Format And Type Fonts CHEMICAL ENGINEERING TRANSACTIONS VOL. 39, 2014 A publication of The Italian Association of Chemical Engineering www.aidic.it/cet Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong Copyright © 2014, AIDIC Servizi S.r.l., ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439034 Please cite this article as: Tangnanthanakan P., Siemanond K., 2014, Comparison of sequential and simultaneous approaches for multiperiod heat exchanger network synthesis and application for crude preheat train, Chemical Engineering Transactions, 39, 199-204 DOI:10.3303/CET1439034 199 Comparison of Sequential and Simultaneous Approaches for Multiperiod Heat Exchanger Network Synthesis and Application for Crude Preheat Train Parawinee Tangnanthanakan a , Kitipat Siemanond* b a The Petroleum and Petrochemical College, Chulalongkorn University, Soi Chulalong korn 12, Phayathai Rd., Pathumwan, Bangkok 10330, Thailand b Center of Excellence on Petrochemical and Materials Technology, Soi Chulalong korn 12, Phayathai Rd., Pathumwan, Bangkok 10330, Thailand kitipat.s@chula.ac.th Global energy demand has increased continuously since the last few decades and it has been a critical issue especially in industrial sector. Heat exchanger network (HEN) has received considerable attention for improving heat recovery in industrial processes. In this work, HEN synthesis for multiperiod operation has been studied. Sequential and simultaneous approaches for multiperiod HEN design are proposed and compared by a case study. The most efficient method will be applied to a case study of crude distillation unit (CDU) where different kinds of crudes are used. The objective for both methods is to minimize total annualized cost (TAC) including capital cost and utility cost. The sequential approach consists of three steps. First, an MINLP superstructure-based model is used to generate an initial HEN for a chosen period. Then it will be adapted by NLP model to generate HENs which are fitted to other period conditions. Lastly, HENs for each period are integrated to obtain the multiperiod HEN design. By varying the chosen period in the first step with all periods, it will result in different multiperiod HEN candidates. The best one will be selected as the final solution for sequential method. For simultaneous approach, an MINLP simultaneous model takes into account all periods concurrently and solve at once. Maximum-area-per-period concept is used in area calculation. The results demonstrate that the simultaneous approach showed better performance than sequential approach. Thus, the simultaneous approach is then applied further to the industrial case study of crude preheat train in CDU to assure that the model can deal with larger problem. In this case, an initialization strategy has been carried out to find an initial feasible solution. It showed that the initialization technique can reduce computational time substantially. Moreover, the final solution of HEN will be validated by commercial process simulator, PRO/II, to affirm its feasibility in real process. 1. Introduction Energy demand has increased continuously and became more important worldwide issue in the last few decades. As well as other industries, the petroleum refinery industry encounters the similar crisis especially in crude distillation unit (CDU) which is one of the largest energy-consuming units in the refinery plant. Heat exchanger network synthesis (HENS) is a widely used technique to recover excess energy from heat source (hot process streams) and transfer to heat sink (cold process streams). This can help in reducing operating expenditure spent on utilities. In reality, the process streams may have variation in condition due to many causes such as changes in feed/product specifications, control failure, unstable environment, etc. Therefore, multiperiod heat exchanger network design is essential to apply in such processes to maintain feasible operation and plant flexibility over uncertain operating conditions. Many researchers have attempted to propose their algorithms to solve multiperiod problems. Aaltola (2002) proposed a simultaneous mixed-integer nonlinear programming (MINLP) model using mean area of different periods in objective function. A sequential decomposition technique relying on Lagrangean decomposition concept was proposed by Escobar et al. (2014). Pejpichestakul and Siemanond (2013) 200 adopted pinch design method to n-stage model sequentially and applied for retrofitting in crude preheat train. In this study, both sequential and simultaneous approaches for multiperiod problem are proposed based on stage model by Yee and Grossmann (1990). The two methods are compared by a simple case study and the best method will be applied with refinery case study of crude preheat train including initialization technique and validation procedures. 2. Methodology 2.1 Sequential approach For sequential approach, there are three steps in sequence as shown in Figure 1(a). First, one of all periods is chosen for synthesizing initial HEN by MINLP stage-wise superstructure model (Yee and Grossmann, 1990) for single period. Next, the initial HEN is adapted by nonlinear programming (NLP) model in order that it can be operable for each of other period conditions besides the chosen period in the first step. The strategy of the NLP model is to fix heat exchangers topology, and no allowance of addition and/or removal of any exchangers. However, areas of heat exchangers can be changed to satisfy heat balance. The objective function of this NLP model is sum of additional area required as illustrated in Eq(1). Finally, the initial HEN and the adapted HENs are integrated to be a multiperiod HEN. There will be different multiperiod HEN candidates which correspond to a chosen period in the first step. Total annualized cost (TAC) is considered as the decision variable for selecting the best multiperiod HEN design.      HPi CPj STk kjioldAreakjinewAreafunctionobjective )),,(_),,(_,0max(    CPj joldAreaHUjnewAreaHU ))(_)(_,0max(    CPi ioldAreaCUinewAreaCU ))(_)(_,0max( (1) Where HP and CP is a set of hot process stream i and cold process stream j, respectively. ST is a set of stage in the superstructure. 2.2 Simultaneous approach In this approach, multiperiod HEN is generated by multiperiod MINLP superstructure-based model. All process streams data are input into the model and solve simultaneously as shown in Figure 1(b). The isothermal mixing assumption is made. The maximum-area-per-period concept proposed by Verheyen and Zhang (2006) is used in area calculation. 2.3 Application for refinery case study One of two approaches which performs better is applied with refinery case study of crude preheat train to assure the performance of the model when dealing with larger problem. 2.4 Initialization technique In this step, an initialization technique is presented since the refinery case study is a large problem that requires more computational time. This technique can provide an initial feasible solution before solving for the real optimal solution. This can be done by executing mixed-integer linear programming (MILP) model which neglects the nonlinear terms of log mean temperature difference (LMTD) calculations. The average LMTD (ALMTD) is introduced to use instead of real LMTD. It is calculated by constructing composite curves for each period, calculating LMTD for every enthalpy intervals, and estimating the ALMTD by using Eq(2).   NN njiqnLMTDnjiqjiALMTD ),,(/)(),,(),( (2) Where i and j denotes hot and cold stream, respectively. The index n represents enthalpy interval while N is total number of intervals corresponding to the temperature range of match (i,j). 201 2.5 Validation by simulating on PRO/II The best result is validated by using the commercial simulation software, PRO/II. Crude distillation process is simulated and the optimal HEN is applied in crude preheat train. It is assumed that the correction factor (FT) is equal to 1 and flow direction is countercurrent. a) b) Figure 1: Algorithm of a) sequential and b) simultaneous approaches for multiperiod HEN synthesis 3. Case study 3.1 Simple case study The case study adapted from Verheyen and Zhang (2006) is used to demonstrate the performance of both sequential and simultaneous methods. The problem involves vacuum gas oil (VGO) hydrotreater unit of an oil refinery. It consists of three hot streams and four cold streams. There is a catalyst being used in the hydrotreating reactor and will gradually loss its activity as time passes. Thus the inlet temperature to reactor has to be increased in order to compensate the loss of reaction rate. This causes not only changes of inlet and outlet temperature of reactor, but also the effluent compositions (heat capacity flowrates). The operational periods are classified into three periods: start-of-run (SOR), mid-of-run (MOR), and end-of-run (EOR). The stream data of each period is shown in Table 1. Note that the time duration for each period is assumed to be equal. Table 1: Stream and economic data for simple case study Stream h (kW/m 2 .°C) SOR MOR EOR Tin (°C) Tout (°C) FCp (kW/°C) Tin (°C) Tout (°C) FCp (kW/°C) Tin (°C) Tout (°C) FCp (kW/°C) H1 2 393 60 201.6 406 60 205.0 420 60 208.5 H2 2 160 40 185.1 160 40 198.8 160 40 175.2 H3 2 354 60 137.4 362 60 136.4 360 60 134.1 C1 1.5 72 356 209.4 72 365 210.3 72 373 211.1 C2 1.5 62 210 141.6 62 210 141.0 62 210 140.5 C3 2 220 370 176.4 220 370 175.4 220 370 174.5 C4 2 253 284 294.4 250 290 318.7 249 286 271.2 Annualization factor = 0.2, Exchanger capital cost = 8,333.3 + 641.7*(Area in m 2 ), Hot utility cost = $115.2/kW, Cold utility cost = $1.3/kW Synthesize multiperiod HEN for every period using simultaneous MINLP stage model Start Input period P1, P2, … , Pn End Synthesize HEN for period Pi using MINLP stage model to generate HEN-i Do HEN adaptation by NLP model for period Pj where j≠i to generate HEN-i-j Do HEN Integration of HEN-I and set of HEN-i-j to generate muliperiod HEN-i candidate Start Choose period Pi End 202 Table 2: Stream and economic data for refinery case study Stream Light crude Medium crude Heavy crude FCp Tin Tout h FCp Tin Tout h FCp Tin Tout h kW/°C °C °C kW/m 2 .°C kW/°C °C °C kW/m 2 .°C kW/°C °C °C kW/m 2 .°C H1 121.02 201.17 104.44 1.293 125.28 198.28 104.44 1.092 132.07 193.31 104.44 1.075 H2 69.91 274.71 148.89 1.318 71.80 271.63 148.89 1.235 74.03 267.77 148.89 1.221 H3 98.60 321.17 232.22 1.298 101.36 319.12 232.22 1.270 104.43 316.69 232.22 1.270 H4 105.22 32.22 30.00 1.058 91.92 32.22 30.00 1.253 70.57 32.22 30.00 1.309 H5 67.76 234.40 30.00 1.395 56.28 225.57 30.00 1.394 46.81 221.36 30.00 1.393 H6 49.64 273.17 30.00 1.423 34.77 269.78 30.00 1.431 29.33 263.57 30.00 1.438 H7 59.98 326.40 30.00 1.343 41.91 326.26 30.00 1.413 32.46 322.00 30.00 1.419 H8 135.33 341.73 30.00 0.892 210.12 357.39 30.00 0.888 268.65 353.52 30.00 0.826 C1 380.57 25.00 125.00 0.654 387.57 25.00 125.00 0.652 392.24 25.00 125.00 0.651 C2 434.32 125.00 170.00 0.632 443.70 125.00 170.00 0.630 449.76 125.00 170.00 0.630 C3 585.63 166.64 370.00 0.788 587.80 168.84 370.00 0.782 555.77 167.81 370.00 0.780 Exchanger capital cost = 26,460 + 389*(Area in m 2 ), Hot utility cost = $134/kW, Cold utility cost = $6.7/kW 3.2 Refinery case study A crude refinery process is simulated using PRO/II feeding three different types of crude, i.e., light, medium and heavy. Therefore, there are three periods operating 100, 150, and 100 days per year for each crude, respectively. Due to the different compositions of crudes, the design parameters such as temperatures and heat capacity flowrates are varied. The stream data are extracted as presented in Table 2. The problem consists of eight hot streams and three cold streams. Hereby, the average heat capacity flowrates are used and assumed to be constant for each stream. The project life time of 5 years is assumed with 10 % annual interest. 4. Results and discussion The mathematical model was implemented on GAMS 21.4 with DICOPT2x-C (CONOPT3 and CPLEX 9.0) as MINLP solver. The computer platform is a Lenovo Y450 with Intel® Core 2 Duo T6400 CPU at 2.0 GHz. Table 3 shows the comparison of the results between sequential and simultaneous approaches. Grid diagrams of each method are shown in Figure 2 and 3. It can be seen that the simultaneous approach generates HEN design better than the sequential approach as it has the lower TAC. This is because the solution obtained from the sequential approach might fall in sub-optimal solution since there were several optimizing steps, while the simultaneous method solved the problem at a time. Furthermore, the result of simultaneous method has less complexity than another one because there is no stream splitting. Table 3: Summary result of sequential and simultaneous approaches from case study Parameter Sequential approach Simultaneous approach No. of heat exchangers 10 10 Total area (m 2 ) 6,894 6,900 Fixed cost ($/yr) 16,667 16,667 Area cost ($/yr) 884,840 885,515 Utility cost ($/yr) 1,831,833 1,811,172 TAC ($/yr) 2,733,340 2,713,354 Table 4: Summary result of HEN with and without initialization for refinery case study Parameter Without initialization With initialization No. of heat exchangers 29 25 Total area (m 2 ) 15,029 16,079 Fixed cost ($/yr) 202,578 174,636 Area cost ($/yr) 1,543,422 1,651,209 Utility cost ($/yr) 7,395,913 7,304,782 TAC ($/yr) 9,141,913 9,130,627 203 H1 H3 H2 C1 C3 C2 C4 2 2 1 3 5 5 CU1 CU2 CU3 HU2 HU1 41 3 4 7 6 7 .0 m 2 7 4 9 .6 m 2 2 1 4 .1 m 2 2 5 9 6 .9 m 2 1 4 1 6 .2 m 2 153.3 m 2 197.4 m 2 183.9 m 2 74.7 m 2 541.4 m 2 Q(kW ) Period 1 Period 2 Period 3 CU1 5,070.5 5,555.4 5,654.3 CU2 22,212. 0 23,856. 0 21,024. 0 CU3 2,566.3 2,550.5 2,124.2 HU1 6,533.7 8,991.3 4,169.8 HU2 9,587.5 8,535.7 8,863.2 Figure 2: Grid diagram of HEN from sequential approach H1 H3 H2 C1 C3 C2 C4 3 3 1 2 4 4 CU1 CU2 CU3 HU1 HU2 5 1 2 5 1 0 0 1 .2 m 2 3 4 .8 m 2 3 6 7 1 .4 m 2 3 0 6 .3 m 2 167.4 m 2 74.4 m 2 177.0 m 2 224.8 m 2 414.4 m 2 8 2 7 .9 m 2 Q(kW) Period 1 Period 2 Period 3 CU1 5,228.6 5,747.5 6,332.7 CU2 12,510.3 14,019.5 11,476.8 CU3 11,705.3 11,800.6 11,260.0 HU1 9,024.8 7,949.3 8,451.8 HU2 6,691.8 9,183.4 4,848.2 Figure 3: Grid diagram of HEN from simultaneous approach Based on the comparison of two methods, the simultaneous approach was selected to apply with the refinery case study in order to ensure its performance when dealing with larger problem. It was found that the simultaneous model needed significant amount of time to solve the refinery case. Therefore, an initialization technique was adopted to help reduce the computational time. After using the initialization technique, the computational time decreased substantially by over 70 %. Moreover, from Table 4, the obtained solution was more preferable than that without initialization. Finally, simulation of the best HEN design was carried out by using PRO/II to see its functionality in the real process. It was found that some modification had to be made because the outlet temperature of the process streams, which do not have utility exchangers installed at the end, did not reach the desire temperatures. Hence, some exchanger areas had to be changed and one utility exchanger was added in the process. The final applicable HEN is illustrated in Figure 4. 204 H1 H3 H2 C3 C2 C4 CU1 HU1 8 9 5 .1 m 2 33.2 m 2 1669.1 m 2 H4 H5 H7 H8 H6 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 CU2 109.1 m 2 CU3 647.7 m 2 2 3 4 .5 m 2 1 8 5 6 .7 m 2 4 8 6 .6 m 2 2 0 6 .9 m 2 2 1 0 .1 m 2 2 0 4 .1 m 2 1 4 6 3 .6 m 2 1 3 0 .2 m 2 5 3 .2 m 2 1 2 4 .1 m 2 9 0 1 .8 m 2 3 4 4 .6 m 2 3 5 7 .5 m 2 1 7 2 .5 m 2 5 7 7 .4 m 2 3 0 2 .1 m 2 6 1 4 .1 m 2 7 5 6 .4 m 2 7 9 5 .1 m 2 1 5 9 5 .7 m 2 CU1 33.2 m 2 Figure 4: Grid diagram of validated HEN from simultaneous method with initialization for crude refinery process 5. Conclusions In this study, the sequential and simultaneous methods have been developed for multiperiod HEN synthesis. The three-step sequential method composes of HEN synthesis, HEN adaptation, and HEN integration. The simultaneous approach is carried out using simultaneous MINLP model for multiperiod which solves in one step. It has been shown in this work that the simultaneous approach can perform better than the three-step sequential approach by giving lower TAC. Moreover, the simultaneous MINLP model is quite rigorous since no initial feasible solution is needed for both of two case studies. But, as the problem size increases, the computational time required is also increased substantially. An initialization technique is hence applied to find an initial feasible solution. This can help reduce the time resource; moreover, it can improve the solution of HEN design. Acknowledgement The authors would like to express our sincere thank to The Petroleum and Petrochemical College and Ratchadaphiseksomphot Endowment Fund for technical and financial support. References Aaltola J., 2002. Simultaneous synthesis of flexible heat exchanger network. Applied Thermal Engineering, 22(8), 907-918. Escobar M., Trierweiler J.O., Grossmann I.E., 2014. 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