Water impact of an optimal natural gas production and distribution system: An MILP model and the case-study of Mexico

Journal Pre-proof Water impact of an optimal natural gas production and distribution system: An MILP model and the case-study of Mexico Maria G. Laguna-Martinez, Jaime Garibay-Rodriguez, Vicente Rico-Ramirez, Edgar O. Castrejon-Gonzalez, Jose M. Ponce-Ortega

PII:

S0263-8762(19)30557-X

DOI:

https://doi.org/10.1016/j.cherd.2019.11.028

Reference:

CHERD 3913

To appear in:

Chemical Engineering Research and Design

Received Date:

25 April 2019

Revised Date:

23 September 2019

Accepted Date:

21 November 2019

Please cite this article as: Laguna-Martinez MG, Garibay-Rodriguez J, Rico-Ramirez V, Castrejon-Gonzalez EO, Ponce-Ortega JM, Water impact of an optimal natural gas production and distribution system: An MILP model and the case-study of Mexico, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.11.028

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Water Impact of an Optimal Natural Gas Production and Distribution System: An MILP Model and the Case-Study of Mexico

Maria G. Laguna-Martineza, Jaime Garibay-Rodrigueza, Vicente Rico-Ramireza,1 , Edgar O. Castrejon-Gonzaleza, and Jose M. Ponce-Ortegab

Tecnologico Nacional de Mexico en Celaya, Departamento de Ingenieria Quimica, Av.

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Tecnologico y Garcia Cubas S/N, Celaya, Guanajuato, Mexico 38010

Universidad Michoacana de San Nicolas de Hidalgo, Departamento de Ingenieria

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Quimica, Morelia, Michoacan, Mexico, 58060

To whom all correspondence should be addressed. E-mail: [email protected],

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Graphical abstract

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Phone: (+52) 461 611 7575 x 5579, Fax (+52) 461 611 7744

Highlights 1



This work evaluates a macroscopic system for the exploitation and distribution of shale gas



Optimal decisions include both the water management and the gas supply chain



The case study uses real information from various governmental agencies in Mexico

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Data has been processed through the geographic information system ArcGIS

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Even in an optimal scenario, water availability for some municipalities is

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compromised

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Abstract

This study presents a mathematical programming approach for evaluating the exploitation

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and distribution of shale gas from potential reserves at a national level, depending upon existing infrastructure and water availability. The study describes an MILP model that

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simultaneously integrates water management with the design and planning of the supply chain, from basins to distribution markets and fresh water supply from available

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watersheds. The model is applied to a case based on the potential exploitation of shale gas basins in Mexico. The parameters of the model are mostly taken from the databases of the country, processed through the geographic information system ArcGIS. The solution

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provides the optimal decisions for exploitation and distribution, as well as for freshwater source selection and optimal wastewater management. Water management strategies include disposal, wastewater treatment in municipal plants and onsite treatment. The negative impact of water consumption of the optimal exploitation systems is assessed based mainly on the estimation of the water stress index. Results show that the shale gas

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exploitation would favor the energy independence of the country, but the availability of freshwater for some municipalities would be compromised.

Keywords: Sustainable water management, Shale gas production, Shale gas supply chain, Water stress index.

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1. Introduction Natural gas from unconventional sources, also known as shale gas, has become one of the most promising energy sources in recent decades. With the discovery of shale gas reserves around the world, the shale revolution began in 2001 in the US. Currently, almost 44% of total natural gas withdrawal comes from shale gas wells and, according to the US Energy Information Administration (2015), an increase of 53% is projected for 2040. For the US, the gas revolution has caused the reconfiguration of the gas industry,

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contradicting the prediction of shortages front short and long-term demand. Between 1990 and 2000, production experienced a growth of 0.7% each year, while consumption grew

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2%; which caused an increase in imports of 9.4% annually. Between 2001 and 2011, however, production has grown 2%, in contrast to an increase in consumption of 1.3%,

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causing a decline in imports at a rate of 2% each year (US Energy Information Administration, 2011). Due to this continuing trend, US net natural gas exports are

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currently an average of 0.87 billion cubic feet per day. Because of geographical conditions, Mexico has become the consumer of 38% of these exports.

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The dynamics of the natural gas industry in Mexico can be explained by the strong dependence ratio, in terms of supply and prices, which exists on the US market. From 2000 to 2013, the demand in Mexico has grown 6.2% each year, while production experienced

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an increase of 3.6%; the consequence is the increasing trend in imports (19% annually). A study published by the EIA in 2011, placed Mexico in fourth place worldwide with the largest gas shale resources. It has been estimated that the exploitation of shale gas in Mexico could attract between 7 and 10 million dollars, annually. The projections for the next 15 years indicate that 1.5 million direct and indirect jobs could be generated,

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strengthening the national energy industry by developing value chains and reducing imports of natural gas (SENER, 2016). In contrast to the energy and economic benefits that the shale gas industry could provide to Mexico, the sector represents a negative impact on the environment; in particular, the depletion and degradation of watersheds, as well as the potential for groundwater contamination (Clark et al., 2013; Siirola, 2014).

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Around the world, the development of large-scale shale gas production has been possible by the hydraulic fracturing (or fracking) and horizontal drilling technologies (Gregory et al., 2011; Vengosh et al., 2013; Ikonnikova et al., 2015). The application of hydraulic fracturing has resulted in the well known shale water management problem (Nicot and Scanlon, 2012; Small et al., 2014). A whole body of literature is available with the basic operational details and fundamentals of hydraulic fracturing (See for instance: Karapataki, 2012; Nicot et al., 2014; Rivard et al., 2014). In brief, a high-pressure mixture of sand, water, and small amounts of chemical additives is directed at the shale rock to release oil

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and gas from dense rock formations; hence, the process allows the gas to flow out to the head of the well. Fracking is usually combined with horizontal drilling, which helps to

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create new pathways to release gas (or to extend existing channels) and allows production at a large scale. The main environmental concerns about fracking are related to water

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consumption and water quality. Fracking uses huge amounts of water, which must be transported to the site at significant environmental cost; the production of shale gas requires

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a considerably larger amount of water than that of conventional natural gas (13-37 L/GJ against 9.3-9.6 L/ GJ) (Clark et al., 2013). Furthermore, the produced wastewater contains

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salt, naturally occurring heavy metals and small amounts of chemical additives; the produced wastewater therefore needs proper management. Current wastewater management strategies in shale gas sites can be classified into the

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following three strategies: i) injection in disposal wells, ii) treatment in municipal plants and iii) onsite treatment (Rahm and Riha, 2014). In the first strategy, the wastewater is sent to disposal wells and pumped into deep impermeable rock layers. In general, the underground injection is the cost-effective option when nearby disposal wells are available. Nonetheless this option implies a risk of causing water contamination and inducing

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seismicity (US Environmental Protection Agency, 2011). The wastewater from shale gas production can also be transported to wastewater treatment plants. Then, the treated water is discharged to surface water. The final strategy involves onsite treatment for reuse, where water treatment units are installed at the shale site to treat the wastewater to achieve the necessary quality for reuse (Horner et al., 2011; Slutz et al., 2012). Due to the public concern on the water related environmental issues, it is important to develop the best approach to address challenges in the shale water management problem. The water 4

management problem has been addressed mostly by evaluating the environmental impacts of hydraulic fracturing and through the estimation of the techno-economic analysis of specific water management options (Goldstein, 2013; McHugh et al., 2014; Best and Lowry, 2014; Rodriguez and Soeder, 2015). The first mathematical model that addresses the long-term strategic planning and design of the shale gas supply chain was proposed by Cafaro y Grossmann (2014); in their approach, the drilling plan, the location and size of the processing plants, as well as the length and

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location of the pipes and the power of the gas compressors are addressed simultaneously. After the shale gas supply chain is analyzed, a clear dependence between hydraulic

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fracturing and water acquisition could be identified. More recent literature either focuses on the design and operation of the supply chain (Gao and You, 2015; Calderon et al., 2015;

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Cafaro et al., 2016; Arredondo-Ramirez et al., 2016; Knudsen et al., 2014; Knudsen et al., 2014b; Drouven et al., 2017) or is concerned with the problem of water management (Yang et al., 2014; Mauter and Palmer, 2014; Gao and You, 2015b; Lira-Barragan et al., 2016;

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Lira-Barragan et al., 2016b; Bartholomew and Mauter, 2016). An overview of this research area was reported by Gao and You (2017). Shale gas production is limited by several water-

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related constraints though, such as the availability of fresh water and the treatment of wastewater; also, the water management issues are caused by the production of shale gas. Hence, it is clear that, for an impact and feasibility studies, an integrated modeling

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framework considering both shale gas production and water management is required. Therefore, the evaluation of the shale gas supply chain and the water supply chain cannot be studied separately. Some reports present integrated modeling frameworks (Gao and You, 2015b; Guerra et al., 2016; Chen et al., 2017; Carrero-Parreño et al., 2018; He et al., 2018), and very few of them perform the analysis at a national level (Charry-Sanchez et al., 2014;

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Ren et al., 2015; Tan and Barton, 2017). In summary, in order to considering the water supply chain in a complex system where freshwater watersheds can be severely impacted, it is important to develop an integrated approach that considers all the challenges and opportunities that the particular conditions of the water sources of a given region provide. In this work, an optimization framework based on mathematical programming has been developed. Most of the model components are based on the original work by Guerra et al.

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(2016), but the constraints have been redefined so that the model can be used for the particular conditions of the case-study and according to the available and more significant information at a national level. The resulting MILP model includes the evaluation of shale gas resources from the perspective of the supply chain as well as the decisions involved on the wastewater management strategies; in particular, a water stress index is estimated and has been used as one of the objectives for making the optimal decisions. The selection of the optimal shale gas basins to be exploited (an average number of wells in operation is predefined per basin) are also considered. The model has been applied to a case study based

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on the exploitation of shale gas reserves in Mexico. The parameters of the model were defined as close to reality as possible by using the economic and geographic databases of

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the country; all of the information with a geospatial component was processed through the geographic information system ESRI ArcGIS. A description of the Geographic Information

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Systems (GIS) methodology and the layers of information used in this work are provided in

2. Problem Superstructure

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the supporting information file.

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The problem considers a shale gas supply chain with given existing production and distribution infrastructures. The goal is to determine the optimal planning and scheduling for the shale gas production as well as the water management policies. Figure 1 shows

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schematically the problem addressed in this work and the symbols used in the representation; as mentioned, the main conceptual components are similar to those reported by Guerra at al. (2016). The problem superstructure includes a set of potential shale gas basins (𝑤) with a specific number of wells that can be exploited; each basin has a specific location and includes a set of potential watershed freshwater sources with known

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availability (𝑖𝑤 ), as well as water storage facilities and on-site treatment units. The wastewater can be sent to disposal wells (𝑗𝑤 ) or to municipal treatment plants (𝑘𝑤 ) for discharge into aquifers. The shale gas extracted from the basins is transported to the processing plants (𝑝ℎ). Each processing plant is characterized through parameters related to the operation costs and the maximum processing capacity. The natural gas produced is transported to markets (𝑚𝑘), where it is supplied to the consumers. 6

The transportation system from basins to processing plants and then to markets is defined through connections determined by gas pipelines. Compressor stations along a selected pipeline route are required. Depending upon the distances between the locations involved in the transportation (origin and the destination), the shale and natural gas can be sent to their destination through a pipeline route including one main compressor station and some intermediate compressor stations (which are needed when traveling long distances). The compressor stations available for the transportation of shale gas from basins to the

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processing plants are indexed with 𝑐 (main compressor stations) and 𝑐′ (intermediate compressor stations). The compressor stations available for the transportation of natural gas

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produced from processing plants to markets are indexed with 𝑝𝑐 (main compressor stations) and 𝑝𝑐′ (intermediate compressor stations). For a given pipeline route, the available

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compressor stations (main and intermediate) are known. In fact, the decision about the optimal transportation route is made in terms of the selection of the corresponding main and

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intermediate compressor stations. Additional considerations were assumed for the model and for the case study with respect to the gas transportation system and the estimations of

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costs. These will be further explained in Section 3.2; a detailed description of the data and assumptions used in the case-study is also provided in the Supporting Information file

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accompanying this paper.

3. Mathematical Formulation

This section describes the various components of the deterministic optimization model developed in this work for the design and planning of a shale gas supply chain and the corresponding water management policies. All of the symbols used in the modeling

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equations are defined in the supporting information accompanying this manuscript (although the basic information is also provided here). For each variable or parameter, superscripts are used as part of the identifier (variable name or parameter name); subscripts are used to reference the various elements of each set. For instance, in Equation (1), a variable used represents the amount of shale gas produced in a basin and sent to a compressor station is named 𝐹𝑆𝑇 𝑤−𝑐 , and it is indexed for basin 𝑤, compressor station 𝑐,

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𝑤−𝑐 during time period 𝑡 (𝐹𝑆𝑇𝑤,𝑐,𝑡 ). In general, the operator ∑𝑖

indicates the summation over

all of the possible values of index 𝑖. The resulting formulation is an MILP model, which is described in more detail in Section 3.1; the model is linear due to several assumptions, which are summarized in Section 3.2. Section 3.2 also discusses some of the limitations of the proposed formulation.

3.1 Model Formulation

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Table 1 presents a summary of the modeling equations, indicating the meaning of each of them. The formulation is described next.

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3.1.1 Mass balances, capacity constraints, demands and operation constraints 3.1.1.1 Mass balances of shale gas in basins

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𝑤−𝑐 The gas produced in each basin over a given time period (𝐹𝑆𝑇𝑤,𝑐,𝑡 ) can be distributed to

any of the compressor stations 𝑐

∀𝑤, 𝑡

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𝑤−𝑐 𝐹𝑆𝑤,𝑡 = ∑𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑡

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(1)

3.1.1.2 Mass balance of shale gas in compression stations Depending on the distances and the destination, the gas in each compressor station

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𝑐−𝑝ℎ 𝑤−𝑐 𝑐 (𝐹𝑆𝑇𝑤,𝑐,𝑡 ) is sent to either processing plants (𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡 ) or intermediate compressor 𝑐−𝑐′ stations 𝑐′ (𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡 ).

𝑐−𝑝ℎ 𝑤−𝑐 𝑐−𝑐′ 𝐹𝑆𝑇𝑤,𝑐,𝑡 = ∑𝑝ℎ 𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡 + ∑𝑐′ 𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡

∀𝑤, 𝑐, 𝑡

(2)

Similarly, the gas received in the intermediate compressor station 𝑐′ (from the compressor

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𝑐′−𝑝ℎ 𝑐−𝑐′ stations through 𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡 ) is sent to one or several processing plants (𝐹𝑆𝑇𝑤,𝑐′,𝑝ℎ,𝑡 ). 𝑐′−𝑝ℎ 𝑐−𝑐′ ∑𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡 = ∑𝑝ℎ 𝐹𝑆𝑇𝑤,𝑐′,𝑝ℎ,𝑡 ∀𝑤, 𝑐 ′ , 𝑡

(3)

3.1.1.3 Mass balance in processing plants The shale gas in each processing plant 𝑝ℎ (𝑃𝑆𝑤,𝑝ℎ,𝑡 ) is received either from main or intermediate compressor stations: 8

𝑐−𝑝ℎ 𝑐′−𝑝ℎ 𝑃𝑆𝑤,𝑝ℎ,𝑡 = ∑𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡 + ∑𝑐′ 𝐹𝑆𝑇𝑤,𝑐′,𝑝ℎ,𝑡

∀𝑤, 𝑝ℎ, 𝑡

(4)

The natural gas produced in a processing plant depends on the feed of shale gas and on a 𝑝𝑟𝑜𝑐 factor associated to the corresponding losses in production (𝛼𝑤 ). 𝑝𝑟𝑜𝑐 𝐹𝐺𝑤,𝑝ℎ,𝑡 = 𝛼𝑤 𝑃𝑆𝑤,𝑝ℎ,𝑡

∀ 𝑤, 𝑝ℎ, 𝑡

(5)

The values used for the parameter 𝛼𝑝𝑟𝑜𝑐 have been taken from previous reports in the 𝑤 literature. Although the exact value for each reservoir might be uncertain (the value is

assumed to be bounded by the values reported for similar reservoirs.

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determined through the particular composition of the shale gas feed), it is generally

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The natural gas produced in the processing plants is transported either to markets (located

𝑝ℎ−𝑝𝑐 stations for further transportation (𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 ). 𝑝ℎ−𝑚𝑘

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𝑝ℎ−𝑚𝑘 in the same location as that of the processing plant, 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 ) or to the compressor

𝑝ℎ−𝑝𝑐

∀ 𝑝ℎ, 𝑡

(6)

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∑𝑤 𝐹𝐺𝑤,𝑝ℎ,𝑡 = ∑𝑚𝑘 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 + ∑𝑝𝑐 𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡

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3.1.1.4 Mass balance in natural gas compressor stations

𝑝𝑐−𝑚𝑘 The natural gas in a compressor station is sent either to markets (𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 ) or to

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𝑝ℎ−𝑝𝑐 intermediate compressor stations 𝑝𝑐′ (𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 ) for longer transportation distances. 𝑝ℎ−𝑝𝑐 𝑝𝑐−𝑚𝑘 𝑝𝑐−𝑝𝑐′ ∑𝑝ℎ 𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 = ∑𝑚𝑘 𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 + ∑𝑝𝑐′ 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐′,𝑡

∀𝑝𝑐, 𝑡

(7)

The gas in intermediate compressor stations 𝑝𝑐′, received from compressor stations 𝑝𝑐, 𝑝𝑐−𝑝𝑐 ′

𝑝𝑐 ′ −𝑚𝑘

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𝐹𝐺𝑇𝑝𝑐,𝑝𝑐 ′ ,𝑡 , is sent to the available markets (𝐹𝐺𝑇𝑝𝑐 ′ ,𝑚𝑘,𝑡 ). 𝑝𝑐−𝑝𝑐′ 𝑝𝑐′−𝑚𝑘 ∑𝑝𝑐 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐′,𝑡 = ∑𝑚𝑘 𝐹𝐺𝑇𝑝𝑐′,𝑚𝑘,𝑡 ∀𝑝𝑐 ′ , 𝑡

(8)

3.1.1.5 Mass balance in markets The total natural gas in a market is received from processing plants, compressor stations and intermediate compressor stations. 𝑝ℎ−𝑚𝑘 𝑝𝑐−𝑚𝑘 𝑝𝑐′−𝑚𝑘 𝐹𝑀𝐾𝑚𝑘,𝑡 = ∑𝑝ℎ 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 + ∑𝑝𝑐 𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 + ∑𝑝𝑐′ 𝐹𝐺𝑇𝑝𝑐′,𝑚𝑘,𝑡 ∀ 𝑚𝑘, 𝑡

(9) 9

3.1.1.6 Maximum demand constraints The total gas sent to a market (𝐹𝑀𝐾𝑚𝑘,𝑡 ) is bounded by the demand at each time period 𝑑𝑒𝑚𝑎𝑛𝑑 𝐹𝑀𝐾𝑚𝑘,𝑡 ≤ 𝑓𝑚𝑘𝑚𝑘,𝑡

∀𝑚𝑘, 𝑡

(10)

3.1.1.7 Processing capacity constraints 𝑝𝑙𝑎𝑛𝑡 A binary variable (𝑦𝑝ℎ,𝑡 ) is used to represent the potential use of a processing plant. If the

by the maximum capacity: 𝑚𝑎𝑥−

∑𝑤 𝑃𝑆𝑤,𝑝ℎ,𝑡 ≤ 𝑦𝑝𝑙𝑎𝑛𝑡 𝑝𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝ℎ,𝑡 𝑝ℎ

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∀𝑝ℎ, 𝑡

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binary variable is equal to 1, the processing plant is needed and its production is bounded

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3.1.1.8 Transportation capacity constraints

(11)

𝑝𝑐 𝑝𝑐′ 𝑐 Binary variables are also used (𝑦𝑐,𝑡 , 𝑦𝑐𝑐′′ ,𝑡 , 𝑦𝑝𝑐,𝑡 and 𝑦𝑝𝑐′,𝑡 ) to represent the potential use of

′ 𝑦𝑐𝑐′ ,𝑡

𝑤−𝑐 ∑𝑤 𝐹𝑆𝑇𝑤,𝑐,𝑡

≤

𝑚𝑖𝑛− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑐𝑐

𝑝𝑐′ 𝑦𝑝𝑐′,𝑡

≤

𝑐 𝑦𝑐,𝑡

𝑚𝑖𝑛− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑝𝑐𝑝𝑐

𝑚𝑖𝑛− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑝𝑐′𝑝𝑐′

𝑚𝑎𝑥− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑐𝑐

∀𝑐, 𝑡

(12)

𝑚𝑎𝑥−

′

𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑐−𝑐′ ≤ ∑𝑐 ∑𝑤 𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡 ≤ 𝑦𝑐𝑐′ ,𝑡 𝑝𝑐 ′ ′ ∀𝑐 ′ , 𝑡

𝑝ℎ−𝑝𝑐 ∑𝑝ℎ 𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡

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𝑝𝑐 𝑦𝑝𝑐,𝑡

𝑚𝑖𝑛− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑐𝑐

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𝑐 𝑦𝑐,𝑡

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each of the compressor stations and to limit their capacities.

≤

≤

𝑝𝑐−𝑝𝑐′ ∑𝑝𝑐 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐′,𝑡

(13)

𝑐

≤ ≤

𝑝𝑐 𝑦𝑝𝑐,𝑡

𝑚𝑎𝑥− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑝𝑐𝑝𝑐

∀𝑝𝑐, 𝑡

(14)

𝑝𝑐′ 𝑦𝑝𝑐′,𝑡

𝑚𝑎𝑥− 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑝𝑝𝑐′𝑝𝑐′

∀𝑝𝑐 ′ , 𝑡

(15)

Similarly, individual links between the various components of the supply chain are defined

Jo

and bounded through Big-M constraints. The model defines nine possible transportation interconnections. Four potential links are feasible for shale gas. These links include the 𝑐−𝑐′ transportation from the basins to compression stations (𝐹𝑆𝑇𝑤,𝑐,𝑐′,𝑡 ); the transportation from ′

𝑐−𝑝ℎ 𝑐−𝑐 compression stations to processing plants and intermediate stations (𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡 𝐹𝑆𝑇𝑤,𝑐,𝑐 ′ ,𝑡 ); 𝑐 ′ −𝑝ℎ

and the transportation from intermediate stations to the processing plants ( 𝐹𝑆𝑇𝑤,𝑐 ′ ,𝑝ℎ,𝑡 ). Five potential interconnections are also defined for natural gas; they include transportation 10

𝑝ℎ−𝑝𝑐

𝑝ℎ−𝑚𝑘

from processing plants to markets and compression stations(𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 ), from 𝑝𝑐−𝑝𝑐 ′

𝑝𝑐−𝑚𝑘 compression stations to markets and intermediate stations (𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐 ′ ,𝑡 ), and 𝑝𝑐 ′ −𝑚𝑘

from intermediate stations to markets (𝐹𝐺𝑇𝑝𝑐 ′ ,𝑚𝑘,𝑡 ). The Big-M constraints are given by Equations (16)-(24). A binary variable is equal to 1 if the corresponding individual transportation link is included in the supply chain and 0 otherwise. For shale gas: 𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

𝑤−𝑐

𝑤−𝑐 𝑙𝑜𝑤𝑒𝑟 𝑤−𝑐 𝑤−𝑐 𝑦𝑠𝑡𝑤,𝑐,𝑡 𝑓𝑠𝑡𝑤,𝑐 ≤ 𝐹𝑆𝑇𝑤,𝑐,𝑡 ≤ 𝑦𝑠𝑡𝑤,𝑐,𝑡 𝑓𝑠𝑡𝑤,𝑐

𝑐−𝑐′ 𝑙𝑜𝑤𝑒𝑟 𝑓𝑠𝑡𝑐,𝑐′

𝑐 ′ −𝑝ℎ 𝑦𝑠𝑡𝑐 ′ ,𝑝ℎ,𝑡

𝑐 ′ −𝑝ℎ 𝑙𝑜𝑤𝑒𝑟 𝑓𝑠𝑡𝑐′,𝑝ℎ

≤

𝑐−𝑐 ′ ∑𝑤 𝐹𝑆𝑇𝑤,𝑐,𝑐 ′ ,𝑡

≤

𝑐 ′ −𝑝ℎ ∑𝑤 𝐹𝑆𝑇𝑤,𝑐 ′ ,𝑝ℎ,𝑡

≤

𝑐−𝑐 ′ 𝑦𝑠𝑡𝑐,𝑐 ′ ,𝑡

𝑝ℎ−𝑝𝑐

𝑐−𝑝ℎ 𝑢𝑝𝑝𝑒𝑟 𝑓𝑠𝑡𝑐,𝑝ℎ

∀𝑐, 𝑝ℎ, 𝑡

𝑐−𝑐 ′ 𝑢𝑝𝑝𝑒𝑟 𝑓𝑠𝑡𝑐,𝑐 ′

∀𝑐, 𝑐′, 𝑡

≤

𝑐 ′ −𝑝ℎ 𝑦𝑠𝑡𝑐 ′ ,𝑝ℎ,𝑡

re

Similarly for natural gas:

≤

𝑐−𝑝ℎ 𝑦𝑠𝑡𝑐,𝑝ℎ,𝑡

of

𝑐−𝑐 ′ 𝑦𝑠𝑡𝑐,𝑐 ′ ,𝑡

≤

𝑐−𝑝ℎ ∑𝑤 𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡

𝑐 ′ −𝑝ℎ 𝑢𝑝𝑝𝑒𝑟 𝑓𝑠𝑡𝑐 ′ ,𝑝ℎ

𝑝ℎ−𝑝𝑐 𝑢𝑝𝑝𝑒𝑟

lP

𝑝ℎ−𝑝𝑐 𝑝ℎ−𝑝𝑐 𝑝ℎ−𝑝𝑐 𝑙𝑜𝑤𝑒𝑟 𝑦𝑔𝑡𝑝ℎ,𝑝𝑐,𝑡 𝑓𝑔𝑡𝑝ℎ,𝑝𝑐 ≤ 𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 ≤ 𝑦𝑔𝑡𝑝ℎ,𝑝𝑐,𝑡 𝑓𝑔𝑡𝑝ℎ,𝑝𝑐

𝑝ℎ−𝑚𝑘 𝑢𝑝𝑝𝑒𝑟

𝑝ℎ−𝑚𝑘

𝑝ℎ−𝑚𝑘 𝑝ℎ−𝑚𝑘 𝑝ℎ−𝑚𝑘 𝑙𝑜𝑤𝑒𝑟 𝑦𝑔𝑡𝑝ℎ,𝑚𝑘,𝑡 𝑓𝑔𝑡𝑝ℎ,𝑚𝑘 ≤ 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 ≤ 𝑦𝑔𝑡𝑝ℎ,𝑚𝑘,𝑡 𝑓𝑔𝑡𝑝ℎ,𝑚𝑘 𝑝𝑐−𝑚𝑘 𝑙𝑜𝑤𝑒𝑟 𝑓𝑔𝑡𝑝𝑐,𝑚𝑘

𝑝𝑐−𝑝𝑐 ′ 𝑦𝑔𝑡𝑝𝑐,𝑝𝑐 ′ ,𝑡

𝑝𝑐−𝑝𝑐′ 𝑙𝑜𝑤𝑒𝑟 𝑓𝑔𝑡𝑝𝑐−𝑝𝑐′

ur na 𝑝𝑐−𝑚𝑘 𝑦𝑔𝑡𝑝𝑐,𝑚𝑘,𝑡

Jo

𝑝𝑐′−𝑚𝑘 𝑦𝑔𝑡𝑝𝑐′,𝑚𝑘,𝑡

𝑝𝑐′−𝑚𝑘 𝑓𝑔𝑡𝑝𝑐𝑙𝑜𝑤𝑒𝑟 ′ ,𝑚𝑘

≤

𝑝𝑐−𝑚𝑘 𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡

≤

𝑝𝑐−𝑝𝑐 ′ 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐 ′ ,𝑡

≤

𝑝𝑐 ′ −𝑚𝑘 𝐹𝐺𝑇𝑝𝑐 ′ ,𝑚𝑘,𝑡

(16)

ro

𝑐−𝑝ℎ 𝑙𝑜𝑤𝑒𝑟 𝑓𝑠𝑡𝑐,𝑝ℎ

-p

𝑐−𝑝ℎ 𝑦𝑠𝑡𝑐,𝑝ℎ,𝑡

∀𝑤, 𝑐, 𝑡

(17)

(18)

∀𝑐 ′ , 𝑝ℎ, 𝑡

(19)

∀𝑝ℎ, 𝑝𝑐, 𝑡

(20)

∀𝑝ℎ, 𝑚𝑘, 𝑡

(21)

≤

𝑝𝑐−𝑚𝑘 𝑦𝑔𝑡𝑝𝑐,𝑚𝑘,𝑡

𝑝𝑐−𝑚𝑘 𝑢𝑝𝑝𝑒𝑟 𝑓𝑔𝑡𝑝𝑐,𝑚𝑘

∀𝑝𝑐, 𝑚𝑘, 𝑡

(22)

≤

𝑝𝑐−𝑝𝑐 ′ 𝑦𝑔𝑡𝑝𝑐,𝑝𝑐 ′ ,𝑡

𝑝𝑐−𝑝𝑐 ′ 𝑢𝑝𝑝𝑒𝑟 𝑓𝑔𝑡𝑝𝑐,𝑝𝑐 ′

∀𝑝𝑐, 𝑝𝑐′, 𝑡

(23)

≤

𝑝𝑐 ′ −𝑚𝑘 𝑦𝑔𝑡𝑝𝑐 ′ ,𝑚𝑘,𝑡

𝑝𝑐 ′ −𝑚𝑘 𝑢𝑝𝑝𝑒𝑟 𝑓𝑔𝑡𝑝𝑐 ′ ,𝑚𝑘

∀𝑝𝑐 ′ , 𝑚𝑘, 𝑡

(24)

3.1.1.9 Exploitation of a basin The Boolean variable 𝑌𝑤𝑤,𝑡 (associated to the binary variable 𝑦𝑤𝑤,𝑡 ) is used to determine the time period when a basin is exploited. The basin does not produce before its exploitation starts (𝑡′) or after it has ceased its operation (𝑇). Moreover, the produced gas

11

for each basin depends on the operating time; where 𝜏 is the operating time at time period 𝑡, so that 𝜏 = 𝑡 − 𝑡′. This formulation includes the following disjunction, which is then converted into the algebraic Equation (25). 𝑌𝑤𝑤,𝑡 ¬𝑌𝑤𝑤,𝑡 [𝐹𝑆𝑤,𝑡 = 𝑒𝑢𝑟𝑤,𝜏+1 ∀ 𝑡 ′ ≤ 𝜏 ≤ 𝑇] ∨ [𝐹𝑆𝑤,𝑡 = 0] ∀ 𝑤, 𝜏 = 𝑡 − 𝑡′

(25)

of

𝐹𝑆𝑤,𝑡 = 𝑒𝑢𝑟𝑤,𝜏+1 𝑦𝑤𝑤,𝑡

In general, 𝑒𝑢𝑟𝑤,𝑡 is a parameter of the model that represents the shale gas production

ro

profile of the shale basin w in time period 𝑡.

Equation (26) imposes a bound on the number of basins that can be exploited

-p

simultaneously (𝑏 is a known parameter in the model):

∑𝑤 𝑦𝑤𝑤,𝑡 ≤ 𝑏 ∀𝑡

lP

re

(26)

3.1.1.10 Mass balance of water

Fresh water is the primary source to satisfy the water demands in basins; nevertheless,

ur na

flowback water can be reused in the hydraulic fracturing operations. The water requirement for a hydraulic fracturing process is defined in terms of a shale production function. It should be noted that, although the data related to the list of wells drilled and hydraulically fractured is accessible, the exact amount of water needed and the water profiles are not available for some of the wells; that is because the amount of water used depends on the

Jo

exploitation efficiency, the composition of the components in the deposit and the variation in the depth of drilling. During the phase of acquisition of fresh water, the flow of fresh water sent to the shale 𝑓𝑟𝑒𝑠ℎ

basins 𝐹𝑊𝑖𝑤 ,𝑤,𝑡 is bounded by the availability in the watersheds 𝑖𝑤 surrounding the basins. That is represented through Equation (27).

12

𝑓𝑟𝑒𝑠ℎ 𝐹𝑊𝑖𝑤 ,𝑤,𝑡

≤

𝑓𝑟𝑒𝑠ℎ 𝑈𝑝𝑝𝑒𝑟 𝐹𝑊𝑖𝑤 ,𝑤,𝑡

∀ 𝑤, 𝑖𝑤 , 𝑡

(27) 𝑓𝑟𝑒𝑠ℎ

𝑤𝑒𝑙𝑙−𝑖𝑛 The water requirements in each basin (𝐹𝑊𝑤,𝑡 ) are provided by fresh water (𝐹𝑊𝑖𝑤 ,𝑤,𝑡 )

and by the water coming from the storage system, as defined in Equation (28). 𝑠𝑡𝑜𝑟𝑎𝑔𝑒

𝑤𝑒𝑙𝑙−𝑖𝑛 𝐹𝑊𝑤,𝑡 = 𝐹𝑊𝑤,𝑡

𝑓𝑟𝑒𝑠ℎ

+ ∑𝑖𝑤 𝐹𝑊𝑖𝑤 ,𝑤,𝑡

∀ 𝑤, 𝑡

(28)

Notice that the amount of fresh water required in each basin is only necessary if basin 𝑤 is

of

exploited in time period 𝑡. Similar from the gas profile production, the water requirement profile starts with a period of increment that will lead to a peak, followed by a decrease.

ro

The basin does not require water before its exploitation starts (𝑡′) of after it has ceased its operation (𝑇). Also, the water requirement for each basin depends on the operating time; where  is the operating time at time period 𝑡, so that 𝜏 = 𝑡 − 𝑡′. The amount of water

𝑌𝑤𝑤,𝑡 ¬𝑌𝑤𝑤,𝑡 𝑤𝑒𝑙𝑙−𝑖𝑛 ′ = 𝑤𝑟𝑤,𝜏+1 𝐹𝑆𝑤,𝜏+1 ∀𝑤, 𝑡 ≤ 𝜏 ≤ 𝑇] ∨ [𝐹𝑊𝑤,𝑡 = 0]

re

𝑤𝑒𝑙𝑙−𝑖𝑛 [𝐹𝑊𝑤,𝑡

-p

required responds to the profile assigned to the parameter 𝑤𝑟𝑤,𝜏+1 :

lP

𝑤𝑒𝑙𝑙−𝑖𝑛 𝐹𝑊𝑤,𝑡 = 𝑤𝑟𝑤,𝜏+1 𝐹𝑆𝑤,𝑡 𝑦𝑤𝑤,𝑡

∀ 𝑤, 𝜏 = 𝑡 − 𝑡′

𝑜𝑢𝑡 𝑤𝑒𝑙𝑙−𝑜𝑢𝑡 𝑤𝑒𝑙𝑙−𝑖𝑛 𝐹𝑊𝑤,𝑡 = 𝑤𝑟𝑤,𝜏+1 𝐹𝑊𝑤,𝑡

∀ 𝑤, 𝜏 = 𝑡 − 𝑡′

(29)

𝑤𝑒𝑙𝑙−𝑜𝑢𝑡 On the other hand, the amount of flowback and produced wastewater (𝐹𝑊𝑤,𝑡 ) is given

ur na

by Equation (30):

(30)

𝑜𝑢𝑡 where 𝑤𝑟𝑤,𝜏+1 is a known positive parameter (smaller than one) for a given basin.

In this work, three alternatives are considered for flowback and wastewater management: i)

Jo

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑜𝑛𝑠𝑖𝑡𝑒 the wastewater can be treated in the basins and reused (𝐹𝑊𝑤,𝑡 ), ii) it can be injected to

the available disposal wells 𝑗𝑤 (𝐹𝑊𝑗𝑤𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 ) or iii) it can be sent to outside treatment ,𝑤,𝑡 plants

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝑝𝑙𝑎𝑛𝑡 𝑘𝑤 (𝐹𝑊𝑤,𝑘𝑤 ,𝑡 ):

𝑤𝑒𝑙𝑙−𝑜𝑢𝑡 𝐹𝑊𝑤,𝑡

=

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝑜𝑛𝑠𝑖𝑡𝑒 𝐹𝑊𝑤,𝑡

+

∑𝑗𝑤 𝐹𝑊𝑗𝑤𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 ,𝑤,𝑡

+

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝑝𝑙𝑎𝑛𝑡 ∑𝑘𝑤 𝐹𝑊𝑤,𝑘 𝑤 ,𝑡

∀ 𝑤, 𝑡

(31) 13

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑜𝑛𝑠𝑖𝑡𝑒 The wastewater treated onsite (𝐹𝑊𝑤,𝑡 ) is stored to be used in the basin during the

next period, reducing the use of fresh water: 𝑠𝑡𝑜𝑟𝑎𝑔𝑒

𝐹𝑊𝑤,𝑡

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑜𝑛𝑠𝑖𝑡𝑒 = 𝐹𝑊𝑤,𝑡−1

∀ 𝑤, 𝑡

(32)

The total amount of wastewater treated in the basins, sent to the disposal wells or to the municipal treatment plants, is bounded by the corresponding capacities of the existing

∑𝑡 𝐹𝑊𝑗𝑤𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 ≤ 𝑑𝑐𝑗𝑤 ,𝑤,𝑡

∀𝑤, 𝑡

ro

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑜𝑛𝑠𝑖𝑡𝑒 𝐹𝑊𝑤,𝑡 ≤ 𝑑𝑐𝑤,𝑡

of

infrastructure.

∀𝑗𝑤 , 𝑤

𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝑝𝑙𝑎𝑛𝑡

𝑠𝑡𝑜𝑟𝑎𝑔𝑒

𝑠𝑡𝑜𝑟𝑎𝑔𝑒

3.1.2 Costs and investment

≤ 𝑑𝑠𝑤

lP

𝐹𝑊𝑤,𝑡

(35)

is subject to the

re

Similarly, the amount of treated water that can be stored 𝐹𝑊𝑤,𝑡 storage capacity:

(34)

∀𝑤, 𝑘𝑤 , 𝑡

-p

𝑡𝑟𝑒𝑎𝑡𝑒𝑑−𝑝𝑙𝑎𝑛𝑡 𝐹𝑊𝑤,𝑘 ≤ 𝐹𝑊𝑘𝑤 ,𝑡 𝑤 ,𝑡

(33)

∀𝑤, 𝑡

(36)

ur na

3.1.2.1 Natural gas supply chain costs

The implementation of the gas distribution network involves the optimal selection of the transportation links among the existing infrastructure; that is, the selection of the compressor stations (main and intermediate) that define a pipeline route as well as the shale gas sources, processing plants and markets. The capacity and the availability for each

Jo

section of a pipeline route as well as the capacities of the plants are defined a priori. The investment costs considered in this formulation involve only those related to the exploitation of the basins (described below in section 3.1.2.3) and those related to the installation of the pipelines of shale gas from the basins to the compressor stations (which do not exist in the current infrastructure). The costs related to the installation of pipelines from basins to the existing transportation infrastructure are described as follows. When pipelines facilities from the basins to 14

𝑤−𝑐 compressor stations are needed, the gas flow (𝐹𝑆𝑇𝑤,𝑐,𝑡 ) is bounded by the compressor 𝑚𝑎𝑥𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦

stations capacity (𝑝𝑐𝑐 𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

(𝑓𝑠𝑡𝑤,𝑐

), which also limits the maximum pipeline capacity

) through Equation (16); operation and investment cost have to be included in

𝑤−𝑐 that case. Otherwise, if the facility is not needed, the corresponding investment (𝐶𝑐𝑎𝑝𝑤,𝑐 ) 𝑤−𝑐 and operation costs (𝐶𝑜𝑝𝑤,𝑐,𝑡 ) are equal to zero. As a significant assumption, linear unit

costs parameters are used in the cost estimations. This is modeled by the following disjunction:

𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

re

𝑤−𝑐 𝑤−𝑐 𝐶𝑐𝑎𝑝𝑤,𝑐 = 𝐶𝑎𝑝𝑤,𝑐 𝑓𝑠𝑡𝑤,𝑐

[

of

⌉ ⌉∨ ⌉ ⌉ 𝑡 ≥ 𝑡′⌉

𝑤−𝑐 ¬𝑌𝑠𝑡𝑤,𝑐,𝑡 𝑤−𝑐 =0 ⌈ 𝐹𝑆𝑇𝑤,𝑐,𝑡 𝑤−𝑐 𝐶𝑜𝑝𝑤,𝑐,𝑡 = 0 𝑡 =

⌉ 𝑤−𝑐 ¬𝑌𝑝𝑤,𝑐 ⌉ 𝑤−𝑐 ¬𝑌𝑠𝑡𝑤,𝑐,𝑡 ⌉ ⌉⌉ 𝑤−𝑐 ⌉ ⌈𝐹𝑆𝑇𝑤,𝑐,𝑡 = 0 ⌉⌉ 𝑡′ ⌉ ∨ 𝑤−𝑐 𝐶𝑜𝑝𝑤,𝑐,𝑡 =0 ⌉ ⌉ ⌉ 𝑤−𝑐 𝐶𝑐𝑎𝑝𝑤,𝑐 =0⌉ ⌉ ] ⌉ [ ⌉ ]

ro

𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟 𝑤−𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑡 ≤ 𝑓𝑠𝑡𝑤,𝑐 𝑤−𝑐 𝑤−𝑐 𝑙𝑜𝑤𝑒𝑟 𝐹𝑆𝑇𝑤,𝑐,𝑡 ≥ 𝑓𝑠𝑡𝑤,𝑐 𝑤−𝑐 𝑤−𝑐 𝑤−𝑐 𝐶𝑜𝑝𝑤,𝑐,𝑡 = 𝐶𝑆𝑇𝑤,𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑡

-p

𝑤−𝑐 𝑌𝑠𝑡𝑤,𝑐,𝑡

𝑤−𝑐 𝑌𝑝𝑤,𝑐

lP

𝑤−𝑐 The Boolean variable 𝑌𝑝𝑤,𝑐 represents the existence of the pipeline between the basins 𝑤 𝑤−𝑐 and compressor stations 𝑐. 𝑌𝑠𝑡𝑤,𝑐 represents the operation of such pipeline at time 𝑡. Such

ur na

𝑤−𝑐 𝑤−𝑐 disjunction is then reformulated through binary variables 𝑦𝑝𝑤,𝑐 and 𝑦𝑠𝑡𝑤,𝑐 as follows: 𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

𝑤−𝑐 𝑤−𝑐 𝐶𝑐𝑎𝑝𝑤,𝑐 = 𝐶𝑎𝑝𝑤,𝑐 𝑓𝑠𝑡𝑤,𝑐

𝑤−𝑐 𝑦𝑝𝑤,𝑐

𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

𝑤−𝑐 𝑤−𝑐 𝑤−𝑐 𝑤−𝑐 𝐶𝑜𝑝𝑤,𝑐,𝑡 ≥ 𝐶𝑆𝑇𝑤,𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑡 − 𝐶𝑆𝑇𝑤,𝑐 𝑓𝑠𝑡𝑤,𝑐

𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

(37)

𝑤−𝑐 (1 − 𝑦𝑠𝑡𝑤,𝑐,𝑡 )

∀ 𝑤, 𝑐, 𝑡

(38)

𝑤−𝑐 (1 − 𝑦𝑠𝑡𝑤,𝑐,𝑡 )

∀ 𝑤, 𝑐, 𝑡

(39)

Jo

𝑤−𝑐 𝑤−𝑐 𝑤−𝑐 𝑤−𝑐 𝐶𝑜𝑝𝑤,𝑐,𝑡 ≤ 𝐶𝑆𝑇𝑤,𝑐 𝐹𝑆𝑇𝑤,𝑐,𝑡 + 𝐶𝑆𝑇𝑤,𝑐 𝑓𝑠𝑡𝑤,𝑐

∀ 𝑤, 𝑐

𝑤−𝑐 𝑤−𝑐 The relation between the binary variables 𝑦𝑝𝑤,𝑐 and 𝑦𝑠𝑡𝑤,𝑐,𝑡 is given by the Equations

(40)-(41):

𝑤−𝑐 𝑤−𝑐 ∑𝑡 𝑦𝑠𝑡𝑤,𝑐,𝑡 ≥ 𝑦𝑝𝑤,𝑐 ∀ 𝑤, 𝑐

(40)

𝑤−𝑐 𝑤−𝑐 𝑦𝑠𝑡𝑤,𝑐,𝑡 ≤ 𝑦𝑝𝑤,𝑐 ∀ 𝑤, 𝑐, 𝑡

(41)

15

𝑤−𝑐 Equations (37)-(39) are activated when the binary variable 𝑦𝑝𝑤,𝑐 takes the value of 1. Note 𝑤−𝑐 that the investment cost (𝐶𝑎𝑝𝑤,𝑐 ) depends only on the existence of the pipeline. On the 𝑤−𝑐 other hand, the operation cost at a given time period (𝐶𝑜𝑝𝑤,𝑐,𝑡 ) also depends on the binary 𝑤−𝑐 𝑢𝑝𝑝𝑒𝑟

𝑤−𝑐 𝑤−𝑐 variable 𝑦𝑠𝑡𝑤,𝑐,𝑡 . The upper bound (𝐶𝑆𝑇𝑤,𝑐 𝑓𝑠𝑡𝑤,𝑐

) is used to relax Equations (38)-

(39) in case the pipeline is not under operation. The remaining costs related to the supply chain involve the transportation costs. The

of

transportation costs in the network are simplified through the use of fixed tariff rates (costs for gas transportation are not estimated in terms of compression costs). The tariff rates are

ro

parameters dependent on the region where the transportation occurs. Two classes of base tariffs are established: the capacity reservation tariff and the usage tariff. For shale gas, usage tariff rates are used to estimate the transportation costs among basins and processing ′

′

𝑝ℎ−𝑝𝑐

cost

from

𝑝ℎ−𝑚𝑘

processing

plants

𝑝𝑐−𝑝𝑐 ′

to

markets

(involving

flows

𝑝𝑐 ′ −𝑚𝑘

re

transportation

-p

𝑐 −𝑝ℎ 𝑐−𝑐 plants (involving gas flows 𝐹𝑆𝑇𝑤,𝑐−𝑝ℎ 𝑐,𝑝ℎ,𝑡 , 𝐹𝑆𝑇𝑤,𝑐,𝑐 ′ ,𝑡 , 𝐹𝑆𝑇𝑤,𝑐 ′ ,𝑝ℎ,𝑡 ) and, for natural gas, the

𝑝𝑐−𝑚𝑘

𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 , 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 , 𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 , 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐 ′ ,𝑡 𝑎𝑛𝑑𝐹𝐺𝑇𝑝𝑐 ′ ,𝑚𝑘,𝑡 ). Usage tariff rates assume unit

lP

costs defined in terms of the amount of material transported by the pipelines. 𝑐−𝑝ℎ

𝑐−𝑝ℎ

𝑤−𝑐 𝐶𝑇𝐷 = ∑ ∑ ∑ 𝐶𝑜𝑝𝑤,𝑐,𝑡 + ∑ ∑ ∑ ∑ 𝐶𝑆𝑇𝑐,𝑝ℎ 𝐹𝑆𝑇𝑤,𝑐,𝑝ℎ,𝑡 𝑤

𝑐

𝑤

𝑡

𝑐

𝑝ℎ

𝑡

′

𝑐′−𝑝ℎ

ur na

𝑐−𝑐 𝑐−𝑐′ + ∑ ∑ ∑ ∑ 𝐶𝑆𝑇𝑐,𝑐′ 𝐹𝑆𝑇𝑤,𝑐,𝑐 ′ ,𝑡 + ∑ ∑ ∑ ∑ 𝑆𝑇𝑐′,𝑝ℎ

𝑤

𝑐

𝑐′

𝑡

𝑝ℎ−𝑝𝑐

𝑤

𝑐′ 𝑝ℎ

𝑝ℎ−𝑝𝑐

𝑡 𝑝ℎ−𝑚𝑘

𝑐 ′ −𝑝ℎ

𝐹𝑆𝑇𝑤,𝑐 ′,𝑝ℎ,𝑡 𝑝ℎ−𝑚𝑘

+ ∑ ∑ ∑ 𝐶𝐺𝑇𝑝ℎ,𝑝𝑐 𝐹𝐺𝑇𝑝ℎ,𝑝𝑐,𝑡 + ∑ ∑ ∑ 𝐶𝐺𝑇𝑝ℎ,𝑚𝑘 𝐹𝐺𝑇𝑝ℎ,𝑚𝑘,𝑡 𝑝ℎ 𝑝𝑐

𝑡

𝑝𝑐−𝑚𝑘

+ ∑ ∑ ∑ 𝐶𝐺𝑇𝑝𝑐,𝑚𝑘

Jo

𝑝𝑐 𝑚𝑘

𝑡

𝑝𝑐 ′ −𝑚𝑘

+ ∑ ∑ ∑ 𝐶𝐺𝑇𝑝𝑐 ′ ,𝑚𝑘 𝑝𝑐 ′ 𝑚𝑘

𝑝ℎ 𝑚𝑘

𝑡 𝑝𝑐−𝑝𝑐 ′

𝑝𝑐−𝑚𝑘

𝑝𝑐−𝑝𝑐 ′

𝐹𝐺𝑇𝑝𝑐,𝑚𝑘,𝑡 + ∑ ∑ ∑ 𝐶𝐺𝑇𝑝𝑐−𝑝𝑐 ′ 𝐹𝐺𝑇𝑝𝑐,𝑝𝑐 ′ ,𝑡 𝑝𝑐 𝑝𝑐

𝑡

𝑝𝑐′−𝑚𝑘

𝐹𝐺𝑇𝑝𝑐′,𝑚𝑘,𝑡

𝑡

(42)

Reservation tariff rates are also known parameters which represent the cost for using the compressor stations in the interconnections of the pipeline system, as presented by

16

Equation (43). The total cost for using the compressor stations depends on the fixed rates 𝐶𝑠𝑐 and 𝐶𝑔𝑐 (binary variables have been previously defined): 𝑝𝑐 𝑝𝑐 𝑝𝑐′ 𝑝𝑐′ 𝑐 𝑐′ 𝑐′ 𝐶𝑆𝐶 = ∑𝑐 ∑𝑡 𝑦𝑐,𝑡 𝐶𝑠𝑐𝑐𝑐 + ∑𝑐′ ∑𝑡 𝑦𝑐′,𝑡 𝐶𝑠𝑐𝑐′ + ∑𝑝𝑐 ∑𝑡 𝑦𝑝𝑐,𝑡 𝐶𝑔𝑐𝑝𝑐 + ∑𝑝𝑐′ ∑𝑡 𝑦𝑝𝑐′,𝑡 𝐶𝑔𝑐𝑝𝑐′

(43)

3.1.2.2 Processing costs The cost of processing shale gas to natural gas is defined by the unit processing cost

(44)

ro

𝐶𝐺𝑃 = ∑𝑤 ∑𝑝ℎ ∑𝑡 𝐶𝑆𝑃𝑤,𝑝ℎ 𝑃𝑆𝑤,𝑝ℎ,𝑡

of

𝐶𝑆𝑃𝑤,𝑝ℎ

3.1.2.3 Exploitation costs

-p

𝑤) The exploitation costs involve the investment cost per basin (𝐶𝑐𝑎𝑝𝑤 and the 𝑤 corresponding operation costs (𝐶𝑜𝑝𝑤,𝑡 ). These terms are represented through the following

re

disjunction:

𝑌𝑤 ′ 𝑤

ur na

lP

¬𝑌𝑤 ′ 𝑤 𝑌𝑤𝑤,𝑡 ⌉ ¬𝑌𝑤𝑤,𝑡 ¬𝑌𝑤𝑤,𝑡 ⌉ 𝐹𝑆𝑤,𝑡 ≤ 𝑓𝑠𝑤𝑤𝑢𝑝𝑝𝑒𝑟 ⌉ ⌉ 𝐹𝑆 = 0 𝐹𝑆 ⌉⌉∨ ⌈ 𝑤,𝑡 𝑤,𝑡 = 0 ⌉⌉ ⌉∨⌈ 𝐹𝑆𝑤,𝑡 ≥ 𝑓𝑠𝑤𝑤𝑙𝑜𝑤𝑒𝑟 𝑤 𝑤 𝐶𝑜𝑝𝑤,𝑡 = 0 ⌉⌉ ⌉ 𝐶𝑜𝑝𝑤,𝑡 = 0 𝑡 = 𝑡′ ⌉ 𝑤 𝑤 𝐶𝑜𝑝𝑤,𝑡 = 𝐶𝑆𝑇𝑤,𝑡 𝐹𝑆𝑤,𝑡 𝑡 ≥ 𝑡′⌉ 𝑤 ⌉ [ 𝐶𝑐𝑎𝑝𝑤 =0 ] 𝑤 𝑤 [ 𝐶𝑐𝑎𝑝𝑤 = 𝐶𝑎𝑝𝑤 ]

Once again, two Boolean variables are defined. 𝑌𝑤 ′ 𝑤 is used to represent the investment on the exploitation of basin 𝑤; whereas the Boolean variable 𝑌𝑤𝑤,𝑡 is related to the operation cost of the basin at time 𝑡. The binary variables 𝑦𝑤′𝑤 and 𝑦𝑤𝑤,𝑡 are used to

Jo

reformulate the disjunction as follows: 𝑤 𝑤 𝐶𝑐𝑎𝑝𝑤 = 𝐶𝑎𝑝𝑤 𝑦𝑤′𝑤

∀𝑤

(45)

𝑤 𝑤 𝑤 𝐶𝑜𝑝𝑤,𝑡 ≥ 𝐶𝑆𝑇𝑤,𝑡 𝐹𝑆𝑤,𝑡 − 𝐶𝑆𝑇𝑤,𝑡 𝑓𝑠𝑤𝑤𝑢𝑝𝑝𝑒𝑟 (1 − 𝑦𝑤𝑤,𝑡 ) ∀ 𝑤, 𝑡 ≥ 𝑡′

(46)

𝑤 𝑤 𝑤 𝐶𝑜𝑝𝑤,𝑡 ≤ 𝐶𝑆𝑇𝑤,𝑡 𝐹𝑆𝑤,𝑡 + 𝐶𝑆𝑇𝑤,𝑡 𝑓𝑠𝑤𝑤𝑢𝑝𝑝𝑒𝑟 (1 − 𝑦𝑤𝑤,𝑡 ) ∀ 𝑤, 𝑡 ≥ 𝑡′

(47)

Also, the relation between the binary variables 𝑦𝑤′𝑤 and 𝑦𝑤𝑤,𝑡 is given by:

17

∑𝑡 𝑦𝑤𝑤,𝑡 ≥ 𝑦𝑤′𝑤 𝑦𝑤𝑤,𝑡 ≤ 𝑦𝑤′𝑤

∀𝑤

(48)

∀ 𝑤, 𝑡

(49)

3.1.2.4 Water Acquisition costs Fresh water acquisition costs include two terms. The first one depends on the water stress level in the watershed 𝑖𝑤 (unit cost is 𝐶𝐹𝑊𝑖𝐴𝑐 ); the second term involve the transportation 𝑤 𝑖 −𝑤

from the source 𝑖𝑤 to the basin (unit cost is 𝐶𝑊𝑇𝑖𝑤𝑤,𝑤 ). 𝑖 −𝑤

𝑓𝑟𝑒𝑠ℎ

𝑓𝑟𝑒𝑠ℎ

∀ 𝑖𝑤 , 𝑤, 𝑡

(50)

ro

𝐹𝑊𝑖𝑤 ,𝑤,𝑡

of

𝑓𝑟𝑒𝑠ℎ

𝐶𝐹𝑊𝑖𝑤 ,𝑤,𝑡 = 𝐶𝐹𝑊𝑖𝐴𝑐 𝐹𝑊𝑖𝑤 ,𝑤,𝑡 + 𝐶𝑊𝑇𝑖𝑤𝑤,𝑤 𝑤

3.1.2.5 Wastewater management costs

is given by Equation (51): 𝑡𝑟𝑒𝑎𝑡𝑒𝑑

re

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

-p

The total cost for wastewater management including any of the three strategies considered

ur na

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝑡𝑟𝑒𝑎𝑡𝑒𝑑 −𝑝𝑙𝑎𝑛𝑡 −𝑝𝑙𝑎𝑛𝑡 ∑𝑘𝑤 𝐶𝐹𝑊𝑘 ,𝑡 𝐹𝑊𝑤,𝑘𝑤 ,𝑡 𝑤

lP

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝑜𝑛𝑠𝑖𝑡𝑒 𝐶𝐹𝑊𝑤,𝑡 = 𝐶𝐹𝑊𝑤𝑜𝑛𝑠𝑖𝑡𝑒 𝐹𝑊𝑤,𝑡 + ∑𝑗𝑤 𝐶𝐹𝑊𝑗𝑤𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 𝐹𝑊𝑗𝑤𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 + ,𝑤,𝑡

∀ 𝑤, 𝑡

(51)

3.1.2.6 Wastewater transportation cost The costs of transporting the wastewater to the disposal wells and to treatment plants 𝑘𝑤 are estimated in term of unit costs and the corresponding wastewater flows:

Jo

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 𝐶𝑇𝑊𝑤,𝑡

=

𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 ∑𝑗𝑤 𝐶𝑇𝑊𝑗𝑤𝑤−𝑗 ,𝑤 𝐹𝑊𝑗𝑤 ,𝑤,𝑡

+

𝑡𝑟𝑒𝑎𝑡𝑒𝑑 −𝑝𝑙𝑎𝑛𝑡 𝑤−𝑘 ∑𝑘𝑤 𝐶𝑇𝑊𝑤,𝑘𝑤 𝐹𝑊𝑤,𝑘 𝑤 ,𝑡

∀ 𝑤, 𝑡

(52)

3.1.2.7 Storage and treatment investment Investment costs of storage units and treatment plants are defined by Equation (53): 𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑠𝑡𝑜𝑟𝑎𝑔𝑒

𝐶𝑊 𝑜𝑛𝑠𝑖𝑡𝑒 = ∑𝑤 𝐶𝑎𝑝𝑤𝑜𝑛𝑠𝑖𝑡𝑒 𝑦𝑤′𝑤 + ∑𝑤 ∑𝑡 𝐶𝐹𝑊𝑤

𝑠𝑡𝑜𝑟𝑎𝑔𝑒

𝐹𝑊𝑤,𝑡

(53) 18

3.1.3 Objective functions This work considers two objective functions; the minimization water footprint and the maximization of profit. 3.1.3.1 Net profit The net profit of a system for the exploitation of shale gas and the distribution of natural

of

gas includes the various economic estimations presented above (Section 3.1.2). In particular, it includes the costs and investment associated to the processing and distribution

ro

of gas (shale and natural), as well as those related to the transportation, treatment, storage and disposal of water; it also involves the utilities from the sales of natural gas in the

𝑓𝑟𝑒𝑠ℎ

-p

markets.

𝑡𝑟𝑒𝑎𝑡𝑒𝑑

𝑠𝑎𝑙𝑒𝑠 𝑝𝑟𝑜𝑓𝑖𝑡 = ∑𝑚𝑘 ∑𝑡 𝐼𝑚𝑘,𝑡 𝐹𝑀𝐾𝑚𝑘,𝑡 − ∑𝑖 ∑𝑤 ∑𝑡 𝐶𝐹𝑊𝑖,𝑤,𝑡 − ∑𝑤 ∑𝑡 𝐶𝐹𝑊𝑤,𝑡

𝑤

𝑤

𝑤−𝑐

− ∑𝑤 ∑𝑡 𝐶𝑇𝑊𝑡𝑟𝑒𝑎𝑡𝑒𝑑 − 𝑤,𝑡 𝑜𝑛𝑠𝑖𝑡𝑒

(54)

lP

re

∑𝑤 𝐶𝑐𝑎𝑝𝑤 − ∑𝑤 ∑𝑡 𝐶𝑜𝑝𝑤,𝑡 − ∑𝑤,𝑐 𝐶𝑐𝑎𝑝𝑤,𝑐 − 𝐶𝑇𝐷 − 𝐶𝑆𝐶 − 𝐶𝐺𝑃 − 𝐶𝑊

3.1.3.2 Water impact (minimization of water footprint) The impact of the shale gas exploitation on the water resources depends not only on the

ur na

amount of fresh water used but also on the alteration of water quality and its temporal distribution. Water conservation requires careful management of the water supply systems and a minimal impact on the hydrological cycle. The water management plan should focus on reducing the exploitation of the resource and on the recovering and conservation of

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water quality.

One of the objective functions of our formulation involves therefore the minimization of the water footprint. To that end, the water requirements of the exploitation process need to be estimated for the whole time horizon; such estimation includes the summation of the freshwater received from watersheds and the total amount of water that is injected into the disposal wells. The water injected into the disposal wells is included because it does not return to the hydrological cycle and, therefore, it directly affects the potential of water renewability in the region. 19

𝑤𝑎𝑡𝑒𝑟

𝑓𝑟𝑒𝑠ℎ

𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙

𝐹𝑊 𝑡𝑜𝑡𝑎𝑙 = ∑𝑖𝑤 ∑𝑤 ∑𝑡 𝐹𝑊𝑖𝑤 ,𝑤,𝑡 + ∑𝑗𝑤 ∑𝑤 ∑𝑡 𝐹𝑊𝑗𝑤 ,𝑤,𝑡

(55)

Those water flows are used to estimate the water stress index (WSI) used as one of the objective functions; please see section 4.1 of this paper and section 2.6 of the supplementary information file for a discussion about the estimation of the WSI. 3.2 Main Assumptions and Limitations of the Formulation The formulation described above includes the main components needed for the design and

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planning of a shale gas supply chain and the corresponding water management policies on a macroscopic scale. However, several significant assumptions were made with respect to the

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estimation of costs and the expected production of shale gas from basins. Those assumptions will of course limit the scope of the proposed approach. However, most of the

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information used for the numerical optimization of the case-study has been taken from real data repositories provided by national information agencies and has been processed through

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ArcGIS. Therefore, the results are expected to be used as a good approximation of the supply chain planning and the water impact caused by the exploitation of shale gas basins (given an estimation of the recoverable resources). In fact, some of the assumptions were

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made to agree with current policies and practices used for gas transportation and water acquisition in the case-study. A summary of the assumptions made is as follows:

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a. The model only considers existing infrastructure for gas distribution and transportation; that is, no capital investment is considered for either increasing the transportation capacities or building new pipeline routes. The exceptions are the pipelines needed to interconnect a basin with an existing pipeline route (which are not a part of the existing infrastructure). b. Natural gas production in processing plants is assume to depend on the feed of shale gas

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𝑝𝑟𝑜𝑐 and on a factor associated to the corresponding losses in production (𝛼𝑤 ). Such factor is

assumed as a constant for each basin. c. Cost estimations are mainly based on linear unit cost parameters. Such approximation is used for: gas transportation (tariff rates), water acquisition (transportation from fresh water resources), water treatment, water storage, water disposal and shale gas exploitation costs. In particular, no compression costs are estimated for gas transportation. The approach used for gas transportation includes fixed tariff rates. The tariff rates are parameters dependent 20

on the region where the transportation occurs. Two classes of base tariffs are established: the capacity reservation tariff and the usage tariff. These assumptions are consistent with the current policies and practices in the case-study. In fact, as it will be described, the tariff rates definitions meet the current legal regulations imposed in Mexico through the Commission for the Regulation of Energy (CRE) and the National Center for the Control of Natural Gas. d. The water requirement for the exploitation of each basin is estimated in terms of the gas

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shale production. e. The flowback and produced wastewater are estimated in terms of the fresh water usage

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for each well. The estimation involves a simplified constant factor. The factors used in this work were taken from literature reports regarding shale gas water management.

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f. The wastewater (flowback and produced water) management considers three alternatives: i) the wastewater can be treated onsite and reused, ii) it can be sent to disposal wells or iii)

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it can be sent to existing treatment plants.

g. Freshwater acquisition is bounded by the water stress level for each watershed on a given region. Also, only the watersheds surrounding a basin (at given maximum distances) can be

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used as a source for fresh water of such basin.

h. Simplified unit costs are assumed for water acquisition (transportation cost from fresh

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water source to the basin), water transportation (from the basin to treatment plants or disposal wells) and water treatment.

i. For the shale production, typical decay profiles are assumed as given, although variations might exist according to the number of wells in each basin. Uncertainties are not considered. However, because of the multiperiod approach used in this work, variations in

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time are considered by modifying the parameters at each time period. j. Water stress is defined as the ratio between the total annual water withdrawals and the water availability. k. The balances used for both water and natural gas are defined in terms of the physical limitations imposed by the geography of the case-study on a macroscopic scale. For instance, we use balance equations for water involving only the watersheds existing in the region surrounding a basin. We believe that trying to use water for available watersheds in 21

regions located too far from a basin would be impractical (on a macroscopic scale) and could provide misleading results in terms of the feasibility of the basin exploitation. Therefore, no overall water and natural gas balances are included.

4. Case Study and Results: Exploitation of Shale Gas in Mexico and the Use of ESRI ArcGIS

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A discussion is conducted currently in Mexico about the potential exploitation of its shale gas reserves and the consequent impact on the environment. The proposed approach was

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applied to a case study involving a natural gas exploitation and distribution system from unconventional sources in Mexico. There are 6 previously studied shale gas basins recognized as potential sources of shale gas in Mexico: Chihuahua, Burro-Picachos,

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Sabinas, Burgos, Tampico-Misantla, and Veracruz. In addition, the shale gas can be processed in any of 7 existing natural gas processing plants, located in Reynosa, Arenque,

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Poza Rica, Matapioche, La Venta, Cactus and Ciudad Pemex. Market locations and the estimated demands are defined for 5 regions in the country: Northwest, Northeast, Central-

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West, Central and South of Mexico (see Figure S2 in the supplementary information file). Similarly, the time horizon is assumed as 15 years. Finally, 30 major watersheds are available as sources of fresh water in the regions under analysis (See Table S4 in the

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supplementary information file).

A simplified diagram of the currently existing pipeline transportation system in Mexico (Mexican National Gas Transportation System) is considered (CENAGAS, 2016). For the case study, only the currently available transportation capacities are considered for each

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section over the time horizon. Figure 2 presents a general outline of the case study (See also Figures S4 and S5 of the supporting information file). As described in the formulation, the estimation of natural and shale gas transportation is made through the definition of fixed tariff rates. The rates depend on the region where the transportation occurs. Figure S3 of the supplementary information file shows the regions used for the tariff rates definition. The required data for every one of the parameters in terms of costs, availability and demand are taken from databases of governmental agencies (See the supporting information file: 22

Mexican Secretary of Energy, SENER; Mexican National Petroleum Company, PEMEX; Mexican National Commission for Knowledge and Use of Biodiversity, CONABIO; Mexican National Commission for Water, CONAGUA; Mexican Secretary of Environment and Natural Resource, SEMARNAT). Therefore, the parameters of the model were defined as close to reality as possible by using the economic and geographic databases of the country; particularly important for the transportation costs and water availability, the geographic information was processed through the geographic information system ESRI ArcGIS. A detailed description of the case study, as well as the data and the main

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parameters fed to the model are included in the supporting information file of this paper.

4.1 Results and Discussion

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The model for the case study consists of 12,600 binary variables, 85,213 continuous variables and 122,719 constraints. It has been coded in the GAMS (General Algebraic

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Modeling System) modeling environment and solved through the solver CPLEX. As described above, the formulation considers two objectives. The first one is related to the

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net profit of the shale gas production and distribution system; the second one is related to the water impact. To assess the water exploitation impact, it is important to consider not

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only the amount of freshwater extracted, but also the resulting environmental damage caused by the extraction. The environmental impact of water exploitation is tied to many spatial factors, such as the water availability and the patterns of water consumption in the location under study. In this work, to perform a regional analysis of water exploitation, the geographic information available in Mexico (processed with Esri ArcGIS) is used along

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with the Pfister method (Pfister, 2009), which provides an approach to estimate the Water Stress Index (WSI). A detailed description of the WSI estimation is presented in the supporting information file. The estimation of WSI is based on the water stress ratio for each watershed (WTA), which is the ratio between the total annual water withdrawals for consumptive use (WU) with respect to water availability (WA); when such ratio is greater than 0.4, it is implied that the corresponding region is experiencing severe water stress and scarcity. The WSI estimation also includes the precipitation variation and the regeneration capacity of each specific watershed (Pfister, 2009). 23

The Pareto set obtained from the multi-objective approach and the main results of the casestudy are shown in Figure 3 and Table 2, respectively. The Pareto set was determined by the ɛ-constraint method. The approach involves the maximization of the net profit, as well as the minimization of the water footprint of the exploitation process. The value of the water footprint reported in this work corresponds to the Stress Weighted Water Footprint (SWWF), which involves the summation (over all of the watersheds included in a solution) of the product between the water withdrawals required for consumptive use times the corresponding water stress index (WSI). Table 2 includes the use of freshwater as well as

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the management decisions made with respect to the flowback and produced wastewater; in the following discussions, the term produced wastewater will refer to both the flowback

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water and the produced water from fracking. Further, in Table 2, the term injected water refers to the produced wastewater that is not treated and is therefore injected into the

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disposal wells; reused and recycled water refers to produced wastewater which is treated on site and re-cycled to the hydraulic fracturing process (in order to decrease the need for fresh

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water); discharged water is the produced wastewater that is treated on municipal treatment plants and reaches enough quality as to be discharged back to surface water sources.

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The analysis of solutions A, B and C is described next, corresponding to the minimization of the water footprint (A), the tradeoff solution (B) and the net profit minimization (C). For solution A, the net profit throughout the time horizon results in 1,129.5x106 USD, with the

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SWWF equal to 644,670 and a freshwater consumption of 4.58x106 m3. For solution C (maximization of profit), the results include the exploitation of 3 out of the 6 potential shale basins with the net profit of 15,570.75 x106 USD, SWWF of 26,107,110 and freshwater consumption of 68x106 m3. In solution B, the net profit is 9,035.10 x106 USD, with SWWF

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of 12,105,900 and a freshwater consumption of 32x106 m3.

Both Figure 3 and Table 2 also show the optimal results for the produced wastewater management alternatives. Since the water footprint is being minimized in Solution A, no produced wastewater is injected to disposal wells (such water does not return to the hydrological cycle); 90% of the produced wastewater is treated and recycled on site and the 24

remaining 10% is sent to municipal wastewater treatment plants (discharged water). Actually, a minimum of 10% was set as the lower bound for discharged water; so, the optimal solution A reaches such boundary. In solution C the goal is maximizing the net profit; as a result, 54% of the wastewater produced is sent to disposal wells (i.e. it does not receive treatment) and only 1% is treated on site (45% is treated on treatment plants). Notice also that both the total fresh water usage and the total gas production are considerable higher than those of Solution A. Finally, for solution B, 1% of the wastewater produced is sent to disposal wells, whereas 63% is treated on site (36% is treated on

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treatment plants).

Also from Figure 3, when the freshwater consumption is less than 24x106m3 during the

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whole time horizon (solution A), only one shale basin is exploited; for a consumption of more than 35x106m3 (solution C) 3 out of the 6 potential basins are exploited. Given the

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current state of the national gas infrastructure in Mexico, the simultaneous exploitation of the 6 basins is infeasible due to the reduced capacity of transportation currently available.

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Figure 4 shows the cumulative gas production for each solution (time is shown in quarters of a year). For solution A, only the basin located in Chihuahua is exploited. In solution B, the basins exploited are Veracruz (starting at year 1) and Tampico-Misantla (starting at year

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6). For the net profit maximization (solution C), the exploitation starts in the basin located at Veracruz (starting at year 1), then in the basin of Burro-Picachos (starting at year 2) and, finally, the Tampico-Misantla basin (starting at year 4). The demand satisfaction for each solution is shown in Figure 5. In solutions A and B, the

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demands of two out of the five markets are basically unsatisfied. When the profit is maximized (solution C), the natural gas is distributed mainly in the market located in the central-western region, achieving up to 100% satisfaction of the demand during the first five years, but meeting only 19.33% of the total demand for all of the markets during the whole time horizon. Solution A (minimum water footprint) reaches up to 50% of the demand satisfaction in the central-western and northeastern markets in the first year, but the well production curve decays rapidly; throughout the total time horizon, only 1.68% of the demand for all of the markets is satisfied. In solution B, the exploitation of a second basin 25

at year 6 allows the satisfaction of 11.38% of the total demand satisfaction for all of the markets. Currently, the gas demand not met by internal production in Mexico is achieved through importation. It is clear that the exploitation of non-conventional energy sources in Mexico will not be able to satisfy the current demand in Mexico, but its contribution would be important to close the gap towards energy independence.

In terms of water resources, the shale gas basins under study in this work are located within 3 hydrological regions. There are 30 major watersheds available in those three hydrological

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regions. The availabilities of freshwater of the 30 watersheds are enlisted in the supplementary information (Table S4); the list also includes the identifier code and name of

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each watershed. Figure 6 shows the locations of the watersheds exploited in the shale basins located at Chihuahua, Burro Picachos, Tampico-Misantla and Veracruz. For solution

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A, only the impact on watersheds 0842, 0837, 0823 and 0816 (shown in Figure 6a) is analyzed. Similarly, for solution B, watersheds 3008, 3019, 3017 and 2809 (Figures 6c and

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6d) are analyzed. The 13 exploited watersheds of solution C (0522, 0513, 0501, 0514, 0512, 2809, 2813, 3017, 3014, 2419, 2010, 3019 and 3008) are shown in Figures 6b, 6c,

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and 6d. The regions marked with an “X” are regions with known water deficit. The analysis of the water impact on the watersheds located in the Chihuahua and the BurroPicachos shale basins is of particular interest because they are located in a vulnerable zone

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of Mexico (in terms of water availability and domestic demands). The amount of acquired freshwater from each watershed in each year is shown in Figure 7. For solution A, the intensive extraction of freshwater is carried out during the first year; on the other hand, this occurs during the sixth year for solution B, and during the fourth year

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for solution C, respectively. This behavior is consistent with that of the cumulative gas production of solutions B and C shown in Figure 4. Notice that, for instance, the watersheds with high water exploitation in solution B are those identified as 3008, 3019 and 3017, located in the Tampico-Misantla and Veracruz basins (Figure 6). Figure 8 shows the yearly variation of the WSI and compares the current condition of each of the watersheds with the condition caused by each solution at the year of the highest extraction. It is observed that watersheds 3008, 3019, 0512, 0501 and 0522 have the highest 26

vulnerability (since currently they show a high WSI). However, after shale gas and water exploitation, the most important impact occurs to watersheds 0514 and 0513 (solution C). There is a reasonable explanation for such result. The basin located in Burro-Picachos is a basin with high potential for exploitation of shale gas. However, the surrounding region includes a watershed (0501) with a high WSI (0.9946 even before the potential shale gas exploitation); therefore, exploiting such basin will require acquiring water from any other of the surrounding watersheds. 0514 and 0513 are the closest alternatives, which are selected by the optimal solution; as a consequence, the WSI of those watersheds will

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necessarily increase.

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As mentioned before, the water stress ratio (WTA) is also an indicator of water use and availability in a country, watershed or region. If such percentage is greater than 40%, the

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water stress is considered high or very high. This factor is of interest because the basins of Chihuahua, Burro-Picachos, Sabinas and Burgos are located in a region with high current water stress percentage of 77.1%. The basin of Tampico-Misantla has medium water stress

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(20.4%), whereas the Veracruz reservoir has no significant water stress (5.9%) (CONAGUA, 2018). Figure 9 shows the water stress percentage for each watershed after

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the exploitation profiles of solutions A, B and C. As a note, the WTA of some of the watersheds is high already, even without the shale gas exploitation. That is the case of

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watersheds 0522, 0501, 0512 and 0514 in solutions A and B.

As described above, in solution C, the water exploitation impact in the Burro-Picachos basin is significant. Currently, the watersheds 0514 and 0513 have water stress percentages of 55.60% and 20.48%, respectively. If the shale basin in Burro-Picachos were exploited,

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watersheds 0513 and 0514 would increase their water stress to 99.05% and 68.46%, respectively. These watersheds provide the freshwater to the cities located nearby, including Monclova, Piedras Negras and Nuevo Laredo. Therefore, the exploitation of the Burro-Picachos basin will cause a clear undesirable effect on the water availability for those cities. As a general result, a complex environmental issue in the case of Mexico is identified: the northern part of the country includes not only the regions with the greatest potential for 27

shale gas exploitation (Burgos, Burro-Picachos, Sabinas and Tampico-Misantla) but also the areas with lowest water availability. Actually, the only region with potential for shale gas exploitation which is not vulnerable from the water availability perspective is the shale basin located in Veracruz (which is not the basin with greatest potential for exploitation). As a result, the optimal solution tends to select the basins with higher estimated recoverable resources and then to find the best possible solution with respect to water. Unfortunately, whenever two basins or more are selected for exploitation, even the optimal selections

the surrounding regions will present an impact on water stress.

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4.2 Sensitivity Analysis

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result in significant water stress in the northern region of the country, since at least one of

To study the consistency of the results obtained by the formulation proposed, sensitivity

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analyses were performed. The analysis involves variations on i) the production factor used 𝑝𝑟𝑜𝑐 in Equation (5) (𝛼𝑤 ) and ii) the percentage of produced wastewater treated on site

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(reused and recycled). Figures 10 and 11 show the results in dimensionless form. Dimensionless values (between 0 and 1) were obtained by dividing the corresponding

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values of each variable by the maximum value obtained in each of the analyses. 𝑝𝑟𝑜𝑐 The first analysis involves variations on the production factor used in Equation (5) (𝛼𝑤 ).

As described, the value was assumed constant, but an exact value for each reservoir is hard

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to define at the exploratory level since it presents a high degree of uncertainty. Figure 10 shows the behavior of the net profit, the fresh water used, the water footprint and the gas 𝑝𝑟𝑜𝑐 demand satisfaction against 𝛼𝑝𝑟𝑜𝑐 also 𝑤 . Equation (5) indicates that an increment of 𝛼𝑤

causes an increment of the natural gas produced from the same shale gas feed. Therefore, as expected, Figure 10 shows that an increment in 𝛼𝑝𝑟𝑜𝑐 also increases the net profit and the 𝑤

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percentage of the gas demand satisfaction (on the right of the plot); on the other hand, fresh water usage and the water footprint are not significantly impacted, since the need for fresh water is defined in terms of the shale basin conditions and the basin exploitation profiles (which do not vary on this study). An increment in 𝛼𝑝𝑟𝑜𝑐 from 0.5 to 0.8 increases the profit 𝑤 by about 50% (from a dimensionless value of 0.65 to the value equal to 1). In Figure 10, the highest values found and used for the normalization of the results are: USD$16.0321x109 for profit, 6.8997x107 m3 for freshwater and 26.1248 x106 for SWWF. 28

Finally, Figure 11 intends to study further the behavior of the wastewater management alternatives. Therefore, in this case, the basins exploited and the production profiles of the shale gas extraction are fixed. The basins and profiles used are those selected by the maximization of profit (Solution C); in fact, the objective function used is the maximization of profit. A linear variation between 80% and 0% is defined for the produced wastewater treated on site (reused and recycled water). Then, the analysis estimates the behavior of the freshwater, profit, water footprint and the remaining water management alternatives

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(municipal treatment plants or disposal wells). There is an obvious economic advantage of using disposal wells instead of using municipal treatment plants. Results show that, as the

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percentage of recycled water decreases, the wastewater treated on plants remains at the lower bound for such alternative (10%), whereas the wastewater sent to disposal wells

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increases linearly. However, the upper limit for the capacity of disposal wells is reached (when the percentage of treatment on site is around 35%) and then the percentage of

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wastewater treated on municipal plant increases linearly. Notice that the net profit is not strongly affected by the management alternatives in this case (only about 5%). As expected,

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5. Conclusions

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however, a greater variation is obtained for the freshwater used.

This paper evaluates the implementation of a natural gas production system from nonconventional sources by using a mathematical programming approach; the work focuses on the integration of both the water management and the gas supply chain. When compared to the current state of the art, this work provides the following contributions:

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i) The integration of geographical information systems (ArcGIS) to a mathematical programming formulation to assess the current available infrastructure for the supply chain of shale gas in Mexico. Real data, developed by various governmental agencies, was used to analyze the case-study. ii) The water stress of the whole gas exploitation system is analyzed based on the geographic location of each shale gas basin.

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iii) The scope of the case-study is macroscopic; the solutions are analyzed including the most important regions of a country (Mexico), and not only a basin or a particular zone. This issue significantly increases the size of the resulting mathematical programming problem. iv) Although the problem has indeed been extensively studied and many approaches are reported, an MILP formulation was proposed to make it suitable for its application to the case study, given the available information at a national level. Nevertheless, the linearity of the model also involves significant assumptions related to

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the values have a strong support from information databases.

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production and cost estimations, which reduce the scope of our formulation unless

The model used allows the optimal decision making about the basin exploitation and the

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operation of processing plants, as well as for the gas distribution to the markets. The water exploitation impact is also addressed, with particular interest in highly vulnerable zones. In

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summary:

a) Solution A (minimum water footprint) achieves only 1.68% of the natural gas

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demands with the exploitation of the basin located in Chihuahua; no significant impact on the water stress is observed (other than that already present in some watersheds).

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b) In Solution B, the exploitation of two basins (Veracruz and Tampico-Misantla) allows the satisfaction of 11.38% of the total natural gas demand satisfaction. Solution B favors de exploitation of a shale gas basin located in a zone where the values of WSI of the watersheds are the smallest (Veracruz). Such solution is feasible because solution B involves medium levels of the total gas production.

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c) Optimal solution C (maximum profit) reaches up to 20% of natural gas demand satisfaction, without the need for additional investment in transportation systems. Therefore, C is a solution with the highest shale gas production and profit, but it is also a solution with high water impact. In solution C, because of the levels of the total gas production, the optimal solution involves a basin with high potential for exploitation (Burro-Picachos), but such a basin is located in a zone with low water availability; the increase of water stress (mainly of watersheds 0514 and 0513

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located in Coahuila) would impact populations near the towns of Monclova, Piedras Negras and Nuevo Laredo, with the per-capita availability of water being compromised. Finally, the optimization reveals an interesting result. The gas production of Solution B could increase, but that increment would require additional gas transportation capacity or infrastructure; additional pipelines routes would allow the distribution of gas from the region surrounding the optimal basins of solution B (with lower water stress) to other parts

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of the country with higher demands. Although further analysis is needed, that is perhaps a feasible practical solution: exploiting the basins in Veracruz and Tampico-Misantla

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capacities from those basins to the rest of the markets.

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(solution B) with higher production rates through the increment of the transportation

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Declaration of interests

The authors declare that they have no known competing financial interests or personal

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Acknowledgements

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relationships that could have appeared to influence the work reported in this paper.

The authors would like to thank the financial support provided from CONACYT, Mexico,

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through grant 257018, and from TNM, Mexico, through grant 5725.16-P.

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Journal, 2017, 63 (11), 4799-4813. https://doi.org/10.1002/aic.15804 Gao, J.; You, F., Shale gas supply chain design and operations toward Better economic and

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Web References: Governmental Sources of information and Statistics for

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the Case-Study

CENAGAS, Simplified diagram for flow patterns in SISTRANGAS, 2016. Retrieved in

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February 2018, from:

e_flujos_en_el_SISTRANGAS.pdf

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https://www.gob.mx/cms/uploads/attachment/file/181525/Diagrama_simplificado_d

CONAGUA, Water statistics in Mexico, 2018. Retrieved in October, 2018 from:

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SENER, Natural gas prospective 2016-2030, 2016.Retrieved in February, 2017 from https://www.gob.mx/cms/uploads/attachment/file/177624/Prospectiva_de_Gas_Natural_20

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US Energy Information Administration, Annual energy outlook 2015: With projections to 2040, US Department of Energy, Washington, DC, 2015. Retrieved in January, 2018 from https://www.eia.gov/outlooks/aeo/pdf/0383(2015).pdf

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37

https://www.epa.gov/sites/production/files/documents/hf_study_plan_110211_final_508.pd

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Figure 1. Superstructure for shale gas exploitation planning.

Figure 2. Geography of the case-study (Mexico)

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Figure 3. Pareto set (solutions A, B and C are indicated)

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Figure 4. Cumulative gas production in each solution

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Figure 5. Demand satisfaction for each market

Figure 6. Watersheds that provide freshwater to basins in a) Chihuahua, b) Burro Picachos, c) Tampico-Misantla, d) Veracruz. 42

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Figure 7. Freshwater acquired from each watershed for each optimal solution.

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Figure 8. Water stress index for each watershed in the current condition and for each

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optimal solution

Figure 9. Water stress for each watershed in the current condition and for each optimal

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solution

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Figure 10 Behavior of different variables against the production factor 𝛼𝑝𝑟𝑜𝑐 in shale gas 𝑤 sites

45

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Figure 11. Effect of the wastewater management on profit, freshwater usage and water footprint

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Table 1. Summary of the modeling equations proposed

Investment operation costs

and

Water costs

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Objective functions

Equations From (1) to (4) (5) From (6) to (9)

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From (25) to (26)

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Gas transportation and processing costs

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Balances for natural gas distribution Capacity constrains (demand, processing and transportation) Exploitation of shale gas basins Water requirements (water balances)

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Shale gas processing

Description Shale gas obtained from each basin is distributed to processing plants. A constant production factor is assumed in a processing plant for the shale gas coming from each shale basin. Natural gas obtained from each processing plant is distributed to markets. Only existing facilities for processing and transportation are considered; transportation and processing capacities are known a priori. A disjunction is used to optimally decide which basins are to be exploited The amount of fresh water required responds to the shale gas exploitation profiles; fresh water sent to the basins is also bounded by the availability in the watersheds. Wastewater flows treated on site, injected to disposal wells and treated on municipal plants are estimated. Investment and operation costs required for the exploitation of the basins: investment costs include the pipelines needed to transport shale gas from basins to the existing transportation system as well as the investment costs related to the onsite wastewater treatment. Equation (53) represents investment for water storage. The distribution through the gas transportation system involves two tariff rates; the usage rate considers the amount of material transported; the reservation rate considers the use of the compressor stations in the interconnections system. Processing costs also involve expressions containing unit cost parameters. The water acquisition cost depends on the water stress level. The costs associated to wastewater treatment onsite, wastewater treatment on plants and wastewater disposal are estimated. Two objectives functions are considered: the maximization of the profit (Equation (54)) of the overall system and the minimization of the water footprint. Equation (55) shows the estimation of the consumption of fresh water. The supplementary information file shows how to estimate the water footprint. The estimation of net profit involves the utilities from the sales of natural gas in the markets; it also includes costs and investments related to production and distribution of gas (shale and natural) as well as those related to water acquisition, water treatment and water disposal.

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Model component Shale gas balances

From (27) to (36)

From (37) to (41) From (45) to (49) (53)

From (42) to (44)

From (50) to (52)

(54) and (55)

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Table 2. Main results for alternative solutions Solution

A

Profit (106$USD)

1129.50 9035.10

SWWF

644,670 12,105,900 26,107,110

Number of basins used

B

C 15570.75

1

2

3

Fresh Water Usage (10 m )

4.58

32

68

Re-used and Recycled Water (106L)

1853.87 9072.03

6

3

305.98

144.71

16523.81

Discharged Water (106 L)

206.07

5183.84

13769.77

Total gas production(106GJ)

429.45

2933.57

Total gas demand satisfaction (%)

1.68

11.38

Water intensity(L/GJ)

10.66

10.93

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Injected Water (Disposal wells) (106 L) 0

4981.25

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19.33

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13.68

49