply radius to minimize the production cost of a bioenergy facility producing electricity and ethanol. Bai et al.60 proposed game-theory models to incorporate the decisions of farmers for land usage (i.e., producing either biomass for food or energy) and the strategic decisions of biofuel manufacturers (i.e., number of biorefineries, locations, etc.). Parker et al.61 completed a resource assessment for the western U.S. with the identification of the optimal locations, capacities, and technology options for a network of biorefineries. Marvin et al.62 analyzed the biomass-to-ethanol supply chain in the midwest U.S. and identified the optimal locations of the biorefineries and the product capacities produced by the supply chain. Marvin et al.63 developed a facility location framework that simultaneously selected the conversion technology for the biorefinery. A detailed cash flow analysis was incorporated into the optimization model. In addition to the upstream biomass logistics, the optimization of biomass supply chains can include the downstream operations of the biorefineries (i.e., the distribution of the fuel products), and the optimal locations of the biorefineries are determined with respect to the overall configuration of the entire supply chain. The fuel products from biomass include methanol, ethanol, and Fischer−Tropsch (FT) hydrocarbons, such as gasoline, diesel, and jet fuel. Bowling et al.64 included the optimal locations of biomass pre-processing hubs in the biomass supply chain. Lam et al.65 proposed a technique to reduce the model size of biomass supply chain problems by removing connections, variables with zero values, and merging zones. Leduc et al.66 optimized the location of gasificationbased methanol production plants in Austria, where the country was divided into several zones. Leduc et al.67 analyzed the supply chain associated with two methanol conversion plants in Germany. Leduc et al.68 considered ethanol biorefineries with co-production of heat and power in Sweden using spatially explicit transportation infrastructure data sets. Leduc et al.69 identified the locations of methanol production plants in a county in northern Sweden. Natarajan et al.70 studied the optimal locations of methanol plants in eastern Finland with geographically explicit information. Dunnett et al.71 analyzed a bioethanol supply chain produced via the fermentation route using hypothetical demand and supply scenarios based on the U.K. and European Union (EU) data. The spatial distribution of the material flows was represented by a grid, where urban centers could be located at the center or at the corner of the grid. Zamboni et al.72,73 studied a bioethanol supply chain system based on cost minimization72 and simultaneous minimization of environmental impact in a multi-objective optimization framework.73 The framework was applied to a northern Italy region by dividing the region into homogeneous squares. Akgul et al.74 incorporated the biomass and fuel delivery routes to the same regional case study. Akgul et al.75 implemented the multi-objective optimization formulation for bioethanol production via a hybrid of first- and second-generation conversion technologies for a U.K. case study. Akgul et al.76 considered the same system with the minimization of the total cost in the objective function. Corsano et al.77 considered an ethanol supply chain with simultaneous optimization of the plant design. The supply chain included sugar plants that produced molasses, which were transported to fermentation plants that produced ethanol. Vimmerstedt et al.78 analyzed an ethanol supply chain using a system dynamics model, named the biomass scenario model, developed by the National Renewable Energy Laboratory (NREL).

grasses, because the harvesting and transportation infrastructure is already in place from the timber industry. Unlike the carbon-based fossil fuels, such as coal and natural gas which are produced in a centralized manner, biomass production occurs in smaller scales and in a much more dispersed manner.5,10 This feature means that the management of the biomass supply chain will play a significant role in the strategic placement and economic performance of biomassbased facilities. The facility has to be able to receive a steady stream of biomass for a long time horizon that will come from multiple farms and forests in the neighboring counties or states. Further, the placement of the facility has to be strategic with respect to the distribution of its products to the market and to environmental limitations, such as freshwater availabilities in the local region. The logistical challenges in using biomass feedstocks, such as the availability to supply the input requirement of biomass-based facilities and the transportation logistics to deliver biomass from multiple sources, have prompted the development of optimization frameworks that simultaneously consider multiple sectors to maximize the supply chain profitability. The issues associated with biomass supply chains have been highlighted in several recent publications.31−38 In the literature, biomass supply chain studies are generally categorized into those that include (i) biomass supply and distribution upstream to the biorefinery facility, (ii) biomass feedstock and fuel product distribution, and (iii) planning of a multi-period supply chain. The first category includes studies that evaluate the availability of biomass in particular regions as supply for a biorefinery facility or a network of facilities as well as the optimization of biomass delivery to the facility. The second category includes studies that consider the optimal facility locations with respect to the feedstock supply chain and the fuel product distribution. Lastly, the third category considers the supply chain structure over multiple time horizons. Note that, while the studies reviewed in this paper pertain to the biomass supply chains for liquid fuel production, similar upstream logistical challenges are faced by the production of electricity/ heat from biomass.39−47 A number of studies evaluated the availabilities of biomass supply in specific regions and investigated the opportunities for biofuel and bioenergy production. Tyndall et al.48 analyzed the supply of woody biomass in the U.S. Corn Belt. Aksoy et al.49 evaluated the best biorefinery location with respect to the availability and transportation costs of poultry litter in Alabama. Gonzalez et al.50 studied the supply and delivered cost of seven biomass feedstocks in the southern region of the U.S. Hacatoglu et al.51 completed a feasibility study for a facility that co-produced electricity and diesel from lignocellulosic biomass in the Great Lakes region. Suh et al.52 compared the transportation options to deliver corn stover in the state of Minnesota based on total cost and emissions. Bauen et al.53 modeled the availability of coppice and Miscanthus biomass species in the U.K. Leboreiro and Hilaly54 proposed a model for the upstream collection, transportation, and storage of biomass. Ravula et al.55 implemented a simulation-based model to generate an efficient cotton transportation system and applied the framework to a case study in Virginia. Sultana and Kumar56 optimized the transportation of multiple biomass feedstocks to a biorefinery in different forms. van Dyken et al.57 focused on the upstream supply chain of biomass that incorporated the supply, pretreatment, storage, and demand of biomass feedstocks. Č uček et al.58 considered the upstream logistics and pre-processing of biomass for central Europe. Gan and Smith59 optimized the plant size B


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The model incorporated policy scenarios in the analysis. Bai et al.79 proposed a formulation that identified the optimal locations of biorefineries with traffic congestion. The route selections for the feedstock and product shipments were taken into account, and the framework was applied to an Illinois case study. Kocoloski et al.80 analyzed a cellulosic ethanol supply chain in Illinois. Zhang et al.81 developed a geographically explicit model using geographic information system (GIS) technology for woody biofuel production in the upper peninsula of Michigan. Tittmann et al.82 proposed a model for power and biofuels production in California based on explicit data from the geographical profile, demand, and transportation infrastructure of the state. Ekşioğlu et al.83 analyzed the biomass-to-ethanol supply chain that included intermediate biomass collection and fuel-blending facilities on top of the biomass harvesting sites, biorefinery locations, and fuel demand locations. The framework was applied to the state of Mississippi. You et al.84 proposed a multi-objective mixed-integer linear programming (MILP) model that incorporated the social impacts of a biorefinery by taking into account the number of jobs created and the improvement to the regional economy. The multi-objective MILP model included economic, environmental, and social impact objective functions and was applied to an Illinois case study. Kim et al.85 studied the biomass supply chains that produced gasoline and biodiesel via a two-step conversion processes (i.e., fast pyrolysis and gasification with a bio-oil intermediate) for the southeast U.S. Kim et al.86 incorporated uncertainties in the biomass supply, fuel demands, prices, and conversion technologies in a two-stage mixed integer stochastic programming framework. Elia et al.5,10 studied a nationwide U.S. supply chain analysis for hybrid coal, biomass, and natural gas to liquids system that incorporated water supply, electricity need, and projected CO2 sequestration capacities. To take into account the seasonal variability of biomass feedstock supply and the planning of biomass supply chains, several studies have proposed multi-period supply chain optimization models.87−103 Zhu et al.87 considered a facility location problem by taking into account the upstream operation of the facility during harvesting and non-harvesting seasons for switchgrass. Zhu and Yao88 considered the seasonal variability of multiple feedstocks in a multi-commodity network flow model for a biorefinery. Giarola et al.89−91 and Dal-Mas et al.92 proposed frameworks for the planning of multi-period bioethanol supply chains, applied to the northern Italy region. Giarola et al.91 studied the upstream planning of the supply chain with the incorporation of a carbon-trading scheme that simultaneously selected the technology options to produce bioethanol through first- or second-generation technologies. Giarola et al.90 formulated a multi-objective MILP for the selection of the bioethanol conversion technology and capacity planning of a single production plant. Giarola et al.89 studied the upstream and downstream planning of the supply chain, and Dal-Mas et al.92 considered uncertainties in biomass costs and product selling prices by incorporating the expected net present value and conditional value-at-risk (CVaR) in the objective function. Ekşioğlu et al.93 proposed a mathematical model that distinguished long-, medium-, and short-term decisions for the biomass-toethanol supply chains applied to a Mississippi case study. An et al.94 analyzed a region in central Texas and incorporated the variability in biomass availability, moisture content, and demand profile of fuel by dividing a 1-year planning horizon into four quarters. Huang et al.95 and Chen and Fan96 studied the waste biomass-to-ethanol systems in the state of California. Huang et al.95 completed a sensitivity analysis on the transportation cost, refinery capacity, and feedstock availability, and Chen and Fan96

implemented a two-stage stochastic programming model to incorporate the uncertainties in fuel demands and feedstock supplies. You and Wang97 proposed a multi-objective, multi-period MILP model to simultaneously maximize the economic performance and minimize the environmental impacts of a biorefinery that produced hydrocarbons via gasification systems, followed by FT conversions or fast pyrolysis, and followed by hydroprocessing steps, such as hydrotreating and hydrocracking. Gebreslassie et al.98 considered the optimal hydrocarbon biorefinery supply chains under supply and demand uncertainties using CVaR and downside risk. The objective function minimized the annualized cost and financial risk of the supply chain. Sharma et al.99 formulated a MILP financial planning model to maximize stakeholder value in the design of a biorefinery with its supply chain configuration. Liu et al.100 considered a case study in the U.K. for a coal and biomass-to-liquid (BTL) system producing diesel and naphtha. Papapostolou et al.101 studied a case study in Greece for a biodiesel supply chain with water and land usage under consideration. Andersen et al.102 proposed a formulation for the biodiesel supply chain in Argentina with land usage consideration, and Walther et al.103 incorporated the technology selection for the secondgeneration biodiesel production in northern Germany in the supply chain framework. In this paper, the second of a two-part study (Baliban et al., DOI 10.1021/ef302003f),1 an optimization framework and a series of computational results are presented on nationwide U.S. hardwood BTL supply chains of a fixed total capacity. The supply chain takes advantage of the optimized BTL refineries described in part 1 (Baliban et al., DOI 10.1021/ef302003f) of the study via an optimization-based process synthesis approach.1 Previously, methods for the optimized single-plant design and supply chain analysis have been developed for a hybrid system that combines coal, biomass, and natural gas to produce liquid fuels (i.e., gasoline, diesel, and jet fuel).3−10 In this study, these methods are adapted and expanded for the hardwood biomass systems to produce multiple ratios of liquid fuels. The rest of the paper is organized as follows. Section 2 defines the specific scope of the problem addressed in this paper. Section 3 details how the data inputs for hardwood biomass were obtained. Section 4 describes the BTL processes and refineries used to convert hardwood biomass to liquid fuels. The locations to which liquid fuels are delivered from the BTL refineries are described in section 5, and the transportation cost analysis for biomass is described in section 6. Water considerations in the supply chain are included in section 7, and the supply chain optimization model is detailed in section 8. Finally, section 9 presents in detail all computational results generated in this study, which include four sets of supply chain case studies with various targets of fuel ratios and a ranking scheme to identify the most economical locations for each type of BTL refinery.

2. PROBLEM DEFINITION This study follows up on the development of hardwood BTL refineries detailed in part 1 (Baliban et al., DOI 10.1021/ef302003f) of the study.1 The goal of this paper is to investigate the optimal facility locations for hardwood BTL refineries using an optimizationbased supply chain optimization framework. The refineries can convert hardwood biomass (45 wt % moisture) to gasoline, diesel, and kerosene in three different product ratios, namely, (i) production of gasoline, diesel, and jet fuel in ratios commensurate with the 2010 United States demand, (ii) maximization of C


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and (iii) perennial grasses and other dedicated energy crops. This study focuses on the forest residues of the United States that include logging residues, fuelwood, and mill residues.30 The availabilities of forest residues for the BTL supply chain are taken from the currently unexploited logging, fuel treatments, fuelwood, forest products, and urban wood residues, as reported by the Federal Forest Service (FFS).105 Timber removals on a per county basis, categorized as hardwood and softwood, are reported in Table C10 of ref 105. Fuelwood is reported in Table C5 of ref 105. Mill residues, which include residues from the forest products industry, are reported in Table C11 of ref 105. The densities of each of these woody resources are calculated from Tables 11 and 12 of ref 30 and are used to convert the volumetric data to mass units. The State of Garbage in America study106 is used to calculate the amount of available urban wood residues. The report gives the total amount of landfilled municipal solid waste, composted organics, and yard trimmings collected on a per state basis. In this study, urban wood residues and municipal solid wastes are not considered as feedstocks to the BTL supply chain. All of these woody biomass resources in the United States are grouped and represented as one species in this study, namely, hardwood biomass with a 45% moisture content, because of the higher capacities of timberland removal residues (79.5 MDTY) compared to the mill residues (1.9 MDTY). The representative composition of the hardwood biomass is shown in Table 1, which is taken from the ECN Phyllis database.107

diesel products (i.e., 75 vol % diesel), and (iii) maximization of jet fuel products (i.e., 75 vol % jet fuel). In part 1 (Baliban et al., DOI 10.1021/ef302003f) of the study,1 topological and economic trade-offs between the three product ratios produced by the BTL refineries were established. In this study, these trade-offs are further analyzed on a spatial basis for the United States and will involve the relationship between required inputs into the BTL refineries (e.g., biomass, electricity, and water), the amount of fuels produced, and the geographical distributions of the input availabilities and fuel demand profile in the United States. No coal and natural gas feedstocks will be input to the refinery, and no CO2 sequestration system is included to reduce greenhouse gas emissions. Electricity required by the facilities will be provided by the grid, and no additional renewable sources, such as solar or wind electricity will be allowed. The supply chain begins at the feedstock locations, which are the counties where hardwood biomass residues exist. These counties also serve as the candidate locations for hardwood BTL plants, which can have 0.8 thousand barrels per day (kBD), 1, 2.5, or 10 kBD capacities. Each of these BTL refineries has been optimized in a process synthesis framework described in part 1 (Baliban et al., DOI 10.1021/ef302003f) of the study,1 complete with heat, power, and water integration, which is solved to global optimality using a rigorous deterministic branch-andbound global optimization approach. The outputs of the process synthesis step for each BTL refinery, which include (i) biomass requirement, (ii) electricity requirement, (iii) butane requirement, (iv) water requirement, (v) investment cost, (vi) liquid fuel flow rates, (vii) CO2 vented, and (viii) byproduct propane/liquefied petroleum gas (LPG) flow rates, serve as parameter inputs into the supply chain optimization model. The supply chain is required to produce a total of 40 kBD liquid fuels across the nation, comparable to the needs of the U.S. Department of Defense.104 These fuels are delivered to known locations of oil refineries, Defense Logistics Agency (DLA) blending locations, and state centers, when there is no oil refinery or DLA locations within the state. The objective of the supply chain optimization framework is to obtain the optimal topology that minimizes the total cost of fuel production for the whole supply chain, including the feedstock purchase, the feedstock transportation, the product transportation, and investment costs of the BTL refineries. The problem is formulated as a large-scale MILP optimization model to represent the discrete decisions, such as the locations and capacities of the BTL refineries, and the continuous decisions, such as where and how much the feedstocks and products should be delivered. Four different sets of case studies will be performed, namely, case studies that include (1) only BTL refineries that produce fuels in ratios commensurate with the United States demands, (2) only BTL refineries that maximize the production of diesel in the supply chain, (3) only BTL refineries that maximize the production of jet fuel in the supply chain, and (4) a combination of BTL refineries with the aforementioned product ratios (i.e., 1, 2, and 3) in the supply chain. In addition, a ranking of the top 5 locations for each of the BTL refinery capacities and product ratios are identified through the optimization framework. Results from the optimization model elucidate the quantitative economic trade-offs between each case study and provide a basis for strategic decision making.

Table 1. Feedstock Proximate and Ultimate Analyses for Hardwood107 proximate analysis (db, wt %) moisture (ar)

ash

45

a

VM

heating values (kJ/kg) FC

b

2.14 N/A N/A ultimate analysis (db, wt %)

HHVc

LHVd

19130

17842

C

H

N

Cl

S

O

50.19

5.9

0.32

0

0.03

41.42

VM = volatile matter. bFC = fixed carbon. cHHV = higher heating value. dLHV = lower heating value. a

The map of available forest residues for the BTL supply chain network is displayed in Figure 1. Because the available data are discretized on a county basis, the hardwood biomass is assumed to be located at the centroid of the county. A total of 2311 counties in the United States possess hardwood biomass resources, and the same counties also serve as candidate locations for a BTL facility.

4. BTL FACILITIES The design and topology of the facilities that will convert the hardwood biomass into gasoline, diesel, and jet fuels are developed in part 1 (Baliban et al., DOI 10.1021/ef302003f) of this study1 based on previous successes on process synthesis approaches on single and hybrid feedstock refineries.6−9 Four refinery capacities, namely, plants that produce 0.8, 1, 2.5, and 10 kBD total liquid fuels are included in the analysis to examine the benefits of scale. These capacities are selected on the basis of the estimated project scale for a technology, such as the hardwood BTL refineries in the United States. The 0.8 kBD capacity corresponds to approximately 12 million gallons/year production of liquid fuels.

3. BIOMASS RESOURCES The biomass resource that does not compete with the food chain in the United States is generally grouped into three major categories, namely, (i) agricultural residues, (ii) forest residues, D


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Figure 1. Map of forest residues locations in the United States.

(v) investment cost, (vi) liquid fuel flow rates, (vii) CO2 vented, and (viii) byproduct propane/LPG flow rates, serve as parameter inputs into the supply chain optimization model. Depending on the composition of the produced liquid fuels, the topologies of the BTL refinery will differ. This is especially true in the hydrocarbon generation and upgrading sections. For example, in the case studies that maximize diesel production, liquid fuel production is performed via the methanol route, which is converted to hydrocarbons in the methanol-to-olefins (MTO) and the Mobil olefins-to-gasoline/ distillate (MOGD) processes. A total of 75 vol % diesel is produced, with the balance being gasoline products. In the maximization of jet fuel, liquid fuel production is performed via the cobalt-based low-temperature FT units that generates a range of hydrocarbon products rich in waxes. The topologies produce 75 vol % jet fuel and 25 vol % gasoline, although the gasoline is aromatic-rich and must be blended to meet the appropriate physical property specification for gasoline fuels. These topological selections are consistent for the four capacities in these case studies. In the case where the fuel composition matches the United States demand ratios, there are topological switches as the refinery capacity increases. At smaller capacities, methanol synthesis is favored over the FT reactions to produce liquid fuels. However, at 10 kBD, the iron-based low-temperature FT unit is selected to produce the distillate cuts and the methanol route is used to produce gasoline.1 The overall cost of liquid fuels production is based on the purchase of the biomass and freshwater feedstocks, the capital charges associated with investment cost, the operation and maintenance (O&M) costs, and the cost of electricity. The sum of these costs is represented as a break-even price of crude oil (BEOP), at which value the BTL refineries would be economically competitive with petroleum-based processes. The BEOP ranges from $112 to 120/bbl for a 0.8 kBD plant, from $101 to 111/bbl for a 1 kBD plant, from $87 to 89/bbl for a 2.5 kBD plant, and from $63 to 68/bbl for a 10 kBD plant. The costs associated with the refinery capital investment (i.e., capital charges, operation, and maintenance) contribute the largest fraction to the overall cost for each capacity level. As the refinery capacity increases from

In addition to the varying capacities, three different product ratios are included in this study. The design and topologies of the BTL refineries are optimized to meet the following specifications: (i) production of gasoline, diesel, and jet fuel in ratios commensurate with the 2010 United States demand (i.e., 67 vol % gasoline, 22 vol % diesel, and 11 vol % jet fuel),108 (ii) maximization of diesel products (i.e., 75 vol % diesel), and (iii) maximization of jet fuel products (i.e., 75 vol % jet fuel). The three product ratios and the four refinery capacities give rise to a total of 12 distinct BTL refineries that may exist in the supply chain. The optimal topologies of these 12 BTL refineries are determined via an optimization-based process synthesis approach described in detail in part 1 (Baliban et al., DOI 10.1021/ef302003f) of the study.1 A process superstructure that includes multiple alternatives to convert hardwood biomass to gasoline, diesel, and jet fuel is postulated, comprised of process units for (i) syngas generation by biomass gasification, (ii) syngas cleaning units to remove acid gases that may poison catalysts during conversion to liquid fuels and to recover sulfur using a Claus process, (iii) liquid fuel production from syngas via FT synthesis or methanol synthesis and subsequent conversion in methanol-to-gasoline or methanolto-olefins technologies, (iv) hydrocarbon upgrading using ZSM-5 zeolite catalysis, olefin oligomerization, and a series of fractionation processes, (v) hydrogen and oxygen production through pressure swing adsorption, and an air separation unit, respectively, and (vi) simultaneous heat, power, and water integration to minimize utility usage of the refinery. Recycling of gases and CO2 from and to various sections of the refinery is allowed to maximize fuel production or limit CO2 emissions.6−9 Each process unit and its input−output relationships are modeled mathematically, and the entire superstructure is formulated as a large-scale mixed-integer nonlinear programming (MINLP) optimization model. The model is solved to global optimality using a rigorous deterministic branch-and-bound strategy, and this process synthesis approach is applied to each of the 12 BTL refineries. The outputs of the process synthesis step for each BTL refinery, which include (i) biomass requirement, (ii) electricity requirement, (iii) butane requirement, (iv) water requirement, E


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Table 2. Cost Parameters, Including the Distance Fixed Cost (DFC) and the Distance Variable Cost (DVC) feedstock/product

distance fixed cost (DFC)

unit

distance variable cost (DVC)

unit

reference

3.318 3.318

$/tonne $/bbl

0.124 0.124

$ tonne−1 mile−1 $/bbl

a a

0.0003

$/kg

5 × 10−6

$/kg

a

1.218

$/bbl

0.0063

$/bbl

a

truck biomass, forest residue fuel products pipeline water barge fuel products a

From ref 111.

per mile per volumetric flow rate basis. Informational postings of the 10 largest pipeline companies in the United States,5 which consist of information on pipeline origin and end locations as well as usage fees, are used to estimate an average transportation cost of liquid fuel products. Connections between BTL refinery locations, ports (origin and destination), and demand locations are allowed for transportation by pipeline and barge. The transportation costs for barge transportation follow the assumptions in a previous publication.5 Transportation costs by truck, barge, and water pipeline are calculated using eq 1, where DFC is the distance fixed cost, DVC is the distance variable cost, distance is the distance traveled, and DM is the distance multiplier. Distance is the straight line distance calculated from the latitude and longitude coordinates of two points, and to account for path curvatures, DM is equal to 1.1 for truck transportation and water pipeline.111 The parameter values are given in Table 2.

0.8 to 10 kBD, this fraction decreases from 71−75% of the total cost to 56−59% of the total cost. The decrease in the investment and O&M charges is very pronounced at these low-capacity levels because the major sections within the BTL refinery will require only one unit to operate. Thus, there is a large benefit for increasing the size of these units to their maximum operational capacity to secure the cost benefit. To examine the full details of the 12 BTL refineries used in this study, the readers are directed to part 1 (Baliban et al., DOI 10.1021/ef302003f).1

5. LIQUID FUEL DELIVERY LOCATIONS The 2010 demand data for petroleum-based products are extracted from the U.S. Energy Information Administration (EIA) website, which are available on a statewide basis. Among the list of products, motor gasoline, distillate fuel oil, and jet fuel represent a large majority of the total product volumes.109 However, in this study, the desired end destinations for the fuel products are the oil refineries and the DLA blending locations. Thus, the statewide demand data are distributed over these locations. The EIA database provides the maximum operating capacities of United States operating petrochemical refineries.110 These refineries serve as end points of fuel delivery in this study. In addition, 51 locations of DLA blending locations, on the basis the town locations, are identified in the United States through correspondence with Lockheed Martin representatives. The capacities for these blending locations, however, are not available, and hence, the statewide demand data are distributed to the oil refineries within the state such that the demand amount at oil refineries does not exceed their capacities. If the total state demand amount is greater than the total capacities of the oil refineries within the state, the remaining demand amount is allocated equally to the DLA locations within the state. If the total state demand amount is less than the total capacities of the oil refineries, the demand is allocated to the refineries proportional to their capacities. For the states that do not have oil refineries or DLA locations, the demand point is located at the state center. With these assumptions, the total fuels delivered to a state will not exceed the total demand of that state. In this study, the desired total fuel production for the whole supply chain is at 40 kBD, which is equivalent to 613.2 million gallons/year, approximately comparable to the needs of the U.S. Department of Defense.104 The optimization model will determine where these 40 kBD of fuels are produced and where they should be distributed across the country.

transportation cost = DFC + DVC × distance × DM (1)

While the transportation of fuel products may take advantage of current infrastructure and can be performed in large amounts, the transportation of biomass can only be performed in a much smaller scale and requires many more connections between biomass sources and the BTL refineries. It is important to account as closely as possible the costs associated with each connection, because an underestimation of these costs can affect the location of the BTL refineries. In this study, the data on forest residues biomass are discretized on a county basis. Thus, we assume that biomass is available at the county centroid, where the feedstock supply chain begins. Because the candidate locations of the hardwood BTL facilities are also at the county centroid, all interconnections for the feedstock transportation are between county centroids. In the case where hardwood biomass is transported from another county to the facility location, the intercounty transportation is applied using eq 1. Distance will be the straight line distance calculated from the latitude and longitude coordinates of the two county centroids, and these intercounty connections represent the average distances that biomass will travel from one county to another. In other words, the actual locations of the farms or forests in a given county may be farther or closer to the facility, but the county centroid represents the average point of all farms or forests for a given county. When biomass is delivered within the county (i.e., the location of hardwood biomass is equal to the facility location), however, eq 1 may underestimate the true transportation cost because of the zero distance value. Thus, it is necessary to estimate the intracounty transportation cost for the cases where biomass is delivered to a facility within the same county. The development of biomass intracounty transportation cost is as

6. TRANSPORTATION COSTS In the supply chain, biomass is transported by truck, water is transported by pipeline, and fuel products are transported by a combination of truck, pipeline, and barge.5 Fuel transportation by pipeline is calculated on the basis of an average value on a F


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follows. First, all county area data are obtained from the United States Census Bureau County and City Data Book: 2007.112 Second, an estimated radius is calculated for each United States county using the area data. Third, an average distance of all points to the county centroid is calculated on the basis of the estimated county radius (AVD). This average distance to the county centroid becomes the distance parameter in the intracounty biomass transportation cost, which is added to the total transportation cost in two ways. Figure 2 shows two counties with hardwood biomass resources. The squares represent the county centroid, with the

Figure 4. Graphical representation of scenario 2 of biomass transportation cost assumptions.

county B to the BTL facility is modeled by the intracounty cost using the average distance AVD estimate. In the second scenario (Figure 4), the intercounty transportation distance from county A to county B is modeled by two segments, namely, (1) the intracounty transportation within county A and (2) the intercounty transportation between the centroids of the two counties. Additionally, the intracounty transportation in county B is applied in the same way as in scenario 1. Thus, in scenario 2, each county is associated with an intracounty transportation cost based on its AVD value. This representation is an overestimation of the biomass transportation costs, because in the intercounty transportation cost, forest locations in county A that are closer to county B would not deliver biomass to the center of county A. However, this scenario is still applied to examine the instances where biomass transportation costs are higher than previously estimated, and the case studies associated with scenario 2 are indicated with the acronym IC in the Computational Studies.

Figure 2. Graphical representation of intra- and intercounty biomass transportation.

dark square representing a selected location of a BTL facility. The circles represent the actual locations of farms or forests in the county, whose information are not available to be input explicitly in the model. Thus, biomass resources located at the circles are accounted to be located at the squares (i.e., county centroid). The dotted lines are the distances that would be traveled by the biomass from the forests to the BTL facility. In Figures 3 and 4, the solid lines represent how the dotted lines are modeled mathematically.

7. WATER RESOURCES In addition to the biomass and liquid fuels supply chain, it is also important to consider the supply of water as required by the hardwood BTL plants. To prevent excessive water consumption in the hardwood BTL plants and stress on the local water resources, this study takes mitigating strategies on two levels, namely, on the single plant level and the supply chain level. On the single plant level, the water network superstructure is incorporated in the process synthesis framework to minimize the freshwater input and wastewater discharge of the hardwood BTL plants.1 On the supply chain level, a regional constraint on water supplies is included in the optimization model such that the water requirement for any hardwood BTL plant can be satisfied by the available local resources. Water usage data in the United States are obtained from the United States Geological Survey (USGS) database,113 where estimates of freshwater consumption for domestic, agricultural, and industrial sectors are reported for each county. The available water for the hardwood BTL supply chain is calculated by taking the minimum of 1.5 times of current industrial use or 15% of total freshwater use in the county to prevent excessive expansion of the current water supply. All water resource locations can supply all candidate facility locations within 5 miles, and the water transportation costs by pipeline is included in the total cost of the BTL supply chain.

Figure 3. Graphical representation of scenario 1 of biomass transportation cost assumptions.

In the first scenario (Figure 3), the intercounty transportation distance from county A to county B is modeled by the distance between the centroids of counties A and B. Additionally, intracounty transportation from the forest in G


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8. BIOMASS ENERGY SUPPLY CHAIN OPTIMIZATION MODEL The previous subsections detail the parameter inputs required in the energy supply chain optimization model. These parameter inputs include (i) the location, availabilities, and purchase prices of hardwood biomass residues, (ii) the transportation costs of biomass resources, water, and fuel products, (iii) investment costs, feedstock requirement, electricity requirement, fuel product amounts, and other input−output material flow rates of the BTL refineries, (iv) locations of fuel product destination (i.e., oil refineries, DLA blending locations, and state centers), and (v) price of utilities (i.e., water and electricity). Formulated as a MILP model, the optimization model gives (a) the strategic locations of BTL refineries for a 40 kBD total supply chain capacity, (b) the capacity of the BTL refinery at each location, (c) the supply chain topology from the feedstocks to product destination, and (d) the cost breakdown associated with each segment of the supply chain. The complete formulation of the mathematical model is as follows. The indices used in the mathematical model include s to denote the state index, c to denote the county or in the case of oil refineries and DLA locations, a representative location index, f to denote the feedstock index, p to denote the product index, t to denote the plant size index, q to denote the fuel ratio index, l to denote the plant location index, and m to denote the model of transportation index. Continuous variables are used to represent the levelized investment cost for a selected facility location (costlI), the total electricity requirement (EllT), electricity produced (ElPl ), the grid electricity required (ElGl ), the water requirement (WFl), the flow of feedstock f from the producing locations c to the plant facility l using mode of transportation m (xf,c,l,m), the required flow rate of biomass feedstock to a refinery (FRf,l), the flow of product p transported from the plant facility l to the demand locations c using mode of transportation m (zp,l,c,m), and the flow of freshwater to the facilities (wc,l). The model allows for electricity production in the supply chain, but because all of the BTL refineries have net electricity input, ElPl values are zero in all cases and the total electricity requirement ElTl is equal to the grid electricity required ElGl . Binary variables (yf,l,t,q) represent the selection of a specific BTL refinery at location l with forest biomass feedstock (f) ∈ FC, capacity t, and fuel product ratio q. The complete list of indices, sets, parameters, and variables used in the optimization model can be found in the Nomenclature section. Equation 2 restricts the selection of BTL refineries such that, at most, one facility can be selected at a given candidate location, which is specified at the county centroid where hardwood biomass exists. Set FL is defined as a set of possible combinations between biomass feedstock f, BTL capacity t, candidate location l, and fuel ratio q, and set LF is the set of candidate facility locations. Equations 3−5 impose lower and upper limits in the number of selected BTL refineries for the entire network, both overall and per plant capacity. Typical bounds used in this paper are N = 100, with Nmax and Nmin t t customized for each case study, and set T includes all BTL plant sizes.

∑

yf , t , l , q ≤ 1

(f , t , l , q) ∈ FL

∑ (f , t , l , q) ∈ FL

yf , l , t , q ≤ N

∑

yf , l , t , q ≤ Ntmax

∀t∈T

yf , l , t , q ≥ Ntmin

∀t∈T

(4)

(f , t , l , q) ∈ FL

∑

(5)

(f , t , l , q) ∈ FL

Selections of the investment cost parameters and the feedstock requirements associated with selected facilities are determined by eqs 6 and 7, where LCf,t,q and FRBf,t,q are the levelized investment cost and biomass feedstock requirement for a BTL refinery that uses feedstock f, of size t, and produces liquid fuels in ratio q, respectively. yf , l , t , q LCf , t , q = costlI

∑

∀ l ∈ LF (6)

(f , t , l , q) ∈ FL

FR Bf , t , qyf , l , t , q

∑

FR f , l =

∀ f ′ ∈ F B , l ∈ LF (7)

(f , t , l , q) ∈ FL

Equation 8 constrains the flow rates from each feedstock source locations not to exceed the amount available at that location (FAf,c), where CF is the set of all counties c that produces feedstock f. The total biomass flow rate arriving at a particular plant has to match the feedstock requirement (FRf,l) of the selected BTL refinery at the given location (eq 9). Equation 10 constrains the product ratios exiting for each BTL refinery to match either the 2010 United States demands for gasoline, diesel, and jet fuel, maximum diesel production, or maximum jet fuel production. Finally, the total product flow rates arriving at each demand location must be less than or equal to the known maximum capacities of the refineries or blending locations and less than the total demand amount within the state. Set CP is defined as a set of all locations c that has a positive demand of fuel product p. All product flows in the supply chain must amount to 40 kBD (total fuel) capacity (eqs 11 and 12).

∑

xf , c , l , m ≤ FA f , c

∀ (f , c ) ∈ C F (8)

(f , c , l , m) ∈ FT

∑

xf , c , l , m = FR f , l

∀ f ∈ F , l ∈ LF (9)

(f , c , l , m) ∈ FT

∑

zp , l , c , m =

(p , l , c , m) ∈ PT

∑

yf , l , t , q PR p , t , q

(f , t , l , q) ∈ FL

∀ l ∈ LF , p ∈ P

∑

zp , l , c , m ≤ DM p , c

(10)

∀ (p , c ) ∈ C P (11)

(p , c , l , m) ∈ PT

∑

zp , l , c , m = total fuel

∀ (p , c) ∈ C P (12)

(p , c , l , m) ∈ PT

The constraints associated with electricity requirement and production by the selected facilities include eqs 13−15. Produced electricity is assumed to be sold to the grid at $0.07/kWh. Equations 13 and 14 define the electricity requirement (ElTl ) and electricity produced (ElPl ) for each selected facility, respectively. The electricity requirement is fulfilled entirely by the grid (eq 15). Note that, in this paper, ElPl values are zero in all cases because all BTL refineries considered do not produce electricity.

∀ l ∈ LF (2)

∑ (3)

(f , t , l , q) ∈ FL

H

yf , l , t , q ELf , t , q = EllT

∀ l ∈ LF (13)


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yf , l , t , q EPf , t , q = EllP

∑

∀ l ∈ LF

EllT = EllG

Table 3. Two Sets of Upper Bounds (UB) Imposed on the Supply Chain Case Studies

(14)

(f , t , l , q) ∈ FL

∀ l ∈ LF

(15)

Equation 16 defines the freshwater input requirement for each selected facility (WFl). This value has to be matched with all water flow rates from various sources (eq 17), and they cannot exceed the water availabilities (WAc) in each source location (eq 18).

∑

yf , l , t , q FWf , t , q = WFl

WFl =

∑

wc , l

(16)

F

∀l∈L

(17)

c∈CW

∑ wc ,l ≤ WAc

∀ c ∈ CW

l ∈ LF

(18)

The objective function includes the total overall cost of the energy supply chain network, which covers (i) the investment costs associated with the new BTL refineries, (ii) the electricity costs/gains, (iii) feedstock purchase and transportation costs, (iv) product transportation costs, and (v) freshwater purchase and transportation costs. Note that the electricity sales and purchases are treated separately in the objective function to allow for a degree of flexibility for the system to sell or purchase electricity at different costs. These sales and purchases of electricity will occur at different locations throughout the country, meaning that, even though on a nationwide basis there will be a net selling or purchasing of electricity, it does not necessarily mean that all selected facilities will uniformly sell or purchase electricity. In this paper, however, no sales of electricity applies because of the properties of the BTL refineries.

+

l ∈ LF

∑∑

wc , l(costWP c

+ costWT c ,l )

F

c∈C l∈L

+

∑

xf , c , l , m(costFf , c + costFT f , c , l , m)

(f , c , l , m) ∈ FT

+

∑ (p , c , l , m) ∈ PT

UB2

30 8 4 0

30 8 4 2

case study name

fuel product ratio

upper bounds

R-UB1 R-UB1-IC R-UB2 R-UB2-IC D-UB1 D-UB1-IC D-UB2 D-UB2-IC K-UB1 K-UB1-IC K-UB2 K-UB2-IC A-UB1 A-UB1-IC A-UB2 A-UB2-IC

U.S. demand ratio U.S. demand ratio U.S. demand ratio U.S. demand ratio maximum diesel maximum diesel maximum diesel maximum diesel maximum jet fuel maximum jet fuel maximum jet fuel maximum jet fuel all product ratios all product ratios all product ratios all product ratios

UB1 UB1 UB2 UB2 UB1 UB1 UB2 UB2 UB1 UB1 UB2 UB2 UB1 UB1 UB2 UB2

biomass transportation cost assumption scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario scenario

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

Table 5. Supply Chain Profiles for Fuel Production in United States Demand Ratio

∑ costlI − EllPcostEl,P + ∑ EllGcostEl,G l ∈ LF

UB1

0.8 1 2.5 10

Table 4. Case Study Labeling Conventions

∀ l ∈ LF

(f , t , l , q) ∈ FL

BTL refinery capacity (kBD)

zp , l , c , mcostPT p,l ,c ,m (19)

Equations 2−19 represent a large-scale MILP optimization model that can be solved using CPLEX. The model consists of 11 369 binary variables, 944 317 continuous variables, and 17 165 constraints, whose solution gives the binary variables representing the selection of BTL refineries and their locations. The continuous variables give the flow rates of hardwood biomass feedstock and product, water, CO2, and electricity amounts in the supply chain topology. The computation is performed on a single computer containing 8 Intel Xeon 2.83 GHz processors and shared memory parallelization, and the optimization model is solved using CPLEX and eight parallel threads. The best incumbent solutions are reported after 24 central processing unit (CPU) hours, and the optimality gap for all performed computational studies is below 1%.

case study

R-UB1

R-UB1-IC

R-UB2

R-UB2-IC

overall cost ($/GJ) BEOP ($/bbl) electricity (MW) biomass usage (MTPY) average costs ($/GJ) biomass purchase biomass transportation product transportation investment cost electricity cost water purchase and transportation propane sale

22.18 113.62 47 12.4

22.77 116.98 47 12.4

17.63 87.69 42.5 12.1

18.28 91.39 42.5 12.1

5.99 0.72 0.04 15.35 0.35 0.01

5.99 1.31 0.07 15.35 0.35 0.01

5.87 0.74 0.04 10.92 0.31 0.01

5.87 1.41 0.06 10.92 0.31 0.01

0.28

0.30

0.26

0.31

namely, supply chains that include (1) only BTL refineries that produce fuels in ratios commensurate with the United States demand (i.e., 67 vol % gasoline, 22 vol % diesel, and 11 vol % jet fuel), (2) only BTL refineries that maximize the production of diesel (i.e., 75 vol % diesel and 25 vol % gasoline), (3) only BTL refineries that maximize the production of jet fuel (i.e., 75 vol % jet fuel and 25 vol % gasoline), and (4) a combination of all BTL refineries with the three product ratios and four capacities. In the mathematical model, these case studies represent variations in the set FL, where only the relevant combinations of f, t, l, and q are allowed. Specifically, index q for the different BTL refinery types is turned on or off depending upon the case studies. For example, in the R case studies, only BTL refineries that produce fuels in United States ratio are active. In the A case studies, all fuel combinations q are active. Each of the supply chain computational study yields a total

9. COMPUTATIONAL STUDIES We completed four sets of case studies in which different sets of BTL refineries are allowed to exist in the supply chain network, I


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Figure 5. Graphical representation of the locations of selected facilities for case study R-UB1. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 6. Distribution of hardwood biomass feedstock transportation distances from the source locations of forest residues to the BTL refineries.

allows for the existence of at most two 10 kBD refineries with the same upper bounds for all of the other capacities. These upper bounds are listed in Table 3. For each set of upper bounds, two scenarios of biomass transportation cost assumptions are applied, as described in section 6. Individual case study labeling conventions are listed in Table 4. In addition to the supply chain case studies, another set of computational results is presented where the optimization framework is used to identify the top 5 locations for each of the 12 BTL refinery types. Only one facility is allowed to exist, and the optimization model is solved 5 times with an integer cut

of 40 kBD total fuels, with differing gasoline, diesel, and jet fuel composition ratios. For each set of case study, there are four distinct runs. Two sets of upper bounds on the number of BTL refineries for each capacity (Nmax l ) are imposed. The first set of upper bounds disallows the existence of any 10 kBD facilities and limits the number of 0.8 kBD refineries to 30, 1 kBD refineries to 8, and 2.5 kBD refineries to 4. This case study represents the scenario where initial developments of BTL refineries would tend to minimize the risk associated with building a larger facility, such as one with a 10 kBD capacity. The second set of upper bounds J


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Figure 7. Graphical representation of the locations of selected facilities for case study R-UB1-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 8. Graphical representation of the locations of selected facilities for case study R-UB2. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend. K


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Figure 9. Graphical representation of the locations of selected facilities for case study R-UB2-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 10. Cost breakdown for the entire supply chain network for case study R-UB1.

constraint added in each iteration such that the previous solution is excluded from the feasible space and the trade-offs for each solution are established. 9.1. Commensurate Demand Ratio. 9.1.1. Optimal Network Topology. For each case study in this series, the whole supply chain produces a total of 40 kBD fuels with 26.9 kBD

gasoline, 8.6 kBD diesel, and 4.5 kBD jet fuel. The summary of the results can be found in Table 5, and the state and county locations of the selected BTL refineries can be found in Tables S1 and S2 of the Supporting Information. In the case where no 10 kBD refineries are allowed and the biomass intercounty assumptions are applied (i.e., case study R-UB1), a total of L


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Figure 11. Cost breakdown for the entire supply chain network for case study R-UB1-IC.

distances is plotted for the R case studies in Figure 6. Note that there is no maximum distance requirement imposed on the optimization model and the solution maximizes short-distance hardwood biomass delivery. To account for additional costs that may be incurred in the intracounty biomass transportation cost, case study R-UB1-IC is completed and compared to case study R-UB1. The supply chain network profile resembles the previous case study, with 40 total BTL refineries, 30 of 0.8 kBD capacity, 6 of 1 kBD capacity, and 4 of 2.5 kBD capacity. Note that all UB1 case studies have this same breakdown on the number of BTL refineries. The same amounts of electricity requirement (47 MW) and total biomass usage (12.4 MTPY) also apply in this case study. However, there are changes in the optimal locations of the facilities and in the distribution of cost contributions of the entire network. Figure 7 shows that the facility locations are more concentrated in the Southeast region compared to case study R-UB1. The largest facilities are located in Arkansas, Illinois, Louisiana, and Mississippi, where the surrounding areas have more dense biomass resources compared to the locations in case study R-UB1. In Figure 6, there is an increase in the amount of biomass delivered within 10 miles (72.62%) and slight variations in the other distance bins. The longest distance traveled by biomass is 47.7 miles for the 0.8 kBD refinery in Nebraska. Case studies R-UB1 and R-UB1-IC represent scenarios when early developments of BTL refineries and supply chains tend to favor smaller scale refineries to avoid the risks in investment and operation associated with large-scale facilities. However, there are gains in allowing larger capacities to be built in the supply chain because of economies of scale.1 Thus, BTL supply chains with 10 kBD refineries are examined in the next two case studies (i.e., R-UB2 and R-UB2-IC), where at most 2 facilities of 10 kBD refineries are allowed. In other words, at most 50% of the total fuel (i.e., 50% of 40 kBD) may be produced in large BTL refineries.

Table 6. Supply Chain Profiles for Maximization of Diesel Case Studies case study

D-UB1

D-UB1-IC

D-UB2

D-UB2-IC


20.11 101.82 44 12.61

20.72 105.30 44 12.61

16.84 83.19 46 12.85

17.68 87.97 46 12.85

5.80 0.66 0.04 13.31 0.31 0.01

5.80 1.22 0.09 13.31 0.31 0.01

5.91 0.69 0.03 9.90 0.32 0.01

5.91 1.51 0.05 9.90 0.32 0.01

0.03

0.03

0.03

0.03

40 refineries are selected in the supply chain network, 30 of which are of 0.8 kBD capacity, 6 of which are of 1 kBD capacity, and 4 of which are of 2.5 kBD capacity. These facilities are spread across the Midwest and Southeast regions of the United States, as shown in Figure 5. The 2.5 kBD refineries are located in Indiana, Iowa, Kentucky, and Tennessee, and the smaller refineries are dispersed throughout the Midwest, Southeast, and Northeast regions. The supply chain uses 12.4 million as-received tonnes/year (MTPY) of hardwood biomass residues, which is satisfied by the currently existing forest residues in the United States of 82 MTPY.105 The most distant connection for case study RUB1 is 46.1 miles, with 70.04% of the total feedstock usage being delivered within a 10 mile radius, 17.10% of the total feedstock usage being delivered between a 10 and 20 mile radius, 9.61% of the total feedstock usage being delivered between a 20 and 30 mile radius, and 0.37% of the total feedstock usage being delivered between a 40 and 50 mile radius (see Figure 6). The distribution of biomass transportation M


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Figure 12. Graphical representation of the locations of selected facilities for case study D-UB1. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 13. Distribution of hardwood biomass feedstock transportation distances from the source locations of forest residues to the BTL refineries for maximization of diesel case studies.

In case study R-UB2, a total of 17 refineries are selected in the supply chain, 5 of 0.8 kBD capacity, 6 of 1 kBD capacity, 4 of 2.5 kBD capacity, and 2 of 10 kBD capacity. Note that all UB2 case studies have the same breakdown on the number of BTL refineries. The 2 facilities of 10 kBD are located in Kentucky and Tennessee, and the smaller refineries are dispersed throughout the Midwest and Southeast regions of the United States (see Figure 8 and Table S2 of the Supporting Information). Electricity usage is equal to 42.5 MW for the entire supply chain, a reduction from case study R-UB1 because of the 10 kBD refineries. Biomass

usage for the whole supply chain amounts to 12.1 MTPY, and in comparison to case study R-UB1, there is more biomass delivered from more than 30 miles in this case study (see Figure 6). The largest distances of biomass transportation are associated with the 10 kBD refinery in Kentucky, while the 10 kBD refinery in Tennessee is surrounded by abundant biomass resources such that all of its feedstock requirements are satisfied within a 10 mile radius. Finally, the effect of biomass intracounty transportation cost is observed in case study R-UB2-IC. The same breakdown on N


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Figure 14. Graphical representation of the locations of selected facilities for case study D-UB1-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 15. Graphical representation of the locations of selected facilities for case study D-UB2. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend. O


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Figure 16. Graphical representation of the locations of selected facilities for case study D-UB2-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

distance delivery, the 10 kBD refineries would require higher amounts of feedstocks that need to be satisfied by more surrounding counties, increasing the radius of biomass delivery. The optimization model then allows for larger delivery distances and selects locations that would ensure enough biomass for all refineries and would minimize the total overall cost for the whole supply chain. 9.1.2. Overall Costs of Fuel Production. In the case where no 10 kBD refineries are allowed and scenario 1 of the biomass transportation cost assumptions are applied (i.e., case study R-UB1), the overall average cost of fuel production in the entire supply chain is $22.18/GJ lower heating value (LHV) of fuels produced. This cost in $/GJ can be converted into a price of crude oil at which the BTL supply chain would be economically competitive with petroleum-based processes, using the refiner’s margin for gasoline, diesel, and jet fuel.6,17 This break-even oil price (BEOP) is expressed in $/barrel (bbl) of oil and is reported in Table 5. For case study R-UB1, the BEOP is equal to $113.62/bbl. The contributing factors of the fuel production cost for each case study are comprised of (1) biomass purchase cost, (2) biomass transportation cost, (3) BTL refinery investment cost, (4) water purchase cost, (5) water transportation cost, (6) butane purchase cost, (7) electricity cost, and (8) fuel product transportation cost. Biomass, water, butane, and electricity are inputs to the BTL refineries, but because no butane purchase is required in all of the BTL refineries,1 no butane purchase cost is incurred in all case studies. These refineries can also produce a byproduct of propane/LPG, whose sale profits can reduce the cost of fuel production and are accounted for in the total cost

Table 7. Supply Chain Profiles for Maximization of Jet Fuel Case Studies case study

K-UB1

K-UB1-IC

K-UB2

K-UB2-IC


22.24 113.96 56.5 12.67

23.00 118.29 56.5 12.67

17.72 88.20 51.5 12.48

18.59 93.16 51.5 12.48

5.95 0.67 0.04 15.16 0.40 0.01

5.95 1.41 0.06 15.16 0.40 0.01

5.86 0.67 0.03 10.77 0.37 0.01

5.86 1.52 0.05 10.77 0.37 0.01

0

0

0

0

the number of facilities applies as in case study R-UB2, as well as the electricity requirement and total biomass usage. The 2 facilities of 10 kBD capacity are now located in Arkansas and Maine, and the shift toward areas with denser biomass resources is observed (see Figure 9). The biomass transportation profile changes significantly from the other three case studies, as seen in Figure 6. A decrease in biomass delivery within 10 miles is observed (i.e., 54.69%) compared to the previous case studies, and more biomass is delivered between 30 and 40 miles. It is interesting to note that the opposite effect takes place when the intracounty biomass transportation cost is applied in case study R-UB1-IC. In this case study, although a higher biomass transportation cost is expected to drive short P


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Figure 17. Graphical representation of the locations of selected facilities for case study K-UB1. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

In case study R-UB2, a significant drop is observed in the overall cost of fuel production, which is priced at $17.63/GJ or $87.69/bbl, a 20.5% reduction from case study R-UB1. This cost reduction is influenced by a few factors. First, the total electricity requirement for the entire supply chain is reduced from 47 to 42.5 MW in this case study. Second, a slight decrease in the amount of biomass usage from 12.4 to 12.1 MTPY takes place. However, these factors do not have large contributions in the overall cost, and the major driving force for the cost reduction is in the investment costs of the refineries. The average investment cost is $10.92/GJ, a significant drop from $15.35/GJ in case study R-UB1, contributing to 61% of the total overall cost. The average biomass purchase is at $5.87/GJ, accounting for 32% of the total cost. Consistent with the findings on a single-plant basis in part of the study, the biomass purchase cost on a per GJ basis is roughly constant across all capacity levels, and thus, its relative contribution increases in higher refinery capacities.1 With the inclusion of 10 kBD refineries in the supply chain, the relative contribution of biomass purchase grows from 27 to 33%. Finally, upon incorporation of biomass intracounty transportation cost in case study R-UB2-IC, the overall cost is equal to $18.92/GJ or $95.04/bbl, with 59% contribution from investment costs, 31% from biomass purchase, 8% from biomass transportation, 2% from electricity purchase, and 1% each for product transportation, water purchase, and water transportation. 9.2. Maximization of Diesel. 9.2.1. Optimal Network Topology. For each case study in this series, the whole supply chain produces a total of 40 kBD fuels with 30 kBD diesel and 10 kBD gasoline. The summary of the results can be found in Table 6, and the state and county locations of the selected BTL

value. For case study R-UB1, the cost breakdown for the entire supply chain is shown in Figure 10. The highest contributing factor is the investment cost to build the BTL refineries ($15.35/GJ), amounting to 68% of the total cost, followed by the biomass purchase cost ($5.99/GJ) at 27%. This pattern is consistent with the results from the process synthesis step in part 1 (10.1021/ef302003f) of this study,1 which also states the investment cost and biomass purchase as the two highest cost contributing factors. The biomass transportation cost incurs a higher percentage of cost (3%) than the product transportation cost, suggesting that the facility locations favor the locations of biomass resources as opposed to the product destination locations. Finally, electricity and water costs contribute minimally to the overall cost value. The supply chain requires a total of 47 MW electricity for the production of 40 kBD fuels, which will be satisfied by the grid. In case study R-UB1-IC, where additional costs are added for the intracounty biomass transportation cost, the overall cost of fuel production increases to $22.77/GJ or $116.98/bbl. Biomass transportation accounts for 6% of the total cost (see Figure 11), an increase compared to 3% in the previous case study (R-UB1). Investment costs and biomass purchase costs account for 67 and 26% of the total cost, respectively. The high investment costs in case studies R-UB1 and R-UB1-IC are directly related to the capacities of the refineries. From the single-plant process synthesis results (section 4), the economies of the scale effect can be observed as the capacity increases from 0.8 to 2.5 kBD but is even more pronounced in the 10 kBD case. Thus, it is important to observe how the supply chain would be affected when larger capacities of BTL refineries are allowed to exist. Q


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Figure 18. Graphical representation of the locations of selected facilities for case study K-UB1-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

Figure 19. Distribution of hardwood biomass feedstock transportation distances from the source locations of forest residues to the BTL refineries for maximization of jet fuel case studies.

When biomass intracounty cost is added in case study D-UB1IC, the locations of the 2.5 kBD refineries shift to Arkansas, Louisiana, and Washington, and the rest of the facilities are located in areas with denser biomass resources (see Figure 14). Most of the biomass delivery is performed within 30 miles, with a small percentage (i.e., 0.36%) delivered within 40 miles. In case study D-UB2, the 2 largest facilities are located in Tennessee and Georgia, while the 4 2.5 kBD refineries are in Iowa, Indiana, Kentucky, and Mississippi (see Figure 15).

refineries can be found in Tables S3 and S4 of the Supporting Information. In case study D-UB1, the 4 refineries of 2.5 kBD capacity are located in Iowa, Indiana, Kentucky, and Tennessee, with smaller refineries spread out in the Midwest, Southeast, Northeast, and Northwest regions (see Figure 12). A total of 44 MW of electricity is required for the entire supply chain, and 12.6 MTPY biomass is used. A total of 77.87% of the hardwood biomass is delivered within a 10 mile radius, and all of the biomass is delivered within 30 miles (see Figure 13). R


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Figure 20. Graphical representation of the locations of selected facilities for case study K-UB2. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

compensated by the significant reduction in the average investment costs because of economies of scale. The total electricity usage increases to 46 MW, and the biomass usage also increases to 12.85 MTPY, highlighting that the 10 kBD refineries require more biomass and electricity input on average. In case study D-UB2-IC, the total cost is equal to $17.68/GJ or $87.97/bbl, with an increased biomass transportation cost to $1.51/GJ and product transportation cost to $0.05/GJ. 9.3. Maximization of Jet Fuel. 9.3.1. Optimal Network Topology. For each case study in this series, the whole supply chain produces a total of 40 kBD fuels with 30 kBD jet fuel and 10 kBD gasoline. The summary of the results can be found in Table 7, and the state and county locations of the selected BTL refineries can be found in Tables S5−S6 of the Supporting Information. In case study K-UB1, where no 10 kBD refineries are allowed, the 4 refineries of 2.5 kBD capacity are located in Iowa, Indiana, Kentucky, and Georgia, with smaller refineries spread out in the Midwest, Southeast, Northeast, and Northwest regions (see Figure 17). A total of 56.5 MW of electricity is required for the entire supply chain, and 12.67 MTPY biomass is used. When biomass intracounty cost is added in case study K-UB1-IC, the locations of the 2.5 kBD refineries shift to Arkansas, Louisiana, and Mississippi and the rest of the facilities are located in areas with denser biomass resources (see Figure 18). Contrary to the R and D case studies when no 10 kBD refineries are allowed, the inclusion of the intracounty biomass transportation cost reduces the amount of biomass delivery within 10 miles in the K case studies (see Figure 19). In case study K-UB1, 81.36% of the total biomass usage is delivered within 10 miles, 16.80% is delivered between

In case study D-UB2-IC, The locations of the two largest facilities shift to Oregon and Arkansas, and the 2.5 kBD facilities are in Illinois, Mississippi, and Louisiana (see Figure 16). Similar trends in the biomass transportation distances for the R case studies are observed. A drop in the short distance delivery is compensated by the increase of delivery between 20 and 40 miles in case study D-UB2-IC, and 0.60% of the biomass is delivered within 50 miles (see Figure 13). 9.2.2. Overall Costs of Fuel Production. Case study D-UB1, where no 10 kBD refinery is allowed, has a total cost of $20.11/GJ or $101.82/bbl. The average investment cost is $13.31/GJ, accounting for 66% of the total cost, and the average biomass purchase cost is $5.80/GJ, accounting for 29% of the total cost. Other factors that add to the costs include the biomass transportation ($0.66/GJ), product transportation ($0.04/GJ), electricity cost ($0.31/GJ), and water purchase and transportation ($0.01/GJ). When biomass intracounty cost is added in case study D-UB1-IC, the total cost increases to $20.72/GJ or $105.30/bbl, which is due to the increase in the biomass transportation cost from $0.66 to 1.22/GJ and in the product transportation cost from $0.04 to 0.09/GJ. In case study D-UB2, where 2 refineries of 10 kBD capacity are allowed to exist, the total cost is equal to $16.84/GJ or $83.19/bbl. The average values for the different cost factors are equal to $9.90/GJ for refinery investment, $5.91/GJ for biomass purchase, $0.69/GJ for biomass transportation, $0.21/GJ for butane purchase, $0.03/GJ for product transportation, $0.32/GJ for electricity, and $0.01/GJ for water purchase and transportation. Note that, in comparison to case study D-UB1, the biomass purchase and transportation costs increase but are S


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Figure 21. Graphical representation of the locations of selected facilities for case study K-UB2-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

10 and 20 miles, and 1.84% is delivered between 20 and 30 miles. In case study K-UB1-IC, 64.36% of biomass is delivered within 10 miles, 28.95% is delivered within between 10 and 20 miles, and 6.69% is delivered between 20 and 30 miles. In case study K-UB2, where 2 refineries of 10 kBD capacity are allowed to exist, the 2 largest facilities are located in Tennessee and Georgia, while the 4 refineries of 2.5 kBD capacity are in Iowa, Indiana, Kentucky, and Arkansas (see Figure 20). The total electricity usage is equal to 51.5 MW, and the biomass usage is equal to 12.48 MTPY. In case study K-UB2-IC, the locations of the two largest facilities shift to Maine and Arkansas, and the 2.5 kBD facilities are in Georgia, Mississippi, and Louisiana (see Figure 21). When larger facilities are allowed to exist, larger biomass transportation distances occur. In both of these case studies, hardwood biomass is delivered within 40 miles. 9.3.2. Overall Costs of Fuel Production. In case study K-UB1, where no 10 kBD refinery is allowed, the total cost of fuel production is equal to $22.24/GJ or $113.96/bbl. The average investment cost is $15.16/GJ, accounting for 68% of the total cost, and the average biomass purchase cost is $5.95/GJ, accounting for 27% of the total cost. Other factors that add to the costs include the biomass transportation ($0.67/GJ), product transportation ($0.04/GJ), electricity cost ($0.40/GJ), and water purchase and transportation ($0.01/GJ). When biomass intracounty cost is added in case study K-UB1-IC, the total cost increases to $23/GJ or $118.29/bbl, which is due to the increase in the biomass transportation cost from $0.67/GJ to $1.41/GJ, accounting for 6% of the total cost, and in the product transportation cost from $0.04/GJ to $0.06/GJ.

In case study K-UB2, where 2 refineries of 10 kBD capacity are allowed to exist, the total cost is equal to $17.72/GJ or $88.20/bbl. The average values for the different cost factors are equal to $10.77/GJ for refinery investment, $5.86/GJ for biomass purchase, $0.67/GJ for biomass transportation, $0.03/GJ for product transportation, $0.37/GJ for electricity, and $0.01/GJ for water purchase and transportation. In case study K-UB2-IC, the total cost is equal to $18.59/GJ or $93.16/bbl, with an increased biomass transportation cost to $1.52/GJ and product transportation cost to $0.04/GJ. 9.4. Comparison. Comparisons across the supply chain to commensurate ratios with the United States fuel demands (i.e., R case studies), maximized diesel production (i.e., D case studies), and maximized jet fuel production (i.e., K case studies) elucidate the economic trade-offs between supply chains with differing targets of fuel production. On a single plant level, these fuel ratios determine what kinds of optimal topologies the BTL refineries should adopt, and on the supply chain level, they determine the interactions between the biomass and fuel markets, as well as the overall cost performances. In the case studies where no 10 kBD refineries are allowed and scenario 1 of the biomass transportation cost assumptions are applied (i.e., case studies R-UB1, D-UB1, and K-UB1), we observe that the supply chain that maximizes diesel (D-UB1) has the lowest cost of fuel production ($20.11/GJ or $101.82/ bbl), followed by case studies R-UB1 ($22.18/GJ or $113.62/ bbl) and K-UB1 ($22.24/GJ or $113.96/bbl). The major driving force is the investment cost of the BTL refineries, which is averaged at $13.31/GJ for D-UB1, about $2/GJ lower than the K-UB1 ($15.16/GJ) and R-UB1 ($15.35/GJ) case studies. From the process synthesis results, we observe that the plant T


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Figure 22. Graphical representation of the locations of selected facilities for case study A-UB2. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

costs. Case study D-UB1-IC has the lowest biomass transportation cost at $1.22/GJ, followed by R-UB1-IC at $1.31/GJ and K-UB1-IC at $1.41/GJ. Note that the differences between these costs are more pronounced in the IC case studies. Finally, while case studies R-UB1, D-UB1, and K-UB1 have the same average product transportation cost ($0.04/GJ), case study D-UB1-IC averages at $0.09/GJ, case study R-UB1-IC averages at $0.07/GJ, and case study K-UB1-IC averages at $0.06/GJ. Further cost reductions by propane sales only apply to case studies D-UB1-IC ($0.03/GJ) and R-UB1-IC ($0.30/GJ). In the second set of upper bounds, where at most 2 refineries of 10 kBD capacity are allowed, case study D-UB2 yields the lowest cost of fuel production at $16.84/GJ or $83.19/bbl, followed by R-UB2 at $17.63/GJ or $87.69/bbl and K-UB2 at $17.72/GJ or $88.20/bbl. The average investment cost is equal to $9.90/GJ for D-UB2, $10.77/GJ for K-UB2, and $10.92/GJ for R-UB2. Biomass purchase cost is the lowest for K-UB2 at $5.86/GJ, followed by R-UB2 at $5.87/GJ and D-UB2 at $5.91/GJ, even though the total amount of biomass usage is lowest for R-UB2 at 12.1 MTPY, followed by K-UB2 at 12.48 MTPY and R-UB2 at 12.85 MTPY. Biomass transportation cost is also the lowest for K-UB2 compared to D-UB2 and R-UB2 at $0.67/GJ, $0.69/GJ, and $0.74/GJ, respectively. Finally, electricity cost is the highest for K-UB2 ($0.37/GJ), followed by D-UB2 ($0.32/GJ) and R-UB2 ($0.31/GJ). Note that, in comparison to the UB1 case studies, the inclusion of 10 kBD refineries in the supply chain reduces the total electricity requirement for the R and K case studies but the total amount is increased for the D case studies. When biomass intracounty transportation costs are applied, case studies D-UB2-IC has the lowest overall cost of $17.68/GJ

topology of the BTL refineries that maximize diesel production have simpler topologies compared to those that produce the three fuel products or that maximize jet fuel. The biomass purchase cost for case study D-UB1 is also lower ($5.80/GJ) than case studies K-UB1 ($5.95/GJ) and R-UB1 ($5.99/GJ). It is important to mention, however, that the biomass usage of case study R-UB1 is in fact lower (12.3 MTPY) than D-UB1 (12.6 MTPY) and K-UB1 (12.67 MTPY), but they incur a higher averaged price, signifying that the supply chain purchases biomass from regions with more expensive feedstocks and locates the BTL refineries such that the transportation cost to deliver the three fuel products to their respective destinations is balanced. The biomass transportation and electricity costs for D-UB1 are also the lowest among the three case studies, further driving the cost differences between case study D-UB1 and the rest. Between case studies K-UB1 and R-UB1, trade-offs exist between the electricity and propane sales. Case study K-UB1 requires a higher amount of total electricity input (56.5 MW) compared to case studies R-UB1 (47 MW) and D-UB1 (44 MW). Thus, the electricity cost for K-UB1 is higher than R-UB1. In addition, case study K-UB1 does not produce byproduct propane and does not gain from its sales, while case study R-UB1 gains a cost reduction of $0.28/GJ from propane sales. When scenario 2 of the biomass transportation cost assumptions is applied in case studies R-UB1-IC, D-UB1-IC, and K-UB1-IC, similar patterns emerge. Case study D-UB1-IC has the lowest cost at $20.72/GJ or $105.30/bbl, followed by R-UB1-IC at $22.77/GJ or $116.98/bbl and K-UB1-IC at $23.00/GJ or $118.29/bbl. All individual cost comparisons also follow the same pattern, except for biomass and product transportation U


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Figure 23. Graphical representation of the locations of selected facilities for case study A-UB2-IC. The facilities are represented by dark brown circles, with sizes that correspond to their respective capacities. The green areas of the map are the United States counties with available forest residues biomass, and their relative amounts are represented by the proposed color scheme in the map legend.

maximize the production of diesel, while the two 10 kBD refineries produce fuels in ratios commensurate with the United States demands. For the entire supply chain, the combination of these refineries produce 46 vol % gasoline, 48 vol % diesel, and 6 vol % jet fuel in total. The same distribution on the number of refinery types in the supply chain also applies for case study A-UB2-IC (see Figure 23). The total electricity requirement is 41 MW, the lowest among all case studies, and the biomass usage is 12.25 MTPY. When case study A-UB2 is compared to the supply chain with the next lowest cost (D-UB2), case study A-UB2 has a higher average investment cost at $10.04/GJ instead of $9.90/GJ but lower biomass purchase, transportation, and electricity costs at $5.77, $0.67, and $0.29/GJ, respectively. Additionally, the case study also has a higher yield from propane sales at $0.16/GJ. Thus, in these A case studies where the optimizer is free to select a combination of fuel ratios, the selection of smaller sized refineries favor the maximization of diesel and the selection of the 10 kBD refineries favor the production of fuels in United States demand ratios. 9.6. Ranking of Facility Locations. The optimization framework can be used to address the question on where to locate a single BTL refinery such that the overall cost of the supply chain associated with that one refinery is minimized. By adjusting the upper bounds on the number of facilities allowed in the supply chain (eq 4) and the total fuel constraint (eq 12), the top 5 locations for each of the 12 BTL refineries are identified. The optimization model is solved 5 times in a loop, and for each iteration, an integer cut constraint is introduced such that the previous optimal solution is infeasible and excluded from the solution space. Tables 8, 9, and 10 detail all ranking results for all

or $87.97/bbl, followed by R-UB2-IC at $18.28/GJ or $91.39/bbl and K-UB2-IC at $18.59/GJ or $93.16/bbl. The increase in costs compared to the UB2 cases is due to the increase in the biomass transportation costs, which are equal to $1.41/GJ for R-UB2-IC, $1.51/GJ for D-UB2-IC, and $1.52/GJ for K-UB2-IC. 9.5. Combined Fuel Ratios. Given the above comparisons between the R, D, and K case studies, we investigated whether the benefits of each case study can be combined in a synergistic way if the supply chain is allowed to have a mixture of R-, D-, and K-type BTL refineries. In this set of case studies, all alternatives of the BTL refineries may exist in the supply chain that produces a total of 40 kBD liquid fuels. In other words, all 12 BTL refineries (i.e., 4 capacities × 3 product ratios) can be selected at any given location. When there is no 10 kBD refineries allowed in the supply chain, the resulting selected BTL refineries correspond almost exactly to the maximization of the diesel case (D-UB1), except for three locations. All of the selected refineries maximize the production of diesel, producing a total of 75 vol % diesel and 25 vol % gasoline for the entire supply chain. The overall cost of fuel production is equal to $20.11/GJ or $101.82/bbl, which resembles the value for case study D-UB1. A similar phenomenon also occurs when the intracounty transportation cost of biomass is added. When 10 kBD refineries are allowed to exist in case study A-UB2, however, the resulting supply chain topology yields a lower cost than any of the previous three counterparts. The total average fuel cost is $16.67/GJ or $82.22/bbl, and the topology of the supply chain is given in Figure 22. A total of 17 facilities are selected. The 0.8, 1, and 2.5 kBD refineries V


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Table 8. Top 5 Locations for BTL Refineries That Produce Fuels in Ratio Commensurate with the United States Demand rank

state

county

scenario 1 cost ($/GJ)

state

county


Mississippi Louisiana Kentucky Minnesota Wisconsin

Warren West Baton Rouge Marion Ramsey (State Center)

24.15 24.16 24.21 24.25 24.26

New Hampshire Mississippi Kentucky Wisconsin Minnesota

(State Center) Warren Marion (State Center) Ramsey

22.94 23.06 23.16 23.18 23.19

Mississippi Louisiana Wisconsin Illinois Minnesota

Warren Bossier (State Center) Will Ramsey

19.40 19.42 19.57 19.59 19.62

Maine Arkansas Louisiana Oregon Louisiana

Cumberland Union Webster Multnomah Bossier

15.19 15.29 15.31 15.33 15.35

0.8 kBD 1 2 3 4 5

Indiana Kentucky Iowa Tennessee Wisconsin

Marion Marion Story Cannon (State Center)

23.39 23.44 23.47 23.51 23.55

1 2 3 4 5

Indiana Kentucky Iowa Tennessee Wisconsin

Marion Marion Story Cannon (State Center)

22.31 22.35 22.39 22.43 22.47

1 2 3 4 5

Georgia Indiana Kentucky Iowa Tennessee

Bibb Marion Marion Story Cannon

18.49 18.55 18.59 18.63 18.67

1 2 3 4 5

Tennessee Georgia Kentucky Tennessee Wisconsin

Cannon Bibb Marion DeKalb Wood

14.31 14.34 14.58 14.63 14.74

1 kBD

2.5 kBD

10 kBD

Table 9. Top 5 Locations for BTL Refineries That Maximize the Production of Diesel rank

state

county


state

county


New Hampshire Louisiana Wisconsin Minnesota Kentucky

(State Center) West Baton Rouge (State Center) Ramsey Marion

21.86 21.96 21.96 21.96 21.97

New Hampshire Mississippi Georgia Wisconsin Minnesota

(State Center) Warren Muscogee (State Center) Ramsey

20.94 21.00 21.00 21.02 21.05

Mississippi Louisiana Louisiana Wisconsin Illinois

Warren Bossier Webster (State Center) Will

17.84 17.85 17.89 17.91 17.95

Louisiana Oregon Washington Mississippi Georgia

Webster Multnomah Clark Warren Muscogee

15.85 15.86 15.88 15.91 15.91

0.8 kBD 1 2 3 4 5

Iowa Indiana Kentucky Tennessee Wisconsin

Story Marion Marion Cannon (State Center)

21.18 21.18 21.22 21.26 21.27

1 2 3 4 5

Iowa Indiana Kentucky Tennessee Wisconsin

Story Marion Marion Cannon (State Center)

20.24 20.24 20.28 20.32 20.33

1 2 3 4 5

Iowa Indiana Georgia Kentucky Tennessee

Story Marion Bibb Marion Cannon

16.98 16.98 16.99 17.02 17.06

1 2 3 4 5

Tennessee Georgia Tennessee Maine Kentucky

Cannon Bibb DeKalb Cumberland Marion

14.71 14.90 15.03 15.03 15.09

1 kBD

2.5 kBD

10 kBD

capacities of the BTL refineries using the two scenarios for biomass transportation cost. First, it can be seen that in each series that the costs for the top 5 locations for each facility are very close to each other. The trade-offs between the costs are mostly contributed to the biomass and product transportations, because the investment cost and amount of biomass required would be the same in each series. The contrast between scenarios 1 and 2 in the

biomass transportation cost assumptions follow the pattern seen in the supply chain case studies, where the preferred locations shift from the Midwest region to the Southeast and Northeast regions of the United States. If one were to build a single BTL refinery, the cheapest combination of BTL refinery type and location would be building a 10 kBD refinery that produce liquid fuels in United States demand ratio in Tennessee (see Table 8) under scenario 1 and the same refinery in Maine W


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Table 10. Top 5 Locations for BTL Refineries That Maximize the Production of Jet Fuel rank

state

county


state

county


New Hampshire Georgia Mississippi Rhode Island Minnesota

(State Center) Muscogee Warren Kent Ramsey

24.19 24.25 24.26 24.27 24.28

New Hampshire Mississippi Georgia Rhode Island Wisconsin

(State Center) Warren Muscogee Kent (State Center)

23.13 23.19 23.20 23.21 23.21

Mississippi Georgia Georgia Massachusetts Wisconsin

Warren Muscogee Bibb Hampden (State Center)

19.58 19.62 19.63 19.64 19.65

Maine Arkansas Louisiana Oregon Mississippi

Cumberland Union Webster Multnomah Warren

15.52 15.58 15.60 15.62 15.64

0.8 kBD 1 2 3 4 5

Iowa Indiana Georgia Kentucky Rhode Island

Story Marion Bibb Marion Kent

23.47 23.48 23.49 23.52 23.52

1 2 3 4 5

Iowa Indiana Georgia Kentucky Rhode Island

Story Marion Bibb Marion Kent

22.40 22.41 22.42 22.45 22.45

1 2 3 4 5

Iowa Indiana Georgia Kentucky Tennessee

Story Marion Bibb Marion Cannon

18.69 18.70 18.71 18.73 18.77

1 2 3 4 5

Tennessee Georgia Maine Tennessee Kentucky

Cannon Bibb Cumberland DeKalb Marion

14.51 14.67 14.81 14.82 14.83

1 kBD

2.5 kBD

10 kBD

10. CONCLUSION An optimization-based framework for the supply chain of hardwood biomass to liquid transportation fuels was proposed. BTL refineries of 0.8, 1, 2.5, and 10 kBD capacities, whose topologies are optimized via a process synthesis approach, are allowed to exist in the supply chain. The problem formulation takes into account the locations of hardwood biomass in the United States, the delivery locations of fuel products, transportation costs of every input and output of the refinery, water resources, and electricity requirement of the supply chain. A large-scale MILP optimization model was developed to identify strategic locations of BTL refineries to produce a total of 40 kBD fuels across the country such that the overall cost of fuel production will be minimized. Four sets of case studies with differing fuel product ratios (i.e., ratios in accordance to United States demand, maximization of diesel, maximization of jet fuel, and a mixture of all ratios) were completed to assess the overall supply chain profiles when certain targets of fuel amounts are imposed. Additionally, the framework is adapted to generate a rank order list of the top 5 most profitable locations for each of the BTL refinery types. Quantitative trade-offs are established for each factor that contributes to the overall cost. The resulting average costs of fuel production for all supply chain case studies producing 40 kBD total fuels range between $82.22 and 118.29/bbl. When a mixture of fuel ratios is allowed in the supply chain, the selections of smaller scale refineries favor the refineries that maximize diesel production and the large-scale refineries (i.e., 10 kBD) produce fuels in ratios commensurate with the United States demand. Optimal locations for the BTL refineries are dispersed in the Midwest, Southeast, Northeast, and in a few instances, the Northwest regions of the United States. Biomass transportation costs to the BTL refineries can affect these locations in a significant way, as reflected by the two sets of assumptions on the intracounty delivery cost of hardwood biomass. The most

under scenario 2. The overall costs of the facilities are equal to $14.31/GJ or equivalent to $68.77/bbl and $15.19/GJ or $73.78/bbl, respectively. Note also that, for refineries with capacities 0.8, 1, and 2.5 kBD, those that maximize diesel achieve the lowest costs, while the 10 kBD refinery that maximizes diesel becomes the refinery with the highest costs compared to the United States ratio and maximization of jet fuel counterparts. Iowa, Indiana, Kentucky, Tennessee, and Wisconsin appear consistently as one of the top 5 locations for smaller refineries in all three product ratios under scenario 1 of biomass transportation cost assumptions. Under scenario 2, the locations shift to Mississippi, Louisiana, Kentucky, Minnesota, New Hampshire, and Wisconsin. For the 10 kBD refineries, Tennessee, Georgia, Kentucky, and Maine are generally in the top 5 list under scenario 1 and Arkansas, Louisiana, Oregon, Maine, and Mississippi are selected under scenario 2. In general, the counties listed in the top 5 ranking for 0.8 and 1 kBD refineries are generally part of the solutions in the supply chain case studies. A total of 4 of the top 5 locations for 2.5 kBD and 2 of the top 5 locations for 10 kBD refineries are also selected. In other cases, all of the locations in Tables 8−10 are usually selected, even though the selected refinery may be of a different capacity than in the ranking list. An exception, however, is observed in the case of DeKalb County in Tennessee. DeKalb County is always selected as one of the top 5 locations for the 10 kBD refineries, however, it is always ranked lower than Cannon County, Tennessee. Because Cannon County, Tennessee is always in the supply chain, the existence of another 10 kBD refinery in the same state would not be optimal for the supply chain solutions, because it will put high stress on the biomass resources in the area. Thus, DeKalb County is never selected in the nationwide supply chain solutions (see Tables S2, S4, S6, and S8 of the Supporting Information). X


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FL = {( f,t,l,q) ∈ FC × T × L × Q} FT = {( f,c,l,m)|(p,c) ∈ CF,l ∈ L, (f,m) ∈ MF, costFE f,c,l,m ≤ maxcostFE f } PT = {(p,l,c,m)|(p,c) ∈ CP,l ∈ L, (p,m) ∈ MP, costPE p,c,l,m ≤ maxcostPE p } CF = {( f,c)|(f,c) ∈ F × C,FAf,c > 0} CP = {(p,c)|(p,c) ∈ P × C,DMp,c > 0} CW = {c|c ∈ C,WAc > 0}

significant factor in the overall cost figure, however, is the investment cost of the BTL refineries, which, in turn, is a function of their topological configurations. Supply chains that allow for larger refineries to be selected (i.e., 10 kBD) have significantly lower costs because of economies of scale.

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ASSOCIATED CONTENT

S Supporting Information *

County locations of all facilities selected in the supply chain case studies (Tables S1−S8). This material is available free of charge via the Internet at http://pubs.acs.org.

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Parameters

N = maximum number of BTL refineries built in the United States Nmax = maximum number of BTL refineries for size t t = minimum number of BTL refineries for size t Nmin t LCf,t,q = BTL levelized investment cost for feed f, size t, and fuel ratio q FRBf,t,q = BTL biomass requirement for feed f, size t, and fuel ratio q ERf,t,q = BTL electricity requirement for feed f, size t, and fuel ratio q EPf,t,q = BTL electricity produced for feed f, size t, and fuel ratio q FWf,t,q = BTL freshwater requirement for feed f, size t, and fuel ratio q FAf,c = availability of feedstock f in county c DMp,c = demand of product p in county c PRp,t,q = amount of liquid fuel product p for a plant of size t and fuel ratio q WAc = water availability in location c capG = maximum grid electricity usage for the country costFf,c = cost per unit mass of feedstock f at county c costFT f,c,l,m = cost per unit mass flow to transport feedstock f from county c to facility l using mode m costPT p,l,c,m = cost per unit mass flow to transport product p from facility l to county c using mode m costEl,G = total investment cost per unit energy of grid electricity costEl,P = total profit per unit energy of produced electricity costWP = cost of water purchase at location c per unit flow c rate costWT = cost of water transportation by pipeline from c,l source c to facility l

AUTHOR INFORMATION

Corresponding Author

*Telephone: 609-258-4595. Fax: 609-258-0211. E-mail: fl[email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the National Science Foundation (NSF EFRI-0937706 and NSF CBET1158849) and support from Lockheed Martin Corporation.

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NOMENCLATURE

Index

s = state index c = county index f = feedstock index p = product index t = plant size index l = plant location index m = transportation mode index r = port index q = fuel product ratio index Sets

S = U.S. states C = U.S. counties FB = biomass feedstocks (i.e., forest residues) F = feedstocks P = products (i.e., gasoline, diesel, and jet fuel) CF = feedstock−county pairs CP = product−location pairs CW = locations of water resources LF = candidate plant locations M = modes of transportation (i.e., truck, pipeline, and barge) MF = feedstock−mode pairs MP = product−mode pairs MPpipe = product pipelines R = 50 U.S. ports with high liquid fuel capacity T = plant sizes (i.e., 0.8, 1, 2.5, and 10 kBD) Q = fuel product ratios (i.e., commensurate with U.S. demands, maximized diesel, and maximized jet fuel production) FL = candidate facility locations FT = feasible feedstock flow quadruplets PT = feasible product flow quadruplets

Continuous Variables

costIl = levelized investment cost of facility l FRf,l = amount of feedstock f required at facility l ElTl = total electricity required at facility l ElPl = total electricity produced at facility l ElGl = grid electricity required at facility l WFl = freshwater requirement for facility l wc,l = freshwater flow from source c to facility l xf,c,l,m = flow of feedstock f from county c to facility l using transportation mode m zp,l,c,m = flow of product p from facility l to county c using transportation mode m Binary Variables

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Set Definitions

f ∈ F = FB FC = {( f)|f ∈ FB} MF = {( f,m) ∈ FB × truck} MP = {(p,m) ∈ P × {pipeline, truck, barge}}

yf,t,l,q = BTL plant binary variable at location l with feed f, size t, and fuel ratio q

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