A capacity expansion planning model for integrated water desalination and power supply chain problem

Energy Conversion and Management 122 (2016) 462–476

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

A capacity expansion planning model for integrated water desalination and power supply chain problem Y. Saif, A. Almansoori ⇑ Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, P.O. Box 2533, United Arab Emirates

a r t i c l e

i n f o

Article history: Received 5 March 2016 Received in revised form 5 June 2016 Accepted 6 June 2016 Available online 11 June 2016 Keywords: Desalination and power supply chain Capacity expansion Mixed integer linear program UAE

a b s t r a c t Cogeneration of water and power in integrated cogeneration production plants is a common practice in the Middle East and North Africa (MENA) countries. There are several combinations of water desalination and power technologies which give significant adverse environmental impact. Renewable and alternative energy technologies have been recently proposed as alternative power production paths in the water and power sector. In this study, we examine the optimal capacity expansion of water and power infrastructure over an extended planning horizon. A generic mixed integer linear programming model is developed to assist in the decision making process on: (1) optimal installation of cogeneration expansion capacities; (2) optimal installation of renewable and alternative power plants; (3) optimal operation of the integrated water and power supply chain over large geographical areas. Furthermore, the model considers the installation of carbon capture methods in fossil-based power plants. A case study will be presented to illustrate the mathematical programming application for the Emirate of Abu Dhabi (AD) in the United Arab Emirates (UAE). The case study is solved reflecting different scenarios: base case scenario, integration of renewable and alternative technologies scenario, and CO2 reduction targets scenario. The results show that increased carbon tax values up to 150 $/ton-CO2 gives a maximum 3% cost increase for the supply chain net present value. The installation of carbon capture methods is not an economical solution due to its high operation energy requirements in the order of 370 kW h per ton of captured CO2. Thus, the Cplex solver in GAMS chooses optimal solutions without installation of carbon capture processes. In addition, higher degree of alternative and renewable energy technologies penetration within the energy mix reduces the overall net present value of the network, and the carbon emissions by 40%, and 12%, respectively. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Water and power are two important interlinked commodities that are identified as essential elements for sustainable development. Demand for both water and power is accelerating while supply is limited by resource availability, production cost, and environmental considerations. Prior considerations of water and power supply identified synergies and opportunities for enhanced overall resource use efficiencies. Identification of such opportunities requires detailed information of the present and emerging water/power pairing. Many countries have set plans to build communication channels between stakeholders within these sectors, and to frame policies and production coordination to meet future water and power demands [1,2]. Nowadays, polygeneration systems are an emerging research area [3], and the cogeneration of water desalination and power represents a facet in this area [4]. ⇑ Corresponding author. E-mail address: [email protected] (A. Almansoori). http://dx.doi.org/10.1016/j.enconman.2016.06.011 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

In the Middle East and North Africa (MENA) region, water scarcity and power demand growth pose great challenges. Power generation, in these countries, relays on fossil fuel power plants which cause great environmental impact. In addition, the water supply in these countries depends heavily on water desalination; which consumes significant amount of power. Accordingly, these countries show a large interdependence and nexus between the water and power sectors. In the future, large scale capacity expansions are expected to sustain water and power demand in the MENA region [5]. Greenhouse gas (GHG) emissions have been identified to produce significant negative environmental impacts. Power production can be achieved through several technologies such as renewables and non-renewables. Water production through desalination depends on two technologies: thermal and membrane. Several countries have set future targets for the adoption of renewable and alternative energy technologies (e.g., solar, nuclear) in their energy production mix as a tool for GHG

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Nomenclature Symbol and abbreviations AD Abu Dhabi CCS carbon capture and storage CLT construction lead time GAMS General Algebraic Modeling System GHG greenhouse gases GT gas turbine HRSG heat recovery steam generator LP linear program MED multi effect distillation MENA Middle East and North Africa MILP mixed integer linear program MSF multi stage flash NLP nonlinear program NPV net present value RO reverse osmosis SB steam boiler ST steam turbine UAE United Arab Emirates Sets ape com czs dese e ffe level nczs nfe phs prs rpe siz T zs Variables CACO2 CC CuCap EMIS EnC

set set set set set set set set set set set set set set set

of of of of of of of of of of of of of of of

alternative power equipment the water and power commodities the coast zone in the network desalination technologies process equipment fossil fuel power equipment levels in a cogeneration phase the interior zone non-fossil fuel power equipment production phases production sites renewable power equipment equipment or technology sizes time periods the zone in the network

and continuous total CO2 captured (kg/s) capital cost ($) current capacity of process equipment at time t, m3/h for desalination, kW for power, kg/s for steam flowrate emission flowrate (kg/s) thermal or electrical energy consumption by a desalination technology (kW)

emissions reduction [6–10]. Carbon capture and storage (CCS) is another mitigation option to reduce carbon emissions from traditional fossil fuel power plants. Therefore, it is of interest to study the problem of future water and power supply chain developments while taking into consideration the existing infrastructure. This integrated supply chain problem represents the main research focus of the current study. Several research optimization studies on water and power supply chain problems, including different scope and objectives, have been done. Those research studies consider different scales including: process plant networks, plants’ set on a regional level, distribution networks, and combinations of the aforementioned in a single problem. Water supply chain optimization studies were considered separately from power supply chain optimization in the available literature [11–18]. These studies focused on the strategic capacity expansion and operation of distributed water desalination plants. In parallel, power generation planning and capacity expan-

ExpCap F FP OC OUO POW Q RCO2 TCO2 UO x, y

expansion capacity of process equipment at time t, m3/h for desalination, kW for power, kg/s for steam flowrate flowrate of water (m3/h) and power (kW) between adjacent zones production rate of water (m3/h) and power (kW) operation cost ($/year) summation of an output from energy process units, kW for power, kg/s for steam flowrate power production (kW) water desalination production (m3/h) total CO2 released to the atmosphere (kg/s) total CO2 production (kg/s) energy unit output of process equipment in cogeneration phase, kW for power, kg/s for steam flowrate decision variables for energy unit in a fossil fuel power plant in Eq. (19)

Discrete variables NUE integer variable for process unit number ync binary variable for the construction of a new phase under different design sizes thought the planning time horizon ynIns binary variable for the construction a new phase yop binary variable for a commodity transport direction Parameters a, b, c coefficients of a process unit in Eq. (19) CLT construction lead time, years D demand of power (kW) or water (m3/h) ExpCapD a given size of process unit, (m3/h) for desalination, (kW) for power, (kg/s) for steam flowrate POWD power demand (kW) a yield from process unit b thermal or electrical energy consumption for a desalination technology (kW/m3/h) Superscript Brine designate a property for seawater brine EL designate electrical energy In water desalination intake THM thermal energy of water desalination Total designate total water production UP upper bound on a continuous variable Water designate a property for water desalination

sions were addressed in many research studies. Multiperiod optimization models were developed for the power generation expansion problem [19–25]. Those models took into consideration the investment and financial planning constraints of the power plant projects. All the previously mentioned water and power supply chain problems represent deterministic mathematical programming models dealing with different aspects of the water and power supply chain problems separately [11–25]. Water and power generation coupling and interaction were analyzed for many countries, such as the western region of United States [1], and MENA region [4,5]. A long term aggregate LP model was developed to examine the water and power interactions for the MENA region countries [2]. Another study presented an NLP model for the short-term optimal planning and distribution for the co-production of water and power [26]. The model analyzes existing infrastructure of water and power, and provides optimal operation conditions for the integrated system to satisfy water

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and power demand. To the best of our knowledge, an integrated long term water and power capacity expansion and operation planning model is not available in the literature. Such a model represents the main focus of the current research study. The present capacity expansion model takes into account the capacity expansion of the process equipment in the cogeneration plants. In addition, it investigates possible renewable and alternative energy technologies integration within the cogeneration mix. CO2 mitigation options (e.g., carbon tax, carbon capture) are also included in the model to study the overall environmental impact cost on the cogeneration supply chain problem. The previous research studies on the capacity expansion modeling either consider water desalination or power supply chain network separately. This study presents an extension of our previous work on water desalination supply chain optimization [17]. Specifically, this research study presents a simultaneous long term capacity expansion planning model for the water desalination and power supply chain problem. The mathematical formulation is a generic deterministic multiperiod mixed integer linear programming (MILP) model; which projects the future necessary infrastructure expansion for water and power on a regional scale. Several water desalination and power technologies will be included in the optimization model to provide several design alternatives for water and power cogeneration. Tactical decisions of optimal production planning for water desalination and power are also included in the model to optimize the supply chain network; while satisfying the water, power, and environmental constraints along the planning time horizon. The following section presents the problem definition of the proposed water and power supply chain model, followed by the MILP formulation in Section 3. Section 4 presents a case study of Abu Dhabi (AD) in the United Arab Emirates (UAE) to show the application of the mathematical programming model. In the case study section, several scenarios will be analyzed to discuss the capacity expansion for the AD power and water infrastructure. Our aim from the case study is to analyze the global supply chain network under different scenarios and the analysis is presented for the global network power to water ratio. Finally, Section 5 provides the conclusions from the research study. 2. Problem definition This section provides the description of the integrated water desalination and power supply chain problem. Section 2.1 presents the integrated water desalination and power supply chain problem scope, and gives the network representation of the problem. Section 2.2 defines the integrated water desalination and power supply chain problem statement. 2.1. Integrated water and power problem scope 2.1.1. The integrated supply chain network The abovementioned supply chain problem is analyzed in this study on a regional scale. This region is divided into several zones, and every zone may have standalone desalination or power plants, cogeneration plants, renewable power plants, and alternatives power plants. Fig. 1 depicts the UAE map which shows the different emirates over large geographical area. In this study, we consider only the AD emirate (e.g., the yellow1 highlighted area) which is divided into several zones. We classify every zone in the supply chain problem as zones located on the coast (czs) and interior zones (nczs). nczs zones normally do not include a direct access for seawater intake. Therefore these zones only include standalone 1 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.

power plants, renewable and alternative power plants. By comparison, czs include direct access to seawater intake, and consequently these zones may include standalone desalination plants, cogeneration plants, renewable and alternative power plants. In general, there is exchange of water and power among adjacent zones. Power plants can be classified as fossil fuel power plants, renewable (e.g., solar, wind, etc.), and alternative (e.g., nuclear) power plants. Desalination plants can be classified as thermal (e.g., multistage flash distillation (MSF), multi effect distillation (MED), etc.) and membrane (e.g., RO) desalination plants. Cogeneration plants include process equipment for water desalination and power production. 2.1.2. The integrated cogeneration plant Standalone water desalination and power plants, as well as cogeneration plants are different in terms of their inputs (e.g., feedstock materials, fuel types), power technology type, desalination technology type, output products (e.g., power, water, coproducts), utility consumption (e.g., electricity, steam, etc.), and environmental impacts. In addition, cogeneration plants include several process units. Every process unit performs specific tasks (e.g., steam generation, power production, water desalination) by transforming the states of the input/output streams of the process unit. In addition, within a cogeneration plant, there are several streams connecting the process units. These process streams are under different conditions (e.g., different temperature and pressure conditions). Therefore, a comprehensive representation of the process streams, process units, and their inter-linkage (i.e., options of several design alternatives of a cogeneration phase) is a useful tool to assist in the design of grassroots and retrofit cogeneration plants. Thermal desalination plants require electricity and steam for their operation; whereas membrane-based desalination plants require mainly electricity for their operation. Fossil fuel power plants include different configurations for power production. Fuel can be burned to generate high pressure and temperature gas streams in order to operate gas turbines (GT) and electrical generators for power production. Steam turbines (ST) can also be used for power production by steam expansion under high pressure and temperature. Heat recovery steam generator (HRSG) units can also be used to generate steam for the operation of steam turbines. Furthermore, steam boilers (SB) can be used to generate steam under high pressure and temperature for the operation of steam turbine units. Fig. 2 shows layouts for different phases of water and power cogeneration. All these cogeneration phases represent different process layouts; which simultaneously deliver water and power products. Normally the capacity expansion of cogeneration plants goes through the addition of several cogeneration phases with different layouts. Therefore, simultaneous optimization of these configurations for the retrofit of existing power plants is an important step to seek minimal power and water production cost from the cogeneration plants. Cogeneration plants can be divided into several sections as shown in Fig. 3. The global box represents a generic cogeneration plant which exchanges several products with its surrounding (e.g., the zone itself). Seawater and fuel are external resources for the generic cogeneration plant to allow the production of water and power. As a result of the cogeneration processes, CO2 and brine are transported outside the plant for appropriate disposal. In addition, water product is transported outside the plant to satisfy water demand for the zone itself, or other adjacent zones. Cogeneration plants are normally composed by several cogeneration production phases. Every phase has distinct structure as previously described in Fig. 2. Furthermore, the operation of these phases is independent from each other. However, the produced water and power from all the existing phases are combined to meet production targets.

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Iran

Z6

Arabian Gulf

Z1

Z2

Oman

Z4 Z5 Z3

Saudi Arabia

Fig. 1. UAE map with distributed water and power production plants for Abu Dhabi Emirate.

The retrofit of cogeneration plants is assumed to be carried out by adding additional cogeneration phases to existing ones in czs production sites. Fig. 4 depicts the alternatives cogeneration phase layouts that can be added to existing phases in a cogeneration plant. There are several levels (e.g., LV1-LVn) that are representations of different steam conditions (e.g., high to low pressure steam headers). Between any adjacent pressure headers, there are unit operations which serve the purpose of power generation and steam production. At the upper level, water is distributed over the SB and HRSG units. These units may be different and have different rated capacities. Also, at the upper level, standalone gas turbines may exist for single power production. Steam generation at the upper level must be at high pressure and temperature conditions to enhance power production. At the lower levels, the steam headers are normally under relatively low pressure and temperature conditions to supply steam for thermal desalination operations. It is also worth mentioning that water may be fed to units between any adjacent levels to generate suitable steam for specific desalination units. Therefore, Fig. 4 accommodates several design alternatives suitable for the retrofit of cogeneration plants. The overall desalination and power supply chain problem can be represented by combining the previously mentioned Figs. 1–4. Fig. 1 represents the transportation of the products among different zones. Figs. 2–4 form the basis of the integrated cogeneration plants, and provide a tool for the cogeneration plants retrofit over the planning time horizon. It is also worth mentioning that renewable power plants (e.g., solar, and wind) or alternative power plants (e.g. nuclear) can be included in Fig. 1 for power production; and also as CO2 mitigation options. These plants are assumed to be standalone facilities for power production. The following section covers the integrated water desalination and power supply chain problem statement. 2.2. Problem statement The water desalination and power supply chain model examines strategic and tactical decisions over a long time planning horizon for distributed production plants. The geographical area under

study is assumed to be composed of several zones (zs), and every zone exchanges water and power across its boundaries (e.g., with its adjacent zones). Furthermore, the zones are classified as zones located at the sea coast (czs), and interior zones (nczs). At the beginning of the planning time horizon, we assume that the existing cogeneration plants, standalone power and desalination plants have known capacities. The capacity expansion of the production plants in every zone is carried out by adding new production phases (phs). Possible capacity expansion or new installation of renewable and alternative power plants are incorporated in the model. The capacity expansion for the new production phases is modeled through binary variables. These binary variables will be optimized while solving the MILP model. The optimal solution ultimately will provide two potential values for a binary variable describing the existence of a new production phase. Zero value for the binary variable implies non-existence of the new production phase. Otherwise, another value implies the existence of a new production phase for the optimal solution of the supply chain network. Furthermore, the configuration of the new production phase is determined by the integer variable values of the process units that may exist in the optimal solution (e.g., as explained by Fig. 4). Any non-zero value for the process unit integer variable implies the existence of the process unit in the new production phase. Otherwise, zero value for the process unit integer variable determines the non-existence of the process unit in the optimal solution of the supply chain network. The modeling of the new production phases will be explained later in the model development section. The problem statement can be summarized as given:
Planning time horizon T divided into equal yearly time periods (t).
Zone set (zs) which reflects the divided area of the region under study. In addition, these zones are classified as czs, and nczs subsets.
Set of production sites (prs) for every zone. Every production site has several existing phases and potential new phases (phs).
Set of products (com) which represents water and power.

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Emission

Fuel Low pressure Steam

High pressure Steam

Water

Steam boiler (SB) Emission

Back pressure steam turbine

(a)

Fuel Low pressure Steam

High pressure Steam

Water

Steam boiler (SB)

Emission

Thermal desalination unit

Thermal desalination unit

Extraction steam turbine

(b)

Fuel

Water Low pressure Steam

Exhaust gas

Thermal desalination unit

Heat recovery steam generator (HRSG)

Gas turbine (GT)

(c) Emission

Fuel

Back pressure steam turbine

Water High pressure Steam

Exhaust gas

Low pressure Steam Gas turbine (GT)

Heat recovery steam generator (HRSG)

Thermal desalination unit

(d) Emission

Fuel

High pressure Steam

Exhaust gas

Gas turbine (GT)

Extraction steam turbine

Water

Heat recovery steam generator (HRSG) Low pressure Steam

Thermal desalination unit

(e) Fig. 2. Different layouts of cogeneration phases.


Set of process equipment (e) which includes all the process equipment types for water desalination and power generation. This set can be further divided into desalination equipment set (dese), fossil fuel power equipment set (ffe), and non-fossil fuel power plant equipment set (nfe) (e.g., renewable (rpe) and nuclear (ape)).


Set of sizes (siz) which gives different design capacities of the process equipment.
Forecast of the water and power demand at every time period for every zone in the region.
Cost and technical data for the design and operation of the production plants.

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Vent

CO2

CO2 capture process

Flue gas

Electricity and steam production

Thermal and membrane desalination units

Water Steam

Electricity

Electricity

Seawater

Brine

Fuel

Water Product

CO2

Fig. 3. A global representation of a cogeneration plant.

Water Production and CO2 Control Vent

E

E

F

F

E

F

CO2 Capture Processes LV1 Electricity

VHPS

Steam

Fuel

Flue gas

Electricity Seawater

LV2

Thermal Desalination Processes

HPS

Electricity

LV3

Seawater MPS

Water Product

Water

LV4 LPS

Brine

Electricity

Condensate

Seawater

Mechanical Desalination Processes

Water Makeup

Electricity and Steam Production Steam

Electricity

Flue gas

Water

Fig. 4. Alternatives cogeneration phase layouts.

Water

Brine

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It is required to minimize the net present value of the whole supply chain problem over the planning time horizon by solving the multiperiod mathematical programming model in order to find the following:
Optimal capacity installation of process equipment at more suitable zones over the planning time horizon.
Optimal operation conditions for the production of water and power at every zone, and the transportation of products between adjacent zones over the planning time horizon. Fig. 5 shows the general structure for the input-output of the mathematical programming model. The following section covers the multiperiod mathematical programming formulation for the integrated water desalination and power supply chain problem.

3. Model formulation 3.1. Design and capacity constraints The capacity expansion constraint is a relation that describes the new capacity (ExpCapzs;prs;phs;e;t ) of a new phase (phs) at a production site (prs) and at a given time period (t) (as explained in the previous section). Therefore, the capacity expansion constraint relates the existing capacity of a new phase (CuCapzs;prs;phs;e;t ) at a given time period with its capacity at a pervious time period (CuCapzs;prs;phs;e;t1 ) through an additional required expansion capacity (as shown in Eq. (1)). The Eq. (1) is general and can be formulated for all the equipments in a new phase that may exist in a new production site under consideration (e.g., desalination plants, fossil and non-fossil fuel power plants). This is given as follow: • • • • • •

Model Key Input

þ ExpCapzs;prs;phs;e;t

•

Model Constraints

• • •

8 zs; prs; phs; e; t

ð2Þ

t X siz X ynczs;prs;phs;siz;t 6 1 8 zs; prs; phs

ð3Þ

Binary and integer variables relations with process unit capacities. Binary variables relation with water and power transportation. Water and power demand constraints. Operation for water and power technologies. Operation boundaries for the process units. • • • •

Products

• • • • •

ð1Þ

siz X ExpCapzs;prs;phs;e;t ¼ ExpCapDe;siz NUEzs;prs;phs;e ynczs;prs;phs;siz;t

Minimize NPV subject to Model constraints •

8 zs; prs; phs; e; t

The equations describing the installation of a new production phase make use of binary variables (ynczs;prs;phs;siz;t ). These binary variables are related to parameters that reflect equipment sizes (ExpCapDe;siz ) that may exist in the new phase; and an integer variable which reflect the total number of this equipment (NUEzs;prs;phs;e ) as given by Eq. (2). Therefore, this equation determines the equipment size and number in the new production phase. The search algorithm optimizes the binary and integer variables for a new production phase. A zero value for the binary variable of the new production (ynczs;prs;phs;siz;t ) implies that the new production phase does not exist in the optimal solution of the supply chain, and consequently there will not be any process units for the given phase (e.g., all NUE will have zero values). Otherwise, the new production phase will exist in the optimal solution, and the integer variable values for the process units will determine the configuration for the new production phase. In addition, the selected size of the equipment to be installed in a new phase is limited to a single value throughout the planning time horizon, as given by Eq. (3). This equation keeps the equipment arrangement fixed for all successive time periods. It is worth mentioning that the right hand side of Eq. (2) is a bilinear function which can be exactly modified to a linear form through the introduction of additional variables and constraints [27,28].

Water and Power demand forecast. Existing capacities of water and power plants. Sizes of power equipment. Maximum number of production phases. Prices of process units. CO2 tax values.

Problem Statement

Model Key Output

CuCapzs;prs;phs;e;t ¼ CuCapzs;prs;phs;e;t1

Water. Electricity. Brine. CO2..

Net present value. Production profiles for every production phase at every time period. Capacity expansion of the production phases at every time period. CO2 emission flowrate. Prediction of CO2 capture processes installation. Fig. 5. The optimization model structure.

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The installation of any new phase in a production site is defined through a binary variable (ynInszs;prs Þ. This binary variable is related to ðyncÞ as given by Eq. (4). This constraint forces all the expansion decisions for the equipment in a new phase to vanish if the new phase does not exist in the final optimal solution. t X siz X ynczs;prs;phs;siz;t 6 ynInszs;prs

8 zs; prs; phs

There are operation constraints related to every zone in the region (e.g., the overall network), and operation constraints for the production sites. The following section defines the zone operation constraints, and followed by the operation constraints of the production sites. 3.2.1. Zone operational constraints Every zone (zs) is connected with a subset of adjacent zones ðzs0 Þ where the exchange of products (e.g., water and power) takes place in every time period. The flow of these products should satisfy the demand in every zone as given by the following equation: prs X phs zs0 zs0 X X X FPzs;prs;phs;com;t þ Fzs0 ;zs;com;t  Fzs;zs0 ;com;t

8 zs; com; t

ð5Þ

FP represents the available quantity of product (e.g., water and power) at any time period; which can be produced through the available assets in zone (zs). F gives the amount of product that can be exchanged between zone (zs) and its neighbor zones ðzs0 Þ. It is also important to define the products transfer direction across the boundaries of any zone. Binary variables (yop) are defined to determine the transport directions of the products across any adjacent zones, as given by the following equations:

Fzs;zs0 ;com;t 6 FUP zs;zs0 ;com;t yopzs;zs0 ;com

8 zs;zs0 ; com; t

ð6Þ

Fzs0 ;zs;com;t 6 FUP zs0 ;zs;com;t yopzs0 ;zs;com

8 zs;zs0 ; com; t

ð7Þ

yopzs;zs0 ;com þ yopzs0 ;zs;com 6 1 8 zs;zs0 ; com

ð8Þ

Constraint (8) insures that the transfer direction of any product between adjacent zones is only in one direction throughout the planning time horizon. 3.2.2. Plant operation constraints 3.2.2.1. Renewable and alternative power plants. The operation requirements for the production sites are different depending on the equipment types available on site. Renewable and alternative power plants are assumed to be standalone facilities. These plants can be located on the coast and interior zones. The amount of power produced (POWzs;rpe;phs;t ) by these plants should not exceed its available capacity as given by the following equations:

POWzs;rpe;phs;t 6 CuCapUP zs;rpe;phs;t

8 zs; rpe; phs; t

ð9Þ

POWzs;ape;phs;t 6 CuCapUP zs;ape;phs;t

8 zs; ape; phs; t

ð10Þ

In addition, renewable power plants can have limited maximum capacity which reflects the degree of the technology penetration in the power mix. Therefore, a fraction from the total power demand (POWD) at every time period is assumed to be supplied from renewable power plants as given by Eq. (11). Similar constraint can be set if one has an interest on the maximum power penetration of alternative power plants. rpe zs X zs X X POWzs;rpe;t 6 % POWDzs;t

8t

POWzs;rpe;phs;t ¼ arpe CuCapUP zs;rpe;hs;t

8 zs; rpe; phs; t

ð12Þ

ð4Þ

3.2. Operation constraints

P Dzs;com;t

The operation of renewable power plants is related to the current capacity through a conversion factor; which reflects the availability and efficiency of the technology as given by the following equation:

ð11Þ

3.2.2.2. Fossil fuel power plants. The generic representation of cogeneration plants presented in Figs. 2–4 shows different design alternatives. Considering desalination units (e.g., standalone desalination plant or desalination technology in a cogeneration plant), the amount of water that can be produced by a desalination technology, existing on the coast sites, is a function of the seawater intake flowrate as given by Eq. (13). The total amount of brine produced by every desalination technology, and the energy consumption (e.g., thermal and electrical energy) for water production are given by Eqs. (14) and (15), respectively. In Q Water czs;prs;dese;phs;t ¼ adese Q czs;prs;dese;phs;t 8 czs;prs;dese;phs; t

ð13Þ

¼ ð1  a 8 czs; prs;dese; phs;t ð14Þ   Water EL EnCczs;prs;dese;phs;t ¼ bTHM þ b Q czs;prs;dese;phs;t 8 czs;prs; dese;phs; t dese dese Q Brine czs;prs;dese;phs;t

In dese ÞQ czs;prs;dese;phs;t

ð15Þ In addition, the total water production from all the desalination technology existing in every phase, and every production site is given by Eq. (16). A restriction on the maximum water production capacity on the desalination technologies is related to the maximum available capacity (see Eq. (17)). Moreover, the total production of water by zone and time period is the summation of all water produced from all existing production sites as given by Eq. (18).

Q Total czs;prs;phs;t ¼

dese X Q Water czs;prs;dese;phs;t

Q In czs;prs;dese;phs;t Q Total czs;t

8 czs; prs; phs; t

6 CuCapczs;prs;dese;phs;t

prs X ¼ Q Total czs;prs;t

8 czs; prs; dese; phs; t

8 czs; t

ð16Þ ð17Þ ð18Þ

Common performance models for utility systems are inherently nonlinear in nature due to the relations involved between the unit size and load. However, linear models are available in the literature for energy equipment performance [29]. The general structure for the unit models (e.g., steam boiler, steam turbines, etc.) follows a linear function as given by the following equation:

UOczs;prs;e;phs;t ¼ ae xzs;prs;e;phs;t þ be yzs;prs;e;phs;t þ ce

8 czs; prs; e; phs; t

ð19Þ

where a, b, and c represent constant parameters for a specific unit. (UO) gives the unit output as a function of x, and y. Table 1 shows the input variables x and y for some of the energy units covered in this study. The overall unit output (OUO) is related to the total number units (of the same type) existing in a given level (NUE) as shown in Eq. (20). This equation can be modified to a linear form as previously described for Eq. (2). Additionally, Eq. (21) limits the unit performance output to a maximum value; which is related to the unit design limit. There are also mass balance constraints for the steam flow at each level present at the new and existing cogeneration phases.

OUOczs;prs;e;phs;t ¼ NUEzs;prs;phs;e UOczs;prs;e;phs;t 8 czs;prs;e; phs; t

ð20Þ

OUOczs;prs;e;phs;t 6 CuCapzs;prs;phs;e;t 8 czs; prs; e; phs;t

ð21Þ

The total emission (TCO2) balance from fossil fuel power plants over the region under study is necessary; this is given by Eq. (22). The net amount of released CO2 (RCO2) is the difference between the net CO2 production from all zones and the captured CO2

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Table 1 Key variables for the energy equipment models in the fossil fuel power plants. Key variables

x

y

Gas turbine

Design power Design power _ _

Fuel heat input

Steam turbine Steam boiler Heat recovery steam generator

Steam flow rate Fuel heat input Gas turbine exhaust gas plus supplementary fuel firing

(CACO2) as described by Eq. (23). Furthermore, Eq. (24) gives the emission reduction target; which can be met through the installation of carbon capture processes.

TCO2t ¼

prs X phs zs X X EMISczs;prs;phs;t

RCO2t ¼ TCO2t  CACO2t CACO2t P %TCO2t 8 t

8t

8t

ð22Þ ð23Þ ð24Þ

3.3. Cost model The objective function of this model is to minimize the net present value (NPV) of the supply chain network; which takes into account the capital and operation cost along the planning time horizon. The capital cost (CC) is related to the expenditure for the capacity expansion of the integrated water desalination and power supply chain assets taking into account an interest rate (ir) as given by the following equation:

CC ¼

prs X phs X zs X e X t X ExpCapzs;prs;phs;e;t COCe tCLT ð1 þ irÞ

ð25Þ

COC is the capital cost coefficient for the expansion of any equipment as a function of its size in the supply chain network. It is worth pointing out that the capital cost for any equipment is evaluated at a time period that takes into account the construction lead time (CLT). Every process operation requires several operation tasks, and therefore every equipment operation cost is a combination of several terms (e.g., fuel consumption, thermal energy consumption, electrical energy consumption, waste disposal, maintenance, labor, etc.). The following equation gives the operation cost for the network along the planning time horizon. OP represents the operation variable and OCC gives an operation cost coefficient of specific equipment.

OC ¼

prs X zs X e X t X OPzs;prs;e;t OCCe t ð1 þ irÞ

ð26Þ

The following section analyzes the integrated water desalination and power supply chain network problem, and shows the application of the proposed mathematical programming model. 4. Case study The case study considered here examines the design and operation of the water desalination and power supply chain for the Emirate of Abu Dhabi in the United Arab Emirates. UAE is part of the Gulf Cooperation Council (GCC) countries; and it is surrounded by Saudi Arabia and Oman. The Emirate of Abu Dhabi is the largest of the emirates by area (67,340 km2), accounting for approximately 87% of the total land area of the UAE. The Abu Dhabi Emirate also has the largest population of the seven emirates. In June 2011, it was estimated to be 2,120,700 people; which has risen to 2.3 million in 2012. It would be a better option to consider

the UAE as a whole as a comprehensive case study, however, information of water desalination and power production plants in other emirates is not available. Therefore, we consider the case study of the AD Emirate as it represents the largest Emirate in terms of geographical area and population. The Abu Dhabi Water and Electricity Company is the one handling the responsibilities of water and power supply for the AD Emirate. In addition, the company handles a long term contract of water and power supply for other emirates. In general, the AD Emirate can be divided into six zones as depicted by Fig. 1 (e.g., the yellow highlighted area). All the production zones are within the Emirate of Abu Dhabi; whereas zone number six is outside the boundary of AD Emirate for the purpose of water and power supply for other emirates. There are nine production plants which are distributed over the emirate. Existing capacities and configurations for the production plants are given in supplementary data section. The AD Emirate considered nuclear energy integration in zone number five. Solar energy technology exists in zone number three. Most of the production plants are natural gas fuel based power plants. Water desalination is mainly based on the MSF technology with minor RO technology capacity. Fig. 6 shows the projected total power to water ratio demand for the AD Emirate over a ten years planning time horizon, starting from 2015 up to 2025 [30,31]. In this case study, we examine different scenarios of carbon tax values, renewable and alternative energy technologies integration, and GHG emission reduction. These scenarios are: (1) Scenario one: Base case scenario. (2) Scenario two: Integration of nuclear and solar energy technologies. (3) Scenario three: CO2 capture from fossil fuel production plants. Section 4.1 examines the capacity expansion of the integrated water desalination and power supply chain problem without considering renewable and alternative energy technologies penetration, and under various carbon tax values (first scenario). Section 4.2 considers the renewable and alternative energy technology penetration effects on the integrated water desalination and power supply chain network with various carbon tax values (second scenario). Section 4.3 examines the effects of CO2 emission reduction targets on the integrated supply chain problem with various capacities integration of nuclear technology (third scenario). The cost and technical data for the model are given in supplementary data section. The mathematical programming model was coded in the General Algebraic Modeling System (GAMS) and solved using the Cplex solver [32]. In general, the model is composed by 68,500 equations, 33,300 continuous variables, and 2200 binary variables.

Powr to water ratio, kWh/m3

470

70 60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9

10

Time, years Fig. 6. The global network demand of power to water ratio for the integrated water desalination and power supply chain over the planning time horizon.

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4.1. Scenario one Renewable and alternative energy technologies are recently proposed options for power supply in the MENA region. The adoption of these technologies is still limited and their integration within the power energy mix should bring environmental benefits (e.g., reduction in the GHG emissions). However, under the given scenario, we consider only the expansion of the production plants by installation of new production phases as shown in Figs. 2–4. These new capacities can be cogeneration and standalone power phases. Consequently, one can establish a basis for comparison with other scenarios (e.g., the effect of renewable and alternative energy technologies integration, and GHG emission reduction targets). In addition, the MSF and RO desalination technologies are considered for the desalination capacity expansion. Table 2 gives the net present value for the water desalination and power supply chain expansion under different carbon tax values. In general, the cost contribution of CO2 tax has insignificant values compared with the overall cost of the integrated supply chain expansion and operation. However, these values represent significant overhead (e.g., the values are in the order of billions). In addition, the total estimated CO2 production does not significantly vary by increasing the carbon tax values. Fig. 7 shows the network global design of power to water ratio for the integrated supply chain along the planning time horizon. This variable represents the ratio of total available power capacity to the total water desalination capacity in the supply chain network at every time period. It can be observed that the network global design of power to water ratio is insensitive with respect to carbon tax values. It is also worth mentioning that there are no carbon capture processes at any production plants. This trend of the results shows that the optimal solutions satisfy the power to water ratio demand without a need for additional CO2 capture power. In fact, the CO2 energy consumption from natural gas fuel based emission (e.g., 370 kW h/ton) is high [33]; and this trend of the results is consistent with other studies which showed that CO2 capture from natural gas fuel based power plants is not economical [34,35]. Moreover, the MSF desalination technology represents the main

Table 2 Summary of the optimal solutions for the first scenario. Carbon tax values, $/ton-CO2 Cogeneration cost, billions $ Emission cost, billions $ Net present value, billions $ Total CO2 production, kg CPU time, s

0 115,020 0 115,020 2.53  1013 460

50 116,120 57 116,170 2.48  1013 5200

150 118,780 166 118,950 2.26  1013 1400

471

option for meeting the water demand; with minor installation of RO capacity (e.g., the RO technology capacity does not exceed 6% of the total water desalination capacity by the end of the planning time horizon). Fig. 8 shows the water and power transport directions among the zones. In general, the model is sensitive with respect to the water and power transport directions among the zones in the integrated supply chain network. In addition, the water and power expansion capacities in every production zone are sensitive with respect to the carbon tax values. This implies that reconfiguration of the water and power infrastructure under various carbon tax values is an important decision in order to minimize the net present value of the network. 4.2. Scenario two Diversification of the power mix has been addressed to reduce UAE’s reliance on fossil fuel power plants [36]. Nuclear and solar power plants represent the major technological options to be deployed in the region in the near-to-medium term future. Nuclear energy is expected to contribute with 25% of the total power mix in the Abu Dhabi Emirate by 2020. Besides, the Abu Dhabi Emirate has planned to set a target of approximately 10% of the power generation from renewable energy technology. Therefore, we examine the effects of nuclear and solar energy technologies integration on the integrated water and power supply chain taking into account their penetration limits. Table 3 presents the summary of the optimal solutions under the given scenario for various carbon tax values. In general, it can be observed that the major cost is affected by the installation of fossil fuel based cogeneration phases. Nuclear and solar energy technologies cost contribution is a relatively minor cost compared with the net present value of the network. Similarly, the CO2 tax cost also is a relatively minor cost compared with the net present value of the network. In addition, there is a reduction of CO2 emission as carbon tax increases without installation of carbon capture processes. Overall, the net present value of the network practically remains unchanged with the introduction of nuclear and solar energy technologies Similar to the previous condition (e.g., Fig. 7), the network global design of power to water ratio for the given scenario is insensitive to the carbon tax values as shown in Fig. 9. However, the financial planning for the water and power supply chain assets at the zones is sensitive to the carbon tax values. In other words, the installation of new production phases in a zone varies as a function of the carbon tax values. Besides, the water and power transport directions change as the carbon tax values increase (see Fig. 10). It is also worth mentioning that the MSF technology is the main option for water supply. 4.3. Scenario three

150$ tax value

Power to water ratio, kWh/m3

120

50 $ tax value

0 $ tax value

100 80 60 40 20 0

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

time, years Fig. 7. The global network design of power to water ratio for the supply chain network under various carbon tax values from 50 to 150 $/ton-CO2, scenario one.

The results from the previous scenarios show that the optimal solutions are insensitive to the carbon tax values. Also, the general results show that the installation of carbon capture processes is not preferable at the optimal solutions. This implies that the release of CO2 emission option is a more economical solution than the installation of carbon capture processes as a result of CO2 capture energy requirements. Furthermore, the expansion capacity constraints of nuclear and solar technologies are binding the optimal solutions (e.g., the solver selects the maximum capacities for the renewable and alternative technologies). Under the current scenario, we examine the effects of higher capacity integration of the nuclear energy technology as proposed in another study and ignore the carbon tax values [37]. Another objective considered under the present scenario is the achievement of a CO2 emission reduction target of 17% (see Eq. (24)) [38]. Such an emission reduction target

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Z6

Z1 Z4

Z2

Z5 Z3 Water transport

(a)

Power transport

Z6

Z1 Z2

Z4 Z5 Z3 Water transport

(b)

Power transport

Z6

Z1 Z2

Z4 Z5 Z3 Water transport

(c)

Power transport

Fig. 8. Water and power transport directions for the first scenario, (a) zero $ tax value, (b) 50 $ tax value, (c) 150 $ tax value.

Table 3 Summary of the optimal solutions for the second scenario. 0 77,104 50.3 10.7 0 77,165 2.3  1013 1800

50 77,509 50.3 10.7 49.7 77,620 2.25  1013 2200

150 77,658 50.3 10.7 149.5 77,869 2.26  1013 2700

will bring environmental and social benefits. Furthermore, this scenario forms a basis for comparison with the previous scenarios under zero carbon tax value. Table 4 presents the summary of the optimal solutions for various capacities of nuclear technology integration. The general trend of the results shows a reduction of the net present value at higher

50 $ tax value

0 $ tax value

120

Power to water ratio, kWh/m3

Carbon tax, $/ton-CO2 Cogeneration cost, billions $ Nuclear technology cost, billions $ Solar technology cost, billions $ Emission cost, billions $ Net present value, billions $ Total CO2 production, kg CPU time, s

150 $ tax value

100 80 60 40 20 0

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

time, years Fig. 9. The global design of power to water ratio for the supply chain network under various carbon tax values from 50 to 150 $/ton-CO2, scenario two.

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Z6

Z1 Z2 Z4 Z5 Z3 Water transport

(a)

Power transport

Z6

Z1 Z2

Z4 Z5 Z3 Water transport Power transport

(b)

Z6

Z1 Z5

Z2

Z4

Z3 Water transport Power transport

(c)

Fig. 10. Water and power transport directions for the second scenario, (a) zero $ tax value, (b) 50 $ tax value, (c) 150 $ tax value.

Table 4 Summary of the optimal solutions for the third scenario. 4 90,734 52.0 10.4 8 90,804 2.48  1013 1200

8 66,196 104.0 9.1 7.5 66,317 2.27  1013 1360

12 45,612 150.8 10.7 6.8 45,780 2.02  1013 33,200

nuclear capacity adoption in the energy mix. The higher integration of nuclear energy into the energy mix also reduces the capacities and cost of the cogeneration plants. In general, the nuclear power capital cost is high compared to the fossil fuel power plants. However, their daily operating costs and fuel costs are significantly low compared with conventional plants. Additionally, the heavy burden of the nuclear plant cost can be amortized over the long life

8 reactors

4 reactors

180 160 140

power to water ratio, kWh/m3

Reactor number Cogeneration cost, billions $ Nuclear technology cost, billions $ Solar technology cost, billions $ CO2 capture cost, billions $ Net present value, billions $ Total CO2 production, kg CPU time, s

12 reactors

200

120 100 80 60 40 20 0

t1

t2

t3

t4

t5

t6

t7

t8

t9

t10

time, years Fig. 11. The global design of power to water ratio for the supply chain network under various nuclear technology capacities, scenario three.

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reduction target as shown by Eq. (24)), and the continuous increased demand of the power and water over time. The renewable and alternative power technologies come online at early years to satisfy power demand and avoid CO2 emission over time. However, these technologies are limited by their maximum penetration in the energy mix. Therefore, the increased power and water demand over the planning time horizon are met by the installation of cogeneration plants at later years. It is worth pointing out that the MSF technology is dominant for the satisfaction of water demand due to the thermal energy coupling between the power production and the water desalination in the cogeneration plants. In general, the water and power transport directions are sensitive with respect to the various nuclear technology capacities as given in Fig. 12. The computational time for the analyzed case studies are given in Tables 2–4. For optimization problems with discrete variables,

of the nuclear reactors. Furthermore, the cost and emission release rate are both reduced as a result of adopting clean energy options such as nuclear and solar energy technologies. Fig. 11 shows the network global design of power to water ratio distribution over the planning time horizon. Under the present scenario, one can see a clear variation of the global network power to water ratio under various degree of the nuclear technology penetration within the energy mix. In general, the nuclear technology comes online at early years considering the construction lead time of these plants. (e.g., four years). A similar trend is observed with the installation of solar energy technology. Then, the network global design of power to water ratio is stabilized at a reasonable constant level by the construction of cogeneration plants at time periods following the construction of the nuclear plants. This trend of the results is due to the CO2 capture energy requirement (e.g., 17%

Z6

Z1 Z2

Z4 Z5 Z3 Water transport

(a)

Power transport

Z6

Z1 Z2

Z4 Z5 Z3

Water transport

(b)

Power transport

Z6

Z1 Z2 Z4 Z5 Z3

Water transport Power transport

(c)

Fig. 12. Water and power transport directions for the third scenario, (a) 4 reactors value, (b) 8 reactors, (c) 12 reactors.

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the Cplex solver in GAMS uses a branch and cut algorithm that solves a series of linear program sub-problems. Since a single mixed integer problem involves solving many sub-problems, even small mixed integer problems can be compute intensive. In our future work, we will consider the proposed integrated water desalination and power supply chain problem under water and power demand uncertainty. Computation difficulties are expected and convergence to optimal solutions can be achieved by designing proper decomposition algorithms [39,40]. These issues will be covered in our future work.

5. Conclusions This paper addresses the capacity expansion of the integrated water desalination and power supply chain problem through a deterministic multiperiod mixed integer linear programming model. The optimization model takes into account strategic and operation decisions through a long term planning time horizon. The capacity of the production plants is expanded through the installation of new production phases. The design of new production phases in the cogeneration plants is modeled through binary variables in order to provide design alternatives of the integrated water desalination and power production phases. Other binary variables were selected for the installation of new standalone fossil fuel power plants, renewable and alternative energy technologies. Tactical decisions consider the operation of fossil fuel power plants, renewable and alternative power plants, and the distribution of water and power through the network zones in order to satisfy the water and power demand over the planning time horizon. Furthermore, the environmental impact of the integrated water and power supply chain problem is considered by the installation of carbon capture processes in fossil fuel power plants. A case study of AD in UAE is presented to illustrate the application of the mathematical programming model. This case study is considered under various carbon tax values (e.g., values range from 0 to 150 $/ton-CO2), various expansion capacities of nuclear technology integration, and an emission reduction target. These conditions were examined to study their effects on the net present value, the required capacities of fossil fuel power plants, the capacities of different desalination technologies, the required capacities of solar and nuclear technologies, and the environmental impact of the supply chain network. The results showed in the first scenario that the network net present value is insensitive with respect to increased carbon tax values. Within the CO2 tax range values (e.g., 0–150 $/ton-CO2), the CO2 tax cost increases the net present value of the supply chain cost by 3% within the carbon tax range. The installation of carbon capture processes is not an economical option due to carbon capture energy requirement. This result is consistent with other research studies [34,35]. In the second scenario with the renewable and nuclear energy integration, similar trend of the results is observed as for the first scenario. However, within the CO2 tax range values (e.g., 0–150 $/ton-CO2), the net present value of the supply chain cost is increased by 1% within the range of CO2 tax values. This is due to the clean power production from the renewable and nuclear technologies. In general, the total CO2 emission flowrate is reduced by the adoption of renewable and nuclear technologies in the energy mix. By comparing the first and second scenarios under 0 $/tonCO2, the total CO2 flowrate is reduced by 9.1%. Under 50 $/tonCO2, fossil fuel power plants operation is further optimized, and 8.9% reduction of CO2 flowrate is gained. However, further reduction of CO2 flowrate cannot be achieved by imposing high carbon tax value, for example under 150 $/ton-CO2. This implies higher integration of clean power technologies would reduce the total CO2 emission flowrate. Under the third scenario, higher capacity

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integration of nuclear technology (e.g., 12 nuclear reactors) was adopted, and the CO2 tax cost was dropped in the objective function. Furthermore, 17% reduction target of CO2 emission is considered by installation of carbon capture processes. By comparing the second and third scenarios under 0 $/ton-CO2 and 4 nuclear reactors, one observes 18% cost increase for the net present value of the network. This is mainly due to the installation of carbon capture processes in order to reach the CO2 reduction target. Higher degree of nuclear reactors (e.g., 12 reactors) in the energy mix leads to the reduction of the network NPV and the CO2 emission by 40%, and 12%, respectively. The MSF desalination technology is the dominant one to satisfy future water demand as a result of the thermal energy coupling between the power production and water desalination in the cogeneration plants. Finally, a research extension from the current study is proposed to study the effects of the water and power demand uncertainty on the integrated water desalination and power supply chain problem configuration. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.enconman.2016. 06.011. References [1] Ackerman F, Fisher J. Is there water–energy nexus in electricity generation? Long-term scenarios for the western United States. Energy Policy 2013;59:235–41. [2] Dubreuil A, Assoumou E, Bouckaert S, Selosse S, Maızi N. Water modeling in an energy optimization framework – the water-scarce middle east context. Appl Energy 2013;101:268–79. [3] Mancarella P. MES (multi-energy systems): an overview of concepts and evaluation models. Energy 2014;65:1–17. [4] Serra LM, Lozano M, Ramos J, Ensinas AV, Nebra AA. Polygeneration and efficient use of natural resources. Energy 2009;34:575–86. [5] Siddiqi A, Anadon LD. The water–energy nexus in Middle East and North Africa. Energy Policy 2011;39:4529–40. [6] Ghaffour N, Bundschuh J, Mahmoudi H, Goosen MFA. Renewable energydriven desalination technologies: a comprehensive review on challenges and potential applications of integrated systems. Desalination 2015;356:94–114. [7] Luciani G. Nuclear energy developments in the mediterranean and the gulf. Int Spectator: Ital J Int Aff 2009;44:113–29. [8] Bhutto AW, Bazmi AA, Zahedi G, Klemeš JJ. A review of progress in renewable energy implementation in the Gulf Cooperation Council countries. J Clean Prod 2014;71:168–80. [9] Farnoosh A, Lantz F, Percebois J. Electricity generation analyses in an oilexporting country: transition to non-fossil fuel based power units in Saudi Arabia. Energy 2014;69:299–308. [10] Ahmad A, Ramana MV. Too costly to matter: economics of nuclear power for Saudi Arabia. Energy 2014;69:682–94. [11] Medellín-Azuara J, Mendoza-Espinosa LG, Lund JR, Ramírez-Acosta RJ. The application of economic-engineering optimization for water management in Ensenada, Baja California, Mexico. Water Sci Technol 2007;55:339–47. [12] Leitão JP, Matos JS, Gonçalves AB, Matos JL. Contribution of geographic information systems and location models to planning of wastewater systems. Water Sci Technol 2005;52:1–8. [13] Cunha MC, Pinheiro L, Zeferino J, Antunes A, Afonso P. Optimization model for integrated regional wastewater systems planning. J Water Resour Plann Manage 2009;135:23–33. [14] Han Y, Xu S, Xu X. Modelling multisource multiuser water resources allocation. Water Resour Manage 2008;22:911–23. [15] Kondili E, Kaldellis JK, Papapostolou C. A novel systematic approach to water resources optimization in areas with limited water resources. Desalination 2010;250:297–301. [16] Liu S, Konstantopoulou F, Gikas P, Papageorgiou LG. A mixed integer optimization approach for integrated water resources management. Comput Chem Eng 2011;35:858–75. [17] Saif Y, Almansoori A. Design and operation of water desalination supply chain using mathematical modeling approach. Desalination 2014;351:184–201. [18] Al-Nory MT, Brodsky A, Bozkaya B, Graves SC. Desalination supply chain decision analysis and optimization. Desalination 2014;347:144–57. [19] Sharma D, Bhattacharya K. A planning model for investor firms in the generation sector and financial analysis. In: IEEE power & energy society general meeting. p. 1–7. [20] Majumdar S, Chattopadhyay D. A model for integrated analysis of generation capacity expansion and financial planning. IEEE Trans Power Syst 1999;14:466–71.

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