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Systematic Design, Analysis and Optimization of Water-Energy Nexus
Salvador Garcia Muñoz, Carl Laird, Matthew Realff (Eds.) Proceedings of the 9WK International Conference on Foundations of Computer-Aided Process Design July 14th to 18th , 2019, Copper Mountain, Colorado, USA. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818597-1.50036-9
SYSTEMATIC DESIGN, ANALYSIS AND OPTIMIZATION OF WATER-ENERGY NEXUS S. D. Tsolas, M. N. Karim, and M. M. F. Hasan* Artie McFerrin Department of Chemical Engineering, Texas A&M University College Station, TX 77843-3122, USA Abstract Responsible use of water and energy resources is critical for environmental sustainability while satisfying the increasing water, energy and fuel demands for end-use consumption. The interdependence of water and energy must be considered and quantified for developing efficient water-energy nexus systems. We first present a systematic and scalable method for the design and optimization of water-energy nexus (WEN). The method is based on a graph-theoretic representation of a nexus and a WEN diagram that enables us to identify potential redundancies in a nexus. We can also design systems with (i) minimum generation of water and energy, for specified grid demands, or (ii) maximum yield of water and energy to the grid supplies for specified generation limits. Next, we present a superstructure optimization-based approach to solve large-scale complex nexus problems. The superstructure encapsulates all plausible connections and phenomena between nexus entities, input-to-output conversions (water-for-water, energy-for-energy), intensities (water-for-energy, energy-for-water), contamination/purification levels, and location allocation and reuse features. Both methods are demonstrated using case studies on waterenergy nexus systems focusing on power generation, seawater desalination, groundwater and surface water at regional and national scales. Keywords Water-Energy Nexus, Energy-Water Supply Chain, Energy Networks, Water Networks, Optimization Introduction The satisfaction of increasing energy and water demands while securing energy and water resources, has always been a challenge and a driving force for economic and societal growth. As population increases, the demands to satisfy their water and energy needs increase as well. Fossil fuels have finite reserves, and as the climate intensifies and the freshwater resources diminish, the availability of resources diminishes. On top of that, the popularity of non-conventional energy and water sources, like shale gas and desalination, gives rise to a high interdependency between water and energy networks in contemporary systems. As a result, increased demands and deficits in water resources highly impact the energy side and vice versa. This interdependence is typically regards as the water-energy nexus and poses an additional challenge in designing energy and water systems [Garcia and You (2016)].
* To whom all correspondence should be addressed
Plethora of works exist that deal with heat and mass integration problems in isolation. Linnhoff and Hindmarsh (1983) introduced the pinch design method for optimal heat source and sink matching in heat exchanger networks, while El-Halwagi and Manousiouthakis (1989) developed similar methods for mass integration. Papoulias and Grossmann (1983) developed a mathematical program to obtain heat exchanger networks with minimum cost. In recent time, designing energy networks with minimum water requirements and/or designing optimal water networks for energy applications have gained interest [Gao and You (2015), Yang et al., (2015)]. Gonzalez-bravo et al. (2016) addressed integrated design of energy and water systems for dual-purpose plants. Nie et al. (2018) developed a framework for land allocation in food-energy-water nexus. There is also a growing interest in integrated operation and expansion planning of deterministic and stochastic systems
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Systematic design, analysis and optimization of water-energy nexus
[Saif and Almansoori (2016)] and tools development [Mroue et al. (2018)]. In this work, we first present a network representationbased graph-theoretic approach for the analysis of waterenergy nexus while capturing the interdependence of energy and water [Tsolas et al., (2018)]. We then propose a simple, graphical method to identify and eliminate redundant subsystems in a nexus. By introducing a water-energy nexus (WEN) diagram, we can infer whether excess water and energy are generated due to system redundancy. Finally, we propose a WEN superstructure-based optimization formulation which encapsulates all different connections in a water-energy nexus, and includes the resources, extensive water reuse and location allocation features. A Graph-theoretic Approach for WEN Representation We define a WEN as a system of two interconnected water and energy networks with one or more common processing nodes. The nexus receives energy and water from resources, processes and exchanges them via the two networks and delivers them to final consumers or external grids. In the extreme case where there is no exchange of energy and water between the two networks, a nexus reduces to two independent water and energy networks. In a regional WEN, the energy and water resources correspond to the fossil fuel, solar and wind resources, as well as the surface, groundwater and seawater reserves of the specific ecosystem. The output corresponds to the various fuel, power, and different quality water demands of the region. The processing nodes can be characterized as sources or sinks, depending on their operation and net production of energy and water. Processing nodes that return output of greater quantity and/or quality than the input they received, act as sources. Processing nodes that return output of lower quantity and/or quality than the input act as sinks. In contrast to classic energy and water networks, a nexus has shared nodes, hence sources of a stream can also act as sources or sinks of another stream. For example, a shale gas processing facility, extracts the crude hydrocarbons and delivers upgraded gas. Therefore, the facility acts as an energy source in a regional water-energy nexus, but it also requires water in order to pump and upgrade the fuel, acting as a water sink. A water source, like a surface water treatment plant, or a desalination facility, uses energy in heat and power to deliver freshwater. A nexus is highly scalable and in a regional system, each processing node can be viewed as a lower level nexus. Similarly, the different equipment comprising the processing facility can be also characterized as lower level source or sink, depending on its role. Water-energy Nexus (WEN) Graph A water-energy nexus can be viewed as a bipartite directed graph, whose oppositely-directed arcs incident to the same vertex, correspond two different product flows. There are two types of vertices, energy sources and water sources. The graph is bipartite since, we do not allow two sources of the same product to connect with each other.
An illustrative example of a water-energy nexus graph is depicted on Fig. 1. The energy sources/water sinks (E1, E2, and E3) are depicted with red circles, and the water sources/energy sinks (W1, and W2) with blue circles. E1 provides 4 units of energy, while it receives 5 units of water from W1. E2 generates 6 units of energy, providing 5 units to W2 and 1 unit to W1. E3 provides 2 units of energy to W2 and 7 units to the energy grid. On the water side, W1 provides 5 units to E1, 4 units to E2, 3 units to E3, and 6 units to the water grid WG. In total, 19 units of energy are generated, while 12 units of water are used for that generation, and 24 units of water are generated, while requiring 12 units of water. The energy and water inputs to the energy and water sources, respectively from the resources, are not depicted.
Figure 1. An illustrative example of a waterenergy nexus graph [Tsolas et al., (2018)]. Different sources of energy have different water requirements, based on the generating technology and the resource utilized (similarly for water sources). This interdependence of water and energy is captured via the intensity factor ሺ߮ሻ of a source, which is defined as follows: ߮ ൌ ߮௪ ൌ
௪௧௦௨௧ ௬ௗ௨௧ ௬௦௨௧ ௪௧ௗ௨௧
(1) (2)
where, ߮ and ߮௪ correspond to the intensity factor for energy sources and water sources, respectively. In the illustrative example, the water intensity of E1 and E2 are 5/4 and 4/6, respectively. A source with higher intensity is more dependent from the other stream. It is worth noting that, even in a simple nexus example like this, there can be redundant generation of water and energy. This means that a part of the networks can be completely omitted (redundant subsystem), while the rest of the network (essential subsystem) will still provide the existing grid supplies. Keeping the intensity factor constant, we can split a source’s generation and discard part of it, since some nodes might partially take part in both redundant and essential subsystems. The question now is, how to identify and optimally split the two subsystems. Lastly, in cases of not extensive water reuse, we can safely assume that by minimizing the total generation, the resource withdrawal is minimized as well. Therefore we can omit the
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resource to source connection in this graphical part of nexus analysis. Water-energy Nexus (WEN) Diagram To systematically identify redundant subsystems a twodimensional water-energy nexus diagram is constructed. The x-axis corresponds to water production, and the y-axis corresponds to energy consumption. The diagram corresponding to the illustrative WEN graph is illustrated in Fig 3. The piecewise red line represents the composite curve for energy sources, while the piecewise blue line represents the water source composite curve. Each linear segment corresponds to each source of the nexus. Energy sources, contribute to the negative x-direction, while water sources to the positive y-direction. Similarly, energy sources contribute to the negative x-direction and water sources to the positive x-direction. For example, E1 which produces 4 units of energy and consumes 5 units of water and is placed as depicted on the diagram.
Figure 3. WEN diagram corresponding to illustrative water-energy nexus graph [Tsolas et al., (2018)]. The slope of each segment corresponds to the intensity factor of the corresponding source ሺ߮ ሻ. Therefore, the steeper the energy composite curve, the less dependent the energy sources are from water. Inversely, the slope of each water segment corresponds to the inverse of the intensity factor of the corresponding source ሺͳΤ߮௪ ሻ. The projection of the energy composite curve corresponds to the total energy generated, while the projection of the water curve to the total energy needed for water generation. Similarly, the projection of the water composite curve on the x-axis corresponds to the total water generated in the nexus, while the protection of the energy composite curve to the water needed for energy generation. Minimization of total generation In order to identify the existence of redundancies in a nexus, a graphical procedure is introduced utilizing the water-energy diagram. Assuming that all the connections
between the sources are equivalent, we can interchange the positions of the source segments. - Step 1: Arrange the linear segments of the energy composite curve in ascending order of their slopes - Step 2: Arrange the linear segments of the water composite curve in descending order of their slopes. - Step 3: Eliminate any overlapping section of the WEN diagram, which corresponds to redundant subsystems. The resulting diagram after following these steps is illustrated in Fig. 4. In the reconfigured nexus, W2 provides water to E1 and E2, instead of the water grid. Also, the W2 linear segment and part of W1 lie above of the linear segments of E1 and part of E2. This part of the nexus where overlapping occurs, corresponds to redundant part of the system. By discarding this part of the nexus, the total generation of energy is reduced by 39% (19 units to 11.6 units) and the total generation of water by 30% (24 units to 16.7). However, the original grid demands are still satisfied.
Figure 4. Reconfigured WEN diagram for identification of redundancies [Tsolas et al., (2018)]. Maximization of grid supplies In the case of minimizing the total generation, all redundant sources are discarded. Given that a redundant subsystem exists, part of the subsystem can be utilized to maximize the energy or water grid, in the expense of an increase in total generation compared to the minimized generation. However, the increased generation will be still less than the original generation of the partially-redundant system. For the maximization of the energy grid, the WEN diagram is rearranged according to steps 1-2. Then, the energy composite curve is shifted vertically to the positive direction, as depicted in Fig. 5. By doing so, the total energy and water generation along with the energy grid increase. The shift of the energy composite curve stops at the pinch point of maximum energy grid supply, where the two composite curves still intersect. The water grid can be similarly maximized, while keeping the energy grid constant.
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Importantly, the connectivity is assumed to be reconfigurable without any consequences. Extensive properties of water-energy nexus graph, diagram and optimization methods for restricted connectivity between sources and for water with different quality by the sourcessinks are analyzed in [Tsolas et al., (2018)].
water, and species balances on the different blocks of the superstructure, along with the distance definitions, the logical disjunctions governing the connectivity of the superstructure and the objective function.
Figure 6. WEN Superstructure illustrating all plausible connections between resources, sources and final consumers.
Figure 5. WEN diagram for energy grid maximization [Tsolas et al., (2018)]. Superstructure-based WEN optimization We presented a graph-theoretic approach as a screening tool to identify redundancies, with respect to the intensity factors of different generating technologies. Now, for given sets of resources with known availabilities and locations, consumers with known location and fuel, power and water demands, one seeks to select and allocate (existing and/or potential) intermediate energy and water sources with optimal technologies. The objective is to satisfy the consumer demands, while minimizing the withdrawal of resources, the total generation and/or the total network cost. To this end, a WEN superstructure (Fig. 6) is proposed, consisting of resources, sources/sinks and consumer blocks, which follow the previous definition of a nexus. Connectivity of sources of the same kind is allowed and also, the water needed for energy is captured both as withdrawal and consumption. Reclaim and reuse of water from the final consumers is also considered, captured by the returning water streams to the water sources. Finally, the water streams are characterized by concentration levels of specified contaminants. Consequently, each energy source has a given contamination ratio, and each water source has a removal ratio for every contaminant. The water resources have a specified concentration of contaminants, and the water consumers a contaminant concentration level tolerance to be satisfied. Model Formulation In order to achieve optimal nexus configuration, an MINLP model is formulated. The model includes continuous variables for the stream flows, generating capacities, distances and contaminant concentrations, along with binary variables, for the selection of sources and existence of streams. The model is comprised of energy,
Energy resource i: ݁ǡ ݁ܽݎ
ሺ͵ሻ
Water resource j: ݓǡ ܽݎݓ
ሺͶሻ
Energy source k: ߚ ڄ൭ ݁ǡ ݁ ᇲǡ ൱ ൌ ݁ݏ
ሺͷሻ
ᇲ
݁ݏ ൌ ݁ǡ ݁ǡ ݁ǡ ᇲᇲ
ᇱᇱ
߮௪௧ ݏ݁ ڄ ൌ ݓǡ
ሺሻ
ݓǡ ൌ ߮௦ ݏ݁ ڄ ݓǡᇲ ݓ௪௦௧ ᇲ
௦ǡூே ௪௦ ܥǡ ڄ ݓǡ ൌ ܥǡ ݓ ڄǡ
௦ ௦ ܥǡ ൌ ൫ͳ ܿݎǡ ൯
ሺሻ
௦ǡூே ܥ ڄǡ
ሺͺሻ ሺͻሻ ሺͳͲሻ
Water source l: ݓǡ ݓᇲǡ ݓǡ ݓǡ ൌ ݏݓ
ᇲ
ݏݓ ൌ ݓǡ ᇲ ݓǡᇲ ݓǡᇲᇲ ᇲ
ሺͳͳሻ
ᇲ
ᇲᇲ
߮௪ ݏݓ ڄ ൌ ݁ǡ
ሺͳʹሻ ሺͳ͵ሻ
௪௦ǡூே ௪ ܥǡ ݏݓ ڄ ൌ ܥǡ ݓ ڄǡ ܥ௪௦ ᇲ ǡ ݓ ڄ ᇲ ǡ
ᇲ ௪ǡை் ܥǡ
ݓ ڄǡ
ሺͳͶሻ
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௪௦ǡூே ௪௦ ܥǡ ൌ ሺͳ െ ݎݎǡ ሻ ܥ ڄǡ
ሺͳͷሻ
Energy consumer p: ݁ǡ ݁ܿ݀
(16)
Water consumer q: ௪ ௪௦ ܥǡ ڄ ݓǡ ൌ ܥǡ ݓ ڄǡ
ݓ௪௦௧
(17)
ൌ ൫ͳ െ
ߚ௦௧
െ ߚ ൯
ڄ ݓǡ
ݓǡᇲ ൌ ߚ ڄ ݓǡ ᇲ
(19)
ݓǡ ݀ܿݓ
௪ ܥǡ
(18)
The resulting WEN diagram was constructed for power generation sources and water sources (Fig. 7). There is overlapping between the intensive sources of Spain’s nexus, which correspond to open-loop nuclear power plant, and seawater desalination. In particular, 11,652 GWh of nuclear power (4%) and 2,691 Mm3 of desalinated water (7%) can be omitted from the network, while the grid demands for power and water are still satisfied. For average values of intensity factors, the redundant subsystem corresponds to 11,279 GWh (3.95%) and 1,906 Mm3 (5%) from total generation.
(20)
௪ǡ ܥǡ
(21)
Distance calculations: To obtain the optimal location of intermediate sources, the distances are calculated for these variables: di,k, dj,l, dk,l, dk,k’, dl,l’, dk,p, dl,q, dk,waste: ଶ ݀ǡ ൌ ሺݔ െ ݔ ሻଶ ሺݕ െ ݕ ሻଶ
(22230)
Objective function: ݖൌ ݖ ݁ݏ ݖ ݏݓ ݓ௪௦௧
൫ݖǡ ݁ǡ ݀ ڄǡ ൯ ൫ݖǡௗ ݓǡௗ ݀ ڄǡௗ ൯ ǡ
(31)
ǡௗ
Results In this section two case studies are presented to demonstrate the optimization of regional systems, with the graphical method for redundancy identification, and the superstructure optimization for a more comprehensive analysis which includes water reuse. Country-level Nexus: Spain The country of Spain offers an extended and diverse pool of energy and water sources, including open-loop cooled power plants, biofuels and desalination, due to its uneven climate. Fuel, power and water data, assorted by source were acquired for 2013 (International Energy Agency, AQUASTAT), along with literature intensity factors [Tsolas et al. (2018)]. The total fossil energy utilized was 8,907,520 TJ. From fossil energy along with renewables, 285,632 GWh of electricity was generated. By using maximum values of intensity factors (withdrawal) and a 45/55 ratio of open loop and closed loop cooling in power plants, it was calculated that 26,750 Mm3 of water was utilized for energy. Analytically, 7,878 Mm3 was utilized solely for fuel, while 18,878 Mm3 are withdrawn for fuel which was used for power generation. In total, 38,106 Mm3 of water was estimated to have bene withdrawn of which, 78% corresponds to surface water treatment, 18% to groundwater treatment, and the rest 4% to desalinated water. For the desalination plants the maximum capacity was used. It was estimated, that 25,335 GWh of power was required for water generation. More analytical data can be found at (Tsolas et al. [2018]).
Figure 7. Reconfigured WEN diagram for the country of Spain in 2013 [Tsolas et al., (2018)]. Regional Nexus: Jack County (Texas) For the WEN superstructure optimization, a Texas county was investigated in the year of 2015. The county has a population of 9,236, and a major city (Jacksboro) in the middle of the region. Plant-level data were acquired for power generation [U.S. Energy Information Administration]. The inputoutput conversion was available, along with the location of the plants. There is one natural gas and three wind parks operating in the region, with installed capacities of 1,280, 150, 120, and 110 MW respectively. The natural gas plant has an estimated intensity factor of 0.22 gal/KWh. The wind parks have no water requirement. In 2015, a measured of 11,455, 1,365, and 751, and 1,154 GWh of power were generated, requiring 1,512 MGal of water. There are no gas processing facilities in the county. It is assumed that, the fuel needed for power generation is obtained from other counties as a resource. The locations of the energy sources are fixed and are illustrated in Fig. 8, with red circles. Water generation data were available by source (surface, groundwater, reuse) and consumption sector (municipal, manufacturing, mining, steam electric, irrigation, livestock) [TWDB]. Since there are no plantlevel data, we assume that three major water facilities provide water to the county, specifically to two major consumers of (domestic, agricultural), along with the requirements for energy generation. The locations of the two water resources (surface and groundwater) and the two water consumers can be seen in Fig. 8, with blue triangles and blue squares respectively. The optimal locations of the
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three water facilities will be determined by the solution of the problem. The three water sources in 2015, were estimated to produce 1,662, 136 and 0.65 MGal respectively, with 0.0014, 0.0018 and 0.009 Kwh/gal requirement of power. Thus, 2,557 MWh of electricity was needed. In total, the consumer demands were 6,553 GWh of power (the city in the middle of the region), 319 MGal of residential water, and 250 MGal of irrigation water. The objective in this case study was to obtain the minimum generation from the sources, and the optimal connectivity and the locations of the water sources to satisfy the existing demands. The resulting nexus has decreased power and water generation, as the second water resource and the third water source were omitted from the nexus, and no reuse of water was necessary. The ratio of water recovery was also a variable to be determined. For the scenario of increased water demands (600 and 500 MGal), the resulting nexus is depicted in Figure 8. No groundwater (wr2) is utilized in the nexus, but all three water sources are chosen to operate. Source ws3 receives wastewater from the consumers, with a recovery ratio of 80%. Finally, all three sources provide water and receive energy from the natural gas power plant and are allocated close to each other.
Figure 8. Regional resulting Nexus for Jack County for increased water demands. Conclusions We presented a graphical, systematic method for the analysis of water-energy nexus, that led to the optimal grass-root and retrofit design of complex systems. We showed that a nexus can be viewed as special type of graph, and proposed a graphical method using a novel WEN diagram, to identify redundancies based on the intensity of energy and water sources. As a result, we are able to obtain the minimum nexus that satisfies existing supplies, or for given generation maximize the output to the grids. Then, a WEN superstructure was introduced to include the utilization of resources by the sources and expand the graphical procedure. Additional phenomena of a regional
WEN are also captured, like location allocation and reuse and treatment of wastewater. Therefore, a systematic set of tools has been demonstrated that can analyze existing regional systems and derive optimal networks, like the case studies that were presented. The superstructure formulation is highly scalable and can be easily extended for generalized multi-product supply-chain analysis (deterministic or stochastic) with multiple intensity and conversion factors, beyond energy, water and food. Future work should be directed towards solution strategies of large-scale as well as imposing economic objectives using the WEN superstructure. References El‐Halwagi, M. M., & Manousiouthakis, V. (1989). Synthesis of mass exchange networks. AIChE Journal, 35(8), 12331244. Gao, J., & You, F. (2015). Optimal design and operations of supply chain networks for water management in shale gas production: MILFP model and algorithms for the water‐ energy nexus. AIChE Journal, 61(4), 1184-1208. Garcia, D. J., & You, F. (2016). The water-energy-food nexus and process systems engineering: a new focus. Computers & Chemical Engineering, 91, 49-67. González-Bravo, R., Nápoles-Rivera, F., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2016). Multiobjective optimization of dual-purpose power plants and water distribution networks. ACS Sustainable Chemistry & Engineering, 4(12), 68526866. Linnhoff, B., & Hindmarsh, E. (1983). The pinch design method for heat exchanger networks. Chemical Engineering Science, 38(5), 745-763. Mroue, A. M., Mohtar, R. H., Pistikopoulos, E. N., Holtzapple, M. T. Energy Portfolio Assessment Tool (EPAT): Sustainable energy planning using the WEF nexus approach–Texas case. Science of The Total Environment 648, 1649-1664. Nie, Y., Avraamidou, S., Li, J., Xiao, X., & Pistikopoulos, E. N. (2018). Land use modeling and optimization based on foodenergy-water nexus: a case study on crop-livestock Papoulias, S. A., & Grossmann, I. E. (1983). A structural optimization approach in process synthesis—II: Heat recovery networks. Computers & Chemical Engineering, 7(6), 707-721. Saif, Y., & Almansoori, A. (2016). A capacity expansion planning model for integrated water desalination and power supply chain problem. Energy conversion and management, 122, 462-476. Yang, L., Grossmann, I. E., Mauter, M. S., & Dilmore, R. M. (2015). Investment optimization model for freshwater acquisition and wastewater handling in shale gas production. AIChE Journal, 61(6), 1770-1782. Tsolas, S., Karim, N. M., & Hasan, M. M. F. Optimization of Water-Energy Nexus: A Network Representation-based Graphical Approach. Applied Energy, 2018, 224, 230–250. International Energy Agency: https://www.iea.org, Last accessed on 12/18/2018. AQUASTAT: www.fao.org/nr/water/aquastat/data/query/, Last accessed on 12/18/2018. U.S. Energy Information Administration: https://www.eia.gov/electricity/data/browser/, Last accessed on 12/18/2018. Texas Water Development Board: http://www2.twdb.texas.gov/, Last accessed on 12/18/2018.
SYSTEMATIC DESIGN, ANALYSIS AND OPTIMIZATION OF WATER-ENERGY NEXUS S. D. Tsolas, M. N. Karim, and M. M. F. Hasan* Artie McFerrin Department of Chemical Engineering, Texas A&M University College Station, TX 77843-3122, USA Abstract Responsible use of water and energy resources is critical for environmental sustainability while satisfying the increasing water, energy and fuel demands for end-use consumption. The interdependence of water and energy must be considered and quantified for developing efficient water-energy nexus systems. We first present a systematic and scalable method for the design and optimization of water-energy nexus (WEN). The method is based on a graph-theoretic representation of a nexus and a WEN diagram that enables us to identify potential redundancies in a nexus. We can also design systems with (i) minimum generation of water and energy, for specified grid demands, or (ii) maximum yield of water and energy to the grid supplies for specified generation limits. Next, we present a superstructure optimization-based approach to solve large-scale complex nexus problems. The superstructure encapsulates all plausible connections and phenomena between nexus entities, input-to-output conversions (water-for-water, energy-for-energy), intensities (water-for-energy, energy-for-water), contamination/purification levels, and location allocation and reuse features. Both methods are demonstrated using case studies on waterenergy nexus systems focusing on power generation, seawater desalination, groundwater and surface water at regional and national scales. Keywords Water-Energy Nexus, Energy-Water Supply Chain, Energy Networks, Water Networks, Optimization Introduction The satisfaction of increasing energy and water demands while securing energy and water resources, has always been a challenge and a driving force for economic and societal growth. As population increases, the demands to satisfy their water and energy needs increase as well. Fossil fuels have finite reserves, and as the climate intensifies and the freshwater resources diminish, the availability of resources diminishes. On top of that, the popularity of non-conventional energy and water sources, like shale gas and desalination, gives rise to a high interdependency between water and energy networks in contemporary systems. As a result, increased demands and deficits in water resources highly impact the energy side and vice versa. This interdependence is typically regards as the water-energy nexus and poses an additional challenge in designing energy and water systems [Garcia and You (2016)].
* To whom all correspondence should be addressed
Plethora of works exist that deal with heat and mass integration problems in isolation. Linnhoff and Hindmarsh (1983) introduced the pinch design method for optimal heat source and sink matching in heat exchanger networks, while El-Halwagi and Manousiouthakis (1989) developed similar methods for mass integration. Papoulias and Grossmann (1983) developed a mathematical program to obtain heat exchanger networks with minimum cost. In recent time, designing energy networks with minimum water requirements and/or designing optimal water networks for energy applications have gained interest [Gao and You (2015), Yang et al., (2015)]. Gonzalez-bravo et al. (2016) addressed integrated design of energy and water systems for dual-purpose plants. Nie et al. (2018) developed a framework for land allocation in food-energy-water nexus. There is also a growing interest in integrated operation and expansion planning of deterministic and stochastic systems
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Systematic design, analysis and optimization of water-energy nexus
[Saif and Almansoori (2016)] and tools development [Mroue et al. (2018)]. In this work, we first present a network representationbased graph-theoretic approach for the analysis of waterenergy nexus while capturing the interdependence of energy and water [Tsolas et al., (2018)]. We then propose a simple, graphical method to identify and eliminate redundant subsystems in a nexus. By introducing a water-energy nexus (WEN) diagram, we can infer whether excess water and energy are generated due to system redundancy. Finally, we propose a WEN superstructure-based optimization formulation which encapsulates all different connections in a water-energy nexus, and includes the resources, extensive water reuse and location allocation features. A Graph-theoretic Approach for WEN Representation We define a WEN as a system of two interconnected water and energy networks with one or more common processing nodes. The nexus receives energy and water from resources, processes and exchanges them via the two networks and delivers them to final consumers or external grids. In the extreme case where there is no exchange of energy and water between the two networks, a nexus reduces to two independent water and energy networks. In a regional WEN, the energy and water resources correspond to the fossil fuel, solar and wind resources, as well as the surface, groundwater and seawater reserves of the specific ecosystem. The output corresponds to the various fuel, power, and different quality water demands of the region. The processing nodes can be characterized as sources or sinks, depending on their operation and net production of energy and water. Processing nodes that return output of greater quantity and/or quality than the input they received, act as sources. Processing nodes that return output of lower quantity and/or quality than the input act as sinks. In contrast to classic energy and water networks, a nexus has shared nodes, hence sources of a stream can also act as sources or sinks of another stream. For example, a shale gas processing facility, extracts the crude hydrocarbons and delivers upgraded gas. Therefore, the facility acts as an energy source in a regional water-energy nexus, but it also requires water in order to pump and upgrade the fuel, acting as a water sink. A water source, like a surface water treatment plant, or a desalination facility, uses energy in heat and power to deliver freshwater. A nexus is highly scalable and in a regional system, each processing node can be viewed as a lower level nexus. Similarly, the different equipment comprising the processing facility can be also characterized as lower level source or sink, depending on its role. Water-energy Nexus (WEN) Graph A water-energy nexus can be viewed as a bipartite directed graph, whose oppositely-directed arcs incident to the same vertex, correspond two different product flows. There are two types of vertices, energy sources and water sources. The graph is bipartite since, we do not allow two sources of the same product to connect with each other.
An illustrative example of a water-energy nexus graph is depicted on Fig. 1. The energy sources/water sinks (E1, E2, and E3) are depicted with red circles, and the water sources/energy sinks (W1, and W2) with blue circles. E1 provides 4 units of energy, while it receives 5 units of water from W1. E2 generates 6 units of energy, providing 5 units to W2 and 1 unit to W1. E3 provides 2 units of energy to W2 and 7 units to the energy grid. On the water side, W1 provides 5 units to E1, 4 units to E2, 3 units to E3, and 6 units to the water grid WG. In total, 19 units of energy are generated, while 12 units of water are used for that generation, and 24 units of water are generated, while requiring 12 units of water. The energy and water inputs to the energy and water sources, respectively from the resources, are not depicted.
Figure 1. An illustrative example of a waterenergy nexus graph [Tsolas et al., (2018)]. Different sources of energy have different water requirements, based on the generating technology and the resource utilized (similarly for water sources). This interdependence of water and energy is captured via the intensity factor ሺ߮ሻ of a source, which is defined as follows: ߮ ൌ ߮௪ ൌ
௪௧௦௨௧ ௬ௗ௨௧ ௬௦௨௧ ௪௧ௗ௨௧
(1) (2)
where, ߮ and ߮௪ correspond to the intensity factor for energy sources and water sources, respectively. In the illustrative example, the water intensity of E1 and E2 are 5/4 and 4/6, respectively. A source with higher intensity is more dependent from the other stream. It is worth noting that, even in a simple nexus example like this, there can be redundant generation of water and energy. This means that a part of the networks can be completely omitted (redundant subsystem), while the rest of the network (essential subsystem) will still provide the existing grid supplies. Keeping the intensity factor constant, we can split a source’s generation and discard part of it, since some nodes might partially take part in both redundant and essential subsystems. The question now is, how to identify and optimally split the two subsystems. Lastly, in cases of not extensive water reuse, we can safely assume that by minimizing the total generation, the resource withdrawal is minimized as well. Therefore we can omit the
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resource to source connection in this graphical part of nexus analysis. Water-energy Nexus (WEN) Diagram To systematically identify redundant subsystems a twodimensional water-energy nexus diagram is constructed. The x-axis corresponds to water production, and the y-axis corresponds to energy consumption. The diagram corresponding to the illustrative WEN graph is illustrated in Fig 3. The piecewise red line represents the composite curve for energy sources, while the piecewise blue line represents the water source composite curve. Each linear segment corresponds to each source of the nexus. Energy sources, contribute to the negative x-direction, while water sources to the positive y-direction. Similarly, energy sources contribute to the negative x-direction and water sources to the positive x-direction. For example, E1 which produces 4 units of energy and consumes 5 units of water and is placed as depicted on the diagram.
Figure 3. WEN diagram corresponding to illustrative water-energy nexus graph [Tsolas et al., (2018)]. The slope of each segment corresponds to the intensity factor of the corresponding source ሺ߮ ሻ. Therefore, the steeper the energy composite curve, the less dependent the energy sources are from water. Inversely, the slope of each water segment corresponds to the inverse of the intensity factor of the corresponding source ሺͳΤ߮௪ ሻ. The projection of the energy composite curve corresponds to the total energy generated, while the projection of the water curve to the total energy needed for water generation. Similarly, the projection of the water composite curve on the x-axis corresponds to the total water generated in the nexus, while the protection of the energy composite curve to the water needed for energy generation. Minimization of total generation In order to identify the existence of redundancies in a nexus, a graphical procedure is introduced utilizing the water-energy diagram. Assuming that all the connections
between the sources are equivalent, we can interchange the positions of the source segments. - Step 1: Arrange the linear segments of the energy composite curve in ascending order of their slopes - Step 2: Arrange the linear segments of the water composite curve in descending order of their slopes. - Step 3: Eliminate any overlapping section of the WEN diagram, which corresponds to redundant subsystems. The resulting diagram after following these steps is illustrated in Fig. 4. In the reconfigured nexus, W2 provides water to E1 and E2, instead of the water grid. Also, the W2 linear segment and part of W1 lie above of the linear segments of E1 and part of E2. This part of the nexus where overlapping occurs, corresponds to redundant part of the system. By discarding this part of the nexus, the total generation of energy is reduced by 39% (19 units to 11.6 units) and the total generation of water by 30% (24 units to 16.7). However, the original grid demands are still satisfied.
Figure 4. Reconfigured WEN diagram for identification of redundancies [Tsolas et al., (2018)]. Maximization of grid supplies In the case of minimizing the total generation, all redundant sources are discarded. Given that a redundant subsystem exists, part of the subsystem can be utilized to maximize the energy or water grid, in the expense of an increase in total generation compared to the minimized generation. However, the increased generation will be still less than the original generation of the partially-redundant system. For the maximization of the energy grid, the WEN diagram is rearranged according to steps 1-2. Then, the energy composite curve is shifted vertically to the positive direction, as depicted in Fig. 5. By doing so, the total energy and water generation along with the energy grid increase. The shift of the energy composite curve stops at the pinch point of maximum energy grid supply, where the two composite curves still intersect. The water grid can be similarly maximized, while keeping the energy grid constant.
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Importantly, the connectivity is assumed to be reconfigurable without any consequences. Extensive properties of water-energy nexus graph, diagram and optimization methods for restricted connectivity between sources and for water with different quality by the sourcessinks are analyzed in [Tsolas et al., (2018)].
water, and species balances on the different blocks of the superstructure, along with the distance definitions, the logical disjunctions governing the connectivity of the superstructure and the objective function.
Figure 6. WEN Superstructure illustrating all plausible connections between resources, sources and final consumers.
Figure 5. WEN diagram for energy grid maximization [Tsolas et al., (2018)]. Superstructure-based WEN optimization We presented a graph-theoretic approach as a screening tool to identify redundancies, with respect to the intensity factors of different generating technologies. Now, for given sets of resources with known availabilities and locations, consumers with known location and fuel, power and water demands, one seeks to select and allocate (existing and/or potential) intermediate energy and water sources with optimal technologies. The objective is to satisfy the consumer demands, while minimizing the withdrawal of resources, the total generation and/or the total network cost. To this end, a WEN superstructure (Fig. 6) is proposed, consisting of resources, sources/sinks and consumer blocks, which follow the previous definition of a nexus. Connectivity of sources of the same kind is allowed and also, the water needed for energy is captured both as withdrawal and consumption. Reclaim and reuse of water from the final consumers is also considered, captured by the returning water streams to the water sources. Finally, the water streams are characterized by concentration levels of specified contaminants. Consequently, each energy source has a given contamination ratio, and each water source has a removal ratio for every contaminant. The water resources have a specified concentration of contaminants, and the water consumers a contaminant concentration level tolerance to be satisfied. Model Formulation In order to achieve optimal nexus configuration, an MINLP model is formulated. The model includes continuous variables for the stream flows, generating capacities, distances and contaminant concentrations, along with binary variables, for the selection of sources and existence of streams. The model is comprised of energy,
Energy resource i: ݁ǡ ݁ܽݎ
ሺ͵ሻ
Water resource j: ݓǡ ܽݎݓ
ሺͶሻ
Energy source k: ߚ ڄ൭ ݁ǡ ݁ ᇲǡ ൱ ൌ ݁ݏ
ሺͷሻ
ᇲ
݁ݏ ൌ ݁ǡ ݁ǡ ݁ǡ ᇲᇲ
ᇱᇱ
߮௪௧ ݏ݁ ڄ ൌ ݓǡ
ሺሻ
ݓǡ ൌ ߮௦ ݏ݁ ڄ ݓǡᇲ ݓ௪௦௧ ᇲ
௦ǡூே ௪௦ ܥǡ ڄ ݓǡ ൌ ܥǡ ݓ ڄǡ
௦ ௦ ܥǡ ൌ ൫ͳ ܿݎǡ ൯
ሺሻ
௦ǡூே ܥ ڄǡ
ሺͺሻ ሺͻሻ ሺͳͲሻ
Water source l: ݓǡ ݓᇲǡ ݓǡ ݓǡ ൌ ݏݓ
ᇲ
ݏݓ ൌ ݓǡ ᇲ ݓǡᇲ ݓǡᇲᇲ ᇲ
ሺͳͳሻ
ᇲ
ᇲᇲ
߮௪ ݏݓ ڄ ൌ ݁ǡ
ሺͳʹሻ ሺͳ͵ሻ
௪௦ǡூே ௪ ܥǡ ݏݓ ڄ ൌ ܥǡ ݓ ڄǡ ܥ௪௦ ᇲ ǡ ݓ ڄ ᇲ ǡ
ᇲ ௪ǡை் ܥǡ
ݓ ڄǡ
ሺͳͶሻ
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௪௦ǡூே ௪௦ ܥǡ ൌ ሺͳ െ ݎݎǡ ሻ ܥ ڄǡ
ሺͳͷሻ
Energy consumer p: ݁ǡ ݁ܿ݀
(16)
Water consumer q: ௪ ௪௦ ܥǡ ڄ ݓǡ ൌ ܥǡ ݓ ڄǡ
ݓ௪௦௧
(17)
ൌ ൫ͳ െ
ߚ௦௧
െ ߚ ൯
ڄ ݓǡ
ݓǡᇲ ൌ ߚ ڄ ݓǡ ᇲ
(19)
ݓǡ ݀ܿݓ
௪ ܥǡ
(18)
The resulting WEN diagram was constructed for power generation sources and water sources (Fig. 7). There is overlapping between the intensive sources of Spain’s nexus, which correspond to open-loop nuclear power plant, and seawater desalination. In particular, 11,652 GWh of nuclear power (4%) and 2,691 Mm3 of desalinated water (7%) can be omitted from the network, while the grid demands for power and water are still satisfied. For average values of intensity factors, the redundant subsystem corresponds to 11,279 GWh (3.95%) and 1,906 Mm3 (5%) from total generation.
(20)
௪ǡ ܥǡ
(21)
Distance calculations: To obtain the optimal location of intermediate sources, the distances are calculated for these variables: di,k, dj,l, dk,l, dk,k’, dl,l’, dk,p, dl,q, dk,waste: ଶ ݀ǡ ൌ ሺݔ െ ݔ ሻଶ ሺݕ െ ݕ ሻଶ
(22230)
Objective function: ݖൌ ݖ ݁ݏ ݖ ݏݓ ݓ௪௦௧
൫ݖǡ ݁ǡ ݀ ڄǡ ൯ ൫ݖǡௗ ݓǡௗ ݀ ڄǡௗ ൯ ǡ
(31)
ǡௗ
Results In this section two case studies are presented to demonstrate the optimization of regional systems, with the graphical method for redundancy identification, and the superstructure optimization for a more comprehensive analysis which includes water reuse. Country-level Nexus: Spain The country of Spain offers an extended and diverse pool of energy and water sources, including open-loop cooled power plants, biofuels and desalination, due to its uneven climate. Fuel, power and water data, assorted by source were acquired for 2013 (International Energy Agency, AQUASTAT), along with literature intensity factors [Tsolas et al. (2018)]. The total fossil energy utilized was 8,907,520 TJ. From fossil energy along with renewables, 285,632 GWh of electricity was generated. By using maximum values of intensity factors (withdrawal) and a 45/55 ratio of open loop and closed loop cooling in power plants, it was calculated that 26,750 Mm3 of water was utilized for energy. Analytically, 7,878 Mm3 was utilized solely for fuel, while 18,878 Mm3 are withdrawn for fuel which was used for power generation. In total, 38,106 Mm3 of water was estimated to have bene withdrawn of which, 78% corresponds to surface water treatment, 18% to groundwater treatment, and the rest 4% to desalinated water. For the desalination plants the maximum capacity was used. It was estimated, that 25,335 GWh of power was required for water generation. More analytical data can be found at (Tsolas et al. [2018]).
Figure 7. Reconfigured WEN diagram for the country of Spain in 2013 [Tsolas et al., (2018)]. Regional Nexus: Jack County (Texas) For the WEN superstructure optimization, a Texas county was investigated in the year of 2015. The county has a population of 9,236, and a major city (Jacksboro) in the middle of the region. Plant-level data were acquired for power generation [U.S. Energy Information Administration]. The inputoutput conversion was available, along with the location of the plants. There is one natural gas and three wind parks operating in the region, with installed capacities of 1,280, 150, 120, and 110 MW respectively. The natural gas plant has an estimated intensity factor of 0.22 gal/KWh. The wind parks have no water requirement. In 2015, a measured of 11,455, 1,365, and 751, and 1,154 GWh of power were generated, requiring 1,512 MGal of water. There are no gas processing facilities in the county. It is assumed that, the fuel needed for power generation is obtained from other counties as a resource. The locations of the energy sources are fixed and are illustrated in Fig. 8, with red circles. Water generation data were available by source (surface, groundwater, reuse) and consumption sector (municipal, manufacturing, mining, steam electric, irrigation, livestock) [TWDB]. Since there are no plantlevel data, we assume that three major water facilities provide water to the county, specifically to two major consumers of (domestic, agricultural), along with the requirements for energy generation. The locations of the two water resources (surface and groundwater) and the two water consumers can be seen in Fig. 8, with blue triangles and blue squares respectively. The optimal locations of the
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three water facilities will be determined by the solution of the problem. The three water sources in 2015, were estimated to produce 1,662, 136 and 0.65 MGal respectively, with 0.0014, 0.0018 and 0.009 Kwh/gal requirement of power. Thus, 2,557 MWh of electricity was needed. In total, the consumer demands were 6,553 GWh of power (the city in the middle of the region), 319 MGal of residential water, and 250 MGal of irrigation water. The objective in this case study was to obtain the minimum generation from the sources, and the optimal connectivity and the locations of the water sources to satisfy the existing demands. The resulting nexus has decreased power and water generation, as the second water resource and the third water source were omitted from the nexus, and no reuse of water was necessary. The ratio of water recovery was also a variable to be determined. For the scenario of increased water demands (600 and 500 MGal), the resulting nexus is depicted in Figure 8. No groundwater (wr2) is utilized in the nexus, but all three water sources are chosen to operate. Source ws3 receives wastewater from the consumers, with a recovery ratio of 80%. Finally, all three sources provide water and receive energy from the natural gas power plant and are allocated close to each other.
Figure 8. Regional resulting Nexus for Jack County for increased water demands. Conclusions We presented a graphical, systematic method for the analysis of water-energy nexus, that led to the optimal grass-root and retrofit design of complex systems. We showed that a nexus can be viewed as special type of graph, and proposed a graphical method using a novel WEN diagram, to identify redundancies based on the intensity of energy and water sources. As a result, we are able to obtain the minimum nexus that satisfies existing supplies, or for given generation maximize the output to the grids. Then, a WEN superstructure was introduced to include the utilization of resources by the sources and expand the graphical procedure. Additional phenomena of a regional
WEN are also captured, like location allocation and reuse and treatment of wastewater. Therefore, a systematic set of tools has been demonstrated that can analyze existing regional systems and derive optimal networks, like the case studies that were presented. The superstructure formulation is highly scalable and can be easily extended for generalized multi-product supply-chain analysis (deterministic or stochastic) with multiple intensity and conversion factors, beyond energy, water and food. Future work should be directed towards solution strategies of large-scale as well as imposing economic objectives using the WEN superstructure. References El‐Halwagi, M. M., & Manousiouthakis, V. (1989). Synthesis of mass exchange networks. AIChE Journal, 35(8), 12331244. Gao, J., & You, F. (2015). Optimal design and operations of supply chain networks for water management in shale gas production: MILFP model and algorithms for the water‐ energy nexus. AIChE Journal, 61(4), 1184-1208. Garcia, D. J., & You, F. (2016). The water-energy-food nexus and process systems engineering: a new focus. Computers & Chemical Engineering, 91, 49-67. González-Bravo, R., Nápoles-Rivera, F., Ponce-Ortega, J. M., & El-Halwagi, M. M. (2016). Multiobjective optimization of dual-purpose power plants and water distribution networks. ACS Sustainable Chemistry & Engineering, 4(12), 68526866. Linnhoff, B., & Hindmarsh, E. (1983). The pinch design method for heat exchanger networks. Chemical Engineering Science, 38(5), 745-763. Mroue, A. M., Mohtar, R. H., Pistikopoulos, E. N., Holtzapple, M. T. Energy Portfolio Assessment Tool (EPAT): Sustainable energy planning using the WEF nexus approach–Texas case. Science of The Total Environment 648, 1649-1664. Nie, Y., Avraamidou, S., Li, J., Xiao, X., & Pistikopoulos, E. N. (2018). Land use modeling and optimization based on foodenergy-water nexus: a case study on crop-livestock Papoulias, S. A., & Grossmann, I. E. (1983). A structural optimization approach in process synthesis—II: Heat recovery networks. Computers & Chemical Engineering, 7(6), 707-721. Saif, Y., & Almansoori, A. (2016). A capacity expansion planning model for integrated water desalination and power supply chain problem. Energy conversion and management, 122, 462-476. Yang, L., Grossmann, I. E., Mauter, M. S., & Dilmore, R. M. (2015). Investment optimization model for freshwater acquisition and wastewater handling in shale gas production. AIChE Journal, 61(6), 1770-1782. Tsolas, S., Karim, N. M., & Hasan, M. M. F. Optimization of Water-Energy Nexus: A Network Representation-based Graphical Approach. Applied Energy, 2018, 224, 230–250. International Energy Agency: https://www.iea.org, Last accessed on 12/18/2018. AQUASTAT: www.fao.org/nr/water/aquastat/data/query/, Last accessed on 12/18/2018. U.S. Energy Information Administration: https://www.eia.gov/electricity/data/browser/, Last accessed on 12/18/2018. Texas Water Development Board: http://www2.twdb.texas.gov/, Last accessed on 12/18/2018.