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Optimal Supply Chains for Biofuel Production
CHAPTER
Optimal Supply Chains for Biofuel Production
20
W. Alex Marvin, Prodromos Daoutidis1 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA 1 Corresponding author: E-mail: [email protected]
20.1 INTRODUCTION The current U.S. biofuel industry is dominated by ethanol (mainly produced from corn grain starch) and biodiesel (mainly produced from soybean oil and recycled cooking oils), but cellulosic biofuels (based on nonfood resources such as agricultural waste, grasses, and woody crops) are predicted to play a large role in the future. Annual ethanol production has quickly expanded from 83 million gallons in 1981 to nearly 15 billion gallons today, and biodiesel production has similarly grown to 700 million gallons. Biofuels became controversial during this rapid growth for influencing the price of food by acting as a competing outlet for agricultural commodities. About a third of US corn production is used to produce ethanol, resulting in ethanol comprising 9.5% of finished gasoline blends in the US (McPhail et al., 2011). Alternatively, cellulosic biofuels are produced from low resource-intensive biomass, and can provide much greater supplies and environmental benefits than food-based biofuels (Hill et al., 2006). The US EPA determined that 0.81 million gallons of cellulosic biofuel were produced in 2013 (U.S. Environmental Protection Agency, 2014), while government mandates require the use of 16 billion gallons of cellulosic biofuel in motor-vehicle fuel by 2022. Development of the cellulosic biofuel industry to meet these mandates will impose significant logistical challenges at each stage of the biofuel supply chain (biomass production, harvesting, storage, processing and transportation, and biofuel distribution). This industry will require about a billion tons of biomass annually from a variety of sources that each may be seasonally available, with uncertainty in composition, quantity, and price. Furthermore, there are many proposed technologies (e.g., crop residue fermentation and biomass gasification with syngas upgrading) competing for biomass processing, and their adoption will determine the economic and environmental impacts of the industry as a whole. Biofuel supply chain optimization has emerged as a popular method for understanding the expected expansion of the biofuel industry. These studies seek to determine the optimum supply chain configuration, including all activities from the Computer Aided Chemical Engineering, Volume 36. ISSN 1570-7946. http://dx.doi.org/10.1016/B978-0-444-63472-6.00020-3 © 2015 Elsevier B.V. All rights reserved.
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biomass production to the biofuel end-use, which maximizes a desired performance index (e.g., profitability, greenhouse gas emissions, water use or net energy use). Often a real-world study region is chosen with high-resolution spatial information about the type, quantity, and location of biomass availability or production capability, harvest and logistics, and biorefinery plant capabilities to convert biomass to biofuels. A number of thorough reviews have been done of the research in this area, including its overlap with petroleum and chemical operations research (An et al., 2011), with hybrid energy system process and supply chain optimization (Floudas et al., 2012), and with the broader set of multiscale challenges surrounding biomass-to-bioenergy supply chains (Yue et al., 2014; Daoutidis et al., 2013). In our previous study (Marvin et al., 2013), we proposed a biofuel supply chain optimization problem for determining economical biomass processing facility locations and capacities and applied it to a 9-state region in the Midwestern United States to assess the feasibility of meeting governmental biofuel mandates in 2015. This was formulated as a mixed integer linear program with an objective of maximizing total net present value (TNPV). A detailed cash flow analysis that includes capital depreciation and taxation was embedded into the model formulation to give insights into the minimum biofuel selling price for each facility and for each Renewable Fuel Standard biofuel classification (renewable fuel, advanced biofuel, and cellulosic biofuel). This chapter builds off of that work by adding a second objective of minimizing total greenhouse gas emissions (TGHG) relative to gasoline (i.e., produced biofuel is assumed to offset an energy-equivalent amount of gasoline). Thus the scope of the life cycle analysis is from cradle to grave (or in the case of biofuels, from field to wheels). Recent life cycle analysis literature on biofuels is leveraged to quantify the impact of each activity in the biofuel supply chain. The resulting multiobjective mixed integer linear program is solved using an ε-constraint approach that yields the Pareto Frontier of efficient supply chain designs. This allows for the identification of supply chain decisions that greatly reduce greenhouse gas emissions for minimal economic losses. The remainder of this article is organized as follows. Multiobjective optimization techniques are reviewed in Section 20.2. The supply chain optimization scope and formulation is described in Section 20.3, and its solution strategy is described in Section 20.4. Life cycle analysis for each activity in the biofuel supply chain is described in Section 20.5. The Pareto Frontier for the multiobjective supply chain optimization is identified and discussed in Section 20.6, along with two Pareto points that have particularly interesting supply chain configurations. Concluding remarks are in Section 20.7.
20.2 MULTIOBJECTIVE OPTIMIZATION Multiobjective optimization seeks to identify one or a set of Pareto optimal solutions (Pareto points) (Gonzalez, 2007). Pareto points are solutions that are noninferior to all other feasible solutions. This is shown in Figure 20.1 for the two objectives of maximizing TNPV and minimizing TGHG for the entire supply chain. Point (b) is
20.2 Multiobjective Optimization
(a) (b)
(c)
FIGURE 20.1 Example Pareto Frontier for maximization of TNPV and minimization of TGHG. The feasible region for the optimization problem is shown with its efficient boundary being the Pareto Frontier. Point (a) is infeasible, point (b) is a Pareto point, and point (c) is feasible but is dominated by point (b).
a Pareto point, because there is no feasible solution that simultaneously improves both objectives. There are usually many Pareto points, and the whole set of them is referred to as the Pareto Frontier or surface. It is desirable to lower TGHG and raise TNPV, so the upper left boundary in Figure 20.1 is the Pareto Frontier. Each solution along the Pareto Frontier is mathematically equal (i.e., a solution that is better for one objective cannot be found without necessarily worsening at least one other objectives) and thus it depends on the preference of a decision maker to select a “right” solution. The general form of a multiobjective optimization problem involving K objectives to be minimized is min ðf1 ðxÞ;:::; fK ðxÞÞ s:t:
x˛X
where x is the vector of decision variables with feasible set X defined by constraints. Multiobjective optimization techniques vary in how a decision maker may express their preference, and the techniques fall into three major groups (Grossmann and Guille´n-Gosa´lbez, 2010; Collette and Siarry, 2003; Miettinen, 1999): • • •
A priori methods A posteriori methods Interactive methods
A priori methods require preference information to be specified before finding a solution. The solution returned is a Pareto point that best satisfies the decision maker’s preference. Examples include scalarization (agglomeration), no-preference methods and utility function methods. Applying a so-called carbon tax to
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greenhouse gas emissions is a common example of linear scalarization to convert a multiobjective problem involving emissions and economics into a single-objective problem. In general, the weights assigned to the objectives convert them into uniform units (e.g., dollars) and represent the relative importance for each objective. Minimizing the Euclidean norm (L2) to an ideal state (i.e., desired value for the objectives that is unobtainable) is an example of a no-preference method. A posteriori methods generate a representative set of Pareto points that the decision makers can then evaluate based on their preferences. These methods require additional computational effort, as determining each Pareto point may require as much time as an a priori method. For example, many well-known a posteriori methods (e.g., Normal-boundary Intersection (Das and Dennis, 1998) and Successive Pareto Optimization (Mueller-Gritschneder et al., 2009)) construct and solve several scalarization problems. Metaheuristics, such as simulated annealing, particle swarm optimization, and evolutionary algorithms, generate a representative set of solutions by searching the feasible region quickly, allowing for an approximation of the Pareto Frontier, but Pareto optimality of the solutions is not guaranteed. The ε-constraint method is the most widely applied a posteriori method in multiobjective optimization. In this method, single-objective problems are solved where one of the original objectives is minimized while the other objectives are constrained: min s:t:
f1 ðxÞ x˛X fK ðxÞ εk ;
cks1
εLk
where the parameters εk are varied between and εU k . These bounds are determined by solving the K single-objective problems for each objective function separately. Thus,
εU k
εLk ¼ min
fk ðxÞ
s:t:
x˛X
and is the maximum value of fk(x) among the solutions when minimizing the other objectives. Solution filtering ensures that the ε-constraint method returns Pareto points, as the solved single-objective problems themselves do not ensure feasibility or that they dominate the solutions with other {εk} values. The advantages of the ε-constraint method are that it (1) obtains a representation of the Pareto Frontier that can be quickly improved with a finer grid of {εk} values, (2) does not suffer from scaling problems of scalarization (e.g., numerical precision and comparable order of magnitude), and (3) can identify islanded (unsupported) Pareto points that are common to integer and mixed integer problems (Mavrotas, 2009). Interactive methods require that the decision maker is continuously interacting with the method while searching for the most preferred Pareto point (Geoffrion et al., 1972; Miettinen et al., 2008). Instead of the method converging mathematically, these methods end when the decision maker has psychologically converged on a desirable solution. At each iteration of the method, the decision maker can
20.3 Supply Chain Scope
modify their preferences in a number of ways. Some methods allow for tradeoff information, where the decision maker ranks objective trade-offs for a number of possible search directions. Other methods allow for modifying the target objectives f ideal within a no-preference method search for Pareto points. Classification of objective functions is another approach in which the objectives are ranked at the current Pareto point and then the method seeks to find a better Pareto point. Although intuitive and transparent for the decision maker, iterative methods suffer from the drawbacks of requiring constant decision-maker attention and limiting the decision maker to seeing only a subset of the whole range of possibilities available along the Pareto Frontier.
20.3 SUPPLY CHAIN SCOPE This chapter builds off of our previous work (Marvin et al., 2013) by adding a second objective of minimizing TGHG and focusing on identifying the Pareto Frontier. Interested readers can find a more complete description of the mathematical formulation and parameter values for the supply chain optimization problem, specifically for the economic objective of maximizing TNPV, in our previous work (Marvin et al., 2013). Those details are not all repeated here, for simplicity. This article considers the biofuel supply chain as a network of biomass producers, conversion facilities, and markets that performs the functions of biomass production, harvesting, storage, processing and transportation, and biofuel distribution to markets. The optimization problem is to determine how to best utilize the biomass resources in the 12-state region of the Midwestern United States to satisfy the market demands for biofuels in 2015 (driven by government mandates). This model includes • • • •
• •
•
3109 biomass producers, each corresponding to a county in the contiguous US 159 existing biofuel facilities and 98 candidate sites for new biofuel facilities Three markets, corresponding to the three RFS2 biofuel classifications: renewable fuel (RF), advanced biofuel (AB), and cellulosic biofuel (CB) Eight biomass types with availability estimates in 2015 from the Billion Ton Study 2011 update (U.S. Department of Energy, 2011): corn, corn stover, five types of forest biomass and wood wastes, and perennial grasses Four biofuel types: RF ethanol, AB ethanol, CB ethanol, and CB naphtha and diesel Seven biomass processing technologies: • Dry-grind starch fermentation of corn • Integrated corn and stover process • Dilute acid pretreatment and C5 þ C6 cofermentation of corn stover • Indirect gasification and syngas upgrading to mixed alcohols of wood • Direct gasification and syngas upgrading to mixed alcohols of wood • Fast pyrolysis and bio-oil upgrading of corn stover • AFEX pretreatment and C5 þ C6 cofermentation of perennial grasses Two transportation methods: road and rail
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Note that the seven biomass processing technologies included here can produce four unique biofuel types from the eight biomass types. These technologies were chosen because each is expected to be commercialized in the near-term and the set is intended to be representative of the diversity seen in biomass processing. Furthermore, detailed technoeconomic models are available for each technology from National Laboratory reports and related publications (Wallace et al., 2005; Humbird et al., 2011; Dutta et al., 2011; Dutta and Phillips, 2009; Wright et al., 2010; Tao et al., 2011). The mathematical formulation from our previous study (Marvin et al., 2013) was expanded to incorporate an environmental objective function. Thus, the multiobjective optimization problem examined in this chapter has the objectives to (1) maximize TNPV and (2) minimize TGHG. TGHG for the entire supply chain is the sum of the greenhouse gas emissions corresponding to each of the facility sites: TGHG ¼
X
GHGr
r
Each facility site r in the study has emissions associated with •
• •
• •
Biomass production, EFBiomass r • Fertilizer production • Fertilizer N2O • Farming • Land use change Biomass transportation, EFTransportBiomass r Biorefinery, EFBiorefinery r • Operations • Coproduct credit Biofuel transportation, EFTransportProducts r Market, EFMarket r • Biofuel combustion • Fuel credit The greenhouse gas emission for each facility is then
GHGr ¼ EFBiomass þ EFTransportBiomass þ EFBiorefinery þ EFTransportProducts þ EFMarket ; r r r r r
cr
Emissions from each of these sources are assumed proportional to the corresponding supply chain activity, as described in the following equations: EFBiomass ¼ r
X
NR EbN $fn;r;v;b ;
cr
n;v;b
where EbN is the amount of emissions associated with producing a unit of biomass type b (e.g., t CO2,eq/dt): EFTransportBiomass ¼ r
X n;v;b
NR NR Eb;v $DNR n;r $fn;r;v;b ;
cr
20.4 Solution Strategy
where DNR n;r is the round-trip distance between biomass producer n and facility site r, NR is the amount of emissions associated with transporting a unit of biomass and Eb;v type b via method v per unit distance (e.g., t CO2,eq/mi/dt): EFBiorefinery ¼ r
X
RB R Eb;l $ur;b;l ;
cr
b;l
RB is the amount of emissions associated with converting a unit of biomass where Eb;l type b using biorefinery technology l (e.g., t CO2,eq/mi/dt):
X
EFTransportProducts ¼ r
RM RM Ep;v $DRM r;m $fr;m;v;p ;
cr
m;v;p
RM where DRM r;m is the round-trip distance between facility site r and market m, and Ep;v is the amount of emissions associated with transporting a unit of product p via method v per unit distance (e.g., t CO2,eq/mi/gal):
EFMarket ¼ r
X
RM EpM $fr;m;v;p ;
cr
m;v;p
where EpM is the amount of emissions associated with the market/customer use of a unit of product p (e.g., t CO2,eq/gal). The multiobjective mixed integer linear program is then max s:t:
ðTNPV; TGHGÞ TGHG equations TNPV equations mass balance equations
where the TGHG equations include all others listed in this section. The TNPV equations and mass balance equations, along with their associated parameter values, are described in detail in our previous study (Marvin et al., 2013). It is important to note a few things about the equations adopted from our previous study: (1) it includes a detailed cash flow analysis for the lifetime of the facilities complete with capital depreciation and taxation, (2) installed capacity for each facility is allowed to vary, and (3) piecewise linear functions for capital investment of each biomass processing technology are used to approximate the effect of economies of scale.
20.4 SOLUTION STRATEGY The ε-constraint method is used to solve the multiobjective mixed integer linear program, by first transforming it into the single-objective mixed integer linear program (SoMP): max s:t:
ε1 $ðTNPV ð1 ε1 Þ$TGHGÞ TGHG equations TNPV equations mass balance equations TGHG ε2
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and then identifying Pareto points iteratively, following the strategy: Step 1: Maximize TNPV without considering TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 ¼ inf. Store the solution value of TGHG as the highest TGHG along the Pareto Frontier TGHGmax. Step 2: Minimize TGHG without considering TNPV by solving problem (SoMP) with ε1 ¼ 0 and ε2 ¼ inf. Store the solution value for all decision variables as the initial guess for the next problem. Store the solution value of TGHG as the lowest TGHG along the Pareto Frontier TGHGmin. Step 3: Maximize TNPV while constraining TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 ¼ TGHGmin. Store the solution value of all decision variables as the initial guess for the next problem. Step K (K ‡ 4): Maximize TNPV while constraining TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 set to a value within the range (TGHGmin, TGHGmax). Store the solution value for all decision variables as the initial guess for the next problem. Note that this initial guess is only a feasible solution for the next problem if the next problem has a higher value for ε2; therefore, there is an advantage to monotonically increasing ε2 in the search for Pareto points. End when the desired number of Pareto points (e.g., resolution of the Pareto Frontier) has been obtained. Solution filtering is then required to confirm that each step returned a feasible solution that is not dominated by any other solution and is thus Pareto optimal.
20.5 LIFE CYCLE ANALYSIS Biofuels are promoted as alternatives to petroleum-based transportation fuels, in part, for their reduced greenhouse gas emissions, determined by thorough life cycle analysis. This attribute of biofuels has been recognized in policies aimed at reducing the transportation sector’s GHG emissions (e.g., the Low-Carbon Fuel Standard in California (CARB (California Air Resources Board), 2010), the US Renewable Fuel Standard program (U.S. Environmental Protection Agency, 2010), and the Renewables Directive in the European Union (European Parliament, 2009)). However, there is still active debate and research over the emissions of biofuels. The emissions of the widespread corn ethanol dry-grind process are even disputed, with some authors concluding that it offers lower emissions when compared with gasoline (Hsu et al., 2010; Wang et al., 2011), some authors concluding the opposite (Searchinger et al., 2008), and others concluding that emissions are nearly equal (Farrell et al., 2006). Most studies agree that cellulosic biofuels offer lower emissions when compared with gasoline (Wang et al., 2012; Tilman et al., 2009; Wu et al., 2006; Han et al., 2011; Schmer et al., 2008). Such life cycle analysis studies differ in their system boundary assumptions for biofuels or petroleum fuels (e.g., including land use change, coproduct credits,
20.5 Life Cycle Analysis
petroleum supply defense via military actions) and in their parameter values (e.g., biorefinery technology updates, better estimates). This chapter utilizes results for the life cycle analysis of select biofuels performed using the GREET (Greenhouse gases, Regulated Emissions, and Energy Use in Transportation) model. The GREET model was developed at Argonne National Laboratory and is a trusted tool for researchers and politicians to examine greenhouse gas emissions from vehicles and transportation fuels on a consistent basis (Argonne National LaboratoryeTransportation Technology R&D Center, 2010). Parameters and assumptions are continuously updated as the biofuel technologies develop, small-scale experiments are performed, and large-scale field trials are completed. Furthermore, numerous national laboratory reports and papers have been published on biofuel life cycle analysis using GREET, with some based on technoeconomic models corresponding to the seven biorefinery technologies considered in this chapter. The system boundary considered for the biofuel life cycle analysis is shown in Figure 20.2. Greenhouse gases considered here are measured in CO2-equivalent tonnes (t CO2,eq). This measure is an aggregation of emissions of CO2, CH4, and N2O, weighted by their 100-year global warming potentials of 1, 25, and 298, respectively. In other words, 1 unit of CH4 is predicted to have the same global warming potential as 25 units of CO2 over a 100-year time horizon. These global warming potentials are as specified by the International Panel on Climate Change’s 2007 assessment (International Panel on Climate Change (IPCC), 2007).
FIGURE 20.2 System boundary of the biofuel life cycle analysis (inspired by Figure 20.2 in (Wang et al., 2012)).
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The specific emission parameter values used in this chapter are shown in Tables 20.1e20.5. They are mainly determined from the GREET model and associated literature (Wang et al., 2012; Han et al., 2011; Wu et al., 2006), using process data from the technoeconomic models corresponding to each of the seven considered biorefinery technologies. Many of those values are obtained from a report, Table 20.1 Emission Parameter Values for Biomass Production Biomass Type b
EbN
Corn Corn-stvr All wood Perngrass
0.00916 t CO2,eq/Bu 0.0636 t CO2,eq/dt 0.111 t CO2,eq/dt 0.111 t CO2,eq/dt
Table 20.2 Emission Parameter Values for Biomass Transportation Biomass Type b
Method v
NR Eb;v
Corn all biomass
Rail Truck
8.58E-7 t CO2,eq/mi/bu 1.98E-4 t CO2,eq/mi/dt
Table 20.3 Emission Parameter Values for Biorefinery Operation Biomass Type b
Technology l
RB Eb;l
Corn Corn Corn-stvr Corn-stvr All wood All wood Corn-stvr Perngrass
1 2 2 3 4 5 6 7
0.00389 t CO2,eq/Bu 0.00389 t CO2,eq/Bu 0.0557 t CO2,eq/dt 0.0557 t CO2,eq/dt 0.145 t CO2,eq/dt 0.145 t CO2,eq/dt 0.145 t CO2,eq/dt 0.0477 t CO2,eq/dt
Table 20.4 Emission Parameter Values for Biofuel Transportation Product p
Method v
RM Ep;v
RF ethanol AB ethanol CB ethanol CB naphtha & diesel
Truck Truck Truck Truck
5.91E-7 5.91E-7 5.91E-7 5.54E-7
t CO2,eq/mi/gal t CO2,eq/mi/gal t CO2,eq/mi/gal t CO2,eq/mi/gal
20.6 Results
Table 20.5 Emission Parameter Values for Market/Customer Product Use (e.g., Biofuel Combustion) Product p
EpM
RF ethanol AB ethanol CB ethanol CB naphtha & diesel
0.00746 t CO2,eq/gal 0.00746 t CO2,eq/gal 0.00746 t CO2,eq/gal 0.0112 t CO2,eq/gal
which summarizes the recent GREET model updates and performs life cycle analysis on a number of biorefinery technologies along with gasoline (Wang et al., 2012). This is the 2012 update of their earlier study from 2006 (Wu et al., 2006). Transportation emission values for biomass and biofuels are taken from Zamboni et al. (2009). A comparison of two competing products (e.g., a biofuel and gasoline) requires a choice of functional unit. Functional unit options for fuels include volume or mass basis, energy equivalence, and end-use equivalence. Conclusions depend on the choice of functional unit. For example, comparing ethanol and gasoline using a volume functional unit (i.e., per gallon) leads to the conclusion that ethanol is cheaper, which may not be the case for the consumer considering its lower energy density compared to gasoline. In this article, we will consider the functional unit of gasoline equivalent gallon (i.e., volumes with equal energy content). Thus, the effect of lower energy density in some biofuels is removed. Additionally, the market/customer product use in Table 20.5 accounts for the biofuel offsetting an equal energy volume of gasoline. A value of 94 g CO2,eq/MJ, found by Wang et al. (2012), was assumed for gasoline. It should also be noted that end-use equivalence functional units may be appropriate in some cases. Most notably, miles per gallon of gasoline equivalent gallon is useful for vehicles designed to take advantage of the properties of ethanol (e.g., higher compression ratio and different fuel-air mixture) to extract additional engine performance. However, as the gasoline equivalent gallon functional unit does not depend on particular vehicle design or performance, it is more suitable for the present supply chain optimization.
20.6 RESULTS The mixed integer linear program (SoMP) from Section 20.4 was coded in IBM ILOG CPLEX Optimization Studio v12.2 (IBM, 2011) and has 156,947 continuous variables, 5488 binary variables, and 40,982 constraints. The Pareto Frontier of supply chains is presented along with some notable Pareto points, with an evaluation of the tradeoff between economic and environmental performance.
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20.6.1 PARETO FRONTIERS The two scenarios of no biofuel mandates and strict mandates were considered, and their corresponding Pareto Frontiers are shown in Figure 20.3. Note that strict mandates are enforced in the mathematical formulation by including a constraint such that the biofuel sales meet or exceed the RFS2 mandates in 2015 for each RFS2 biofuel classification type. The Pareto points are identified using the ε-constraint approach described in Section 20.4. Each of the single-objective problems are solved with a target optimality gap of 0.5% and a time limit of 10 h. Most of the Pareto points are identified to an optimality gap less than 2.0% in 10 h. The addition of the biofuel mandate constraints reduces the size of the feasible region, and thus the Pareto Frontier for the no biomass mandates scenario dominates the Pareto Frontier of the strict mandates scenario (i.e., has higher TNPV for the same TGHG values). This is largely the result of the strict mandate scenario hitting the upper bound on production of biofuels, whereas the no mandates scenario can improve both economics and emission objectives by producing more biofuel than is truly demanded. For this reason, the remainder of this section will focus on results for the strict mandates scenario. The effect of constraining TGHG can be seen by plotting the total biofuel production for each Pareto point, as shown in Figure 20.4. Recall that the 2015 RFS2 mandates are for the production of 3 B gal/y cellulosic biofuel, 2.5 B gal/y of other advanced biofuel, and 15 B gal/y of implicit nonadvanced biofuel. CB produced by technologies l ¼ {3, 4, 5, 6, 7} may be sold in each of those three categories, whereas AB produced by technology l ¼ 2 may be sold in the latter two categories, and RF produced by technology l ¼ 1 may only be sold in the last category. Much of the
FIGURE 20.3 Pareto Frontiers for the scenarios of no biofuel mandates and strict mandates.
20.6 Results
FIGURE 20.4 Total biofuel production for each Pareto point.
biofuel demand is satisfied then by CB for low TGHG Pareto points. Limited cellulosic biomass availability prevents all of the demand to be satisfied this way, and thus AB and RF are also produced. As the ε-constraint is relaxed, an increasing amount of the biofuel demand is satisfied by RF. Also, recall that technology 2 competes for corn (also an RF feedstock) and corn stover (also a CB feedstock) as feedstocks; thus AB production from technology 2 remains relatively constant. CB naphtha and diesel-range is produced in small amounts from technology 6, as it competes for corn stover with technologies that typically have lower greenhouse gas emissions.
20.6.2 KEY PARETO POINTS This section will provide some analysis of the strict mandates scenario Pareto Frontier, by examining key Pareto points. The goal is to identify modest supply chain changes that may lead to large emission gains for a small loss of profit.
20.6.3.1 Highest TNPV It turns out that the same supply chain configuration identified in our previous study (Marvin et al., 2013) for the strict mandates scenario is a Pareto point for the multiobjective problem. For simplicity, those results are summarized here. In the solution, five different technologies are installed with a total of 168 facilities producing RF (15,000 M gal/y), 26 producing AB (2500 M gal/y), and 24 producing CB (3000 M gal/y). All produced biofuels are sold in their highest RFS fuel classification. By examining the breakeven prices for each facility, it was found that all facilities are economical for facility-gate prices of 2.39, 2.13, and 1.71 $/gal for CB, AB, and RF, respectively.
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20.6.3.2 Lowest TGHG The Pareto point with the lowest TGHG is found by first minimizing TGHG without considering TNPV, then maximizing TNPV while constraining TGHG to be less than or equal to the previous solution value. Recall that the previous solution is used as an initial guess to expedite the solution of the second problem. The supply chain configuration for this Pareto point is shown in Figure 20.5. Five of the seven technologies are installed by developing 90 of the 98 candidate sites, with a total of 60 facilities producing RF (4020 M gal/y), 33 producing AB (6211 M gal/y), and 57 producing CB (10,269 M gal/y). CB and AB are produced far in excess of the RFS mandates for their classifications, so they are also sold at lower fuel classifications. Limited supply of cellulosic material in 2015 prohibits CB from dominating the biofuel markets, although that would have resulted in a lower TGHG. Technology 4 (indirect gasification) is favored over technology 5 (direct gasification), which was installed in the highest TNPV Pareto point, for production of CB ethanol from all-wood, because it has higher product yield for nearly identical emissions. The average distribution of discounted costs for each installed technology is shown in Figure 20.6. By examining the breakeven prices for each facility, it was found that all facilities are economical for facility-gate prices of 4.18, 2.28, and 1.74 $/gal for CB, AB, and RF, respectively. Thus, CB costs are 75% higher for this Pareto point than the highest TNPV Pareto point, while the costs of AB and RF are equivalent. The average distribution of emissions is shown in Figure 20.7. Technologies 2, 3, and 7 have lower net emissions than technology 1 in the solution due to lower emission biomass feedstock(s) and emission-negative biorefinery operation (the result of emission credits for coproducts like electricity). Compressor operation in the high-pressure gasification of technology 4, along with no turbine installation for possible electricity generation, leads it to have emission-positive biorefinery operation. Technology 4 still has lower emissions than technology 1 due to wood being a lower emission biomass feedstock than corn.
20.6.3.3 Balanced The “balanced” Pareto point described here offers large emissions gains for a small loss on profit, compared to the highest TNPV case. This point was chosen by examining the Pareto Frontier (see Figure 20.3) as a decision maker would. The highest TNPV Pareto point offered TNPV of 19.4 B$ and TGHG of 71.4 M t CO2,eq/y, while the lowest TGHG Pareto point offered TNPV of 72.0 B$ and TGHG of 102 M t CO2,eq/y. Thus, there is an opportunity to reduce biofuel production emissions by nearly half, from the highest TNPV case. Presented here is the Pareto point that captures more than half of those emission reductions, with a TNPV of 11.3 B$ and a TGHG of 87.7 M t CO2,eq/y. This Pareto point was calculated in 7.6 h with a 0.50% gap and is shown in Figure 20.8. Three of the seven technologies are installed by developing 60 of the 98 candidate sites, with a total of 161 facilities producing RF (11,900 M gal/y), 43 producing AB (5600 M gal/y), and 15 producing CB (3000 M gal/y). Just enough CB is produced to satisfy the mandate, but excess
(a)
(b)
FIGURE 20.5 Optimum supply chain configuration for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Installed facility capacity shown in million gallons per year (mgy). RF, AB, and CB are produced. Subfigure (a): Corn grain utilization with corn-utilizing facilities shown. RF and AB ethanol are produced from corn using technology 1 and 2, respectively. Existing facilities are denoted with an asterisk (*). Maximum corn utilization is 34%. In this Pareto point, many existing facilities are idled (zero production) in favor of lower emission biofuel technologies. Subfigure (b): Corn stover utilization with associated facilities shown. AB and CB ethanol and CB naphtha and diesel are produced from corn stover. Subfigure (c): Aggregated forest biomass and wood waste utilization with associated facilities shown. CB ethanol is produced from all wood. Subfigure (d): Perennial grass utilization with associated facilities shown. CB ethanol is produced from perennial grasses.
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(c)
(d)
FIGURE 20.5dCont’d
AB is produced and sold as the lower classification (RF). This offsetting of some RF (produced from corn grain) with AB (produced from in an integrated process that utilizes corn and corn stover) is what gives this Pareto point improved emissions. The average distribution of discounted costs for each installed technology is shown in Figure 20.9. By examining the breakeven prices for each facility, it was
20.6 Results
FIGURE 20.6 Breakdown of cost sources for installed technologies for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {5, 6} were not constructed in the optimum supply chain.
FIGURE 20.7 Breakdown of emission sources for installed technologies for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Net emissions per gallon of produced biofuel are also shown. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {5, 6} were not constructed in the optimum supply chain.
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(a)
(b)
FIGURE 20.8 Optimum supply chain configuration for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Installed facility capacity shown in million gallons per year (mgy). RF, AB, and CB are produced. Forestry resources and perennial grasses were available but were not utilized in the optimum supply chain. Subfigure (a): Corn grain utilization with corn-utilizing facilities shown. RF and AB ethanol are produced from corn using technology 1 and 2, respectively. Existing facilities are denoted with an asterisk (*). Maximum corn utilization is 34%. Subfigure (b): Corn stover utilization with associated facilities shown. AB and CB ethanol and CB naphtha and diesel are produced from corn stover.
20.7 Conclusions
FIGURE 20.9 Breakdown of cost sources for installed technologies for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {4, 5, 6, 7} were not constructed in the optimum supply chain.
found that all facilities are economical for facility-gate prices of 2.47, 2.23, and 1.71 $/gal for CB, AB, and RF, respectively. Thus, the biofuel prices are at most only 0.10 $/gal higher than in the Pareto point with highest TNPV. The average distribution of emissions is shown in Figure 20.10. As expected, the emissions distribution for technologies 1, 2, and 3 are similar to what was found in the other Pareto points; however, there are small differences in the transportation emissions.
20.7 CONCLUSIONS This chapter proposed a multiobjective mixed integer linear program to determine biofuel supply chain configurations that are Pareto optimal for profit and emissions. It was applied to the Midwestern US 2015 case study introduced in Marvin et al. (2013) to determine facility location, capacity, and technology selection. Pareto Frontiers were found for the two case studies of strict RFS mandates and no mandates. In the strict mandates case study, it was found that the lowest TGHG Pareto point offers an additional 50% reduction in emissions compared to the highest TNPV Pareto point. Unfortunately, the lowest TGHG Pareto point corresponds with a large negative TNPV. One of the Pareto points showed that half of these
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FIGURE 20.10 Breakdown of emission sources for installed technologies for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Net emissions per gallon of produced biofuel are also shown. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {4, 5, 6, 7} were not constructed in the optimum supply chain.
emission reductions are obtainable by shifting some renewable fuel production to advanced biofuel technologies, with biofuel prices only 0.10 $/gal higher than in the Pareto point with highest TNPV.
ACKNOWLEDGMENTS Partial financial support from the National Science Foundation, CBET award number 1307089, is gratefully acknowledged.
REFERENCES An, H., Wilhelm, W.E., Searcy, S.W., 2011. Biofuel and petroleum-based fuel supply chain research: a literature review. Biomass Bioenergy 35 (9), 3763e3774. Argonne National LaboratoryeTransportation Technology R&D Center, 2010. GREET Model: The Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation Model. CARB (California Air Resources Board), 2010. Low Carbon Fuel Standard (LCFS) Regulation. California Environmental Protection Agency, Air Resources Board, Sacramento, CA.
References
Collette, Y., Siarry, P., 2003. Multiobjective Optimization: Principles and Case Studies. Springer. Daoutidis, P., et al., 2013. Engineering biomass conversion processes: a systems perspective. AIChE J. 59 (1), 3e18. Das, I., Dennis, J.E., 1998. Normal-boundary intersection: a new method for generating the pareto Surface in Nonlinear Multicriteria optimization problems. SIAM J. Optim. 8 (3), 631e657. Dutta, A., et al., 2011. Process Design and Economics for Conversion of Lignocellulosic Biomass to Ethanol: Thermochemical Pathway by Indirect Gasification and Mixed Alcohol Synthesis. National Renewable Energy Laboratory. NREL/TPe5100e51400. Dutta, A., Phillips, S.D., 2009. Thermochemical Ethanol via Direct Gasification and Mixed Alcohol Synthesis of Lignocellulosic Biomass. National Renewable Energy Laboratory. NREL/TPe510e45913. European Parliament, 2009. Directive 2009/28/EC: On the Promotion of the Use of Energy from Renewable Sources and Amending and Subsequently Repealing Directives 2001/ 77/EC and 2003/30/EC. Farrell, A.E., et al., 2006. Ethanol can contribute to energy and environmental goals. Science 311 (5760), 506e508. Floudas, C.A., Elia, J.A., Baliban, R.C., 2012. Hybrid and single feedstock energy processes for liquid transportation fuels: a critical review. Comput. Chem. Eng. 41, 24e51. Geoffrion, A.M., Dyer, J.S., Feinberg, A., 1972. An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Manage. Sci. 19 (4), 357e368. Gonzalez, T.F., 2007. Handbook of Approximation Algorithms and Metaheuristics. Chapman & Hall/CRC, Boca Raton. Grossmann, I.E., Guille´n-Gosa´lbez, G., 2010. Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes. Comput. Chem. Eng. 34 (9), 1365e1376. Han, J., et al., 2011. Well-to-Wheels Analysis of Fast Pyrolysis Pathways with GREET. Argonne National Laboratory. ANL/ESD/11e8. Hill, J., et al., 2006. Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels. Proc. Natl. Acad. Sci. U.S.A. 103 (30), 11206e11210. Hsu, D.D., et al., 2010. Life cycle environmental impacts of selected US ethanol production and use pathways in 2022. Environ. Sci. Technol. 44 (13), 5289e5297. Humbird, D., et al., 2011. Process Design and Economics for Biochemical Conversion of Lignocellulosic Biomass to Ethanol: Dilute-acid Pretreatment and Enzymatic Hydrolysis of Corn Stover. National Renewable Energy Laboratory. NREL/TPe5100e47764. IBM, 2011. IBM ILOG CPLEX Optimization Studio 12.2. International Panel on Climate Change (IPCC), 2007. Climate Change 2007: Synthesis Report. Switzerland, Geneva. Marvin, W.A., Schmidt, L.D., Daoutidis, P., 2013. Biorefinery location and technology selection through supply chain optimization. Ind. Eng. Chem. Res. 52 (9), 3192e3208. Mavrotas, G., 2009. Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems. Appl. Math. Comput. 213 (2), 455e465. McPhail, L., Westcott, P., Lutman, H., 2011. The Renewable Identification Number System and U.S. Biofuel Mandates. United States Department of Agriculture. Miettinen, K., 1999. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston.
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Miettinen, K., Ruiz, F., Wierzbicki, A.P., 2008. Introduction to multiobjective optimization: interactive approaches. In: Multiobjective Optimization. Springer, pp. 27e57. Mueller-Gritschneder, D., Graeb, H., Schlichtmann, U., 2009. A successive approach to Compute the Bounded pareto Front of Practical multiobjective optimization problems. SIAM J. Optim. 20 (2), 915e934. Schmer, M.R., et al., 2008. Net energy of cellulosic ethanol from switchgrass. Proc. Natl. Acad. Sci. U.S.A. 105 (2), 464e469. Searchinger, T., et al., 2008. Use of US croplands for biofuels increases greenhouse gases through emissions from land-use change. Science 319 (5867), 1238e1240. Tao, L., et al., 2011. Process and technoeconomic analysis of leading pretreatment technologies for lignocellulosic ethanol production using switchgrass. Bioresource Technol. 102 (24), 11105e11114. Tilman, D., et al., 2009. Beneficial biofuelsethe food, energy, and environment trilemma. Science 325 (5938), 270e271. U.S. Department of Energy, 2011. U.S. Billion-ton Update: Biomass Supply for a Bioenergy and Bioproducts Industry, R.D. Perlack and B.J. Stokes (Leads), ORNL/TMe2011/224. Oak Ridge National Laboratory, Oak Ridge, TN. U.S. Environmental Protection Agency, 2010. EPA Finalizes Regulations for the National Renewable Fuel Standard Program for 2010 and beyond, EPAe420efe10e007. United States Environmental Protection Agency. U.S. Environmental Protection Agency, 2014. Regulation of fuels and fuel additives: 2013 cellulosic biofuel standard. U.S. Environ. Prot. Agency 79 (85), 25025e25031. Wallace, R., et al., 2005. Feasibility Study for Co-locating and Integrating Ethanol Production Plants from Corn Starch and Lignocellulosic Feedstocks. National Renewable Energy Laboratory. NREL/TPe510e37092. Wang, M., Han, J., Dunn, J.B., Cai, H., Elgowainy, A., 2012. Well-to-wheels energy use and greenhouse gas emissions of ethanol from corn, sugarcane and cellulosic biomass for US use. Environ. Res. Lett. 7 (4), 045905. Wang, M.Q., et al., 2011. Energy and greenhouse gas emission effects of corn and cellulosic ethanol with technology improvements and land use changes. Biomass Bioenergy 35 (5), 1885e1896. Wright, M.M., et al., 2010. Techno-economic Analysis of Biomass Fast Pyrolysis to Transportation Fuels. National Renewable Energy Laboratory. NREL/TPe6A20e46586. Wu, M., Wang, M., Huo, H., 2006. Fuel-cycle Assessment of Selected Bioethanol Production Pathways in the United States. Argonne National Laboratory. ANL/ESD/06e7. Yue, D., You, F., Snyder, S.W., 2014. Biomass-to-bioenergy and biofuel supply chain optimization: overview, key issues and challenges. Comput. Chem. Eng. 66, 36e56. Zamboni, A., Bezzo, F., Shah, N., 2009. Spatially explicit static model for the strategic design of future bioethanol production systems. 2. Multi-objective environmental optimization. Energy Fuels 23 (10), 5134e5143.
Optimal Supply Chains for Biofuel Production
20
W. Alex Marvin, Prodromos Daoutidis1 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA 1 Corresponding author: E-mail: [email protected]
20.1 INTRODUCTION The current U.S. biofuel industry is dominated by ethanol (mainly produced from corn grain starch) and biodiesel (mainly produced from soybean oil and recycled cooking oils), but cellulosic biofuels (based on nonfood resources such as agricultural waste, grasses, and woody crops) are predicted to play a large role in the future. Annual ethanol production has quickly expanded from 83 million gallons in 1981 to nearly 15 billion gallons today, and biodiesel production has similarly grown to 700 million gallons. Biofuels became controversial during this rapid growth for influencing the price of food by acting as a competing outlet for agricultural commodities. About a third of US corn production is used to produce ethanol, resulting in ethanol comprising 9.5% of finished gasoline blends in the US (McPhail et al., 2011). Alternatively, cellulosic biofuels are produced from low resource-intensive biomass, and can provide much greater supplies and environmental benefits than food-based biofuels (Hill et al., 2006). The US EPA determined that 0.81 million gallons of cellulosic biofuel were produced in 2013 (U.S. Environmental Protection Agency, 2014), while government mandates require the use of 16 billion gallons of cellulosic biofuel in motor-vehicle fuel by 2022. Development of the cellulosic biofuel industry to meet these mandates will impose significant logistical challenges at each stage of the biofuel supply chain (biomass production, harvesting, storage, processing and transportation, and biofuel distribution). This industry will require about a billion tons of biomass annually from a variety of sources that each may be seasonally available, with uncertainty in composition, quantity, and price. Furthermore, there are many proposed technologies (e.g., crop residue fermentation and biomass gasification with syngas upgrading) competing for biomass processing, and their adoption will determine the economic and environmental impacts of the industry as a whole. Biofuel supply chain optimization has emerged as a popular method for understanding the expected expansion of the biofuel industry. These studies seek to determine the optimum supply chain configuration, including all activities from the Computer Aided Chemical Engineering, Volume 36. ISSN 1570-7946. http://dx.doi.org/10.1016/B978-0-444-63472-6.00020-3 © 2015 Elsevier B.V. All rights reserved.
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biomass production to the biofuel end-use, which maximizes a desired performance index (e.g., profitability, greenhouse gas emissions, water use or net energy use). Often a real-world study region is chosen with high-resolution spatial information about the type, quantity, and location of biomass availability or production capability, harvest and logistics, and biorefinery plant capabilities to convert biomass to biofuels. A number of thorough reviews have been done of the research in this area, including its overlap with petroleum and chemical operations research (An et al., 2011), with hybrid energy system process and supply chain optimization (Floudas et al., 2012), and with the broader set of multiscale challenges surrounding biomass-to-bioenergy supply chains (Yue et al., 2014; Daoutidis et al., 2013). In our previous study (Marvin et al., 2013), we proposed a biofuel supply chain optimization problem for determining economical biomass processing facility locations and capacities and applied it to a 9-state region in the Midwestern United States to assess the feasibility of meeting governmental biofuel mandates in 2015. This was formulated as a mixed integer linear program with an objective of maximizing total net present value (TNPV). A detailed cash flow analysis that includes capital depreciation and taxation was embedded into the model formulation to give insights into the minimum biofuel selling price for each facility and for each Renewable Fuel Standard biofuel classification (renewable fuel, advanced biofuel, and cellulosic biofuel). This chapter builds off of that work by adding a second objective of minimizing total greenhouse gas emissions (TGHG) relative to gasoline (i.e., produced biofuel is assumed to offset an energy-equivalent amount of gasoline). Thus the scope of the life cycle analysis is from cradle to grave (or in the case of biofuels, from field to wheels). Recent life cycle analysis literature on biofuels is leveraged to quantify the impact of each activity in the biofuel supply chain. The resulting multiobjective mixed integer linear program is solved using an ε-constraint approach that yields the Pareto Frontier of efficient supply chain designs. This allows for the identification of supply chain decisions that greatly reduce greenhouse gas emissions for minimal economic losses. The remainder of this article is organized as follows. Multiobjective optimization techniques are reviewed in Section 20.2. The supply chain optimization scope and formulation is described in Section 20.3, and its solution strategy is described in Section 20.4. Life cycle analysis for each activity in the biofuel supply chain is described in Section 20.5. The Pareto Frontier for the multiobjective supply chain optimization is identified and discussed in Section 20.6, along with two Pareto points that have particularly interesting supply chain configurations. Concluding remarks are in Section 20.7.
20.2 MULTIOBJECTIVE OPTIMIZATION Multiobjective optimization seeks to identify one or a set of Pareto optimal solutions (Pareto points) (Gonzalez, 2007). Pareto points are solutions that are noninferior to all other feasible solutions. This is shown in Figure 20.1 for the two objectives of maximizing TNPV and minimizing TGHG for the entire supply chain. Point (b) is
20.2 Multiobjective Optimization
(a) (b)
(c)
FIGURE 20.1 Example Pareto Frontier for maximization of TNPV and minimization of TGHG. The feasible region for the optimization problem is shown with its efficient boundary being the Pareto Frontier. Point (a) is infeasible, point (b) is a Pareto point, and point (c) is feasible but is dominated by point (b).
a Pareto point, because there is no feasible solution that simultaneously improves both objectives. There are usually many Pareto points, and the whole set of them is referred to as the Pareto Frontier or surface. It is desirable to lower TGHG and raise TNPV, so the upper left boundary in Figure 20.1 is the Pareto Frontier. Each solution along the Pareto Frontier is mathematically equal (i.e., a solution that is better for one objective cannot be found without necessarily worsening at least one other objectives) and thus it depends on the preference of a decision maker to select a “right” solution. The general form of a multiobjective optimization problem involving K objectives to be minimized is min ðf1 ðxÞ;:::; fK ðxÞÞ s:t:
x˛X
where x is the vector of decision variables with feasible set X defined by constraints. Multiobjective optimization techniques vary in how a decision maker may express their preference, and the techniques fall into three major groups (Grossmann and Guille´n-Gosa´lbez, 2010; Collette and Siarry, 2003; Miettinen, 1999): • • •
A priori methods A posteriori methods Interactive methods
A priori methods require preference information to be specified before finding a solution. The solution returned is a Pareto point that best satisfies the decision maker’s preference. Examples include scalarization (agglomeration), no-preference methods and utility function methods. Applying a so-called carbon tax to
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greenhouse gas emissions is a common example of linear scalarization to convert a multiobjective problem involving emissions and economics into a single-objective problem. In general, the weights assigned to the objectives convert them into uniform units (e.g., dollars) and represent the relative importance for each objective. Minimizing the Euclidean norm (L2) to an ideal state (i.e., desired value for the objectives that is unobtainable) is an example of a no-preference method. A posteriori methods generate a representative set of Pareto points that the decision makers can then evaluate based on their preferences. These methods require additional computational effort, as determining each Pareto point may require as much time as an a priori method. For example, many well-known a posteriori methods (e.g., Normal-boundary Intersection (Das and Dennis, 1998) and Successive Pareto Optimization (Mueller-Gritschneder et al., 2009)) construct and solve several scalarization problems. Metaheuristics, such as simulated annealing, particle swarm optimization, and evolutionary algorithms, generate a representative set of solutions by searching the feasible region quickly, allowing for an approximation of the Pareto Frontier, but Pareto optimality of the solutions is not guaranteed. The ε-constraint method is the most widely applied a posteriori method in multiobjective optimization. In this method, single-objective problems are solved where one of the original objectives is minimized while the other objectives are constrained: min s:t:
f1 ðxÞ x˛X fK ðxÞ εk ;
cks1
εLk
where the parameters εk are varied between and εU k . These bounds are determined by solving the K single-objective problems for each objective function separately. Thus,
εU k
εLk ¼ min
fk ðxÞ
s:t:
x˛X
and is the maximum value of fk(x) among the solutions when minimizing the other objectives. Solution filtering ensures that the ε-constraint method returns Pareto points, as the solved single-objective problems themselves do not ensure feasibility or that they dominate the solutions with other {εk} values. The advantages of the ε-constraint method are that it (1) obtains a representation of the Pareto Frontier that can be quickly improved with a finer grid of {εk} values, (2) does not suffer from scaling problems of scalarization (e.g., numerical precision and comparable order of magnitude), and (3) can identify islanded (unsupported) Pareto points that are common to integer and mixed integer problems (Mavrotas, 2009). Interactive methods require that the decision maker is continuously interacting with the method while searching for the most preferred Pareto point (Geoffrion et al., 1972; Miettinen et al., 2008). Instead of the method converging mathematically, these methods end when the decision maker has psychologically converged on a desirable solution. At each iteration of the method, the decision maker can
20.3 Supply Chain Scope
modify their preferences in a number of ways. Some methods allow for tradeoff information, where the decision maker ranks objective trade-offs for a number of possible search directions. Other methods allow for modifying the target objectives f ideal within a no-preference method search for Pareto points. Classification of objective functions is another approach in which the objectives are ranked at the current Pareto point and then the method seeks to find a better Pareto point. Although intuitive and transparent for the decision maker, iterative methods suffer from the drawbacks of requiring constant decision-maker attention and limiting the decision maker to seeing only a subset of the whole range of possibilities available along the Pareto Frontier.
20.3 SUPPLY CHAIN SCOPE This chapter builds off of our previous work (Marvin et al., 2013) by adding a second objective of minimizing TGHG and focusing on identifying the Pareto Frontier. Interested readers can find a more complete description of the mathematical formulation and parameter values for the supply chain optimization problem, specifically for the economic objective of maximizing TNPV, in our previous work (Marvin et al., 2013). Those details are not all repeated here, for simplicity. This article considers the biofuel supply chain as a network of biomass producers, conversion facilities, and markets that performs the functions of biomass production, harvesting, storage, processing and transportation, and biofuel distribution to markets. The optimization problem is to determine how to best utilize the biomass resources in the 12-state region of the Midwestern United States to satisfy the market demands for biofuels in 2015 (driven by government mandates). This model includes • • • •
• •
•
3109 biomass producers, each corresponding to a county in the contiguous US 159 existing biofuel facilities and 98 candidate sites for new biofuel facilities Three markets, corresponding to the three RFS2 biofuel classifications: renewable fuel (RF), advanced biofuel (AB), and cellulosic biofuel (CB) Eight biomass types with availability estimates in 2015 from the Billion Ton Study 2011 update (U.S. Department of Energy, 2011): corn, corn stover, five types of forest biomass and wood wastes, and perennial grasses Four biofuel types: RF ethanol, AB ethanol, CB ethanol, and CB naphtha and diesel Seven biomass processing technologies: • Dry-grind starch fermentation of corn • Integrated corn and stover process • Dilute acid pretreatment and C5 þ C6 cofermentation of corn stover • Indirect gasification and syngas upgrading to mixed alcohols of wood • Direct gasification and syngas upgrading to mixed alcohols of wood • Fast pyrolysis and bio-oil upgrading of corn stover • AFEX pretreatment and C5 þ C6 cofermentation of perennial grasses Two transportation methods: road and rail
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Note that the seven biomass processing technologies included here can produce four unique biofuel types from the eight biomass types. These technologies were chosen because each is expected to be commercialized in the near-term and the set is intended to be representative of the diversity seen in biomass processing. Furthermore, detailed technoeconomic models are available for each technology from National Laboratory reports and related publications (Wallace et al., 2005; Humbird et al., 2011; Dutta et al., 2011; Dutta and Phillips, 2009; Wright et al., 2010; Tao et al., 2011). The mathematical formulation from our previous study (Marvin et al., 2013) was expanded to incorporate an environmental objective function. Thus, the multiobjective optimization problem examined in this chapter has the objectives to (1) maximize TNPV and (2) minimize TGHG. TGHG for the entire supply chain is the sum of the greenhouse gas emissions corresponding to each of the facility sites: TGHG ¼
X
GHGr
r
Each facility site r in the study has emissions associated with •
• •
• •
Biomass production, EFBiomass r • Fertilizer production • Fertilizer N2O • Farming • Land use change Biomass transportation, EFTransportBiomass r Biorefinery, EFBiorefinery r • Operations • Coproduct credit Biofuel transportation, EFTransportProducts r Market, EFMarket r • Biofuel combustion • Fuel credit The greenhouse gas emission for each facility is then
GHGr ¼ EFBiomass þ EFTransportBiomass þ EFBiorefinery þ EFTransportProducts þ EFMarket ; r r r r r
cr
Emissions from each of these sources are assumed proportional to the corresponding supply chain activity, as described in the following equations: EFBiomass ¼ r
X
NR EbN $fn;r;v;b ;
cr
n;v;b
where EbN is the amount of emissions associated with producing a unit of biomass type b (e.g., t CO2,eq/dt): EFTransportBiomass ¼ r
X n;v;b
NR NR Eb;v $DNR n;r $fn;r;v;b ;
cr
20.4 Solution Strategy
where DNR n;r is the round-trip distance between biomass producer n and facility site r, NR is the amount of emissions associated with transporting a unit of biomass and Eb;v type b via method v per unit distance (e.g., t CO2,eq/mi/dt): EFBiorefinery ¼ r
X
RB R Eb;l $ur;b;l ;
cr
b;l
RB is the amount of emissions associated with converting a unit of biomass where Eb;l type b using biorefinery technology l (e.g., t CO2,eq/mi/dt):
X
EFTransportProducts ¼ r
RM RM Ep;v $DRM r;m $fr;m;v;p ;
cr
m;v;p
RM where DRM r;m is the round-trip distance between facility site r and market m, and Ep;v is the amount of emissions associated with transporting a unit of product p via method v per unit distance (e.g., t CO2,eq/mi/gal):
EFMarket ¼ r
X
RM EpM $fr;m;v;p ;
cr
m;v;p
where EpM is the amount of emissions associated with the market/customer use of a unit of product p (e.g., t CO2,eq/gal). The multiobjective mixed integer linear program is then max s:t:
ðTNPV; TGHGÞ TGHG equations TNPV equations mass balance equations
where the TGHG equations include all others listed in this section. The TNPV equations and mass balance equations, along with their associated parameter values, are described in detail in our previous study (Marvin et al., 2013). It is important to note a few things about the equations adopted from our previous study: (1) it includes a detailed cash flow analysis for the lifetime of the facilities complete with capital depreciation and taxation, (2) installed capacity for each facility is allowed to vary, and (3) piecewise linear functions for capital investment of each biomass processing technology are used to approximate the effect of economies of scale.
20.4 SOLUTION STRATEGY The ε-constraint method is used to solve the multiobjective mixed integer linear program, by first transforming it into the single-objective mixed integer linear program (SoMP): max s:t:
ε1 $ðTNPV ð1 ε1 Þ$TGHGÞ TGHG equations TNPV equations mass balance equations TGHG ε2
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and then identifying Pareto points iteratively, following the strategy: Step 1: Maximize TNPV without considering TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 ¼ inf. Store the solution value of TGHG as the highest TGHG along the Pareto Frontier TGHGmax. Step 2: Minimize TGHG without considering TNPV by solving problem (SoMP) with ε1 ¼ 0 and ε2 ¼ inf. Store the solution value for all decision variables as the initial guess for the next problem. Store the solution value of TGHG as the lowest TGHG along the Pareto Frontier TGHGmin. Step 3: Maximize TNPV while constraining TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 ¼ TGHGmin. Store the solution value of all decision variables as the initial guess for the next problem. Step K (K ‡ 4): Maximize TNPV while constraining TGHG by solving problem (SoMP) with ε1 ¼ 1 and ε2 set to a value within the range (TGHGmin, TGHGmax). Store the solution value for all decision variables as the initial guess for the next problem. Note that this initial guess is only a feasible solution for the next problem if the next problem has a higher value for ε2; therefore, there is an advantage to monotonically increasing ε2 in the search for Pareto points. End when the desired number of Pareto points (e.g., resolution of the Pareto Frontier) has been obtained. Solution filtering is then required to confirm that each step returned a feasible solution that is not dominated by any other solution and is thus Pareto optimal.
20.5 LIFE CYCLE ANALYSIS Biofuels are promoted as alternatives to petroleum-based transportation fuels, in part, for their reduced greenhouse gas emissions, determined by thorough life cycle analysis. This attribute of biofuels has been recognized in policies aimed at reducing the transportation sector’s GHG emissions (e.g., the Low-Carbon Fuel Standard in California (CARB (California Air Resources Board), 2010), the US Renewable Fuel Standard program (U.S. Environmental Protection Agency, 2010), and the Renewables Directive in the European Union (European Parliament, 2009)). However, there is still active debate and research over the emissions of biofuels. The emissions of the widespread corn ethanol dry-grind process are even disputed, with some authors concluding that it offers lower emissions when compared with gasoline (Hsu et al., 2010; Wang et al., 2011), some authors concluding the opposite (Searchinger et al., 2008), and others concluding that emissions are nearly equal (Farrell et al., 2006). Most studies agree that cellulosic biofuels offer lower emissions when compared with gasoline (Wang et al., 2012; Tilman et al., 2009; Wu et al., 2006; Han et al., 2011; Schmer et al., 2008). Such life cycle analysis studies differ in their system boundary assumptions for biofuels or petroleum fuels (e.g., including land use change, coproduct credits,
20.5 Life Cycle Analysis
petroleum supply defense via military actions) and in their parameter values (e.g., biorefinery technology updates, better estimates). This chapter utilizes results for the life cycle analysis of select biofuels performed using the GREET (Greenhouse gases, Regulated Emissions, and Energy Use in Transportation) model. The GREET model was developed at Argonne National Laboratory and is a trusted tool for researchers and politicians to examine greenhouse gas emissions from vehicles and transportation fuels on a consistent basis (Argonne National LaboratoryeTransportation Technology R&D Center, 2010). Parameters and assumptions are continuously updated as the biofuel technologies develop, small-scale experiments are performed, and large-scale field trials are completed. Furthermore, numerous national laboratory reports and papers have been published on biofuel life cycle analysis using GREET, with some based on technoeconomic models corresponding to the seven biorefinery technologies considered in this chapter. The system boundary considered for the biofuel life cycle analysis is shown in Figure 20.2. Greenhouse gases considered here are measured in CO2-equivalent tonnes (t CO2,eq). This measure is an aggregation of emissions of CO2, CH4, and N2O, weighted by their 100-year global warming potentials of 1, 25, and 298, respectively. In other words, 1 unit of CH4 is predicted to have the same global warming potential as 25 units of CO2 over a 100-year time horizon. These global warming potentials are as specified by the International Panel on Climate Change’s 2007 assessment (International Panel on Climate Change (IPCC), 2007).
FIGURE 20.2 System boundary of the biofuel life cycle analysis (inspired by Figure 20.2 in (Wang et al., 2012)).
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The specific emission parameter values used in this chapter are shown in Tables 20.1e20.5. They are mainly determined from the GREET model and associated literature (Wang et al., 2012; Han et al., 2011; Wu et al., 2006), using process data from the technoeconomic models corresponding to each of the seven considered biorefinery technologies. Many of those values are obtained from a report, Table 20.1 Emission Parameter Values for Biomass Production Biomass Type b
EbN
Corn Corn-stvr All wood Perngrass
0.00916 t CO2,eq/Bu 0.0636 t CO2,eq/dt 0.111 t CO2,eq/dt 0.111 t CO2,eq/dt
Table 20.2 Emission Parameter Values for Biomass Transportation Biomass Type b
Method v
NR Eb;v
Corn all biomass
Rail Truck
8.58E-7 t CO2,eq/mi/bu 1.98E-4 t CO2,eq/mi/dt
Table 20.3 Emission Parameter Values for Biorefinery Operation Biomass Type b
Technology l
RB Eb;l
Corn Corn Corn-stvr Corn-stvr All wood All wood Corn-stvr Perngrass
1 2 2 3 4 5 6 7
0.00389 t CO2,eq/Bu 0.00389 t CO2,eq/Bu 0.0557 t CO2,eq/dt 0.0557 t CO2,eq/dt 0.145 t CO2,eq/dt 0.145 t CO2,eq/dt 0.145 t CO2,eq/dt 0.0477 t CO2,eq/dt
Table 20.4 Emission Parameter Values for Biofuel Transportation Product p
Method v
RM Ep;v
RF ethanol AB ethanol CB ethanol CB naphtha & diesel
Truck Truck Truck Truck
5.91E-7 5.91E-7 5.91E-7 5.54E-7
t CO2,eq/mi/gal t CO2,eq/mi/gal t CO2,eq/mi/gal t CO2,eq/mi/gal
20.6 Results
Table 20.5 Emission Parameter Values for Market/Customer Product Use (e.g., Biofuel Combustion) Product p
EpM
RF ethanol AB ethanol CB ethanol CB naphtha & diesel
0.00746 t CO2,eq/gal 0.00746 t CO2,eq/gal 0.00746 t CO2,eq/gal 0.0112 t CO2,eq/gal
which summarizes the recent GREET model updates and performs life cycle analysis on a number of biorefinery technologies along with gasoline (Wang et al., 2012). This is the 2012 update of their earlier study from 2006 (Wu et al., 2006). Transportation emission values for biomass and biofuels are taken from Zamboni et al. (2009). A comparison of two competing products (e.g., a biofuel and gasoline) requires a choice of functional unit. Functional unit options for fuels include volume or mass basis, energy equivalence, and end-use equivalence. Conclusions depend on the choice of functional unit. For example, comparing ethanol and gasoline using a volume functional unit (i.e., per gallon) leads to the conclusion that ethanol is cheaper, which may not be the case for the consumer considering its lower energy density compared to gasoline. In this article, we will consider the functional unit of gasoline equivalent gallon (i.e., volumes with equal energy content). Thus, the effect of lower energy density in some biofuels is removed. Additionally, the market/customer product use in Table 20.5 accounts for the biofuel offsetting an equal energy volume of gasoline. A value of 94 g CO2,eq/MJ, found by Wang et al. (2012), was assumed for gasoline. It should also be noted that end-use equivalence functional units may be appropriate in some cases. Most notably, miles per gallon of gasoline equivalent gallon is useful for vehicles designed to take advantage of the properties of ethanol (e.g., higher compression ratio and different fuel-air mixture) to extract additional engine performance. However, as the gasoline equivalent gallon functional unit does not depend on particular vehicle design or performance, it is more suitable for the present supply chain optimization.
20.6 RESULTS The mixed integer linear program (SoMP) from Section 20.4 was coded in IBM ILOG CPLEX Optimization Studio v12.2 (IBM, 2011) and has 156,947 continuous variables, 5488 binary variables, and 40,982 constraints. The Pareto Frontier of supply chains is presented along with some notable Pareto points, with an evaluation of the tradeoff between economic and environmental performance.
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20.6.1 PARETO FRONTIERS The two scenarios of no biofuel mandates and strict mandates were considered, and their corresponding Pareto Frontiers are shown in Figure 20.3. Note that strict mandates are enforced in the mathematical formulation by including a constraint such that the biofuel sales meet or exceed the RFS2 mandates in 2015 for each RFS2 biofuel classification type. The Pareto points are identified using the ε-constraint approach described in Section 20.4. Each of the single-objective problems are solved with a target optimality gap of 0.5% and a time limit of 10 h. Most of the Pareto points are identified to an optimality gap less than 2.0% in 10 h. The addition of the biofuel mandate constraints reduces the size of the feasible region, and thus the Pareto Frontier for the no biomass mandates scenario dominates the Pareto Frontier of the strict mandates scenario (i.e., has higher TNPV for the same TGHG values). This is largely the result of the strict mandate scenario hitting the upper bound on production of biofuels, whereas the no mandates scenario can improve both economics and emission objectives by producing more biofuel than is truly demanded. For this reason, the remainder of this section will focus on results for the strict mandates scenario. The effect of constraining TGHG can be seen by plotting the total biofuel production for each Pareto point, as shown in Figure 20.4. Recall that the 2015 RFS2 mandates are for the production of 3 B gal/y cellulosic biofuel, 2.5 B gal/y of other advanced biofuel, and 15 B gal/y of implicit nonadvanced biofuel. CB produced by technologies l ¼ {3, 4, 5, 6, 7} may be sold in each of those three categories, whereas AB produced by technology l ¼ 2 may be sold in the latter two categories, and RF produced by technology l ¼ 1 may only be sold in the last category. Much of the
FIGURE 20.3 Pareto Frontiers for the scenarios of no biofuel mandates and strict mandates.
20.6 Results
FIGURE 20.4 Total biofuel production for each Pareto point.
biofuel demand is satisfied then by CB for low TGHG Pareto points. Limited cellulosic biomass availability prevents all of the demand to be satisfied this way, and thus AB and RF are also produced. As the ε-constraint is relaxed, an increasing amount of the biofuel demand is satisfied by RF. Also, recall that technology 2 competes for corn (also an RF feedstock) and corn stover (also a CB feedstock) as feedstocks; thus AB production from technology 2 remains relatively constant. CB naphtha and diesel-range is produced in small amounts from technology 6, as it competes for corn stover with technologies that typically have lower greenhouse gas emissions.
20.6.2 KEY PARETO POINTS This section will provide some analysis of the strict mandates scenario Pareto Frontier, by examining key Pareto points. The goal is to identify modest supply chain changes that may lead to large emission gains for a small loss of profit.
20.6.3.1 Highest TNPV It turns out that the same supply chain configuration identified in our previous study (Marvin et al., 2013) for the strict mandates scenario is a Pareto point for the multiobjective problem. For simplicity, those results are summarized here. In the solution, five different technologies are installed with a total of 168 facilities producing RF (15,000 M gal/y), 26 producing AB (2500 M gal/y), and 24 producing CB (3000 M gal/y). All produced biofuels are sold in their highest RFS fuel classification. By examining the breakeven prices for each facility, it was found that all facilities are economical for facility-gate prices of 2.39, 2.13, and 1.71 $/gal for CB, AB, and RF, respectively.
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20.6.3.2 Lowest TGHG The Pareto point with the lowest TGHG is found by first minimizing TGHG without considering TNPV, then maximizing TNPV while constraining TGHG to be less than or equal to the previous solution value. Recall that the previous solution is used as an initial guess to expedite the solution of the second problem. The supply chain configuration for this Pareto point is shown in Figure 20.5. Five of the seven technologies are installed by developing 90 of the 98 candidate sites, with a total of 60 facilities producing RF (4020 M gal/y), 33 producing AB (6211 M gal/y), and 57 producing CB (10,269 M gal/y). CB and AB are produced far in excess of the RFS mandates for their classifications, so they are also sold at lower fuel classifications. Limited supply of cellulosic material in 2015 prohibits CB from dominating the biofuel markets, although that would have resulted in a lower TGHG. Technology 4 (indirect gasification) is favored over technology 5 (direct gasification), which was installed in the highest TNPV Pareto point, for production of CB ethanol from all-wood, because it has higher product yield for nearly identical emissions. The average distribution of discounted costs for each installed technology is shown in Figure 20.6. By examining the breakeven prices for each facility, it was found that all facilities are economical for facility-gate prices of 4.18, 2.28, and 1.74 $/gal for CB, AB, and RF, respectively. Thus, CB costs are 75% higher for this Pareto point than the highest TNPV Pareto point, while the costs of AB and RF are equivalent. The average distribution of emissions is shown in Figure 20.7. Technologies 2, 3, and 7 have lower net emissions than technology 1 in the solution due to lower emission biomass feedstock(s) and emission-negative biorefinery operation (the result of emission credits for coproducts like electricity). Compressor operation in the high-pressure gasification of technology 4, along with no turbine installation for possible electricity generation, leads it to have emission-positive biorefinery operation. Technology 4 still has lower emissions than technology 1 due to wood being a lower emission biomass feedstock than corn.
20.6.3.3 Balanced The “balanced” Pareto point described here offers large emissions gains for a small loss on profit, compared to the highest TNPV case. This point was chosen by examining the Pareto Frontier (see Figure 20.3) as a decision maker would. The highest TNPV Pareto point offered TNPV of 19.4 B$ and TGHG of 71.4 M t CO2,eq/y, while the lowest TGHG Pareto point offered TNPV of 72.0 B$ and TGHG of 102 M t CO2,eq/y. Thus, there is an opportunity to reduce biofuel production emissions by nearly half, from the highest TNPV case. Presented here is the Pareto point that captures more than half of those emission reductions, with a TNPV of 11.3 B$ and a TGHG of 87.7 M t CO2,eq/y. This Pareto point was calculated in 7.6 h with a 0.50% gap and is shown in Figure 20.8. Three of the seven technologies are installed by developing 60 of the 98 candidate sites, with a total of 161 facilities producing RF (11,900 M gal/y), 43 producing AB (5600 M gal/y), and 15 producing CB (3000 M gal/y). Just enough CB is produced to satisfy the mandate, but excess
(a)
(b)
FIGURE 20.5 Optimum supply chain configuration for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Installed facility capacity shown in million gallons per year (mgy). RF, AB, and CB are produced. Subfigure (a): Corn grain utilization with corn-utilizing facilities shown. RF and AB ethanol are produced from corn using technology 1 and 2, respectively. Existing facilities are denoted with an asterisk (*). Maximum corn utilization is 34%. In this Pareto point, many existing facilities are idled (zero production) in favor of lower emission biofuel technologies. Subfigure (b): Corn stover utilization with associated facilities shown. AB and CB ethanol and CB naphtha and diesel are produced from corn stover. Subfigure (c): Aggregated forest biomass and wood waste utilization with associated facilities shown. CB ethanol is produced from all wood. Subfigure (d): Perennial grass utilization with associated facilities shown. CB ethanol is produced from perennial grasses.
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(c)
(d)
FIGURE 20.5dCont’d
AB is produced and sold as the lower classification (RF). This offsetting of some RF (produced from corn grain) with AB (produced from in an integrated process that utilizes corn and corn stover) is what gives this Pareto point improved emissions. The average distribution of discounted costs for each installed technology is shown in Figure 20.9. By examining the breakeven prices for each facility, it was
20.6 Results
FIGURE 20.6 Breakdown of cost sources for installed technologies for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {5, 6} were not constructed in the optimum supply chain.
FIGURE 20.7 Breakdown of emission sources for installed technologies for the lowest TGHG Pareto point in the case of strict biofuel mandates with fuel credits. Net emissions per gallon of produced biofuel are also shown. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {5, 6} were not constructed in the optimum supply chain.
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(a)
(b)
FIGURE 20.8 Optimum supply chain configuration for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Installed facility capacity shown in million gallons per year (mgy). RF, AB, and CB are produced. Forestry resources and perennial grasses were available but were not utilized in the optimum supply chain. Subfigure (a): Corn grain utilization with corn-utilizing facilities shown. RF and AB ethanol are produced from corn using technology 1 and 2, respectively. Existing facilities are denoted with an asterisk (*). Maximum corn utilization is 34%. Subfigure (b): Corn stover utilization with associated facilities shown. AB and CB ethanol and CB naphtha and diesel are produced from corn stover.
20.7 Conclusions
FIGURE 20.9 Breakdown of cost sources for installed technologies for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {4, 5, 6, 7} were not constructed in the optimum supply chain.
found that all facilities are economical for facility-gate prices of 2.47, 2.23, and 1.71 $/gal for CB, AB, and RF, respectively. Thus, the biofuel prices are at most only 0.10 $/gal higher than in the Pareto point with highest TNPV. The average distribution of emissions is shown in Figure 20.10. As expected, the emissions distribution for technologies 1, 2, and 3 are similar to what was found in the other Pareto points; however, there are small differences in the transportation emissions.
20.7 CONCLUSIONS This chapter proposed a multiobjective mixed integer linear program to determine biofuel supply chain configurations that are Pareto optimal for profit and emissions. It was applied to the Midwestern US 2015 case study introduced in Marvin et al. (2013) to determine facility location, capacity, and technology selection. Pareto Frontiers were found for the two case studies of strict RFS mandates and no mandates. In the strict mandates case study, it was found that the lowest TGHG Pareto point offers an additional 50% reduction in emissions compared to the highest TNPV Pareto point. Unfortunately, the lowest TGHG Pareto point corresponds with a large negative TNPV. One of the Pareto points showed that half of these
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FIGURE 20.10 Breakdown of emission sources for installed technologies for the “balanced” Pareto point in the case of strict biofuel mandates with fuel credits. Net emissions per gallon of produced biofuel are also shown. Existing facilities are denoted by an asterisk (*). New facilities of technologies l ¼ {4, 5, 6, 7} were not constructed in the optimum supply chain.
emission reductions are obtainable by shifting some renewable fuel production to advanced biofuel technologies, with biofuel prices only 0.10 $/gal higher than in the Pareto point with highest TNPV.
ACKNOWLEDGMENTS Partial financial support from the National Science Foundation, CBET award number 1307089, is gratefully acknowledged.
REFERENCES An, H., Wilhelm, W.E., Searcy, S.W., 2011. Biofuel and petroleum-based fuel supply chain research: a literature review. Biomass Bioenergy 35 (9), 3763e3774. Argonne National LaboratoryeTransportation Technology R&D Center, 2010. GREET Model: The Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation Model. CARB (California Air Resources Board), 2010. Low Carbon Fuel Standard (LCFS) Regulation. California Environmental Protection Agency, Air Resources Board, Sacramento, CA.
References
Collette, Y., Siarry, P., 2003. Multiobjective Optimization: Principles and Case Studies. Springer. Daoutidis, P., et al., 2013. Engineering biomass conversion processes: a systems perspective. AIChE J. 59 (1), 3e18. Das, I., Dennis, J.E., 1998. Normal-boundary intersection: a new method for generating the pareto Surface in Nonlinear Multicriteria optimization problems. SIAM J. Optim. 8 (3), 631e657. Dutta, A., et al., 2011. Process Design and Economics for Conversion of Lignocellulosic Biomass to Ethanol: Thermochemical Pathway by Indirect Gasification and Mixed Alcohol Synthesis. National Renewable Energy Laboratory. NREL/TPe5100e51400. Dutta, A., Phillips, S.D., 2009. Thermochemical Ethanol via Direct Gasification and Mixed Alcohol Synthesis of Lignocellulosic Biomass. National Renewable Energy Laboratory. NREL/TPe510e45913. European Parliament, 2009. Directive 2009/28/EC: On the Promotion of the Use of Energy from Renewable Sources and Amending and Subsequently Repealing Directives 2001/ 77/EC and 2003/30/EC. Farrell, A.E., et al., 2006. Ethanol can contribute to energy and environmental goals. Science 311 (5760), 506e508. Floudas, C.A., Elia, J.A., Baliban, R.C., 2012. Hybrid and single feedstock energy processes for liquid transportation fuels: a critical review. Comput. Chem. Eng. 41, 24e51. Geoffrion, A.M., Dyer, J.S., Feinberg, A., 1972. An interactive approach for multi-criterion optimization, with an application to the operation of an academic department. Manage. Sci. 19 (4), 357e368. Gonzalez, T.F., 2007. Handbook of Approximation Algorithms and Metaheuristics. Chapman & Hall/CRC, Boca Raton. Grossmann, I.E., Guille´n-Gosa´lbez, G., 2010. Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes. Comput. Chem. Eng. 34 (9), 1365e1376. Han, J., et al., 2011. Well-to-Wheels Analysis of Fast Pyrolysis Pathways with GREET. Argonne National Laboratory. ANL/ESD/11e8. Hill, J., et al., 2006. Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels. Proc. Natl. Acad. Sci. U.S.A. 103 (30), 11206e11210. Hsu, D.D., et al., 2010. Life cycle environmental impacts of selected US ethanol production and use pathways in 2022. Environ. Sci. Technol. 44 (13), 5289e5297. Humbird, D., et al., 2011. Process Design and Economics for Biochemical Conversion of Lignocellulosic Biomass to Ethanol: Dilute-acid Pretreatment and Enzymatic Hydrolysis of Corn Stover. National Renewable Energy Laboratory. NREL/TPe5100e47764. IBM, 2011. IBM ILOG CPLEX Optimization Studio 12.2. International Panel on Climate Change (IPCC), 2007. Climate Change 2007: Synthesis Report. Switzerland, Geneva. Marvin, W.A., Schmidt, L.D., Daoutidis, P., 2013. Biorefinery location and technology selection through supply chain optimization. Ind. Eng. Chem. Res. 52 (9), 3192e3208. Mavrotas, G., 2009. Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems. Appl. Math. Comput. 213 (2), 455e465. McPhail, L., Westcott, P., Lutman, H., 2011. The Renewable Identification Number System and U.S. Biofuel Mandates. United States Department of Agriculture. Miettinen, K., 1999. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston.
519
520
CHAPTER 20 Optimal Supply Chains for Biofuel Production
Miettinen, K., Ruiz, F., Wierzbicki, A.P., 2008. Introduction to multiobjective optimization: interactive approaches. In: Multiobjective Optimization. Springer, pp. 27e57. Mueller-Gritschneder, D., Graeb, H., Schlichtmann, U., 2009. A successive approach to Compute the Bounded pareto Front of Practical multiobjective optimization problems. SIAM J. Optim. 20 (2), 915e934. Schmer, M.R., et al., 2008. Net energy of cellulosic ethanol from switchgrass. Proc. Natl. Acad. Sci. U.S.A. 105 (2), 464e469. Searchinger, T., et al., 2008. Use of US croplands for biofuels increases greenhouse gases through emissions from land-use change. Science 319 (5867), 1238e1240. Tao, L., et al., 2011. Process and technoeconomic analysis of leading pretreatment technologies for lignocellulosic ethanol production using switchgrass. Bioresource Technol. 102 (24), 11105e11114. Tilman, D., et al., 2009. Beneficial biofuelsethe food, energy, and environment trilemma. Science 325 (5938), 270e271. U.S. Department of Energy, 2011. U.S. Billion-ton Update: Biomass Supply for a Bioenergy and Bioproducts Industry, R.D. Perlack and B.J. Stokes (Leads), ORNL/TMe2011/224. Oak Ridge National Laboratory, Oak Ridge, TN. U.S. Environmental Protection Agency, 2010. EPA Finalizes Regulations for the National Renewable Fuel Standard Program for 2010 and beyond, EPAe420efe10e007. United States Environmental Protection Agency. U.S. Environmental Protection Agency, 2014. Regulation of fuels and fuel additives: 2013 cellulosic biofuel standard. U.S. Environ. Prot. Agency 79 (85), 25025e25031. Wallace, R., et al., 2005. Feasibility Study for Co-locating and Integrating Ethanol Production Plants from Corn Starch and Lignocellulosic Feedstocks. National Renewable Energy Laboratory. NREL/TPe510e37092. Wang, M., Han, J., Dunn, J.B., Cai, H., Elgowainy, A., 2012. Well-to-wheels energy use and greenhouse gas emissions of ethanol from corn, sugarcane and cellulosic biomass for US use. Environ. Res. Lett. 7 (4), 045905. Wang, M.Q., et al., 2011. Energy and greenhouse gas emission effects of corn and cellulosic ethanol with technology improvements and land use changes. Biomass Bioenergy 35 (5), 1885e1896. Wright, M.M., et al., 2010. Techno-economic Analysis of Biomass Fast Pyrolysis to Transportation Fuels. National Renewable Energy Laboratory. NREL/TPe6A20e46586. Wu, M., Wang, M., Huo, H., 2006. Fuel-cycle Assessment of Selected Bioethanol Production Pathways in the United States. Argonne National Laboratory. ANL/ESD/06e7. Yue, D., You, F., Snyder, S.W., 2014. Biomass-to-bioenergy and biofuel supply chain optimization: overview, key issues and challenges. Comput. Chem. Eng. 66, 36e56. Zamboni, A., Bezzo, F., Shah, N., 2009. Spatially explicit static model for the strategic design of future bioethanol production systems. 2. Multi-objective environmental optimization. Energy Fuels 23 (10), 5134e5143.