DOI: 10.3303/CET2188115 Paper Received: 27 May 2021; Revised: 1 August 2021; Accepted: 14 October 2021 Please cite this article as: Sa’ad S.F., Wan Alwi S.R., Lim J.S., Manan Z.A., 2021, Pricing Mechanism for Centralised Reused Water System with Multiple Water Headers, Chemical Engineering Transactions, 88, 691-696 DOI:10.3303/CET2188115 CHEMICAL ENGINEERING TRANSACTIONS VOL. 88, 2021 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 Copyright © 2021, AIDIC Servizi S.r.l. ISBN 978-88-95608-86-0; ISSN 2283-9216 Pricing Mechanism for Centralised Reused Water System with Multiple Water Headers Siti Fatimah Sa’ad, Sharifah Rafidah Wan Alwi*, Jeng Shiun Lim, Zainuddin Abdul Manan Process Systems Engineering Centre (PROSPECT), Research Institute for Sustainable Environment (RISE), School of Chemical and Energy Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia syarifah@utm.my Reasonable water pricing is essential for long-term sustainability and financing. The selling prices of reused/regenerated water should enable the generation of revenue that could cover the production costs. In this work, reused/regenerated water prices at different qualities are determined based on the total annualised cost of the centralised system with and without subsidy, quality factor, and profit factor. This paper presents a mathematical programming formulation that aims to maximise the centralised system’s profit in the industrial site considering multiple qualities of reused/regenerated water. A case study of numerous scenarios, each with various numbers of water headers and different water prices, is used to test the model. The results obtained show that as the total annualised cost increases, the selling prices of reused/regenerated water increase, the centralised system’s profit also increases, and there is a possibility to surpass the freshwater price. For scenarios with subsidy and low total annualised cost, there is an opportunity to increase the centralised system’s profit by increasing the profit factor in determining the reused/regenerated water price without exceeding the freshwater price. Based on the case study, Scenario 7 with the highest number of water headers is chosen as it has the highest freshwater reduction, which is 70 %, low total annualised cost, a comparable profit with a profit margin of more than 15 % and the highest profit factor can be applied compared to the other scenarios. 1. Introduction The reused water is described as wastewater-generated water that has been treated to meet the quality requirements for reuse (EU Water Directors, 2016). Offering the best price for reused water is a strategy for increasing the appeal of potential buyers. It was expected that reused water prices would be lower than freshwater prices to encourage current users of freshwater to convert to reused water. According to USEPA (2012), two techniques are used to develop reused water prices, either the price covers all costs associated with reused water production, allocation, administration and operation, or the price is reduced by cost subsidisation from other sources. Full cost recovery prices comprise the capital and annual costs of the reused water system. Reused water prices are supposed to be lower than potable water prices to encourage existing potable water consumers to switch to reused water. As a result, reused water prices are often subsidised to keep it at or below the level of potable water. EU Water Directors (2016) stated a few options in considering the price of water reuse. Firstly, there are no charges for the use of treated wastewater, as there are in some cases in Australia. Secondly, the price is determined based on the costs of treatment and distribution to the end-user. Thirdly, treated wastewater is normally less costly than drinking water. Fourthly, the price is determined by the consumers' willingness to pay. Fifthly, the price is determined by market value. Sixthly, prices for both conventional and reused water are the same. Lastly, the price is determined by the cost of recovering environmental and resource costs. According to EU Water Directors (2016), the relationship between conventional water supply and water reuse prices is crucial and must be clearly defined. Setting an overly low price for water reuse may lead to over-use of the water and failing to represent the external cost. EU Water Directors (2016) suggested the increasing block tariff to solve the problem in which as consumption and demand increase, the tariff will increase as well. 691 Aviso et al. (2010) presented a fuzzy bi-level optimisation model in the determination of the freshwater and treatment costs associating with water reuse subsidy. The study did not consider reused water price. Tan et al. (2011) proposed a fuzzy bi-level optimisation model in the determination of freshwater, effluent treatment and regenerated water costs. The study did not consider regenerated water price at different quality. Cooley and Phurisamban (2016) adopted a levelised cost approach taking into account all of the capital and operating costs to estimate the cost of alternative water supply. The work did not consider quality and profit factors. Misrol et al. (2020) proposed a model with the combination of domestic and industrial wastewater intending to maximise profit. The study did not clearly state the selling price of water generated from the centralised system. Fadzil et al. (2020) applied the Pinch Analysis method to determine the number of water header. The study assumed the price of water for each header and did not clearly state the pricing mechanism. Misrol et al. (2021) developed a model with the generation of reused water and biogas from wastewater. The study did not clearly state the mechanism of the selling price of water produced. Although there were a lot of past researches regarding water integration between plants, research regarding the pricing of reused water is still required. Various characteristics of reused water may be required with more than one form of the reused water consumer. If so, it becomes more complex to calculate the user charge for different qualities of reused water. This gap is the subject to be explored in this paper. In this paper, the term ‘regenerated water’ was used to refer to the treated wastewater for reuse. The main aim is to present a mathematical model that could help the industrial players to identify the best setting price of water at different qualities. 2. Methodology Figure 1 shows the water integration network of the centralised system between different plants. The subscript 𝑖 defines water source, 𝑗 defines water demand, 𝑘 defines water header collector, 𝑟 defines regeneration unit, 𝑑 defines water header distributor, and 𝑚 defines contaminant. In this mathematical model, the units used are L/h for flowrate, ppm for concentration, kg/h for mass load, and USD/y for total annual costs, total annual revenue, and total annual profit. Figure 1: Water integration network of the centralised system Eq(1a) is the objective function to maximise the centralised system’s profit by selling regenerated water. Eq(1b) is the objective function with the addition of subsidy. 𝑇 𝑅𝐸𝑉 is the total annual revenue, 𝑇 𝐴𝐶 is the total annualised cost and 𝑠 is the fraction of subsidy. Max 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇 𝑅𝐸𝑉– 𝑇 𝐴𝐶 (1a) Max 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇 𝑅𝐸𝑉– [𝑇 𝐴𝐶 x (1- 𝑠)] (1b) Eq(2) and Eq(3) are applied for water source. 𝐹𝐼 𝑖 is the flowrate of source 𝑖, 𝐹𝐼𝐾 𝑖,𝑘 is the flowrate from source 𝑖 to header collector 𝑘, 𝐶𝐼 𝑖,𝑚 is the contaminant concentration of type 𝑚 of source 𝑖 and 𝐶𝐼𝐾 𝑖,𝑘,𝑚 is the contaminant concentration of type 𝑚 from source 𝑖 to header collector 𝑘. 𝐹𝐼 𝑖 = ∑ 𝐹𝐼𝐾 𝑖,𝑘𝑘 ∀𝑖 (2) 𝐹𝐼 𝑖 x 𝐶𝐼 𝑖,𝑚 = ∑ (𝐹𝐼𝐾 𝑖,𝑘𝑘 x 𝐶𝐼𝐾 𝑖,𝑘,𝑚) ∀𝑖,𝑚 (3) Eq(4) and Eq(5) are applied for water header collector. 𝐹𝐾 𝑘 is the flowrate in header collector 𝑘 and 𝐶𝐾 𝑘,𝑚 is the contaminant concentration of type 𝑚 in header collector 𝑘. 692 𝐹𝐾 𝑘 = ∑ 𝐹𝐼𝐾 𝑖,𝑘𝑖 ∀𝑘 (4) 𝐹𝐾 𝑘 x 𝐶𝐾 𝑘,𝑚 = ∑ (𝐹𝐼𝐾 𝑖,𝑘𝑖 x 𝐶𝐼𝐾 𝑖,𝑘,𝑚) ∀𝑘,𝑚 (5) Eq(6) to Eq(11) are applied for regeneration unit. 𝐹𝐾𝑅 𝑘,𝑟 is the flowrate from header collector 𝑘 to regenerator 𝑟, 𝐶𝐾𝑅 𝑘,𝑟,𝑚 is the contaminant concentration of type 𝑚 from header collector 𝑘 to regenerator 𝑟, 𝐹𝑅 𝑟 is the flowrate in regenerator 𝑟, 𝐶𝑅 𝑟,𝑚 is the contaminant concentration of type 𝑚 in regenerator 𝑟, 𝐶𝑂𝑈𝑇𝑅 𝑟,𝑚 is the outlet contaminant concentration of type 𝑚 from regenerator 𝑟, 𝑅𝑅𝑟,𝑚 is the removal ratio of contaminant type 𝑚 in regenerator 𝑟, and 𝑀𝑅 𝑟,𝑚 is the mass contaminant removed of type 𝑚 from regenerator 𝑟. ∑ 𝐹𝐾𝑅 𝑘,𝑟𝑟 = 𝐹𝐾 𝑘 ∀𝑘 (6) ∑ (𝐹𝐾𝑅 𝑘,𝑟𝑟 x 𝐶𝐾𝑅 𝑘,𝑟,𝑚) = 𝐹𝐾 𝑘 x 𝐶𝐾 𝑘,𝑚 ∀𝑘,𝑚 (7) 𝐹𝑅 𝑟 = ∑ 𝐹𝐾𝑅 𝑘,𝑟𝑘 ∀𝑟 (8) 𝐹𝑅 𝑟 x 𝐶𝑅 𝑟,𝑚 = ∑ (𝐹𝐾𝑅 𝑘,𝑟𝑘 x 𝐶𝐾𝑅 𝑘,𝑟,𝑚) ∀𝑟,𝑚 (9) 𝐶𝑂𝑈𝑇𝑅 𝑟,𝑚 = 𝐶𝑅 𝑟,𝑚 x (1-𝑅𝑅𝑟,𝑚) ∀𝑟,𝑚 (10) 𝑀𝑅 𝑟,𝑚 = [(𝐶𝑅 𝑟,𝑚 - 𝐶𝑂𝑈𝑇𝑅 𝑟,𝑚 ) x 𝐹𝑅 𝑟 ]/1,000,000 ∀𝑟,𝑚 (11) Eq(12) to Eq(15) are applied for water header distributor. 𝐹𝑅𝐷 𝑟,𝑑 is the flowrate from regenerator 𝑟 to header distributor 𝑑, 𝐶𝑅𝐷 𝑟,𝑑,𝑚 is the contaminant concentration of type 𝑚 from regenerator 𝑟 to header distributor 𝑑, 𝐹𝐷 𝑑 is the flowrate in header distributor 𝑑, and 𝐶𝐷 𝑑,𝑚 is the contaminant concentration of type 𝑚 in header distributor 𝑑. ∑ 𝐹𝑅𝐷 𝑟,𝑑𝑑 = 𝐹𝑅 𝑟 ∀𝑟 (12) ∑ (𝐹𝑅𝐷 𝑟,𝑑𝑑 x 𝐶𝑅𝐷 𝑟,𝑑,𝑚) = 𝐹𝑅 𝑟 x 𝐶𝑂𝑈𝑇𝑅 𝑟,𝑚 ∀𝑟,𝑚 (13) 𝐹𝐷 𝑑 = ∑ 𝐹𝑅𝐷 𝑟,𝑑𝑟 ∀𝑑 (14) 𝐹𝐷 𝑑 x 𝐶𝐷 𝑑,𝑚= ∑ (𝐹𝑅𝐷 𝑟,𝑑𝑟 x 𝐶𝑅𝐷 𝑟,𝑑,𝑚) ∀𝑑,𝑚 (15) Eq(16) to Eq(19) are applied for water demand. 𝐹𝐷𝐽 𝑑,𝑗 is the flowrate from header distributor 𝑑 to demand 𝑗, 𝐹𝐹𝑊𝑗 is the freshwater flowrate to demand 𝑗, 𝐹𝐽𝑗 is the flowrate of demand 𝑗, 𝐶𝐹𝑊 is the contaminant concentration of freshwater, and 𝐶𝐽𝑗,𝑚 is the contaminant concentration of type 𝑚 of demand 𝑗. ∑ 𝐹𝐷𝐽 𝑑,𝑗𝑗 ≤ 𝐹𝐷 𝑑 ∀𝑑 (16) ∑ (𝐹𝐷𝐽 𝑑,𝑗𝑗 x 𝐶𝐷 𝑑,𝑚 ) ≤ 𝐹𝐷 𝑑 x 𝐶𝐷 𝑑,𝑚 ∀𝑑,𝑚 (17) 𝐹𝐹𝑊𝑗 + ∑ 𝐹𝐷𝐽 𝑑,𝑗𝑑 = 𝐹𝐽𝑗 ∀𝑗 (18) (𝐹𝐹𝑊𝑗 x 𝐶𝐹𝑊) + ∑ (𝐹𝐷𝐽 𝑑,𝑗𝑑 x 𝐶 𝐷 𝑑,𝑚) ≤ 𝐹 𝐽 𝑗 x 𝐶𝐽𝑗,𝑚 ∀𝑗,𝑚 (19) Eq(20) to Eq(24) are applied for the determination of pipes existence. 𝑈 is a large positive number. 𝑄𝐼𝐾 𝑖,𝑘 , 𝑄𝐾𝑅 𝑘,𝑟 , 𝑄𝑅𝐷 𝑟,𝑑 are the binary parameters. 𝑉𝐷𝐽 𝑑,𝑗 is the binary variable. 𝐹𝐼𝐾 𝑖,𝑘 ≤ 𝑈 x 𝑄𝐼𝐾 𝑖,𝑘 ∀𝑖,𝑘 (20) 𝐹𝐾𝑅 𝑘,𝑟 ≤ 𝑈 x 𝑄𝐾𝑅 𝑘,𝑟 ∀𝑘,𝑟 (21) 𝐹𝑅𝐷 𝑟,𝑑 ≤ 𝑈 x 𝑄𝑅𝐷 𝑟,𝑑 ∀𝑟,𝑑 (22) 693 𝐹𝐷𝐽 𝑑,𝑗 ≤ 𝑈 x 𝑉𝐷𝐽 𝑑,𝑗 ∀𝑑,𝑗 (23) 𝑉𝐷𝐽 𝑑,𝑗 ≤ 𝐹𝐷𝐽 𝑑,𝑗 ∀𝑑,𝑗 (24) Eq(25) is applied to determine the total annual revenue. 𝐻ℎ𝑜𝑢𝑟 is the operating hours per year and 𝑃𝑅𝑊 𝑑 is the volumetric price of regenerated water. 𝑇 𝑅𝐸𝑉 = 𝐻ℎ𝑜𝑢𝑟 x ∑ [(𝐹𝐷𝐽 𝑑,𝑗𝑑,𝑗 /1,000) x 𝑃𝑅𝑊 𝑑 ] (25) Eq(26) is applied to determine the total annualised cost. 𝑇 𝐶𝐶 is the total capital cost, 𝐴𝐹 is the annualised factor and 𝑇 𝑂𝐶 is the total annual operating cost. 𝑇 𝐴𝐶 = (𝑇 𝐶𝐶 x 𝐴𝐹) + 𝑇 𝑂𝐶 (26) Eq(27) is applied to determine the total capital cost. 𝑇 𝐶𝐶𝑝𝑖𝑝𝑒 , 𝑇 𝐶𝐶𝑝𝑢𝑚𝑝, 𝑇 𝐶𝐶𝑚𝑜𝑡𝑜𝑟, 𝑇 𝐶𝐶𝑟𝑒𝑔 are the capital costs of pipe, pump, motor, and regeneration unit. 𝑇 𝐶𝐶 = 𝑇 𝐶𝐶𝑝𝑖𝑝𝑒 + 𝑇 𝐶𝐶𝑝𝑢𝑚𝑝 + 𝑇 𝐶𝐶𝑚𝑜𝑡𝑜𝑟 + 𝑇 𝐶𝐶𝑟𝑒𝑔 (27) Eq(28) is applied to determine the total annual operating cost. 𝑇 𝑂𝐶𝑤𝑤 is the annual costs of buying high-quality wastewater. 𝑇 𝑂𝐶𝑝𝑢𝑚𝑝 and 𝑇 𝑂𝐶𝑟𝑒𝑔 are the annual operating costs of pumping and regeneration. 𝑇 𝑂𝐶 = 𝑇 𝑂𝐶𝑤𝑤 + 𝑇 𝑂𝐶𝑝𝑢𝑚𝑝 + 𝑇 𝑂𝐶𝑟𝑒𝑔 (28) The details of the cost equations are not shown due to the limited spaces and pages. The MINLP model is solved with a DICOPT solver by using GAMS software (GAMS, 2016). The model is initially run at the baseline freshwater price to get the total annualised cost. The total annualised cost is used to determine the base or minimum regenerated water price as shown in Eq(29). The regenerated water price at different qualities is determined based on the quality factor and profit factor as shown in Eq(30). The quality factor is used to classify the regenerated water price at different quality. The profit factor is used to cover any miscellaneous cost and provide extra profit to the centralised system. The model then is run at the new regenerated water prices. 𝐵𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 = 𝑇𝑜𝑡𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙𝑖𝑠𝑒𝑑 𝑐𝑜𝑠𝑡 (𝑇 𝐴𝐶) 𝑇𝑜𝑡𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑟𝑒𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑤𝑎𝑡𝑒𝑟 (29) 𝑃𝑟𝑖𝑐𝑒 = 𝐵𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝑥 (1 + 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 + 𝑝𝑟𝑜𝑓𝑖𝑡 𝑓𝑎𝑐𝑡𝑜𝑟) (30) 3. Case study The water data for the centralised system were modified from Yu et al. (2013) with three plants and two types of contaminants which are total suspended solids (TSS) and chemical oxygen demand (COD) as shown in Table 1. The case study was tested with the different number of water header. Table 1: The water data for the centralised system Sources Demands Plant Number Flowrate Concentration (ppm) Plant Number Flowrate Concentration (ppm) (m3/h) TSS COD (m3/h) TSS COD A 1 10.417 45 80 A 1 10.417 10 40 2 14.583 70 120 2 41.667 20 50 3 12.5 100 350 3 6.25 30 65 B 4 20.833 50 75 B 4 33.333 10 40 5 37.5 65 110 5 83.333 20 50 6 35.417 100 300 6 8.333 30 65 C 7 12.5 50 80 C 7 16.667 10 40 8 17.5 60 110 8 54.167 20 50 9 18.75 110 350 9 4.167 30 65 For one water header in Scenarios 1, 2 and 3, wastewater sources are mixed and produced one quality of regenerated water. For two water headers in Scenarios 4, 5 and 6, wastewater sources are segregated into two classes based on quality and produced two qualities of regenerated water. For three water headers in Scenario 7, wastewater sources are segregated into three classes and produced three qualities of regenerated water. 694 The quality factor is assumed zero for low-quality water as this quality is assumed to apply the minimum price, 0.1 for medium-quality water, and 0.2 for high-quality water. The profit factor, as well as subsidy fraction, are assumed 0.1 for all scenarios. 4. Results and discussion Table 2 shows the regenerated water price based on the total annualised cost at different scenarios. Scenarios 1, 2, 4 and 7 achieved the highest freshwater reduction, which was 70 %, whilst Scenario 3 achieved the lowest freshwater reduction, which was 61.3 % because it only produced low-quality regenerated water. The lower total annualised cost was achieved with subsidy which also reflected the lower regenerated water price. The highest price was achieved by Scenario 1 because it had the highest total annualised cost and the price was almost the same as the freshwater price, which was USD 0.75/m3. The regenerated water prices of the remaining scenarios were still below the freshwater price. Table 3 shows the economic results at different regenerated water prices. The high total annual revenue and total annual profit were achieved by Scenario 1, followed by Scenario 4 and Scenario 5 due to the selling of high-quality regenerated water at a high price. The opposite was achieved by Scenario 3 because low-quality regenerated water was sold at a low price. The profit margin is the same either with or without subsidy because as the total annualised cost increases, resulting in a high regenerated water price, thus, increasing the total annual revenue. Table 2: The results of regenerated water prices Scenario Quality Freshwater Flow TAC (USD/y) Price (USD/m3) reduction (%) (m3/y) Without subsidy With subsidy Without subsidy With subsidy 1 High 70 1,440,000 829,850 746,865 0.749 0.674 2 Medium 70 719,250 647,325 0.599 0.539 3 Low 61.3 511,710 460,539 0.391 0.352 4 High 70 758,410 682,569 0.685 0.616 Medium 0.632 0.569 5 High 69.6 717,500 645,750 0.648 0.583 Low 0.548 0.493 6 Medium 65.5 660,930 594,837 0.551 0.496 Low 0.505 0.454 7 High 70 694,380 624,942 0.627 0.564 Medium 0.579 0.521 Low 0.530 0.477 Table 3: The results of economic analysis Scenario Total Annual Revenue (USD/y) Total Annual Profit (USD/y) Profit margin (%) Without subsidy With subsidy Without subsidy With subsidy 1 1,078,600 970,560 248,750 223,695 23.1 2 862,560 776,160 143,310 128,835 16.6 3 495,330 445,930 -16,380 -14,609 -3.3 4 958,130 861,970 199,720 179,401 20.8 5 879,410 791,180 161,910 145,430 18.4 6 725,400 652,730 64,470 57,893 8.9 7 824,430 741,820 130,050 116,878 15.8 The regenerated water price increased as the profit factor increased. Thus, a further analysis was conducted at each scenario to study the effects of profit factor in determining the regenerated water price, starting with 0.1 and increased up to 0.5 as shown in Figures 2a and 2b. The percentage changes of the regenerated water price from the baseline freshwater price at the increasing profit factor were most likely more than 10 %. The low percentage change indicated that the regenerated water price was close to the freshwater price. However, the regenerated water price must be below the freshwater price. A negative percentage change means that the price does not exceed the freshwater price and vice versa. For without subsidy, Scenario 4 can apply up to 0.2 and Scenarios 2, 5 and 7 can apply up to 0.3 to achieve high profit. For with subsidy, Scenario 1 can apply up to 0.2, Scenario 4 up to 0.3, Scenario 5 up to 0.4, and Scenarios 2 and 7 up to 0.5 to achieve high profit. The higher profit factor could be applied when there was a subsidy and at the same time, the regenerated water 695 prices were still below the freshwater price. Based on the case study, Scenario 7 is chosen as it has a low total annualised cost, a comparable profit and the highest profit factor can be applied. (a) (b) Figure 2: The percentage changes of regenerated water prices from the baseline freshwater price at different profit factor (a) without subsidy, and (b) with subsidy 5. Conclusions The high total annualised cost resulting in a high regenerated water price and gave high profit to the centralised system. The disadvantage is that there is a possibility to surpass the freshwater price. The advantage is the prices have not been directly affected by the fluctuation of the freshwater price. However, the prices might surpass the freshwater price if the fluctuation occurred. For scenarios with low total annualised cost, there is an opportunity to have high profit by increasing the profit factor in determining regenerated water price without exceeding the freshwater price. In this case study, Scenario 7 is chosen with 70 % freshwater reduction, low total annualised cost, more than 15 % of profit margin and the highest profit factor can be applied. In future work, the proposed method can consider maintenance costs as well as the effect of different subsidy factor. Acknowledgements The authors would like to express gratitude to Universiti Teknologi Malaysia (UTM) for funding this project through Vote Number Q.J130000.2409.08G86, Q.J130000.3509.05G94, Q.J130000.3509.05G96 and Q.J130000.3551.05G97. References Aviso K.B., Tan R.R., Culaba, A.B., Cruz Jr. J.B., 2010, Bi-level fuzzy optimization approach for water exchange in eco-industrial parks, Process Safety and Environmental Protection, 88, 31-40. 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