Structural design of fully thermally coupled distillation columns using a semi-rigorous model

Structural design of fully thermally coupled distillation columns using a semi-rigorous model

Computers and Chemical Engineering 29 (2005) 1555–1559 Structural design of fully thermally coupled distillation columns using a semi-rigorous model ...

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Computers and Chemical Engineering 29 (2005) 1555–1559

Structural design of fully thermally coupled distillation columns using a semi-rigorous model Young Han Kim∗ Department of Chemical Engineering, Dong-A University, 840 Hadan-dong, Saha-gu, Pusan 604-714, Republic of Korea Received 1 August 2003; received in revised form 7 December 2004; accepted 7 December 2004 Available online 13 January 2005

Abstract A new structural design procedure for fully thermally coupled distillation columns (FTCDC) utilizing semi-rigorous material balances is proposed and applied to the design of example systems of butanol, BTX and hexane–heptane mixtures. The structural design can be directly incorporated in the design of commercial design software, giving basic information which is required at the beginning of simulation. The performance of the proposed design evaluated from the application to the three example systems with three different feed compositions indicates that the new procedure gives useful design information for the commercial simulation software. It is shown that the proposed procedure provides a comparable result to an existing rigorous structural design method. © 2004 Elsevier Ltd. All rights reserved. Keywords: Thermally coupled distillation; Petlyuk column design; Structural design; Semi-rigorous model; Ternary separation

1. Introduction The structural information of a distillation column is useful when commercial design software is utilized in the design of the column. Without the information iterative calculations have to be conducted until an acceptable structure is found. Although short-cut design equations can be used in the structural design, equations are not applicable to the design of a fully thermally coupled distillation column (FTCDC) due to the unknown compositions of interlinking streams. A practical design rule utilizing twice the minimum tray number as tray number of a practical column was implemented in the design of the FTCDC (Kim, 2002) and an extended FTCDC (Kim, 2001). The operating lines of a prefractionator and a main column of the FTCDC in a minimum tray distillation column configuration are developed from a stageto-stage computation beginning with feed and side product compositions. This structural design for a column with minimum trays is proportionally expanded, resulting in the design ∗

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of a practical FTCDC. However, this procedure may produce an alternative design from the optimum structure for a nonideal system (Seader & Henley, 1998). In this study, a new structural design for the FTCDC is proposed and its performance is tested using example systems containing butanol, BTX and hexane–heptane mixtures. The design procedure employs material balances and equilibrium calculated using UNIQUAC activity model and the Peng–Robinson EOS for the computation of tray compositions. The design outcome is compared with that from an existing design procedure (Kim, 2002).

2. Design procedure A schematic of an FTCDC is shown in Fig. 1, in which stream and tray indications are included. The proposed structural design procedure of this study begins with feed and side product compositions and liquid flow rates in a prefractionator and a main column. Whereas the compositions are given from the design specification, the flow rates are not and therefore the rates are derived from the calculated minimum liquid

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Nomenclature B D F L NF NP NR NS NT NT2 S V x y z

flow rate of bottom product (kmol/h) flow rate of overhead product (kmol/h) flow rate of feed (kmol/h) liquid flow rate (kmol/h) feed tray number side draw tray number location of upper interlinking tray location of lower interlinking tray number of trays in a main column number of trays in a prefractionator flow rate of side draw (kmol/h) vapor flow rate (kmol/h) liquid composition (mol fraction) vapor composition (mol fraction) feed composition (mol fraction)

Greek letters β intermediate component split ratio defined in Eq. (2) γ transport ratio Subscripts A lightest component B intermediate component C heaviest component i component m tray number n tray number

the intermediate and C is the heaviest, and the stage number is given from the top of the prefractionator. β is the optimum split of intermediate component through the upper linking (Fidkowski & Krolikowski, 1986). The stage-to-stage computation is repeated up to the top of the prefractionator until a negative composition results for the computation. The tray number of the upper section is determined from a set of interlinking trays in the prefractionator and main column resulting in a minimum difference of tray liquid composition. The vapor composition in the lower section of the prefractionator is calculated from the following material balance, again beginning with the feed composition:

Superscript II prefractionator

flow (Fidkowski & Krolikowski, 1986). In this procedure, the flow rates are taken as 1.5 times the minimum flow (Seader & Henley, 1998). When feed tray composition is assumed to be same as the feed composition of a saturated liquid, the liquid composition of one stage above the feed tray is calculated from the following material balance, Eq. (1). In this study, the UNIQUAC activity model and the Peng–Robinson EOS are used to determine the equilibrium computation. The parameters for the equations are found from the HYSYS database (Hyprotech, 2002). II xn,i =

II V2 yn+1,i − Fzi γ1,i

L2

Fig. 1. Schematic diagram of a fully thermally coupled distillation column.

(1)

where the symbols for liquid and vapor flows are given in Fig. 1 and γ1,i is the transport ratio of component i through upper linking from the prefractionator to the main column. In this case, it is one for component A, β for component B and zero for component C. Note, component A is the lightest, B is

II yn,i =

II L3 xn−1,i − Fzi γ2,i

V3

(2)

Instead of the stage liquid composition as in the upper section, vapor composition is successively calculated in the lower section until a negative composition is found. The design procedure for the prefractionator is also used for the middle section of a main column. Because the side product composition is equal to the liquid composition of side draw tray, the mid-section of the main column—trays between upper and lower interlinking trays—is designed with the same procedure as that used in the prefractionator design. The liquid composition in the mid-upper section between NR and NP in Fig. 1 is computed from: xn,i =

V4 yn+1,i + Fzi γ3,i L4

(3)

However, the end of the section, i.e., the upper interlinking tray number has to be determined to give as small difference

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between the top tray composition of the prefractionator as possible. Because composition difference between two interlinking trays—the top tray of the prefractionator and the upper interlinking tray of the main column—induces mixing that will lower the distillation column tray efficiency (Triantafyllou & Smith, 1992), the composition difference should be minimized. Hence, the following objective function is used to find the upper interlinking tray:  II Min |(xn,i − xm,i )Fzi γ1,i | (4)

Using the results of the presented structural design procedure for an FTCDC system a HYSYS (Hyprotech, 2002) simulation is conducted. The column pressure is taken as an atmospheric pressure for the processes of this study. The initial liquid flow rates, reflux flow in the main column and liquid flow in the prefractionator, are taken from the numbers used in the proposed structural design procedure, and then the flow rates are adjusted until the key compositions of three products, overhead, bottom and side draw, meet the given product specifications.

Then, the liquid composition in the upper interlinking tray is found from:

3. Example processes

m,n

i

xNR,i =

II V4 yNR+1,i + V2 y1,i

− Fzi γ4,i

(5)

L

Again, the liquid composition of the top section from the interlinking tray to the top of the main column is calculated with the following material balance until the composition satisfies the specification of overhead product. xn,i =

Vyn+1,i − Fzi γ4,i L

(6)

Like the design of the upper section, the lower section of the main column is designed using the composition of side product. The design of mid-lower section begins with Eq. (2) using the side draw composition. The lower interlinking tray is found from an objective function similar to Eq. (4), and its tray composition is from Eq. (5). The tray compositions of bottom section below the interlinking tray are also computed from a modification of Eq. (6). From the structural design of the FTCDC, total tray numbers in the prefractionator, in the main column, feed location, side draw location and the two interlinking trays are determined by adding tray numbers computed from Eqs. (1) through (6). The composition at feed tray is different from the feed composition in a practical prefractionator, and thus the mixing at the feed tray has to be considered in the practical design. In this study, 1.7 times the originally computed number of trays is actually implemented in the prefractionator, and the basis for this increase is explained in the following.

The proposed design procedure is applied to three real systems in order to validate the design procedure. The systems are ternary mixtures of s-butanol/i-butanol/n-butanol (S1), benzene/toluene/p-xylene (S2) and hexane/2-methyl hexane/heptane (S3). The systems are selected because they are representative of three different groups of organic compounds. Also, three different feed compositions are provided: equi-molar (F1), 0.1/0.8/0.1 (F2) and 0.8/0.1/0.1 (F3). The butanol mixture with equi-molar feed is used as a base system for the explanation of the results. A feed flow rate of 1 kg mol/h is used for all the cases. The design specification for the products in the example systems is arbitrarily set to 0.975 mol fraction of the lightest component in overhead product, 0.975 of the heaviest in bottom product and 0.95 of intermediate component in side draw. The vapor–liquid equilibrium for systems S1 and S2 is computed using UNIQUAC, and that for system S3 uses Peng– Robinson EOS.

4. Results and discussion Using the material balances from the structural design, the tray liquid composition is obtained and used in the count of the number of total, interlinking, feed and side draw trays. The results of the proposed structural design procedure are summarized in Table 1. In addition, the operational variables

Table 1 Design results of example systems Item

S1

S2

S3

F1

F2

F3

F1

F2

F3

F1

F2

F3

NT NT2 NR NS NF NP L (kmol/h) V (kmol/h) L2 (kmol/h) V3 (kmol/h)

74 19(11) 15 66 8(5) 42 4.63 4.71 1.57 2.04

72 26(15) 6 71 9(5) 48 4.26 4.82 1.43 2.19

73 10(6) 20 57 6(4) 43 3.90 3.77 1.51 1.98

27 9(5) 5 21 5(3) 11 1.39 1.54 0.33 0.73

21 10(6) 5 19 3(2) 12 1.07 1.65 0.21 1.00

23 5(3) 7 16 3(2) 10 1.99 1.79 0.21 1.00

79 17(10) 4 55 10(6) 13 4.95 4.86 1.23 1.55

76 17(10) 4 67 10(6) 20 3.70 4.14 0.44 1.18

82 21(12) 5 59 12(7) 14 6.60 6.11 1.02 1.70

Tray numbers are counted from top. The numbers in parentheses represent the tray location where the feed tray composition equals to feed composition.

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Fig. 2. Tray liquid composition profile in practical FTCDC. Plus symbols are of a prefractionator and circles are of a main column.

obtained from the HYSYS simulation for the specified products are also listed in the table. The liquid composition profile for the base system practical column using the HYSYS simulation are shown in Fig. 2. The profile of the main column is denoted in circles, and the interlinking trays are marked with NR and NS. The profile of plus symbols is for the prefractionator. The flat composition profile near the side draw tray indicates a flat temperature profile, which is employed as a HYSYS simulation quality guideline. The tray number of the prefractionator and feed location are modified in Table 1, the numbers in parentheses being those obtained from the proposed design procedure. This modification is necessary due to the difference between the compositions of feed tray and feed itself. In the proposed structural design the two are assumed to be same, but they are not as is shown in the simulation results (Fig. 2). Unless an infinite number of trays are used around feed tray, the two compositions are not equal because two operating lines do not meet at the equilibrium curve in a practical distillation column. When a practical liquid flow rate is taken as 1.3 times the reflux flow of 3.6 kmol/h (the infinite number of the prefractionator trays) (Seader & Henley, 1998), the resulting number of trays is 19. This number is 1.7 times the originally estimated tray number for the prefractionator. Therefore, the practical tray number and feed tray location in Table 1 are modified from that estimated using the assumption of the equal composition at the feed tray. The comparison between the minimum liquid flow and the practical flow in Table 1 indicates that the ratios between the two vary widely. However, the basis used in the structural

design of 1.5 times the minimum for liquid flow is not far from the actual design outcome for the example processes. Since the minimum liquid flow is computed using an average relative volatility, it results in some error for a practical non-ideal equilibrium system. It is shown from the practical design results that the proposed structural design did provide reasonable liquid flow rate estimates. The results of the proposed design procedure is compared for the base case to that of a previous structural design (Kim, 2002). It shows that the previous design procedure results in a reduction of the total reflux flow by 8% while total tray number is increased by 19%. Although the two structural designs give different tray numbers, the latest proposed design study shows a comparable outcome to the previous procedure. For a rigorous determination of the optimum structure for a given process specification, a decision on the trade-off between tray number and vapor boil-up is necessary, and can be based on investment economics and operating costs. In the process of the tray number adjustment, the structural design outcome of this study is useful because the six tray numbers, NT, NT2, NR, NS, NF and NP, can be proportionally varied until economic parameters are satisfied.

5. Conclusion A structural design procedure for fully thermally coupled distillation columns using a semi-rigorous model is proposed and tested on three systems, butanol, BTX and hexane–heptane mixtures having different compositions of feed. The structural information was utilized in HYSYS sim-

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ulations to find the operating variables that would meet a given set of product specification. The outcome of the proposed structural design procedure provides a good estimate for the rigorous simulation. The application result of the proposed design procedure to the example systems indicates that the procedure is applicable to various systems having different equilibrium relations and feed compositions.

Acknowledgements Financial support from the Korea Science and Engineering Foundation (Grant No. R01-2003-000-10218-0) and partially through the CANSMC is gratefully acknowledged.

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References Fidkowski, Z., & Krolikowski, L. (1986). Thermally coupled system of distillation columns: optimization procedure. AIChE Journal, 32, 537–546. Hyprotech (2002). User guide. Calgary, Canada: Hyprotech Ltd. Kim, Y. H. (2001). Structural design of extended fully thermally coupled distillation columns. Industrial and Engineering Chemistry Research, 40, 2460–2466. Kim, Y. H. (2002). Structural design and operation of a fully thermally coupled distillation column. Chemical Engineering Journal, 85, 289–301. Seader, J. D., & Henley, E. J. (1998). Separation process principles (pp. 509–512). New York: John Wiley & Sons Inc. Triantafyllou, C., & Smith, R. (1992). The design and optimisation of fully thermally coupled distillation columns. Transactions IChemE, 70(A), 118–132.