Optimal configuration of ternary distillation columns using heat integration with external heat exchangers

Optimal configuration of ternary distillation columns using heat integration with external heat exchangers

Journal Pre-proof Optimal configuration of ternary distillation columns using heat integration with external heat exchangers N. Khalili, N. Kasiri, J...

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Journal Pre-proof Optimal configuration of ternary distillation columns using heat integration with external heat exchangers

N. Khalili, N. Kasiri, J. Ivakpour, Amirhossein Khalili-Garakani, M.H. Khanof PII:

S0360-5442(19)32174-7

DOI:

https://doi.org/10.1016/j.energy.2019.116479

Reference:

EGY 116479

To appear in:

Energy

Received Date:

26 May 2019

Accepted Date:

03 November 2019

Please cite this article as: N. Khalili, N. Kasiri, J. Ivakpour, Amirhossein Khalili-Garakani, M.H. Khanof, Optimal configuration of ternary distillation columns using heat integration with external heat exchangers, Energy (2019), https://doi.org/10.1016/j.energy.2019.116479

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

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Optimal configuration of ternary distillation columns using heat integration with external heat exchangers

N. Khalili a, N. Kasiri a,*1, J. Ivakpour b, Amirhossein Khalili-Garakanic, M. H. Khanof a a

Computer Aided Process Engineering (CAPE) Laboratory, School of Chemical, Petroleum and Gas Engineering, Iran University of Science & Technology (IUST), Tehran, Iran b

Petroleum Refining Technology Division, Research Institute of Petroleum Industry, Tehran, Iran

c

Chemistry & Process Engineering Department, Niroo Research Institute, Tehran, Iran

ABSTRACT The subject of energy saving in distillation column sequencing is of critical importance. Heat integration in a multicomponent separation can be industrialized by saving considerable energy and cost. In this work, external heat-integrated distillation column with external heat exchanger has been studied and the annual cost function has been optimized using Genetic Algorithm. Introducing the layout and binary matrices enabled the investigation of all possible locations for the heat exchanger arrangement successfully. Moreover, exchangers heat loads and compressors pressure, have also been considered as optimization variables. Benzene, toluene, xylene and n-alkanes, separations have been studied as case studies. It has been demonstrated that the proposed optimization method in the alkane separation case decreased the total annual cost by 22.6% in comparison with the proposed thermally coupled distillation sequence columns. The heat integration of external heat exchangers in an external heat-integrated distillation column configuration and the proposed dived-wall column resulted in decreasing the total annual cost by 17% and 39% respectively, in comparison with conventional distillation columns.

Keywords: Heat integrated distillation column, Heat exchanger, Optimization, Genetic Algorithm, layout and binary matrices, total annual cost

1. Introduction The energy assessment of the United States shows that the chemical and petroleum industries are the first and second energy consumers with approximately 24 and 10 percent of the total energy consumption in 1*Corresponding

author at: Computer Aided Process Engineering (CAPE) Laboratory, School of Chemical, Petroleum and Gas Engineering, Iran University of Science & Technology (IUST), Narmak, Tehran, Iran Tel: +98-21-77240540, Fax: +98-2173021652. E-mail address: [email protected] (N. Kasiri).

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the United States, respectively. Distillation processes constitute 57 percent of the total energy consumption in the refining industries comprising of about 40000 columns in 200 different processes [1]. Consuming this high amount of energy in a distillation process is due to the low thermodynamic efficiency resulted from absorbing heat at high temperature in the reboiler and stripping it at low temperature in the condenser [2]. Three main problems of conventional distillation columns are large size, high energy consumption and high operating costs [3]. Thus, researchers have been trying to develop new and efficient technologies from the thermodynamic and economic point of view by changing distillation column configurations [4]. Thermal efficiency improvement methods have been developed since 1950. These methods include distillation using a heat pump [5] such as a vapor recompression distillation column, mechanical recompression of vapor by compressing the working fluid, compression resorption heat pump (CRHP) and absorption heat pump (AHP) using absorption equilibrium, and thermos-acoustic heat pump (TAHP) using temperature driving force and also heat integration distillation column [5] and thermally coupled double-column like divided-wall column (DWC) [6] and Kaibel column [7]. Some of these methods such as heat integration are regarded as more successful and have been tested in pilot scale [8]. In the internal heat integration of distillation columns (HIDiC) the required energy for liquid and vapor at the top and the bottom of the column is provided from the liquid and vapor inside the column. Therefore, the need for vapor/liquid from the reboiler / condenser is reduced and energy consumption, which is supplied from the utility system, is decreased. This is more economical from an energy consumption aspect. In internal heat integration there are some problems such as the complexity of exchanging heat between the two parts of the column and the limitation of heat transfer area [9] as well as the controlling of the process [10]. Because of these problems, Suphanit completely studied two different designs of heat distribution: uniform heat transfer area and uniform heat load distribution [11]. He also suggested the internal heat integration in multiple discrete places and investigated the results of propane-propylene separation [12]. Exergy and pinch analysis were utilized by researchers for configuration selection, performance analysis and structural optimization of different type of HIDiCs [13]. Mancera et al. presented an exergy based method for selecting the type of HIDiC column in separation of the propylene-propane [14]. Besides Gadalla et al. [15] suggested the pinch analysis as a rapid approaching tool which might help researchers to better understanding of the nature of HIDiC designs. Also, Cong et al. [16] proposed two concepts of available energy efficiency and duty drop ratio to improve the designing procedure of the Multi-tube type HIDiCs. But these approaches are out of scope of this paper. The concept of external heat integration, which is known as external heat-integrated distillation column (EHIDiC), was proposed by Huang et al. [17], for azeotropic mixtures using two high and low-pressure columns for the separation of binary mixtures. Later, they used three heat exchangers instead of expensive panels and studied their size and the amount of heat transfer in them [18]. It is found that if the place of heat transfer is chosen optimally, this configuration could show a better performance than the internal heat integration considering the energy saving [19]. The effects of different external heat integration configurations in dynamic simulation and control of ethylene-ethane process have also been studied [20]. Alcántara-Avila et al. [21], found the best structure by Linearization the decreasing effect of tray heat loads on the duties of the reboiler and condenser. In distillation columns, in which integration is done using compressors, the method of weighted function is used to employ MILP for optimizing energy requirement (ER) and total annual cost (TAC). In order to find the optimum structure of the distillation columns with heat integration, the problem is converted to MINLP. A combination of superstructure

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representation and rigorous simulations, was also being studied using complex mathematical programming [22]. As stated in the above descriptions, there are different approaches for structural assessment of the HIDic and EHIDiC columns, but the main gaps are not having considered heat integration among more than one column in the distillation column sequences. To the authors best knowledge there is no research on possibility of heat integration between the rectifying and stripping sections of two or more distillation columns in the sequence. The application of external heat exchanger gives more flexibility in changing the structure of the integrated columns and heat integration scenarios in the sequences. It is represented that by integrating of the rectifying and stripping sections of different columns in the sequence new opportunities might be possible for reducing energy consumptions in the system. Following the previous assessments of HIDiC applications by the authors [23-25], these features are considered: - Heat integration is considered for the specified distillation column sequencing in more than one column which are rarely considered by other researchers. - In previous research, simplifying assumptions have been considered, due to the complexity of the calculations. But in this study, in order to approach reality, simplifying assumptions have been limited to minimal levels. - In former publications, in the field of optimal heat integration with exchangers, all the trays have not been considered. In this study, all possible trays for heat integration using an external exchangers are considered in sequential distillation columns. - In the proposed method, optimal trays for the heat exchangers, heat duties and the corresponding pressure of compressors are systematically determined by the optimization of TAC. - A new systematic procedure based on binary matrices are developed which might lead to the new optimized configurations in the field of sequential distillation columns.

2. Theory & Methods 2.1. Simulation Assumptions In a ternary separation, each of the distillation columns is divided into rectifying and stripping parts, thus there are overall four integration scenarios for heat integration between two columns comprising of: rectifying and stripping sections in the first column, rectifying and stripping sections of the second column, rectifying of the first and stripping of the second column, rectifying of the second and stripping of the first column. Then by considering the existing equipment (compressor, throttling valve and so on), integration is possible for each four scenario. The assumptions considered for the simulation are as follows: 

Liquid and vapor are in equilibrium on each tray.



The problem is considered to be steady state.



There is no reaction in the trays.



The components do not form azeotrope.

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2.2. Objective Function In this research the optimization of heat integration with external heat exchanger is done in a multicomponent separation by considering all possible integration options between rectifying and stripping sections. The aim is to minimize the total annual cost in the case study and show the profitability of this method in comparison with a normal distillation column sequencing. The optimization problem in this research could be considered as a mixed integer nonlinear programming (MINLP) one which is solved by Genetic Algorithm (GA). In this research, optimization of the total annual cost is accomplished by changing continuous and discrete variables. These variables include the existence and absence and location of the heat exchanger location and the amount of heat exchanged which will be discussed in more detail in the following sections. As an iterative procedure is used, the randomly guessed initial values of the variables are chosen such that they lay within predefined reasonable boundaries to have a fewer number of iterations.

2.3. Economic Assessment Cost assessment of different equipment installation for establishing distillation column is taken from Olujic et al. [26]. The cost of installing the column shell is a function of the diameter, height and operational pressure and material of construction, which in the present work is assumed to be carbon steel. The distance between trays is considered to be 18 inches. In order to assess the cost of installing heat exchangers, the range of design pressure and the type of heat exchanger need to be known. It is presumed that reboilers are kettle type, condensers are floating-head type and the side-heat exchangers are fixed-tube type. The total annual cost is a function of the capital and the operating costs. In this study the interest rate is set at 7 percent and also the average lifetime of the equipment is considered to be 10 years. Therefore, according to the equation (1), the capital cost coefficient is 0.1423 which means that the contribution of the operational cost is greater than the capital cost in the total annual cost function. A large amount of the total annual cost is due to utility costs, which can be reduced through integration. Table 1 shows data for utilities cost. (1) $ i  (1  i ) n

TAC (

year

)  UC 

(1  i ) n  1

 CC

Table 1. Utility cost Utility Steam($/ton) LP MP HP Electricity($/Kw.h) Cooling water($/ton) Refrigeration (moderately low temp.)(30)($/GJ) Refrigeration (low temp.)(30)($/GJ)

Price 13 16 20 0.1 0.03 4.43 7.89

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According to the following equations (2) and (3), capital costs which are functions of diameters of stripping and rectifying columns, pressures, number of trays of rectifying and stripping columns, area of heat exchangers, the duty of compressors, area of condensers and reboilers. Also, utility costs which are functions of duty of compressors, area of condensers and reboilers.

CC  f ( Ds , Dr , P , ns , nr , Ahex ,Wcomp , Acondenser , Areboiler )

(2)

UC  f (Wcomp , Acondenser , Areboiler )

(3)

2.4. The New Binary Matrix Method Variables of the problem are the ratio of compressor pressure, the number and positions of side-heat exchangers shown by the binary and layout matrices and the amount of heat loads by the side-heat exchangers determined by the heat load matrix. The number of these variables is different for each separation depending on the number of trays and the number of columns. The pressure matrix Pj is also linear, in which “j” shows the number of columns. The lower and the upper limits depend on the design conditions. In general, the number of variables is(𝑛 - 1)[1 + (𝑛 - 1) + 2 * ∑n - 1 n𝑠,𝑗]. In which, ns and nr are equal to the number of integration options and each entry is equal to the 𝑗=𝑛

number of rectifying or stripping trays corresponding to that integration option. The layout number for a binary separation was previously suggested by Shahandeh et al. [23]. In order to expand the application of the theory, for the multicomponent separation of the current work, this number is considered to be a matrix. Therefore, the elements of the layout matrix would be determined by row index “i” and the column index “j”. “i” and “j” designate the number of rectifying column and stripping column respectively. “i” and “j” for a separation of n components by n-1 column, would change from 1 to n-1. There are (n-1)2 elements here. Each of the elements in the layout matrix is an integer number which could change from 1 to the total number of rectifying and stripping trays minus 1.

[

𝐿𝑖𝑗 = ⋮

]

⋯ ⋱ ⋮ ⋯

𝑖×𝑗

The heating load on each tray in the stripping section is defined as the following matrix and the heating load in the rectifying section would be defined as the negative of this matrix:

[

𝑄𝑠𝑖𝑗 = ⋮

]

⋯ ⋱ ⋮ ⋯

i × n𝑠,𝑚𝑎𝑥

The number of columns in the heat load matrix is equal to the maximum number of trays in the rectifying or stripping sections which specifies the domain of the matrix. The number of rows is equal to the number of possible integration options. In each row, the number of variables is equal to the number of trays corresponding to each state and the remaining entries of that row are considered zero. In this section the n-1 n𝑠,𝑗. The domain of these entries is from the minimum number of variables is also equal to(n - 1) × ∑ 𝑗=𝑛

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value of the heat load (5 percent of the reflux heat load here) to the lower heat load of the corresponding condenser or reboiler of that state. The binary matrix’s entries are zero and 1. If the design by GA is such that there is no exchanger or the minimum temperature difference is lower than the heat integration domain, then the corresponding binary matrix’s entry of that tray is zero, otherwise it is 1.The number of binary matrix’s variables is equal to the number of variables in the heat load matrix. The amount of heat load of each heat exchanger is determined by the matrix multiplication of the binary matrix and the heat load on the trays, which are chosen by the layout matrix. ⋯ 𝐵𝑖𝑗 = ⋮ ⋱ ⋮ ⋯

[

]

i × n𝑠,𝑚𝑎𝑥

Since it is difficult to match the heat integration options with the variable entries of the heat load and binary matrices, thus the square layout matrix is changed to a linear matrix in which the number of columns is equal to the number of integration options. Therefore, “j” represents the integration options. It should be noted that the number of columns in the linear matrices ns and nr are equal to the number of integration options and each entry is equal to the number of rectifying or stripping trays corresponding to that integration option. There are three ways of specifying the location of the heat exchanger using the layout matrix:  The first way: If the entry is between 1 to the minimum number of corresponding stripping or rectifying trays, then the corresponding location of the counter “m” which is between 1 to L(1,j) can be found as follows:

L(1, j )  1 & L(1, j )  min(ns (1, j ), nr (1, j )) Qs ( j , m )  Qs ( j , m )  B ( j , m ) Qr ( j ,[nr (1, j )  L(1, j )]  m)  Qs ( j , m)



(4)

(5)

The second way: If the entry is chosen between the minimum and maximum number of the corresponding rectifying and stripping trays, the corresponding location for the counter “m”, which is from 1 to the minimum number of rectifying and stripping trays, can be found as follows:

L(1, j )  min(ns (1, j ), nr (1, j )) & L(1, j )  max(ns (1, j ), nr (1, j ))

(6)

a) If the number of corresponding stripping trays is less than the number of rectifying trays then:

Q s ( j , m)  Q s ( j , m)  B ( j , m) Qr ( j , (nr (1, j )  L(1, j ))  m)  Qs ( j , m)

(7)

b) If the number of corresponding stripping trays is greater than the number of rectifying trays, then:

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Qs ( j , ( L(1, j )  nr (1, j ))  m)  Qs ( j , ( L(1, j )  nr (1, j ))  m)  B( j , ( L(1, j )  nr (1, j ))  m) Qr ( j , m)  Qs ( j , ( L(1, j )  nr (1, j ))  m)



(8)

The third way: the last remaining option is, when the entry is chosen greater than the maximum number of stripping and rectifying trays, the location for counter “m”, which is from 1 to L(1, j )  [ns (1, j )  ns (1, j )] , is found as follows:

L(1, j )  max(n s (1, j ), nr (1, j ))

(9)

Qs ( j , m  ( L(1, j )  nr (1, j )))  Qs ( j , m  ( L(1, j )  nr (1, j )))  B( j , m  ( L(1, j )  nr (1, j ))) Qr ( j , m)  Qs ( j , m  ( L(1, j )  nr (1, j )))

(10)

Figure 1 illustrates the flowchart for generating the binary matrices through the above equations. The order of the binary matrices generation are also represented in the figure. Bij

Qsij & Qrij

Lij

Determine ns & nr

Pj

Lij changet to liner matrix

If

L(1, j )  1 & L(1, j )  min( ns (1, j ), nr (1, j ))

No

If

L(1, j )  min( ns (1, j ), nr (1, j )) & L(1, j )  max( ns (1, j ), nr (1, j ))

Yes

No

Eq. (10)

Yes

Eq. (5)

If

No

ns < nr

Eq. (8)

Yes Eq. (7)

Figure 1. The flowchart of the binary matrices generation.

The optimization problem has two constraints. The first one is that the total summation of entries of the binary matrix must not be zero, and the other is the location of the heat exchanger must be chosen such that leads to positive heat transfer driving force. 𝑗

i

1

1

∑∑𝐵(𝑖,𝑗) ≥ 1

& 𝑇𝑟(i,n) ― Ts(j,n) ≥ 0

(11)

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The algorithm for information exchange between the optimizer and simulator is as follows (figure 2). The aim of this section is to change the variables systematically and assess their effects on the objective function without using simplifications for multicomponent systems and optimizing the objective function. In order to predict the liquid-vapor equilibrium in the operational conditions in this simulation, the PengRobinson equation of state is used, which is valid over a large operational conditions. In this study cost assessments are based on the routine proposed by Douglas [27]. Some of the other studies referred to here for comparison purposes have used other cost estimation references. In order to overcome this their process cost estimates have been carried out once again using the Douglas routine.

Figure 2. A schematic diagram of the algorithm between the optimizer and simulator.

1. Choosing the compressor pressure for heat integration is faced with the challenge of compressor cost. If the pressure is increased, by increasing the temperature, the appropriate driving force for heat transfer is provided. But, on the other hand, the compressor cost should be considered because it has a great impact on the total annual cost. The trade-off between these two problems in this study has been done systematically. The upper pressure limit should be considered reasonable, which is different for each separation. 2. Each tray diameter is a function of vapor flow rate. Therefore, after increasing pressure and temperature, the amount of liquid and vapor flow rates on each tray, change and each tray diameter can be found based on the Smith relations. In this study, the effect of the design pressure on the column diameter is taken into consideration. The vapor velocity is set at 80 percent of the flooding velocity and the length of the segment is 70 percent of the tray diameter [28]. 3. After applying pressure, the simulator solves the mesh equations simultaneously using the NewtonRaphson method and considering a specific equation of state for each separation. Then the information required for the heat load of the condenser and reboiler in each column is determined in order to specify the required range of the heat load variable on each tray. This range is then returned to the problem and lower values of the condenser and reboiler heat loads in each corresponding column are considered as thresholds. The amount of the condenser heat load which can be returned is

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the difference between Product trim-Condenser Duty (PCD) and Reflux trim Condenser Duty (RCD) [23]. PCD is part of the trim-condenser duty which is required for the top product condensation. The difference between total trim-condenser duty and PCD, which is called RCD, is the amount of duty which might be saved through heat integration in HIDiC. The details of the mesh equations on each tray are provided in Appendix A. 4. Now the specifications of the heat exchanger must be determined and applied in the simulator. The heat load on each tray is chosen by the GA by within the range specified in the previous part. Having determined the heat load, the location of the heat exchanger is chosen by the binary and layout matrices simultaneously. After determining the location of the heat exchanger, the simulator applies necessary changes and the required information is obtained in order to determine the annual cost.

2.5. Case studies Two case studies are considered in this work. The first case study is separation of ethane and methane from a mixture of alkanes. The Peng-Robinson equation of state is used for describing liquid and vapor states under the operating conditions. The operating conditions (table 2) are reported according to Van Duc Long & Lee [27]. Table 2. Specification of n-alkanes in a conventional column. Component

Feed (kg/h)

Methane Ethane Propane iso-Butane n-Butane iso-Pentane n-Pentane n-Hexane n-Heptane Temperature (ºC) Pressure (bar)

267.15 23485.72 23509.56 7220.74 15404.07 5562.95 3933.33 4730.34 2451.37 55.83 31.37

Deethanizer product (kg/h) 267.15 22211.57 1164.27 2.77 0.93 13.38 30.98

Depropanizer products (kg/h) 1274.15 22325.00 606.33 92.96 0.01 44.44 17.5

Other heavy product (kg/h) 20.29 6611.64 15310.19 5562.93 3933.33 4730.34 2451.37 123.3 18.10

The characteristics of the feed and products in the 2nd case study are shown in table 3 for the separation in the normal distillation column. The Peng-Robinson equation of state is used for describing liquid and vapor states under the operating conditions. The operating pressures of the towers are considered 10 atm in accordance with Premkumar & Rangaiah [29]. Table 3. Specification of BTX in conventional column. Component Benzene Toluene p-Xylene

Feed composition 0.33 0.33 0.34

Feed condition 100kgmol 10 atm Saturated liquid

Specification of products 0.995 0.91 0.92

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3. Results & Discussion 3.1. Comparing the external heat Integration by heat exchanger with the thermally coupled column In this comparison, normal distillation column is used for the separation of ethane and propane from the alkane feedstock. There are two columns: the first one is used for the separation of 95 percent ethane and the second one for the separation of 90 percent propane. The first column is designed for the pressure of 30.98 bar with 18 trays and the second column for the pressure of 17.5 bar with 34 trays. In the simulation, the condenser and reboiler heat loads of the first column are different from the corresponding reference by 0.48 and 2 percent respectively. For the second column, these values are 0.8 and 0.2 percent, respectively [29]. The extent of the effect of GA adjustments on optimization time and the value of the optimized function must initially be clarified. One of the adjustments, which affect choosing the population diversity, is done by the scaling function, which determines the number of parents at each domain of competence. Figure 3 has been drawn by changing the scaling function by the adjustment of the algorithm. Population diversity in Rank’s method is more than other methods, which has a positive effect on the domain of exploration. Another effective parameter is the selection function. This function is used to choose the rated selected parents. Figure 4 shows the best selection function for the separation posed in this sample as reported by the Tournament. Now the manner in which children are produced by the selected parents is considered. The effect of the scaling function is shown in figure 5. The above values for selecting elite children have reduced the efficiency of the GA. The effect of the crossover fraction is demonstrated in figure 6. The more the value of this fraction, the less mutation and diversity are seen in the population. If this value reaches 1, it will eliminate mutation in its usual GA form, which has undesirable effects. But, the less this value is, the more mutation occurs which leads to more diversity in the population and has negative effects on the performance. It should be noted that there are 138 variables in this sample. Table 4 shows the adjustments used in this study.

Table 4. GA parameters set for the deethanizer separation. Parameters Population Size Creation function Scaling function Selection function Elite count Crossover function Crossover fraction Mutation

Values 138 Feasible population Rank Tournament 2 Single point 0.9 Adapt feasible

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Figure 3. The effect of scaling function on the GA process.

Figure 4. The effect of selection function on the GA process.

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Figure 5. The effect of crossover function on the GA process.

Figure 6. The effect of crossover fraction.

By these adjustments, the reboiler heat load, RCD, PCD and so on are shown in the most optimized state and have been shown in table 5. The optimized integrated distillation column in this research has been compared with the thermally coupled column with heat pump which has been noticed as the best case in the reference. In this sample the pressure range for the output of the first compressor is between 31.47 to 40 bar and for the second one is between 18.1 to 36.2 bar. In this table the information related to the integration for this sample with different stripping pressure (𝐻𝐼𝐷𝑖𝐶2) has been shown, which will be discussed later.

Table 5.Characteristic for estimation capital &operating costs.

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𝑃𝑗(Pressure Matrix)(kpa)

-

𝐿𝑖𝑗(Layout Matrix)

-

External HIDiC with heat exchanger [3098 2000] 2 3 13 6

[4069 5614]

[4554.4 390]

Parameters

𝑅𝐶𝐷𝑗(Recycle Condenser Duty Matrix)(kW) 𝑃𝐶𝐷𝑗(Product Condenser Duty Matrix)(kW) 𝑄𝑐𝑜𝑛𝑗(Condenser Duty Matrix)(kW) 𝑊𝑐𝑜𝑝𝑚𝑗(Comperessor Duty Matrix)( kW) 𝑄𝑟𝑒𝑏𝑗(Reboiler Duty Matrix)( kW) Heat exchanger Duty(kW) Utility cost of comperessor($/yr) Utility cost of Condenser($/yr) Utility cost of reboiler($/yr) Capital Cost($) TAC($/yr)

Conventional Column

[―

2010]

[

[―

]

1835]

Retrofit TCDS with heat Pump -

External 𝑯𝑰𝑫𝒊𝑪𝟐 with heat exchanger [2400 1450] 7 9 11 23

-

[3682 2955]

3625

-

[4069 7624]

[4554.4 2225]

[3683 2826]

-

[0 181.4]

[0 712]

[7838 6489] -

[2568 6509] 5899 Utility cost($/yr) 145120 229608 133122.76 2467825.75 1563513.25 2394400.383 3452864.348 3037438.604 2332062.737

[0 7918] 1997 569600 521435 1363875.5 3940828.09 3014598.089

[

[―

]

2149]

[3682 5104] [645 [―

0]

7657.02] 6134

516480 133782.54 1318921.695 4639993.302 2715735.089

Temperature on each tray for the ethanizer and propanizer can be seen in figure 7. As it can be understood from the figure, by applying small pressure changes, the end of the trays in the second tower can be heat integrated by the end of the first stripping tower. One might think that integration can be done without using a compressor because the temperature difference is enough between the trays of the second rectifying column and the first stripping column. The threshold of the heat integration between rectifying and stripping are the lower amount of RCD and reboiler heat loads. Therefore, by increasing the pressure of the rectifying column, RCD and also heat transfer in the heat exchanger increase. Moreover, more driving force and the less heat transfer area can be achieved. This results in eliminating more heat load of the reboiler for a given compressor work. The cost of the compressor should be considered because too much increase in the compressor pressure is not economically justifiable.

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140

Temperature

120 100 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Tray number Deethanizer

Depropanizer

Figure 7. Temperature profiles of deethanizer and depropanizer columns.

As it was noted before, the utility cost function has a great effect on the total annual cost function. Therefore, the best optimization must be arranged in a way that for less compressor cost, more integration and consequently more decrease in the reboiler heat load are attained. Figure 8 shows the external heat integration using an external heat exchanger for the separation of ethane and propane at the given pressure. The consumption powers of the equipment are also shown. As it can be understood, if the goal was to reduce exergy, for eliminating the remaining reboiler heat load, thermal integration could have been used between the first rectifying and striping sections. But, since the goal is to reduce the total annual cost, this task is not economically justifiable because of lower boiling temperature of the components in the deethanizer column and the increase of the compressor pressure for raising the driving force.

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4554.4 kW

2225 kW

5899 kW Feed

181.4 kW

2568 kW

6509 kW

Figure 8. Optimized design using an external exchanger for the separations in deethanizer & depropanizer.

As it can be seen in figure 8, diameter change has been implemented. The diameter change has been studied systematically having analyzed the pressure change and determined the location of the heat exchanger. The large diameter difference (usually about 20 percent) in some trays leads to the construction of a two diameters tower. Increasing pressure results in decreasing the volumetric flow rate of the produced vapor and the tower diameter and increasing the thickness of the tower. This diameter change is monotonic. The existence of an exchanger causes a tray diameter change and the location of the exchanger determines the location of the diameter change. As it has been discussed in Appendix A, removing heat from trays in the rectifying section, results in reducing vapor and liquid flow rates in the trays above, consequently resulting in a diameter reduction. Injecting heat to the trays in the rectifying section, results in a reduction of the vapor flow rate in the trays below will lead to a diameter reduction in that section. Diameter calculations and applying changes in this research lead to the prevention of flooding or drying in the rectifying and stripping trays. In this comparison, the thermal integration applies in the normal distillation tower sequencing [22]. The column equipped with thermally coupled distillation sequence columns (TCDS) at a pressure of 14.5bar and vapor recompression, is introduced as the optimum column. In this section, the pressure range has been changed by assuming that decreasing pressure could make the existence of the compressor seem more economical and the elimination of the deethanizer more possible, thus the pressure has been reduced to 14.5 bar. Therefore, the pressure range in the first and the second rectifying columns is between 14.5 to 40 and 15.1 to 36.2 bar respectively. Decreasing pressure causes the temperature of the top product of the deethanizer column to change from 13.38 to -10.8 C hence forcing the utilization of the more expensive refrigeration costs compared to the conventional cooling water costs. By applying the integration design under these conditions, increasing

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the first rectifying column pressure leads to an increase in the temperature profile of the upper trays and consequently the elimination of the refrigerant. Another advantage of increasing pressure is the possibility of integrating rectifying and stripping trays in the first column, which leads to the elimination of reboiler heat load. Figures 9 and 10 shows the optimization of this sample using Genetic Algorithm and a schematic diagram of this design which is shown by two heat exchangers.

Figure 9.The GA performance during HIDiC with external exchanger.

3682 kW

5104 kW

208 kW 645 kW 4053 kW

Feed

8166 kW

Figure 10. Optimized design using some external exchangers for the separations in deethanizer & depropanizer at lower pressure.

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As it is clear in figure 10, in designing the second alternative in which the rectifying tower has a lower pressure, two compressors are used for the thermal integration. The first compressor needs to consume more power because the temperature level in the rectifying tower is low and a larger temperature difference should be used. Therefore, the compressor power has been multiplied in comparison with the previous one and consequently costing 3.5 times the one in which the rectifying pressure was kept intact. Along this increase in compressor cost, 911 KW of thermal energy is reduced in the reboiler. In this case, the trays at the end of the first and the second rectifying columns are integrated with the trays in the first stripping column. This results in increasing the reboiler heat load. Because of this the annual cost of the second one is 16 percent greater than the first. But both of them have lower annual costs in comparison with the TCDS tower. These results as well as comparisons against normal distillation columns have been shown in table 6. The difference in the reported annual cost with the reference is due to different ways of evaluating it.

Table 6. Comparison of the specifications with TCDs. Parameter Reboiler energy reduction (%) Condenser energy reduction (%) Comparison in total utility cost (%) Comparison in total capital cost (%) cost (%) Comparison in total annual Payback period(yr) CPU time(h)

External HIDiC with heat exchanger 36.64 42.02 28.83 -44.2 23.22 4.035 72

𝑯𝑰𝑫𝒊𝑪𝟐External with heat exchanger 43 24.86 30.68 -93 10.59 7.24 60

Retrofit TCDS with heat Pump 44.36 63.02 17.27 -64.59 0.75 16.25 -

3.2. Comparison with dividing wall column In this part the BTX case has been studied and used for the comparison. Having applied heat integration using heat exchangers, the scheme shown in figure 11 is the most favorable one. In the separation of this sample there are also 150 variables. Because of decreasing the heat load of the condenser in the second column, the integration has not led to the elimination of the reboiler.

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1114 kW

280 kW

655 kW

1442 kW

79 kW

22.7 kW

303 kW

975 kW

Feed

Figure 11. Optimized design using some external exchangers for the separation of BTX.

The characteristics of the DWC and the conventional columns and the proposed integration have been reported in table 7. In table 8, these comparisons with the normal distillation column are reported in percentage. Table 7. Characteristics for estimation of capital & operating costs. Conventional Column -

Parameters 𝑃𝑗(Pressure Matrix) (kpa) 𝐿𝑖𝑗(Layout Matrix) 𝑅𝐶𝐷𝑗(Recycle Condenser Duty Matrix) (kW) 𝑃𝐶𝐷𝑗(Product Condenser Duty Matrix) (kW) 𝑄𝑐𝑜𝑛𝑗(Condenser Duty Matrix) (kW) 𝑊𝑐𝑜𝑝𝑚𝑗(Comperessor Duty Matrix) (kW) 𝑄𝑟𝑒𝑏𝑗(Reboiler Duty Matrix) (kW) Heat exchanger Duty (kW) Utility cost of Electricity ($/yr) Utility cost of Cooling water ($/yr) Utility cost of steam ($/yr) Capital Cost ($) TAC ($/yr)

-

External HIDiC with heat exchanger [1300 1150] 11 5 26 4

[1273.8 640.9]

[902.8 48.4]

-

[223.2 239.1]

[211.2 231.6]

-

[1114 280] [79 22.77]

1306

[303 945] 2097

1355 -

81416 27373.09 330720 1710202.898 682357.9024

25645.09 359075 826725.9 502115.1678

[1485 880] 1506 900] [ Utility cost($/yr) 46440 637590 999107.88 825903.319

[

Table 8. Comparison of the specifications with DWC.

]

DWC -

-

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parameters Reboiler energy reduction (%) Condenser energy reduction (%) Comparison in total utility cost (%) Comparison in total capital cost (%) Comparison in total annual cost (%) Payback period (yr) CPU time(h)

External HIDiC with heat exchanger 43.13 41.05 35.7 -71.17 17 6.99 52

DWC 43.6 44.77 43.75 17.25 39 1.67 -

The heat exchanger has a great effect on decreasing the reboiler and condenser heat loads. The farther the location of the reboiler or condenser is, the less effective the amount of heat transferred is on decreasing the reboiler or condenser heat loads by the heat exchanger. Therefore, the trays closer to the reboiler should be integrated. In order to do this, the temperature of the stripping trays should be raised above the temperature of the trays near the reboiler and this requires increasing the compressor power resulting in cost increases. In this study all of these cases have been studied systematically. figure 11 is the result of the optimization using integration. In the BTX separation, the divided-wall column is more favorable compared to the heat integration proposed in this research. DWC is a built in shell with no compressor and heat exchanger. Therefore, the capital cost decreases significantly in comparison with the normal distillation columns. Basically, for the separations in which by low compressor power, considerable heat load from the reboiler can be eliminated, the integration design is more economical. It is even more economical for components with a low boiling point.

4. Conclusions In distillation columns sequencing, heat integration can have a very important role in determining better configurations and decreasing energy. In this study, HIDiC by external heat exchangers have been used for distillation towers sequencing. Taking into consideration of all possible heat transfer scenarios between trays using external heat exchangers without the use of the layout matrix and the related formulas developed here, is so complex and near impossible. In contrast to the previous studies about external heat integration, in which heat integration was just considered between the second rectifying and the first stripping column, in this study heat integration has been studied within a domain containing all thermodynamic possibilities, between all trays. In addition to the location, the amount of heat transfer by the exchanger and pressure was also considered as variables in the optimization. The optimization problem in this work is an MINLP one and the annual cost function has been considered as the objective function in using Genetic Algorithm as the optimization methodology. Determining the location of the exchanger, the tower diameter was also studied systematically in order to avoid flooding possibility. The optimized HIDiC structure was compared against DWC and TCDs. In the alkane sample separation with external heat integration, two optimal models are compared. In the first optimal model, the pressure interval for the genetic algorithm is considered in accordance with the reference pressure. In this optimal configuration, the compressor is located in the second distillation column. Therefore, heat integration between the trays of the second rectifying column and the first stripping column has occurred. This model

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is optimally 23% in terms of the total annual cost in comparison to conventional distillation column. While, the total annual cost of the TCDs column in the reference is 0.75% optimal relative to the conventional distillation column. Therefore, the total annual cost of the proposed optimal model is 22.6% lower than the reference model. It should be noted that increasing total annual cost of the reference due to the high utility cost of the compressor. In the second model, the pressure interval for the genetic algorithm is considered lower than the reference pressure. In this optimal configuration, the compressor is located in the first distillation column. Therefore, heat integration between the trays of the second rectifying column and the first stripping column and between the trays of the first rectifying column and the first stripping column has occurred. The annual cost of the optimal model is 10% less than the conventional distillation column. The high total annual cost of this optimal model is also due to the utility cost of the compressor. Findings show reasonable rates of return for such investments. For the BTX sample this structure is not economical compared to the divided-wall column, due to a larger total annual cost although they are almost the same in saving energy. This model is optimally 17% in terms of the total annual cost compared to conventional distillation column. While, the total annual cost of the DWC column in the reference is 39% optimal relative to the conventional distillation column. In the BTX separation, the heat pump method was not an appropriate method for heat integration in order to reduce energy consumption. The DWC structure has lower total annual cost as it is built in a single shell with no need of compressors. The lack of pressure change in DWC causes it less flexible in utilization and not as comprehensive as HIDiC. Increasing the number of components significantly raises the number of variables and thus required CPU time in simulations requiring more robust solution schemes and better initial guesses to make simulation assessments possible. Appendix 1 In order to determine the characteristics of all trays in the simulation, mesh equations in all trays must be solved simultaneously. The mesh equations of tray “i” in the rectifying and tray “j” in the stripping sections, which exchange heat, are shown below.

Rectifying Section

Stripping Section

The mass balance for n components in tray “i” is as follows: 𝑀𝑛,𝑖 = 𝐿𝑖 ― 1𝑥𝑛,𝑖 ― 1 + 𝑉𝑖 + 1𝑦𝑛,𝑖 + 1 ― [𝑉𝑖 + 𝑊𝑖]𝑦𝑛,𝑖 ― [𝐿𝑖 + 𝑈𝑖]𝑥𝑛,𝑖 = 0 The equilibrium equation for n components on each tray is given by: 𝐸n,i = yn,i ― Kn,ixn,i

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In which Kn,iis the equilibrium constant of the component n on tray “i” which is determined by thermodynamic relations for the components in the separation. The summation equations of the mole fractions are: c

(𝑆y)i =

∑y

n,i

―1=0

n,i

―1=0

n=1 c

(𝑆x)i =

∑x

n=1

Instead of this equation, the mass balance equation can be written: 𝐿𝑖 ― 1 + 𝑉𝑖 + 1 ― [𝑉𝑖 + 𝑊𝑖] ― [𝐿𝑖 + 𝑈𝑖] = 0 The heat balance equation: 𝐿𝑖 ― 1 + 𝑉𝑖 + 1 ― [𝑉𝑖 + 𝑊𝑖] ― [𝐿𝑖 + 𝑈𝑖] = 0 The same equations may be written for tray “j” with the only difference of positive heat load in the energy balance equation. References [1] Ozokwelu, D., Hybrid Separations/Distillation Technology: Research Opportunities for Energy and Emissions Reduction. Washington DC: US Dept. of Energy, 2005. [2] Khalili-Garakani A., Ivakpour J., Kasiri N. A New Search Space Reduction Method Based on Exergy Analysis for Distillation Column Synthesis. Energy 2016, 116: 795-811. [3] Rix A., Hecht C., Paul N., Schallenberg J. Design of Heat-Integrated Columns: Industrial Practice. Chemical Engineering Research and Design 2019, 147: 83-89. [4] Kiss A.A., Flores Landaeta S.J., Infante Ferreira C.A. Towards energy efficient distillation technologies making the right choice. Energy 2012, 47(1): 531-42 [5] Blahušiak M., Kiss A.A., Babic K., Kersten S.R.A., Bargeman G., Schuur B. Insights into the selection and design of fluid separation processes. Separation and Purification Technology 2018, 194: 301-318. [6] Jana A.K. A Novel Divided-Wall Heat Integrated Distillation Column: Thermodynamic and Economic Feasibility. Industrial & Engineering Chemistry Research 2018, 57(36): 12127-12135. [7] Ghadrdan M., Halvorsen I.J., Skogestad S. Optimal operation of Kaibel distillation columns. Chemical Engineering Research and Design 2011, 89(8), 1382-1391. [8] Kiss A.A. Advanced Distillation Technologies: Design, Control and Applications. John Wiley & Sons, UK, 2013. [9] Bruinsma O.S.L., Krikken T., Cot J., Sarić M., Tromp S.A., Olujić Z., Stankiewicz A.I. The structured heat integrated distillation column. Chemical Engineering Research and Design 2012, 90(4), 458-470. [10] Nakaiwa, M., et al. (1998). Operating an ideal heat integrated distillation column with different control algorithms. Computers & Chemical Engineering 1998, 22: 389-393. [11] Suphanit, B. Design of internally heat-integrated distillation column (HIDiC): Uniform heat transfer area versus uniform heat distribution. Energy 2010, 35(3): 1505-1514. [12] Suphanit, B. Optimal heat distribution in the internally heat-integrated distillation column (HIDiC). Energy 2011, 36(7): 4171-4181. [13] Fang J., Cheng X., Li Z., Li H., Li H. A review of internally heat integrated distillation column. Chinese Journal of Chemical Engineering 2019, 27(6): 1272-1281. [14] Mancera J.A., Mendoza D.F., Riascos C.A.M. HIDiC Configuration Selection Based on Exergetic Analysis. Chemical Engineering Transactions 2018, 69. [15] Gadalla M., Olujic Z., Sun L., De Rijke A., Jansens P.J. Pinch Analysis-Based Approach to Conceptual Design of Internally Heat-Integrated Distillation Columns. Chemical Engineering Research and Design 2005, 83(A8): 987-993. [16] Cong H., Li X., Li H., Patrick J.M., Gao X. Performance Analysis and Structural Optimization of Multi-Tube Type Heat Integrated Distillation Column (HIDiC). Separation and Purification Technology 2017, 188: 303-315.

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[17] Huang, K., Shan L., Zhu Q., Qian J. Adding rectifying/stripping section type heat integration to a pressure-swing distillation (PSD) process. Applied thermal engineering 2008, 28(8-9): 923-932. [18] Huang, K., Liu W., Ma J., Wang S. Externally Heat-Integrated Double Distillation Column (EHIDDiC): Basic Concept and General Characteristics. Industrial & Engineering Chemistry Research 2010, 49(3): 1333-1350. [19] Chen, H., Huang K., Wang S. A novel simplified configuration for an ideal heat-integrated distillation column (ideal HIDiC). Separation and Purification Technology 2010, 73(2): 230-242. [20] Zhang, X., Huang K., Chen H., Wang S. Comparing three configurations of the externally heat-integrated double distillation columns (EHIDDiCs). Computers & Chemical Engineering 2011, 35(10): 2017-2033. [21] Alcántara-Avila J.R., Kano M., Hasebe S. Multiobjective Optimization for Synthesizing Compressor-Aided Distillation Sequences with Heat Integration. Industrial & Engineering Chemistry Research 2012, 51(17): 5911-5921. [22] Alcántara-Avila J. R., Hasebe S., Kano M. New Synthesis Procedure to Find the Optimal Distillation Sequence with Internal and External Heat Integrations. Industrial & Engineering Chemistry Research 2013, 52(13): 4851-4862. [23] Shahandeh H., Ivakpour J., Kasiri N. Internal and external HIDiCs (heat-integrated distillation columns) optimization by genetic algorithm. Energy 2014, 64: 875-886. [24] Shahandeh H., Ivakpour J., Kasiri N. Feasibility study of heat-integrated distillation columns using rigorous optimization. Energy 2014, 74: 662-674. [25] Shahandeh H., Jafari M., Kasiri N., Ivakpour J. Economic optimization of heat pump-assisted distillation columns in methanol-water separation. Energy 2015, 80: 496-508. [26] Olujić, Ž., Sun L., de Rijke A., Jansens P.J. Conceptual design of an internally heat integrated propylene-propane splitter. Energy 2006, 31(15): 3083-3096. [27] Van Duc Long N., Lee M. Debottlenecking the Retrofitted Thermally Coupled Distillation Sequence. Industrial & Engineering Chemistry Research 2013, 52(35): 12635-12645. [28] Branan, C.R. Rules of Thumb for Chemical Engineers (Fourth Edition). Burlington, Gulf Professional Publishing, 2005. [29] Premkumar R., Rangaiah G.P. Retrofitting conventional column systems to dividing-Wall Columns. Chemical Engineering Research and Design 2009, 87(1): 47-60.

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 Heat integration of distillation column sequences using external exchangers are carried out.  All different possible scenarios are presented through introduction of layout and binary matrices  Each scenario is optimized using genetic algorithm in a simulation environment  Total annual cost is used as the objective function with operating conditions as parameters  Comparisons provided the overall optimum scenario