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Economic and Environmental Life Cycle Optimization of Noncooperative Supply Chains and Product Systems: Modeling Framework, Mixed-Integer Bilevel Fractional Programming Algorithm, and Shale Gas Application Jiyao Gao and Fengqi You* Robert Frederick Smith School of Chemical Engineering and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: In this work, we propose a general modeling framework for the economic and environmental life cycle optimization of supply chains and product systems with noncooperative stakeholders. This framework is based on the functional-unit-based life cycle optimization approach and the leader−follower Stackelberg game structure to capture the decentralized feature and noncooperative relationships between multiple stakeholders across the product life cycle. The leader enjoys the priority of decision-making to optimize both its own economic performance and the life cycle environmental performance of the supply chain or product system. After the observation of leader’s decisions, the follower takes actions correspondingly to optimize its own economic performance. The resulting problem is formulated as a mixed-integer bilevel fractional program to account for conflicting objectives and interactions among different stakeholders. Design and operational decisions for both leader and follower are taken into consideration, including facility allocation, technology selection, production planning, transportation and storage scheduling, etc. To tackle the computational challenge of the resulting mixed-integer bilevel fractional programs, a tailored solution algorithm is developed based on a parametric algorithm and a projection-based reformulation and decomposition method. An application to a well-to-wire Marcellus shale gas supply chain is presented to demonstrate the applicability of the proposed life cycle optimization modeling framework and the efficiency of the solution algorithm. KEYWORDS: Life cycle optimization, Sustainability, Noncooperative, Shale gas, Game theory

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INTRODUCTION In the past decade, sustainable design and operations of supply chains and product systems considering both economic and environmental performance have become increasingly important in industries.1−4 Inspired by the life cycle analysis (LCA) approach and multiobjective optimization method, life cycle optimization methods are proposed to for sustainability optimization from a life cycle perspective.5−7 A functionalunit-based life cycle optimization approach is further developed, which provides a systematic approach to optimize the life cycle economic and environmental performance of supply chains and product systems.8 Such a product-centric life cycle optimization approach has proved its effectiveness toward more cost-effective and environmentally sustainable designs compared with the traditional life cycle optimization approaches.9−12 To the best of our knowledge, all existing studies on life cycle optimization rely on centralized models, which assume that all the components in a supply chain or a product system operate in a cooperative way toward a universal objective.13,14 However, © XXXX American Chemical Society

some life cycle optimization problems may involve multiple noncooperative stakeholders across the product life cycle. Different life cycle stages of a certain product, such as feedstock production and acquisition, manufacturing, transportation, and end use of final products, are normally managed in a decentralized way by different stakeholders. Besides, each stakeholder may pursue distinct objectives, which leads to conflicts of interest and compromised strategies in reality. As a consequence, the optimal strategies obtained from a centralized life cycle optimization model may be overly optimistic or even infeasible under a noncooperative environment.15−19 Existing studies on optimization of noncooperative supply chains and product systems solely focus on the economic performance and fail to take into account the corresponding environmental performance, especially from a life cycle perspective.20−25 To Received: January 1, 2017 Revised: February 22, 2017 Published: February 28, 2017 A

DOI: 10.1021/acssuschemeng.7b00002 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering

economic and environmental performance, making it capable of addressing conflict of interest from different criteria and different stakeholders. Second, functional-unit-based fractional objectives are employed, which results in a complex MIBLFP problem and is expected to provide more sustainable solutions than its linear counterparts. More importantly, a drastically different application is considered investigating the interactions between shale gas producers and power generation sector in a noncooperative shale gas supply chain. Special features such as third parties and adoption of CCS technologies are also taken into account. To illustrate the applicability of proposed modeling framework and solution algorithm, a case study based on Marcellus shale gas supply chain is considered. The major novelties of this work are summarized below: • A novel life cycle optimization framework for the sustainable design and operations of supply chains and product systems with noncooperative stakeholders; • A specific case study on life cycle optimization of a noncooperative shale gas supply chain in Marcellus shale play; • Comprehensive comparisons with centralized life cycle optimization and existing LCA results. The rest of this article is organized as follows. The General Problem Statement section formally states the modeling framework for life cycle optimization of noncooperative supply chains and product systems. The resulting MIBLFP model formulation and tailored solution algorithm are given in the Model Formulation and Tailored Solution Algorithm section. To illustrate and validate the proposed modeling framework and solution algorithm, an application to the life cycle optimization of a well-to-wire shale gas supply chain is presented and compared with the existing LCA studies in the next section. Conclusions are drawn at the end.

investigate the impact of noncooperative environment and the decentralized feature on life cycle optimization and to better capture the corresponding life cycle performance, it is important to model and analyze explicitly the noncooperative feature in the life cycle optimizations of supply chains and product systems. The objective of this paper is to propose a general life cycle optimization framework for noncooperative supply chains and product systems. To address this challenge, we couple the sophisticated game theory models with the state-of-the-art life cycle optimization approaches. Because in typical supply chains and product systems, some stakeholders (e.g., customer in a buyer’s market, supplier in a seller’s market, large wholesaler, etc.) possess certain power over other stakeholders (e.g., supplier in a buyer’s market, customer in a seller’s market, small retailers, etc.), we need to choose a game theory model that can capture the priority feature of stakeholders in the decision making process.26 There are a number of game theory models that are widely applied in the noncooperative supply chain optimization problems, including the Cournot model, the Bertrand model, and the Stackelberg game.27−29 However, both Cournot model and Bertrand model are commonly applied in modeling the competition among stakeholders with simultaneous decisions (e.g., different manufacturers compete for the market with same products). By contrast, the Stackelberg game enables us to capture the different roles of players in a noncooperative system.29 This advantage also leads to its wide application in noncooperative optimization problems.25,30,31 Therefore, the Stackelberg game model is adopted in this study to model the noncooperative feature of the supply chain across the product life cycle. Different from traditional life cycle optimization models, this framework takes a noncooperative perspective on life cycle optimization by explicitly considering the objectives of different stakeholders. Following the Stackelberg game, two types of stakeholders, namely a leader and a follower, are identified in the optimization problem.25,32 The leader enjoys the priority of making decisions and has the knowledge of potential reactions of the follower. Because of the essential position and information advantage, the leader senses more responsibility of proposing sustainable strategies in terms of its economic and life cycle environmental performance. Once the leader’s decisions are made, the follower reacts rationally to optimize its own decisions. Because of the limited information, the follower is mainly driven by its economic objective. Although it is possible to consider a common environmental objective for both the leader and the follower, the resulting problem will degrade to a single-level optimization problem with identical solution to a centralized model due to the lack of conflict between different stakeholders. The conflicting objectives from different stakeholders will eventually lead to a Stackelberg equilibrium.29 This modeling framework is general enough to allow for the consideration of both design and operational decisions for the leader and the follower. Because of the sequential decision-making process, the resulting problem can be formulated as a mixed-integer bilevel linear fractional program (MIBLFP), which cannot be solved directly using any off-the-shelf optimization solvers.33 Therefore, we present a tailored solution strategy integrating the parametric algorithm with a projection-based reformulation and decomposition algorithm to tackle this computational challenge.34 Notably, although a similar bilevel structure is employed in previous studies,25,32 this modeling framework exceeds in two main aspects: First, the perspective is extended to life cycle

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GENERAL PROBLEM STATEMENT In this section, we formally state the life cycle optimization framework of noncooperative supply chains and product systems. This framework integrates the four phases of a classical LCA methodology, namely the goal and scope definition, inventory analysis, impact assessment, and interpretation,35 with a noncooperative game-based multiobjective optimization model. It provides a systematic way to identify the optimal strategy that achieves the best economic and environmental performance across the life cycle in the noncooperative environment. The details of this framework are introduced in the following subsections. Goal and Scope Definition. In the first phase, the basic settings and features of the LCA, including the goal of the study, system boundaries, and functional unit, are elucidated. The common goal of an LCA study is to quantify the environmental impacts of design alternatives or to compare the environmental performance between different products. However, in the proposed framework, the goals are to determine the optimal design and operational decisions and to investigate the life cycle economic and environmental performance of noncooperative supply chains and product systems. The system boundary of an LCA study covers the processes that contribute to the environmental impacts of a product. Typically, it consists of several life cycle stages, such as feedstock acquisition, product manufacturing, transportation and storage, end use of product, and waste disposal or recycling. According to the life cycle stages included, LCA B


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ACS Sustainable Chemistry & Engineering studies can be categorized into “cradle-to-grave”, “cradle-togate”, etc. A cradle-to-grave LCA covers the full life cycle of a product from the resource extraction (cradle) to the end use and disposal (grave). A cradle-to-gate LCA, however, is a partial version from the resource extraction (cradle) to the exit gate of product factory (gate), where the end use and disposal phases in the full life cycle of product are excluded. In this framework, because a noncooperative supply chain or product system with different stakeholders is considered, the system boundary needs to reflect the decentralized feature such that processes corresponding to different stakeholders can be clearly identified and included. The functional unit is another key element of LCA. It is a measure of the function of the studied product system and it provides a reference to which the inputs and outputs can be related. Therefore, the same functional unit enables the comparison of two essentially different systems. In the proposed framework, the functional unit is incorporated in the objective function to optimize the life cycle economic and environmental performance associated with one functional unit. More importantly, function unit provides a product-centric perspective and its definition is largely dependent on the actual roles of stakeholders that are making sustainable design decisions. For instance, from a producer’s perspective the functional unit can be chosen as the one unit of product produced. However, for a customer, unit amount of functionality provided by the product is a more appropriate choice of functional unit. Inventory Analysis. In this second phase, the life cycle inventory (LCI) is established to describe the mass and energy input−output relationships of each process. A flow model is first constructed and illustrated with a flowchart, which consists of all the process blocks and corresponding input and output flows within the predefined system boundary. The input and output data of each process block are then collected based on the selected functional unit. In the life cycle optimization model, the mass and energy balance relationships of processes are formulated as mathematical constraints. Therefore, the LCI of a set of design and operational alternatives can be simultaneously evaluated. Moreover, when establishing the LCI, processes need to be linked with their corresponding stakeholders, and the input and output flows between two stakeholders require clear identification. The LCI lays the foundation of all the following steps. Impact Assessment. Impact assessment is the process of translating the LCI results into a selected set of environmental impact categories for further analysis. There are two types of impact categories: the midpoint impact categories and the end point impact categories. A midpoint impact category reflects the direct environmental impacts of interventions. Some commonly used midpoint impact categories include climate change, ozone depletion, acidification, eutrophication, etc. The end point impact categories go beyond the midpoint and evaluate the ultimate environmental impacts from interventions or midpoints to the areas of protection (e.g., human health, ecosystem diversity, and resource availability). The basic interventions, midpoint impact category, and end point impact category are connected with each other through corresponding environmental mechanisms. Based on the two types of environmental impact categories, there are midpoint-oriented methods, such as the one defined by the Handbook on Life Cycle Assessment,35 and end point-oriented methods, including the Eco-indicator 9936 and the state-of-the-art ReCiPe methods37

for life cycle environmental impact assessment. In this framework, the selected impact indicators are employed as the environmental objective function, which allows us to automatically quantify the environmental impacts of different design and operational decisions. Interpretation. Interpretation is the last phase in the classical LCA methodology, where the life cycle inventory or impact assessment results are summarized and discussed as a basis for conclusions, recommendations, and decision-making in accordance with the goal and scope definition. Based on the selected impact indicators, the environmental objectives associated with different stakeholders are defined. By solving the resulting multiobjective life cycle optimization problem, a set of Pareto-optimal solutions can be obtained that demonstrate the trade-offs between economic and environmental objectives as well as the conflicts of interest among distinct stakeholders. With a comprehensive analysis of the optimal solutions, we are able to evaluate the life cycle environmental impacts of noncooperative supply chains and product systems. In addition, more insights into the impacts of noncooperative environment on life cycle optimization can be obtained by comparing this optimization result with its centralized counterpart and existing LCA results. Life Cycle Optimization Model of Noncooperative Supply Chains and Product Systems. In this section, we present the life cycle optimization model for noncooperative supply chains and product systems. As mentioned above, in this study we choose the Stackelberg game as the illustrative game theory model. Two types of players are identified, namely the leader and the follower. The leader takes the leading role in the noncooperative supply chain or product system to pursue more sustainable strategies. Accordingly, the leader’s objectives are optimizing both its own economic performance and the life cycle environmental performance based on the predefined functional unit, LCI results, and environmental impact indicators. Specifically, the economic objective is to optimize the economics (e.g., minimize cost, maximize NPV, etc.) by generating one functional unit; the environmental objective is to minimize the life cycle environmental impacts per functional unit, which can be evaluated using either midpoint or end point environmental impact indicators. Meanwhile, the follower is only driven by economics to optimize its own economic objective. The system boundary covers all the processes related to the leader’s and the follower’s activities in this noncooperative supply chain across the product life cycle. Within this system boundary, the following data are considered as known information. • A set of candidate locations for feedstock supply sites, product manufacturing facilities, storage sites, and demand zones; • Technology and logistic options, including the types of feedstocks, transportation modes, alternative technologies, storage methods, and end uses; • Capacity constraints regarding availability of feedstock, productivity at manufacturing facilities, inventory level at storage sites, and demands of final products; • Time related parameters, including planning horizon of the project, length of time period considered, lead time of design and operational decisions, and discount rate; • Economic data, including feedstock procurement cost, capital investment for infrastructure construction, operation and maintenance (O&M) cost, transportation and C


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ACS Sustainable Chemistry & Engineering x u ∈ +mR , y u ∈ +mz

inventory cost, transfer price of products, penalty cost for purchase from external sources, tax payments, and government incentives; • Environmental impact data obtained from the basic LCI and selected impact indicators with corresponding characterization factors, including the data on feedstock acquisition, processing and manufacturing, transportation and inventory, product distribution; • Problem specific data, including the resource reserve, production efficiency, availability of facilities, conversion rate of technologies, composition of materials, reference capital cost, price fluctuation, and policy constraints. Notably, in addition to the above information shared by both the leader and the follower, the leader should know the rational behavior of the follower based on the leader’s decisions on its life cycle optimization problem. On the other hand, the leader’s decisions are considered as given information in the follower’s problem. Both the leader and the follower need to make their own design and operational decisions in the corresponding processes based on the information they have. Strategic decisions, such as technology selection, lead to distinct LCI results for that process. Other operational decisions, such as the production profile, result in different total life cycle environmental consequences. These decisions include, but are not limited to Design Decisions. • Locations and capacities of major facilities and corresponding infrastructure; • Selection of feedstock suppliers, processing or manufacturing facilities, storage units, end use customers, and associated transportation links; • Selection of feedstocks and products, processing or conversion technologies, and transportation methods. Operational Decisions. • Procurement planning of feedstocks; • Scheduling of processing and/or production; • Inventory planning; • Transportation activities; • Sales of final products.

where (xl, yl) solves: max TP follower = wRtx l + wZty l s. t. Q Rx u + Q Zy u + PRx l + PZy l ≤ s x l ∈ +nR , y l ∈ +nz

where UCleader denotes the leader’s economic performance per functional unit, such as the leader’s total cost divided by the corresponding quantity of the functional unit; UE denotes the life cycle environmental impacts associated with one functional unit throughout the supply chain across the product life cycle; and TPfollower denotes the follower’s economic indicator (e.g., total profit). xu and yu indicate the continuous variables and integer variables in the upper-level leader’s problem, respectively. Correspondingly, xl and yl indicate the continuous variables and integer variables in the lower-level follower’s problem, respectively. The constraints for both the leader and the follower can be classified into five types. • Mass balance constraints for LCI describe the relationships between the input and output streams of each node based on mass conservation of every species. • Environmental constraints link various activities across the product life cycle with their corresponding environmental impacts. • Economic constraints calculate the economic performance of different players based on their decisions, including the leader’s total cost and the follower’s total profit. • Capacity constraints describe the capacity limits of different activities, including supply availability, manufacturing capacity, transportation, inventory level, market demand, etc. • Logic constraints describe the logical relationships of activities and basic assumptions, especially those regarding infrastructure construction and technology selection for both leader and follower. Despite similar model structures, it is worth noting that the proposed bilevel modeling framework is essentially different from two-stage optimization models. In the bilevel optimization model, the upper-level problem and the lower-level problem are two individual optimization problems corresponding to two distinct decision makers. Both optimization problems need to be solved simultaneously instead of being solved sequentially to reach an optimum defined by Nash equilibrium. Moreover, because both integer and continuous variables are considered for the upper-level problem and the lower-level problem, the resulting problem is far more complex than traditional twostage optimization problems where integer variables only appear in the first stage. Tailored Global Optimization Algorithm. As mentioned above, the resulting problem is a multiobjective MIBLFP problem, which involves multiple fractional objective functions in the upper-level program of a typical mixed-integer bilevel linear program (MIBLP). Notably, MIBLP has been known to be intrinsically difficult to globally optimize. Because the feasible region of the upper-level program is partially dependent on the lower-level program, mixed-integer bilevel programs cannot be solved directly using any general-purpose optimization solver.38 Besides, an MIBLP involves continuous and

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MODEL FORMULATION AND TAILORED SOLUTION ALGORITHM Model Formulation. According to the problem statement in the previous section, a multiobjective, mixed-integer bilevel linear fractional programming (MIBLFP) model is developed to address the functional-unit-based life cycle optimization of supply chains and product systems with noncooperative stakeholders. A general form of this MIBLFP problem denoted as (P0) is presented as follows. Economic Objective: min UC leader =

cRtx u + cZty u + dRtx l + dZty l gRt x u + hRt x l

Environmental Objective: (P0) min UE =

eRtx u + eZty u + f Rt x l + f Zt y l gRt x u + hRt x l

s. t. AR x u + AZ y u + BR x l + BZ y l ≤ r D


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Figure 1. Pseudocode of the tailored solution algorithm.

global optimum. Thus, an efficient projection-based reformulation and decomposition algorithm is considered.34 This solution algorithm is guaranteed to converge in finite number of iterations. In Figure 1, we provide a pseudocode for the detailed steps. We note that Iterout and Iterin are the iteration counting numbers for the outer loop and inner loop, respectively. Tolout is the optimality gap for the parametric algorithm in the outer loop. ξ is the optimality gap for the inner loop reformulation and decomposition algorithm. UB and LB are the upper bound and lower bound for the inner loop, respectively. Θ* and θ are both auxiliary parameters to record the optimal objective values. YL is a subset of integer variables for the lower level problem. This solution algorithm is based on the general form of proposed modeling framework, and there are no specific assumptions. As long as the problem can be formulated into an MIBLFP as given in (P0), this tailored solution algorithm would be applicable.

integer variables in both upper-level and lower-level problems, so it is challenging to be directly reformulated into a single-level program.33,39 The fractional objectives add more complexity to the MIBLFP problem. Because of its combinatorial natural and pseudoconvexity, the upper-level program, identified as a mixed-integer linear fractional program with an embedded lower-level mixed-integer linear program (MILP), can be computationally intractable.40,41 To tackle this computational challenge, we present a tailored solution algorithm targeting the special features of this MIBLFP problem, namely the fractional objectives and mixed-integer bilevel linear program. Specifically, two state-of-the-art algorithms, including a parametric algorithm40−42 and a projection-based reformulation and decomposition algorithm,34 are coupled together to optimize globally the challenging MIBLFP problems. The computational challenge resulted from fractional objectives can be circumvented by applying a parametric algorithm. Specifically, the fractional objective function is reformulated into a linear form as the difference between the numerator and the denominator multiplied by an auxiliary parameter q, denoted as F(q). When F(q*) = 0, the corresponding optimal solution of the reformulated program is identical to the original one.31 In each iteration of the parametric algorithm, we need to solve a MIBLP problem to its

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APPLICATION TO THE WELL-TO-WIRE LIFE CYCLE OPTIMIZATION OF A NONCOOPERATIVE SHALE GAS SUPPLY CHAIN To illustrate the applications of the proposed life cycle optimization framework and the corresponding tailored solution algorithm, we address the life cycle optimization of a E


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Figure 2. Illustrative shale gas supply chain superstructure.

LCA, and the most up-to-date data from U.S. databases are prioritized. These LCI data are further aggregated to match the decision variables of the leader and the follower, so that the direct environmental impacts can be directly linked with the interactions of different stakeholders in the noncooperative shale gas supply chain. Detailed input data are provided in the Supporting Information.43,45,52,55−59 Impact Assessment. In this study, the impact category to assess the life cycle environmental performance of shale gas is dedicated to midpoint indicator greenhouse gas (GHG) emissions, which is the most widely used one in related shale gas LCA studies.45,52,56,60 To compare our results with existing studies, the GHG emissions are calculated in units of CO2equivalents as specified by the International Panel on Climate Change (IPCC).61 Specifically, a 100-year GWP (25 kg CO2eq/kg CH4, 298 kg CO2-eq/kg N2O, and 22 800 kg CO2-eq/kg SF6) is considered following the previous LCA studies.55−57 Although other environmental issues, such as those regarding water footprint and water contamination are of great importance as well, they are not considered in this study mainly due to the following reasons. First, most of the waterrelated environmental concerns are mainly restricted to the shale gas production phase, especially in the hydraulic fracturing and production processes. Considering the well-towire system boundary in this study, the water-related metrics are not the best choice. Second, most existing shale gas supply chain models take either the water consumption or water treatment cost as the objective function.62−64 However, the water management cost is much less significant compared with other cost incurred in the shale gas development. On the other hand, the environmental impacts associated with water in shale gas development are still challenging to quantify and involve a high level of uncertainty. A well-recognized systematic approach has yet to be developed. Therefore, although the noncooperative life cycle optimization framework is general enough and capable of handling any impact categories, we focus on the impact indicator of life cycle GHG emissions for this case study to be consistent with most shale gas LCA studies.45,52,56,60 Interpretation. The interpretation phase is combined with solving the following noncooperative shale gas life cycle optimization model. Through a detailed analysis of the optimal results and comprehensive comparisons with existing literature, we target on providing insight and strategic recommendations

well-to-wire Marcellus shale gas supply chain in a noncooperative environment in this section. Specific Problem Statement. Goal and Scope. The primary goal of this case study is to investigate the impact of noncooperative environment on the optimal life cycle economic and environmental performance of a shale gas supply chain. Specifically, a well-to-wire life cycle of Marcellus shale gas from the well sites to the generation of electricity at power plants is considered, as shown in Figure 2.43−46 The system boundary of this well-to-wire life cycle of shale gas covers three major life cycle stages: shale gas production, shale gas processing, and end use of shale gas.43,45,47−49 The shale gas production stage involves all the development activities of the shale gas wellhead, including the predrilling phase, the drilling phase, and the production phase. The shale gas processing stage covers all the activities regarding shale gas gathering, processing, storage, marketing, and distribution. The shale gas goes through a set of processing plants where shale gas can be further separated.50 After the processing plant, impurities are removed, and two major products known as “pipeline-quality” natural gas and natural gas liquids (NGLs) are obtained. In the end use stage, we focus on the electricity generation at gas turbine combined cycle (GTCC) power plants.51−53 Other customers, including the industrial, commercial, and residential customers, are considered as third parties in this noncooperative shale gas supply chain.54 In this study, because we consider a well-to-wire life cycle of shale gas and focus on the electric power generation using shale gas, we employ a functional unit of one Megawatt-hour (MWh) of electric power generated following most shale gas LCA studies.43,45,55 Accordingly, both the economic and life cycle environmental objectives are evaluated based the functional unit and formulated as fractional functions. Inventory Analysis. The life cycle inventory analysis is conducted based on the predefined life cycle settings. The mass and energy relationships are determined for processes and activities throughout the shale gas life cycle, including well drilling, shale gas production, gathering, processing, transmission, and end use. In this phase, we need to build up the LCI that is compatible to the life cycle optimization model of a noncooperative shale gas supply chain. The first step is to identify the major design and operational decisions for both the leader and the follower. Next, the basic LCI data are gathered based on existing literature and databases of Marcellus shale gas F


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• Amount of natural gas to purchase from each shale gas processing plant; • Amount of conventional natural gas to purchase from external sources. The decisions are made according to the following information: • Local demand and transfer price of natural gas; • Emissions data on the end use of natural gas; • Techno-economic data regarding different CCS technologies. The shale gas producer is the follower in this game that reacts rationally according to the leader’s decisions. The follower’s decisions include: • Drilling schedule at each shale site; • Selection of location and capacity for each potential processing plant; • Amount of raw shale gas transported to each existing processing plant; • Production profile at each processing plant; • Amount of processed natural gas transported to each power plant; • Amount of processed natural gas sold to other types of customers. These decisions are made based on the following information: • Potential shale wells that can be drilled at each shale site; • Estimated ultimate recovery (EUR) of each shale well; • A set of potential processing plants that can be built; • Planning horizon of this project; • Cost data on capital investment, operations and maintenance (O&M); • Emissions data on all the operations in this supply chain; • Demand of natural gas at each power plant; • Demand of natural gas from other types of customers. With full knowledge of this shale gas supply chain, the power plants tend to care about not only its life cycle economic performance but also its life cycle environmental performance embedded in its final products, namely electricity generated from shale gas. Accordingly, in this case study the functional unit is defined as one MWh of electricity generated from shale gas. Thus, the objectives of the power plants include: • Minimizing the total cost for building and operating power plants to generate one MWh electricity in this shale gas supply chain, also known as the levelized cost of electricity (LCOE);71 • Minimizing the life cycle GHG emissions for generating one MWh electricity. Notably, in addition to transforming the environmental objective into a constraint in the resulting optimization problem, a carbon price can also be employed to convert the GHG emissions into monetary units. Correspondingly, the leader’s problem becomes a single objective optimization problem, although the modeling framework remains a bilevel mixed-integer optimization problem due to the noncooperative structure of the supply chain. Meanwhile, because of limited information, the shale gas producer takes action after the power plants and is only driven by its own profitability. Thus, after the realization of the power plants’ decisions, the producer reacts accordingly to optimize its own objective, which is • Maximizing producer’s net present value (NPV).

on the life cycle economic and environmental optimization of a noncooperative shale gas supply chain. Details of the analysis and discussion are provided in the Results and Discussion section. In the following, we present the modeling details of this noncooperative life cycle optimization model. Life Cycle Optimization Model of Noncooperative Shale Gas Supply Chains. On the basis of the predefined life cycle of shale gas, we formally state this life cycle optimization model of noncooperative shale gas supply chains. Compared with the existing models for shale gas supply chain,10,65,66 we highlight three major developments: (1) Instead of relying on a centralized model optimizing the overall life cycle performance, we introduce a game theory model to address the noncooperative feature of the shale gas life cycle. Conflicts of interest and interactions among different stakeholders are taken into account. (2) Potential applications of CCS technologies are considered to mitigate the life cycle GHG emissions of electricity generated by shale gas. (3) Third parties are taken into account to provide a full picture of the shale gas life cycle, including the external suppliers of natural gas and other end use customers of shale gas in addition to power plants. In a shale gas supply chain, an intimate cooperation can be observed between shale gas operators and processors, which correspond to well development activities and shale gas processing activities, respectively.50,67 For instance, according to the U.S. Energy Information Administration (EIA), the extensive shale gas development has led to the construction of several large processing plants, as well as the expansion of existing plants.68 Besides, the processing service is normally provided through different types of contracts.69 Therefore, in this study we consider the shale gas operator and processor as a cooperative whole based on fee-based processing contracts, managed by an incorporated stakeholder and named as the producer.69,70 The producer makes decisions related to all the shale sites, processing plants, pipeline networks, and corresponding infrastructure involved in the upstream and midstream shale gas supply chain. In this study, we focus on the “well-to-wire” life cycle of shale gas, and the downstream decision maker is limited to power plants.43−45 As the largest consumer of natural gas that accounts for more than 30% of the total natural gas consumption in the U.S., power plants also contribute the most GHG emissions (up to 78%) in the full life cycle of shale gas.43 We name the power generation sector as the customer in this supply chain. The power plants need to make decisions on not only the procurement plan of natural gas from the producer but also proper CCS technology selection for emissions abatement. Notably, other players involved in the shale gas supply chain, including the external supplier of natural gas and other types of natural gas customers, are considered as third parties in this model.24 Considering the sufficient shale gas supply and relatively low price of shale gas, a buyer’s market is considered here, so the customer in this specific application (i.e., the power plants in this supply chain) acts as the leader and enjoys the decision-making priority. However, it is worth noting that the proposed modeling framework is general enough, and its application is not restricted to the specific selection of the leader. In this well-to-wire shale gas supply chain, the customer’s decisions include: • Decisions on the adoption of CCS technology and the corresponding technology selection in the existing power plants; G


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ACS Sustainable Chemistry & Engineering In this case study, a total of 20 potential shale sites72 are taken in to account, each of which allows for drilling of up to 4−8 shale wells.73 The EUR of each shale well is estimated based on existing data reported in Marcellus shale play.74,75 There are 3 potential conventional shale gas processing plants,67 with 3 capacity ranges considered for each of them. Five GTCC power plants are considered.52,76 For each power plant, they can choose whether or not to incorporate a CCS technology into the original processes. We consider 3 different CCS technologies for power plants, including two postcombustion capture technologies and one oxyfuel combustion process.77,78 The postcombustion processes separate CO2 from combustion exhaust gases using a liquid solvent or other separation methods. Two postcombustion capture technologies considered here are the Fluor’s Econamine FG PlusSM process that uses monoethanolamine (MEA) solvent, and MHI’s KS-1 process that uses a proprietary, sterically hindered amine solvent, although other CCS technologies could be easily incorporated into the model.79−81 Because of similar processes, these two postcombustion technologies share close performance in terms of GHG emissions reduction and economic performance. The oxyfuel combustion processes use oxygen rather than air for combustion of fuel, which results in an exhaust gas that can be easily separated to produce a high purity CO2 stream.82 The oxyfuel combustion process offers the most effective way in mitigating GHG emissions. However, the corresponding capital and operating cost are the highest, and it results in the lowest net thermal efficiency in power generation. The total planning horizon is 10 years, which is close to the real productive life of Marcellus shale gas wells.83−85 All detailed input data are based on existing literature and are provided in the Supporting Information. Notably, we have taken into account the energy consumption from all the steps of CCS for the GHG emissions of power generation with CCS technologies. Because of the development of performance and regulation standards, some of the assumptions applied in the data sources may need to be updated according to the latest practice. Nevertheless, the proposed framework and solution method are general enough to be easily adapted to these updates. Additionally, although uncertainty is ubiquitous in shale gas energy systems,66,86 all the input data are considered deterministic because the main focus of this study is to address the life cycle optimization of noncooperative supply chains and product systems. Specific Model Formulation. According to the problem statement in the previous section, a multiobjective MIBLFP model is developed to address the life cycle optimization of noncooperative shale gas supply chain networks. The detailed model formulation (constraints 1−35) is provided in Appendix A. The leader’s economic objective is to minimize the LCOE generated from shale gas, denoted as UCleader and given in constraint 1. The leader’s environmental objective is to minimize the life cycle GHG emissions per MWh electricity generation, denoted as UE and given in constraint 5. The follower’s objective, denoted as TPfollower, is maximizing its total NPV as given in constraint 17. All the constraints can be classified into five types. • Mass balance constraints describe the LCI details based on mass conservation of all the species in the supply chain network, given by constraints 12 and 13 for the leader’s problem and constraints 25−30 for the follower’s problem, respectively.

■

• Environmental constraints calculate the GHG emissions generated from various activities from shale gas production to electric power generation in the supply chain, given by constraints 6−11. • Economic constraints are used to measure the economic performance of different stakeholders, given by constraints 2−4 for the leader’s problem and constraints 17−24 for the follower’s problem, respectively. • Capacity constraints describe the capacity limits of different activities in the shale gas supply chain, including supply availability, shale gas processing, transportation, market demand, etc., given in constraints 14 for the leader’s problem and constraints 31 and 32 for the follower’s problem, respectively. • Logic constraints describe the relationships of activities and basic assumptions, especially those involving infrastructure construction and technology selection, given by constraints 15 and 16 for the leader’s problem and constraints 33−35 for the follower’s problem, respectively.

RESULTS AND DISCUSSION Based on the aforementioned model formulation, the resulting upper-level problem (leader’s problem) has 20 integer variables, 42 continuous variables, and 62 constraints. The lower-level problem (follower’s problem) includes 32 integer variables, 117 continuous variables, and 160 constraints. All of the models and solution procedures are coded in GAMS 24.7.387 on a PC with an Intel Core i7−6700 CPU @ 3.40 GHz and 32.00 GB RAM, running a Window 10 Enterprise, 64-bit operating system. Furthermore, the MILP problems are solved using CPLEX 12.6.3 The absolute optimality tolerance for all solvers is set to 10−6. The outer loop corresponding to the parametric algorithm converges in 4 to 6 iterations, and the inner loop normally takes 6 to 15 iterations to converge. The total computational time varies from a few hundred CPU seconds to a few thousand seconds depending on the number of inner and outer iterations involved. Notably, solution of the master problem is the most time-consuming step mainly due to the complex formulation and large scale with added KKTcondition-based cuts. Meanwhile, both subproblems can be solved within a few seconds. Pareto-Optimal Curve. The resulting MIBLFP problem is solved using the presented solution algorithm and 10 Paretooptimal solutions are obtained which form the Pareto-optimal curve shown in Figure 3. The x-axis represents the life cycle GHG emissions for generating functional unit electricity in the shale gas supply chain. The y-axis represents the LCOE at power plants. Similar to the results from centralized models, the LCOE increases as the unit GHG emissions limit decreases, which explicitly reveals the trade-offs between the economic and environmental objectives in the power plants’ problem. The region above the Pareto-optimal curve is the suboptimal region, and the region below the curve is the infeasible region. In Figure 3, point A indicates the optimal solution with the lowest life cycle GHG emissions of 107 kg CO2-eq/MWh, and the accumulated total GHG emissions are 7.3 billion kg CO2-eq throughout the planning horizon; meanwhile, it has the highest LCOE of $128/MWh, and the total cost is $5.1 billion (in USD) for the power plants. Therefore, we identify point A as the environment-oriented solution. On the contrary, point B is identified as the economics-oriented solution, which has the H


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With different preferences toward economic and environmental performance, the leader (power plants) will choose different strategies, and the follower (shale gas producer) will react accordingly with distinct decisions. In Figure 4, we

Figure 3. Pareto-optimal curve demonstrating the trade-offs between LCOE and life cycle GHG emissions with corresponding breakdowns: pie charts represent breakdowns of cost; donut charts represent breakdowns of life cycle GHG emissions.

Figure 4. Follower’s NPV vs life cycle GHG emissions with corresponding breakdowns.

lowest LCOE known as $72/MWh, and a total cost of $1.5 billion. The life cycle GHG emissions of point B are 477 kg CO2-eq/MWh, with 14.3 billion kg CO2-eq total GHG emissions. Solutions between points A and B are all equivalently optimal according to the definition of Paretooptimality, and they have lower LCOE than A and lower life cycle GHG emissions than B. Here we take point C as an example; the life cycle GHG emissions are 231 kg CO2-eq/ MWh, and the total GHG emissions are 11.0 billion kg CO2-eq. With more than twice higher life cycle GHG emissions than point A, the LCOE can be reduced significantly to $84/MWh, and the corresponding total cost for power plants is $2.0 billion. We note that the actual selection of strategy depends on the power plants’ preference toward both economic and environmental criteria. Apart from the Pareto-optimal curve, the detailed breakdowns of life cycle GHG emissions and corresponding total cost for points A, B and C are also provided in Figure 3. For the cost breakdowns, all the three points share a similar pattern. The O&M cost account for more than half of the power plants’ total cost, followed by procurement cost and capital investment. As the unit GHG emissions decrease, the portions of O&M cost and capital investment increase largely due to the adoption of advanced CCS technologies. Besides, the total cost for power plants increases as a direct result of larger production profile, which is expected to bring more efficient operations and thus reducing the GHG emissions per functional unit. In contrast, the breakdowns of GHG emissions are significantly different. For point B without CCS technology applied, power generation is identified as the primary source of GHG emissions, accounting for 54% of the total GHG emissions. Other end use customers contribute one-third of the GHG emissions. Other sections, including production, processing, and transportation, all share similar amounts of GHG emissions ranging from 1% to 7%. For point A with the oxyfuel combustion process implemented for CCS, the portion of power generation emissions is drastically reduced from 54% to only 6%, and the portions of other sectors increase correspondingly. However, due to the higher capital and O&M cost as well as lower generation efficiency, the total cost of point A increases accordingly as expected. Point C, as a balanced solution, provides an intermediate performance between these two extreme points.

present the follower’s total NPV, revenue, and costs at different life cycle GHG emissions. Because the follower’s objective remains maximizing its NPV despite the leader’s preference, the follower’s NPV does not follow the same pattern as LCOE in the previous Pareto-optimal curve. However, two major conclusions can be drawn from this figure: First, as the leader leans toward minimizing the LCOE instead of the life cycle GHG emissions, the leader inclines to procure less shale gas, and thus lower profit is expected to be made for the follower. Second, the cost breakdown for the follower is relatively consistent despite the change of its total profit, which potentially indicate that the follower may not change its strategic decisions dramatically with different decisions from the leader. Next, to illustrate the trade-offs made between two extreme solutions A and B, we provide a comprehensive performance comparison in Figure 5. As can be observed, the major differences in strategic decisions applied in these two solutions can be summarized in two aspects: adoption of CCS technology in power plants and the overall production profile in the shale gas supply chain. Because of the effectiveness of CCS technology in reducing GHG emissions in power generation, the life cycle GHG emissions are significantly reduced by up to 78% in the environment-oriented solution. As a consequence, the LCOE of electricity increases 78% correspondingly because of the extra capital and operating cost as well as loss in power generation efficiency. The difference in terms of production profile can be easily seen by comparing the total electricity generation in the two solutions. Although the environment-oriented solution produces 96% more electricity than the economics-oriented one, the total GHG emissions is even 49% lower thanks to the CCS technology. Besides, more electricity and lower power generation efficiency require a larger shale gas supply, so both the leader’s total cost and follower’s total profit increase, by 249% and 59%, respectively. Comparison with LCA Studies and Other Models. All the results obtained from the proposed model are consistent with data from existing LCA publications.76 According to the EIA, the estimated LCOE for natural gas-fired power plants ranges from $73/MWh to $142/MWh depending on the specific technology applied.88 Correspondingly, a recent LCA review paper by Heath et al. gives a range from around 440 to 760 kg CO2-eq/MWh regarding shale gas life cycle GHG I


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Figure 5. Comprehensive comparison between extreme points A (environment-oriented model) and point B (economics-oriented solution).

Figure 6. Comparison of results regarding life cycle GHG emissions and upstream GHG emissions associated with 1 MWh of electricity generation from shale gas.10,43,57,60,89

Table 1. Model Statistics and Computational Times for the Four Life Cycle Optimization Problems Considered in This Case Study Model Name

Type of Problems

Centralized fractional Noncooperative fractional

Mixed-integer linear fractional program Mixed-integer bilevel linear fractional program

Centralized linear Noncooperative linear

Mixed-integer linear program Mixed-integer bilevel linear program

emissions for electric power generation.60 To verify the results as well as to clarify the impacts of noncooperative modeling of supply chains, we present a detailed comparison of unit life cycle GHG emissions per MWh electricity generation in Figure 6, which includes the results from this noncooperative optimization models, results from conventional centralized life cycle optimization models, and results reported by existing LCA studies. In addition, linear models minimizing the total GHG emissions generated throughout the life cycle and fractional models minimizing unit life cycle GHG emissions per MWh electricity generation are all considered. All the results are based on the application in Marcellus shale play. To give a fair comparison, the centralized models and non-

Integer Variables

Continuous Variables

Constraints

52 upper: 20 lower:32 52 upper: 20 lower:32

159 upper: 42 lower: 117 159 upper: 42 lower: 117

221 upper: 62 lower: 160 221 upper: 62 lower: 160

Computational Time (CPUs) 2 1975 1 447

cooperative models are formulated based on the same data without considering the CCS technology, which is not included in the LCA studies. The modeling details of different life cycle optimization models are summarized in Appendix B. Corresponding model statistics and computational performance are summarized in Table 1. As can be seen, all the results are within the same range.43,57,60,89 Compared with the results reported by LCA studies, the optimal solutions of life cycle optimization models have relatively lower unit life cycle GHG emissions per MWh electricity generation thanks to optimization techniques. The reduction of unit life cycle GHG emissions per MWh electricity generation is more significant in the “upstream” (the shale gas J


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Figure 7. Summary of shale gas supply chain design and flow information in (A) environment-oriented solution and (B) economics-oriented solution.

supply chain before the downstream end use sector).43,52 This result indicates the great potential of mitigating unit life cycle GHG emissions per MWh electricity generation by optimizing upstream decisions in a shale gas supply chain; on the other hand, it implies that the power generation technology may still be the dominating factor affecting the downstream GHG emissions.90 Because of the noncooperative feature, the optimal solution of noncooperative fractional model has 3% higher unit

life cycle GHG emissions per MWh electricity generation than that obtained from the centralized fractional model. Additionally, when focusing on the “upstream”, we notice a more significant difference: the optimal solution of noncooperative fractional model has 21% higher unit life cycle GHG emissions per MWh electricity generation in the upstream than the optimal solution of centralized fractional model. A similar pattern can be observed in the comparison of results between K


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Figure C1. Benchmark of CCS technologies regarding economic and environmental criteria.78,82

gas supply, respectively. Customers other than power plants accounts for 12.6% of the gas supply. NGLs produced at the processing plant are sold to their corresponding market. For the economics-oriented solution of point B, no CCS technology is applied in any of the five power plants. A total of 239 Bscf raw shale gas is produced, and most of the gas (36.7%) is sent to power plant 5 for electricity generation. The less procurement of shale gas has two causes: the leader’s strategies based on different leading objectives and the change of power generation efficiency with and without CCS technologies. In addition, more sales gas (34.7%) is sent to other customers in point B that grants the follower opportunity of making more profit. For both solutions, external source of natural gas is not chosen considering the shale gas production is enough to satisfy the downstream demand. From the producer’s perspective, its strategic decisions largely rely on the decisions realized by the leader. For point A where more shale gas is required by the power plants, all 20 potential shale sites are active, with a total of 105 wells drilled. For point B with smaller order from the power plants, 12 shale sites are active, and 57 wells are drilled in total. The number of active wells reflects the production profiles of the shale gas producer in these two cases. The design decisions regarding processing plants are also different. For point A, processing plant 1 is constructed with capacity of 42.6 Bscf shale gas per year. For point B, processing plant 1 is constructed with a capacity of 23.9 Bscf shale gas per year. Benchmark of CCS Technologies. Through a detailed review of the decisions in both the economics-oriented (point B) and environment-oriented (point A) solutions, the application of CCS technology is identified as a pivotal technology in this noncooperative shale gas supply chain. Therefore, making proper decisions on the selection of CCS technologies becomes crucial toward a more sustainable shale gas supply chain. To present a better comparison between different CCS technologies in terms of economic and environmental performance, a detailed benchmark is presented in Figure C1 and included in Appendix C. Through this comparison, a few important conclusions are obtained: (1) Without CCS technology, both the O&M cost and capital cost for the power plant are significantly lower, but much higher GHG emissions in electric power generation are observed, and the net thermal efficiency increases as well; (2) Both postcombustion technologies, namely the postcombustion (Flour) and postcombustion (MHI), have similar economic and environmental performance due to their similar processes. Around 85−90% of the direct CO2 emissions can be removed

two linear models on the right of Figure 6. Such results verify the advantage of our optimization model in improving the overall life cycle environmental performance of a shale gas supply chain. They also reveal that the noncooperative environment affects the optimal results of life cycle optimization, especially for the upstream of a shale gas supply chain. Although centralized models are easier to solve and lead to better results in most cases, the life cycle economic and environmental performance is overoptimistic, and the corresponding optimal strategy can be infeasible in a noncooperative shale gas supply chain. The proposed modeling framework provides an effective way to address the life cycle optimization problems for a noncooperative supply chain or product system. Additionally, by comparing the proposed fractional models optimizing functional-unit-based life cycle economic and environmental objectives with linear models, we can see the advantage of fractional ones in providing more sustainable solutions. The environmental impacts associated with one functional unit is less in the optimal solutions of fractional models than those obtained in the linear ones.91 The linear models minimizing the total GHG emissions generated throughout the life cycle always lead to the smallest production scale. For instance, the optimal solution of noncooperative linear model results in 10.8 million MWh total electric power generation, which equals the minimum demand of power generation. By contrast, the optimal solution of noncooperative fractional model corresponds to 29.8 million MWh total electric power generation, which is almost three times of that in the solution of its linear counterpart. Therefore, the fractional models enable us to find the optimal amount of functional units to generate for the best sustainability performance. Supply Chain Network and Flow Summary. In this section, we investigate the detailed strategies applied in environment-oriented solution A and economics-oriented solution B. The optimal shale gas supply chain designs with corresponding mass flows are summarized in Figure 7, where the width of each flow is proportional to its amount. First of all, for both solutions corresponding to point A and point B, the leader takes distinct strategies. For the environment-oriented solution of point A minimizing the life cycle GHG emissions, all the five power plants are equipped with the oxyfuel-combustion CCS technology. The power generation in this supply chain requires a total of 426 Bscf raw shale gas from the shale gas producer, and most of the processed gas is sent to power plant 2, power plant 3, and power plant 5 to generate electricity, accounting for 22.1%, 32.3%, and 25.1% of the total L


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multiobjective mixed-integer bilevel linear fractional program. The general formulation is provided in the main text. Here we present the specific model formulation applied in this case study. All the parameters are denoted with lower-case symbols, and all of the variables are denoted with upper-case symbols. Notably, this model formulation is developed based on the existing shale gas supply chain life cycle optimization model.10 Compared with the previous one, the following improvements need to be highlighted: (1) a bilevel structure is adopted to address the conflicting objectives from different stakeholders; (2) third parties including the external source of natural gas and other customers in addition to power plants are considered; (3) adoption of CCS technologies is taken into account for the natural gas-based power generation.

by contacting with the amine solvent. However, because extra energy is required by the stripper vessel to regenerate the amine and compress the CO2, the net GHG emissions for these two technologies are slightly higher than the direct emissions. By sacrificing some extra operating cost and capital investment as well as nearly 5%−10% thermal efficiency, the GHG emissions can be reduced by up to 6 times; (3) The most effective CCS technology is identified as the oxyfuel combustion process, where more than 90% of the gas turbine exhaust is cooled and recycled to the turbine, and the remaining flue gas is compressed to achieve a high CO2 concentration. As a result, the oxyfuel combustion technology can reduce the GHG emissions by more than 10 times. However, it suffers from the highest capital investment and operating cost as well as the lowest thermal efficiency; (4) For power plants that only focus on minimizing the life cycle GHG emissions, the oxyfuel combustion technology would be chosen. However, in practice both postcombustion technologies are reasonable choices with effective emissions reduction and decent economic performance.

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Leader’s Problem

The power generation sector is identified as the leader in this game. Here we present the detailed model formulation for the leader’s problem. Objectives. The power plants have two conflicting objectives. The economic objective is to minimize the LCOE, defined as the total cost, including the procurement cost, capital cost, operations and maintenance cost, and transportation cost, divided by the total electricity generation. Notably, we attribute the transportation cost of shale gas from processing plants to power plants to the power generation sector.

CONCLUSION

An MIBLFP-based general modeling framework was proposed to address the functional-unit-based life cycle optimization of noncooperative supply chains and product systems. A tailored solution strategy incorporating a parametric algorithm and a projection-based reformulation and decomposition algorithm was introduced to tackle this computationally challenging problem. To demonstrate the complex interactions among different stakeholders and trade-offs between conflicting objectives, a case study based on the Marcellus shale gas supply chain is presented. In this noncooperative shale gas supply chain, two major decision makers are identified as the operator of power plants and shale gas producer. Multiple decisions with respect to well drilling, production, processing, transmission, and power generation are considered. Through a detailed analysis and discussion, we come to a few important conclusions: (1) the noncooperative perspective provides more insights into the life cycle optimization of a shale gas supply chain, and it normally results in worse but more realistic performance than the centralized counterparts regarding both economic and environmental criteria; (2) proper applications of CCS technologies can lead to significant improvement of the overall environmental performance of a shale gas supply chain by sacrificing economic performance to some extent; (3) the interactions between power plants and shale gas producer are so complex that may lead to different design and performance depending on the power plants’ preference; (4) the proposed modeling framework provides an effective way to address the life cycle optimization problems in a noncooperative environment, and the tailored solution algorithm is proved efficient in globally optimizing the resulting MIBLFP problem. In the future work, this modeling framework can be further extended to take into account the competitions among same type of stakeholders and to consider various types of uncertainty.

min UC leader =

TC shale + TC conv TEE

(1)

shale

where UC is the LCOE generated from shale gas, and TCconv is the total cost related to external conventional natural gas. TEE is the total electricity generation. TCshale can be calculated using the following equation: TC shale =

∑ ∑ (vsalmshale + vlccm,k + vomm,k + vtm,k) m∈M k∈K

·TSGm , k +

∑ ∑

vtcm ·lpmp , m ·STPM p , m

p∈P m∈M

(2)

vsalshale m

where indicates the transfer price of shale gas at power plant m, vlccm,k is the levelized capital cost for electricity generated per unit natural gas at power plant m with CCS technology k. vomm,k is the variable operations and maintenance cost for electricity generated per unit natural gas at power plant m with CCS technology k. vtm,k indicates the transmission cost of electricity generated per unit natural gas at power plant m with CCS technology k. TSGm,k denotes the amount of shale gas gathered at power plant m and used for electric power generation with CCS technology k. vtcm is the unit variable transportation cost for the pipeline transporting natural gas. lpmp,m is the distance from processing plant p to power plant m. STPMp,m denotes the amount of shale gas transported from processing plant p to power plant m. TCconv is the total cost corresponding to conventional natural gas, which can be calculated as follows TC conv =

■

∑ ∑ (vsalmconv + vlccm,k + vomm,k + vtm,k)· m∈M k∈K

APPENDIX A: DETAILED MODEL FORMULATION FOR THE WELL-TO-WIRE LIFE CYCLE OPTIMIZATION OF A NONCOOPERATIVE SHALE GAS SUPPLY CHAIN The mathematical model for the proposed noncooperative shale gas supply chain life cycle optimization problem is a

EXMm , k

(3)

vsalconv m

where indicates the transfer price of conventional natural gas at power plant m. EXMm,k stands for amount of conventional natural gas purchased at power plant m and used for power generation with CCS technology k. M


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TEpow indicates the GHG emissions corresponding to electric power generation processes, calculated by

The total electricity generation TEE can be calculated by

∑ ∑ uek ·TNGm,k

TEE =

m∈M k∈K

TEpow =

(4)

∑ ∑ empm,k ·TNGm,k

where uek denotes the amount of electricity generated per unit natural gas input with CCS technology k. TNGm,k is the amount of natural gas obtained from different sources at power plant m to generate electricity with CCS technology k. The environmental objective is to minimize the life cycle GHG emissions of the well-to-wire shale gas supply chain, which accounts for drilling activities, shale gas production, gas processing, transportation, procurement of external natural gas, and power generation.

where empm,k indicates the emissions associated with electricity generation per unit amount of natural gas at power plant m with technology k. Constraints. Mass Balance Constraints. The total amount of shale gas gathered at a power plant equals that of shale gas purchased from different processing plants.

∑ TSGm,k = ∑ STPMp,m , ∀ m k∈K

min UE = TE drill + TEprod + TEproc + TEtran + TE ex + TEpow TEE (5)

TE is the total GHG emissions from drilling activities, which can be calculated by

∑ esdi·NNi

TNGm , k = TSGm , k + EXMm , k , ∀ m , k

where esdi indicates the emissions associated with the drilling process of a shale well at shale site i. NNi is an integer variable that stands for the number of wells drilled at shale site i. TEprod accounts for the GHG emissions generated at shale gas production processes, which can be calculated by TEprod =

∑ ewfi ·SPi

dmm ≤

∑ ∑ espp ·STPi ,p i∈I p∈P

dmm ·XCSm , k ≤ uek ·TNGm , k ≤ dmupm ·XCSm , k , ∀ m , k (15)

where XCSm,k is a binary variable and equals 1 if CCS technology k is applied in power plant m. Only one CCS technology can be selected at a certain power plant; this constraint is given by

(8)

where espp is the emissions for processing unit amount of shale gas at processing plant p. STPi,p indicates the amount of shale gas transported from shale site i to processing plant p. TEtran indicates the GHG emissions generated in all the transportation activities, which is given by TEtran =

∑ XCSm,k = 1, ∀ m Follower’s Problem

Objectives. The shale gas producer’s objective is solely maximizing its total NPV, which contains the income from sales of shale gas and natural gas liquids (NGL), as well as the capital and operating costs from well drilling, gas production, gas processing, and transportation processes, given as follows

i∈I p∈P

∑ ∑

emt · lpmp , m ·STPMp , m

p∈P m∈M

(9)

where est is the emissions associated with transportation of a unit amount of shale gas by pipeline. emt indicates the emissions associated with transportation of a unit amount of natural gas by pipeline. TEex stands for the GHG emissions embedded in the conventional natural gas purchased from external sources, which can be calculated by TE ex =

∑ ∑ eex·EXMm,k m∈M k∈K

(16)

k∈K

∑ ∑ est ·lspi ,p ·STPi ,p +

(14)

where dmm is the minimum demand of electricity generation at power plant m, and dmupm stands for the maximum demand of electricity generation at power plant m. uek indicates the amount of electricity generated per unit natural gas input with CCS technology k. Logic Constraints. A certain CCS technology can be applied in electric power generation only when it is selected at a power plant; this relationship is described by the following constraint:

where ewf i stands for the emissions associated with the production process of unit shale gas at shale site i. SPi is the total shale gas production at shale site i. TEproc is the GHG emissions generated at processing plants, which is calculated by the following equation: TEproc =

∑ uek ·TNGm,k ≤ dmupm , ∀ m k∈K

(7)

i∈I

(13)

Capacity Constraints. The total electric power generated at power plant m should satisfy the corresponding demand, given by the following constraint:

(6)

i∈I

(12)

p∈P

The total amount of natural gas gathered at a power plant equals the summation of shale gas from shale gas supply chain and the conventional natural gas from external natural gas sources. This relationship is given by

drill

TE drill =

(11)

m∈M k∈K

max TP follower = IN SG + IN NGL − TC drill − TC prod proc proc − TCfix − TCvar − TC tran

(17)

SG

IN indicates the income from sales of shale gas to the power plants, which can be calculated by IN SG =

(10)

∑ ∑ p∈P m∈M

where eex is the emissions associated with a unit of conventional natural gas at the power plant gate.

vsalmshale·STPM p , m +

∑ vse·STEp p∈P

(18)

where vse is the average transfer price of natural gas at downstream customers except power plants. STEp is the N


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where sppi denotes the reference shale gas production profile of a shale well at shale site i. euri denotes the estimated ultimate recovery (EUR) of wells at shale site i. The total amount of shale gas production at each shale site should equal the total amount of shale gas transported to different processing plants,

amount of natural gas sold to other downstream customers (excluding power plants). INNGL is the income from sales of NGL, calculated by

IN NGL =

∑ pl·SPLp (19)

p∈P

where pl is the average unit price of NGL. SPLp is the total amount of NGL produced at processing plant p. TCdrill stands for the total cost associating with drilling activities. Notably, a linear function is considered here. Although a nonlinear function may provide more accurate estimation of well drilling cost, some necessary parameters are still missing, and the nonlinear terms will add extra complexity to the resulting problem. Therefore, we adopt such a simplified linear function to formulate the model in a tractable form.

TC drill =

∑ sdci·NNi

SPi =

The total methane produced at a processing plant is determined by the methane composition of the total shale gas transported from different shale sites taking into account processing efficiency. The amount of NGL produced at a processing plant is calculated by a similar equation.

∑ STPi ,p·pefp ·mci = SPMp , ∀ p i∈I

∑ STPi ,p·pef p ·lci = SPLp , ∀ p

where sdci is the unit cost for shale well drilling and completion at shale site i. TCprod is the total cost regarding shale gas production at shale sites, calculated by TC prod =

∑ spci·SPi

i∈I

where spci indicates the unit cost for shale gas production at shale site i. TCfproc indicates the capital investment of constructing ix processing plants, which is calculated by proc = TCfix

SPM p =

∑ ∑ prir− 1·YPp,r ∑ ∑ (PCp,r p∈P r∈R

∑ ∑ vpp ·STPi ,p i∈I p∈P

TC

=

∑ ∑ vtcs·lspi ,p ·STPi ,p i∈I p∈P

(30)

p∈P

∑ STPi ,p ≤ ∑ PCp,r , ∀ p i∈I

r∈R

(31)

where PCp,r denotes the designed capacity of processing plant p with capacity range r. The total amount of shale gas sold to other downstream customers cannot exceed their demand.

(23)

∑ STEp ≤ dme (32)

p∈P

where dme is the maximum demand of natural gas for downstream customers apart from power plants. Logic Constraints. If a processing plant is established, its processing capacity should be bounded by the corresponding capacity range; otherwise, its capacity should be zero. This relationship can be modeled by the following inequality:

(24)

where vtcs is the levelized unit transportation cost for pipeline transporting shale gas. Constraints. Mass Balance Constraints. The total shale gas production rate at a shale site equals the sum of that of different wells. Thus, the total shale gas production at each shale site in each time period can be calculated by SPi = NNi·sppi ·euri , ∀ i

(29)

Notably, this constraint is shared by both the leader’s problem and the follower’s problem. Capacity Constraints. The total amount of shale gas from all the shale sites processed by each processing plant should not exceed its processing capacity,

where vpp is the unit processing cost for shale gas at processing plant p. TCtran stands for the total cost regarding transportation activities, calculated by tran

STPM p , m + STEp , ∀ p

∑ TSGm,k = ∑ STPMp,m , ∀ m k∈K

where prir is the reference capital investment for processing plant with capacity range r. YPp,r is a binary variable which equals 1 if processing plant p is set up with capacity range r. PCp,r is the designed processing capacity for processing plant p with capacity range r. prcr indicates the reference capacity for processing plant with capacity range r. TCproc var. stands for the variable costs regarding shale gas processing, which is calculated by =

(28)

The total amount of shale gas gathered at a power plant equals that of shale gas purchased from different processing plants.

⎛ pri − prir − 1 ⎞ − prcr − 1·YPp , r ) ·⎜ r ⎟ ⎝ prcr − prcr − 1 ⎠ (22)

proc TCvar

∑ m∈M

p∈P r∈R

+

(27)

where pef p is the processing efficiency in terms of raw shale gas at processing plant p. mci denotes the average methane composition in shale gas at shale site i. SPMp is the amount of processed natural gas obtained at processing plant p. lci is the average NGL composition in shale gas at site i. The total amount of natural gas produced at a processing plant equals the summation of natural gas transported from the processing plant to power plants and other customers.

(21)

i∈I

(26)

p∈P

(20)

i∈I

∑ STPi ,p , ∀ i

prcr − 1·YPp , r ≤ PCp , r ≤ prcr ·YPp , r , ∀ p , r

(33)

Only one capacity range can be chosen for a processing plant, given as

(25) O


Research Article


∑ YPp,r ≤ 1, ∀ p r∈R

10−6 optimality gap, and the total computational time is less than 1 CPU second.

(34)

Noncooperative Linear Model

The total number of wells that can be drilled at shale site i over the planning horizon is bounded, given by

NNi ≤ tmni , ∀ i

min TC leader = TC shale + TC conv

(35)

min TE = TE drill + TEprod + TEproc + TEtran + TE ex

where tmni denotes the maximum number of wells that can be drilled at shale site i over the planning horizon.

+ TEpow

■

s.t. constraints 1−16. where (xl, yl) solves:

APPENDIX B: MATHEMATICAL FORMULATIONS AND COMPUTATIONAL DETAILS OF ALTERNATIVE LIFE CYCLE OPTIMIZATION MODELS In the case study, we compared the optimization results of four different types of life cycle optimization models. The first one is the noncooperative fractional model as presented above. The other three life cycle optimization models include the centralized fractional model, the centralized linear model, and the noncooperative linear model. Both centralized models result in a single-level problem optimizing uniform objectives. The linear models are minimizing the total GHG emissions generated throughout the well-to-wire life cycle, whereas the fractional ones are minimizing the unit life cycle GHG emissions per MWh electricity generation. In the following, we present the specific model formulations of the latter three life cycle optimization models. The corresponding model statistics and computational time are given as well.

max TP follower = IN SG + IN NGL − TC drill − TC prod proc proc − TCfix − TCvar − TC tran

s.t. constraints 17−35. The resulting problem of this noncooperative linear model also features a bilevel structure, where the feasible region of the upper-level problem is partially dependent on the lower-level problem. The objectives functions and constraints for both the upper-level problem and lower-level problem are linear. Therefore, it results in a mixed-integer bilevel linear program (MIBLP). The upper-level problem (leader’s problem) has 20 integer variables, 42 continuous variables, and 62 constraints. The lower-level problem (follower’s problem) has 32 integer variables, 117 continuous variables, and 160 constraints. This MIBLP is solved using the projection-based reformulation and decomposition algorithm. The MILP solver applied in this algorithm is CPLEX 12.6.3 with 10−6 optimality gap, and the relative optimality gap for this algorithm is set to 10−3. The total computational time is 447 CPU seconds. It is worth noting that the bilevel structure adds more complexity to the noncooperative models than their centralized counterparts. Both noncooperative models require more than a few hundred CPU seconds to optimize, while the centralized ones can be solved within seconds despite their similar problem scales. The parametric algorithm handles fractional objective efficiently and only a few more seconds is required than the linear models.

Centralized Fractional Model

min UC =

TC shale + TC conv TEE

min UE = TE drill + TEprod + TEproc + TEtran + TE ex + TEpow TEE

■

s.t. constraints 1−16 and 25−35. The resulting problem of this centralized fractional model is a single-level problem with fractional objective functions formulated as a ratio of two linear functions. We note that TEE denotes the total electricity generation as given by constraint 4. All the constraints are identified as linear ones. Thus, it is identified as a mixed-integer linear fractional program (MILFP), which has 52 integer variables, 159 continuous variables, and 221 constraints. This problem is solved using the parametric algorithm with 10−6 absolute optimality gap. For each iteration in the parametric algorithm, solver CPLEX 12.6.3 is used with 10−6 optimality gap. The total computational time is less than 2 CPU seconds.

APPENDIX C: COMPARISON OF CCS TECHNOLOGIES CONSIDERED IN THE POWER PLANTS The detailed comparison of different carbon capture and storage (CCS) technologies considered in the power plants are summarized in Figure C1.

■

* Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.7b00002. Detailed input data of the case study on life cycle optimization of Marcellus shale gas supply chain (PDF)

Centralized Linear Model

min TC = TC shale + TC conv

■

min TE = TE drill + TEprod + TEproc + TEtran + TE ex + TE

ASSOCIATED CONTENT

S

pow

AUTHOR INFORMATION

Corresponding Author

*F. You. Phone: (607) 255-1162; Fax: (607) 255-9166; E-mail: [email protected].

s.t. constraints 1−16 and 25−35. This centralized linear model leads to a single-level problem, where all the objective functions and constraints are linear. Therefore, it is a mixed-integer linear program (MILP), which has 52 integer variables, 159 continuous variables, and 221 constraints. This MILP is solved by CPLEX 12.6.3 directly with

ORCID

Fengqi You: 0000-0001-9609-4299 Notes

The authors declare no competing financial interest. P


Research Article


■

ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the National Science Foundation (NSF) CAREER Award (CBET1643244).

■

vomm,k Variable operations and maintenance cost for electricity generated from unit natural gas at power plant m with CCS technology k vpp Unit processing cost of shale gas at processing plant p vse Unit average transfer price of natural gas at downstream customers excluding power plants-citygates price vsalshale Transfer price of natural gas from shale gas supply m chain at power plant m vsalconv Transfer price of conventional natural gas at power m plant m vtm,k Transmission cost of electricity generated from unit natural gas at power plant m vtcm Unit variable transportation cost for pipeline transporting natural gas vtcs Unit variable transportation cost for pipeline transporting shale gas

NOMENCLATURE

Sets

I Set of shale sites indexed by i K Set of CCS technology indexed by k (k1, No CCS; k2, Postcombustion (Flour); k3, Postcombustion (MHI); k4, Oxyfuel combustion) M Set of power plants indexed by m P Set of processing plants indexed by p R Set of capacity ranges indexed by r Subscripts/Superscripts

shale Shale gas conv Conventional natural gas

Continuous Variables

EXMm,k

Parameters

dmm dmupm dme eex eepm,k emt esdi ese espp est ewf i lci lmpp,m lspi,p mci pef p pl prcr prir sdci spci sppi tmni uek vlccm,k

Minimum demand of electricity generation at power plant m Maximum demand of electricity generation at power plant m Maximum demand of natural gas for other downstream customers excluding power plants Emissions associated with a unit of conventional natural gas at the power plant gate Emissions associated with electricity generation per unit amount of natural gas at power plant m with CCS technology k Emissions associated with transportation of a unit amount of natural gas by pipeline Emissions associated with the drilling process of a shale well at shale site i Emissions associated with usage of unit amount of natural gas by other customers Emissions associated with processing a unit amount of shale gas at processing plant p Emissions associated with transportation of a unit amount of shale gas by pipeline Emissions associated with producing a unit amount of shale gas at shale site i NGL composition in shale gas at shale site i Distance from processing plant p to power plant m Distance from shale site i to processing plant p Methane composition in shale gas at shale site i Processing efficiency of shale gas at processing plant p Average unit sales price of NGL Reference capacity for processing plant with capacity range r Reference capital investment for processing plant with capacity range r Unit cost for shale well drilling and completion at shale site i Unit cost for shale gas production at shale site i Shale gas production of a shale well at shale site i Maximum number of wells that can be drilled at shale site i over the planning horizon Amount of electricity generated per unit natural gas input with CCS technology k Levelized capital cost for electricity generated from unit natural gas at power plant m with CCS technology k

PCp,r SPi SPLp SPMp STPp STPi,p STPMp,m TNGm,k

Amount of natural gas obtained from external conventional natural gas sources at power plant m to generate electricity with CCS technology k Processing capacity for processing plant p with capacity range r Shale gas production rate at shale site i Amount of NGL produced at processing plant p Amount of natural gas produced at processing plant p Amount of natural gas transported from processing plant p to customers other than power plants Amount of shale gas transported from shale site i to processing plant p Amount of natural gas transported from processing plant p to power plant m Amount of natural gas obtained from different sources at power plant m to generate electricity with CCS technology k

Integer Variables

NNi Number of wells drilled at shale site i Binary Variables

XCSm,k 0−1 variable. Equal to 1 if CCS technology k is applied in power plant m YPp,r 0−1 variable. Equal to 1 if processing plant p is set up with capacity range r

■

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