An environmental and economic optimization of Algal Biofuel Supply

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Process Systems Engineering

An environmental and economic optimization of Algal Biofuel Supply Chain with multiple technological pathways Keivan Ghasemi Nodooshan, Reinaldo J. Moraga, Shi-Jie (Gary) Chen, Christine Nguyen, Ziteng Wang, and Shayan Mohseni Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02956 • Publication Date (Web): 02 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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Industrial & Engineering Chemistry Research

An environmental and economic optimization of Algal Biofuel Supply Chain with multiple technological pathways

Keivan Ghasemi Nodooshana, Reinaldo J. Moragaa*, Shi-Jie (Gary) Chena, Christine Nguyena, Ziteng Wanga and Shayan Mohsenib a

Department of Industrial and Systems Engineering, Northern Illinois University, DeKalb, IL

b

School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

* Corresponding author

KEYWORDS Keywords: algal biofuel, supply chain network optimization, multi-objective optimization, sustainable production, fuzzy ε-constraint 1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

This article optimizes the design and configuration of algal biofuel supply chain networks (SCN) under economic and environmental objectives. Minimization of the total supply chain cost and the total life cycle greenhouse gas (GHG) emission are the economic and environmental objectives, respectively. The SCN has been modeled by a multi objective Mixed Integer Linear Programming approach which incorporates multiple production pathways and time periods, seasonality factors, water evaporation, recycling opportunities and other major traits of the algal biofuel SCN. The model determines the optimal strategic and tactical level decisions of all SCN echelons. A fuzzy solution-based 𝜀-constraint method has been utilized to obtain Pareto-optimal solutions that illustrate the trade-off between economic and environmental objectives. The performance of the model has been assessed in a case study carried out in seven states of the U.S which intends to develop the algal biofuel SCN from the year 2018 to the year 2024. Essential information with regard to the future of different technological pathways, relative importance of various supply chain factors, and sensitivity analysis have been discussed with respect to the case study results.

2 ACS Paragon Plus Environment

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1. Introduction Energy is becoming a growing concern around the world. Pressing issues such as rapid depletion of fossil fuel reservoirs, energy security, economic stability, and global climate balance have prompted governments to invest in the renewable energy industry. Even petroleum giants are investigating the potential of this industry. Exxon Mobil Corporation for instance has partnered with Synthetic Genomics, Inc., Massachusetts Institute of Technology, and other institutions to assess the potential of algal biofuel.1 Today, renewable energy sources contribute to meeting 14% of the global primary energy demand and biomass from which biofuel is produced boasts meeting about 11.5% of the global energy demand, which is 82% of all renewable energies. Biomass is still attracting interest from researchers and investors and its contribution is estimated to increase to 15-50% of primary global energy by the year 2050.2 Specifically, biofuel demand for the transportation sector has significantly increased as transportation has the biggest share of the world energy demand and the need for a sustainable energy source is strongly felt in this sector.3 As an example, the Energy Independence and Security Act of 2007 (EISA) established a Renewable Fuel Standard (RFS) which mandates the transportation fuel sold in United States to include a blending of 36 billion gallons of renewable fuels by 2022. This is due to the fact that two-thirds of the petroleum consumed in United States is imported, out of which 60% is used in the transportation sector. RFS also requires that the Green House Gas (GHG) emission of advanced biofuels production be at least 50% less than that of petroleum-based transportation fuels. In order for the biofuel industry to meet the ambitious expectations of RFS, this industry should overcome numerous challenges. A number of next generation biofuels, however, demonstrate great promise in meeting such goals.4



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Algal biofuel which is the third generation of biofuels and one of the promising next generation biofuel candidates, has been attracting interest due to several characteristics of microalgae including: 1) High productivity: Microalgae doubling time (i.e. time required for doubling the biomass) is commonly 24 hours with the potential of being reduced to periods as short as 3.5 hours. In addition, oil content (i.e. percent of oil in dry weight biomass) of 20-50% is quite common for microalgae and can even exceed 80% in certain species.5 Table 1 compares the oil yield and land requirement of microalgae with some of the commercial sources of biodiesel in the United States. Table 1. Oil yield and land requirements of biodiesel sources5 Crop

Oil Yield (Gallon/ha)

Percent of existing US cropping area*

Corn

45

846

Soybean

118

326

Canola

314

122

Jatropha

500

77

Oil Palm

1572

24

Microalgae

15507

2.5

*Required for meeting 50% of all transport fuel needs of the United States. 2) Minimized competition with agriculture and food industries: Microalgae can be cultivated in non-arable lands and utilize saline, brackish, and wastewater in addition to fresh water.4 3) Production of multiple biofuels: biodiesel, methane, bio hydrogen, and also valuable coproducts are amongst the microalgae products.4-5 4) Recycling CO2: CO2 required for algae cultivation can be provided from sources such as power plants and other industries and hence mitigate greenhouse gas (GHG) emissions6. 4 ACS Paragon Plus Environment

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5) Compatibility with existing infrastructure: existing tanks, pipelines, and vehicles need not be changed to use algal biofuels which saves astronomically high capital investment costs.7 In spite of all algal biofuel potential, a significant amount of research and development is necessary for sustainable, cost-competitive, and scalable production of algal-based biofuels. This is due to the fact that the technology state of this field is described to be in its infancy by the experts. Such efforts are being supported and initiated recently. The United States Department Of Energy (DOE), as an example, has recently revived its investment in research related to production of economically viable and environmentally sound algal biofuels.4 The current study would design a supply chain network with the goal of commercial scale and sustainable production of micro algal biofuels.

2. Literature Review One of the prominent factors hindering the development of the biomass industry is the high supply chain cost of biomass.8 Hence, the supply chain of biofuels as one of the most promising alternatives of fossil fuels needs to be studied if biofuels are to replace the fossil fuels and contribute to meeting the world’s energy demand. A growing interest has been cultivated in studying optimal network design of Biomass Supply Chain (BSC) over the recent decades as the economic, environmental, and efficiency indexes of BSC heavily depend on optimality of its network design. The Biomass literature can be divided into research that focus on technical issues (i.e. algae biology, conversion technologies, etc.) and ones that study the Biomass Supply Chain Network Design (BSCND) with a focus on optimization and commercialization of BSC. In this section, the BSCND literature would be discussed and the contributions of this study will be outlined.



In a review by Ghaderi et al.9, 146 BSCND articles published from 1997 to 2016 have been discussed, out of which only three articles have algae as their feedstock. To the best of our knowledge, two BSCND articles with algae as their feedstock have been published ever since Ghaderi et al.9 published their review of the literature. These five articles will be reviewed briefly in the following paragraphs. Ahn et al.10 used different Mixed Integer Linear Programs (MILPs) tailored for their specific problem which focus on the strategic decisions of the supply chain network with the ultimate goal of minimizing the total cost. They developed a multiple time period model of the strategies to manage a biodiesel supply chain to determine the system configuration that is most effective when the amounts and locations of biodiesel demand change with time. Mohseni et al.11 proposed a twostage model for the BSCND. Their macro-stage performs a spatial filtering using GIS and Analytical Hierarch Process (AHP) to identify the most suitable candidate locations for facility construction which are later applied in the micro-stage. The micro-stage uses a MILP that provides a trade-off between system cost and reliability to determine the strategic and tactical supply chain decisions. Their model uses multiple time periods to capture the seasonal behavior of biomass yield, pipe line capacity, and fertilizer price, etc. Use of a robust optimization method ensures that their strategic and tactical supply chain decisions remain optimal for almost all possible realizations of the uncertain parameters. Gong and You12 developed a Mixed Integer Non Linear Program (MINLP) model. They utilized a global optimization strategy integrating a branch-andrefine algorithm based on successive piecewise linear approximations along with an exact parametric algorithm based on Newton’s method to efficiently solve the nonconvex MINLP model with separable concave terms and mixed-integer fractional terms in the objective functions. The developed model simultaneously optimized the unit cost and the unit global warming potential 6 ACS Paragon Plus Environment

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(GWP). Two Pareto-optimal curves were obtained. The first one pertains to biofuel production illustrating a trade-off between production cost and GWP. The second pertains to biological carbon sequestration (i.e. a set of technologies to store CO2 emissions from industrial power plants) which demonstrates a tradeoff between sequestration cost and GWP.13 Gong and You14 worked on the design and optimization of a large-scale processing network capable of producing multiple algaebased fuels and bio products under uncertainty. 46,704 alternative processing pathways leading to a wide variety of final products have been considered in that article. A two-stage adaptive robust mixed integer fractional programming model was proposed to incorporate the uncertainty and select the robust optimal processing pathway with the highest return of investment. Biodiesel and poly-3-hydroxybutyrate were introduced as the final optimum fuel and bio product, respectively. Mohseni and Pishvaee15 developed a MILP to design and optimize the micro algal biofuel supply chain. Two production scenarios (i.e. centralized and decentralized) have been compared in that article along with a comparison between the performances of two robust optimization approaches on supply chain decisions. After discussing the five BSCND algal biofuel articles published to date, a broader and more statistical perspective is provided in the following paragraphs that is beneficial to gain a better understanding of the literature. As discussed earlier, only a small number of the articles have focused on algae as biomass in the BSCND literature. Figure 1 shows the feedstock-based distribution of articles gathered by Ghaderi et al.9 plus the additional two algal biofuel articles. The total number does not add up to 148 as some articles have multiple feedstock and some have not determined the feedstock. Generally, there are three generations of biofuels. The first generation of biofuels is produced from food crops which are mostly corn, wheat, and sugar cane;



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200 180 13 6

160

31

140 120

49

100 80

29

60 40

7

20

39

51

5

0

First Generation (20%)

Second Generation (77.8%)

Third Generation (2.7%)

Starch and Sugar Crops (39)

Oily Crops (7)

Animal/Agriculture Waste (51)

Urban/Industrial Wood Waste (29)

Forestry Biomass (49)

Hebaceous energy crops (31)

Short Rotation Woody Crops (6)

Energy Crops (13)

Algae (5)

Figure 1. Distribution of Biomass Generation the second generation from energy crops, food crop residues, and food crops themselves after fulfillment of their food purposes; and the third generation from algae.16 As illustrated, the second generation of biofuels is the most studied generation as it overcomes the shortcoming of the first generation by not competing with the food industry. However, the limitations of the second generation in commercial scale production environment (i.e. limited sources of food crop residues and the low efficiency of energy crops compared to algae) have spurred an increasing interest in the third generation biofuels and other sources of renewable energy. Moreover, most of the optimization models comprise of a single objective function while in reality multiple criteria play 8 ACS Paragon Plus Environment

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a role in the optimal design and configuration of many supply chain networks. In the BSCND literature, 117 articles have been published with a single objective (80%); and 29 with multiple objectives (20%). The main objective in designing and planning a biofuel supply chain is for it be cost competitive. However, the fact that a major incentive of biofuel production is alleviating the environmental problems such as global warming and air pollution should not be neglected. Figure 2 shows the different objectives of the literature and their popularity. Economic & Social 1%

Environmental 2%

Social 1%

Sustainable 5%

Economic & Environmental 13%

Economic 78%

Economic

Economic & Environmental

Sustainable

Economic & Social

Social

Environmental

Figure 2. Popularity of different objectives9 Furthermore, 71 articles have a single time period and 75 have considered multiple periods but a trend can be observed indicating that the number of models with multiple time periods is meaningfully higher than the single period in the last five years. The comprehensiveness of the 9 ACS Paragon Plus Environment


supply chain network, consideration of different technologies, and decision variables are some of the other characteristics based on which, literature can be analyzed. To summarize the gaps observed in the literature, we can mention (1) lack of enough BSCND articles with algae biomass, (2) multi-objective models comprising only 20% of the literature models, (3) not enough articles with multi-period models, and (4) nondeterministic models comprising only 20% of the literature models. Regarding the algal biofuel BSCND literature, however, these gaps are more profound and critical. This is due to the fact that very few articles are published in this subject which needs to be addressed so that the potential of algae in the future of renewable energies is assessed. To address these research gaps, the present work develops one of the first microalgae supply chain networks. This article also introduces the following contributions to the literature: 

A comprehensive but tractable mathematical model encompassing the algal biofuel supply chain from raw material procurement for algae growth to the distribution of biofuel to the market. The model is capable of addressing strategic decisions such as determining the location, capacity level, and technology type of biorefinery facilities in addition to tactical decisions, including inventory levels, production amounts, and shipments among the network.



Consideration of environmental issues (i.e. GHG emissions) as the second objective so that the network design is not only economic, but it is also sustainable, making this work one of the first multi-objective studies of micro algal biofuel supply chain optimization. In addition, incorporating features such as water recycling, nutrient recycling, and multiple water resources are some of the other efforts made in alignment with the environmental objective of the model.


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

Consideration of multiple technological pathways will help the literature gain a better understanding with regard to the potential of different biofuel production technologies and the necessity of further investigations. The technological pathways considered in this have been narrowed to 16 pathways that show the most promise in terms of their final product, being well-established, and being economic. This is accomplished by a review of biomass literature to reduce the computational complexity of the model.



A fuzzy solution-based ε-constraint method proposed by Pishvaee and Razmi17 is employed to solve the developed Multi Objective Microalgae Biofuel Supply Chain (MO-MBSC). This method overcomes the major drawback of the ε-constraint method, the prevalent method of solving multi objective models in the literature, which is the possibility of generating weakly Pareto-optimal solutions.

3. Problem description As discussed in the literature review, there are not enough tools to determine the optimal configuration of algal biofuel supply chain networks. In this article, an algal biofuel supply chain network with three echelons of procurement, production, and distribution is modeled with the goal of determining the optimal configuration of the algal biofuel network that minimizes the total supply chain cost and its total GHG emission. In doing so, the model deals with strategic level decisions (such as the location, technology, and capacity of biorefineries) and also tactical level decisions (like the flow of raw materials from their sources to facilities and inventory levels). The known elements of the problem are the raw material sources necessary for different stages of the supply chain (i.e. CO2, water, fertilizer, etc.); candidate locations and capacities for biorefineries; production pathways at biorefineries; final products and their markets; and finally the planning horizon of the supply chain. Figure 3 depicts a schematic diagram of the supply chain in question. 11 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Figure 3. Three echelons of algal biofuel supply chain network with the details of production echelon. 12 ACS Paragon Plus Environment

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The three echelons are shown and the production echelon is further broken down into production stages as it includes the majority of model parameters, constraints, and decision variables. In the following sections the supply chain echelons of the problem would be discussed. 3.1 Procurement In order to grow algae and process it into biofuels, different types of resources are required. The major and more crucial resources required for algal biofuel production are discussed further in this section. CO2: CO2 is one of the necessary resources for the photosynthesis process by which micro-algae grows and produces lipids that will be turned into fuels in the downstream parts of the supply chain. CO2 absorption from the atmosphere does not result in the desirable micro-algae yields necessary for biofuel production.11 Hence, the micro-algae should be provided with an external source of CO2. Electricity power plants equipped with carbon capture and storage systems are the external source of CO2 in this article like the other articles in literature.11, 13a, 15, 18 Capture and use of CO2 emitted by fossil fuel power plants helps mitigate the negative environmental effects of the energy industry. CO2 will be transported via pipelines between power plants and production facilities and in supercritical fluid form. This is due to the fact that gas-phase transportation is not suitable because of low density and the subsequent need for large diameter pipes along with high pressure drop.19 CO2 transportation in supercritical fluid form overcomes the disadvantages of gasphase transportation and is an efficient means of transporting CO2 which has been used in different industries since 1980.19b, 20 Water: Water is the other essential element of photosynthesis. To produce a gallon of biodiesel, between 189 to 1655 gallons of water are consumed.18,

21

Three types of water have been

considered in this article for algae cultivation since there are numerous strains of algae capable of 13 ACS Paragon Plus Environment


being grown in different types of water. These three types are fresh water, waste water, and brackish water. Use of wastewater and brackish water will help not worsen the water crisis of the world. Pipelines would be the means of transportation for water in this study. Raw materials: Other resources necessary for the production of algal biofuel include the nitrogen and phosphorus fertilizers necessary for algae growth, flocculants required for harvesting the algae, and the chemicals needed for oil extraction and conversion. In particular, nitrogen and phosphorus fertilizers are of importance in algal biofuel production. This is due to the relative high consumption of these two nutrients for algae cultivation and the subsequent competition created with the agricultural industry over the mutual resources.22 There are three sources of nitrogen and phosphorus nutrients in this supply chain network. The first source is purchase of fertilizers; the second is waste water which contains nitrogen and phosphorus; and the third is the algae residue returned to the cultivation stage after the anaerobic digestion stage. Algae residue is returned to cultivation ponds as digester effluent and this source of nutrients is accounted for in the calculation of nutrient requirements based on the work by Lundquist et al.23 The two additional sources of nutrients are incorporated in this study in an effort to help solve the high nutrient consumption problem of the algal biofuel production. All the raw materials will be transported to the production facilities by trucks. 3.2 Production The algae-to-biodiesel production process commences with the cultivation of algae in open ponds which is the more established, cost effective, and prevalent of the two algae cultivation technologies18 (i.e. open pond cultivation and photobioreactor cultivation). After algae is grown, they should be separated from growth culture in the harvesting stage and then proceed to the drying stage to further increase the algae density. Then the convertible lipids are extracted from the algae 14 ACS Paragon Plus Environment

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in the lipid extraction stage. The extracted lipids proceed to the conversion stage where they are converted into biofuels while the algae residues are sent to the residue recovery stage after lipid extraction. In the residue recovery stage, the protein and carbohydrate content of algae is used to produce biogas by biologic reactions in the absence of oxygen in an efficient process called anaerobic digestion.24 The technologies and the consequent production pathways (i.e. a unique combination of technologies starting from cultivation stage to the conversion stage) are adapted from Delrue et al.25, however, the literature has been consulted to select only the well-established and effective technologies so that the results are not plagued with technological uncertainties. As mentioned earlier, only open pond cultivation has been considered in article as it is the superior method of cultivation in this field. Raceway cultivation is the open pond technology of choice due to its prevalence and cost effectiveness.18 The drying technologies considered in this article include centrifugation, belt filter press, solar drying, and bed drying, which cover the variety of drying technologies available. Each of these technologies offer different advantages such as high algae density, minimal energy usage, high lipid content and quality (i.e. ratio of different lipids that exist in the lipid blend), and different costs which would be compared by the model performing tradeoffs. The thermal drying step shown in Figure 3 should be used in addition to any of the four drying technologies if n-hexane dry extraction is to be used in the next stage. The lipid extraction technologies include n-hexane dry extraction and DME wet extraction. The latter of the two technologies yields less algal lipid but is less energy intensive and hence costs less and produces less GHG.25 Transesterification and hydrotreating are the two conversion technologies which produce biodiesel and renewable biodiesel as their final products, respectively.26 Table 2 presents the 16 production pathways considered in this study. The production stages with only one 15 ACS Paragon Plus Environment


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Table 2. Technological production pathways.

Pathway Drying Technology

Lipid Technology

Extraction Conversion Technology

1

Centrifugation

DME wet extraction

Transesterification

2

Centrifugation

DME wet extraction

Hydrotreating

3

Centrifugation + Thermal drying

N-hexane dry extraction

Transesterification

4

Centrifugation + Thermal drying


Hydrotreating

5

Belt filter press

DME wet extraction

Transesterification

6

Belt filter press

DME wet extraction

Hydrotreating

7

Belt filter press + Thermal drying N-hexane dry extraction

Transesterification

8

Belt filter press + Thermal drying N-hexane dry extraction

Hydrotreating

9

Solar drying

DME wet extraction

Transesterification

10

Solar drying

DME wet extraction

Hydrotreating

11

Solar drying + Thermal drying


Transesterification

12

Solar drying + Thermal drying


Hydrotreating

13

Bed drying

DME wet extraction

Transesterification

14

Bed drying

DME wet extraction

Hydrotreating

15

Bed drying + Thermal drying


Transesterification

16

Bed drying + Thermal drying


Hydrotreating

technology have not been included in the table as there is only one choice available. The data related to cost and GHG emission of each technology has been adapted from the work by Delrue et al. who have used different references and methods such as calculation based on lipid content and microalgae formula, and the quantities of consumed process fuels according to carbon conservation

to determine these parameters. 25, 27 16 ACS Paragon Plus Environment

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3.3 Distribution Transportation of biofuels from production facilities to the fuel markets will be achieved by ground transportation and specifically trucking. Trucking has proved to be an effective means of transportation for the petroleum-based fuels and is hence selected for the distribution of fuels in this study.11 Finally, technical issues such as water evaporation, seasonality of factors such as biomass yield, loss of CO2 in cultivation ponds, algae moisture content, and cultivation requirements of different algae strains have also been taken into account in the calculation production pathway parameters, requirement parameters, etc. so that the final results are reliable and applicable to the real world conditions.

4. Mathematical formulation This section presents the mathematical model of the described problem. The indices, parameters and variables used to formulate the model are given in appendix A. First, the objective functions will be discussed and then the constraints are explained based on their category. 4.1 Economic objective function Equation (1) is the economic objective function which minimizes the expected cost throughout the entire planning horizon. The objective consists of two types of components. The first two components are the supply chain network revenues and the rest are costs. The different components of Equation (1) respectively refer to the: (1) revenue from the sale of biodiesel; (2) revenue from the sale of glycerin; (3) procurement and transportation cost of CO2; (4) procurement and transportation cost of fresh water; (5) procurement and transportation cost of waste water; (6) procurement and transportation cost of brackish water; (7) procurement and transportation cost of nitrogen; (8) procurement and transportation cost of phosphorus; (9) procurement and 17 ACS Paragon Plus Environment


𝑡 𝑡 𝑡 𝑀𝑖𝑛 𝑐𝑜𝑠𝑡 = − ∑ ∑ ∑ ∑ ∑ 𝑝𝑏𝑦,𝑏 𝑥𝑏𝑦,𝑝,𝑙,𝑏 − ∑ ∑ ∑ 𝑝𝑔𝑔𝑡 𝑥𝑔𝑙,𝑔 𝑦

𝑏

𝑡

𝑝

𝑙

𝑙

𝑔

+ +

𝑡 𝑡 ∑ ∑ ∑ 𝑡𝑤𝑤,𝑙 𝑥𝑤𝑤,𝑙 + ∑ ∑ ∑ 𝑡𝑘𝑘,𝑙 𝑥𝑟𝑘,𝑙 𝑤 𝑙 𝑡 𝑘 𝑙 𝑡 𝑡 𝑡 ∑ ∑ ∑ 𝑡𝑛𝑛,𝑙 𝑥𝑛𝑛,𝑙 + ∑ ∑ ∑ 𝑡ℎℎ,𝑙 𝑥ℎℎ,𝑙 𝑛 𝑙 𝑡 ℎ 𝑙 𝑡 𝑡 𝑡 ∑ ∑ ∑ 𝑡𝑟𝑠𝑟 ,𝑙 𝑥𝑟𝑠𝑟 ,𝑙 + ∑ ∑ ∑ ∑ ∑ 𝑡𝑏𝑙,𝑏 𝑥𝑏𝑦,𝑝,𝑙,𝑏

+

𝑠𝑟

𝑙

𝑡

(1)

𝑡

𝑡 ∑ ∑ ∑ 𝑡𝑜𝑂,𝑙 𝑥𝑜𝑜,𝑙 𝑜 𝑙 𝑡

+

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𝑡 + ∑ ∑ ∑ 𝑡𝑓𝑓,𝑙 𝑥𝑓𝑓,𝑙 𝑓

𝑙

𝑙

𝑏

𝑡

𝑦

𝑝

𝑡

𝑡 𝑡 𝑡 + ∑ ∑ ∑ 𝑡𝑔𝑙,𝑔 𝑥𝑔𝑙,𝑔 + ∑ ∑ ∑ ∑ 𝑐𝑐𝑙,𝑝,𝑐 𝑈𝑙,𝑝,𝑐 𝑙

+

𝑔

𝑡

𝑙

𝑝

𝑡 𝑡 ∑ ∑ ∑ ∑ ∑ 𝑝𝑐𝑦,𝑙,𝑝 𝑥𝑏𝑦,𝑝,𝑙,𝑏 𝑦 𝑙 𝑝 𝑏 𝑡

𝑐

𝑡

+ ∑ ∑ ℎ𝑔𝑙 𝑖𝑔𝑙𝑡 𝑙

𝑡

𝑡 + ∑ ∑ ∑ ℎ𝑏𝑦,𝑙 𝑖𝑏𝑦,𝑙 𝑦

𝑙

𝑡

transportation cost of other raw materials; (10) biodiesel transportation cost; (11) glycerin transportation cost; (12) capital cost of biorefineries; (13) production cost of biodiesel; (14) inventory holding cost of glycerin and (15) inventory holding cost of biodiesel. Capital cost of pipelines has been considered in coefficients 𝑡𝑜𝑂,𝑙 , 𝑡𝑓𝑓,𝑙 , 𝑡𝑤𝑤,𝑙 , and 𝑡𝑘𝑘,𝑙 . In addition, 𝑡𝑜𝑂,𝑙 encompasses the costs associated with capturing, compressing, and recompressing of CO2.19a, 28 It should also be mentioned that in order to capture the cost of transporting CO2 in supercritical form, 𝑡𝑜𝑂,𝑙 is calculated under the assumption that the pipeline operates at an inlet pressure and temperature greater than the CO2 critical point and based on the model developed by Peters et al.28b Moreover, production cost of biodiesel encompasses all the costs associated with the six stages of biofuel production from cultivation to anaerobic digestion. Cost of pumps for water circulation in cultivation ponds, cost of CO2 delivery to the ponds in bubble form, sedimentation cost for harvesting, all drying technologies costs, pumping, extraction, and distillation cost for N-hexane 18 ACS Paragon Plus Environment

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dry extraction, cost of decantation for DME wet extraction, and liquid-liquid extraction cost for transesterification are instances of biodiesel production cost which have been estimated based on the supplemental data of the work by Delrue et al. and the work of Lundquist et al.23, 25 4.2 Environmental objective function Equation (2) is the environmental objective function which minimizes total CO2-equivalent GHG emission caused by supply chain operations.

𝑡 𝑡 𝑀𝑖𝑛 𝐺𝐻𝐺 = ∑ ∑ ∑ 𝐺𝑂𝑂,𝑙 𝑥𝑜𝑜,𝑙 + ∑ ∑ ∑ 𝐺𝐹𝑓,𝑙 𝑥𝑓𝑓,𝑙 𝑜

𝑙

𝑡

𝑓

𝑙

(2)

𝑡

𝑡 𝑡 + ∑ ∑ ∑ 𝐺𝑊𝑤,𝑙 𝑥𝑤𝑤,𝑙 + ∑ ∑ ∑ 𝐺𝐾𝑘,𝑙 𝑥𝑟𝑘,𝑙 𝑤

+ +

𝑙

𝑡

𝑘 𝑙 𝑡 𝑡 𝑡 ∑ ∑ ∑ 𝐺𝑁𝑛,𝑙 𝑥𝑛𝑛,𝑙 + ∑ ∑ ∑ 𝐺𝐻ℎ,𝑙 𝑥ℎℎ,𝑙 𝑛 𝑙 𝑡 ℎ 𝑙 𝑡 𝑡 𝑡 ∑ ∑ ∑ 𝐺𝑅𝑠𝑟,𝑙 𝑥𝑟𝑠𝑟 ,𝑙 + ∑ ∑ ∑ ∑ 𝐺𝐸𝑙,𝑝,𝑐 𝑈𝑙,𝑝,𝑐 𝑠𝑟 𝑙 𝑡 𝑙 𝑝 𝑐 𝑡

𝑡 + ∑ ∑ ∑ ∑ 𝐺𝑃𝑙,𝑡 𝛾𝑙𝑡 𝜑𝑐 𝑈𝑙,𝑝,𝑐 + ∑ ∑ 𝐺𝐺𝑙 𝑖𝑔𝑙𝑡 𝑙

+

𝑝

𝑐

𝑡

𝑙

𝑡 ∑ ∑ ∑ 𝐺𝑆𝑙 𝑖𝑏𝑦,𝑙 𝑙 𝑦 𝑡

𝑡

𝑡 + ∑ ∑ ∑ ∑ ∑ 𝐺𝐵𝑦,𝑝 𝑥𝑏𝑦,𝑝,𝑙,𝑏 𝑦

𝑝

𝑙

𝑏

𝑡

𝑡 𝑡 + ∑ ∑ ∑ 𝐺2𝑙,𝑔 𝑥𝑔𝑙,𝑔 + ∑ ∑ ∑ ∑ ∑ 𝐺3𝑙,𝑏 𝑥𝑏𝑦,𝑝,𝑙,𝑏 𝑙

𝑔

𝑡

𝑦

𝑙

𝑏

𝑝

𝑡

The different components of Equation (2) respectively represent the: (1) GHG emissions of CO2; (2) GHG emissions of fresh water; (3) GHG emissions of waste water; (4) GHG emissions of brackish water; (5) GHG emissions of nitrogen; (6) GHG emissions of phosphorus; (7) GHG emissions of other raw materials; (8) GHG emissions of establishing biorefineries; (9) GHG emissions released from open ponds during microalgae growth; (10) GHG emissions of storing glycerin; (11) GHG emissions of storing biodiesel; (12) GHG emissions of producing biodiesel; 19 ACS Paragon Plus Environment


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(13) GHG emissions of glycerin transportation and (14) GHG emissions of biodiesel transportation. 4.3 Raw material allocation constraints Constraint sets (3)-(8) state that in each raw material source, the amount of raw material sent to biorefineries should not exceed the maximum raw material that can be obtained from that source.

𝑡 𝑎𝑜𝑜𝑡 ≥ ∑ 𝑥𝑜𝑜,𝑙

∀𝑜, 𝑡

(3)

∀𝑓, 𝑡

(4)

𝑙 𝑡 𝑎𝑓𝑓𝑡 ≥ ∑ 𝑥𝑓𝑓,𝑙 𝑙 𝑡 𝑎𝑤𝑤𝑡 ≥ ∑ 𝑥𝑤𝑤,𝑙

(5)

∀𝑤, 𝑡

𝑙 𝑡 𝑎𝑘𝑘𝑡 ≥ ∑ 𝑥𝑘𝑘,𝑙

∀𝑘, 𝑡

(6)

∀𝑛, 𝑡

(7)

∀ℎ, 𝑡

(8)

𝑙 𝑡 𝑎𝑛𝑛𝑡 ≥ ∑ 𝑥𝑛𝑛,𝑙 𝑙 𝑡 𝑎ℎℎ𝑡 ≥ ∑ 𝑥ℎℎ,𝑙 𝑙

With sources ensured not to be used more than their capacity, it should be made sure that the necessary raw materials for production are procured. Constraint set (9) shows the water requirement of each biorefinery in each time period is satisfied by the fresh, waste and brackish water transported. Since only one of either the fresh water or brackish water algae species can be used in cultivation stage, constraint sets (10)-(12) ensures fresh water and brackish water are not transported to a biorefinery simultaneously. Constraint sets (13) and (14) ensure that the required 20 ACS Paragon Plus Environment

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amounts of nitrogen and phosphorus for each biorefinery are provided. Constraint set (15) satisfies the need for other raw materials. The required resource amounts in these constraints are calculated through the multiplication of the total cultivated biomass (𝛿𝐶 𝜑𝑙.𝑡), the binary variable of facility 𝑡 foundation (𝑈𝑙,𝑝,𝑐 ), and the resource requirements of producing a unit of biomass

(𝑚𝑤, 𝑚𝑛, 𝑚ℎ, 𝑚𝑟,𝑝 ).

𝑡 𝑡 𝑡 𝑡 ∑ 𝑥𝑓𝑓,𝑙 + ∑ 𝑥𝑤𝑤,𝑙 + ∑ 𝑥𝑘𝑘,𝑙 ≥ ∑ ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑚𝑤 𝑓

𝑤

𝑘

𝑝

(10)

𝑡

𝑡 ∑ ∑ 𝑥𝑘𝑘,𝑙 ≤ 𝑀 ∗ 𝑍𝐾𝑙 ∀𝑙 𝑘

(9)

𝑐

𝑡 ∑ ∑ 𝑥𝑓𝑓,𝑙 ≤ 𝑀 ∗ 𝑍𝐹𝑙 ∀𝑙 𝑓

∀𝑙, 𝑡

(11)

𝑡

(12)

𝑍𝐹𝑙 + 𝑍𝐾𝑙 ≤ 1 ∀𝑙 𝑡 𝑡 𝑡 ∑ 𝑥𝑤𝑤,𝑙 𝑛𝑎 + ∑ 𝑥𝑛𝑛,𝑙 ≥ ∑ ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑚𝑛 𝑤

𝑛

𝑝

𝑡 𝑡 𝑡 ∑ 𝑥𝑤𝑤,𝑙 ℎ𝑎 + ∑ 𝑥ℎℎ,𝑙 ≥ ∑ ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑚ℎ 𝑤

ℎ

𝑝

𝑡 𝑡 𝑥𝑟𝑟,𝑙 ≥ ∑ ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑚𝑟,𝑝 𝑝

∀𝑙, 𝑡

(13)

∀𝑙, 𝑡

(14)

𝑐

𝑐

∀𝑙, 𝑟, 𝑡

(15)

𝑐

4.4 Final product constraints Constraint set (16) ensures that for each biorefinery, the total amount of biodiesel shipped to all markets at time period 𝑡 plus the biodiesel inventory at the end of time period 𝑡 is not greater than the maximum amount of biodiesel that can be produced at time period 𝑡 (equals to total cultivated biomass (= 𝛿𝐶 𝜑𝑙.𝑡 ) multiplied by conversion rate 𝑐𝑏𝑦,𝑝 ) plus the biodiesel inventory at the end of 21 ACS Paragon Plus Environment


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the previous time period. A similar condition is held for the production and storage of glycerin, which is given by constraint set (17). Constraint set (18) ensures that the amount of biodiesel shipped from all biorefineries to each demand zone 𝑏 is equal to its biodiesel requirement. Constraint set (19) ensures that the amount of glycerin sent to each demand zone 𝑔 is not greater than the maximum amount of glycerin which can be sold at that zone.

𝑡 𝑡−1 𝑡 𝑡 ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑐𝑏𝑦,𝑝 + 𝑖𝑏𝑦,𝑙 ≥ ∑ 𝑥𝑏𝑦,𝑝,𝑙,𝑏 + 𝑖𝑏𝑦,𝑙 𝑐

∀𝑙, 𝑡, 𝑝, 𝑦

𝑡 𝑡 ∑ ∑ 𝛿𝐶 𝜑𝑙.𝑡 𝑈𝑙,𝑝,𝑐 𝑐𝑔𝑝 + 𝑖𝑔𝑙𝑡−1 ≥ ∑ 𝑥𝑔𝑙,𝑔 + 𝑖𝑔𝑙𝑡 ∀𝑙, 𝑡 𝑐

𝑝

𝑝

(17)

𝑔

𝑡 ∑ ∑ ∑ 𝑥𝑏𝑦,𝑝,𝑙,𝑏 = 𝑑𝑏𝑏𝑡 𝑦

(16)

𝑏

∀𝑏, 𝑡

(18)

𝑙

𝑡 ∑ 𝑥𝑔𝑙,𝑔 ≤ 𝑑𝑔𝑔𝑡

∀𝑔, 𝑡

(19)

𝑙

4.5 Biorefineries constraints Constraint set (20) ensures that at most one type of production pathway and capacity level can be assigned to each biorefinery. Constraint set (21) makes sure that even if biorefinery 𝑙 is closed, its capital cost is still considered during the years after the closure. This is due to the fact that the 𝑡 𝑡 capital cost of biorefineries are calculated by the clause 𝑈𝑙,𝑝,𝑐 𝑐𝑐𝑡𝑙,𝑝,𝑐 where 𝑐𝑐𝑙,𝑝,𝑐 is the annualized

capital cost of biorefineries. Constraint sets (22) and (23) enforce an upper bound on the total amount of biodiesel and glycerin stored during time period 𝑡 at biorefinery 𝑙.

𝑡 ∑ ∑ 𝑈𝑙,𝑝,𝑐 ≤1 𝑝

∀𝑙, 𝑡

(20)

𝑐


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𝑡−1 𝑡 𝑈𝑙,𝑝,𝑐 ≤ 𝑈𝑙,𝑝,𝑐 𝑡 𝑖𝑏𝑦,𝑙 ≤ 𝑠𝑏𝑦,𝑙

𝑖𝑔𝑙𝑡 ≤ 𝑠𝑔𝑙

(21)

∀𝑙, 𝑝, 𝑐, 𝑡

(22)

∀𝑦, 𝑙, 𝑡

(23)

∀𝑙, 𝑡

5. Multi objective solution approach The methods developed for solving the Multi Objective Mathematical Programming (MOMP) problems are categorized in three categories of (1) Priori, (2) Interactive, and (3) Posteriori.29 In the priori method, the goals or objective functions’ weights are determined based on decision makers’ preferences prior to the problem solving. The quantification of preferences beforehand and prior to solving the problem, however, is quite difficult. The interactive method tries to find the most preferred solution by gradually incorporating the decision makers’ preferences in the solving process. The major disadvantage of this method is that it only calculates one solution that the decision maker believes to be the preferred solution instead of providing a whole picture of efficient solutions by Pareto sets.17, 29 With the posteriori method, all the Pareto optimal solutions are determined and then the decision maker chooses the most preferred solution among them. The ε-constraint method is one of the most famous posteriori methods that is employed extensively for solving MOMP problems in different literatures due to its simplicity of implementation.29 There are two key points that should be considered when using this method: (1) determining the range of the objective functions over the efficient solutions set, (2) ensuring the efficiency of the produced solution.29 The pay-off table which is obtained by individual optimization of the objective functions is usually used to obtain the range (optimal and nadir values) of each objective function. This might lead to weakly efficient solutions which are not acceptable for multi-objective optimization since they are dominated by other efficient solutions. To escape this drawback, the 23 ACS Paragon Plus Environment


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proposed MO-MBSC is solved using a fuzzy solution-based 𝜀-constraint method which was developed by Pishvaee and Razmi.17 The steps of this method which enable the decision maker to find the most preferred solution by adjusting the satisfaction degree of each objective function can be summarized as follows: Step 1: Determine the optimal value (𝑂𝐹 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 ) and the nadir value (𝑂𝐹 𝑛𝑎𝑑𝑖𝑟 ) of each objective function over the efficient set. To obtain the optimal value for the first and second 𝑜𝑝𝑡𝑖𝑚𝑎𝑙

objective functions, i.e., (𝑂𝐹1

𝑜𝑝𝑡𝑖𝑚𝑎𝑙

, 𝑂𝐹2

), each objective should be solved separately, and

then the corresponding nadir value for each one can be calculated as follows:

𝑂𝐹1𝑛𝑎𝑑𝑖𝑟 = min {𝑂𝐹1 (𝑥)|𝑂𝐹2 (𝑥) ≤ 𝑂𝐹2𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑎𝑛𝑑 𝑥 ∈ 𝑆}

(24)

𝑂𝐹2𝑛𝑎𝑑𝑖𝑟 = min {𝑂𝐹2 (𝑥)|𝑂𝐹1 (𝑥) ≤ 𝑂𝐹1𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑎𝑛𝑑 𝑥 ∈ 𝑆}

(25)

where x is the vector of decision variables and S represents the feasible region which satisfies all the constraints of the model. Step 2: define a linear membership function for each objective function as follows:

𝑖𝑓 𝑂𝐹1 (𝑥) < 𝑂𝐹1𝑜𝑝𝑡𝑖𝑚𝑎𝑙

1, 𝑂𝐹1𝑛𝑎𝑑𝑖𝑟 − 𝑂𝐹1 (𝑥)

𝜇1 (𝑥) =

𝑂𝐹1𝑛𝑎𝑑𝑖𝑟 {

−

𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑂𝐹1

𝑖𝑓 𝑂𝐹1 (𝑥) > 𝑂𝐹1𝑛𝑎𝑑𝑖𝑟

1,

𝑖𝑓 𝑂𝐹2 (𝑥) < 𝑂𝐹2𝑜𝑝𝑡𝑖𝑚𝑎𝑙

𝑂𝐹2𝑛𝑎𝑑𝑖𝑟 {

𝑖𝑓 𝑂𝐹1𝑜𝑝𝑡𝑖𝑚𝑎𝑙 ≤ 𝑂𝐹1 (𝑥) ≤ 𝑂𝐹1𝑛𝑎𝑑𝑖𝑟

0,

𝑂𝐹2𝑛𝑎𝑑𝑖𝑟 − 𝑂𝐹2 (𝑥)

𝜇2 (𝑥) =

,

0,

−

𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑂𝐹2

,

(26)

𝑖𝑓 𝑂𝐹2𝑜𝑝𝑡𝑖𝑚𝑎𝑙 ≤ 𝑂𝐹2 (𝑥) ≤ 𝑂𝐹1𝑛𝑎𝑑𝑖𝑟 𝑖𝑓 𝑂𝐹1 (𝑥) > 𝑂𝐹1𝑛𝑎𝑑𝑖𝑟 24

ACS Paragon Plus Environment

(27)

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where 𝜇𝑖 (𝑥) indicates the satisfaction degree of 𝑖th objective function. Step 3: Consider the satisfaction degree function of one of the objective function as the objective function and incorporate the satisfaction degree function of the other objective function with right hand side 𝜀 in the constrains as shown below:

(28)

𝑀𝑎𝑥 𝜇1 (𝑥) 𝑠. 𝑡. 𝜇2 (𝑥) ≥ 𝜀 𝑥𝜖𝑆

where epsilon takes a value in the range [0,1]. Step 4: Divide the range [0,1] into n equal intervals by defining n+1 equidistant grid points and use the defined points as the values of the epsilon to produce different Pareto-optimal solutions. Step 5: If the decision maker is satisfied with one of the produced solutions, stop and choose it as the final solution, otherwise consider the interval that is most preferred by the decision maker as the new range and go to step 4 to obtain new Pareto-optimal solutions.

6. Case study To evaluate the performance of the proposed MO-MBSC model, a case study was devised to apply the model in an area covering seven Midwestern states of the U.S. These seven states are Indiana, Illinois, Kentucky, Missouri, Nebraska, Iowa, and Kansas. The rest of this section is organized as follows: First, the assumptions made in the case study and the data collection resources and process will be discussed. Then the obtained results will be shown and analyzed. The assumptions used in the model are described below: 25 ACS Paragon Plus Environment


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(1) The planning horizon is 7 years which is broken up into 28 three-month periods in order to enable the model to take into account seasonal variations in microalgae growth, water evaporation, and other seasonal factors mentioned in many research.9, 18 7 years have been assumed in the planning horizon so that the plan is long enough to justify the investment that has been put in the biorefineries but not too long so that the technologies of the biorefineries are not outdated by the ongoing technological advances. (2) The annual amortized capital cost of each biorefinery is estimated by the following annuity formulation:11

𝐴𝑛𝑛𝑢𝑙𝑖𝑧𝑒𝑑 𝑐𝑜𝑠𝑡 = 𝑄 × 𝑖⁄[1 − (1 + 𝑖)−𝑛 ]

(29)

where 𝑄 is the initial capital cost; 𝑖 the internal rate of return; and 𝑛 the project lifetime. 𝑄 is adapted from the work by Lundquist et al.23 (3) The transportation costs are categorized into three categories of solid commodities trucking, liquid commodities trucking, and transportation by pipeline. The cost of solid commodities trucking is calculated using the following formulation:30

𝑡𝑡 (𝑡𝑏𝑑 + 𝑣𝑏 ) ∗ 𝑑𝑗𝑚 𝑥𝐼𝑡𝑙𝑗 𝑇𝐶1 = ∑ ∑ ∑ [ + 𝑙𝑢𝑏 ] ∗ 𝑐𝑎𝑝𝑏 1 − 𝑀𝐶𝑙 𝑙 𝐼𝑙 𝑗

(30)

where 𝑡𝑏𝑑 is the distance dependent cost and 𝑡𝑏𝑡 is the time dependent cost of transportation, 𝑣 is the truck speed, 𝑐𝑎𝑝𝑏 is the capacity of each truck, 𝑑𝑗𝑚 the distance between locations, and 𝑙𝑢𝑏


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the loading/unloading cost. 𝑥𝐼𝑡𝑙𝑗 is the amount of material being transported and finally 𝑀𝐶𝑙 is the moisture content of the material being handled. The cost of liquid commodities trucking is calculated using the following formulation:30

𝑡 𝑡𝑙𝑞 𝑑 (𝑡𝑙𝑞 + 𝑣 ) ∗ 𝑑𝐼𝑙𝑗 𝑡 𝑇𝐶2 = ∑ ∑ [ + 𝑙𝑢𝑙𝑞 ] ∗ 𝑦𝑗𝑚 𝑐𝑎𝑝𝑙𝑞 𝑗 𝑚

(31)

𝑡 𝑑 where 𝑡𝑙𝑞 is the distance dependent cost and 𝑡𝑙𝑞 is the rime dependent cost of transportation, 𝑣 is

the truck speed, 𝑐𝑎𝑝𝑙𝑞 is the capacity of each truck, 𝑑𝐼𝑙𝑗 is the distance between locations, 𝑙𝑢𝑙𝑞 is 𝑡 the loading/unloading cost, and 𝑦𝑗𝑚 is the amount of material being transported. The value of all

these parameters are adopted from the work by Huang et al.30 To fine-tune these parameters for Midwest region, the trucking rate data of Midwestern and Western regions from the year 2012 to 2015 was collected from United States Department of Agriculture.31 It was concluded that the difference between truck rates in Midwestern and Western regions of U.S is negligible. Pipeline transportation cost includes the water transportation cost and the CO2 transportation cost. CO2 transportation cost has been adapted from the work by Zhang et al.19a ; and the water transportation cost from the article by Zhou and Tol.32 (4) Algal biomass productivity is a function of numerous factors such as temperature, light intensity, oxygen concentration, cultivation culture PH, and nutrient availability which makes it hard to calculate the productivity.6 To overcome this complexity, algal biomass productivity has been considered a function of temperature and light intensity. This is due to the fact that these two



factors have the strongest correlation with productivity.33 The following formulation has been used to calculate algal biomass productivity which has been tested against experimental results.34

1/𝑃 = −0.0802 + (1.676 ∗ 1/𝑇) + (73.491 ∗ 1/𝐼)

(32)

where P is productivity (g dry weight/𝑚2 day), T is the temperature of cultivation culture in centigrade and I is the irradiance (KJ/𝑚2 day). In the following paragraphs the data collection resources and process will be discussed. 

CO2: The number of fossil fuel power plants selected as a source of CO2 in this study sums up to 26 locations. These power plants have been selected based on their CO2 emission capacity and location.35 The seven states in which the case study is carried out have been divided to counties and the suitable locations have been selected based on the average temperature and sunshine hours obtained from U.S Climate Data. 36 The total amount of CO2 available by the selected 26 power plants is approximately 250 million metric tons per year.



Fresh water: The 23 fresh water sources used in the case study have been selected using the National Water Information System Mapper of United States Geological Survey.37 The suitability of locations has been determined using the same method employed for CO2 power plant locations.



Waste water: The information of waste water sources has been retrieved from different county and state websites in which the waste water treatment plants are located. In total, 16 waste water treatment plants have been selected to provide waste water to production facilities. 28 ACS Paragon Plus Environment

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

Brackish water: Brackish water sources of the supply chain network are Mississippi McNairy-Nacatoch aquifer of River Valley alluvial aquifer and Mississippian aquifer. The location, capacity, depth of water, and other necessary information related to these aquifers has been obtained from an article by Osborn et al.38



Nitrogen: In order to provide the nitrogen required for algae cultivation, ammonia production facilities have been selected with respect to their capacity and location.39 The total amount of nitrogen available by purchase of fertilizer is 6.719 million tons per year.



Phosphorus: Six phosphorus fertilizer facilities producing a total of 6.7 million tons of phosphorus fertilizer per year have been considered as the available sources of phosphorus for the supply chain.40 The distance between phosphorus facilities and the candidate locations of biorefineries are longer in comparison to that of other necessary resources. However, this does not affect the supply chain decisions drastically as the phosphorus requirement of algae production is approximately one tenth of the nitrogen requirement.



Other raw materials: The other required raw materials will be procured from the local markets as the amounts consumed are relatively low.15, 22, 25, 41



Biorefinery locations: The candidate locations for biorefinery foundation have been selected using Land Cover Data Viewer map of National Gap Analysis Program administrated by United States Geological Survey.42 The priority of selection has been given to shrub lands and grasslands, nonvascular and sparse vascular rock vegetation, and recently disturbed or modified land cover categories.



Demand zones: The demand zones to which the produced biofuels and co-products will be distributed, are the most populous city of each of the seven states included in the case 29 ACS Paragon Plus Environment


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study. Biofuel demand of each city starts as 0.3% of state’s total gasoline consumption for transportation and grows by 0.15% of state’s total gasoline annually. 6.1. Results and discussion This section analyzes the results of the proposed MO-MBSC model which includes optimal objective functions (total supply chain cost and GHG emission), optimal supply chain design (facility location, production pathway and capacity) as well as sensitivity analysis evaluating the effect of different input parameters on the optimal results. The model was coded in GAMS software and solved by the commercial solver CPLEX on a personal computer equipped with CPU 3.16 GHz and 4G RAM. 6.1.1. Supply chain cost and GHG emission To solve the MO-MBSC problem, the range [0, 1] is divided into five equal sections by six grid points (0, 0.2, 0.4, 0.6, 0.8, 1) which are used as the values of 𝜀 to generate six Pareto-optimal solutions. Table 3 includes optimal values of the total cost and GHG emission objective functions. Table 3. Computational results under different satisfaction degrees of objective functions. Solution

Satisfaction degree 𝜇2 (𝑥)

Objective function value

𝜇1 (𝑥)

Ofcost

OfGHG

CPU time (sec)

A

1

0

9.448 × 109

7.291 × 109

1145

B

0.8

0.614

1.09 × 1010

6.871 × 109

3451

C

0.6

0.799

1.234 × 1010

6.745 × 109

3251

D

0.4

0.874

1.379 × 1010

6.694 × 109

2589

E

0.2

0.929

1.524 × 1010

6.656 × 109

3210

F

0

1

1.668 × 1010

6.608 × 109

1945


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As might be expected, it is clear that two objective functions are in conflict with each other, meaning that as GHG emission value is reduced, total cost rises and vice versa. According to this, obtaining a more environmentally friendly biodiesel leads to increased supply chain cost. However, it is of great importance to find an acceptable trade-off between cost and GHG emission which satisfies decision maker criteria. To this aim, it should be considered how much supply chain cost would increase by reducing different amounts of GHG emission. For example, when GHG emission decreases from 7.3 × 109 to 6.6 × 109 (kg CO2-eq), supply chain cost grows significantly to a peak of $1.66 × 1010 which is about two times the cost of the supply chain emitting 7.3 × 109 (kg CO2-eq) GHG, but the cost rises only marginally from $9.44 × 109 to $1.09 × 1010 by reducing GHG emission from 7.3 × 109 to 6.9 × 109 (kg CO2-eq). In other words, as reduction in GHG emission increases, the cost of environmental protection grows exponentially. This trend is clearly seen from the Pareto optimal frontier shown in Figure 4.

1.655

Total supply chain cost (×1010 $)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.555

F E

1.455 1.355 1.255 1.155

D C

B

1.055

A

0.955

0.855 6.555 6.605 6.655 6.705 6.755 6.805 6.855 6.905 6.955 7.005 7.055 7.105 7.155 7.205 7.255

Total GHG emissions (×109 kg CO2-eq)

Figure 4. Trade-off between economic and environmental objective functions for 𝜇2 (𝑥) ∈ [0,1]. 31 ACS Paragon Plus Environment


Therefore, GHG emissions of microalgae biodiesel supply chain can become close to the most environmental optimum solution with a small increase in production cost, which shows an obvious advantage in considering economic and environmental objective functions in microalgae biodiesel supply chain simultaneously. The last column of Table 3 shows that the computational time of all model iterations is under 1 hour which is satisfactory as the proposed model is aimed at optimizing strategic supply chain decisions. Although the calculated results provide the decision maker with an overall image of the Pareto-optimal set obtained by a course grid, it is of great importance to generate more efficient solutions in the area which is more interesting for the decision maker when there are decision-making factors such as budget restriction or environmental regulations. In the next iteration, a denser grid in the preferred area is used to guide the decision maker towards the final decision. Accordingly, the area between solutions B and C (𝜇2 (𝑥) ∈ [0.2 0.4]) is considered as the preferred area of decision maker since it makes a reasonable trade-off between supply chain cost and GHG emission (as the cost slope is not steep for GHG emission reduction), then four grid points (0.24, 0.28, 0.32, 0.36) are chosen as the value of 𝜀. From the new Pareto-optimal frontier depicted in Figure 5, the decision maker can more precisely investigate the effect of changes in GHG emission on supply chain cost which helps with finding the most preferred Pareto-optimal solution. 6.1.2. Supply chain design Figure 6 shows the optimal facility locations, production pathways and capacities between 2018 and 2024 for two efficient solutions B and E chosen from Table 3. In solution B, five biorefineries with production pathway 14 will be built in 2018. This will increase to ten biorefineries with production pathway 14 and two with production pathway 16 three years later and then to fourteen biorefineries with production pathway 14, five with production pathway 16 and two with 32 ACS Paragon Plus Environment

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1.405 1.355

Total supply chain cost (×1010 $)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.305 1.255

C

1.205 1.155

B

1.105 1.055

1.005 6.699 6.719 6.739 6.759 6.779 6.799 6.819 6.839 6.859 6.879 6.899 6.919 6.939

Total GHG emission (×109 kg CO2-eq)

Figure 5. Trade-off between economic and environmental objective functions for 𝜇2 (𝑥) ∈ [0.2, 0.4] production pathway 12 in 2024. On the other hand, solution E suggests that five and thirteen biorefineries with production pathway 12 should be founded by the year 2018 and 2021 respectively. As the demand of biodiesel continues to rise, six biorefineries with production pathway 12 and two with production pathway 14 will be additionally needed in 2024. This difference seen between the types of optimal production pathways chosen by each design can be justified by the fact that solution B focuses on the reduction of supply chain cost more than GHG emission. It determines the most economic pathways with lower GHG emission such as pathways 14 and 16 while solution E selects more environmental pathways such as pathway 12 to achieve lower GHG emission than solution B. The results also indicate that two optimal designs select different locations for biorefineries. In 2018, for example, locations 5, 6, 7, 8 and 10 are optimal locations in solution B compared to locations 6, 8, 9, 12 and 21 in solution E. 33 ACS Paragon Plus Environment


Figure 6. Optimal supply chain design for solutions B and E between 2018 and 2024. Consequently, the location and the type of pathway are highly influenced by changing the preferences in the objective functions. This can be justified by the fact that GHG emissions and the cost resulting from transportation of raw materials and final products is heavily correlated with the locations chosen for biorefineries. Another important aspect illustrated by Figure 6 is the clear importance of economy of scale. In other words, both designs almost prescribe maximum capacity level for biorefineries which leads to fewer biorefineries with higher capacities, that is to say a 34 ACS Paragon Plus Environment

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centralized supply chain structure. Therefore, economy of scale is of benefit to the proposed MOMBSC, while in some biomass supply chains, lower production cost of larger biorefineries as a result of economy of scale might be counteracted by the increased cost of transporting heavy raw materials and final products for longer distance.43 The numbers mentioned in Figure 6 follow the format of (location, production pathway, capacity). Three capacities have been considered for each biorefinery which are 400, 1000, and 2000 (ha) cultivation ponds. The capacities are adapted from the work by Lundquist et al.23 400 ha has been considered the base capacity as it is determined as the most efficient option out of the 5 scenarios in their work and then 1000 ha and 2000 ha are considered as multiple ponds options for higher capacities. 6.1.3. Sensitivity analysis As emphasized by many researchers,18, 44 there are a number of factors that play a significant role in determining the production cost of microalgal biodiesel, including: (1) growth rate, (2) conversion rate, (3) CO2 demand, (4) land cost, (5) water transportation cost and (6) CO2 transportation cost. To evaluate the effect of these factors, a sensitivity analysis was performed in this section which helps analyze how the total cost can be reduced to a competitive cost in comparison to traditional fossil fuels. The value of factors considered in the analysis are changed according to ranges shown in Table 4. The results illustrated in Figure 7 reveal that growth rate and lipid content have the greatest effect on the unit production cost. A positive change of 20% in these parameters, respectively, leads to reductions of around 14% and 19% in the optimal production cost, and a negative change of 20% in these parameters, respectively, increase the cost by over 10% and 15%. Based on this finding, more focus should be put on increasing microalgae lipid content than growth rate as there is a traditional trade-off between improvements in these two parameters.44 35 ACS Paragon Plus Environment


Table 4. Sensitivity analysis parameters. Scenario No

Sensitivity parameter

0

Base model

1+

Growth rate

+20

1-

Growth rate

-20

2+

Conversion rate

+20

2-

Conversion rate

-20

3+

CO2 demand

+20

3-

CO2 demand

-20

4+

Land cost

+20

4-

Land cost

-20

5+

Demand

+20

5-

Demand

-20

6+

water transportation cost

+20

6-

water transportation cost

-20

7+

CO2 transportation cost

+20

7-

CO2 transportation cost

-20

Variation range (%)

Land cost constituting a high proportion of the unit cost is the next important parameter which can be considered as one of the significant cost reduction potentials. For example, a 20% reduction in land cost causes a change of approximately 10% in the unit cost. Accordingly, the government can help make microalgae biodiesel cost-competitive by offering low-cost land for microalgae production. Among the other parameters evaluated, the effect of change in water and CO2 transportation cost is noticeable as they reduce the unit cost by around 4% and 5% respectively. This suggests that future waste water treatment stations and power plants should be constructed 36 ACS Paragon Plus Environment

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4.5 4 3.5

Unit cost ($/liter)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 2.5 2 1.5 1 0.5 0 -0.5 -1

0

1+

1-

Capital costs

2+

2-

3+

Operation costs

3-

Revenue

4+

4-

Land costs

5+

5-

6+

6-

Other costs

Figure 7. Results of the sensitivity analysis. near locations with high average temperature and solar irradiance which is suitable for microalgae production. Finally, the unit cost is less sensitive to change in nitrogen and phosphorus requirements which indicates the proposed MO-MBSC does not depend on use of expensive fertilizers heavily because nitrogen and phosphor requirements can be met by waste water nutrients and residues after anaerobic digestion as a source of nutrients. This suggests that future waste water treatment stations and power plants should be constructed near locations with high average temperature and solar irradiance which is suitable for microalgae production. Finally, the unit cost is less sensitive to change in nitrogen and phosphor requirements which indicates the proposed MO-MBSC does not depend on use of expensive fertilizers heavily because nitrogen and phosphor requirements can be met by waste water nutrients and residues after anaerobic digestion as a source of nutrients.



As stated previously, one of the advantages of the MO-MBSC is satisfying the water requirements through various water sources (i.e., fresh, brackish, and waste water) to address the concern of high water consumption of microalgae production which raises the issue of sustainability. To evaluate the impact of using various water sources instead of only fresh water on the unit cost, one of these sources is considered in each iteration and the model is forced to use it by replacing the availability parameters of the other two sources with zero, then the amount of water requirement (𝑚𝑤) is changed by ±20 and the model is run again. The result of this experiment along with basic model which can use all sources without restriction are shown in Figure 8. 3.4 3.3

Unit cost ($/liter)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.2 3.1 3 2.9 2.8 -20% Freshwater only

basic case Brackishwater only

20% Wastewater only

Combined

Figure 8. Impact of individual use of different water sources on unit cost. At first sight, it can be clearly seen that sole use of fresh and brackish water increase the unit cost much more than individual use of waste water. This is because waste water not only provides the water required to grow microalgae, but it also reduces the need of fertilizer which accounts for a high proportion of production cost. In addition, use of wastewater for algae cultivation would 38 ACS Paragon Plus Environment

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reduce the GHG emissions and also the cost associated with its treatment in waste water treatment plants by assimilating nutrients, disinfecting the waste water, and reducing the amount of phosphorus and ammonia emitted to the air.45 Another point is that the effect of sole use of fresh water on the unit cost is bigger than that of brackish water which is due to the higher price of fresh water than brackish water. The results also indicate that the difference between unit costs becomes larger with increase in water requirement factor. This highlights the importance of using various water sources in regions where microalgae need more water for growth. Therefore, besides the fact that the combined use of fresh, brackish and waste water reduces the barriers of large scale production due to the limited fresh water resources, it can be considered as one of important cost reduction potentials.

7. Conclusion The present study develops a comprehensive algal biofuel supply chain multi objective model for a sustainable biodiesel production. The model demonstrates that environmental factors (i.e. GHG emission) can be considered without compromising the main objective of cost competitiveness drastically. As illustrated, a 420,000-ton reduction in GHG emission (i.e. 5% from point A to B) can be achieved with 15% increase in the total supply chain cost which is noticeable considering the new challenges the world is facing such as global warming. This also addresses plans, such as RFS, established by EISA which mandate at least 50% reduction in GHG emission in production of biofuels in comparison to that of their petroleum counterparts. This study also provides guidelines for future research endeavors such as focusing on lipid content improvement which would offer more economic benefits than focusing on productivity improvement as typically there is a tradeoff between these two improvements in reality. Moreover, the benefits of using multiple water resources in the algal biofuel supply chain networks were shown and it can be 39 ACS Paragon Plus Environment


concluded that the use waste water can reduce the sensitivity of the unit cost to the availability and cost of fertilizers that are of great importance in the supply chains not utilizing waste water. As for future improvements, a thorough GIS analysis for candidate facility locations and resources would help the applicability and reliability of the solutions offered. It was observed that the locations play a major role in the optimality of different scenarios which highlights the benefits of utilizing more precise locating tools like GIS. Moreover, assessing the feasibility of utilizing brownfields for biorefinery foundation would help the literature as land cost was amongst the factors playing a significant role in production cost. In addition, a non-deterministic model capturing the uncertainties of the nascent algal biofuel industry would be a meaningful improvement of the current study. Due to the lack of information on different factors of the algal biofuel supply chain network, a robust optimization approach would be recommended as opposed to stochastic programming which requires a well-collected data base of all influential factors.


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ASSOCIATED CONTENT Supplemental Data Values of input parameters used in the case study: CO2 resources (Table 1 and S2), fresh water resources (Table 2 and S3), wastewater resources (Table 3 and S4)), brackish water resources (S5), nitrogen resources (Table 4 and S6), phosphorus resources (Table 5 and S7), biorefinery locations (Table 6 and S8), capital and transportation costs calculations (S9)

Corresponding Author E-mail: [email protected], Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ABBREVIATIONS EISA, Energy Independence and Security Act; RFS, Renewable Fuel Standard; GHG, Green House Gas; DOE, United States Department Of Energy; BSC, Biomass Supply Chain; BSCND, Biomass Supply Chain Network Design; MILP, Mixed Integer Linear Program; GWP, Global Warming Potential; AHP, Analytical Hierarch Process; MO-MBSC, Multi Objective Microalgae Biofuel Supply Chain; MOMP, Multi Objective Mathematical Programming;



Nomenclature Indices 𝑜

Index of CO2 sources

𝑓

Index of fresh water sources

𝑤

Index of waste water sources

𝑘

Index of brackish water sources

𝑛

Index of nitrogen sources

ℎ

Index of phosphorus sources

𝑟

Index of other raw material types

𝑠𝑟

Index of sources of raw material type 𝑟

𝑙

Index of possible locations for biorefineries

𝑝

Index of production pathways at biorefineries

𝑦

Index of biodiesel types

𝑐

Index of capacity options for biorefineries

𝑔

Index of consumption market of glycerin

𝑏

Index of consumption market of biodiesel

𝑡

Index of time stages

Parameters 𝑎𝑜𝑜𝑡

Available CO2 at source 𝑜 at time stage 𝑡

𝑎𝑓𝑓𝑡

Available fresh water at source 𝑓 at time stage 𝑡

𝑎𝑤𝑤𝑡

Available waste water at source 𝑤 at time stage 𝑡

𝑎𝑘𝑘𝑡

Available brackish water at source 𝑘 at time stage 𝑡

𝑎𝑛𝑛𝑡

Available nitrogen at source 𝑛 at time stage 𝑡

𝑎ℎℎ𝑡

Available phosphorus at source ℎ at time stage 𝑡

𝑎𝑟𝑠𝑡𝑟

Available raw material type 𝑟 at source 𝑠𝑟 at time stage 𝑡

𝑡𝑜𝑜,𝑙

Purchase and transportation cost of CO2 from source 𝑂 to biorefineries 𝑙

𝑡𝑓𝑓,𝑙

Purchase and transportation cost of fresh water from source 𝑓 to biorefineries 𝑙


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𝑡𝑤𝑤,𝑙

Purchase and transportation cost of waste water from source 𝑤 to biorefineries 𝑙

𝑡𝑘𝑘,𝑙

Purchase and transportation cost of brackish water from source 𝑘 to biorefineries 𝑙

𝑡𝑛𝑛,𝑙

Purchase and transportation cost of nitrogen from source 𝑛 to biorefineries 𝑙

𝑡ℎℎ,𝑙

Purchase and transportation cost of phosphorus from source ℎ to biorefineries 𝑙

𝑡𝑟𝑠𝑟 ,𝑙

Purchase and transportation cost of raw material type 𝑟 from source 𝑠𝑟 to biorefineries 𝑙

𝑡𝑔𝑙,𝑔

Transportation cost of glycerin from biorefineries 𝑙 to market 𝑔

𝑡𝑏𝑙,𝑏

Transportation cost of biodiesel from biorefineries 𝑙 to market 𝑏

𝑡 𝑐𝑐𝑙,𝑝,𝑐

Annualized capital cost of biorefinery 𝑙 with production pathway 𝑝 and capacity option 𝑐 at time stage 𝑡

𝑡 𝑝𝑐𝑦,𝑙,𝑝

Unit production cost of biodiesel type 𝑦 at biorefinery 𝑙 with production pathway 𝑝 at time stage 𝑡

ℎ𝑏𝑦,𝑙

Unit inventory holding cost of biodiesel type 𝑦 at biorefinery 𝑙

ℎ𝑔𝑙

Unit inventory holding cost of glycerin at biorefinery 𝑙

𝑟𝑚𝑟,𝑦,𝑝

Requirement of raw material type 𝑟 to produce biodiesel type 𝑦 by pathway 𝑝

𝑐𝑏𝑦,𝑝

Conversion rate of biomass to biodiesel type 𝑦 under production pathway 𝑝

𝑐𝑔𝑝

Conversion rate of biomass to glycerin under production pathway 𝑝

𝜑𝑙,𝑝,𝑐

maximum amount of biomass produced at biorefinery 𝑙 with production pathway 𝑝 and capacity option 𝑐

𝑑𝑏𝑏𝑡

Demand for biodiesel at market 𝑏 at time stage 𝑡

𝑑𝑔𝑔𝑡

Maximum amount of glycerin which can be sold at market 𝑔 at time stage 𝑡

𝑝𝑟𝑠𝑡𝑟

Price of raw material 𝑟 at source 𝑠𝑟 at time stage 𝑡

𝑡 𝑝𝑏𝑦,𝑏

Price of biodiesel type 𝑦 at market b at time stage 𝑡

𝑝𝑔𝑔𝑡

Price of glycerin at market 𝑔 at time stage 𝑡

𝑠𝑏𝑦,𝑙

Maximum storage capacity of biodiesel type 𝑦 at biorefinery 𝑙

𝑠𝑔𝑙

Maximum storage capacity of glycerin at biorefinery 𝑙

𝑚𝑜

CO2 requirement for production one unit of biomass

𝑚𝑤

water requirement for production one unit of biomass

𝑚𝑛

nitrogen requirement for production one unit of biomass



𝑚ℎ

phosphorus requirement for production one unit of biomass

𝑛𝑎

Amount of nitrogen available per unit of waste water

ℎ𝑎

Amount of phosphorus available per unit of waste water

𝑚𝑟,𝑝

raw material 𝑟 requirement for processing one unit of biomass by production pathway 𝑝

𝐺𝐶𝑜,𝑙

GHG emissions of production and transporting one unit of CO2 from source 𝑜 to biorefinery 𝑙

𝐺𝐹𝑓,𝑙

GHG emissions of production and transporting one unit of fresh water from source 𝑓 to biorefinery 𝑙

𝐺𝑊𝑤,𝑙

GHG emissions of production and transporting one unit of waste water from source 𝑤 to biorefinery 𝑙

𝐺𝐾𝑘,𝑙

GHG emissions of production and transporting one unit of brackish water from source 𝑘 to biorefinery 𝑙

𝐺𝑁𝑛,𝑙

GHG emissions of production and transporting one unit of nitrogen from source 𝑛 to biorefinery 𝑙

𝐺𝐻ℎ,𝑙

GHG emissions of production and transporting one unit of phosphorus from source ℎ to biorefinery 𝑙

𝐺𝑅𝑠𝑟,𝑙

GHG emissions of production and transporting one unit of raw material 𝑟 from source 𝑠𝑟 to biorefinery 𝑙

𝐺𝐸𝑙,𝑝,𝑐

GHG emissions of establishing biorefinery 𝑙 with production pathway 𝑝 and capacity 𝑐

𝐺𝑃𝑙,𝑡

GHG emissions per unit quantity of biomass cultivated at biorefinery 𝑙 at time stage 𝑡

𝐺𝑆𝑙

GHG emissions of storing unit quantity of biodiesel at biorefinery 𝑙

𝐺𝐺𝑙

GHG emissions of storing unit quantity of glycerin at biorefinery 𝑙

𝐺𝐵𝑦,𝑝

GHG emissions of producing unit quantity of biodiesel using production pathway 𝑝

𝐺2𝑙,𝑔

GHG emissions of transporting one unit of glycerin from biorefinery 𝑙 to market 𝑔

𝐺3𝑙,𝑏

GHG emissions of transporting one unit of biodiesel from biorefinery 𝑙 to market 𝑏

Decision variable 𝑡 𝑥𝑜𝑜,𝑙

Flow of CO2 from source 𝑜 to biorefinery 𝑙 at time stage 𝑡

𝑡 𝑥𝑓𝑓,𝑙

Flow of fresh water from source 𝑓 to biorefinery 𝑙 at time stage 𝑡

𝑡 𝑥𝑤𝑤,𝑙

Flow of waste water from source 𝑤 to biorefinery 𝑙 at time stage 𝑡

𝑡 𝑥𝑘𝑘,𝑙

Flow of brackish water from source 𝑘 to biorefinery 𝑙 at time stage 𝑡


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𝑡 𝑥𝑛𝑛,𝑙

Flow of nitrogen from source 𝑛 to biorefinery 𝑙 at time stage 𝑡

𝑡 𝑥ℎℎ,𝑙

Flow of phosphorous from source ℎ to biorefinery 𝑙 at time stage 𝑡

𝑥𝑟𝑠𝑡𝑟,𝑙

Flow of raw material 𝑟 from source 𝑠𝑟 to biorefinery 𝑙 at time stage 𝑡

𝑡 𝑥𝑏𝑦,𝑝,𝑙,𝑏

Flow of biodiesel type 𝑦 from biorefinery 𝑙 with production pathway 𝑝 to market 𝑏 at time stage 𝑡

𝑡 𝑥𝑔𝑙,𝑔

Flow of glycerin from biorefinery 𝑙 to market 𝑔 at time stage 𝑡

𝑡 𝑖𝑏𝑦,𝑙

Inventory level of biodiesel type 𝑦 at location 𝑙 at time stage 𝑡

𝑖𝑔𝑙𝑡

Inventory level of glycerin at location 𝑙 at time stage 𝑡

𝑡 𝑈𝑙,𝑝,𝑐

1 if a biorefinery with capacity 𝑐 and production pathway 𝑝 is opened at location 𝑙 at time stage 𝑡; 0 otherwise

𝑍𝐹𝑙

1 if fresh water is chosen for biorefinery 𝑙; 0 otherwise

𝑍𝑘𝑙

1 if brackish water is chosen for biorefinery 𝑙; 0 otherwise



For Table of Contents Only


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An environmental and economic optimization of Algal Biofuel Supply

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