CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 2017 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš Copyright © 2017, AIDIC Servizi S.r.l. ISBN978-88-95608-51-8; ISSN 2283-9216 A Modified Method for Design of Distributed Wastewater Treatment Systems: Each Unit Removing Multiple Contaminants Chang-Zhan Liua, Ai-Hong Lia, Zhi-Yong Liub,* aDepartment of Chemical Engineering, Chengde Petroleum College, Hebei 067000, China bSchool of Marine Science and Engineering, Hebei University of Technology, Tianjin 300130, China liuzhiyong@hebut.edu.cn A modified method is presented for the design of distributed wastewater treatment systems, in which each process can remove multiple contaminants, based on our previous work. In the design procedure, the value of Total Mixing Influence Potential (TMIP), which can be obtained based on the pinch principle, reflects the influence of performing a process on the total treatment flowrate of the system. The process with the smallest TMIP value will be performed first, when designing of the treatment system. However, when a process can remove multiple contaminants, it is difficult to obtain the values of the TMIP. This paper improves the calculation of TMIP values for the processes, which can remove multiple contaminants, by combining pinch principle with a linear programming approach. The investigation of a literature example shows that the result obtained with the method proposed is comparable to the optimal solution obtained in the literature. In addition, the method proposed is low computational complexity and of clear engineering insight. 1. Introduction Developing advanced wastewater treatment systems is an effective way to reduce water pollution, which is threatening the health of humans and aggregating the shortage of water resource. Wang and Smith (1994) pointed out that the distributed treatment (also named decentralized treatment) can often result in lower costs than centralized treatment. In addition, Opher and Friedler (2016) drew a conclusion that the distributed urban wastewater treatment system is environmentally better than the centralized system by performing a Life Cycle Assessment. This paper focuses on the wastewater treatment systems of multiple contaminants. Wang and Smith (1994) introduced Pinch Analysis method for the design of distributed wastewater treatment systems. Kuo and Smith (1997) improved the method of Wang and Smith (1994) mainly by addressing the important features of multiple treatment units and by developing a staged design approach for multiple contaminant systems. Soo et al. (2013) extended the Wastewater Composite Curve proposed by Ng et al. (2007) to the synthesis of distributed wastewater treatment systems of one or two contaminants with multiple treatment units. In general, the Pinch Analysis method is conceptually clear and suitable for the systems of single contaminant or simple ones of multiple contaminants. Mathematical programming method is the major tool for the integration of distributed wastewater treatment systems of multiple contaminants. Takama et al. (1980) initiated the study of water allocation network optimization with nonlinear programming (NLP) approach. However, they failed to obtain the global optimal solution. Later, many solving strategies, successive relaxed solution (Galan and Grossmann, 1998), superstructure decomposition and parametric optimisation strategies (Hernandez-Suarez et al., 2004), two- stage strategy (Castro et al., 2007), discretization optimal approach (Burgara-Montero et al., 2012), were presented for acquiring the global optimal solution of the system. Kollmann et al. (2014) discussed the energy potential of wastewater treatment plants which has yet unexploited. Alnouri et al. (2015) integrated on-site decentralized and off-site central treatment systems into the synthesis of industrial city water networks. Sueviriyapan et al. (2016) proposed a retrofit method for existing complex industrial wastewater systems by DOI: 10.3303/CET1761200 Please cite this article as: Liu C.-Z., Li A.-H., Liu Z.-Y., 2017, A modified method for design of distributed wastewater treatment systems: each unit removing multiple contaminants, Chemical Engineering Transactions, 61, 1213-1218 DOI:10.3303/CET1761200 1213 means of recycling and rerouting. Although mathematical programming approach is robust in handling complex systems, it is often computational complexity and lack of clear engineering insights. To reduce the solving difficulty and provide clear engineering insights for the synthesis of distributed wastewater treatment systems of multiple contaminants, Li et al. (2015) proposed the concept of Total Mixing Influence Potential (TMIP) and develop a design procedure based on the concept. The system Li et al. (2015) considered is that the main task of a process is to remove only one contaminant (the contaminant is called as the main contaminant of the process, Liu et al., 2013) based on the pinch principle. However, in industrial cases, one treatment process can usually remove multiple contaminants. As mentioned above, it is difficult to deal with the systems of multiple contaminants with pinch method. This paper will provide the calculation of TMIP values for the processes which have multiple main contaminants by combining the pinch method with a linear programming (LP) approach. 2. The concept of Total Mixing Influence Potential (TMIP) It is important to determine the preference order of treatment processes because unnecessary stream mixing caused by unreasonable performing order would reduce the contaminant concentrations and consequently increase the flowrates of downstream processes (Kuo and Smith, 1997). Based on this insight, Li et al. (2015) introduced the concept of TMIP to identify the reasonable performing order of treatment processes. The definition of TMIP is shown in Eq(1) and Eq(2). In the jth column vector of Eq (1), which is referred to as Mixing Influence Treatment Flowrate (MITF) matrix, FTPj is the minimum treatment flowrate of treatment process TPj and the other elements are those of its downstream processes, where NT is the number of treatment processes. The sum of all the elements in the jth column vector, as shown in Eq (2), can reflect the influence of performing TPj on the total treatment flowrate of the system and defined as Total Mixing Influence Potential (TMIP). The process with the minimum TMIP value should be performed first. 1 ,1 ,1 1, , 1, , NT TP j NT j TPj NT j j,k NT j NT TP F MI MI MI F MI MI MI MI F                       (1) , 1 NT j j i i MI MI    (2) 3. The calculation of TMIP value for a process removing multiple contaminants It can be seen from Eq(1) and Eq(2) that the calculation of TMIP value is essentially based on the minimum treatment flowrates of treatment processes. The minimum treatment flowrates for the processes which remove only one contaminant can be obtained with pinch principle (Li et al., 2015). To obtain the minimum treatment flowrates for the processes which can remove multiple contaminants, an LP approach is needed to be combined with the pinch method, which will be discussed in the following. 3.1 The minimum treatment flowrate for a process removing multiple contaminants Let us denote the set of main contaminants of TPj as CTPj, for example, CTPj={A, B}. For removing contaminant A, the set of the streams to be treated by TPj, STPj,A, can be obtained with the pinch method of Li et al. (2015). Similarly, the set of the streams to be treated for removing contaminant B, STPj,B, can be obtained. Then, in order to remove contaminants A and B simultaneously, the set of the streams that TPj might treat is STPj= STPj,AUSTPj,B. The minimum removal mass load for each main contaminant of TPj (MTPj,k) is shown in Eq(3), where Fi is the flowrate of wastewater stream Si, Ci,k is the concentration of contaminant k in Si, C lim env,k is the environmental limit concentration of contaminant k, and RRj,k is the removal ratio of TPj for contaminant k. lim , , , , i i k env k i i i TPj k j k F C C F M k RR        TPj TPjS S TPj C (3) 1214 The mass load removed by TPj for each main contaminant should be equal to or higher than the corresponding minimum removal mass load, as shown in Eq (4), where FTPj,i is the flowrate of Si to be treated by TPj. , , ,TPj i i k TPj k i F C M k    TPj TPj S C (4) The constraint of flowrate of Si to be treated by TPj is: , 0 TPj i i F F  (5) The objective is to obtain the minimum treatment flowrate of TPj, which is the sum of flowrates of wastewater streams it should treat. , min TPj i i F   TPjS (6) 3.2 The design procedure Based on the minimum treatment flowrate obtained above, the MITF matrix and the TMIP values of a system can be calculated easily. The detailed procedure can be referred to Li et al. (2015), which is summarized as follows: (1) Identify the main contaminants and calculate the minimum treatment flowrate for each treatment process; (2) Calculate the minimum treatment flowrates of downstream processes for each treatment process based on the streams after it is performed and list the MITF matrix; (3) Calculate the TMIP value with Eq(2) for each treatment process and identify the first process to be performed; (4) Return to step (1) to identify the next process based on the current streams till the removed mass load of each contaminant is equal to or larger than the corresponding minimum removal mass load shown in Eq (3). 4. Case study The stream and treatment process data for this example taken from Castro et al. (2007) are shown in Table 1. Each process can remove two contaminants. The environmental limit for each contaminant is 100 ppm. Table 1: The stream and treatment process data (a) Stream data Stream Flowrate (t·h-1) Concentration (ppm) A B C D E F S1 19 1,100 500 500 200 800 100 S2 7 40 0 100 300 910 200 S3 8 200 220 200 500 150 0 S4 6 60 510 500 200 780 100 S5 17 400 170 100 300 900 0 (b) Treatment process data Process Removal ratio (%) A B C D E F TP1 99 99 TP2 99 99 TP3 99 99 The design procedure is as follows: 1. Identifying the main contaminants and calculating the minimum treatment flowrate for each process Let us take process TP1 as an example. It can be seen from Table 1(b) that TP1 is required to remove contaminants A and B, i.e., CTP1={A, B}. For removing contaminant A, the set of the streams that TP1 should treat is {S1, S5} and the minimum treatment flowrate is 27.96 t·h-1, which can be obtained based on pinch method shown in Table 2. Similarly, for removing contaminant B, the set of the streams that TP1 should treat is {S4, S1} and the minimum treatment flowrate is 23.13 t·h-1, as shown in Table 3. For removing contaminants 1215 A and B simultaneously, TP1 might treat streams S1, S4 and S5. The minimum treatment flowrate of TP1 can be obtained by solving Formula (7). Table 2: The minimum treatment flowrate of TP1 for removing contaminant A Stream Ci,A (ppm) Fi (t·h-1) Mi,A (g·h-1) ∑Mi,A (g·h-1) FTP1,A (t·h-1) S1 1,100 19 20,900 20,900 19 S5 400 17 6,800 27,700 8.96 S3 200 8 1,600 29,300 S2 40 7 280 29,580 S4 60 6 360 29,940 Sum 57 29940 27.96 The streams printed in bold and italics are those TP1 should treat for removing contaminant A Table 3: The minimum treatment flowrate of TP1 for removing contaminant B Stream Ci,B (ppm) Fi (t·h-1) Mi,B (g·h-1) ∑Mi,B (g·h-1) FTP1,B (t·h-1) S4 510 6 3,060 3,060 6 S1 500 19 9,500 12,560 17.13 S3 220 8 1,760 14,320 S5 170 17 2,890 17,210 S2 0 7 0 17,210 Sum 57 17210 23.13 The streams printed in bold and italics are those TP1 should treat for removing contaminant B       1,1 1, 4 1,5 1,1 1, 4 1,5 1,1 1, 4 1,5 1,1 1, 4 1,5 min 1100 60 400 29940 57 100 /0.99 500 510 170 17210 57 100 /0.99 0 19 0 6 0 17                          TP TP TP TP TP TP TP TP TP TP TP TP F F F F F F F F F F F F (7) It can be obtained from Formula (7): -1 1,1 -1 1, 4 -1 1,5 =19 t h =1.24 t h =8.78 t h       TP TP TP F F F FTP1 = 19+1.24+8.78 = 29.02 t·h-1. Similarly, the minimum treatment flowrates of other processes can be obtained, as listed in Table 4. Table 4: The minimum treatment flowrate of each process Process Main contaminants Streams treated FTP1 (t·h-1) TP1 A, B S1, S4, S5 29.02 TP2 C, D S1, S3, S4, S5 35.49 TP3 E S1, S2, S4, S5 43.71 2. Determining the first process to be performed Let us take MI1,2 as an example to illustrate the calculation of MITFs. When TP1 is performed, according to the results of Step 1, the streams after TP1 can be shown in Figure 1. Based on the streams in Figure 1, the minimum treatment flowrate of TP2 for removing contaminants C and D can be obtained as 35.49 t·h-1, which is the value of MI1,2 according to the definition of the MITF. Similarly, we can obtain other elements of MITF matrix. The MITF matrix is shown in Eq(8) and the TMIP values for all the processes are shown in Eq(9). 1216 TP1S1 S4 Sm1 S4b Concentration of contaminant A high low 19 6 17 1.24 29.02 4.76 S5 7 S2 8 S3 8.78 8.22 S5b Streams for the downstream processes Figure 1: Streams after TP1 for the downstream processes 1 2,1 3,1 1,2 2 3,2 1,3 2,3 3 37.54 39.10 35.49 35.49 36.60 43.74 49.19 43.71 TP TP TP F MI MI MI F MI MI MI F                   29.02 (8)    1 2 3 = 122.22 119.41MI MI MI 108.25 (9) It can be seen from Eq(9) that TP1, whose TMIP value is the smallest, should be performed first (Li et al. 2015). The flowrate of TP1 is 29.02 t·h-1, which is the element of FTP1 in Eq(8) and printed in bold and italics. 3. Determining the second process to be performed Obtain the MITFs for TP2 and TP3 based on the streams after TP1, which have been shown in Figure 1. The MITF matrix for TP2 and TP3 is: 2 3,2 2,3 3 35.49 49.21 TP TP F MI MI F            36.67 43.74 (10) The TMIP values for TP2 and TP3 are:    2 3 = 84.70MI MI 80.41 (11) It can be seen from Eq(11) that the second process to be performed is TP3 and the last one is TP2. The flowrate of TP3 is 43.74 t·h-1 and that of TP2 is 36.67 t·h-1, which are printed in bold and italics in Eq(10). The total treatment flowrate is 29.02+43.74+36.67=109.43 t·h-1 and the final design is shown in Figure 2. The total treatment flowrate is very close to the global optimal solution of Castro et al. (2007), 109.401 t·h-1, in which an LP formulation in the first stage is used to generate starting points for the solution of the NLP program in the second stage. The network interconnection number is also the same as the work of Castro et al. (2007). However, as can be seen from the above design procedure, the method proposed in this work is low calculation effort and of clear engineering insights. 1.24 25.12 5736.67 29.02 S4 6 S1 19 S3 8 S5 17 8.78 TP1 28.52 43.74 TP3 S2 7 TP2 6.29 0.5 4.76 8.22 1.71 18.62 Figure 2: Design for the example 1217 5. Conclusions A modified method of Li et al. (2015) is presented for the design of distributed wastewater treatment systems, in which each process can remove multiple contaminants. The value of Total Mixing Influence Potential (TMIP), which can reflect the influence of performing a process on the total treatment flowrate of a system, is obtained by combining the Pinch Method with a linear programming approach. In the design procedure, the treatment process with the smallest TMIP value will be performed first. It is shown that the value of TMIP is a good indicator for determining the preference order of treatment processes. The method proposed is low computational complexity and of clear engineering insights. The investigation of a literature example shows that the results obtained with the method proposed is very close to the global optimal solution obtained with mathematical programming method. Acknowledgments This work is supported by the Foundation of Educational Commission of Hebei Province, Hebei, China (Grant No. Z2017032) and the Natural Science Foundation of Hebei Province, Hebei, China (Grant No. B2017202073). References Alnouri S.Y., Linke P., El-Halwagi M., 2015, A synthesis approach for industrial city water reuse networks considering central and distributed treatment systems, Journal of Cleaner Production, 89, 231-250. Burgara-Montero O., Ponce-Ortega J.M., Serna-González M., El-Halwagi M.M., 2012, Optimal design of distributed treatment systems for the effluents discharged to the rivers, Clean Technologies and Environmental Policy, 14, 925-942. 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