Abstract
The demand for water often necessitates desalination, particularly in arid coastal environments. Desalination is often integrated with electrical cogeneration. The demands for water and electricity change over time and are subject to uncertainty. A country-wide large-scale energy and water cogeneration planning model for Kuwait is formulated as a multi-period mixed integer linear programming problem and solved to minimize the net present value over the time period of 2013–2050. Five different plant technology options were considered for desalination and cogeneration including Oil & Multi Stage Flash, Natural Gas & Multi-Effect Distillation, Natural Gas & Reverse Osmosis, Solar Energy & Multi-Effect Distillation, and Solar Energy & Reverse Osmosis. Both water and energy usage in Kuwait and data from existing plants were utilized in providing the parameters and forecasts necessary for solution of the mathematical programming model. The model provides technology choice and associated capacity decisions for existing plants, new plants at green sites, and existing plant capacity expansions as well as their timing to meet the demands.
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Abbreviations
- i :
-
Plant technology defined as follows: 1 Oil-MSF, 2 NG-MED, 3 NG-RO, 4 SWEP-MED, and 5 SEW-RO (\(i\; = \;1,\; 2,\; \ldots ,\;N\))
- j :
-
Production inputs, including oil, sun, water, natural gas among others. Different plant technologies use different sets of inputs (\(j\; = \;1,\;2,\; \ldots ,\;J\))
- k :
-
Plant number (\(k\; = \;1,\; 2,\; \ldots ,\;K\)). This set indicates the number of plant of each type
- t :
-
Planning horizon in years, \(t = 1 , { 2, } \ldots ,\; 3 7\) . Data is based from year 2013 until 2050 (\(1,\; 2,\; \ldots \;,\; T\))
- m :
-
Markets to be supplied it consists of the set {water, electricity}. For representation purposes the set m is indexed as \(m\; = \; 1,\; 2,\; \ldots ,\;M\)
- \(A_{ji}^{\hbox{min} }\) :
-
Minimum amount of input j that can be purchased for plant of technology i (oil: barrels, natural gas: ft3)
- \(A_{ji}^{\hbox{max} }\) :
-
Maximum amount of input j that can be purchased for plant of technology i (oil: barrels, natural gas: ft3)
- a jikt :
-
Amount of input j purchased by plant k of technology i at time t (oil: barrels, natural gas: ft3)
- \(C_{i}^{\text{inv}}\) :
-
Plant investment cost (fixed-charge) for plants of technology i ($/Plant)
- \(C_{i}^{\exp }\) :
-
Improvement cost (fixed-charge) for plants of technology i ($/Improvement)
- \(C_{im}^{\text{cap}}\) :
-
Investment cost (variable) for plants of technology i for generation of product m ($/M US Gal/year, $/MW/year)
- \(C_{i}^{\text{oper}}\) :
-
Operational cost of plant \(i\)($/utilization percent)
- \(C_{jt}^{\text{inp}}\) :
-
Estimated cost of input \(j\)at time t (Oil: $/barrel: Natual Gas: $/ft3)
- \({\text{d}}_{mt}^{\hbox{min} }\) :
-
Minimum demand estimate for product of market m for planning period \(t\) (M US Gal/year, MW/year)
- \({\text{d}}_{mt}^{\hbox{max} }\) :
-
Maximum demand estimate for product of market ym for planning period t (M US Gal/year, MW/year)
- I ijm :
-
Requirement of input j by plant of technology i to generate product for market m (Oil: barrels/MW, barrels/M US Gal Natural Gas: ft3/MW, ft3/M US Gal natural gas: ft3)
- P mt :
-
Sales price of product m at time t ($/M US Gal, $/MW)
- \(Q_{im}^{\hbox{min} }\) :
-
Minimum or starting capacity for plants of technology i (M US Gal/year, MW/year)
- \(Q_{im}^{\hbox{max} }\) :
-
Maximum capacity for plants of technology i (M US Gal/year, MW/year)
- q ikmt :
-
Installed capacity for plant k of technology i for product m at time t (water: M US Gal/year electricity MW/year)
- v ikmt :
-
Capacity expansion for plant k of technology i for product m at period t (water: M US Gal/year electricity MW/year)
- w ikt :
-
Operating level for plant k of technology i at time t (Dimensionless from 0 to 1)
- x ikmt :
-
Amounts of product m generated by plant k of technology i at time t (water: M US Gal electricity MW)
- y ikt :
-
1 if plant k of technology i is open at the beginning of period t; 0 otherwise (dimensionless)
- z ikt :
-
1 if plant k of technology i is expanded at the beginning of period t; 0 otherwise (dimensionless)
- α :
-
Maximum operating level for new plants (Dimensionless from 0 to 1)
- \(\gamma_{im}^{\hbox{min} }\) :
-
Minimum capacity expansion for plants of technology i (M US Gal/year, MW/year)
- \(\gamma_{im}^{\hbox{max} }\) :
-
Maximum capacity expansion for plants of technology i (M US Gal/year, MW/year)
- \(\psi^{\text{up}}\) :
-
Maximum increase in operating levels between successive periods expressed as a factor of the operating level of the previous period (dimensionless from 1 to infinite, used 1)
- \(\psi^{\text{lo}}\) :
-
Minimum operating level for a plant based on the operating level of the previous period (dimensionless from 0 to 1, used 0)
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Acknowledgments
Nael AlQattan acknowledges the support of fellowship Kuwaiti government for his doctorate studies.
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AlQattan, N., Ross, M. & Sunol, A.K. A multi-period mixed integer linear programming model for water and energy supply planning in Kuwait. Clean Techn Environ Policy 17, 485–499 (2015). https://doi.org/10.1007/s10098-014-0806-8
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DOI: https://doi.org/10.1007/s10098-014-0806-8