Navigating the Water–Energy Nexus: A Mathematical Approach
Abstract
:1. Introduction
2. The Water–Energy Nexus
3. Mathematical Modelling and Simulation
3.1. Mathematical Modeling
3.2. Simulation
4. Application of Mathematical Modelling to the Water–Energy Nexus
4.1. Water Footprint of Renewable Energy Technologies
4.1.1. Hydroelectric Power
4.1.2. Geothermal Energy
4.2. Energy Consumption in Advanced Water Treatment and Distribution
4.2.1. Advanced Oxidation Processes (AOPs)
4.2.2. Membrane Separation Processes
4.2.3. Water Distribution Systems
5. Process Simulation in the Water–Energy Nexus
5.1. Simulation of Hydroelectric Power Water Footprint
5.2. Simulation of Geothermal Energy Water Footprint
5.3. Simulation of Energy Consumption in Advanced Oxidation Processes
5.4. Simulation of Energy Consumption in Membrane Separation Processes
5.5. Simulation of the Water Distribution Energy Demands
6. Importance of Mathematical Modelling and Simulation-BasedApproach of the Water–Energy Nexus
6.1. Securing the Future of Hydropower
6.2. Optimization of Water Consumption and Reducing Damage of Equipment in Geothermal Cooling Systems
6.3. Achieving the Desired Overall Efficiency at Minimal Energy Consumption in Advanced Oxidation Processes
6.4. Minimizing Energy Consumption in Membrane Separation Processes
6.5. Paving the Way for Smart Water Distribution Networks
7. Challenges and Prospects
8. Conclusions and Future Research Directions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Energy Generation Technology | Description | Water Footprint (m3/GJ) | References |
---|---|---|---|
Hydroelectric power | Water lost evaporation from the large reservoirs creating behind the dam. | 16.5 | [11] |
Nuclear energy | Significant amounts of water are lost in the cooling reactors through evaporation. | 0.42–0.76 | [12] |
Geothermal energy | Tower and once-through Cooling systems and extraction of geothermal fluids (steam) | 0.005 | [13] |
Solar energy | Minimal, mostly through cleaning the photovoltaic panels and cooling, especially in concentrated solar power (CSP) mirrors. | 0.021 | [14] |
Wind energy | Negligible water consumption during operation, usually for some cleaning operations. However, much water is consumed during manufacturing and construction. | 0.001 | [15] |
Coal energy | Cooling systems and fuel preparation (washing) | 0.15–0.58 | [16] |
Biofuels | Irrigation in growing raw material like corn and sugarcane and in the conversion process. | 121.51 | [17] |
Natural gas | Cooling systems and gas extraction processes. | 2.9474 | [14] |
Water Treatment Technology | Description | Energy Consumption (kWh/H2O Treated) | References |
---|---|---|---|
Coagulation | Mechanical mixing to distribute coagulants evenly. | 0.008–0.022 | [21] |
Sedimentation | Energy is negligible with most of the sedimentation basins operating solely under gravity. | 0.0005–0.001 | [18] |
Dissolved air flotation (DAF) systems | Compressors and pumps are utilized to dissolve air under pressure, creating bubbles that lift particles. | 9.5–35.5 | [21] |
Filtration | Pump water through filters and backwashing particularly in sand filters | 0.4–0.45 | [22] |
Adsorption | Pumping water through adsorption media and regeneration. | 0.225 | [23] |
Advanced oxidation processes | Energy intensive as they utilize UV lamps, Xenon and mercury lamps. | 6.4–41.1 | [24] |
Membrane separation | High pressure pumps needed to push water through membranes | 2.5 (Desalination) | [25] |
Category | Classification | Description | References |
---|---|---|---|
Formulation | Fundamental models | Formulated based on fundamental chemical and physical principles such as mass and energy balances, thermodynamics, chemical reaction kinetics. | [28] |
Empirical models | Formulated based on data and observations of the system’s behavior mainly through least squares or factorial experimental designs. | ||
Linearity | Linear models | Models in which the dependent variable and/or their derivatives appear only to the first power. | [29] |
Non-linear models | Models where the dependent variable and/or their derivatives are raised to powers greater than one. | ||
Temporality | Steady state | Also known as time invariant or static refers to models in which the dependent variable remains constant with respect to time. | [30] |
Unsteady state | Also called transient or dynamic represent situations where the dependent variable changes with time. | ||
Spatial variation | Lumped parameter model | The spatial variations are ignored, and the dependent variable is considered homogeneous throughout the system. | [31] |
Distributed parameter model | Considers the detailed variations in the dependent variable from point to point throughout the system. | ||
Nature of variables | Continuous models | Deals with variables that can take on any value within a specific interval. | [32] |
Discrete models | Dealing with variables that take only distinct separate values in the interval. |
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Kiteto, M.K.; Mecha, C.A. Navigating the Water–Energy Nexus: A Mathematical Approach. Foundations 2024, 4, 713-737. https://doi.org/10.3390/foundations4040045
Kiteto MK, Mecha CA. Navigating the Water–Energy Nexus: A Mathematical Approach. Foundations. 2024; 4(4):713-737. https://doi.org/10.3390/foundations4040045
Chicago/Turabian StyleKiteto, Moses Kayanda, and Cleophas Achisa Mecha. 2024. "Navigating the Water–Energy Nexus: A Mathematical Approach" Foundations 4, no. 4: 713-737. https://doi.org/10.3390/foundations4040045
APA StyleKiteto, M. K., & Mecha, C. A. (2024). Navigating the Water–Energy Nexus: A Mathematical Approach. Foundations, 4(4), 713-737. https://doi.org/10.3390/foundations4040045