_{1}

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Water, Energy and Food (WEF) nexus systems are developed to model and analyze interactions across and between WEF sectors. WEF nexus simulation models permit evaluating the direct and indirect WEF quantitative interaction effects in response to change of technology and/or demand. Optimization models can help to find the optimal combinations of WEF nexus system policy options and parameters that lead to the best performance of the system. This paper describes a framework for integrating quantitative WEF nexus simulation model (the Q-Nexus Model) with an optimization tool, which will give policy makers the ability to compromise best policy options based on WEF nexus simulator. The developed method is then applied to the numerical experiment and the results are discussed. Lastly, the conclusions and further developments are presented.

Numerous water, energy and food nexus systems are developed to analyze interactions between WEF sectors with the purpose of managing vital resources in the context of various competing interests [

The water, energy and food nexus interactions are complex and dynamic, and they directly and indirectly affect one another [

To better highlight the direct and indirect WEF interaction effects,

As shown in

Evidently, the accurate analysis of WEF nexus systems necessitates evaluating the direct and indirect quantitative effects. Despite the utility of evaluating these effects, they have yet to be used in a decision making framework by applying optimization algorithms to seek optimal policies for WEF nexus systems management. Facilitating the use of WEF nexus simulation models with independently developed optimization software provides a powerful tool for decision makers. The Q-Nexus Model as a WEF nexus simulator has already been used to influence policy and planning [

Two types of simulation could be performed using the Q-Nexus Model, the first type consists of analyzing scenarios related to variation of resources demand or reducing losses; the second type of simulation consists of analyzing scenarios of changing the technology by considering “High Efficient” and “Best Practice” technology alternatives. Moreover, the model permits to simulate different WEF intersectoral allocation policies and evaluate the performance of the system [

Our focus in this work is the applicability of optimization techniques to aid in WEF nexus decision making in terms of selection of best policy options using Q- Nexus Model simulator outputs. A flexible simulation and optimization framework that can easily be used for various WEF planning or management objectives is proposed.

Coupling WEF nexus simulation and optimization techniques (S-O) will certainly lead to investigate valuable knowledge that the simulation model may yield. The motif is to explore instantaneously the great detail provided by simulation and the ability of optimization techniques to find optimal results. The application of optimization techniques will derive the greatest benefit from a simulation model, as a matter of fact; the optimization model can be used to execute the WEF nexus simulation many times, to determine the best input values to achieve desired system outputs. Important optimization questions that can be answered to inform the sustainable WEF planning by combining simulation and optimization techniques include:

- What combinations of WEF nexus system policy options and input parameters lead to the best and worst performance of the system?

- What are the best tradeoffs between multiple competing objectives?

Combining S-O techniques can provide answers to these crucial questions and key insights for policy makers.

A thoroughly study of classification and discussion on this approach is presented in [

tion tools or approaches to build up a closed loop system. The coupled simulation and optimization approach has been applied in different fields to resolve optimization problems in the literature [

One of the advantages of coupled simulation and optimization is the ability to define objective functions outside the simulation tool; that is, the objective functions rely only on output from the simulation model. Thus, any modeling input or output could be adapted as a decision variable or used within objective function and constraint evaluations, respectively.

The optimization techniques treat the Q-Nexus Model as a black box, requiring only that each set of input values yields corresponding output values. This pairing of optimization with WEF nexus simulation model can be used beneficially anytime a WEF nexus system is being modeled and many combinations of input parameters are being considered.

Spreadsheet tools could be used as wrapper for the proposed framework where the simulation model and optimization tool could be implemented and

easily operated. This allows policy maker to identify decision variables from the input parameters and specify outputs of the Q-Nexus Model needed for evaluation of the objective functions and constraints.

The Q-Nexus Model is built on the input-output theory and is being able to evaluate quantitatively both the direct and indirect intersectoral WEF quantities [

A set of inflows were identified to represent the WEF sectors, for example, surface water, groundwater, desalination, wastewater and drainage water reuse inflows covering the water sector, imported petroleum and all types of electricity including renewable energy, covering the energy sector, and irrigated cereals, irrigated roots and other food production items covering the area of food. These inflows are particularly identified for the Lebanese case study presented in [

A set of equations are developed in [

If we denote by:

n: number of water resources inflows;

m: number of energy resources inflows;

h: number of food resources inflows;

^{th} water resource inflow in the j^{th} energy resource inflow;

^{th} water resource inflow in the j^{th} food resource inflow;

^{th} energy resource inflow in the j^{th} water resource inflow;

^{th} energy resource inflow in the j^{th} energy resource inflow;

^{th} energy resource inflow in the j^{th} food resource inflow;

^{th} food resource inflow in the j^{th} energy resource inflow;

^{th} food resource inflow in the j^{th} food resource inflow;

and ^{th} energy inflow;

^{th} food inflow;

^{th} water inflow;

^{th} food inflow;

^{th} energy inflow.

The WEF intersectoral use intensities (t) are defined as follows:

where^{th} water resource inflow, total use of the j^{th} energy resource inflow and total use of the j^{th} food resource inflow, respectively.

The WEF intersectoral allocation coefficients (c) are defined as follows:

The technology matrix A was demonstrated in [

where

The water for water and food for water relationships are considered quantitatively negligible, so they are set equal to zero in the above equation.

The total outputs (x) caused by end use quantities (y) are linked by the following equation [

where I is the identity matrix.

The changes in end use and the resulting changes in intersectoral quantities are linked by the following equation [

In quantitative-based WEF nexus system, several water and energy inflows are used in the production of the water, energy and food resources [

Additional food quantities will generate within the WEF nexus system needs for total (direct and indirect) additional water and energy resources (

Hereafter, the objective function and constraints are presented.

The total additional intersectoral water use (direct and indirect) could be evaluated using the Q-Nexus Model simulator, where:

Similarly, the total additional intersectoral energy use (direct and indirect) could be evaluated using the Q-Nexus Model simulator, where:

These simulation output values will serve as objective function for the optimization tool:

If the cost in US dollars per meter cube of water resource produced is denoted (^{3}), and the cost in US dollars per tons of oil equivalent of energy resource produced is denoted (

The estimation of (

The objective function: Minimum Cost (21)

The decision variables are the water and energy allocations in WEF sectors:

Subject to the following constraints:

(27)

(28)

where

The S-O framework will be used to find the best water and energy resource allocations that minimize the total cost to produce the required additional water and energy resources.

The additional resource cost (in USD) covers building and operating a generating resource plants over an assumed financial life and duty cycle. Key inputs to calculating additional resource cost include construction costs, financing costs, and an assumed utilization rate for each plant type [^{3}) and the cost in US dollars per tons of oil equivalent of energy resource produced (

If we denote by:

To take into account the capacity factors when estimating the costs per unit of resource produced, a gradual decline cost is assumed with increasing of water and energy plant sizes, starting from the estimated maximum costs per unit of resource i produced

If

If

If

If

Similarly, if

If

If

If

It is important to mention that the parameters

In order to put the developed framework in an application, a hypothetical case study of WEF nexus is presented. WEF nexus inflows that are considered are as follows:

Water inflows (including extraction, treatment, conveyance & distribution) (Mm^{3}/year): i) surface water (W1); ii) groundwater (W2); iii) desalination (W3); iv) wastewater reuse (W4); v) recycled water and agricultural drainage water reuse (W5).

Energy inflows (evaluated in terms of primary energy equivalent in ktoe/year on a net calorific value basis): i) imported petroleum (E1); ii) electricity (petroleum) (E2); iii) electricity (hydro) (E3); iv) imported electricity (E4); v) electricity (wind/solar) (E5); vi) biofuels (E6).

Food inflows (including agriculture, food processing & transportation) (kt/year): i) irrigated cereals (F1); ii) irrigated roots and tubers (F2); iii) irrigated vegetables (F3); iv) irrigated fruits (F4); v) Other Agriculture, Forestry & Food products (F5).

Microsoft Excel provides a platform to build the WEF nexus simulator and it includes an optimizer (Frontline Excel Solver), so it is easy and direct coupling both simulator and optimizer without the need to construct a software coupling between an optimizer and the simulation tool. This will abstract both the WEF nexus simulation and the optimization problem into easily managed modules. The Q-Nexus Model is used for WEF nexus simulation and the Frontline Excel Solver [

The WEF intersectoral allocation coefficients (

(direct and indirect) are

W1 | W2 | W3 | W4 | W5 | E1 | E2 | E3 | E4 | E5 | E6 | F1 | F2 | F3 | F4 | F5 | End Use | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

W1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 16.66 | 0.00 | 0.00 | 0.00 | 0.00 | 85.13 | 60.45 | 79.46 | 114.15 | 257.57 | 64.0 |

W2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 26.79 | 23.50 | 32.47 | 55.76 | 79.27 | 320.0 |

W3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 30.0 |

W4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.18 | 0.24 | 0.30 | 0.54 | 0.0 |

W5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.34 | 1.01 | 1.34 | 1.68 | 1.52 | 7.0 |

E1 | 2.87 | 4.39 | 0.03 | 0.21 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 12.13 | 4.54 | 6.95 | 10.77 | 20.42 | 1895.7 |

E2 | 104.68 | 130.74 | 65.37 | 0.06 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.92 | 1.92 | 1.92 | 3.92 | 13.81 | 3095.9 |

E3 | 1.35 | 1.43 | 1.55 | 0.00 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | 0.88 | 0.04 | 99.7 |

E4 | 0.39 | 0.47 | 0.46 | 0.00 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 | 0.88 | 0.04 | 40.5 |

E5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.35 | 5.1 |

E6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 26.0 |

F1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 | 144.0 |

F2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 352.0 |

F3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.00 | 854.0 |

F4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 508.0 |

F5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 60.87 | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 | 3449.0 |

W1 | W2 | W3 | W4 | W5 | E1 | E2 | E3 | E4 | E5 | E6 | F1 | F2 | F3 | F4 | F5 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

W1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.52 | 0.52 | 0.59 | 0.54 |

W2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.34 | 0.34 | 0.34 | 0.29 | 0.21 |

W3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

W4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

W5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.13 | 0.13 | 0.11 | 0.25 |

E1 | 0.05 | 0.06 | 0.00 | 0.76 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.70 | 0.78 | 0.65 | 0.58 |

E2 | 0.93 | 0.92 | 0.97 | 0.23 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.30 | 0.22 | 0.24 | 0.42 |

E3 | 0.02 | 0.02 | 0.02 | 0.01 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |

E4 | 0.01 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |

E5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

E6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

The estimated parameters of the cost of any projected additional water and energy resources

A scenario of increasing the food products by 20% is considered. Based on the Q-Nexus Model simulator, and by assuming that the intersectoral intensities and allocation coefficients are unchanged, the total (direct and indirect) additional intersectoral quantities of water and energy are

By applying the proposed S-O framework, the best water and energy allocation coefficients that minimize the total provision cost of the additional water and energy resources will be calculated. The objective function (Equation (21)) and constraints (Equations (22)-(28)) will be considered. The maximum envisaged capacities of the additional water and energy resources inflows

W1 | W2 | W3 | W4 | W5 | |
---|---|---|---|---|---|

^{3}) | 2.1 | 0.15 | 0.58 | 0.5 | 0.25 |

^{3}) | 5.4 | 0.45 | 1 | 0.81 | 0.85 |

^{3}) | 10 | 5 | 1 | 2 | 2 |

^{3}) | 100 | 50 | 10 | 20 | 20 |

E1 | E2 | E3 | E4 | E5 | E6 | |
---|---|---|---|---|---|---|

1 | 820 | 1800 | 150 | 1700 | NA | |

2 | 1000 | 2200 | 200 | 2100 | NA | |

10 | 100 | 10 | 100 | 1 | NA | |

100 | 1000 | 100 | 1000 | 10 | NA |

NA: Not Applicable

Mm^{3} | ktoe | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

W1 | W2 | W3 | W4 | W5 | E1 | E2 | E3 | E4 | E5 | E6 |

120.00 | 70.00 | 20.00 | 20.00 | 20.00 | 12.00 | 100.00 | 10.00 | 0.50 | 10.00 | 0.00 |

W1 | W2 | W3 | W4 | W5 | E1 | E2 | E3 | E4 | E5 | E6 | F1 | F2 | F3 | F4 | F5 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

W1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.66 | 0.64 | 0.57 | 0.58 |

W2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.28 | 0.31 | 0.33 | 0.39 | 0.36 |

W3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

W4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

W5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.03 | 0.03 | 0.04 | 0.06 |

E1 | 0.01 | 0.04 | 0.00 | 0.76 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.70 | 0.78 | 0.67 | 0.59 |

E2 | 0.98 | 0.96 | 0.97 | 0.23 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.30 | 0.22 | 0.24 | 0.38 |

E3 | 0.00 | 0.00 | 0.02 | 0.00 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |

E4 | 0.01 | 0.01 | 0.01 | 0.00 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |

E5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 |

E6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

The cost of the additional water and energy resources of the optimized scenario is 259.09 million USD, which is 12% less than the cost calculated based on the allocation coefficients of the BAU scenario. The use of the proposed S-O framework allows policy maker to identify allocation coefficients from input parameters and to calculate direct and indirect intersectoral quantities by using the Q-Nexus Model to verify constraints and to minimize the objective cost function.

This study presents an effort to take advantage of the detailed evaluation capabilities of direct and indirect interactions of a WEF nexus simulation model within an optimization framework. The proposed approach shows that Q-Nexus Model can be used in a simulation-based analysis framework to allow for flexibility in choosing optimization tools, analyzing the impacts of model variables on WEF planning decisions, and considering a broad range of vital objective functions. Preliminary results from the proposed S-O framework show its ability to advance sustainable WEF sectors performance and resource use.

The proposed WEF nexus simulation and optimization framework will be used to guide policy making, where user could set any objective representing its own interest, given that WEF nexus simulator can provide the relevant outputs for objective function and constraints evaluation.

The Q-Nexus Model incorporates handling of multiple technological strategies that can also be considered in other management objectives. The extension of this work will be in the development and testing of relevant objective functions to represent the interest of WEF stakeholders, and will also include a comparison of multi-objective optimization approaches. These issues are still under development at our university.

Karnib, A. (2017) Water-Energy-Food Nexus: A Coupled Si- mulation and Optimization Framework. Journal of Geoscience and Environment Pro- tection, 5, 84-98. https://doi.org/10.4236/gep.2017.54008