Feasibility study of heat-integrated distillation columns using rigorous optimization

Energy xxx (2014) 1e13

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Feasibility study of heat-integrated distillation columns using rigorous optimization Hossein Shahandeh a, Javad Ivakpour b, Norollah Kasiri a, * a

Computer Aided Process Engineering (CAPE) Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran b Petroleum Refining Technology Division, Research Institute of Petroleum Industry, Tehran 1485733111, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 January 2014 Received in revised form 2 July 2014 Accepted 9 July 2014 Available online xxx

In this work, rigorous optimization of HIDiC (Heat-Integrated Distillation Column) and VRC (Vapor Recompression Column) is implemented by GA (Genetic Algorithm) to find an alternative for CDiC (Conventional Distillation Column). The objective function is TAC (Total Annual Cost). Three different case studies are investigated, being composed of benzene-toluene, propane-propylene, and methanol-water. A novel strategy is proposed to consider all the heat integration possibilities resulting in more efficient search space than our previous attempt. It is observed that the heat exchangers arrangement of optimum HIDiCs are very similar to VRCs in ideal case studies. Although CDiC is the optimum configuration in the benzene-toluene separation, 6.6% reduction is achieved for the presented HIDiC compared to previous work. For propane-propylene splitter, VRC is the economical alternative with a 44.1% decrease in the TAC of CDiC. Moreover, VRC and HIDiC optimizations leads to 25.5% and 4.4% reductions in TAC compared to previous work, respectively. However, for the non-ideal methanol-water separation, which has a wide boiling point range, the TAC of optimum HIDiC is surprisingly lower than CDiC and optimum VRC by 3.4% and 31.2%, respectively. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Genetic algorithm Heat exchangers arrangement Heat-integrated distillation column Optimization Vapor recompression column

1. Introduction Distillation is the most widely used separation process in chemical industries. In an industrial plant, the distillation process consumes 40e70% of operating costs and capital investment [1]. Low efficiency of CDiCs (Conventional Distillation Columns) and the global warming have urged companies and governments to find an alternative technology which demands less energy. Since elimination of distillation process from industries is impossible in our modern and competitive world, researchers have focused on finding new effective technologies in the view of thermodynamic and economic. To do so, many heat-integrated configurations have been introduced since 1950s as alternatives. A number of these configurations like VRC (Vapor Recompression Column), DWC (Divided-Wall Column), and petlyuk column have been successfully commercialized and their industrial applications are growing constantly [2].

* Corresponding author. Fax: þ9821 77490416. E-mail addresses: [email protected] (H. Shahandeh), ivakpourj@ ripi.ir (J. Ivakpour), [email protected] (N. Kasiri).

One of the latest configurations in this field is HIDiC (Heat-Integrated Distillation Column) which is a combination of VRC and diabatic distillation columns. Initially, Mah et al. presented HIDiC as SRV (Secondary Reflux and Vaporization) and specifications of an appropriate distillation process in which HIDiC can outperform CDiC [3]. It was also reported that HIDiCs have less entropy production compared to CDiCs [4]. Ever since, many experimental, simulation, and optimization studies have been conducted on HIDiCs and they have been compared with VRCs and CDiCs. There are comprehensive reviews by Nakaiwa et al. [5], Jana [2], Shenvi et al. [6], and Kiss et al. [7]. Simplified schematic diagrams of VRC and HIDiC are shown in Fig. 1. By compressing the overhead vapor of column, this stream is able to be the heating source of the heat-integrated reboiler/ condenser in VRCs (see Fig. 1(A)). There is a rise in temperature profile across distillation columns from the top to the bottom; therefore, the compressor pressure ratio must be high enough for the desired direction of heat transfer. Available latent heat of the high-pressure stream is usually more than required duty in the heat-integrated heat exchanger. Utilizing cooling water, this additional heat can be absorbed in order to entirely condensate the high-pressure stream.

http://dx.doi.org/10.1016/j.energy.2014.07.032 0360-5442/© 2014 Elsevier Ltd. All rights reserved.

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Nomenclature CDiC CoD DWC GA HIDiC LMTD MILP MINLP n N NLP NRTL P PCD Q r RCD ReD

conventional distillation column compressor duty (kW) divided-wall column genetic algorithm heat-integrated distillation column logarithmic mean temperature difference ( C) mixed integer linear programming mixed integer non-linear programming last tray of distillation column number of trays non-linear programming non-random two-liquid pressure (kPa) product condenser duty (kW) heat duty (kW) number of trays in the rectifying section reflux condenser duty (kW) reboiler duty (kW)

On the other hand, by dividing a distillation column into its rectifier and stripper sections and increasing the rectifier operating pressure, transferring heat from the rectifier to the stripper will be feasible (see Fig. 1(B)). As a result, the whole column sections can be applied to heat integration, and there will be also more options for installation of heat-integrated heat exchangers. Furthermore, lower pressure ratio is required to run HIDiCs compared to VRCs, for the same case study due to having more suitable position for the compressor. Under these conditions, HIDiCs are expected to be the most efficient candidate. It should be noted that recycling of the high-pressure stream to the low-pressure column is possible only by passing it through a throttling valve in both VRCs and HIDiCs. It is possible that the heat integration leads to complete elimination of condenser and reboiler in steady-state condition referred to as ideal HIDiC [8,9]. If heat integration leads to elimination of only one or none of them, the structure would be called partial HIDiC [8,9]. Some Researchers have focused on the internal heat integration of trayed HIDiC in their experiments and simulation studies [9e13]. Gadalla used thermo-hydraulic analysis for internal HIDiC

s SQP SRK SRV T TAC VRC

number of trays in the stripping section sequential quadratic programming soave-redlich-kwong secondary reflux and vaporization temperature ( C) total annual cost ($ yr1) vapor recompression column

Greek letter a number of heat-integrated heat exchangers (integer variable) b heat exchangers arrangement matrix g heat exchangers heat load distribution matrix Subscripts i tray counter j coupled heat exchanger counter r the rectifying section s the stripping section T Total

simulation for the first time [14,15]. In the thermodynamic analysis part of his study, temperature profiles of the rectifying and stripping sections were checked to have enough heat transfer driving force in each heat panel. In the hydraulic analysis part of his study, physical limitations of each heat-integrated tray were checked, consisting of their dimensions and maximum available heat transfer area in each tray and each section. Heat panels will be then installed in either the rectifier or the stripper depending on space availability. It was also reported that it is preferred to limit the heat integration to trays with higher temperature differences [14]. On the other hand, some researchers have focused on the internal heat integration of packed HIDiC in their experiments [16e19], while they have considered trayed HIDiCs in their simulation studies [8,20]. Their efforts have been led to a pilot plant HIDiC with a 27 m height and 1.4 m diameter column [18]. It has been recently shown that construction of external HIDiCs is much easier and they are comparatively more energy efficient than their internal counterparts [6,21e24]. External HIDiCs do not require expensive heat panels with physical limitations, and there

Fig. 1. Schematic diagram of a VRC (A) and a HIDiC (B).

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is also no need to put the rectifier into the stripper in an annular form. Moreover, using external HIDiCs leads to a smaller number of heat exchangers with larger heat transfer areas. Chen et al. introduced a trial and error procedure for the heat exchangers arrangement of ideal HIDiC [22]. They claimed that three heat exchangers would be adequate for having external HIDiCs with approximate positions of top, middle, and bottom of the two sections. A new methodology was also proposed for assignment of heat exchangers location based on the temperature profiles of column sections [6]. Some rigorous optimization procedures have also been proposed to find the best configuration and operating conditions of external HIDiCs. Suphanit investigated optimization of the propane-propylene separation with different objective functions [23]. In his work, only continuous variables (compressor pressure ratio and heat distribution) were considered, and SQP (Sequential Quadratic Programming) was selected to solve the existing NLP (Non-Linear Programming) problem. In another work, separation of binary, multicomponent, and non-ideal mixtures studied with a new design methodology based on superstructure, mixed-integer optimization with rigorous thermodynamic modeling [24]. By taking into account various type of variables and also different objective functions, it was reported that VRCs are more effective and economical comparing to HIDiCs. However, the MINLP (Mixed Integer Non-Linear Programming) Problem was simplified into NLP problem in the mentioned study [24]. A new three-level procedure was then presented using MILP (Mixed Integer Linear Programming) for separation of an ideal ternary mixture [25]:

exchangers, three examples are studied as case studies in the present work. Separation specifications of both benzene-toluene and propane-propylene are adapted from Suphanit's works [21,23], and are taken from Gadalla's investigation for methanol-water [15]. Specifications of each case study, consisting of feed characteristics, products purity, number of equilibrium stages in each column section, operating conditions, and equipment duties are briefly reported in Table 1. To meet the minimum TAC, an HIDiC with the uniform heat transfer scenario was recommended for the benzene-toluene separation [21], and rigorous optimization procedure was carried out for propane-propylene splitter [23]. In both ideal cases, the external heat integration led to elimination of reboiler, which is more costly compared to condenser. In contrast to the first two case studies, the methanol-water mixture is a nonideal mixture which was only studied once with internal HIDiC [15]. However, Gadalla only compared energy consumption of all equipment and the required heat transfer area of each heat integration candidate. The type of heat integration is another difference between the methanol-water case and the other cases (benzenetoluene and propane-propylene). Applying internal heat integration in the methanol-water separation requires 24 heat exchangers due to installing limitations. On the other hand, the benzenetoluene and propane-propylene separations can easily operate with only 2 heat exchangers by external heat integration. In addition, neither reboiler nor condenser is omitted in the methanolwater case.

1. The optimal design and operation conditions of distillation sequences were found without any heat integration. 2. The optimal heat-integrated heat exchangers arrangement was determined by solving the formulated MILP problem. 3. A new MILP problem was then solved considering additional heat integration between reboiler and condenser of columns with different pressure with a superstructure representation.

Modeling and simulation of VRCs and HIDiCs were discussed elaborately in our previous work [26]. The developed simulation algorithm is validated using the optimum results from Suphanit [23]. All necessary formulations and economic constants are adapted from the same works [12,21,23]. It must be noted that only propane-propylene splitter results are chosen for validation due to unavailability of some reported information on operating conditions of the benzene-toluene and methanol-water case studies. For instance, only location of the heat exchangers (1st and 16th trays), compressor pressure ratio (1.88), and TAC ($342,320/yr) were reported for the benzene-toluene case [21]. According to Table 2, there is a good agreement among results of the proposed model and reference with the maximum error of 5.3% for the total amount

In the most recent study about rigorous optimization of both internal and external HIDiCs GA (Genetic Algorithm) was used as a stochastic method for the benzene-toluene separation [26]. In our previous work, a new integer variable was presented (Layout number) for the first time in order to increase the number of heat integration options. However, Layout number did not consider all the heat integration possibilities. When TAC (Total Annual Cost) of both internal and external configurations was improved compared to previous work, external HIDiC was found more economical than the internal one. It still seems necessary to propose a systematic procedure for consideration of all the possible options for arrangement of coupled heat exchangers without any simplification during optimization. All aforementioned investigations have shown that arrangement of heat-integrated heat exchangers is as important as compressor pressure ratio. Hence, a novel method is proposed here in order to consider all heat integration possibilities in HIDiCs. Genetic algorithm is then developed and used for systematic optimization of HIDiCs and VRCs. TAC is chosen as the objective function, and the optimum results are also compared with previous attempts. To reach general results, benzene-toluene [21], propane-propylene [23], and methanol-water [15] mixtures are chosen as the case studies by adapting required data from the references. 2. Case studies In order to extensively demonstrate the capabilities of GA and also our new method for arrangement of heat-integrated heat

3. Validation

Table 1 Specifications of HIDiC for three case studies. Characteristic

Benzenetoluene [21]

Propanepropylene [23]

Methanolwater [15]

Feed flow rate (kg/h) Feed temperature ( C) Composition of volatile component in feed (%mol) Purity of volatile component in top product (%mol) Purity of volatile component in bottom product (%mol) Number of stages in rectifying section Number of stages in stripping section Pressure drop per stage (kPa) Compressor inlet pressure (kPa) Compressor outlet pressure (kPa) Reboiler Condenser Heat integration category Number of heat-integrated heat exchangers

8512.5 94 50

112,000 27.23 52

76,000 94 67.4

99.5

99.6

99.9

0.5

1.1

0.1

16

171

65

16

49

30

0 100 188 omitted existed external 2

0.62 1120 1562.5 omitted existed external 2

1.3 120 260 existed existed internal 24

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Table 2 Validation of applied modeling and simulation procedures. (* Not mentioned in Ref. [23]). Optimum parameters

Propanepropylene [23]

Propanepropylene

Error (%)

Vapor through compressor (kmol/h) Total heat-integrated heat exchanger area (m2) Total amount of heat integration (MW) Compressor duty (MW) Reboiler duty (MW) Condenser duty (MW) Utility cost (million$/yr) Capital cost (million$) TAC (million$/yr)

24,432

25,633

4.9

28,787

29,356

2.9

82

86.83

5.3

6.277 0 e* 5.218 35.67 10.30

6.591 0 9.692 5.273 34.13 10.14

0.7 e e 1.0 4.3 1.6

of heat integration. The positive existing errors between the present results and those of Suphanit can be justified with the following differences: 1. While our simulation procedure is based on NewtoneRaphson method, the Aspen Plus software, which was used in the Suphanit's work, applies Inside-Out method for simulation [23]. 2. Different diameter calculation procedure may also be effective for the existing errors in cost indices, whereas constant coefficients are the same as Suphanit's work [23]. Default sizing procedure of Aspen Plus is the Fair tray flooding correlation, but Smith's offered method [27] is used here. The reason is that it was reported that the Fair tray flooding correlation is not an accurate method for the propane-propylene case [12]. 3. Due to unavailability of some reference's coefficients and constants for simulation and economic analysis, we had to tune our own values which seemed more appropriate. 4. Optimization Fig. 2 shows temperature profile of CDiC in all three case studies. According to this figure, there is a different trend, circled by dashed line, in temperature profile of the methanol-water case. A line with small slope in temperature profile of CDiCs means that some of trays are additional. As illustrated in Fig. 3, this discrepancy can be justified by separate optimization of number of trays in the stripper (Fig. 3(A)) and the rectifier (Fig. 3(B)) of CDiC. Despite the fact that number of trays in the stripping section was assumed 30 in Gadalla's work [15], 8 is found to be the optimum for the number of trays in this study. As a result, number of trays in the stripper is reduced to 8 in the rest of our work. 4.1. Optimization procedure Finding the optimum heat pump-assisted configuration (e.g. VRC and HIDiC) as an alternative for CDiCs is the main purpose of this investigation. It consists of two connected parts: (1) simulator, and (2) optimizer. The simulator is programmed based on modified NewtoneRaphson method in order to solve all distillation configurations (e.g. CDiC, VRC, and HIDiC) [26]. It is composed of (i) modeling of each specific equipment such as distillation column(s), compressor, and throttling valve [26], (ii) cost analysis formulations such as capital cost, utility costs, and TAC [12], and (iii) a constraint of having positive temperature difference in each heat exchanger [26]. Top and bottom purities of these columns are specified to make degree of freedom zero. A suitable initial guess helps the solution

Fig. 2. Temperature profile of CDiC for benzene-toluene (A), propane-propylene (B), and methanol-water (C).

algorithm to have less trial and error iterations and hence less computational cost. Adapted and extended McCabe-Thiele method is used for this [28]. While SRK (Soave-Redlich-Kwong) and PengeRobinson equations of state are employed to evaluate thermodynamic properties of benzene-toluene and propane-propylene mixtures, respectively, NRTL (non-random two-liquid) activity coefficient model and SRK equation of state are selected for the methanol-water mixture. Furthermore, a flexible procedure about

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Fig. 3. Number of trays optimization in CDiC for the methanol-water separation in the stripper (A) and rectifier (B).

variations of temperature and pressure is used for column diameter calculation [27]. On the other hand, GA is implemented for optimization of heatintegrated configurations like our previous work [26]. In each generation, the simulator receives a set of variables from GA. After simulation of whole process, diameter of column(s) is/are calculated according to the liquid and vapor flow rates, temperature, and pressure profiles. Afterwards, economic analysis is carried out by importing of (i) temperature profiles, (ii) diameter of column(s), (iii) and reboiler, condenser, compressor, and coupled heat exchanger duties. For the next generation, information of previous generations is used to produce a new one. In this paper, the condenser duty is divided into RCD (Reflux Condenser Duty) and PCD (Product Condenser Duty) [26]. For each case study, RCD, PCD, ReD (Reboiler Duty), and CoD (Compressor Duty) of non-heat-integrated HIDiC (a HIDiC configuration in which removing and adding heat loads have not been taken into account yet) are reported in Table 3. It indicates that the reboiler is the limiting device in the benzene-toluene and propane-propylene cases, while the limiting device in the methanol-water case is the condenser. Some changes should be considered in the optimization program depending on whether condenser or reboiler is the heat integration restriction. Therefore, the reboiler is taken into account as the last tray of the stripper for being able of heat integration in the first and second cases. Despite this, the condenser is considered as the first tray of the rectifier for the same reason in the third case. Fig. 4 shows three different zones for adding/removing duties in both sections to satisfy this concern. While the zones 1 and 3 are for paired heat exchanger, the zone 2 belongs to the reboiler and condenser for utilizing steam and cooling water, respectively. Although HIDiCs can use any zone, VRCs are only allowed to employ the first and second zones. Maximum magnitude of heat load in the zone 1 can omit the reboiler (Fig. 4(A)) or condenser (Fig. 4(B)), and a value larger than that makes the simulation algorithm diverged because the products purity is already fixed. Heat loads summation in the zone 3 also should not exceed than a value which completely removes the ReD (Fig. 4(A)) or RCD (Fig. 4(B)). The optimization program hence must be developed in a way that prevents divergence.

4.2. Objective function To show advantages of genetic algorithm as an optimizer method and our new heat exchangers arrangement method, the optimum results should be compared with the previous works for the same problem [21,23]. Hence, the same objective function, formulations, and constants are considered here. The objective function of this study is TAC, which is combination of capital and utility costs. 7% interest rate, 10-year equipment lifetime, and 8000 annual equipment working life are implemented for calculation of TAC. These values are the same as stated in the references to enable a fair comparison among the previous and present findings [12,21,23]. The details of GA implementation in the optimization problems of the current case studies is the same as that represented in our previous work [26], except that our new coupled heat exchanger arrangement does not used Layout number anymore. 4.3. Variables  Compression Ratio. The first variable is compressor pressure ratio. The lower bound of the pressure ratio is 1 for all three cases, but the upper one is dependent on the mixture features. Since the boiling point difference is relatively small for the benzenetoluene and propane-propylene mixtures, the pressure ratio of 3 seems to be adequately high as the upper bound. Because of the large difference between boiling point of methanol and water, the value of the upper bound is considered to be 7.  Number of Heat Exchangers (a). The abovementioned continuous variable is the only variable of VRCs during optimization, while HIDiCs have more variables consisting of number, location, and duty of heat exchangers. Upper and lower bounds are required for the number of heat-integrated heat exchangers during HIDiCs optimization. At least one coupled heat exchanger is necessary to ensure the existence of heat integration. Moreover, the larger the number of heat exchangers, the less economical the HIDiCs will be [6,21,23,24,26]. In the present study, it is thus assumed that maximum number of heat exchangers is less than or equal to five, which is even larger than the previously proposed numbers [6,21,23,24,26].

1a5

Table 3 Equipment duties of the non-heat-integrated HIDiC. Parameter

Benzene-toluene

Propane-propylene

Methanol-water

Pressure ratio ReD (kW) RCD (kW) PCD (kW) CoD (kW)

2.5 948.8 954.1 406.9 169.7

1.4 74,829.7 78,855.3 5002.6 5789.1

2 31,996.5 17,625.6 17,934.6 2757.9

(1)

 Heat Exchangers Location. Despite Layout number, which only uses horizontal line style for heat integration between the rectifier and stripper [26], any given tray of each section can be heat-integrated with any tray of other section in our new heat exchanger arrangement method. Moreover, Not only is coupling of each tray of stripper and rectifier now feasible, but heat-

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Fig. 4. Three different zones for heat exchanger locating in the stripper (A) and rectifier (B).

integrated heat exchanger can be located as the condenser in the rectifier and as the reboiler in the stripper. For instance, if the number of trays in the stripper and rectifier is 2 and 5, there will be 18 (¼ (2 þ 1)$(5 þ 1)) options for heat integration during placement of the first heat exchanger (Fig. 5). However, only 8 options would be feasible using Layout number. Having determined location of the first heat-integrated heat exchanger, the second one may be placed on any of the remaining

positions. This procedure continues until the last heat exchanger is located. To this aim, a one-dimensional matrix (b) should be produced when its length is equal to the number of heat exchangers (a) for each section. Each parameter in the matrix is a variable between 0 and 1. Location of the first heat exchanger is the nearest integer value to that evaluated from (number of trays-1) b1þ0.5. To avoid reaching the zero number because of rounding values less than 0.5, a constant value of 0.5 is added to the result of multiplication before rounding. Afterwards, location of the second heat exchanger is

Fig. 5. Every possibility of heat integration when Ns ¼ 3 and Nr ¼ 6 in HIDiCs.

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determined by b2, but the number of trays will be less than the previous value by 1. The reason is that the tray associated with the first heat exchanger should be excluded from more heat integration. This procedure will continue until determination of the last coupled heat exchanger. A comprehensive example of abovementioned procedure is illustrated in Fig. 6.  Heat Exchangers Duty. After placement of all heat exchangers, assignment of their heat duties is the next step. It is observed that it is more efficient if the total amount of heat integration (QT) and its distribution among the heat exchangers are considered as the set of variables. The unit of QT is MW, and a matrix of variables (g) with the length of number of heat exchangers (a) is used for its distribution. Members of g matrix can also vary between 0 and 1. It should be highlighted that variables of g matrix should be normalized in order to fairly distribute all the total amount of heat integration. For instance, if

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QT is 100 MW and g matrix is [0.1 0.2 0.3], the normalized g matrix will be [0.17 0.33 0.5]. As a result, heat exchangers duty will be 17, 33, 50 MW.

4.4. Constraint As mentioned before, both VRC and HIDiC configurations need a constraint to impose the positive temperature approach on optimizer:

0  Tr;j  Ts;j

(2)

where Tr,j is temperature of the vapor stream from the rectifier entering into the jth heat-integrated heat exchanger, and Ts,j is temperature of the liquid stream from the stripper entering into the jth heat-integrated heat exchanger.

Fig. 6. Heat exchanger arrangement when Nr ¼ 10, Ns ¼ 10, br ¼ [0.9 0.1 0.1 0.7], and bs ¼ [0.8 0 0.3 0.4].

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4.5. Computational time When desktop computer hardware (Intel@ Core™ i3 CPU M330 @ 2.13 GHz, 4 GB RAM) is used for optimization similar to our previous study [26], the computational time is larger here. Although VRC optimization takes only 1 h for the benzene-toluene separation, GA requires 10 h (2 h larger than the previous work [26]) for optimization of HIDiC owing to consideration of all heat integration possibilities. For the propane-propylene separation, whose column(s) has/have the greatest number of trays, VRC and HIDiC optimizations have computational time of 2 h and 24 h, respectively. It also takes 1.5 h and 14 h to optimize VRC and HIDiC structures for the methanol-water separation. Since number of variables and search zones were increased in this study, using short versions of MINLP problems (i.e. NLP and MILP) would not guarantee the global optimization; therefore, long computational time of optimization by GA can be acceptable.

Table 4 Comparison of different configurations for benzene-toluene separation. Parameters

HIDiC [21]

HIDiC

VRC

CDiC

Heat exchangers location in the rectifying Heat exchangers location in the stripping Vapor through compressor (kmol/h) Compressor outlet pressure (kPa) Minimum LMTD ( C) Compressor duty (kW) Condenser duty (kW) Reboiler duty (kW) Total heat integration (kW) Total heat-integrated heat exchanger area (m2) Utility cost ($/yr) Capital cost ($) TAC ($/yr)

1, 16

1

e

e

1, 16

16

e

e

242.3

158.3

164.6

e

188

255

241

e

6.0 178.2 433.3 e 1708.2 278.2

4.13 173.9 417.7 e 948.7 229.7

4.0 163.5 414.5 e 955.8 240.1

e e 1271.0 955.7 e e

149,027 1,513,971 364,582

144,400 1,377,733 340,558

136,968 1,240,807 313,631

187,687 445,975 251,184

5. Results and discussions In this section, results from TAC minimization of the three aforementioned case studies are presented and discussed, when CDiC, VRC, and HIDiC are the studied configurations. Reported results for VRCs and HIDiCs are based on genetic algorithm optimization. By comparing the previous optimum configurations and the results obtained here, effectiveness of GA and new coupled heat exchanger arrangement method is investigated too. 5.1. Benzene-toluene separation Optimization of the benzene-toluene separation is carried out first. Although we did previously accomplish optimization of this example by GA [26], it is studied again because of new and different heat integration arrangement presented in Section 4. Before minimization, the optimum configuration recommended by Suphanit is simulated and its cost indices are evaluated. While the TAC was reported to equal $342,320/yr in the reference, by using a different distillation simulation procedure and column diameter calculation, and considering some unmentioned constants in the reference (such as reboiler and condenser temperature approaches), simulation leads to a negligible amount of 6.5% error ($364,582/yr). External HIDiC and VRC are then optimized using GA, and optimum results of them are reported in Table 4. Moreover, the separation task is also evaluated using CDiC configuration in order to carry out more general comparison. While schematic diagrams of CDiC, optimum VRC, and optimum HIDiC are sketched in Fig. 7, cost indices (capital and utility costs and TAC) of them are shown beside of Suphanit results in Fig. 8. Despite the significant difference between the two recommended HIDiC configurations in the view of heat exchangers arrangement, Fig. 8 indicates only slight decrease of 6.6% for the TAC of the recommended configuration. As shown in Fig. 7(C), only one coupled heat exchanger, between the first stage of the rectifier (from the zone 3 of Fig. 4(B)) and the last stage of the stripper (from the zone 1 of Fig. 4(A)), is required in the optimum structure. According to Table 4, although this arrangement has less total heat integration and heat transfer area, it demands 35.6% higher compressor pressure ratio in order to generate a positive LMTD (Logarithmic Mean Temperature Difference). Surprisingly, the compressor shaft work is reduced by 3.0% because of the smaller amount of vapor flowing through the compressor (34.7%). The less vapor flow rate, therefore, can compensate the negative effects of the new suggested heat exchangers arrangement especially on the compressor work. It should be highlighted that the optimum HIDiC structure is as the same as our previous work, even though method

of coupled heat exchanger placement is quite different [26]. However, there are slight differences among their operating conditions and their economic analysis. The reason is that GA is a stochastic optimization method, and two consecutive runs of it do not necessarily result in the similar solutions (even with the same first guess). Looking more closely, the HIDiC configuration recommended here is very similar to the VRC configuration in term of paired heat exchangers location, and the only difference is in the compressors location (see Fig. 7(B) and (C)). According to Table 4, the obtained results demonstrate economic superiorities of VRC and CDiC over HIDiC. The TAC of HIDiC is more by 8.6% compared to VRC, which is itself more expensive than CDiC by 24.9%. The TAC of HIDiC is higher than VRC because of; (1) more capital and utility costs due to larger compressor pressure ratio, (2) more capital costs for having two separate columns, and (3) multiplication of the stripper capital cost by 1.5 [21,23]. On the other hand, the main cost difference between VRC and CDiC is due to compressor and electricity requirements of VRC. This obviously means that HIDiC and VRC configurations would be economical for more difficult separation tasks like mixtures with close boiling points. As benzene and toluene have an approximately large boiling point difference of 30.5 C (¼110.6e80.1), the stated conclusion is somehow predictable. Other advantages of the CDiCs are their less construction and control costs. 5.2. Propane-propylene separation The propane-propylene splitter has all the features that make heat-integrated configurations (i.e. HIDiCs and VRCs) more economical than CDiCs. The difference between the boiling point of propane and propylene is very small (42.10  (47.75) ¼ 5.65 C) and heat duties of reboiler and condenser are very large. Operating conditions of an industrial VRC and optimum HIDiC, recommended by Suphanit, are reported in Table 5 [23]. While the TAC of VRC and HIDiC were previously evaluated and reported as 11.61 and 10.30 million$/yr [23], respectively, simulation and economic analysis of these two configurations for the same operating conditions are accomplished with small errors. According to Table 5, these values are being different from those reported in the reference with only 2.8% and 1.6% errors, respectively. Simulation of CDiC and optimization of heat-integrated distillation columns are then carried out for the same separation task from the reference [23]. It should be mentioned here that all

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Fig. 7. Schematic diagram of CDiC (A), optimal VRC (B), and optimal HIDiC (C) for the benzene-toluene separation.

H. Shahandeh et al. / Energy xxx (2014) 1e13

9

columns include 171 trays in the rectifier and 62 trays in the stripper as illustrated in Table 5, except for one of the reference work in which the stripping section of the HIDiC has 49 trays. GA is successfully used for finding better operating conditions for both HIDiC and VRC compared to the previous study. Diagrams of CDiC, optimum VRC, and optimum HIDiC are schematically presented in Fig. 9. By providing more options for heat integration, search zone expansion leads to economic improvements of 4.4% reduction on the TAC of HIDiC compared to Suphanit's work. Not only does the presented optimum HIDiC require only one heat exchanger (one less than the previous work), but its position is quite different (Fig. 9(C)). Like the benzene-toluene separation, the first stage of the rectifier (from the zone 3 of Fig. 4(B)) and the last stage of the stripper (from the zone 1 of Fig. 4(A)) are chosen for the optimum HIDiC. Therefore, the optimal heat exchangers arrangement in HIDiC is similar to VRC, but not the compressor position and number of columns (Fig. 9(B) and (C)). Based on Table 5, the compressor shaft work is decreased up to 12.1% mainly because of 13.1% reduction in vapor flow rate passing through it like the previous case. It should be noted here that this reduction is achieved when the pressure ratio is even 1.4% higher than the Suphanit's work. Although the proposed configuration demands less operating costs, its smaller LMTD makes the heat transfer area 70.4% larger and increases capital investment. On the other hand, the new optimum VRC has less annualized cost compared to its industrial counterpart owing to lower pressure ratio by 14.5% [23]. As reported in Table 5, the paired heat exchanger area of the introduced VRC is about 4.25-times larger than the industrial one due to smaller LMTD. Furthermore, all cost indices of the optimized VRC, especially utility cost and TAC, are decreased in this work as a result of 37.2% reduction in the compressor horsepower. Working at lower operating pressure also provides 31.2% reduction in condenser duty. It is important to know that the presented VRC configuration by Suphanit is just adapted from industry [12], and it was not optimized rigorously. Economic analysis of all propane-propylene separation candidates are also illustrated in Fig. 10. To show improvements of this study, optimum results from Suphanit's work are also presented. Compared to other candidates, the optimized VRC reaches optimum results when its TAC is $8,405,040/yr. Not only is the electricity requirement in the optimum VRC less than the optimum HIDiC (3.5% less utility costs), but its coupled heat exchanger and column (including trays) capital costs are lower up to 36.2% and 23.6% as well, respectively. Due to separation of close boiling point mixture and large reboiler and condenser duties, utility cost of CDiC is high enough to economically rank it as the worst candidate. Like the previous case, the TAC of VRC is lower compared to HIDiC for the same separation task. Therefore, the optimized VRC is the best candidate for the propane-propylene separation. In addition, this conclusion is in agreement with findings of a recently published article in which numerical simulation was employed [29]. 5.3. Methanol-water separation The third case is separation of non-ideal methanol-water mixture in which heat-integrated configurations were rarely considered in literature. The main reason for this unwillingness is the large boiling point difference between the two components (100  64.6 ¼ 35.4 C). This imposes higher pressure ratio on the compressor and larger horsepower requirement, consequently, pushing cost indices to the higher values for heat-integrated alternatives. Regardless of the mentioned fact, this case is considered for more investigation from the previous work in which only

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10

H. Shahandeh et al. / Energy xxx (2014) 1e13

internal HIDiC was studied [15]. The separation of methanol-water by external HIDiC has not been carried out before. Only energy consumption of all equipment and the total required heat transfer area were compared in Gadalla's work for each heat integration candidate [15]. Therefore, Economic comparison of our optimum results with previous ones does not seem fair. However, available information of internal HIDiC from the reference is compared to our optimum external one in Table 6. As it can be seen, the reboiler and condenser duties are decreased significantly in spite of small increases in the compressor shaft work and total heat-integrated heat transfer area. In this case study, the required reboiler and condenser duties are large because of high products purity (Table 1). Consequently, the TAC of CDiC would be high, and hence, VRC and HIDiC may be good alternatives. CDiC is simulated while VRC and HIDiC are optimized in order to determine the optimum candidate for this case. Schematic diagrams of CDiC, optimum VRC, and optimum HIDiC are shown in Fig. 11. Table 7 and Fig. 12 present detailed operating

Table 5 Comparison of different configurations for propane-propylene separation. Parameters

HIDiC [23] VRC [23]

HIDiC

VRC

CDiC

Heat exchangers location in the rectifying Heat exchangers location in the stripping Vapor through compressor (kmol/h) Compressor outlet pressure (kPa) Minimum LMTD ( C) Compressor duty (MW) Condenser duty (MW) Reboiler duty (MW) Total heat integration (MW) Total heatintegrated heat exchanger area (m2) Utility cost ($/yr) Capital cost ($) TAC ($/yr)

29, 49

e

1

e

e

29, 49

e

62

e

e

25,632.6

23,254.7

22,278.1

21,705.2

e

1562

1810

1568

1547

e

2.6

11.4

1.6

2.5

e

6.6

8.6

5.8

5.4

e

9.7

9.3

9.0

6.4

78.9

e

e

e

e

75.0

86.7

76.4

74.8

76.3

e

27,151.9

6677.6

46,277.4

28,395.0

e

Fig. 9. Schematic diagram of CDiC (A), optimal VRC (B), and optimal HIDiC (C) for the propane-propylene separation.

Fig. 8. Economic analysis of optimum configurations for the benzene-toluene separation.

5,270,000 7,039,736 4,631,252 4,469,475 13,240,773 34,178,773 29,768,688 35,540,830 27,641,759 12,661,193 10,139,397 11,278,127 9,691,467 8,405,040 15,043,442

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Fig. 10. Economic analysis of optimum configurations for the propane-propylene separation.

conditions and economic analysis of the candidates for the methanol-water separation. As explained before, higher pressure ratio will be required in VRC structure to have an adequate positive driving force. The reason is that the temperature rapidly increases in the last five stages in the stripping section (see Fig. 2(C)). The vapor should be then pressurized in 686 kPa, which is high for a single compressor and could cause mechanical damages during operation. Hence, it is more logical to use two consecutive compressors with similar pressure ratios of 2.39 (see Fig. 11(B)). The influence of high-pressure ratio on capital costs is very clear in Fig. 12, where economic analysis of three mentioned configurations is illustrated. As a result, the VRC is the most expensive option in terms of TAC among the candidates. In contrary with VRCs, it is possible to have another heat integration location on stages of the stripper and rectifier in HIDiCs. Using genetic algorithm for TAC minimization, the overhead vapor of the rectifier (from the zone 1 of Fig. 4(B)) and liquid of the first stage of the stripper (from the zone 3 of Fig. 4(B)) are found as the optimum locations for the heat integration (see Fig. 11(C)). According to Table 7, the utility cost of HIDiC is about 26.4% lower than CDiC, but its capital cost is 3.4-time higher, and the optimized HIDiC can only reduce TAC by 3.4% compared to CDiC. Furthermore, there are two differences between locations of coupled heat exchanger in this example compared to the previous cases (benzene-toluene and propane-propylene). First, the vapor leaving the top of the rectifier (instead of the vapor from the first stage of the rectifier) is selected as the hot stream (Fig. 11(C)). Large reduction of the reboiler duty is not feasible by only having heat integration in the zone 3 of Fig. 4(B), because the value of RCD is much less than ReD in this case. Consequently, the zone 1 of Fig. 4(B) is chosen in which both RCD and PCD can be utilized for heat integration in order to significantly decrease the reboiler duty. Since ReD was less than RCD in the benzene-toluene and propane-propylene separations, this event did not occur in the previous cases.

11

Fig. 11. Schematic diagram of CDiC (A), optimal VRC (B), and optimal HIDiC (C) for the methanol-water separation.

H. Shahandeh et al. / Energy xxx (2014) 1e13

Table 6 Comparison of available data between internal HIDiC from the reference and optimal external HIDiC for methanol-water separation. Parameters

Internal HIDiC [15]

External HIDiC

Difference (%)

Compressor duty (MW) Condenser duty (MW) Reboiler duty (MW) Total heat-integrated heat exchanger area (m2)

3.5 17.9 19.5 9410.0

3.8 13.1 9.2 10,449.6

8.6 26.8 52.8 11.0

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12

H. Shahandeh et al. / Energy xxx (2014) 1e13

Table 7 Comparison of different configurations for methanol-water separation when r ¼ 65 & s ¼ 8. Parameters

HIDiC

VRC

CDiC

Heat exchangers location in the rectifying Heat exchangers location in the stripping Vapor through compressor (kmol/h) Compressor outlet pressure (kPa) Minimum LMTD ( C) Compressor duty (MW) Condenser duty (MW) Reboiler duty (MW) Total heat integration (MW) Total heat-integrated heat exchanger area (m2) Utility cost ($/yr) Capital cost ($) TAC ($/yr)

1 1 3532.4 293 2.4 3.8 13.1 9.2 24.9 10,449.6

e e 4037.1 287, 686 13.6 3.9, 4.6 5.7 e 34.3 2535.0

e e e e e e 35.0 34.0 e e

4,949,644 6,944,635 6,725,088 15,256,644 23,915,408 4,536,914 7,121,847 10,349,651 7,371,043

Second, the coupled heat exchanger is chosen at the furthest tray from the reboiler in the stripping section this time (Fig. 11(C)). There is no doubt that a single heat exchanger with a large area is more economical than multiple heat exchangers with small areas. Nevertheless, it should be explained why the farthest stage from the reboiler is found as the optimum location in the stripper. This can be understood by adding a large constant heat load on different stages of the stripper and comparing it with its non-heatintegrated counterpart. As indicated in Fig. 13, the whole temperature profile in the stripper is changed by adding a 20 MW heat load separately. Only the first five stages are analyzed, since temperature of the bottom stages near the reboiler is high and heat integration with them makes the HIDiC uneconomical. Besides this, there would be a jump in the temperature profile and its intensity depends on the heat load and its location. For instance, temperature of the first stage of the stripper is raised about 4.8 C compared to the temperature of the non-heatintegrated HIDiC. Like VRC configuration, even using the first five trays imposes a huge shaft work on the compressor due to the temperature jump occurrence. Under these circumstances, the best option is choosing a stage in the stripper with the lowest temperature for heat integration, which is the first one (see Fig. 13). This figure shows that pressure in the rectifier should be high enough to increase the temperature of the hot stream from the rectifier more than 78.9, 79.8, 81.1, 84.4, or 91.0 C, when the first, second, third, fourth, or fifth stage of the stripper is selected for having 20 MW heat integration, respectively. As it can be seen, heat integration

Fig. 13. Effect of heat integration placement on temperature profile of the stripper.

close to the reboiler can negatively affect compressor pressure ratio and, hence, TAC. From another viewpoint, the mean temperature difference between two consecutive trays across the whole stripper in the methanol-water case is much more than the others (see Table 8). Even though heat integration near the reboiler is thermodynamically more efficient, rapid growth in temperature profile of the stripper imposes the selection of the farthest stage from the reboiler on GA. 6. Conclusions HIDiCs and VRCs are two promising heat-integrated structures for replacement of CDiCs. Although control and construction of these configurations are harder, finding their optimum steady-state operating conditions is still attractive for energy and cost savings. In this study, rigorous optimizations of HIDiC and VRC configurations have been carried out implementing genetic algorithm method. Considering heat-integrated systems for distillation (especially HIDiC) required additional variables compared to CDiCs; number, size, and place of coupled heat exchangers and compressor pressure ratio. In order to determine the best heat-integrated structure, TAC was used as the objective function. GA was programmed such that all heat integration options were considered for the heat exchangers arrangement in HIDiC compared to the previous studies. Optimum HIDiCs and an industrial VRC suggested in the references were also simulated in this study for validation and economic comparison with the proposed configurations. It should be noted that optimum heat-integrated configurations were economically and thermodynamically improved compared to the previous studies. Based on the obtained results by GA, the best candidates for separation of benzene-toluene, propane-propylene, and methanolwater mixtures were CDiC, VRC, and HIDiC, respectively. When the boiling point difference is relatively large and separation is not a difficult task in the benzene-toluene case, using CDiC was the best choice. Dealing with a much closer boiling point mixture in the propane-propylene case, separation task was much more difficult and heat-integrated configurations were found more efficient. In the two abovementioned ideal mixtures, VRCs

Table 8 Mean temperature difference between two consecutive trays in different examples.

Fig. 12. Economic analysis of optimum configurations for the methanol-water separation.

Case study

Benzene-toluene

Section

Rectifier Stripper Rectifier

1st tray 113.33 nth tray 128.16 Mean temperature 0.93 difference

94.61 109.81 0.95

Propane-propylene Methanol-water

34.91 40.76 0.03

Stripper

Rectifier Stripper

26.76 33.31 0.11

83.75 107.72 0.37

81.16 107.11 3.24

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H. Shahandeh et al. / Energy xxx (2014) 1e13

outperformed HIDiCs; even though, the optimal heat exchangers arrangement in HIDiCs had many resemblances with VRCs. Although the methanol-water case is neither ideal nor close boiling mixture, the CDiC was not being the most economical option due to high products purity requirement. Owing to the rapid growth in temperature of the last five trays near the reboiler, the VRC could not reduce energy consumption or cost indices too. Moreover, different optimal heat exchangers arrangement was found in the HIDiC compared to the other cases. As a result, the optimum HIDiC used the most beneficial position of heat integration, and it economically outperformed the CDiC and VRC. Acknowledgments The authors are gratefully acknowledged the financial support of Iranian Fuel Conservation Organization (IFCO) under Grant no. 1105-2758 during one of the author's (Hossein Shahandeh) M.Sc. education.

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Please cite this article in press as: Shahandeh H, et al., Feasibility study of heat-integrated distillation columns using rigorous optimization, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.07.032