Shale gas wastewater management under uncertainty

Journal of Environmental Management 165 (2016) 188e198

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Journal of Environmental Management journal homepage: www.elsevier.com/locate/jenvman

Research article

Shale gas wastewater management under uncertainty Xiaodong Zhang a, b, *, Alexander Y. Sun b, Ian J. Duncan b a b

EES-16, Earth and Environmental Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78713, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 April 2015 Received in revised form 24 September 2015 Accepted 26 September 2015 Available online xxx

This work presents an optimization framework for evaluating different wastewater treatment/disposal options for water management during hydraulic fracturing (HF) operations. This framework takes into account both cost-effectiveness and system uncertainty. HF has enabled rapid development of shale gas resources. However, wastewater management has been one of the most contentious and widely publicized issues in shale gas production. The flowback and produced water (known as FP water) generated by HF may pose a serious risk to the surrounding environment and public health because this wastewater usually contains many toxic chemicals and high levels of total dissolved solids (TDS). Various treatment/ disposal options are available for FP water management, such as underground injection, hazardous wastewater treatment plants, and/or reuse. In order to cost-effectively plan FP water management practices, including allocating FP water to different options and planning treatment facility capacity expansion, an optimization model named UO-FPW is developed in this study. The UO-FPW model can handle the uncertain information expressed in the form of fuzzy membership functions and probability density functions in the modeling parameters. The UO-FPW model is applied to a representative hypothetical case study to demonstrate its applicability in practice. The modeling results reflect the tradeoffs between economic objective (i.e., minimizing total-system cost) and system reliability (i.e., risk of violating fuzzy and/or random constraints, and meeting FP water treatment/disposal requirements). Using the developed optimization model, decision makers can make and adjust appropriate FP water management strategies through refining the values of feasibility degrees for fuzzy constraints and the probability levels for random constraints if the solutions are not satisfactory. The optimization model can be easily integrated into decision support systems for shale oil/gas lifecycle management. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Shale gas Hydraulic fracturing Wastewater management Uncertainty

1. Introduction Shale gas has become one of the most critical energy resources in the world. Its production has been made possible by advances in drilling technologies and cost reductions (Gregory et al., 2011; Rahm, 2011; Karapataki, 2012; Slutz et al., 2012; USEIA, 2012; Nicot et al., 2014). The USEIA (2012) estimated that annual shale gas production in the United States will increase from 5.0 TCF (trillion cubic feet) (23% of total U.S. dry gas production) in 2010 to 13.6 TCF (49% of total U.S. dry gas production) in 2035. Hydraulic fracturing (HF) is the key technology that has enabled shale gas development. In HF operations, a large amount of fracturing fluid (water and proppants) is injected under high pressure into low-

* Corresponding author. EES-16, Earth and Environmental Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. E-mail addresses: [email protected], [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jenvman.2015.09.038 0301-4797/© 2015 Elsevier Ltd. All rights reserved.

permeability shale formations to induce fracturing and improve the mobility of natural gas. Large-scale production of shale gas has become economic through application of HF technologies. A horizontal fracturing well consumes approximately 2e7 million gallons of water (Vidic et al., 2013). A large quantity of wastewater is generated, including flowback and produced water, together referred to as FP water (Nicot et al., 2014). Flowback is the fluid returned to the surface during the hydraulic fracturing process itself, while produced water is the fluid that returns to the surface once the well is in production (USEPA, 2011a; Ferrar et al., 2013). Volumes of FP water are large and vary from play to play, depending on the characteristics of the basins and formations (Veil and Clark, 2010; Clark et al., 2013; Murray, 2013; Yang et al., 2013). FP water generally contains high levels of total dissolved solids (TDS) and some naturally occurring toxic compounds, including, in some cases, naturally occurring radioactive material (NORM), dissolved from the formations. If FP water is discharged without any

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

treatment or after inadequate treatment, it may pose a threat to the environment and public health due to its high salinity and dissolved chemicals (Kargbo et al., 2010; Rahm, 2011; Shaffer et al., 2013). Thus, FP water needs to be disposed of in permitted disposal wells or treated before it can be discharged to a body of water or else reused. There is growing pressure on industry from stakeholders to increase the reuse of FP water rather than using disposal wells. In regional FP water management planning, multiple drilling sites (FP water sources) and various wastewater treatment/disposal facilities may be considered to comprise an integrated FP water management system (Hammer and VanBriesen, 2012; Penn State Cooperative Extension, 2012). The FP water generated from different sources will be delivered to various treatment and/or disposal facilities in multiple project periods. Because of differences in transportation distances (resulting in varied transportation costs) and variations of treatment and disposal costs, different management strategies for allocation of FP water to various treatment/disposal facilities can lead to significant variations of total treatment/disposal costs for large volumes of FP water. With the increased quantity of FP water, existing treatment facilities will experience pressure to expand their capacity in order to treat more wastewater. From the perspective of a total FP water management system, the best management decisions are those with the minimum overall costs including wastewater delivering, treatment/ disposal, and treatment facility capacity expansion costs (Fig. 1). Achieving this goal of minimum cost control will require effective strategies for FP water management. Over the past decade, a number of research efforts have been conducted regarding FP water issues in shale gas plays. Most of these studies focused on possible impacts of shale gas development on water quality (Osborn et al., 2011; Warner et al., 2012; Barbot et al., 2013), water use for shale gas production (Nicot and Scanlon, 2012), policy analysis for wastewater management (Rahm and Riha, 2012), and review of desalination technologies (Shaffer et al., 2013). There has been a lack of integrated FP water management planning from a total-system perspective, which could provide decision makers with strategies for allocating FP water and expanding treatment facility capacity in an optimal and cost-effective way. An optimization model on the basis of systemsanalysis techniques may help address this gap. Development of such a techno-economic optimization management model will

189

benefit a variety of decision makers and managers in the government and private industry. Recently, Karapataki (2012) developed a mixed-integer linear programming model for wastewater management in the Marcellus Shale. Due to limitations of knowledge and data, many model parameters inevitably contain uncertainty, including capacities of underground injection disposal facilities, cost and capacity of wastewater treatment plants, and the costs to transport FP water. The uncertainties may affect the accuracy (and, therefore, usefulness) of generated FP water management strategies. Most previously published studies have been unsuccessful in addressing and quantifying these uncertainties. Therefore, the objective of this study is to develop an uncertain optimization model for FP water management (UO-FPW), where both FP water allocation to various treatment/disposal options and treatment facility capacity expansion are optimized. The UO-FPW model is based on the fuzzy-stochastic mixed-integer programming method, which can effectively deal with uncertain information expressed as fuzzy membership functions and probability density functions. The model is then applied to a representative hypothetical case study for supporting FP water treatment/ disposal-option management, as well as treatment capacity expansion planning, under uncertainty. Optimal management strategies with a minimized total-system cost are generated to help decision makers select appropriate and cost-effective FP water treatment/disposal options in shale gas plays. Uncertainties in the model parameters expressed as stochastic and non-stochastic forms are effectively reflected. Tradeoffs between economic objective and system reliability are analyzed. 2. Uncertainty optimization model for shale gas wastewater management An FP water management system involves a number of components with unique features. Consider an FP water management system consisting of multiple wastewater sources (drilling sites with one or more hydraulic fracturing wells) and various wastewater treatment/disposal options. The FP water is first collected and stored in on-site open pits and/or storage tanks, and then delivered to on-site/off-site facilities for treatment, disposal, and/or reuse (Gregory et al., 2011; USEPA, 2011a; Hammer and VanBriesen, 2012). Transport of wastewater to treatment and disposal facilities is mainly by truck.

Fig. 1. An integrated FP water management system considering wastewater flow allocation and treatment facility capacity expansion.

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X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

Wastewater management options vary from shale play to shale play as a result of a number of technical, economic, environmental, political, and regulational factors. Investigation of all possible wastewater management options and their practices in different shale plays is not the aim of this study and is not provided. A wastewater management option that is technically and economically viable in one shale gas play may not be suitable in another. For example, underground injection has traditionally been a primary disposal option for oil/gas produced water through injection into subsurface formations for permanent storage (GWPC and ALL Consulting, 2009; Veil and Clark, 2010; USEPA, 2011a,b; Penn State Cooperative Extension, 2012; Nicot et al., 2014). USEPA has established Class II underground injection control (UIC) to regulate wells for disposal of brine and other fluids from oil/gas production (GWPC and ALL Consulting, 2009; USEPA, 2011b, a; Tiemann and Vann, 2012). In the Barnett Shale play in Texas, a number of Class II UIC wells exist, making underground injection a viable option for FP water disposal, whereas in the Marcellus Shale play in Pennsylvania, FP water must be transported to other states such as Ohio for underground injection disposal because the number of Class II wells in Pennsylvania is very limited. If not injected underground for disposal, the wastewater may be delivered to off-site hazardous wastewater treatment plants (HWTPs) before ultimately being discharged to the receiving waterways or reused. Municipal wastewater treatment plants, also called publicly owned treatment works (POTWs), are not considered a management option during the planning periods because they are incapable of treating high concentrations of TDS. FP water has received increasing scrutiny by the public, and more stringent regulation (PADEP, 2011). In 2011 the Pennsylvania Department of Environmental Protection (PADEP) requested that Marcellus gas operators stop delivering FP water to POTWs (PADEP, 2011). The FP water may still be sent to specially designed HWTPs that can treat high salinity and chemicals (PADEP, 2011). Reuse in subsequent hydraulic fracturing processes or other purposes is playing a more and more important role in shale gas wastewater management. Reuse of FP water reduces the need for freshwater and the volume of wastewater, thus helping solving both the problem of water supply and that of disposal. In the Marcellus Shale play, in reponse to the PADEP request, internal reuse of FP water for hydraulic fracturing operations rapidly became the dominant practice, with a nearly 90% reuse rate in 2012 (Maloney and Yoxtheimer, 2012; Vidic et al., 2013). Nevertheless, such reuse is not a long-term solution to wastewater management in any shale gas play. Reuse may be able to deal with the initial flowback water produced in the first few weeks after a well is drilled, but saline formation water will be produced from the well for many years-probably long after hydraulic fracturing has ceased in the area, so that there will be no ready demand for this wastewater for reuse in hydraulic fracturing. Therefore, wastewater will still need to be delivered to specific HWTPs with capability for TDS reduction before external reuse or discharge (Shaffer et al., 2013; Vidic et al., 2013). Reuse of FP water without treatment is also not considered in this study as an option, because reuse of untreated FP water can cause problems such as clogging of wells due to high scaling potential of ions (i.e., calcium, barium, and strontium) (Kargbo et al., 2010; Barbot et al., 2013). In long-term wastewater management planning, the preferred option is to reuse FP water after treatment at specially designed HWTPs with the ability to treat high TDS levels. Although on-site treatment appears to present a convenient solution, allowing reuse of the FP water at the same well sites, this treatment also faces challenges, such as supplying energy for widespread desalination of FP water considering the fact that most of these sites are away from substantial infrastructure, and less competitive for

cost control (Karapataki, 2012; Shaffer et al., 2013). A specially designed and established HWTP that can serve multiple well sites is a better and economically preferable option for the long-term management of wastewater. In this study, based on short-term and long-term considerations, combinations of wastewater management options, including underground injection, treatment at HWTPs specially designed for TDS treatment, and reuse in subsequent hydraulic fracturing processes after treatment are adopted (USEPA, 2011a; Slutz et al., 2012; Lutz et al., 2013; Shaffer et al., 2013; Vidic et al., 2013). Two aspects of FP water management are particularly challenging to decision makers: 1) how to allocate wastewater flows to different treatment/disposal facilities in the most economic way; and 2) how to plan expansions of FP water treatment/disposal facilities over the planning horizon in order to meet future wastewater treatment needs, which are likely to continue long after active HF operations stop in an area. In optimization management of FP water, uncertainties are inherent in many system components, such as the capacities of underground injection disposal sites and wastewater treatment plants due to limited information and data, existing estimation methods and techniques, and changing conditions. Such uncertainties complicate FP water management. Using deterministic parameter values may obscure the uncertain nature of the optimization, making the management schemes thus generated, unreliable and resulting in highly variable costs at the total-system level. Addressing and quantifying these uncertainties will help decision makers identify the optimal FP water management strategies. Tackling the above issues is the goal of the UO-FPW model presented here. The assumptions of the UO-FPW model in this study include: 1) all FP water will be delivered to underground injection disposal sites and/or to planned HWTPs that are specially designed and established for TDS treatment during the project periods; 2) expansion of underground injection is not possible within the planning periods; 3) wastewater will be reused only after treatment in HWTPs. On-site treatment and reuse is not considered in this study due to the economic, technical, environmental, and political challenges in sitting, design, construction, and maintenance of on-site treatment facilities.

2.1. Objective function For problems of FP water management, the objective is to minimize total-system cost, which includes the costs of FP water transportation, wastewater treatment and disposal, and treatment facility capacity expansion, and also incorporates revenues from wastewater reuse after treatment in HWTPs. Fixed costs such as those for taxes and construction of treatment/disposal facilities are not included in the model. Two categories of decision variables are included: 1) continuous variables representing delivered wastewater quantities from generation sources to treatment/disposal facilities during the planning periods; and 2) binary variables representing options to expand the capacity of treatment facilities. The details are presented as follows: Indices and decision variables: i: index for FP water generation sources (i.e., drilling sites), i ¼ 1, 2, …, r; j: index for FP water treatment and disposal facilities, including underground injection disposal (UID) sites and specially designed and planned HWTPs that can treat TDS, j ¼ 1, 2, …, p, UID sites, j ¼ p þ 1, p þ 2, …, s, HWTPs; k: index for the planning periods, k ¼ 1, 2, …, g; r: number of FP water generation sources;

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

s: number of wastewater treatment and disposal facilities, including p underground injection disposal sites and s-p hazardous wastewater treatment plants; g: number of planning periods; n: number of capacity-expansion options for HWTPs; Xijk: continuous decision variables representing daily average quantity of wastewater delivered from source i to treatment and disposal facility j in period k (bbl/day); Yjmk: binary decision variables representing capacity-expansion option m for wastewater treatment and disposal facility j at the start of the period k (j ¼ p þ 1, p þ 2, …, s). The objective function to minimize total-system cost is formulated as follows:

0 Min f ¼Pk @

g  r X s X X

 COPjk þ CTRijk Xijk

i¼1 j¼1 k¼1



g r s X X X

REjk ,RRjk ,Xijk A

(1a)

þ

(3) Wastewater treatment-demand constraints: s X



Xijk ¼ WWGik ;

ci; k

(1d)

j¼1 

where WWGik is the generated wastewater quantity in source i in period k (bbl/day). (4) Technical constraints:

Xijk  0;

ci; j; k

n X

(1e)

Yjmk ¼ integer;

Yjmk  1;

cj; m; k

cj; k

(1f)

(1g)

m¼1

i¼1 j¼pþ1 k¼1 g s n X X X

hazardous wastewater treatment plant j in period k (bbl/day).

0  Yjmk  1;

1

191

(Each wastewater treatment facility can be only expand once in any given time period.)

CEXjmk ,Yjmk

j¼pþ1 m¼1 k¼1

where COPjk is treatment cost of wastewater treatment and disposal facility j in period k ($/bbl); CTRijk is transportation cost of wastewater from source i to treatment and disposal facility j in period k ($/bbl); CEXjmk is capital cost of expanding wastewater treatment and disposal facility j by expansion option m in period k ($ per expansion option); REjk is revenues from wastewater reuse from treatment facility j in period k ($/bbl); RRjk is reuse rate from wastewater treatment facility j in period k (% of incoming wastewater quantity to the facility j); and Pk is duration of each planning period k (days).

The constraints represent the relationships between the decision variables and a series of restrictions related to FP water management, including wastewater treatment facility capacity constraints, wastewater treatment-demand constraints, and technical and political constraints. The detailed descriptions are shown as follows: (1) Underground injection disposal site capacity constraints:



Pk ,Xijk  UIFj ;

cj ¼ 1; 2; …; p

(1b)

i¼1 j¼1 k¼1 

where UIFj is available capacity (bbls) of underground injection disposal site j during the planning periods, expressed as fuzzy membership functions. (2) Hazardous wastewater treatment plant capacity constraints:

r X i¼1

Xijk0  WTPj ðtÞ þ

The above UO-FPW model can be rewritten to a generalized fuzzystochastic mixed-integer linear programming form as follows:

Min

f ¼ CX

n X k0 X

EOjmk Yjmk ;

m¼1 k¼1

(1c)

cj ¼ p þ 1; p þ 2; …; s; k0 ¼ 1; 2; …; g where WTPj(t) is a random parameter representing treatment capacity of hazardous wastewater treatment plant j (bbl/day); and EOjmk is increased treatment capacity of expansion option m for

(2a)

Subject to 



Ai X  Bi ; Aj X  Bj ðtÞ;

2.2. Constraints

p X g r X X

2.3. Solution method

i2M; isj

(2b)

j2M; jsi

(2c)

X  0; or integers 

(2d)



where Ai and Bi are imprecise or ambiguous parameters expressed as fuzzy sets, Bj(t) is a set of random parameters, Bj(t)2B, B2{R}m1, M ¼ {1,2,…,m}, Aj2{R}m  n, C2{R}m  n, X2{R}n  1, and R is a set of real numbers. In order to deal with the fuzzy parameters in the constraints (2b), a fuzzy ranking approach based on expected intervals (EIs) is ~ denoted as used. The membership function of a fuzzy parameter A (a1,a2,a3,a4) can be expressed as follows:

8 0; > > < fA ðxÞ; mA ðxÞ ¼ > gA ðxÞ; > : 1;

x  a1 or x  a4 a1  x  a2 a3  x  a4 a2  x  a3

(3)

where the functions of fA(x) and gA(x) are continuously increasing and ~ is defined as decreasing, respectively. The EI of a fuzzy number A nez,1996; Jime nez et al., 2007; Zhang and Huang, 2013): follows (Jime

2 1 3 Z Z1 i h A A 1 1 EIðAÞ ¼ E1 ; E2 ¼ 4 fA ðxÞdx; gA ðxÞdx5 0

(4)

0

Note that, if fA(x) and gA(x) are linear functions, the fuzzy number is trapezoidal; if a2 is equal to a3, the fuzzy number is triangular. As a result, equation (4) can be written as follows nez, 1996; Jime nez et al., 2007; Zhang and Huang, 2013): (Jime

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X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

 EIðAÞ ¼

a1 þ a2 a3 þ a4 ; 2 2

 (5)

Consider the fuzzy numbers A and B; the degree to which A is nez, 1996; Jime nez not smaller than B is defined as follows (Jime et al., 2007):

mM ðA; BÞ ¼

8 0 > > > > > > <

if E2A  E1B <0

E2A  E1B   A B A B > E  E  E  E > 2 1 1 2 > > > > : 1

i h if 02 E1A  E2B ; E2A  E1B

(6)

 Pr Aj X  Bj ðtÞ  1  g;

if E1A  E2B >0

where ½E1A ; E2A  is the expected interval of the fuzzy number A, and ½E1B ; E2B  is the expected interval of the fuzzy number B; mM(A, B) is the preference degree of fuzzy numbers A over B. mM(A, B)a represents that fuzzy number A is no smaller than B by at least a degree of a, denoted by A  aB. Reconsider the inequalityconstraints (2b). Based on the exten sion principles of fuzzy sets, Ai X is also a fuzzy number since Ai is a nez (1996) and Jime nez et al. fuzzy number. According to Jime (2007), a decision vector X is feasible in the degree of a if

    min mM Bi ; Ai X ¼a i2M

study, six scales of feasibility degrees from 0.5 through 1 are used, representing the acceptability categories of the different solutions. In order to tackle the abovementioned constraints (2c) with random parameters, chance-constrained programming (CCP) method is used. CCP is capable of effectively dealing with random features of the model's right-hand-side coefficients (i.e.,Bj(t)) through conversion of the original random constraints into the crisp ones. By using the CCP method, the original constraints with random features are converted into the crisp forms at a given probability level g as follows (Charnes and Cooper, 1959; Huang, 1998; Zhang et al., 2009b, 2011):

Aj X  Bj ðtÞðgÞ ¼ Fj1 ðgÞ;



Ai X  a Bi

Min f ¼ Pk @

E2Bi  E1Ai X a  E2Bi  E1Ai X  E1Bi  E2Ai X



(14)

r s  X X COPjk þ CTRijk Xijk 

g X

i¼1 j¼pþ1

1

REjk ,RRjk ,Xijk A þ

g s n X X X

CEXjmk ,Yjmk

j¼pþ1 m¼1 k¼1

k¼1

(15a) Subject to: p X g r X X

UIFj

Pk ,Xijk  ð1  aÞE2

UIF

þ a,E1 j ; cj ¼ 1; 2; :::; p

(15b)

i¼1 j¼1 k¼1 r X

(9)

g  r X s X X i¼1 j¼1 k¼1

(8)

The a means the acceptability or feasibility degree of fuzzy constraints, representing that decision makers are willing to admit nez et al., 2007). Accordthe satisfaction of fuzzy constraints (Jime ingly, (1a) means the risk of violating fuzzy constraints, reflecting the system reliability. Based on equations (7) and (8), the fuzzy constraints (2b) can be converted into the following formulation nez, 1996; Jime nez et al., 2007): (Jime

cj2M; jsi

where Bj ðtÞðgÞ ¼ Fj1 ðgÞ, given the cumulative distribution function of Bj(t) (i.e., Fj(Bj)), and the probability level of g. Thus, the original model (1) is converted into the following crisp a,g-parametric linear programming formulation:

The above equation is equivalent to the following formulation: 

(13)

where g is the probability level that the constraints will be violated. The above equations can be reformulated as follows:

0 (7)

cj2M; jsi

Xijk0  WTPj ðtÞðgÞ þ

n X k0 X

EOjmk Yjmk ; cj

m¼1 k¼1

i¼1

¼ p þ 1; p þ 2; :::; s; k0 ¼ 1; 2; :::; g

(15c)

The above equation is equivalent to:



 aE2Ai þ ð1  aÞE1Ai X  ð1  aÞE2Bi þ aE1Bi

(10)

s X

Xijk  ð1  0:5,aÞE2WWGik þ 0:5,aE1WWGik ;

ci; k

(15d)

Xijk  ð1  0:5,aÞE1WWGik þ 0:5,aE2WWGik ;

ci; k

(15e)

j¼1

The fuzzy equality constraints can be transformed into the two equivalent crisp forms, which means they are indifferent (Arenas Parra et al., 2005):





0:5,aE2Ai þ ð1  0:5,aÞE1Ai X  ð1  0:5,aÞE2Bi þ 0:5,aE1Bi

s X j¼1

(11) Xijk  0;



 0:5,aE1Ai þ ð1  0:5,aÞE2Ai X  ð1  0:5,aÞE1Bi þ 0:5,aE2Bi

(12)

The feasibility degree reflects the preferences of decision makers nez et al. (2007), to accept the modeling solutions. According to Jime 11 scales have been identified to distinguish the feasibility levels, including: 0 (unacceptable), 0.1 (practically unacceptable), 0.2 (almost unacceptable), 0.3 (very unacceptable), 0.4 (quite unacceptable), 0.5 (neither acceptable nor unacceptable), 0.6 (quite acceptable), 0.7 (very acceptable), 0.8 (almost acceptable), 0.9 (practically acceptable), and 1 (completely acceptable). Generally, a higher feasibility degree leads to a worse objective value. In this

ci; j; k

0  Yjmk  1; n X

Yjmk  1;

Yjmk ¼ integer;

(15f) cj; m; k

cj ¼ 2; 3; k ¼ 1; 2; 3

(15g)

(15h)

m¼1

The solution processes are summarized as follows: Step 1: formulate the UO-FPW management model; Step 2: identify the membership functions of fuzzy parameters, and the probability density functions of random parameters in the model;

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198 Table 1 FP water transportation and treatment/disposal costs, and revenues from reuse. Source

Treatment and disposal facility

Transportation costs ($/bbl) from source to facility Drilling site 1 UID site Drilling site 1 HWTP 1 Drilling site 1 HWTP 2 Drilling site 2 UID site Drilling site 2 HWTP 1 Drilling site 2 HWTP 2 Drilling site 3 UID site Drilling site 3 HWTP 1 Drilling site 3 HWTP 2 Drilling site 4 UID site Drilling site 4 HWTP 1 Drilling site 4 HWTP 2 Drilling site 5 UID site Drilling site 5 HWTP 1 Drilling site 5 HWTP 2 Operational costs of treatment/disposal facility UID site HWTP 1 HWTP 2 Revenues from wastewater reuse ($/bbl) HWTP 1 HWTP 2

Period k¼1

k¼2

k¼3

2.4 3.2 5.6 6.5 2.9 3.4 4.2 4.8 5.1 2.7 6.0 3.6 7.1 3.2 3.1

3.0 3.6 6.3 6.9 3.7 3.9 4.8 5.3 5.5 3.2 6.7 4.3 7.5 3.6 3.8

3.6 4.0 6.7 7.4 4.4 4.2 5.5 5.9 6.3 3.9 7.3 4.9 7.9 3.9 4.3

1.5 3.8 3.0

2.0 4.5 3.4

2.4 5.0 3.9

1.2 1.0

1.3 1.2

1.5 1.4

Step 3: determine a probability level (g) that the constraints with random features will be violated; Step 4: at a given probability level (g), convert the constraints with fuzzy parameters into crisp a-parametric forms (i.e., and Eqs. (15b), (15d), and (15e)) by using the fuzzy ranking method; Step 5: obtain the solutions corresponding to each feasibility degree (a), determined by the decision makers; Step 6: repeat Steps 3 through 5, obtaining all solutions at each probability level (g) and each feasibility degree (a).

3. Case study

193

shale gas plays in the United States. The study system includes five drilling sites as FP water generation sources, each of which involves multiple drilling wells for generating FP water. The FP water needs to be treated or disposed according to the requirements of environmental and political regulations. Three treatment/disposal facilities, including one underground injection disposal site and two planned HWTPs capable of treating TDS, are available. All FP water from the five sources is assumed to be shipped to treatment/ disposal facilities by truck; pipeline transportation is not considered. The whole planning horizon is 15 years, divided into three planning periods of 5 years each. Table 1 lists the economic parameters, including FP water transportation costs, treatment/disposal costs, and revenues from reuse after treatment in HWTPs (Ely et al., 2011; USEPA, 2011a,b; Hammer and VanBriesen, 2012; IHS, 2012; Karapataki, 2012; Slutz et al., 2012). The FP water generation volumes and reuse rates of two HWTPs are shown in Table 2. Owing to vagueness in information acquisition and data collection, the capacity of the underground injection disposal site is imprecise and expressed as a fuzzy membership function. Without loss of generality, triangular fuzzy membership functions are adopted for the sake of simplicity in computation, to deal with fuzzy parameters, although the proposed model is also applicable to other types of fuzzy membership functions. The capacity of the underground injection disposal site is (9.6, 10.5, 11.5)  106 bbls for the duration of all three 5-year planning periods. The capacities of the two HWTPs are considered random features and expressed as probability density functions. Table 3 shows the distribution information of the uncertain capacities of the two HWTPs. Table 4 presents the expansion options of the two HWTPs, along with related capital costs for expansion (in present value). During the project planning periods, the problem facing decision makers is to effectively plan wastewater treatment/disposal management activities from a wholesystem perspective, including allocating wastewater flow and expanding treatment facility capacity in order to simultaneously achieve a minimum total-system cost and meet demand for wastewater treatment/disposal. The developed UO-FPW model is thus applied to handle this planning problem.

3.1. Overview of the study system 3.2. Results analyses A representative shale gas wastewater management system is presented based on real-world and hypothetical cases, data, information, and a review of published literature and governmental reports (Gaudlip and Paugh, 2008; Soeder and Kappel, 2009; Hammer and VanBriesen, 2012; IHS, 2012; Karapataki, 2012; Penn State Cooperative Extension, 2012; Slutz et al., 2012; Lutz et al., 2013; Rahm et al., 2013; Ziemkiewicz et al., 2013). The proposed model system is designed to reflect the current and future characteristics of FP water treatment and disposal, management options, and socio-economic and technical considerations in major

Table 5 shows the results obtained from the UO-FPW model at different feasibility degrees (i.e., a ¼ 0.5 to 1) when g ¼ 0.01. Wastewater treatment and disposal patterns would vary at various a degrees. For drilling site 1, at a feasibility degree of 0.5, its wastewater in period 1 would be shipped to the underground injection disposal site and to HWTP 1 with flows of 413 and 5198 bbl/ day, respectively; with the increase of the a degree, more wastewater would be disposed of by underground injection and less wastewater would be delivered to HWTP 1 for treatment. In periods

Table 2 FP water generation rate and reuse rate. Source

Treatment and disposal facility

Period k¼1

FP water generation rate (bbl/day) Drilling site 1 Drilling site 2 Drilling site 3 Drilling site 4 Drilling site 5 Reuse rate (%) HWTP 1 HWTP 2

(5500, (4500, (5130, (5970, (5080, 75% 70%

k¼2 5650, 4600, 5200, 6090, 5160,

5780) 4740) 5290) 6130) 5220)

(6220, (4730, (5500, (6240, (5370, 85% 80%

k¼3 6350, 4940, 5650, 6340, 5550,

6500) 5070) 5820) 6440) 5690)

(6740, (5030, (5700, (6480, (5600, 95% 90%

6900, 5160, 5920, 6670, 5780,

7000) 5310) 6060) 6840) 5900)

194

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

Table 3 Distribution information of uncertainty capacities of two HWTPs (bbl/day).

g Level

0

0.01

0.05

0.10

0.25

0.50

0.75

0.90

0.95

0.99

1

HWTP 1 HWTP 2

12400 11200

12900 11600

13400 12000

13600 12200

14000 12500

14500 12900

15000 13300

15400 13600

15600 13800

16100 14200

16600 14600

2 and 3, all wastewater from drilling site 1 would be transported to HWTP 1 for treatment; as the a degree increases, wastewater volumes shipped to HWTP 1 would also increase. For drilling site 2, its wastewater treatment/disposal patterns would vary significantly with the a degrees; in period 1, all of its wastewater would be treated by HWTP 1 at all feasibility degrees; with the increase of the a degree from 0.5 to 1, wastewater flowing to HWTP 1 would increase from 4580 to 4610 bbl/day; in period 2, its wastewater would be totally treated by HWTP 1 at a ¼ 0.5 and by HWTP 2 at a ¼ 0.8, while wastewater at a ¼ 0.6, 0.7, 0.9 and 1 would be shipped to both HWTP 1 and HWTP 2; in period 3, all of its wastewater would be delivered to HWTP 2 at different a degrees, with increased a degree corresponding to increased wastewater flowing to HWTP 2. For drilling site 3, its wastewater in period 1 would be delivered to HWTP 1 and HWTP 2 for treatment at all a degrees; with increasing a degrees, the wastewater volume treated by HWTP 1 would increase and the volume treated by HWTP 2 would decrease. In period 2, wastewater from drilling site 3 would be transported to both HWTP 1 and HWTP 2 at a ¼ 0.5 and 0.8, while the total volume would be treated by HWTP 1 at a ¼ 0.6, 0.7, 0.9, and 1. In period 3, HWTP 1 would be the only treatment option for wastewater from drilling site 3 at a ¼ 0.5, 0.8, and 0.9, whereas HWTP 2 would be used to treat most of the wastewater (with a smaller portion treated by HWTP 1) at a ¼ 0.6, 0.7, and 1. For drilling site 4, all of its wastewater in period 1 would be treated by HWTP 2 at various feasibility degrees; a higher feasibility degree would lead to increased wastewater flow to HWTP 2. In periods 2 and 3, a portion of wastewater would be diverted for underground injection disposal; the volume of wastewater disposed of by underground injection at different feasibility degrees in period 2 would be 1970 (a ¼ 0.5), 2004 (a ¼ 0.6), 1889 (a ¼ 0.7), 2073 (a ¼ 0.8), 2057 (a ¼ 0.9), and 2042 (a ¼ 1) bbl/day; and those in period 3 would be 3385, 3274, 3313, 3052, 2991, and 2930 bbl/day, respectively. Such an allocation pattern is due mainly to the lower transportation costs from drilling site 4 to the underground injection disposal site during the planning periods. For drilling site 5, HWTP 2 would be the sole treatment means in period 1, and the corresponding treated wastewater volumes would increase as the a degree increases. In period 2, all the wastewater from drilling site 5 would be

Table 4 Expansion option and capital costs of two HWTPs. Treatment and disposal facility

Expansion option m

Period k¼1

k¼2

k¼3

Capital costs of expanding treatment and disposal facility (106 present value) HWTP 1 1 15.8 14.0 11.9 HWTP 1 2 18.6 16.7 14.5 HWTP 1 3 20.4 18.2 15.9 HWTP 2 1 12.5 10.6 8.6 HWTP 2 2 14.1 12.0 10.7 HWTP 2 3 16.8 14.6 12.8 Increased treatment capacity (bbl/day) HWTP 1 1 600 600 600 HWTP 1 2 750 750 750 HWTP 1 3 850 850 850 HWTP 2 1 550 550 550 HWTP 2 2 650 650 650 HWTP 2 3 800 800 800

treated by HWTP 2 at all feasibility degrees except the feasibility degree of 0.8 (at which HWTP 1 would be solely used). In period 3, most of the wastewater from drilling site 5 would be treated by HWTP 2, with a portion by HWTP 1 at a ¼ 0.5, 0.8, and 0.9; at a ¼ 0.6, 0.7, and 1, all its wastewater would be shipped to HWTP 1 for treatment. During the planning periods, two HWTPs would be the main wastewater treatment options at different feasibility degrees. This predominance is due mainly to the limited disposal capacity of the underground injection site during the whole planning periods. In addition, expansion of the underground injection site is difficult because of geological, environmental, economic, social, and political factors. For the underground injection site, its wastewater source in period 1 would be drilling site 1 only, and be drilling site 4 only in periods 2 and 3 due to their relatively low transportation costs. For HWTP 1, wastewater sources in period 1 would be drilling sites 1, 2, and 3 at all feasibility degrees; the sources in period 2 would be drilling sites 1, 2, 3 when a ¼ 0.5, 0.6, 0.7, 0.9, and 1, whereas those at a ¼ 0.8 would be drilling sites 1, 3, 5; in period 3, wastewater sources would be drilling sites 1, 3, and 5. For HWTP 2, wastewater in period 1 would come mainly from drilling sites 4 and 5 except a small portion coming from drilling site 3. In period 2, wastewater sources for HWTP 2 would be significantly different at various feasibility degrees; those sources would be drilling sites 3, 4, and 5 at a ¼ 0.5, drilling sites 2, 4, 5 at a ¼ 0.6, 0.7, and 0.9, and drilling sites 2, 3, 4 at a ¼ 0.8 and 1. In period 3, wastewater shipped to HWTP 2 would come mainly from drilling sites 2, 4, and 5 at a ¼ 0.5, 0.8, and 0.9, while this wastewater would come from drilling sites 2, 3, and 4 at a ¼ 0.6, 0.7, and 1. With the increase of a degree, wastewater shipped to the underground injection disposal site during the entire planning periods would decrease, while the volume treated by the two HWTPs would increase. This pattern arises because an increase of a degree (i.e., increased certainty degree of fuzzy constraints) would lead to an increased generation of wastewater and, simultaneously, a reduction in the capacity of the underground injection disposal site. As a result, more wastewater would be shipped to HWTP 1 and HWTP 2 for treatment. Since the capacity of the underground injection site is much less than that of two HWTPs, the two HWTPs would be the primary treatment options for FP water. This model pattern reflects the real situation in Pennsylvania, where underground injection wells are scarce. Wastewater from the Marcellus Shale play in Pennsylvania must be transported to nearby states, such as Ohio, for underground injection disposal; however, high transportation costs make this treatment option uneconomic for large volumes of wastewater (Gregory et al., 2011; USEPA, 2011a,b; Penn State Cooperative Extension, 2012). Table 6 shows the expansion results of two HWTPs during the planning periods at different feasibility degrees when the level of g is 0.01. HWTP 1 should have the same expansion options at all feasibility degrees (from 0.5 to 1); its capacity should have only one expansion in period 1 with an increment of 850 bbl/day; no further expansion is needed in periods 2 and 3. HWTP 2 would have different expansion options at different feasibility degrees. For example, at a ¼ 0.5, HWTP 2 would be expanded with an increased capacity of 800 bbl/day in period 1 and 650 bbl/day in period 2, while at a ¼ 0.8 it would expand capacity by 800 bbl/day in period 1

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

195

Table 5 Results obtained from the UO-FPW model (when g ¼ 0.01). Wastewater flow (bbl/day)

Source

Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling Drilling

X111 X121 X131 X112 X122 X132 X113 X123 X133 X211 X221 X231 X212 X222 X232 X213 X223 X233 X311 X321 X331 X312 X322 X332 X313 X323 X333 X411 X421 X431 X412 X422 X432 X413 X423 X433 X511 X521 X531 X512 X522 X532 X513 X523 X533

Treatment and disposal facility

site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site site

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5

UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2 UID site HWTP 1 HWTP 2

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

and 550 bbl/day in both periods 2 and 3. As a increases, the incremental capacities of the two HWTPs will increase. This expansion occurs because a higher degree of feasibility corresponds to a decreased underground injection capacity and increased wastewater generation rate; in order to meet the requirements for treatment or disposal of more wastewater, more capacity expansions would be carried out. In addition, between the two HWTPs, HWTP 2 should be preferentially expanded due to its lower capital costs for expansions. Table 6 Capacity expansion results of two HWTPs (g ¼ 0.01). Treatment and disposal facility

HWTP HWTP HWTP HWTP HWTP HWTP

1 1 1 2 2 2

Period

1 2 3 1 2 3

Period

Feasibility degree (a) 0.5

0.6

0.7

0.8

0.9

1

850 / / 800 650 /

850 / / 800 800 /

850 / / 800 800 /

850 / / 800 550 550

850 / / 800 650 550

850 / / 800 650 650

Feasibility degree (a) 0.5

0.6

0.7

0.8

0.9

1

413 5198 0 0 6320 0 0 6853 0 0 4580 0 0 4878 0 0 0 5130 0 3973 1213 0 2410 3205 0 5855 0 0 0 6050 1970 0 4345 3385 0 3235 0 0 5138 0 0 5500 0 1043 4685

437 5180 0 0 6327 0 0 6859 0 0 4586 0 0 1510 3376 0 0 5137 0 3984 1205 0 5623 0 0 1156 4708 0 0 6054 2004 0 4316 3274 0 3355 0 0 5141 0 0 5508 0 5735 0

462 5163 0 0 6334 0 0 6866 0 0 4592 0 0 1647 3248 0 0 5144 0 3996 1198 0 5631 0 0 1142 4731 0 0 6058 1889 0 4436 3313 0 3325 0 0 5145 0 0 5516 0 5743 0

486 5145 0 0 6341 0 0 6872 0 0 4598 0 0 0 4903 0 0 5151 0 4007 1190 0 1849 3790 0 5882 0 0 0 6062 2073 0 4257 3052 0 3595 0 0 5148 0 5524 0 0 996 4754

511 5128 0 0 6348 0 0 6879 0 0 4604 0 0 1671 3240 0 0 5158 0 4019 1183 0 5647 0 0 5891 0 0 0 6066 2057 0 4278 2991 0 3665 0 0 5152 0 0 5532 0 981 4777

535 5110 0 0 6355 0 0 6885 0 0 4610 0 0 1708 3212 0 0 5165 0 4030 1175 0 5655 0 0 1100 4800 0 0 6070 2042 0 4298 2930 0 3735 0 0 5155 0 0 5540 0 5765 0

Total-system cost at different feasibility degrees (a) of fuzzy constraints and probability levels (g) of random constraints are presented in Table 7. Correspondingly, treatment cost per barrel of FP water is listed in Table 8. Various decision schemes are generated for different combinations of a degrees and g levels. The developed UO-FPW model can effectively reflect the interactional effects of fuzzy and random uncertainties on the resulting wastewater management strategies, providing more flexibility to interpret the results and generating decision schemes. The a means the feasibility or acceptability degree of decision makers on fuzzy constraints satisfaction, reflecting the preferences of decision makers;

Table 7 Total-system cost at combined a degrees and g levels (million $).

g Level

0.01 0.05 0.10

Feasibility degree (a) 0.5

0.6

0.7

0.8

0.9

1

1126.75 1104.07 1094.26

1130.47 1106.75 1095.87

1132.08 1110.46 1102.96

1138.05 1112.07 1104.57

1140.73 1116.87 1107.25

1144.25 1120.72 1108.99

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X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

Table 8 Treatment cost per barrel of FP water at combined a degrees and g levels ($).

g Level

0.01 0.05 0.10

Feasibility degree (a) 0.5

0.6

0.7

0.8

0.9

1

2.41 2.36 2.34

2.42 2.36 2.34

2.42 2.37 2.35

2.43 2.37 2.35

2.43 2.38 2.36

2.43 2.38 2.36

(1a) means the risks of fuzzy constraints violation, representing nez, 1996; Jime nez et al., 2007). A the reliability of the system (Jime higher feasibility degree means decision makers will not be willing to accept a higher risk of violating fuzzy constraints, leading to increased system reliability, but a higher total cost of the system. Different feasibility degrees of fuzzy constraints would lead to different wastewater management patterns and HWTP capacity expansion options, each with different total-system cost. At a fixed g level, total-system cost would increase with the increase of the a degree. For example, when g ¼ 0.01, total-system cost would increase from $1126.75 to $1130.47, $1132.08, $1138.05, $1140.73, and $1144.25 million, respectively, as the a degree increases from 0.5 to 0.6, 0.7, 0.8, 0.9, and 1, respectively. The lower the feasibility degrees of fuzzy constraints are, the better the objective value (i.e., if the goal is to minimize total-system cost). However, a lower feasibility degree means a lower acceptable degree of fuzzy constraints, corresponding to a higher risk of violating fuzzy constraints. Thus, a lower feasibility degree represents an optimistic attitude of decision makers on the total wastewater treatment/ disposal costs, while a higher feasibility degree corresponds to a more conservative attitude. The g level represents the probabilities that the random constraints will be violated. At a fixed a degree, total-system cost will decrease as the g level increases. An increased g level (corresponding to decreased system reliability) leads to decreased strictness of the random constraints and, at the same time, an expanded decision space (i.e., increased existing capacities of the two HWTPs), resulting in a decreased total-system cost. For example, at a feasibility degree of 0.8, with the increase of the g level from 0.01 to 0.05 and 0.10, total-system cost would decrease from $1138.05 to $1112.07 and $1104.57 million, respectively. A plan to obtain a lower total-system cost (at a higher g level) would lead to an increased risk of violating random constraints, while accepting a higher total-system cost (at a lower g level) would guarantee system reliability (i.e., meeting FP water treatment/disposal requirements). The relationships between totalsystem cost and combined a degrees and g levels reflect the tradeoffs between economic objective and system reliability (i.e., risk of violation of fuzzy and random constraints). The modeling results can facilitate decision makers in making appropriate FP water management strategies under uncertainty. In the case study, wastewater generation rates at the five sources are estimated as fuzzy parameters instead of deterministic values. Such estimations provide more analysis of the effects of uncertain modeling parameters on the results. Fuzzy methods can effectively deal with non-probabilistic uncertainties, which are caused by a lack of knowledge or imprecision or vagueness (Zhang et al., 2009a, 2009b, 2010). Previous wastewater generation rates can be estimated as deterministic values based on the available historical data and information, while prediction of future wastewater generation rates in the project planning periods is inevitably associated with uncertainty. Decision makers frequently estimate wastewater generation (also, including cost-related parameters) based on their incomplete knowledge, data and information; for example, decision makers can give such estimations: the most likely wastewater generation rate is approximately 5650 bbl/day, and the possible

range falls between 5500 and 5780 bbl/day. Using deterministic values (single values) cannot address such uncertainty, while ignoring such uncertainty will lose much useful information for decision making. Fuzzy methods are an effective tool for handling such vague uncertainty. Fuzzy methods have been widely applied in energy and environmental decision making associated with vague or imprecise uncertainty, such as energy systems modeling, air quality management, water resources planning, and waste management. By introducing the concept of feasibility degree, fuzzy constraints are transformed into the crisp ones that are easy to be solved. The feasibility degree is a measure of the degree that decision makers can accept the generated solutions. If decision makers are not satisfied with the solutions, they can adjust the feasibility degree in order to obtain another set of the solutions for meeting their needs. Various feasibility degree can lead to varied total-system cost. However variations of the feasibility degree have small impacts on treatment cost per barrel of FP water (Table 8). That is because total amounts of wastewater generated at all sources in the whole project planning periods (15 years) are slightly different at different feasibility degrees; random parameters (i.e., probability levels) will not affect total amounts of wastewater generated since random uncertainty exists only in treatment capacities of two HWTPs in the case study. The generated results can help decision or policy makers make and adjust appropriate wastewater management strategies through refining the values of feasibility degrees and the probability levels if the solutions are not satisfying, based on their knowledge and preferences on system reliability and wastewater treatment/disposal requirements. The synergistic effects of fuzzy and random uncertainties on wastewater treatment/disposal management strategies can be effectively reflected using the developed UO-FPW model. 4. Conclusions A model (UO-FPW) for optimizing the management of flowback and produced water (together referred to as FP water) is proposed in this study. The model can be used to examine issues such as determining the most cost-effective allocation of the wastewater to various treatment/disposal facilities and predicting the best time to expand wastewater treatment. The challenge in such modeling is the need to account for the uncertainty in the information used. The UO-FPW model, which is based on a fuzzy-stochastic mixedinteger programming method, can effectively deal with stochastic (expressed as probability density functions) and non-stochastic (expressed as fuzzy membership functions) information in the modeling parameters. The model can identify optimal management strategies by minimizing total-system cost. Applying the UO-FPW model to a hypothetical case demonstrates its applicability in shale gas wastewater management. Our main findings are:  The hazardous wastewater treatment plants would be the primary FP water treatment option. This pattern reflects the real situation in Pennsylvania where underground injection wells are scarce; in order to be injected underground, wastewater must be transported to nearby states such as Ohio, while high transportation costs make underground injection uneconomic for large volumes of wastewater. Since capacity of the underground injection disposal site is limited and impossible to be expanded, the two hazardous wastewater treatment plants should have the capacity expansions to meet the needs of treating more wastewater delivered. The hazardous wastewater treatment plant with lower capital expansion costs (i.e., HWTP 2) should be expanded for at least twice at three planning periods to provide more incremental capacities.

X. Zhang et al. / Journal of Environmental Management 165 (2016) 188e198

 Uncertainties in the modeling parameters (i.e., capacities of underground injection disposal and hazardous wastewater treatment plants, and wastewater generation rate) can have an impact on the generated FP water management strategies. Quantification of these uncertainties is important since it is not always possible to provide accurate estimation of some parameters such as capacity of the underground injection well. Incorporation of such uncertainties into the optimization management provides much useful information for decision or policy making, which cannot be achieved through replacing them with deterministic values (although it is easier). The developed UO-FPW model provides the basis for analysis of interactional effects of parameter uncertainty on the resultant decision schemes for wastewater management.  The modeling results reflect the tradeoffs between economic objective (i.e., minimizing total system cost) and system reliability (i.e., risk of violating fuzzy and/or random constraints, and meeting FP water treatment/disposal requirements). Two measures, named feasibility degree and probability level, are introduced to address decision makers' preferences on fuzzy and stochastic constraints, respectively. A high feasibility degree represents a low risk of violating fuzzy constraints (corresponding to decreased underground injection capacity and increased wastewater generation rate simultaneously), while a high probability level means a high risk of violating random constraints (corresponding to increased capacities of two hazardous wastewater treatment plants). From the decision makers' perspective, the preferable decision schemes are those with a minimized total-system cost, corresponding to a low feasibility degree and a high probability level (Table 7). However, such a scenario would lead to increased risk of violating fuzzy and random constraints simultaneously. A desire for achieving high system reliability (i.e., reduced risk of violating fuzzy and random constraints, and meeting FP water treatment/ disposal requirements) would result in a high total-system cost. Decision makers can select the most suitable strategies for managing FP water, based on their preferences on economic objective and system reliability (by identifying various combinations of feasibility degrees and probability levels). Such results are beneficial for decision makers to adjust relevant decision schemes to arrive at the most effective and efficient policies for management of FP water from shale gas development. Importantly, the optimization model developed in this study can be used to support a life-cycle, systems approach to wastewater management during shale gas explorations. Acknowledgments Chris Parker edited the text. Publication is authorized by the permission of the Director, Bureau of Economic Geology. The authors would like to thank the Editor and anonymous reviewers for their helpful comments and suggestions. References rez Gladish, B., Rodrıguez Urıa, M.V., 2005. Arenas Parra, M., Bilbao Terol, A., Pe Solving a multiobjective possibilistic problem through compromise programming. Eur. J. Oper. Res. 164, 748e759. Barbot, E., Vidic, N.S., Gregory, K.B., Vidic, R.D., 2013. Spatial and temporal correlation of water quality parameters of produced waters from Devonian-Age shale following hydraulic fracturing. Environ. Sci. Technol. 47, 2562e2569. Charnes, A., Cooper, W.W., 1959. Chance-constrained programming. Manage. Sci. 6, 73e79. Clark, C.E., Horner, R.M., Harto, C.B., 2013. Life cycle water consumption for shale gas and conventional natural gas. Environ. Sci. Technol 47, 11829e11836. Ely, J.W., Horn, A., Cathey, R., Fraim, M., Jakhete, S., 2011. Game Changing Technology for Treating and Recycling Frac Water. SPE Annual Technical Conference and Exhibition, October 30-November 2, Denver, Colorado, USASPE 145454.

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