PRES22_0231.docx DOI: 10.3303/CET2294187 Paper Received: 09 May 2022; Revised: 04 June 2022; Accepted: 10 June 2022 Please cite this article as: Isafiade A.J., Short M., 2022, Multi-Objective Optimisation of Integrated Renewable Energy Feedstock Supply Chain and Work-Heat Exchanger Network Synthesis Considering Economics and Environmental Impact, Chemical Engineering Transactions, 94, 1123-1128 DOI:10.3303/CET2294187 CHEMICAL ENGINEERING TRANSACTIONS VOL. 94, 2022 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš, Sandro Nižetić Copyright © 2022, AIDIC Servizi S.r.l. ISBN 978-88-95608-93-8; ISSN 2283-9216 Multi-Objective Optimisation of Integrated Renewable Energy Feedstock Supply Chain and Work-Heat Exchanger Network Synthesis Considering Economics and Environmental Impact Adeniyi J. Isafiadea,*, Michael Shortb aDepartment of Chemical Engineerig, University of Cape Town, Rondebosch, 7701, South Africa bDepartmnet of Chemical and Process Engineering, University of Surrey, Guildford, GU2 7XH niyi.isafiade@uct.ac.za This work presents a new method for integrating various renewable energy feedstock sources with the utility systems of combined heat and power generation hubs and heat exchanger networks (HENs). The combined heat and power hub of the integrated network involves two turbines fed with high pressure steam. The steam can be generated from fuel sources such as wood, corn stover, and glycerine. The power system is required to produce a fixed amount of shaft power while optimally satisfying the hot utility demand of the HEN of a process plant through the high-pressure steam and intermediate pressure steams exiting the turbines. The superstructure of the integrated system comprises three layers and is synthesised using the utility hub approach. The first layer of the superstructure, which comprises the feedstock supply chain network, is modelled as a mixed integer linear program. The second layer of the superstructure, which comprises the combined heat and power hub wherein are the steam system and turbines for the power plant, is modelled using linear program to represent the material and energy balances of the turbine system. The third layer, which comprises a HEN, is modelled using the simplified stagewise superstructure (SWS) synthesis approach. The objective function of the integrated model comprises operating costs, capital costs, and environmental impact. The newly developed method is applied to a case study using the weighted method of multi-objective optimisation and the results obtained involves the selection of corn stover and glycerine for the generation of heat and power. Also, only high-pressure steam and medium pressure steam were selected for use as hot utilities in the integrated HEN of the system. 1. Introduction Increasing concerns about climate change has necessitated the design of process plants that are not only economically optimal but environmentally friendly as well. Heat exchanger network synthesis (HENS) has been used over the years by process industries to achieve economically optimal heat integrated systems. However, most of the methods in the literature have failed to consider a holistic view of the benefits inherent in integrating and simultaneously optimising the heat demand of process plants, turbine power systems and renewable energy supply chain. Although the work of Isafiade et al. (2017), which adopted the stage-wise superstructure (SWS) model of Yee and Grossmann (1990) for the synthesis of multiperiod HENs, involves multiple utilities generated from multiple renewable and non-renewable sources, the method did not consider the economics or environmental impact associated with the transportation of the renewable energy feedstocks from their supply locations to the plant site. In terms of combined heat and power generation, a series of studies has been done which incorporates thermodynamic cycles with heat exchanger network synthesis in what can be described as Work and Heat Exchanger Network Synthesis (WHENS). According to Fu et al. (2018), WHENS entails Work Integration and Heat Integration where the requirements for heating and cooling which results from compression and expansion in a thermodynamic cycle can be integrated with the synthesis of HENs. The study of Sun et al. (2019), which incorporated absorption refrigeration cycle with HENS, was aimed at simultaneously optimising the operating parameters of the absorption refrigeration system and the HEN. The HEN component of the integrated system was modelled using the SWS and the objective function comprises capital costs for heat 1123 exchangers in the HEN, capital costs for the generator, evaporator, absorber, and condenser in the refrigeration cycle. The operating cost component of the objective function of the model comprises the utility costs. Another study that integrates thermodynamic cycles with HENS is that of Elsido et al. (2021) where the HENS component of the system involves multiperiod operating profile and thermal storages. Martinelli et al. (2022) also integrated the synthesis of HENs with refrigeration cycles. One of the novelties of the work involves the ability of the developed model to simultaneously optimise the refrigeration cycle structure, including the pressures and temperatures, with the HEN component of the integrated system. It is worth stating that for the papers reviewed, the benefits associated with harnessing process heat from one component of the integrated system to satisfy the heat demand of some other component has been established even for problems involving multiple utilities as is the case in the work of Elsido et al. (2021). However, to have a more robust and sustainable integrated resource and energy system, the inclusion of a supply chain involving multiple energy feedstocks from which renewable energy can be generated, while considering the associated environmental impact of the energy sources must be considered and solved simultaneously. One of the few studies that have integrated renewable energy supply chain with the heat demand of process plants through HENS is that of Cowen et al. (2019). In the study, three co-located process plants whose heat demand is multi- period was considered. However, the study did not include power generation and the only criteria for making a choice among the renewable energy sources is economics. This work involves the development of an integrated energy network that comprises a supply chain of renewable energy sources, a steam and power generation system and a HEN. It should be known that the steam and power generation component of the integrated system only involves the boiler and two turbo generators. 2. Problem statement The problem solved in this paper can be stated as follows. Given a set of biomass and waste-based feedstocks M, from which energy can be generated, given a set of transport modes R (including unit transport costs) by which the feedstocks, or energy generated from the feedstocks, can be transported from the feedstock locations to a combined heat and power generation plant located at an energy hub. Seasonal availability and unit costs for each of the energy feedstocks, is identified by set T, while the distances, including tortuosity factors, between each of the feedstock location and the energy hub is identified by the set D. The process plant, whose heat demand is to be integrated with the combined heat and power generation system, has a set of hot H and cold C process streams with heat capacity flowrates FCP and heat transfer coefficients h. Other parameters given are the heat exchanger installation and area costs and unit costs for the utilities. The goal is to design a renewable energy supply chain network (SCN) that is integrated with a combined heat and power generation system and the heat exchanger network system of a process plant. 3. Methodology The superstructure that describes the integrated network is shown in Figure 1. The top layer of the superstructure comprises the SCN of renewable energy feedstocks. This layer is connected to the heat and power hub, which is the middle layer, through various feedstock/energy transport modes. The third layer of the superstructure comprises the process plant where hot and cold utilities are required. The mathematical model for the renewable energy supply chain component of the integrated model is represented as a mixed integer linear program (MILP). The MILP model of this paper differs from that of Cowen et al. (2019) in that the intermediate demand node of the integrated superstructure constitutes the heat and power generation system hub. This is unlike the model of Cowen et al. (2019) where the demand nodes of their superstructure comprise co-located process plants. However, some of the data used for the SCN of this paper were adapted from Cowen et al. (2019). The mathematical model, including data, for the heat and power generation hub of the integrated superstructure is taken from the boiler/turbo-generator model of Edgar et al. (2001). The model comprises a boiler, where high pressure steam (4,378 kPa(g), 382 °C) is generated, and two turbogenerators with turbine 1 being a double extraction turbine while turbine 2 is single extraction. The two turbines have intermediate steams with pressures 1,344 kPa(g) and 427.5 kPa(g) with 54 °C of superheat. According to Edgar et al. (2001), electric power may be purchased from another producer with a base of 12,000 kW. This may be necessary to meet the electric power demand which is 24,550 kW. However, if the additional electric power needed to meet the system demand is less than the purchased 12,000 kW, then the unused power will attract penalty charges. The characteristics of the turbines, details of steam levels, and demand on the system, can be found in Edgar et al. (2001). The model of Edgar et al. (2001) was modified in this paper by the inclusion of additional high-pressure steam (HPS) stream split that links the power hub to the HEN hub. For the HEN model of this paper, the SWS model of Yee and Grossmann (1990) was used. The three models were systematically integrated to obtain a 1124 superstructure that contains various options of satisfying the stipulated demand for power (24,550 kW) and utilities by the process streams in the HEN. The objective function of the integrated model, which is multi-objective, comprises an economic component and an environmental component. The economic aspect involves annual operating and annualised capital costs of the SCN, annual cost of purchased power and penalty associated with unused purchased power, and annual operating and annualised capital cost of the HEN. The environmental component comprises minimisation of Carbon in the flue gas emissions generated from each of the available feedstocks. Min 𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑇𝑇𝐴𝐴 �𝑇𝑇𝐴𝐴 �� � 𝑦𝑦𝑖𝑖,𝑗𝑗,𝑘𝑘 + 𝑇𝑇𝑇𝑇 �� � 𝑇𝑇𝐴𝐴𝐴𝐴 𝑘𝑘∈𝐾𝐾𝑗𝑗∈𝐶𝐶𝑖𝑖∈𝐻𝐻𝑘𝑘∈𝐾𝐾𝑗𝑗∈𝐶𝐶𝑖𝑖∈𝐻𝐻 � + ��� � 𝑇𝑇𝑗𝑗 ∙ 𝑞𝑞𝑖𝑖,𝑗𝑗,𝑘𝑘 𝑘𝑘∈𝐾𝐾𝑗𝑗∈𝐶𝐶𝑖𝑖∈𝐻𝐻 � + � � ��𝑆𝑆𝑇𝑇𝑆𝑆𝑇𝑇𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚,𝑟𝑟,𝑡𝑡 𝑡𝑡∈𝑇𝑇𝑟𝑟∈𝑅𝑅𝑚𝑚∈𝑀𝑀 � +{(0.0239 ∙ 𝑆𝑆ℎ𝑜𝑜𝑜𝑜𝑟𝑟𝑜𝑜 ∙ 𝑃𝑃𝑃𝑃) + (0.00983 ∙ 𝑆𝑆ℎ𝑜𝑜𝑜𝑜𝑟𝑟𝑜𝑜 ∙ 𝐸𝐸𝑃𝑃)} (1) In Eq(1), AF is annualization factor, CF ($/m) is fixed charge for heat exchanger installation, yi,j,k is the binary variable that indicates whether a heat exchanger is paired between hot stream i and cold stream j in stage k of the stage-wise superstructure, AC ($/m) is the cost per unit of heat exchanger area, A (m2) is the size of a heat exchanger, AE is heat exchanger area cost exponent, Cj is the unit cost of cold utility j. The unit cost of hot utility is not included in Eq(1) because the hot utilities are determined by the quantity of energy feedstock selected in the solution network. In Eq(1) qi,j,k,t is the quantity of heat exchanged between hot stream i and cold stream j in stage k of the SWS, SCNCostm,r,t is the annual cost of the SCN, 0.0239 $/(kW∙h) is the unit cost of purchased power PP, 0.00983 $/(kW∙h) is the unit cost of the penalty for excess power EP. The two costs, i.e., PP and EP, were adapted from Edgar et al. (2001). Nhours in Eq(1) is the number of operating hours in a year (8,160 h). min 𝐸𝐸𝐸𝐸 = ��� 𝑥𝑥𝑚𝑚,𝑟𝑟,𝑡𝑡 𝜂𝜂 ∙ 𝐿𝐿𝐿𝐿𝐿𝐿𝑚𝑚� � 𝑡𝑡 ∙ 𝑇𝑇𝐶𝐶𝑇𝑇𝑚𝑚 ∙ 3.67 ∙ 𝑟𝑟 𝑆𝑆ℎ𝑜𝑜𝑜𝑜𝑟𝑟𝑜𝑜 (2) Eq(2) is adapted from Shenoy (1995). In the equation, EI represent the mass flow of the pollutant (kg/y), 𝑥𝑥𝑚𝑚,𝑟𝑟,𝑡𝑡 is the quantity of energy (in kW) transported from supply m through transport mode r, in season t to the heat and power generation hub. 𝜂𝜂 is the combustion efficiency of the feedstocks, LHVm is the lower heating value (in kWh/kg) of feedstock m, CUAm is the mass percentage of the pollutant in non-oxidized form. In this paper, the CUAm values used for corn stover, glycerine and wood are 47.4% (Kumar et al., 2008), 20.15% (Tamošiūnas et al., 2019) and 53.24% (Shi et al., 2016). The 3.67 was obtained by dividing the molecular mass of CO2 by the atomic mass of carbon. The weighted sum method of multi-objective optimisation as presented by Gxavu and Smaill (2012) is adopted in this paper. The multi-objective equation is shown in Eq(3). min 𝑍𝑍 = 𝑅𝑅𝑔𝑔 ∙ � 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇𝑚𝑚𝑖𝑖𝑚𝑚 � + �1 − 𝑅𝑅𝑔𝑔� ∙ � 𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝑚𝑚𝑖𝑖𝑚𝑚 � (3) In Eq(3), Z is the multi-objective variable, Rg is the weighting factor. Feedstock 1 Feedstock 3Feedstock 2 Supply chain network Energy hub HEN HPS MPS LPS Power generated Purchased power (Excess power) Boiler Turbine 1 Turbine 2 Figure 1: Superstructure of integrated network 1125 4. Case study The case study involves three kinds of feedstocks (corn stover, glycerine, wood), situated at different locations relative to the heat and power generation hub. The costs, capacity, and seasons of availability of the feedstocks are shown in Table 1 while the various modes of transport, including the cost parameters and tortuosity factors, are shown in Table 2. The HEN component of the case study comprises 2 hot process streams, 4 cold process streams and 1 cold utility. The hot utilities are HPS, medium pressure steam (MPS) and low-pressure steam (LPS). These three hot utility streams form the link between the heat and power generation hub and the HEN hub as illustrated in Figure 1. A split branch of the HPS will flow directly from the boiler to the HEN while the MPS and LPS are exit streams from the turbines that then flow to the HEN. Table 3 shows the parameters for the streams in the process plant. Table 1: Types of energy feedstocks, unit costs and available capacity Supply Feedstock Season 1 Season 2 Season 3 LHVm (kWh/kg) Cost ($/kg) Capacity (×106 kg) Cost ($/kg) Capacity (×106 kg) Cost ($/kg) Capacity (×106 kg) Supply 1 Corn stover 4.63 0.024 400 0.022 15 0.027 60 Supply 2 Glycerine 4.75 0.04 500 0.044 50 0.025 50 Supply 3 Wood 4.28 0.05 600 0.030 10 0.070 10 Table 2: Transport options and cost parameters Transport mode Transport specific parameter AF 𝑇𝑇𝑟𝑟𝐹𝐹𝐶𝐶 ($/(t∙km) 𝑇𝑇𝑟𝑟𝑉𝑉𝐶𝐶 ($/km) 𝑇𝑇𝑟𝑟𝐼𝐼𝐶𝐶 ($/(t∙km) 𝜏𝜏𝑟𝑟 𝑆𝑆𝑓𝑓𝑟𝑟 Truck 0.20 0.002 0.0900 5,000 1.27 2 Railway 0.25 0.005 0.0070 50,000 1.10 2 Pipeline 0.50 0.000 0.0001 1.5×105 1.27 1 Table 3: Plant stream data Hot streams Ti s (°C) Ti 𝑡𝑡 (°C) FCPi (kW/°C) Cold streams Tj s (°C) Ti 𝑡𝑡 (°C) FCPj (kW/°C) HU1 (HPS) 257 257 - C1 25 240 140 HU2 (MPS) 197 197 - C2 20 250 150 HU3 (LPS) 154 154 - C3 50 180 70 H1 155 85 150 C4 70 100 120 H2 230 40 285 CU1 5 10 - For AF in Table 2, the discount rates for truck, railway and pipeline are 15 %, 16.5 % and 24 %, and the capital are annualized over 10 y, 7 y, and 3 y. For the heat exchangers, discount rate is 30 % and capital is annualized over 10 y. In Table 3, it is assumed that all streams, including utilities, have the same heat transfer coefficient which is 0.5 (kW/(m2·°C)). For this paper, it was assumed that the HPS exiting the boiler and the intermediate streams exiting the two turbines (MPS and LPS), which are all superheated, were desuperheated to temperatures shown in Table 3 through heat losses in the pipes before being fed to the HEN. This is necessary since superheated steam is less effective at transferring heat. The integrated model, which is a mixed integer non-linear programming model (MINLP) was solved simultaneously using DICOPT solver in General Algebraic Modelling Systems (GAMS) environment. The model comprises 307 equations, 289 variables and 23 discrete variables. To implement the weighting approach of multi-objective optimisation shown in Eq(3), the integrated model was solved for three scenarios. The first is for a case where TAC is the only objective variable being minimised with EI unconstrained. This scenario resulted in a TACmin of $ 2.360 ×107 with an associated EI of 2.781 ×109 kg/y. The second scenario is for a case where EI is the only minimised objective in the integrated model. For this case, the solution obtained has an EImin of 1.373 ×109 kg/y with an associated TAC of $ 5.652 ×107. For the third scenario, the TACmin and EImin obtained in the first two solution scenarios were substituted into Eq(3) with an Rg value of 0.5. The solution obtained involves a TAC of $ 3.218 ×107 and an EI of 1.405 ×109 kg/y. A breakdown of the values for the key variables for each of the three solutions are shown in Table 4. In the table, HEs represents number of heat exchangers. Fig 2 shows the integrated network for the 3rd scenario which is the multi-objective case with equal weightings given to each of the two objectives. In the figure, only corn stover and glycerine are selected as feedstocks for 1126 energy generation with corn stover having to be transported by truck while glycerine (converted to biogas) will be transported through pipeline. Corn stover was selected only in seasons 2 and 3 while glycerine was selected in all seasons. At the heat and power generation hub, the total amount of HPS, i.e., HPSTOT, generated from the boiler is 49.21 kg/s. Of this amount, 15.6 kg/s is fed to turbine 1, 30.74 kg/s is fed to turbine 2 while 2.32 kg/s is fed to the HEN as hot utility. For MPS, 3.80 kg/s exits turbine 1 while 29.87 kg/s exits turbine 2. For LPS, 11.8 kg/s exits turbine 1 while 0.87 kg/s exits turbine 2. In turbine 1, 6,250 kW of power is produced while 9,000 kW is produced by turbine 2. In terms of power purchased and excess power, 9,300 kW of power is purchased while 2,700 kW is excess power. Table 4: Breakdown of costs for the various scenarios investigated Scenarios TAC (×107 $) EI (×109 kg/y) HEs Feedstock Transport mode Feedstock quantity (kW) 1st (TACmin) 2.360 2.781 8 Corn stover Pipeline 629,006 Glycerine Wood Railway Truck 198,074 11,989 2nd (EImin) 5.652 1.373 10 Corn stover Truck 22,796 Glycerine Truck 809,407 3rd (Multi-objective) 3.218 1.405 10 Corn stover Glycerine Truck Pipeline 31,278 809,407 Corn stover Glycerine MPS 197 240 250 180 100 HPSTOT: 49.21 kg/s MPS2: 29.87 kg/s MPS1: 3.80 kg/s LPS1: 11.8 kg/s LPS2: 0.87 kg/s 123456 P2: 19,453.8 kW P3: 11,824 kW EI: 119,867,900 kg/y P1: 665,266 kW P2: 66,526 kW P3: 77,614 Kw EI: 1,285,330,100 kg/y 6,250 kW 9,000 kW 29.66 kg/s HPS1: 15.6 kg/s HPS2: 30.74 kg/s HPS to HEN: 2.32 kg/s PP: 9,300 kW EP: 2,700 kW Power generated 25 20 50 70 155 230 85 40 1 2 3 4 5 6 9 7 8 10 HPS 257 257 197 154 10500 2403 4085 9100 3600 222.8 222.8 148.6 148.6 10388 17309 11087 8827 62.9 6539 CU 5 10 H1 H2 C1 C2 C3 C4 Figure 2: Integrated network for case study involving SCN, power generation and HEN 1127 In the HEN, 10 heat exchangers are selected. Of the 10 exchangers, 4 are hot utility exchangers and 1 is a cold utility exchanger and the remaining 5 are process heat exchangers. In terms of utility usage in the HEN, only HPS and MPS were used as utilities with 6,488 kW coming from HPS while 12,700 kW comes from MPS. It is worthy to note that although HPS has higher temperature driving force compared with MPS, more MPS is still used compared to HPS. This is because the solver tries to minimise the quantity of HPS (with only 2.32 kg/s transported to the HEN) that is generated in the boiler by minimising the quantities of feedstocks selected from the various supply locations. The minimisation of HPS is subject to the stated constraints for the power generation component of the integrated network and these constraints also determine how much of MPS and LPS are generated from the turbines as intermediate streams. Of the total MPS that exits the two turbines, only 4.01 kg/s is transported to the HEN while the LPS is not used in the HEN. 5. Conclusions This paper has presented a superstructure that illustrates how to systematically integrate various options of renewable energy generation feedstocks with a heat and power generation hub that is then further integrated with the HEN of a process plant. The superstructure also captures the seasonality associated with availability of renewable energy sources. The weighted method of multi-objective optimisation was used to simultaneously evaluate TAC and EI as objectives. The integrated superstructure, which was modelled as an MINLP, gave results that illustrate the benefits of combined heat and power generation using renewable energy sources as feedstocks. Future studies will involve detailed pipe design to account for the associated capital costs and pumping costs of fluids. Other issues that will be considered in future studies are desuperheater design for the various steam levels involved in the heat and power hub, interplant heat integration, environmental impacts associated with the transportation in the integrated network and sensitivity analysis of the solutions obtained to investigate the critical parameters involved in the problem considered. Acknowledgments A.J. Isafiade would like to acknowledge the support of the National Research Foundation of South Africa (Grant number: 119140) and Faculty of Engineering and the Built Environment at the University of Cape Town. References Cowen N., Vogel A., Isafiade A.J., Čuček L., Kravanja Z., 2019, Synthesis of combined heat exchange network and utility supply chain, Chemical Engineering Transactions, 76, 391 – 396. Edgar T.F., Himmelblau D.M., Lasdon L.S., 2001, Optimization of Chemical Processes, 2nd Edition, Mc Graw Hill, New York, USA, 435 – 438. 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Yee T.F., Grossmann I.E., 1990, Simultaneous optimization models for heat integration – II, Heat exchanger network synthesis, Computers and Chemical Engineering, 14(10), 1165 – 1184. 1128 PRES22_0388.pdf Multi-Objective Optimisation of Integrated Renewable Energy Feedstock Supply Chain and Work-Heat Exchanger Network Synthesis Considering Economics and Environmental Impact