Quick Decision-Making for Close-Boiling ... - ACS Publications

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Quick Decision-Making for Close-Boiling Distillation Schemes Chengtian Cui,† Xingang Li,†,‡,§ Hong Sui,*,†,‡,§ and Jinsheng Sun*,† †

School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, P. R. China National Engineering Research Center of Distillation Technology, Tianjin, 300072, P. R. China § Collaborative Innovation Center of Chemical Science and Engineering, Tianjin, 300072, P. R. China ‡

S Supporting Information *

ABSTRACT: Separating close-boiling components using distillation is very common in industry. Considering the higher capital and energy intensity of the task, schematic selection of optimal distillation strategies becomes a significant decision of both industrial and methodological importance. In this sense, this paper introduces a reliable shortcut method of simplicity and robustness for optimizing the target of total annualized cost (TAC). In detail, selective analyses are carried out among four schematic candidates for three closeboiling systems. The schemes are conventional distillation column, mechanical vapor recompression (MVR), double-effect distillation, and distillation with a recycle process. The mixtures to be separated are methyltrichlorosilane/dimethylchlorosilane, methylcyclopentane/cyclohexane, and isobutanol/n-butanol. After the first round evaluation, hydraulic calculations through rigorous simulations are worked out to size the equipment, which is necessary for TAC analyses. In the second round comparison, MVR stands out to be a more attractive option for close-boiling separations than other configurations. diagram helps analyze the difficulty of separation.7 For a closeboiling binary system, the much more limited deviation between the equilibrium and the diagonal lines, or relative volatility, means an extreme separation difficulty for a CDiC, requiring a great number of stages and considerable thermal utilities.15 In order to save valuable utilities, the aforementioned heatintegrated distillation configurations are expected to be elaborately integrated into a CDiC. However, not all these design alternatives are good options for the specific close-boiling separations. For example, TCDS and DWC16−20 are not suitable for binary systems because they are usually for ternary1 and quaternary systems.5 HPAD21 is right for the purpose, because it corresponds to a lower capital investment since the required temperature elevation is relatively limited. In practice, the HPAD decision should follow a careful investigation of economic analysis.20 A HIDiC22−24 is expected to result in good energysaving performance in terms of operating costs. However, reported industrial applications are so infrequently encountered or in lack of relevant engineering experience.11 Therefore, a HIDiC is not considered in this work. Considering that the industrial application of DED25 for close-boiling binary systems was exemplified by Chen et al.26 for a 1,2-propanediol/ethylene glycol mixture, it is included in this study.

1. INTRODUCTION Accounting for approximately 95% of liquid separations, distillation is by far the most widely used thermal separation technology in the chemical process industry.1 It is responsible for an estimated 3% of the world’s energy consumption and over 50% of plant operating costs.2−4 Besides, distillation utilizes equipment of the largest scales and is considered to be the most capital intensive process technology.5 All these remarks imply distillation is a major concern within chemical industries. The importance of designing distillation systems of both sustainability and feasibility is continuously challenging chemical engineers. The energy intensive nature of a conventional distillation column (CDiC) is mainly attributed to its low thermodynamic efficiency (typically around 5%), by high-quality energy in and low-grade heat out.6,7 Under this large thermal utilities depletion, any reduction in energy consumption by energy efficient technologies will bring not only considerable economical profits but also environmental and social benefits.8−10 Motivated by this impetus, numerous heat-integrated distillation configurations have been developed,11,12 including thermally coupled distillation sequence (TCDS) and dividing-wall column (DWC), heat pump assisted distillation (HPAD), internally heat-integrated distillation column (HIDiC), and double-effect distillation (DED). These heat-integrated options are expected to provide better energy performances than CDiC. Close-boiling binary mixtures are commonly encountered in the fine-chemical and specialty industries.13,14 Generally, the x−y © 2017 American Chemical Society

Received: Revised: Accepted: Published: 5078

March 5, 2017 March 24, 2017 April 12, 2017 April 12, 2017 DOI: 10.1021/acs.iecr.7b00935 Ind. Eng. Chem. Res. 2017, 56, 5078−5091

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Industrial & Engineering Chemistry Research

the 2 columns do not require stringent purity specifications, the theoretical stage requirements will be reduced. However, the additional recycle stream introduces unexpected extra energy consumption. In this sense, heat integration is a reasonable choice to lower energy requirements from the prototype without heat integration, which has been an industrial completion.38,39 With all the above understanding, this study intends to systematically compare four different design options (CDiC, HPAD, DED, and DRP) for separating close-boiling binary mixtures, providing insights for designers by comparative analyses and evaluations. These methods are highlighted by no request for entrainers that will ruin the generality of the application. Considering both operating and capital costs, the evaluations are carried out utilizing total annualized cost (TAC) based on three proposed case studies.40 After the debut in TAC optimization of the process alternatives, the shortcut method feeds results to initialization of subsequent rigorous simulations. Finally the comparisons between shortcut and rigorous methods are derived to verify the accuracy of the former approach. In this context, the authors provide chemical engineers with computer programmable models with explanations for quick decisionmaking.

Except for the abovementioned heat-integrated distillation alternatives, common industrial applications for close-boiling separations are extractive distillation (ED) and heterogeneous azeotropic distillation (HAD).27 For example, Jongmans et al.28,29 applied ionic liquid as entrainer in an ED process to separate an ethylbenzene/styrene mixture. In an acetic acid dehydration process, acetic esters are customarily added as light entrainer for separating acetic acid/water via HAD.30,31 However, because ED and HAD require an entrainer, it is usually time-consuming to select a suitable solvent.32 The other approaches make full use of melting point differences in either distillation/freezing or distillation/melt crystallization configurations.33−37 Workable for only specific mixtures, these hybrid distillation configurations are not applied as wide as the heatintegrated distillation configurations. Another option is the distillation with recycle process (DRP), shown in Figure 1, which is particularly useful in engineering

2. THEORY 2.1. HPAD. For a CDiC, in order to upgrade the level of the energy discharged from its condenser and reuse it to reduce energy consumption in its reboiler, several HPAD concepts have been proposed.41 The HPAD configurations include vapor compression (VC), mechanical vapor recompression (MVR), thermal vapor recompression (TVR), absorption heat pump (AHP), compression-resorption heat pump (CRHP), etc. Among these alternatives, VC and MVR are commonly available for commercial purposes,4 and their schematics are shown in Figure 2. VC applies a specific working fluid as an intermediate medium, absorbing energy from the condenser (heat source) and rejecting it to the reboiler (heat sink). An additional compressor is used to provide the required work input, with an expansion valve to close the cycle. Because all of the elements involved are external to the column, VC does not require major modifications, except for necessary adjustments to the heat exchangers for changing utilities. This advantage makes VC particularly useful in retrofit designs. It should be noted that, before utilizing VC, a suitable working fluid is required for heat transfer purposes.

Figure 1. DRP for close-boiling separation.

practices. For example, Sun et al.38,39 applied two DRPs in a 9-column organosilicon distillation scheme. Generally for a close-boiling binary system A/B (A and B are light and heavy key components, respectively), the crude feed enters the first column, reaching the separation target of A in the distillate. Because the residue of the first column is designed to contain a certain amount of A, it lowers the operating temperature of the column and, more importantly, the separation difficulty as well, which is a particular benefit for thermal unstable components that decompose or polymerize at elevated reboiler temperatures. When the residue is separated in a subsequent column, the distillate is designed to be the same A/B ratio as the feed to the first column, circulating back to the first column feedstock. Pure B yields within the residue with a reduced separation difficulty as well. Because the residue and the distillate of

Figure 2. Schematics of VC, MVR, and RLF. 5079

DOI: 10.1021/acs.iecr.7b00935 Ind. Eng. Chem. Res. 2017, 56, 5078−5091

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direction of mass flow is consistent with the direction of heat integration. In these two configurations, because the bottoms purification targets of the initial columns are not stringently specified to be pure component, the separation efforts of these columns are reduced, which correspond to less stages required. However, because both top and bottom products are at high purity, the total number of stages of the second columns is expected to be quite large. As for dynamic performance, Sun et al.38 proposed that the coherent direction of heat integration and mass flow makes starting of the unit smoother and easily controllable, facilitating the popularization of the LSF scheme in industry, while the shortcoming blocks LSR from being the most popularized is the relatively complicated starting procedure and longer operative stabilization time. As for the FS pattern, the crude feed stream is split into two approximately equal streams, which are fed to the HPC and LPC, respectively. Because both HPC and LPC should have stringent purity specifications in the distillate and bottoms, resulting in a great number of stages required in both columns, FS may not be suitable for close-boiling separations. Considering energy savings, capital costs, and dynamic performances, only LSF is considered, and this pattern will be integrated into the DRP as well.

In contrast to VC, MVR uses the overhead vapors as the heat transfer medium feeding the compressor. This way, the procedure of choosing a medium can be circumvented. MVR is of particular benefit in close-boiling separations, because only a small temperature lift of the medium is required in such works, which corresponds to a higher coefficient of performance (COP) in the heat pump distillation system. Therefore in this study, MVR is selected as a representative of HPAD technologies. Another interesting variant of MVR is reboiler-liquid flashing (RLF) (Figure 2).7 Instead of upcycling the energy from the reboiler, RLF depressurizes the bottoms and reuses it as cold utility for the condenser. Gao et al.42 compared the performance of MVR and RLF for a close-boiling mixture of n-butanol and isobutanol. They observed that the two alternatives have very close TACs. Therefore, we reckon that RLF will give a similar performance as MVR for separating close-boiling systems. 2.2. DED. Among the heat-integrated distillation operations without extra rotating machines driven by electricity or other power suppliers, DED has been one of the greatest predilections for the majority of pieces of research.43 The basic concept of DED is to combine the condenser of a high-pressure column (HPC) and the reboiler of a low-pressure column (LPC) into one process-to-process heat exchanger to save energy. Chiang and Luyben44,45 investigated the energy saving potentials of five different DED configurations using a methanol−water system. They found that three design patterns can provide significant energy savings for all cases with different feed compositions, compared to the basic case with a CDiC. For low methanol feed concentrations, the light split reverse (LSR) configuration is the best heat-integrated system. While, for high methanol feed concentrations, the light split forward (LSF) configuration gave the best results because it requires the lowest pressure steam. Another better option is the feed split (FS) pattern. These three DED options are shown in Figure 3. In the LSR and LSF patterns, the entire feed stream enters into one of two adjacent columns in a cascaded process. The LSR feed stream is fed to the initial LPC to remove the light key component with a high-purity overhead, which accounts for approximately half of the total light key product. The bottoms containing the remaining light key product is separated in the subsequent HPC overhead. In this case, the mass flow and heat integration are in opposite directions. In the other variation, LSF, approximately 50% of the light key component is purified in the initial HPC, with the remaining bottom product accomplishing the separation target in the subsequent LPC. Herein, the

3. ECONOMIC EVALUATION TACs of different distillation schemes are compared, including the annualized capital and operating costs. Capital costs include columns shells, internals, condensers/reboilers, and compressors. Operating costs include steam for reboilers, cooling water (CW) for condensers, and electrical power for compressors. For simplicity, the capital investments of pumps and associated electrical power consumptions are not considered. In addition, the economic evaluation consists of an annual operating time (AOT, 8,000h/a) and a payback period for capital investment (PBP, 3a). 3.1. Capital Cost. 3.1.1. Distillation Column. The capital cost of the column shell is estimated based on diameter (DC) and height (HC). The cost of internals only involves trays. For the diameter and height shortcut calculation, the correlations of Rathore et al.46 are used. The column diameter DC (m) is estimated as follows: 0.5 ⎡⎛ 4 ⎞ ⎛ TD ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Dc = ⎢ · (D)· (R + 1)· (22.4)· · ·⎜ ⎟⎥ ⎝ 273 ⎠ ⎝ P ⎠ ⎝ 3, 600 ⎠⎦ ⎣⎝ π · V ⎠

(1)

Figure 3. Three configurations of DED. 5080


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Industrial & Engineering Chemistry Research where V (m/s), D (kmol/h), R, TD (K), and P (atm) are the average gas flow rate, distillate molar flow rate, reflux ratio, overhead temperature, and column operating pressure, respectively. The estimation of V is ⎛ 1 ⎞0.5 V = 0.761·⎜ ⎟ ⎝P⎠

Table 2. Cost Data To Calculate Operating Costs

Column height HC (m) is calculated based on (3)

where N is the number of stages, and η is the stage efficiency. For simplicity, this study postulates η = 0.8 for all stages. The capital costs of distillation column shells (CCOL, US$) and trays (CTray, US$) are estimated as follows:47,48 CCOL = 17, 640·Dc1.066 ·Hc0.802

(4)

CTray = 229·Dc1.55·Nt

(5)

(7)

where Q is the heat duty in the heat exchanger, U is the overall heat transfer coefficient, and LMTD is the logarithmic mean temperature difference between hot stream and cold stream. A minimum temperature difference (ΔTmin) is specified to ensure that LMTD ≥ ΔTmin. The overall heat transfer coefficients are adopted from Luyben48 and are summarized in Table 1. Table 1. Overall Heat Transfer Coefficient Estimation Heat exchanger

Overall heat transfer coefficient, kW/(°C·m2)

Condenser Reboiler Process-to-process

0.852 0.568 0.852

3.1.3. Compressor. The mechanical efficiency of the compressor is postulated to be 0.8. The capital cost of the compressor (CCOM, US$) in HPAD is calculated as a function of the work done (Wc, kW):48 CCOM = 9, 560·Wc 0.82

(8)

3.2. Operating Cost. The operating cost mainly involves low pressure (LP) steam, CW, and electricity. The average costs of these utilities are listed in Table 2.48 The operating cost (COPE, US$/a) is written as COPE = AOT ·[∑ (Chu·Q hu) +

PBP

4. SHORTCUT METHOD AND OPTIMAL DESIGN The shortcut method is useful in preliminary conceptual design, in parametric study to find optimal condition, in process synthesis study to establish optimal separation sequence, and as initial approximation for rigorous simulation.49 In this section, a shortcut method for optimizing different distillation alternatives is provided. Because the results of the shortcut method must be verified via rigorous simulation, necessary initial values should be provided, including operating pressure, the number of stages, feed location, reflux ratio, product distribution, recycle flow rate, etc. The minimum temperature difference ΔTmin for process-to-process heat exchangers is specified to be 10 °C. Apparently, the change in column pressure will affect relative volatility, reflux ratio, column heat load, etc. To prevent a time-consuming iterative sequential optimization procedure, the operating pressure is specified before optimization. The column pressure is determined by the saturated dew point temperature versus pressure relationship of different mixtures, which can be retrieved from commercial simulators (i.e., Aspen Plus, Aspen HYSYS, Pro/II, gPROMS, etc.). The CDiC, MVR, DED, and DRP schemes are shown in Figure 4. 4.1. Shortcut Method and Optimal Design of CDiC. 4.1.1. CDiC Shortcut Method. Because CDiC does not involve heat integration, its operating pressure depends on various parameters, such as cold utility at the condenser and the thermodynamic properties of components. Typically, the CDiC is operated at atmospheric pressure if CW could be used as cold utility. Once the product specifications are acquired, the number of stages and reflux ratio can be obtained using the Fenske− Underwood−Gilliland (FUG) method, and the feed location can be calculated using the Kirkbride empirical equation.7 Material and energy balances constrain the product distribution and heat duty. For the CDiC, the material and energy balances are, respectively, (11) F=D+B

(6)

Q U ·LMTD

∑ (CCOL + CTray + CHEX + CCOM ) (10)

The heat transfer area is calculated from the amount of heat load and overall driving force:40

A=

7.78 0.354 16.9

TAC = COPE +

3.1.2. Heat Exchanger. The capital cost of the heat exchanger is estimated based on the heat transfer area (A). Luyben48 proposed a correlation used to estimate the cost of the heat exchanger (CHEX, US$): CHEX = 7, 296·A0.65

Price US$/GJ

3.3. TAC. TAC is an important economic criterion for grassroots process design. TAC intuitively provides engineers with the competitiveness of different distillation schemes, because it accounts for both capital and operating costs. In this work, TAC (US$/a) is calculated by the equation below:47,48

(2)

⎛N⎞ Hc = 0.61·⎜ ⎟ + 4.27 ⎝η⎠

Utility LP steam (6 bar, 160 °C) CW (25 to 35 °C) Electricity

∑ (Ccu·Q cu) + Celec·Wc]

F ·xF = D·xD + B ·xB

(12)

Q R − Q C + F ·HF − D·HD − B ·HB = 0

(13)

In eqs 11 and 12, the crude feed molar flow rate F, molar fraction of light key component in crude feed xF, molar fraction of light key component in distillate xD, and molar fraction of light key component in bottoms xB are design variables, which should be given before design and optimization. Thus, the

(9)

where Chu, Ccu, and Celec are the utility cost for heating, cooling, and electrical power, respectively. Qhu, Qcu, and Wc are the energy consumption of heating, cooling, and electricity, respectively. 5081


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Figure 4. CDiC, MVR, DED, and DRP schemes.

product distribution (D and B are the molar flow rate of distillate and bottoms, respectively) can be rewritten as x − xB D = F· F xD − xB (14) B = F·

xD − xF xD − xB

α ·xD 1·(1 − xD) = R min + 1 + α−θ 1−θ

Combining eqs 20 and 21, R min =

(15)

Herein, crude feed and products are assumed to be saturated liquids, and their enthalpies are assumed to be nearly identical. Then, eq 13 reduces to QR = QC

⎡ xD 1 − xB ⎤ Nmin = lg ⎢ · ⎥ /lgα xB ⎦ ⎣ 1 − xD

The heat duty of the CDiC condenser is expressed as (17)

αi·(xi , D)min αi − θ

= R min + 1

(23)

⎡⎛ 1 + 54.4·X ⎞ ⎛ X − 1 ⎞⎤ N − Nmin ⎟·⎜ ⎟⎥ = 1 − exp⎢⎜ ⎣⎝ 11 + 117.2·X ⎠ ⎝ X 0.5 ⎠⎦ N+1

X=

R − R min R+1

(24)

(25)

The feed location can be made with the Kirkbride empirical equation:

(19)

where αi is the relative volatility of the reference component and q is the thermal condition of the feed. Herein, constant relative volatility and crude feed at boiling condition (q = 1) are specified. The common root θ can be derived from eq 18. xi,F is the molar fraction of component i in the feed, and (xi,D)min is the molar fraction of component i in distillate under minimum reflux ratio. Applying eqs 18 and 19 to binary mixtures, α ·xF 1·(1 − xF ) + =0 α−θ 1−θ

(22)

The actual reflux ratio R and the number of stages N can be calculated using the Gilliland correlations:

where λ = R/Rmin is the ratio of the real reflux ratio over the minimum reflux ratio. λ is usually set in the range 1.1−2.0.40 ΔH is the latent enthalpy of the distillate. The minimum reflux ratio can be obtained using the Underwood equation: α ·x ∑ i i,F = 1 − q αi − θ (18)

∑

1 − xD ⎤ 1 ⎡ xD ·⎢ − α· ⎥ α − 1 ⎣ xF 1 − xF ⎦

Calculation of the minimum number of stages uses the Fenske equation:

(16)

Q C = D·(λ ·R min + 1) ·ΔH

(21)

0.206 ⎡⎛ ⎞ ⎛ xB ⎞2 ⎛ B ⎞⎤ NR − 1 x F = ⎢⎜ ⎟ · ⎜ ⎟⎥ ⎟·⎜ ⎢⎣⎝ xF ⎠ ⎝ 1 − xD ⎠ ⎝ D ⎠⎥⎦ NS

(26)

where NR and NS are the stage numbers of the rectifier and stripper, respectively. 4.1.2. Optimal Design of CDiC. The optimization model of CDiC (M1) is a nonlinear programming (NLP), which is

(20) 5082


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In eqs 32−35, F, B2, xF, xD1, xD2, and xB2 are design variables necessary to initialize the optimization. The remaining variables D1, B1, D2, and xB1 are unknowns. The separation targets for the distillate of each column are identical: xD1 = xD2 = xD. It should be noted that eqs 32−35 have only one degree of freedom (xB1 or B1). Herein, xB1 is selected as the decision variable. Therefore, D1, B1, D2, and B2 can be rewritten as a function of xB1: x − xB1 D1(xB1) = F · F xD − xB1 (36)

formulated as below: min TAC eq 10. (M1) s. t. Capital investments evaluation eqs 1−8. Operating costs evaluation eq 9. Material balance eqs 14 and 15. Energy balance eqs 16 and 17. FUG eqs 22−25. Kirkbride empirical eq 26. CCOM = 0 LMTD ≥ ΔTmin 1.1 ≤ λ ≤ 2.0

B1(xB1) = F ·

To solve M1, some data should be input as initialization. These initial values include α, ΔH, F, xF, xD, xB, P, TD, LMTDC, and LMTDR. The model can be easily solved with commercial programming software, such as LINGO, GAMS, etc. 4.2. Shortcut Method and Optimal Design of MVR. 4.2.1. MVR Shortcut Method. For the MVR, the operating pressure of the compressor must be set below the critical pressure of the distillate, while producing a sufficient temperature lift to drive the reboiler. In practice, the saturated dew point temperature versus pressure relationship of the distillate is required for determining the operating pressure. The MVR material balance is the same as the CDiC. While the MVR energy balance is expressed as Q C + Q R1 − WC = D·(λ ·R min + 1) ·ΔH

(27)

Q R1 + Q R 2 = D·(λ ·R min + 1) ·ΔH

(28)

(37)

x − xB2 D2(xB1) = B1· B1 xD − xB2

(38)

xD − xB1 xD − xB2

(39)

B2 (xB1) = B1·

Based on eqs 16 and 17, the DED energy balance is written as Q R1 = Q C1 = D1·(λ1·R min ,1 + 1) ·ΔH1

(40)

Q R 2 = Q C 2 = D2 ·(λ 2 ·R min ,2 + 1) ·ΔH2

(41)

The product distribution of two columns can be calculated based on the principle that the heat loads of the HPC condenser and the LPC reboiler are equal; thus, the heat integration constraint can be expressed as

The COP of the MVR scheme is defined as COP = Q R1/WC

xD − xF xD − xB1

Q R 2 = Q C1 (29)

4.3.2. Optimal Design of DED. The optimization model of DED (M3) is formulated as a NLP. It is expressed as below: min TAC eq 10. (M3) s. t. Capital investments evaluation eqs 1−8. Operating costs evaluation eq 9. FUG eqs 22−25. Kirkbride empirical eq 26. Material balance eqs 36−39. Energy balance eqs 40 and 41. Heat integration constraint eq 42. CCOM = 0 LMTD ≥ ΔTmin 0 ≤ xB1 ≤ xF 1.1 ≤ λ ≤ 2.0

Combining eq 29 into eqs 27 and 28: Q C + (COP − 1) ·WC = D·(λ ·R min + 1) ·ΔH

(30)

COP·WC + Q R 2 = D·(λ ·R min + 1) ·ΔH

(31)

In the shortcut method, QR2 = 0 is postulated to ensure the reboiler duty is fully provided by the pressured overhead distillate. 4.2.2. Optimal Design of MVR. The optimization model of MVR (M2) is a NLP. M2 is shown as below: min TAC eq 10. (M2) s. t. Capital investments evaluation eqs 1−8. Operating costs evaluation eq 9. Material balance eqs 14−15. FUG eqs 22−25. Kirkbride empirical eq 26. Energy balance eqs 30 and 31. QR2 = 0 LMTD ≥ ΔTmin 1.1 ≤ λ ≤ 2.0

To solve the DED optimization model, the necessary initial values are α1, α2, ΔH1, ΔH2, F, xF, xD, xB2, P1, P2, TD1, TD2, LMTDR1, LMTDC2, and LMTDC1−R2. 4.4. Shortcut Method and Optimal Design of DRP. 4.4.1. DRP Shortcut Method. The material balance for the DRP is written as

For M2, the necessary input values are α, ΔH, F, xF, xD, xB, P, TD, LMTDC, LMTDR1, LMTDR2, and COP. 4.3. Shortcut Method and Optimal Design of DED. 4.3.1. DED Shortcut Method. The material balance equations for the DED are F = D1 + B1

(32)

B1 = D2 + B2

(33)

F ·xF = D1·xD1 + B1·xB1

(34)

B1·xB1 = D2 ·xD2 + B2 ·xB2

(35)

(42)

F + D2 = D1 + B1

(43)

B1 = D2 + B2

(44)

F ·xF + D2 ·xD2 = D1·xD1 + B1·xB1

(45)

B1·xB1 = D2 ·xD2 + B2 ·xB2

(46)

In eqs 43−46, F, D1, B2, xF, xD1, xD2, and xB2 are specified before optimization, leaving the unknowns B1, D2, and xB1. Likewise, eqs 43−46 have only one degree of freedom (xB1 or B1). Herein, xB1 is determined as the decision variable. This way, B1 and D2 can be rewritten as a function of xB1, giving 5083


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xF − xB2 xD1 − xB2

(47)

B1(xB1) =

D1·xD1 + B2 ·xD2 − F ·xF xD2 − xB1

(48)

D2(xB1) =

D1·xD1 + B2 ·xB1 − F ·xF xD2 − xB1

(49)

B2 = F ·

xD1 − xF xD1 − xB2

(50)

The DRP energy balance is the same as eqs 40 and 41, and the heat integration constraint is also eq 42. 4.4.2. Optimal Design of DRP. M4 is the DRP optimization model, and it is a NLP. M4 is formulated as follows: min TAC eq 10 (M4) s. t. Capital investments evaluation eqs 1 to 8. Operating costs evaluation eq 9. FUG eqs 22−25. Kirkbride empirical eq 26. Energy balance eqs 40 and 41. Heat integration constraint eq 42. Material balance eqs 47 and 50. CCOM = 0 LMTD ≥ ΔTmin 0 ≤ xB1 ≤ xF 1.1 ≤ λ ≤ 2.0

Figure 5. x−y diagram of the Me1/Me2 system at different pressures.

to 220 kPa, its relative volatility drops from 1.092 to 1.080. For this system, the SRK (Soave−Redlich−Kwong) equation is selected as the thermodynamic model to predict the vapor− liquid equilibrium (VLE).38,39 For M1, the initial values for the shortcut model are α = 1.091 (at 110 kPa), ΔH = 29,139.62 kJ/kmol (the latent enthalpy of pure Me1 at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 343 K (saturated temperature of pure Me1 at 110 kPa), LMTDC = 40 K, and LMTDR = 85 K. The comparisons of two methods and the rigorous design flow sheet via CDiC for Me1/Me2 separation are shown in Table S1 and Figure 6, respectively.

In this model, the required initial values are α1, α2, ΔH1, ΔH2, F, xF, xD1, xD2, xB2, P1, P2, TD1, TD2, LMTDR1, LMTDC2, and LMTDC1−R2.

5. RIGOROUS SIMULATION 5.1. Explanation of Tasks. Aspen Plus was selected for rigorous simulation using the RadFrac model for distillation columns. Except for column diameters by the Aspen tray sizing option, the rest of the values related to economic evaluations are based on eqs 3−10. The shortcut evaluations were performed using LINGO. The Global Solver option was selected to obtain the global optimization, which can be easily achieved with less computational efforts. The purposes of rigorous simulation are (1) to verify the accuracy of the shortcut method and (2) to compare TACs of each scheme for different mixtures. To accomplish those aims, three close-boiling binary systems with different relative volatilities and latent enthalpy are proposed as case studies. Arranged in order of increasing relative volatilities, these binary systems are methyltrichlorosilane (Me1)/dimethylchlorosilane (Me2), methylcyclopentane (MCP)/cyclohexane (CH), and isobutanol/n-butanol. The molar flow rate of the crude feed is set to be 1,000 kmol/h, the molar fractions of the crude feed are 0.5/0.5, and the separation targets for light and heavy key components are 0.999. In the following case studies, detailed information of shortcut estimations and rigorous simulations can be referred to in the Supporting Information. 5.2. Case Studies. 5.2.1. Me1/Me2 System. Me1 and Me2 are important organosilicon monomer materials.38,39 Currently, distillation is the main technology for their separation.38,39 In this case, the CDiC operates at 110 kPa. The DED/DRP HPCs and the MVR compressor operate at 220 kPa, ensuring sufficient temperature difference for process-to-process heat exchangers. The x−y diagram of the Me1/Me2 system at different pressures is shown in Figure 5. After compressing the mixture from 110 kPa

Figure 6. Rigorous design flow sheet via CDiC for Me1/Me2 separation.

For M2, the initial values are α = 1.091 (at 110 kPa), ΔH = 29,139.62 kJ/kmol (the latent enthalpy of pure Me1 at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 343 K (saturated temperature of pure Me1 at 110 kPa), LMTDC = 40 K, LMTDR1 = 10 K (process-to-process heat exchanger), LMTDR2 = 85 K, and COP = 8.35. The rigorous design flow sheet via MVR is shown in Figure 7, and the results of shortcut and rigorous methods are listed in Table S2. 5084


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Table S4 lists the results of shortcut and rigorous methods. Figure 9 presents the rigorous design flow sheet via DRP. For the CDiC, it is clearly indicated that the economic contribution of energy (23,581,920US$/a) is more significant than the annualized capital investment (10,539,612 US$/a). These values remind us the importance of saving energy. Another fatal problem of the CDiC is its large value of column height (284.87 m). In engineering practices, this CDiC should be divided into several small column shells with additional stream transfer equipment. The MVR has the same problem of column height, although it can significantly reduce energy cost by 71.7% compared with the CDiC. For the DED, an additional column increases annualized capital cost by 28.8%, but the heat integration between two columns can decrease operating cost by 31.6%, leading to a final reduction of 13.0% in TAC. However, DED cannot solve the column height problem. Despite the fact that the first column requires fewer stages, the second column still needs a large number of stages because both distillate and bottoms are at high purity. Finally for the DRP, it can reduce the column height in both columns, but the recycle stream increases the column diameters. The trade off between column height and diameter shows an additional capital investment (28.7%) is required. Besides, the heat integration between two columns cannot fully compromise the additional energy cost caused by the recycle stream. For this reason, the energy cost of the DRP increases by 16.3% compared with the CDiC. 5.2.2. MCP/CH System. MCP/CH is a closing-boiling mixture with α = 1.299 at 110 kPa. The operating pressures of the compressor and HPCs are postulated to be 240 kPa, at which the relative volatility reduces to 1.261. Figure 10 presents the x−y diagram of the MCP/CH system at 110 kPa and 240 kPa. The SRK thermodynamic model is selected to describe the VLE behavior in this system.50 For M1, the initial values are α = 1.299 (at 110 kPa), ΔH = 29,230.00 kJ/kmol (the latent enthalpy of pure MCP at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 348 K (saturated temperature of pure MCP at 110 kPa), LMTDC = 44 K, and LMTDR = 73 K. Figure 11 and Table S5 give the results of the rigorous design flow sheet via CDiC and the comparisons of shortcut and rigorous methods, respectively.

Figure 7. Rigorous design flow sheet via MVR for Me1/Me2 separation.

For M3, the input values are α1 = 1.080 (at 220 kPa), α2 = 1.091 (at 110 kPa), ΔH1 = 27,653.63 kJ/kmol (the latent enthalpy of pure Me1 at 220 kPa), ΔH2 = 29,139.62 kJ/kmol (the latent enthalpy of pure Me1 at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB2 = 0.001, P1 = 2.2 atm, P2 = 1.1 atm, TD1 = 367 K (saturated temperature of pure Me1 at 220 kPa), TD2 = 343 K (saturated temperature of pure Me1 at 110 kPa), LMTDR1 = 58 K,LMTDC2 = 40 K, and LMTDp−p = 10 K (process-to-process heat exchanger). Table S3 presents a summary for two methods. Figure 8 shows the design flow sheet via DED. For M4, the input values are α1 = 1.080 (at 220 kPa), α2 = 1.091 (at 110 kPa), ΔH1 = 27,653.63 kJ/kmol (the latent enthalpy of pure Me1 at 220 kPa), ΔH2 = 29,285.28 kJ/kmol (the latent enthalpy of 0.5/0.5 Me1/Me2 at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD1 = 0.999, xD2 = 0.5, xB2 = 0.001, P2 = 2.2 atm, P2 = 1.1 atm, TD1 = 367 K (saturated temperature of pure Me1 at 220 kPa), TD2 = 344 K (saturated temperature of 0.5/0.5 Me1/Me2 at 110 kPa), LMTDR1 = 58 K, LMTDC2 = 40 K, and LMTDp−p = 10 K (process-to-process heat exchanger).

Figure 8. Rigorous design flow sheet via DED for Me1/Me2 separation. 5085


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Figure 9. Rigorous design flow sheet via DRP for Me1/Me2 separation.

Figure 11. Rigorous design flow sheet via CDiC for MCP/CH separation.

Figure 10. x−y diagram of the MCP/CH system at different pressures.

For M2, the initial values are α = 1.299 (at 110 kPa), ΔH = 29,230.00 kJ/kmol (the latent enthalpy of pure MCP at 110 kPa), F = 1,000 kmol/h,xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 348 K (saturated temperature of pure MCP at 110 kPa), LMTDC = 44 K, LMTDR1 = 10 K (process-to-process heat exchanger), LMTDR2 = 73 K, and COP = 7.125. Figure 12 presents the MVR rigorous design flow sheet. Table S6 lists the comparison of the two approaches. For M3, the input values are α1 = 1.261 (at 240 kPa), α2 = 1.299 (at 110 kPa), ΔH1 = 27,604.75 kJ/kmol (the latent enthalpy of pure MCP at 240 kPa), ΔH2 = 29,230.00 kJ/kmol (the latent enthalpy of pure MCP at 110 kPa), F = 1,000 kmol/h,xF = 0.5, xD = 0.999, xB2 = 0.001, P1 = 2.4 atm, P2 = 1.1 atm, TD1 = 376 K (saturated temperature of pure MCP at 240 kPa), TD2 = 348 K (saturated temperature of pure MCP at 110 kPa), LMTDR1 = 45 K, LMTDC2 = 44 K, and LMTDp−p = 10 K (process-to-process heat exchanger). Figure 13 shows the DED rigorous design flow sheet. Table S7 presents the results of two methods.

Figure 12. Rigorous design flow sheet via MVR for MCP/CH separation.

For M4, the input values are α1 = 1.261 (at 240 kPa), α2 = 1.299 (at 110 kPa), ΔH1 = 27,604.75 kJ/kmol (the latent 5086


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Figure 13. Rigorous design flow sheet via DED for MCP/CH separation.

Figure 14. Rigorous design flow sheet via DRP for MCP/CH separation.

enthalpy of pure MCP at 240 kPa), ΔH2 = 29,667.90 kJ/kmol (the latent enthalpy of 0.5/0.5 MCP/CH at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD1 = 0.999, xD2 = 0.5, xB2 = 0.001, P1 = 2.4 atm, P2 = 1.1 atm, TD1 = 376 K (saturated temperature of pure MCP at 240 kPa), TD2 = 352 K (saturated temperature of 0.5/0.5 MCP/CH at 110 kPa), LMTDR1 = 45 K, LMTDC2 = 49 K, and LMTDp−p = 10 K (process-to-process heat exchanger). Figure 14 and Table S8 give the results. The relative volatility of the MCP/CH system is slightly higher than that of the Me1/Me2 system. But the CDiC still needs 126 theoretical stages, which makes one column very high (100.35m). The advantages of the MVR and DED structures over the CDiC are supported by energy savings of 65.7% and 29.6%, and these savings contribute to overall savings of 19.5% and 14.5% in TACs, respectively. Likewise, these three configurations cannot reduce column height. Although the DRP can significantly decrease the height of both columns, its TAC increases by 31.9% compared with the CDiC. However, the DRP design can make construction and allocation easy to achieve.

5.2.3. Isobutanol/n-Butanol System. Isobutanol and n-butanol are close-boiling compounds with medium relative volatility (1.414 at 110 kPa). The Wilson equation is selected to predict the VLE.42 The operating pressure of the HPCs and the compressor is 270 kPa. At 270 kPa, the relative volatility reduces to 1.398. The x−y diagram of the isobutanol and n-butanol system at 110 kPa and 270 kPa is indicated in Figure 15. For M1, the initial values are α = 1.414 (at 110 kPa), ΔH = 41,570.52 kJ/kmol (the latent enthalpy of pure isobutanol at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 383 K (saturated temperature of pure isobutanol at 110 kPa), LMTDC = 80 K, and LMTDR = 39 K. Table S9 presents a summary for shortcut and rigorous methods. Figure 16 shows the design flow sheet via CDiC. For M2, the initial values are α = 1.414 (at 110 kPa), ΔH = 41,570.52 kJ/kmol (the latent enthalpy of pure isobutanol at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB = 0.001, P = 1.1 atm, TD = 383 K (saturated temperature of pure isobutanol at 110 kPa), LMTDC = 80 K, LMTDR1 = 10 K (process-to-process heat exchanger), LMTDR2 = 39 K, and 5087


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Figure 17. Rigorous design flow sheet via MVR for isobutanol/ n-butanol separation.

(the latent enthalpy of 0.5/0.5 isobutanol/n-butanol at 110 kPa), F = 1,000kmol/h, xF = 0.5, xD1 = 0.999, xD2 = 0.5, xB2 = 0.001, P1 = 2.7 atm, P2 = 1.1 atm, TD1 = 411 K (saturated temperature of pure isobutanol at 270 kPa), TD2 = 388 K (saturated temperature of 0.5/0.5 isobutanol/n-butanol at 110 kPa), LMTDR1 = 12 K, LMTDC2 = 85 K, and LMTDp−p = 10 K (process-to-process heat exchanger). Figure 19 and Table S12 summarize the results. For the isobutanol/n-butanol system, the MVR and DED require 67.2% and 30.0% less energy than the CDiC, respectively. The results from the economic analysis show that the MVR and DED can provide 22.7% and 17.4% TAC savings with respect to the CDiC. For the DRP, except for lowering column height, this configuration does not show an economic benefit compared with others. 5.3. Discussion. A summary of shortcut calculations and rigorous simulations for the three close-boiling binary systems is listed in Table 3. By comparing the relative errors, the predictions from CDiC, MVR, and DED shortcut methods are generally good, while the DRP shortcut method slightly underestimates the TACs compared to rigorous simulations. Conclusively the results from shortcut methods are considerably in agreement with the rigorous simulations, verifying their accuracy. For close-boiling binary systems, the results show that both MVR and DED schemes can reduce the TAC, compared with the CDiC process, of which the MVR is advantageous over DED, in terms of TAC evaluation. However, thinking of the MVR scheme with a necessary compressor, its costly maintenance gives way to DED as an attractive option. It is important to note that the CDiC, MVR, and DED schemes cannot solve the column height problem. Despite the fact that the results show their economic advantages over DRP, unexpected high equipment construction and allocation costs may destroy the benefits in real industry. On the other hand, although the DRP scheme can lower the separation targets as well as the height of distillation columns, the effect of heat integration cannot wholly compensate the additional energy cost caused by the recycle stream. Therefore, DRP does not show economic benefits compared to the corresponding CDiC.

Figure 15. x−y diagram of the isobutanol/n-butanol system at different pressures.

Figure 16. Rigorous design flow sheet via CDiC for isobutanol/ n-butanol separation.

COP = 7.49. The comparisons of two methods and the rigorous design flow sheet via MVR are shown in Table S10 and Figure 17, respectively. For M3, the input values are α1 = 1.398 (at 270 kPa), α2 = 1.414 (at 110 kPa), ΔH1 = 37,938.31 kJ/kmol (the latent enthalpy of pure isobutanol at 270 kPa), ΔH2 = 41,570.52 kJ/kmol (the latent enthalpy of pure isobutanol at 110 kPa), F = 1,000 kmol/h, xF = 0.5, xD = 0.999, xB2 = 0.001, P1 = 2.7 atm, P2 = 1.1 atm, TD1 = 411 K (saturated temperature of pure isobutanol at 270 kPa), TD2 = 383 K (saturated temperature of pure isobutanol at 110 kPa), LMTDR1 = 12 K, LMTDC2 = 80 K, and LMTDp−p = 10 K (process-to-process heat exchanger). The design flow sheet via DED is shown in Figure 18. And the results of shortcut and rigorous methods are shown in Table S11. For M4, the input values are α1 = 1.398 (at 270 kPa), α2 = 1.414 (at 110 kPa), ΔH1 = 37,938.31 kJ/kmol (the latent enthalpy of pure isobutanol at 270 kPa), ΔH2 = 40,333.02 kJ/kmol

6. CONCLUSIONS After investigation into four design options (CDiC, MVR, DED, and DRP) for close-boiling separations, the following conclusions are reached and are believed to be a great reference valuable to other close-boiling binary systems. 5088


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Figure 18. Rigorous design flow sheet via DED for isobutanol/n-butanol separation.

Figure 19. Rigorous design flow sheet via DRP for isobutanol/n-butanol separation.

Table 3. Summary of Shortcut and Rigorous Methods for Three Different Close-Boiling Binary Systems Method

TAC of CDiC (US$/a)

TAC of MVR (US$/a)

TAC of DED (US$/a)

TAC of DRP (US$/a)

Me1-Me2 shortcut Me1-Me2 rigorous Relative error MCP-CH shortcut MCP-CH rigorous Relative error Isobutanol/n-butanol shortcut Isobutanol/n-butanol rigorous Relative error

34,104,962 (0.0%) 34,121,532 (0.0%) 0.0486% 10,487,739 (0.0%) 10,144,000 (0.0%) 3.3886% 10,547,128 (0.0%) 9,768,183 (0.0%) 7.9743%

23,876,678 (−30.0%) 24,370,540 (−28.6%) 2.0265% 8,411,348 (−19.8%) 8,161,048 (−19.5%) 3.0670% 7,949,387 (−24.6%) 7,554,379 (−22.7%) 5.2289%

29,802,699 (−12.6%) 29,702,456 (−13.0%) 0.3375% 8,701,222 (−17.0%) 8,668,538 (−14.5%) 0.3770% 8,162,930 (−22.6%) 8,071,618 (−17.4%) 1.1313%

37,536,107 (+10.1%) 40,995,119 (+20.1%) 8.4376% 11,747,505 (+12.0%) 13,384,494 (+31.9%) 12.2305% 10,853,482 (+2.9%) 12,654,926 (+29.6%) 14.2351%

(3) The DRP can lower the height of distillation columns compared to other options, but this advantage fails to convert into an overall TAC reduction. However, it is still a nice option when columns in the other three options are too high.

(1) The shortcut methods of different design options are provided and verified by rigorous simulations, showing easy realization with the aid of computer programming and effective prediction of TACs with considerable accuracy. They help conceptual design, parametric study, optimization, and quick decision-making. (2) In terms of TAC evaluation, MVR and DED options provide better performance than CDiC and DRP alternatives in close-boiling separations. In addition, the MVR scheme is generally better than the DED process.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00935. 5089


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Hc N Nmin NR NS P Q q R Rmin T V Wc

Detailed comparisons of shortcut method and rigorous simulation (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail addresses: [email protected] (H. Sui). *E-mail addresses: [email protected] (J. Sun). ORCID

Jinsheng Sun: 0000-0002-0665-3841 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by the 973 National Key Basic Research Program of China (No. 2015CB251403) and the International S&T Cooperation Program of China, ISTCP (No. 2015DFR40910).

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Greek Letters

α λ η θ

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NOMENCLATURE

Acronyms

AHP AOT CDiC CH COP CRHP CW DED DRP DWC ED FS HAD HIDiC HPAD HPC LMTD LP LPC LSF LSR MCP Me1 Me2 MVR PBP RLF SRK TAC TCDS TVR VC VLE

Absorption heat pump Annual operating time Conventional distillation column Cyclohexane Coefficient of performance Compression−resorption heat pump Cooling water Double-effect distillation Distillation with a recycle process Divided-wall column Extractive distillation Feed splitting Heterogeneous azeotropic distillation Heat integrated distillation column Heat pump assisted distillation High-pressure column Logarithmic mean temperature difference Low pressure Low-pressure column Light split forward Light split reverse Methylcyclopentane Methyltrichlorosilane Dimethylchlorosilane Mechanical vapor recompression Payback period Reboiler-liquid flashing Soave−Redlich−Kwong Total annualized cost Thermally coupled distillation sequence Thermal vapor recompression Vapor compression Vapor−liquid equilibrium

Relative volatility Ratio of real reflux ratio over minimum reflux ratio Stage efficiency Common root of Underwood equation

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Roman Letters

A B C D Dc F H

Height of distillation column Number of stages Minimum number of stages Rectifier stage number Stripper stage number Pressure Heat duty Thermal condition of feed Reflux ratio Minimum reflux ratio Temperature Average gas flow rate Compression work

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