Reactive Distillation Columns with a Top-Bottom External Recycle

Article pubs.acs.org/IECR

Reactive Distillation Columns with a Top-Bottom External Recycle Haisheng Chen, Kejin Huang,* Liang Zhang, and Shaofeng Wang College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: Although reactive distillation columns represent a promising technology for process intensification between reaction operation and separation operation, it is difficult to use for the separation of reacting mixtures with the most and the least volatile reactants (i.e., the most unfavorable ranking of relative volatilities). To overcome the difficulty, we propose two novel configurations featured a top-bottom external recycle for the separation of exothermic and endothermic reactions, respectively. While the external recycle should be directed from the top to the bottom for the exothermic reactions, it should be from the bottom to the top for the endothermic reactions. With the arrangement of a reactive section at the bottom for the exothermic reactions and at the top for the endothermic reactions, the two process configurations proposed favor considerably internal mass integration and internal energy integration between the reaction operation and the separation operation involved and help, consequently, to enhance the thermodynamic efficiencies of the reactive distillation columns. A simple and effective procedure for process synthesis and design is devised, and four examples, including an ideal quaternary exothermic reaction, an ideal quaternary endothermic one, the esterification of latic acid with methanol, and the esterification of palmitic acid with isopropanol, are chosen to evaluate the two configurations proposed. The obtained results show that they are definitely superior to those with two or one reactive sections at both or either ends in the aspect of capital investment and operating cost. They are also demonstrated to be highly competitive alternatives to the conventional reactor/separator/recycle systems.

1. INTRODUCTION The ranking of the relative volatilities of reacting mixtures can present a great influence to the performance of reactive distillation columns.1−3 In some circumstances, it can even cause the reactive distillation columns to be uncompetitive with their conventional counterparts (e.g., a reactor plus several conventional distillation columns). In the case that the reactants are the light and heavy components, and the products are the lightest and heaviest ones (i.e., the most favorable ranking of relative volatilities), a reactive distillation column with its reactive section between rectifying section and stripping section (c.f., Figure 1a) can offer significant economical benefit (i.e., reduction of capital investment and operating cost). The reasons stem from the facts that the unconverted reactants can be easily separated from the products and recycled back to the reactive section.4−6 In the case that the reactants are the lightest and heaviest components and the products are the ones in-between (i.e., the most unfavorable ranking of relative volatilities), if the reactive distillation column with an intermediate reactive section is still used, the unconverted reactants cannot be easily separated from the products and recycled back to the reactive section (c.f., Figure 1b), incurring therefore significant capital investment and operating cost. The analysis indicates the drawback of the reactive distillation columns in the separation of this kind of reacting mixtures and reminds us of the needs to considering the impact of the ranking of relative volatilities on process synthesis and design. Up to now, only a few studies have been reported on the synthesis and design of reactive distillation columns separating the reacting mixtures with the most unfavorable ranking of relative volatilities. Taking the advantages of the high presence of reactants at the top and the bottom, Tung and Yu1 put forward a process design with two reactive sections at its both ends. Although a certain extent of improvement could be secured in © 2012 American Chemical Society

reaction conversion, adverse internal energy integration emerged. While the thermal heat released from the top reactive section could not be utilized to aid the separation operation in case of exothermic reactions, the thermal heat from the rectifying section could not be used for the reaction operation at the bottom reactive section in case of endothermic reaction. This inevitably lowered the thermodynamic efficiency of this kind of reactive distillation column. In 2009, Thotla and Mahajani7 proposed a process design with a reactive section at its top for the esterification of lactic acid with methanol (an exothermic reaction). Although a relatively high conversion rate was achieved, as compared with the configuration showed in Figure 1b, adverse internal heat integration occurred because the reactive section was arranged at the top of the process. Another problem was that no measure was taken at all to deal with the accumulation of the lightest/heaviest reactants at the top/bottom, respectively. These deficiencies confined the thermodynamic efficiency of this kind of reactive distillation columns. For the esterification of palmitic acid with isopropanol (an endothermic reaction), Bhatia et al.8 suggested a process flow-sheet comprising a reactive distillation column, a recovery column, and a membrane unit or another recovery column. Although the reactive distillation column gave rise to a relatively higher conversion of palmitic acid than did the configuration shown in Figure 1b, the reactive section was placed onto the whole stages and this led to adverse internal energy integration in the lower part of the process, lessening consequently the thermodynamic efficiency of this kind of reactive distillation columns. In terms of the above analysis, it is clarified Received: Revised: Accepted: Published: 14473

July 28, 2012 October 7, 2012 October 16, 2012 October 16, 2012 dx.doi.org/10.1021/ie302014m | Ind. Eng. Chem. Res. 2012, 51, 14473−14488

Industrial & Engineering Chemistry Research

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and the reactive distillation columns with two or one reactive sections, the advantages of the RDC-TBER are highlighted, and extensive application of the external recycle to the RDC-TBER is also attempted. Some concluding remarks are summarized in the last section of the article.

2. PRINCIPLE OF THE RDC-TBER Owing to the most unfavorable relative volatilities of the reacting mixture separated, the lightest and heaviest reactants are hardly to be maintained in close contact no matter how the reactive section is arranged along the height of the reactive distillation column. The inherent difficulty inspires the proposal of the RDC-TBER, as shown in Figure 2. The lightest/heaviest reactants

Figure 1. Advantages and disadvantages of reactive distillation columns with an intermediate reactive section: (a) separation of reacting mixtures with the most favorable relative volatilities, (b) separation of reacting mixtures with the most unfavorable relative volatilities.

that the difficulties given by the most unfavorable ranking of relative volatilities cannot be completely resolved with the careful distributions of the reactive section, and this reflects the structural pitfall of the reactive distillation columns. Considering the fact that the lightest/heaviest reactants are apt to accumulate at the top/bottom, respectively, one may introduce an external recycle between the top and bottom to strengthen their contact in the reactive section, and this is quite likely to enhance the conversion rate in addition to the further reinforcement of internal mass integration and internal energy integration between the reaction operation and the separation operation involved. This modification leads to the creation of a novel reactive distillation column with a top-bottom external recycle (termed, hereinafter, the RDC-TBER), which is certainly worth detailed studies. The purpose of the current work is to assess the performance of the RDC-TBER in the separation of reacting mixtures with the most unfavorable relative volatilities. Two configurations of the RDC-TBER are devised for the separation of exothermic and endothermic reactions, respectively, and a simple procedure is developed for process synthesis and design in terms of the minimization of an economical objective function (EOF). Four reactive distillation columns, comprising the separation of an ideal quaternary exothermic reaction, an ideal quaternary endothermic one, latic acid esterification with methanol, and palmitic acid esterification with isopropanol, are chosen as illustrative examples to evaluate the performance of the RDC-TBER. Through strict comparison with their conventional counterparts

Figure 2. Schemes of the RDC-TBER: (a) for exothermic reactions, (b) for endothermic reactions.

are fed onto the bottom/top of the reactive section, respectively, and the product is withdrawn as an intermediate product in the nonreactive section. An external recycle is added between the top and bottom of the reactive distillation column and serves to suppress the unfavorable separation between the lightest and heaviest reactants. The direction of the external flow should be determined in accordance with the thermodynamic characteristics of the reaction operation involved. More specifically, while it should be from the top to the bottom for an exothermic reaction (c.f., Figure 2a), the reverse is true for an endothermic reaction (c.f., Figure 2b). The external linkage between the top and bottom can present a favorable effect to the 14474

dx.doi.org/10.1021/ie302014m | Ind. Eng. Chem. Res. 2012, 51, 14473−14488


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of the external recycle) are adjusted sequentially to optimize the system performance in terms of the chosen EOF. While the adjustments of the structural variables can be accomplished with a trial and error method because of their discontinuity in nature, the adjustments of the operating variables are conducted by a modified steepest gradient method. Generally, the recursive computation can be converged in a few iterations, and the following convergence criterion is employed here.

reaction operation involved and is quite likely to enhance the thermodynamic performance of the RDC-TBER. The placement of the reactive section should also be decided according to the thermodynamic characteristics of the reaction operation involved. Namely, while it should be superimposed onto the stripping section (frequently including the reboiler as well) for an exothermic reaction (c.f., Figure 2a), it should be onto the rectifying section (frequently including the condenser as well) for an endothermic reaction (c.f., Figure 2b). The two schemes are either advantageous in utilizing the thermal heat generated from the reaction operation to the separation operation or capable of applying the thermal heat released from the rectifying section to the reaction operation. With the incorporation of the external recycle between the top and bottom of the RDC-TBER, a higher degree of internal mass integration and internal energy integration can be expected between the reaction operation and the separation operation involved than those reactive distillation columns with one or two reactive sections. As a result, a certain extent of improvement can be expected in system performance.

|EOF(J + 1) − EOF(J )| /EOF(J ) ≤ ξ

(1)

where ξ is a predetermined error tolerance. Finally, the optimal value of the total number of stages of the RDC-TBER is searched in terms of the chosen EOF. Again, a trial and error search method can be used here. The proposed procedure features great simplicity in principle and high robustness to the guess of the initial process design and the thermodynamic properties of the reacting mixtures separated. It even works effectively for the synthesis and design of some more complicated chemical processes (e.g., the fully thermally coupled distillation columns).9 The EOF is chosen to be the minimization of total annual cost (TAC) in the current work. The TAC is the sum of operating cost (OC) and annual capital investment, which is assumed to be the capital investment (CI) divided by a payback period (c.f., eq 1). The cost of equipments and utilities is estimated with the formulas shown in Appendix A.10

3. SYNTHESIS AND DESIGN OF THE RDC-TBER According to the features of the variables to be determined in the synthesis and design of the RDC-TBER, it is reasonable to divide them into two categories, structural variables and operating variables. For the structural variables, they include the total number of stages of the RDC-TBER, the total kinetic holdups, the number of stages in the reactive section, and the locations for feeding the lightest and heaviest reactants and withdrawing the intermediate product. Since the locations for feeding the lightest and heaviest reactants exhibit quite a limited influence to the separation of the reacting mixtures with the most unfavorable relative volatilities, they are fixed exclusively at the bottom and top of the reactive section in the current work. For the operating variables, they contain the reflux flow rate, the operating pressure, and the flow rate of the external recycle. While the first one is used to keep the intermediate product on the given specification, the others are chosen to maximize the thermodynamic efficiency of the RDC-TBER. To avoid catalyst deactivation, the operating pressure is limited to be less than or equal to 1500 kPa in the current work. Figure 3 demonstrates a simple iterative procedure for the synthesis and design of the RDC-TBER in terms of the optimization of a chosen EOF. With the physicochemical properties and design specifications given, an initial process design is first constructed with a careful guess of the four structural variables (i.e., the total number of stages of the RDC-TBER, the total kinetic holdups, the number of stages in the reactive section, and the location for withdrawing the intermediate product) and two operating variables (i.e., the operating pressure and the flow rate of the external recycle) in addition to the adjustment of another operating variable (i.e., the reflux flow rate). The initial process design serves merely as a framework to confine the structural and operating variables. Except for the attainment of the desired product quality, no strict requirements have actually been made on the performance of the RDC-TBER, making the finding of the initial process design not very difficult with the aid of the steadystate process model. Second, the three structural variables (i.e., the total kinetic holdups, the number of stages in the reactive section, and the location for withdrawing the intermediate product) and the two operating variables (i.e., the operating pressure and the flow rate

TAC = OC + CI/β

(2)

4. EXAMPLE I: SEPARATION OF A HYPOTHETICAL kF

EXOTHERMIC REACTION A + B ⇌ C + D kB 4.1. Problem Description. An ideal quaternary reversible reaction occurs in the reactive section of the RDC-TBER to be developed. kF

A+B⇌C+D kB

(3)

The reactants A and B are the lightest and heaviest components, respectively, and the products C and D are the intermediate boiling components between the two reactants. Ideal vapor and liquid phase behavior is assumed for the reaction system and the vapor−liquid equilibrium relationship can be expressed as s Pj = xA, jPA,s j + x B, jPB,s j + xC, jPC,s j + x DPD, j

(4)

yi , j = xi , jPis, j/Pj

(5)

The vapor saturation pressure is calculated as ln Pis, j = A vp, i − Bvp, i /Tj

(6)

The reaction rate of component i on stage j can be expressed in terms of the mole fractions (xi, j) and the kinetic holdup (Mj). ratei , j = νiMj(kF, jxA, jx B, j − kB, jxC, jx D, j)

(7)

where kF,j and kB,j are the forward and backward specific reaction rates, which are given by

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kF, j = aF e−EF / RTj

(8)

kB, j = aB e−EB / RTj

(9)



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Figure 3. An iterative procedure for the synthesis and design of the RDC-TBER.

Lj = Lj − 1

Owing to the thermal heat of the reaction operation involved, the vapor and liquid flow rates change from stage to stage in the reactive section and can be calculated as Vj = Vj + 1 − rateC, j × ΔHR /ΔHV

(10)

Lj = Lj − 1 + rateC, j × ΔHR /ΔHV

(11)

The physicochemical properties and design specifications are given in Table 1. The sizing and economical basis for process synthesis and design is listed in Table 2. The process simulation is conducted using the steady-state model described in Appendix B. 4.2. Synthesis and Design of the RDC-TBER. Because the reaction involved is an exothermic one, the reactive section is placed at the bottom (including the reboiler as well) of the RDCTBER, and the external recycle is directed from the top to the

The vapor and liquid flow rates are kept constant in the nonreactive section.

Vj = Vj + 1

(13)

(12) 14476



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Table 1. Physicochemical Properties and Design Specifications of Example I parameter product specification (mol %) activation energy (kJ/kmol) specific reaction rate at 366 K (kmol/s·kmol) relative volatility A:B:C:D heat of reaction (kJ/kmol) latent heat of vaporization (kJ/kmol) vapor pressure constants

value C D forward backward forward backward

A (Avp/Bvp) B (Avp/Bvp) C (Avp/Bvp) D (Avp/Bvp)

47.5 47.5 50208 112968 0.008 0.004 8:1:4:2 −62760 29053.7 17.65/3862 15.57/3862 16.95/3862 16.26/3862

Table 2. Economical Basis for Process Synthesis and Design parameter condensers heat transfer coefficient (kW/K·m2) temp. difference (K) reboilers heat transfer coefficient (kW/K·m2) temp. difference (K) payback period (year) steam cost ($/ton)

value 0.852 13.9 0.568 34.8 3 25(0.985 + 0.015 × P/100)

bottom. According to the procedure described in Figure 3, the synthesis and design of the RDC-TBER starts from an initial process design arbitrarily chosen with the total number of stages as 29, the total kinetic holdups as 500 kmol, the number of stages in the reactive section as 5, the intermediate product at 15th stage, the operating pressure as 400 kPa, and the flow rate of the external recycle as 4 × 10−3 kmol/s. The obtained relationships among the TAC and the structural variables (i.e., the total number of stages of the RDC-TBER, the total kinetic holdups, the number of stages in the reactive section, and the stage for withdrawing the intermediate product) and the operating variables (i.e., the operating pressure, and the flow rate of the external recycle) are shown in Figures 4 and 5, respectively. The resultant optimum design of the RDC-TBER is depicted in Figure 6a. 4.3. Economical Assessment of the RDC-TBER. Here, a thorough comparison is made among the RDC-TBER and a conventional scheme, a reactive distillation column with two reactive sections at its both ends (RDC-TRS), and a reactive distillation column with one reactive section at its either end (RDC-ORS). The conventional scheme is chosen to be a continuous stirred tank reactor plus a conventional distillation column (CSTR-CDC) separating the lightest and heaviest reactants from the intermediate products and recycling them back to the continuous stirred tank reactor (CSTR). The process flow-sheet stands for the most efficient technique for the separation of reacting mixtures with the most unfavorable relative volatilities. In Table 3, the outcomes of process synthesis and design are tabulated for the CSTR-CDC, RDC-TRS, RDCORS, and RDC-TBER. With reference to the CSTR-CDC (c.f., Figure 6b), while the RDC-TRS (c.f., Figure 6c) and the RDC-ORS (c.f., Figure 6d) lead to a sharply augmented

Figure 4. TAC versus the structural variables of the RDC-TBER for Example I: (a) total number of stages, (b) total kinetic holdups, (c) stages in the reactive section, and (d) stage of the intermediate product.

TAC by 205.71% (i.e., increased CI and OC by 27.97% and 348.28%, respectively) and 1013.33% (i.e., increased CI and OC by 318.18% and 1570.69%, respectively), the RDCTBER results in a reduced one by 24.76% (i.e., reduced CI and increased OC by 27.97% and 22.41%, respectively). 14477



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Figure 5. TAC versus the operating variables of the RDC-TBER for Example I: (a) operating pressure, (b) flow rate of the external recycle.

The comparison implies the great effect of the external recycle in strengthening internal mass integration and internal energy integration between the reaction operation and the separation operation involved.

5. EXAMPLE II: SEPARATION OF A HYPOTHETICAL kF

ENDOTHERMIC REACTION A + B ⇌ C + D kB 5.1. Problem Description. The problem has been adapted from Example I with the following modifications: The reaction is assumed to be an endothermic one with a heat of reaction ΔHR = 62 760 kJ/kmol (14) The forward and backward activation energies have been exchanged with each other, namely, E F = 112 968 kJ/kmol

(15)

E B = 50 208 kJ/kmol

(16)

5.2. Synthesis and Design of the RDC-TBER. Because the reaction involved is an endothermic one, the reactive section is placed at the top (including the condenser as well) of the RDC-TBER, and the external recycle is directed from the bottom to the top. The synthesis and design of the RDCTBER begins from an initial process design with the total number of stages as 29, the total kinetic holdups as 30 kmol, the number of stages in the reactive section as 5, the stage for withdrawing the intermediate product as 18, the operating pressure as 1200 kPa, and the flow rate of the external recycle as 1.2 × 10−3 kmol/s. The relationships among the TAC and the six decision variables (i.e., the total number of stages of the

Figure 6. Optimum process designs for Example I: (a) RDC-TBER, (b) CTSR-CDC, (c) RDC-TRS, and (d) RDC-ORS.

RDC-TBER, the total kinetic holdups, the number of stages in the reactive section, the stage of withdrawing the intermediate 14478



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Table 3. Comparisons among the Various Process Designs for Example I parameter total no. stages no. reactive stages (including reactor/condenser/reboiler) reactive holdup per reactive stage (kmol) reactive holdup on reboiler/reactor (kmol) reboiler duty (MW) reactor diam. (m) column diam. (m) reactor height (m) column height (m) CI × 106 ($) OC × 106 ($) TAC × 106 ($) comparison in CI (%) comparison in OC (%) comparison in TAC (%)

CSTRCDC 44 1

RDCTRS

RDCORS

RDCTBER

44 11

70 22

32 1

4

4

306

100

542

546

1.63 2.3 1.22 4.6 30 1.43 0.58 1.05 100 100 100

6.93

25.14

1.26

2.01

3.7

1.36

30.72 1.83 2.6 3.21 127.97 448.28 305.71

49.74 5.98 9.69 11.69 418.18 1670.69 1113.33

21.95 1.03 0.45 0.79 72.03 77.59 75.24

product, the operating pressure, and the flow rate of the external recycle) are shown in Figures 7 and 8. The resultant optimum RDC-TBER is shown in Figure 9a. 5.3. Economical Assessment of the RDC-TBER. The comparison among the CSTR-CDC, RDC-TRS, RDC-ORS, and RDC-TBER is made in Table 4. The RDC-TRS (c.f., Figure 9c) and the RDC-ORS (c.f., Figure 9d) are again uncompetitive with the CSTR-CDC (c.f., Figure 9b), presenting an augmented TAC by 253.61% (i.e., increased CI and OC by 132.69% and 282.28%, respectively) and 128.87% (i.e., increased CI and OC by 92.31% and 139.24%, respectively). The RDC-TBER, on the other hand, shows comparable performance with the CSTR-CDC, displaying a reduced TAC by 15.46% (i.e., reduced CI and increased OC by 13.46% and 15.19%, respectively).

6. EXAMPLE III: SEPARATION OF THE LACTIC ACID ESTERIFICATION WITH METHANOL 6.1. Problem Description. The exothermic reaction, esterification of lactic acid with methanol, is separated with the RDC-TBER to be developed.7 Lactic Acid (LA) + Methanol (MeOH) kF

⇌ Methyl Lactate (MLA) + Water (W) kB

(17)

The normal boiling points of the reacting components, which are found from the database of Aspen Plus V7.1, are tabulated in Table 5, and the reaction heat is −7230.91 kJ/kmol. It is noted that there exist no azeotropes in this mixture, with the heaviest and the lightest components being the reactants LA and MeOH, respectively, and the products MLA and W being the intermediate boiling components, respectively. Therefore, the reacting mixture has the most unfavorable ranking of relative volatilities. As described in Appendix C, the process is simulated using the commercial software Aspen Plus V7.1, and the UNIQUAC property method is utilized to calculate the activity coefficients of the reacting components.11 A pseudo-homogeneous activity-based kinetic model is used to calculate the

Figure 7. TAC versus the structural variables of the RDC-TBER for Example II: (a) total number of stages, (b) total kinetic holdups, (c) stages in the reactive section, and (d) stage of the intermediate product.

reaction rate (c.f., eq 18). The relevant binary interaction parameters and the values of kinetic parameters are denoted in Tables 6 and 7, respectively. 14479



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Figure 8. TAC versus the operating variables of the RDC-TBER for Example II: (a) operating pressure, (b) flow rate of the external recycle.

ratei , j = kF exp( −E F /RTj)(αLA, jαMeOH, j) − kB exp( −E B /RTj)(αMLA, jαW, j)

(18)

6.2. Synthesis and Design of the RDC-TBER. Analogous to Example I, the reactive section is placed at the bottom (including the reboiler as well) of the RDC-TBER, and the external recycle is directed from the top to the bottom. The process synthesis and design is commenced from an initial process design with the total number of stages as 13, the total kinetic holdups as 20 kmol, the number of stages in the reactive section as 7, the stage for withdrawing the intermediate product as 6, the operating pressure as 300 kPa, and the flow rate of the external as 3 × 10 −6 kmol/s. The relationships among the TAC and the structural variables (i.e., the total number of stages of the RDC-TBER, the total kinetic holdups, the number of stages in the reactive section, and the stage of withdrawing the intermediate product) and the operating variables (i.e., the operating pressure and the flow rate of the external recycle) are shown in Figures 10 and 11, respectively. The optimum process design is sketched in Figure 12a. 6.3. Economical Assessment of the RDC-TBER. The comparison among the CSTR-CDC, RDC-TRS, RDC-ORS, and RDC-TBER is conducted in Table 8. The RDC-TRS (c.f., Figure 12c) and the RDC-ORS (c.f., Figure 12d) are advantageous over the CSTR-CDC (c.f., Figure 12b), rendering a reduced TAC by 4.94% (i.e., decreased CI and OC by 15.87% and 1.67%, respectively) and 17.28% (i.e., decreased CI and OC by 31.75% and 15%, respectively). The RDC-TBER is far superior to the CSTR-CDC, displaying a considerably reduced TAC by 23.46% (i.e., reduced CI and OC by 26.98% and 21.67%, respectively).

Figure 9. Optimum process designs for Example II: (a) RDC-TBER, (b) CTSR-CDC, (c) RDC-TRS, and (d) RDC-ORS.

It can be noted that the RDC-TBER has still much better economical performance than the RDC-TRS and the RDC-ORS in this case. 14480



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Table 4. Comparisons among the Various Process Designs for Example II parameter total no. stages no. reactive stages (including reactor/condenser/reboiler) reactive holdup per reactive stage (kmol) reactive holdup on condenser/ reactor (kmol) reboiler duty (MW) reactor diam. (m) column diam. (m) reactor height (m) column height (m) CI × 106 ($) OC × 106 ($) TAC × 106 ($) comparison in CI (%) comparison in OC (%) comparison in TAC (%)

CSTRCDC

RDCTRS

RDCORS

RDCTBER

32 1

23 4

29 12

35 5

4

4

4

14

84

60

10

1.12 0.82 0.64 1.65 21.21 0.52 0.79 0.97 100 100 100

7.44

4.48

1.6

1.77

1.31

0.78

15.36 1.21 3.02 3.43 232.69 382.28 353.61

19.75 1 1.89 2.22 192.31 239.24 228.87

24.14 0.45 0.67 0.82 86.54 84.81 84.54

Table 5. Physicochemical Properties and Design Specifications of Example III parameter

value

pressure (kPa) product specification (mol %) boiling point (K)

100 49.7 (MLA) 337.85 (MeOH) 490 (LA) 417.95 (MLA) 373.15 (W)

Table 6. Binary Interaction Parameters of UNIQUAC Model for Example III LA MeOH MLA W

LA

MeOH

MLA

W

0 −1040.75 208.41 −499.38

452.35 0 −41.42 −351.0861

−288.41 −7.37 0 219.62

357.47 165.26 −394.57 0

Table 7. Kinetic Parameters of Pseudo-homogeneous Activity-Based Model for Example III parameter

value

EF × 103 (kJ/kmol) EB × 103 (kJ/kmol) Log kF (kmol/kg·s) Log kB (kmol/kg·s)

53.1 ± 6.51 40.1 ± 16.07 18.84 ± 2.25 13.45 ± 5.56

7. EXAMPLE IV: SEPARATION OF THE PALMITIC ACID ESTERIFICATION WITH ISOPROPANOL 7.1. Problem Description. The endothermic reaction, esterification of palmitic acid with isopropanol, is separated with the RDC-TBER to be developed.

Figure 10. TAC versus the structural variables of the RDC-TBER for Example III: (a) total number of stages, (b) total kinetic holdups, (c) stages in the reactive section, and (d) stage of the intermediate product.

Palmitic Acid (PA) + Isopropanol (IP) kF

⇌ Isopropyl Palmitate (IPP) + Water kB

minimum-boiling azeotrope, its influences can be neglected because of the high conversion rate specified in the current work. It is thus still reasonable to treat the reactants PA and IP are the heaviest and the lightest components, respectively, and the products IPP and W are the intermediate boiling components.

(19)

The normal boiling points of the reacting mixture are found from Bhatia’s work and reproduced in Table 9, and the reaction heat is 18 900.01 kJ/kmol.12 Although W and IP form a 14481



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Figure 11. TAC versus the operating variables of the RDC-TBER for Example III: (a) operating pressure, (b) flow rate of the external recycle.

Therefore, the reacting mixture has the most unfavorable ranking of relative volatilities. As described in Appendix C, the RDC-TBER is simulated with the commercial software Aspen Plus V7.1, and the UNIQUAC property method is applied to calculate the activity coefficients of the reacting components. The reaction rate can be represented by the LHHW model shown in eq 20, and the relevant equilibrium constant is described by eq 21. The binary interaction parameters are listed in Table 10, and the relevant equilibrium constants of the reaction rate and the values of kinetic parameters are given in Table 11.8,12 ⎛ E ⎞ ⎟⎟ ratei , j = kF exp⎜⎜ − ⎝ RTj ⎠ ×

(αPA, jαIP, j − αIPP, jαW, j/Keq) (1 + KPAαPA, j + KIPαIP, j + KW αW, j)2

Keq = 1256 e−1505/ Tj

(20) (21)

7.2. Synthesis and Design of the RDC-TBER. Similar to Example II, the reactive section is placed at the top (including the condenser as well) of the RDC-TBER, and the external recycle is directed from the bottom to the top. The process synthesis and design is initiated from an initial process design with the total number of stages as 20, the total kinetic holdups as 84 kg, the number of stages in the reactive section as 8, the stage for withdrawing the intermediate product as 12, the operating pressure as 200 kPa, and the flow rate of the external as 2 × 10−3 kmol/s. The relationships among the TAC and the total number of stages of the RDC-TBER, the total kinetic holdups, the stage for withdrawing the intermediate product, the number of stages in the reactive section, the operating pressure, and the flow rate of

Figure 12. Optimum process designs for Example III: (a) RDC-TBER, (b) CTSR-CDC, (c) RDC-TRS, and (d) RDC-ORS.

the external recycle are shown in Figures 13 and 14. The optimum process design is depicted in Figure 15a. 7.3. Economical Assessment of the RDC-TBER. The comparison among the CSTR-CDC, RDC-TRS, RDC-ORS, and RDC-TBER is shown in Table 12. The RDC-TRS (c.f., Figure 15c) is inferior to the CSTR-CDC (c.f., Figure 15b), presenting an increased TAC by 187.89% (i.e., an increased CI and OC by 89% and 187.89%, respectively). The RDC-ORS 14482



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Table 8. Comparisons among the Various Process Designs for Example III parameter total no. stages no. reactive stages (including reactor/ condenser/reboiler) reactive holdup per reactive stage (kmol) reactive holdup in reboiler/reactor (kmol) reboiler duty (MW) reactor diam. (m) column diam. (m) reactor height (m) column height (m) CI × 106 ($) OC × 106 ($) TAC × 106 ($) comparison in CI (%) comparison in OC (%) comparison in TAC (%)

CSTRCDC

RDCTRS

RDCORS

RDCTBER

25 1

18 2

14 6

15 4

1

1

8

14

23

5

1.67 0.68 0.93 1.37 18.29 0.63 0.6 0.81 100 100 100

1.68

1.45

1.32

1.27

0.99

1.03

10.97 0.53 0.59 0.77 84.13 98.33 95.06

10.24 0.43 0.51 0.67 68.25 85 82.72

10.97 0.46 0.47 0.62 73.02 78.33 76.54

Table 9. Physicochemical Properties and Design Specifications of Example IV parameter

value

pressure (kPa) product specification (mol %) boiling point (K)

100 49.7 (IPP) 353.46 (IP/W) 355.4 (IP) 624.15 (PA) 599.9 (IPP) 373.15 (W)

Table 10. Binary Interaction Parameters of UNIQUAC Model for Example IV PA IP IPP W

PA

IP

IPP

W

0 −94.050 165.381 418.407

300.239 0 605.248 383.050

−137.681 −150.672 0 417.930

783.613 59.713 1490.770 0

Table 11. Reaction Parameters of LHHW Models for Example IV parameter

value

E0 (kJ/kmol) kF (kmol/kg·s) KPA KIP KW n

35000 5999.98 0.0049 0.0966 0.6483 2

Figure 13. TAC versus the structural variables of the RDC-TBER for Example IV: (a) total number of stages, (b) total kinetic holdups, (c) stages in the reactive section, and (d) stage of the intermediate product.

(c.f., Figure 15d) is advantageous over the CSTR-CDC, displaying a reduced TAC by 4.74% (i.e., a decreased CI and increased OC by 29% and 1.28%, respectively). The RDC-TBER outperforms again the CSTR-CDC, displaying a considerably reduced TAC by 18.42% (i.e., an increased CI and reduced OC by 6% and 23.08%, respectively). It can be noted that the RDCTBER provides the best economical performance among the four process designs examined.

8. DISCUSSION For the entire example systems studied in this work, the RDC-TBER displays a lower TAC than the CSTR-CDC, the 14483



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Figure 14. TAC versus the operating variables of the RDC-TBER for Example IV: (a) operating pressure, (b) flow rate of the external recycle.

Table 12. Comparisons among the Various Process Designs for Example IV parameter total no. stages no. reactive stages (including reactor/ condenser/reboiler) reactive holdup per reactive stage (kg) reactive holdup in condenser/reactor (kg) reboiler duty (MW) reactor diam. (m) column diam. (m) reactor height (m) column height (m) CI × 106 ($) OC × 106 ($) TAC × 106 ($) comparison in CI (%) comparison in OC (%) comparison in TAC (%)

CSTRCDC

RDCTRS

RDCORS

RDCTBER

16 1

24 3

13 6

22 5

84

3 30.5

3 59

3 62

13.76

4.32

3.41

2.97

0.99

2.23

17.56 1.89 4.84 5.47 189 310.26 287.89

8.05 0.71 1.58 1.81 71 101.28 95.26

16.09 1.06 1.2 1.55 106 76.92 81.58

4.45 0.41 1.99 0.81 9.51 1 1.56 1.9 100 100 100

RDC-TRS and the RDC-ORS, irrespective of the design specifications given and the physicochemical properties of the reacting mixtures separated (e.g., whether the reaction involved is exothermic or endothermic, and whether the vapor−liquid equilibrium relationship is ideal or nonideal). This outcome indicates that the addition of an external recycle between the top and bottom of the RDC-TBER can really benefit internal mass integration and internal energy integration between the reaction operation and the separation operation involved and facilitate the process to be a competitive alternative in the separation of reactive mixtures with the most unfavorable relative volatilities. For the RDC-TRS, though it intuitively makes use of the special

Figure 15. Optimum process designs for Example IV: (a) RDC-TBER, (b) CTSR-CDC, (c) RDC-TRS, and (d) RDC-ORS.

feature in the distribution of the lightest and heaviest components, it fails to be competitive with the RDC-TBER. The reason lies probably on the inappropriate internal mass integration and internal energy integration between the reaction operation and the separation operation involved. The RDC-TBER offers better performance than the RDC-ORS and a relatively 14484



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Figure 16. Schemes of the RDC-TER: (a) for exothermic reactions and (b) for endothermic reactions.

Table 13. Comparisons between the RDC-TBER and the RDC-TER reboiler duty (MW)

comparison (%)

example

RDC-TBER

RDC-TER

RDC-TBER

RDC-TER

example I example II example III example IV

1.26 1.6 1.32 3.41

1.1 1.59 1.28 3.35

100 100 100 100

87.3 99.38 96.97 98.24

low operating pressure is usually needed to meet the design specifications. This is indispensable to the addition of a topbottom external recycle, which enhances greatly internal mass integration and internal energy integration between the reaction operation and the separation operation involved. It is interesting to examine the resultant designs of the RDCTBER in the separation of exothermic and endothermic reacting mixtures with the most unfavorable ranking of relative volatilities. While for Examples I and III, the RDC-TBER needs a smaller number of stages than the conventional distillation column in the CSTR-CDC, for Examples II and IV the reverse is true. The phenomenon comes actually from the different strategies applied to locate the reactive section in process synthesis and design, namely, the reactive section is overlapped onto the top end of the RDC-TBER in case of endothermic reaction and onto the

Figure 17. Optimum designs for the RDC-TER: (a) Example I, (b) Example II, (c) Example III, and (d) Example IV.

bottom end of the RDC-TBER in case of exothermic reaction. Because of the temperature and pressure gradients from the top to the bottom, the reaction occurring at the top/bottom end of the RDC-TBER has a relatively lower/higher reaction rate than the continuous stirred tank reactor in the CSTR-CDC, and this leads to the increase/decrease of the total number of stages in the 14485



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RDC-TBER as compared with that in the conventional distillation column of the CSTR-CDC. In fact, the performance of the RDC-TBER can be further improved with the addition of another external recycle from the condenser/reboiler to an intermediate stage of the process and the resultant scheme is termed the RDC-TER in the current work (c.f., Figure 16). This modification favors further internal mass integration between the reaction operation and the separation operation involved and contributes to enhancing system performance. In Table 13, a detailed comparison is made between the RDC-TBER and the RDC-TER in terms of the reboiler duty for all the four example systems studied in the current work (c.f., Figure 17). Here, the same total number of stages and operating conditions are adopted for the two process schemes. It is readily found that the RDC-TER is more efficient than the RDC-TBER and this confirms again the positive effect of the external recycle.

The length of a CSTR reactor is assumed to be twice the diameter

L R = 2DR

Assuming an F factor of 1 in engineering units, the diameter of a distillation column or a reactive distillation column is calculated from the equation DC = 0.01735(MW T100/P)0.25 (1000VT )0.5

(A3)

The height of a distillation column or a reactive distillation column is calculated from the equation LC = 0.73152N

(A4)

The heat transfer areas of the reboiler and condenser are calculated using the steady state vapor flow rates and the heat of vaporization

9. CONCLUSIONS With the inclusion of an external recycle between the top and bottom, two novel configurations of reactive distillation columns (i.e., the RDC-TBER) have been proposed for the separation of reacting mixtures with the most unfavorable relative volatilities. While the external recycle is directed from the top to the bottom in case that the reaction operation involved is exothermic, it is from the bottom to the top in case that the reaction operation involved is endothermic. In cooperation with the effective placement of the reactive section along the height of the RDC-TBER, the external recycle serves to reinforce internal mass integration and internal energy integration between the reaction operation and the separation operation involved and can enhance considerably system performance in the separation of reacting mixtures with the most unfavorable relative volatilities. An iterative procedure for the synthesis and design of the RDC-TBER has been developed, in which six structural and operating variables (i.e., the total number of stages, the total kinetic holdups, the stage for withdrawing the intermediate product, the number of stages in the reactive section, the operating pressure, and the flow rate of the external recycle) are adopted as decision variables to optimize system performance. In terms of the separation of two ideal quaternary reacting mixtures and two real reacting mixtures (i.e., the esterification of LA with MeOH and the esterification of PA with IP), the RDC-TBER has been demonstrated to have a lower TAC than the CSTR-CDC, the RDC-TRS, and the RDC-ORS. The results indicate that the RDC-TBER should be considered as a highly competitive alternative for the separation of reacting mixtures with the most unfavorable relative volatilities. Studies are now underway on the performance sensitivity of the RDC-TBER with respect to the physicochemical properties of the reacting mixtures separated and the design specifications given. Research work will also be conducted on process dynamics and controllability with special attention focused on the impact of the external recycle between the top and bottom of the RDC-TBER in the near future.

A CON = VT × ΔHV /(UCONΔTCON)

(A5)

AREB = VB × ΔHV /(UREBΔTREB)

(A6)

In terms of the above size estimations, the capital and energy costs of the individual equipments of CRDCS, RDC-TRS, RDCORS, and RDC-TBER, are estimated using the following equations: Reactor cost = 52920DR 1.066L R 0.802

(A7)

Column shell cost = 17640DC1.066LC 0.802

(A8)

Tray cost = 229DC1.55N

(A9)

Catalyst cost = CW × 7.71622

(A10)

Total heat exchanger cost = 7296AREB 0.65 + 7296A CON 0.65 (A11)

Energy cost = 348.948ΔHVVS(0.985 + 0.015

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P ) 100

(A12)

APPENDIX B: STEADY-STATE MODELS USED FOR EXAMPLES I AND II The steady-state models of the CSTR-CDC, RDC-TRS, RDCORS, RDC-TBER, and RDC-TER have been developed in terms of the principle of mass and energy balance in conjunction with the given vapor−liquid equilibrium relationship. The following assumptions have been made to simplify the resultant equations: (1) Theoretical stages with perfect mixing and no pressure drop are assumed. (2) Sensible heat is neglected, and the latent heat of all components is equal. (3) Vapor holdups can be neglected, and liquid holdups are constant. (4) Relative volatilities are constant. For the CSTR-CDC, the liquid composition on each stage, the flow rates of the two recycles, and the heat duty of condenser (or reboiler) are chosen as decision variables. For the RDC-TRS and the RDC-ORS, the liquid composition on each stage and the heat duty of condenser (or reboiler) are chosen as decision variables. For the RDC-TBER and RDC-TER, besides the liquid composition on each stage and the heat duty of condenser (or reboiler), the external recycle flow rates must also be chosen as the decision variable. Once the decision variables have been determined, other process variables can be calculated in a

■

APPENDIX A: SIZING AND ECONOMICAL BASIS FOR PROCESS SYNTHESIS AND DESIGN The diameter of a CSTR reactor is described as DR = (3.977 × 10−2 × MRT)0.3333

(A2)

(A1) 14486



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sequential manner. For instance, after the temperature distribution has been searched to match the given operating pressure, the profile of vapor composition can be calculated, and the mass balance and energy balance equations can be solved to give the vapor and liquid flow rates. The decision variables are then updated using a Broyden’s (quasi-Newton) method, and the satisfaction of component mass balance equations (i.e., eq B1 (note that the external recycle flow is directed from the top to the bottom for the exothermic reaction) or eq B2 (note that the external recycle flow is directed from the bottom to the top for the endothermic reaction)) and product specification (i.e., eq B3) are taken as the convergence criterion. For the CSTR-CDC, the satisfaction of composition specifications (i.e., eqs B4 and B5) is chosen to be the convergence criterion as well. The steady-state models appear to be quite robust and can approach the desired steady states fairly quickly for the CSTR-CDC, RDC-TRS, RDCORS, RDC-TBER, and RDC-TER. |Lj − 1xi , j − 1 + Vj + 1yi , j + 1 − Ljxi , j − Vjyi , j + Fjzi ,δj + ratei , j + RF1j xi ,1 + RF2jxi ,nt| < ε

(B1)

|Lj − 1xi , j − 1 + Vj + 1yi , j + 1 − Ljxi , j − Vjyi , j + Fjzi ,δj + ratei , j + RF1j xi ,nt + RF2jxi ,1| < ε sp

■

(B2)

|xsd − xsd | < ε

(B3)

|xA,tr − xA,tr sp| < ε

(B4)

|x B,br − x B,br sp| < ε

(B5)

APPENDIX C: STEADY-STATE MODELS USED FOR EXAMPLES III AND IV The steady-state simulation of the CSTR-CDC, RDC-TRS, RDC-ORS, RDC-TBER, and RDC-TER is conducted using the commercial software Aspen Plus. An external Fortran subroutine is programmed to model the kinetics of the reaction operation involved. For the description of the totally refluxed operation, a trace of the overhead product is deliberately withdrawn and then recycled to the top of the process. Although it is actually an approximation method, the steady-state models can well represent the performance of the totally refluxed reactive distillation columns. In case that an external recycle flow is contained between the top and bottom (i.e., in the RDC-TBER) and/or between the either end to an intermediate stage (i.e., in the RDC-TER) of a reactive distillation column, it should be selected as a tear stream and the Broyden convergence method should be used to find the solution iteratively.

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NOTATION a = pre-exponential factor A = hypothetical component ACON = heat transfer area of condenser, m2 AREB = heat transfer area of condenser, m2 Avp = vapor pressure constant, kPa B = hypothetical component Bvp = vapor pressure constant, kPa·K C = hypothetical component CW = weight of the total catalyst, kg D = hypothetical component DC = diameter of a conventional distillation column or a reactive distillation column, m DR = diameter of a reactor, m E = activation energy, kJ/kmol ΔHR = heat of a reaction, kJ/kmol ΔHV = heat of vaporization, kJ/kmol J = iteration number Keq = chemical equilibrium constant L = liquid flow rate, kmol/s LC = height of a conventional distillation column or a reactive distillation column, m LR = height of a reactor, m M = kinetic holdup on a reactive tray, kmol MRT = kinetic holdup on reactor, kmol MW = average molecular weight, g/mol N = total number of stages P = pressure, kPa R = ideal gas law constant, kJ/(kmol·K) rate = reaction rate, kmol/s RF1 = liquid flow rate of external recycle between the top and bottom, kmol/s RF2 = liquid flow rate of external recycle from bottom/top to a certain stage in the RDC-TER, kmol/s RR = reflux rate, kmol/s T = temperature, K V = vapor flow rate, kmol/s VB = vapor boilup, kmol/s VT = vapor flow rate from the top of a conventional distillation column or a reactive distillation column, kmol/s x = liquid composition xA,tr = liquid composition of component A in the top recycle of the CSTR-CDC xB,tr = liquid composition of component B in the bottom recycle of the CSTR-CDC y = vapor composition

Greek Letters

α = activity β = payback period δ = kronecker function ξ = error tolerance of process design ε = error tolerance of process modeling ν = stoichiometric coefficient

AUTHOR INFORMATION

Corresponding Author

*Phone: + 86 10 64434801. Fax: + 86 10 64437805. E-mail: [email protected].

Superscripts

s = saturated sp = product specification

Notes

The authors declare no competing financial interest.

■

Subscripts

ACKNOWLEDGMENTS The project is financially supported by The National Science Foundation of China (Grant No. 21176015) and the Doctoral Programs Foundation of Ministry of Education of China (Grant No. 20100010110008), and thereby, they are acknowledged.

B = backward F = forward IP = isopropanol IPP = isopropyl palmitate LA = Lactic acid 14487



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MeOH = methanol MLA = methyl lactate sd = side draw PA = palmitic acid W = water

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REFERENCES

(1) Tung, S. T.; Yu, C. C. Effects of Relative Volatility Ranking to the Design of Reactive Distillation. AIChE J. 2007, 53, 1278. (2) Tang, Y. T.; Chen, Y. W.; Huang, H. P.; Yu, C. C.; Huang, S. B.; Lee, M. J. Design of Reactive Distillations for Acetic Acid Esterification. AIChE J. 2005, 51, 1683. (3) Kaymak, D. B.; Luyben, W. L.; Smith, O. J., IV Effect of Reactive Volatility on the Quantitative Comparison of Reactive Distillation and Conventional Multi-unit Systems. Ind. Eng. Chem. Res. 2004, 43, 3151. (4) Sun, J.; Huang, K. J.; Wang, S. J. Deepening Internal Mass Integration in Design of Reactive Distillation Columns, 1: Principle and Procedure. Ind. Eng. Chem. Res. 2009, 48, 2034. (5) Huang, K. J.; Lin, Q. Q.; Shao, H.; Wang, C.; Wang, S. J. A Fundamental Principle and Systematic Procedures for Process Intensification in Reactive Distillation Columns. Chem. Eng. Process. 2010, 49, 294. (6) Wang, S. F.; Huang, K. J.; Lin, Q. Q.; Wang, S. J. Understanding the Impact of Operating Pressure on Process Intensification in Reactive Distillation Columns. Ind. Eng. Chem. Res. 2010, 49, 4269. (7) Thotla, S.; Mahajani, S. Reactive Distillation with Side Draw. Chem. Eng. Process. 2009, 48, 927. (8) Bhatia, S.; Ahmad, A. L.; Mohamed, A. R.; Chin, S. Y. Production of Isopropyl Palmitate in a Catalytic Distillation Column: Comparison Between Experimental and Simulation Studies. Comput. Chem. Eng. 2007, 31, 1187. (9) Wang, P.; Chen, H.; Wang, Y.; Zhang, L.; Huang, K.; Wang, S. J. A Simple Algorithm for the Design of Fully Thermally Coupled Distillation Columns (FTCDC). Chem. Eng. Commun. 2011, 199, 608. (10) Kaymak, D. B.; Luyben, W. L. Quantitative Comparison of Reactive Distillation with Conventional Multiunit Reactor/Column/ Recycle Systems for Different Chemical Equilibrium Constants. Ind. Eng. Chem. Res. 2004, 43, 2493. (11) Aspen Tech. Aspen Plus 11.1 Users Guide. Aspen Tech: Cambridge, MA, 2001. (12) Chin, S. Y.; Ahmad, A. L.; Mohamed, A. R.; Bhatia, S. Characterization and Activity of Zinc Acetate Complex Supported over Functionalized Silica as a Catalyst for the Production of Isopropyl Palmitate. Appl. Catal., A 2006, 297, 8.

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Reactive Distillation Columns with a Top-Bottom External Recycle

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