Understanding the Impact of Operating Pressure on Process

Ind. Eng. Chem. Res. 2010, 49, 4269–4284

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Understanding the Impact of Operating Pressure on Process Intensification in Reactive Distillation Columns Shaofeng Wang, Kejin Huang,* and Quanquan Lin College of Information Science and Technology, Beijing UniVersity of Chemical Technology, Beijing 100029, People’s Republic of China

San-Jang Wang Department of Chemical and Material Engineering, Ta Hwa Institute of Technology, Chiunglin, Hsinchu 307, Taiwan

For a reactive distillation column involving reactions with high thermal effect, process intensification can be reinforced with the prudent adjustment of operating pressure within its feasible region bounded by the given hot and cold utilities. Three specific situations can be identified and should be dealt with cautiously during process synthesis and design. For a reactive distillation column involving reversible endothermic reactions, the enhancement of the operating pressure increases reactant conversion and reaction heat load, thus facilitating process intensification between the reaction operation and the separation operation involved. For a reactive distillation column involving equilibrium-limited exothermic reactions, the abatement of operating pressure increases reactant conversion and the reaction heat load, thus reinforcing process intensification between the reaction operation and the separation operation involved. For a reactive distillation column involving kinetically controlled exothermic reactions, the complicated relationship between operating pressure and reactant conversion and reaction heat load must be dealt with carefully, thus being likely to benefit process intensification between the reaction operation and the separation operation involved. Six hypothetical ideal and two real reactive distillation systems involving either equilibrium-limited or kinetically controlled reactions with high thermal effect are studied to evaluate the proposed philosophy. It has been found that with the appropriate selection of operating pressure, a considerable reduction of utility consumption can be secured beside a possible abatement in capital investment. These striking results evidence the strong necessity of deepening process intensification through the adjustment of operating pressure in the synthesis and design of reactive distillation columns involving reactions with high thermal effect. 1. Introduction Reactive distillation is an excellent example of process intensification which combines reaction operation and separation operation into one unit. To exploit the full potentials of a reactive distillation column involving reactions with high thermal effect, one needs to intensify process intensification through deepening internal mass integration and internal heat integration during process synthesis and design.1,2 So far, a number of methods have been proposed to enhance internal mass integration and internal heat integration within a reactive distillation column, and these include the superimposition of reactive section onto the rectifying and/or stripping sections, the relocation of feed stages, and the redistribution of catalyst in the reactive section.3-5 The essence of these methods is to find out the optimum process configuration to combine effectively the reaction operation and the separation operation involved. Apart from these structural design options, the detailed operating condition of a reactive distillation column, e.g., temperature or pressure, may also affect the combination between the reaction operation and the separation operation involved and their influences should be examined carefully. Operating pressure is a key design parameter for a conventional distillation column and is usually determined according to the temperature levels of the given cold and hot utilities (i.e., to guarantee sufficiently large temperature driving forces in the * To whom correspondence should be addressed. Tel.: +86 10 64434801. Fax: +86 10 64437805. E-mail: [email protected].

condenser and reboiler simultaneously).6 Optimization based on an economic objective (e.g., total annual cost, TAC) is frequently used to balance the associated capital investment and operating cost in process synthesis and design.7 In the case of reactive distillation columns, the above practice cannot be directly applied to the determination of operating pressure because the reaction operation involved must share the same favorable temperature region with the separation operation. Even though the temperature region has been matched between the two operations, operating pressure is still needed to be cautiously adjusted to cope with their intricate interactions, maximizing the thermodynamic efficiency of reactive distillation columns. This issue has long been ignored although it represents the essential philosophy of process intensification. Luyben and coworkers tried an optimization-based method (i.e., in terms of the minimization of boilup or TAC) to find the operating pressure of an ideal reactive distillation column.8-10 Although they detected the strong impact of operating pressure on the process performance, the underlying mechanism was not disclosed. With regard to the effect of operating pressure on process dynamics and controllability, it is common to perturb the operating pressure from its steady-state value and then study its influences.11,12 Although reasonable conclusions sometimes might be obtained, an inappropriate and even wrong interpretation was quite likely to be generated. The reason is mainly due to the fact that the effect of operating pressure on process intensification (and thus process dynamics and controllability) appears to be direction sensitive. With the increase/decrease of

10.1021/ie100067z  2010 American Chemical Society Published on Web 03/29/2010

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operating pressure, while a positive/negative effect can be observed in one region, a negative/positive one can be found in another region. These complicated phenomena indicate also the great importance of understanding the impact of operating pressure on process intensification. The current work examines the impact of operating pressure on process intensification in the reactive distillation columns involving reactions with high thermal effect. Three specific situations are identified according to the physicochemical characteristics of the reaction involved, i.e., reversible endothermic reactions, equilibrium-limited exothermic reactions, and kinetically controlled exothermic reactions. Six hypothetical ideal and two real reactive distillation systems involving either equilibrium-limited or kinetically controlled reactions with high thermal effect are intensively studied, and the implications of operating pressure on process intensification are analyzed. Some important conclusions are summarized in the last section of this article. 2. Impact of Operating Pressure on Process Intensification in Reactive Distillation Columns For a reactive distillation column involving reactions with high thermal effect, operating pressure affects significantly reactant conversion and reaction heat load, giving rise to strong influences to process intensification between the reaction operation and the separation operation involved. It is therefore imperative to designate deliberatively operating pressure during process synthesis and design. For a reactive distillation column involving reversible endothermic reactions, two cases exist. If the involved reaction is equilibrium-limited, increasing operating pressure shifts the equilibrium toward the product side (i.e., Le Chatelier’s principle). If the involved reaction is kinetically controlled, increasing operating pressure accelerates reaction rates. In both cases, the enhancement of operating pressure facilitates reactant conversion and reaction heat load, reinforcing process intensification between the reaction operation and the separation operation involved. For a reactive distillation column involving equilibriumlimited exothermic reactions, decreasing operating pressure shifts the equilibrium toward the product side (i.e., Le Chatelier’s principle) and is favorable to reactant conversion and reaction heat load, thereby reinforcing process intensification between the reaction operation and the separation operation involved. For a reactive distillation column involving kinetically controlled exothermic reactions, the relationship between operating pressure and reactant conversion is not monotonic. Too low an operating pressure retards reaction rates, reducing reactant conversion and reaction heat load. Too high an operating pressure accelerates more intensively the backward reaction rate than the forward reaction rate, decreasing the reactant conversion and reaction heat load. Therefore operating pressure must be selected carefully so as to maximize reactant conversion and reaction heat load, reinforcing process intensification between the reaction operation and the separation operation involved. 3. Impact of Operating Pressure on Process Intensification in Hypothetical Reactive Distillation Columns Involving Equilibrium-Limited Reactions 3.1. Quaternary Reactive Distillation System with Two Reactants and Two Products. 3.1.1. Process Description. This hypothetical ideal system was originally defined by Luyben and co-workers and has been studied intensively by many

Figure 1. Hypothetical quaternary A + B ) C + D (∆HR < 0) reactive distillation column. Table 1. Physical Properties and Operating Conditions of A + B ) C + D (∆HR < 0) System parameter specific equilibrium constant at 366 K heat of reaction (kJ kmol-1) vapor pressure constants A B C D relative volatility A:B:C:D latent heat of vaporization (kJ kmol-1) molecular weights A/B/C/D (g mol-1) number of stages rectifying section reactive section stripping section feed flow rate of reactant A (kmol s-1) feed flow rate of reactant B (kmol s-1) feed location of reactant A feed location of reactant B thermal condition of FA thermal condition of FB overhead product composition (C, mol %) bottom product composition (D, mol %)

value 2 -41 840 Avp 12.3463 11.6531 13.0394 10.9600 4:2:8:1 2953.7 50/50/50/50

Bvp 3862 3862 3862 3862

7 6 7 0.0126 0.0126 14 9 1.0 1.0 95 95

researchers.13-17 In this work, it is modified with the assumption that the reaction on each reactive stage is in chemical equilibrium. Unlike the original process, the liquid holdup is now not an important design parameter because it presents no net influences to the chemical equilibrium, i.e., ViHj(kf,jxA,jxB,j kb,jxC,jxD,j) ) 0. The basic process design has a three-section structure, 7/6/7, i.e., a rectifying section, a stripping section, and a reactive section in between (cf. Figure 1). A total condenser and a partial reboiler are mounted at the top and the bottom, which are counted as the first and last stages, respectively. No pressure drop is assumed between stages, and two pure reactant feeds, FA and FB, are fed onto the bottom and the top of reactive section, respectively. The specifications of the top and the bottom products are set to be 95 mol %, respectively, and the physicochemical properties and nominal steady-state operating conditions are summarized in Table 1. Other relevant information can be found in the corresponding references. The hypothetical reversible reaction occurring on the reactive stages is A+B)C+D

(1)


Figure 2. Effect of operating pressure on heat duties in A + B ) C + D (∆HR < 0) reactive distillation column.

where the equal sign indicates the reaction is equilibriumlimited. The volatilities are such that the products C and D are the lightest and heaviest, respectively, in the reacting mixture. The component composition on stage j in the reactive section is in chemical equilibrium and is limited by Keq,j )

xC,jxD,j xA,jxB,j

(2)

where Keq,j is the chemical equilibrium constant and given by Keq,j ) (Keq)366e-(∆HR/R)(1/Tj-1/366)

(3.1)

∆HR ) Ef - Eb

(3.2)

Ideal vapor and liquid phase behavior is assumed for the reacting mixture, and the vapor-liquid equilibrium relationship can be expressed as Pj ) xA,jPAs + xB,jPsB + xC,jPsC + xD,jPDs

(4.1)

yi,j ) xi,jPsi,j /Pj

(4.2)

The vapor saturation pressure is calculated as ln Psi,j ) Avp,i - Bvp,i /Tj

(5)

Equimolar overflow is assumed, so the vapor and liquid flow rates are constant in the nonreactive rectifying and stripping sections. Since the reaction is exothermic, namely ∆HR < 0, the vapor and liquid flow rates change from stage to stage in the reactive section because the thermal heat of reaction vaporizes a certain amount of liquid on each reactive stage. Vj ) Vj+1 - rj,C∆HR /∆Hv

(6)

Lj ) Lj-1 + rj,C∆HR /∆Hv

(7)

The performance of the quaternary reactive distillation system can be predicted with the steady-state model shown in the Appendix. 3.1.2. Impact of Operating Pressure. In Figure 2, the impact of operating pressure on the system performance is illustrated. The heat duties of condenser and reboiler increase monotonically with the increase of operating pressure, demon-

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Figure 3. Net reaction rate profiles of A + B ) C + D (∆HR < 0) reactive distillation column.

strating that a relatively low operating pressure is beneficial to process intensification in a reactive distillation column involving an exothermic reaction. Figure 3 details the profiles of net reaction rates in the reactive section when the operating pressure is chosen as 2, 5, and 9 bar, respectively. It also reflects the profiles of reactant conversion and reaction heat load because the thermal heat of reaction is independent of temperature and operating pressure. As can be seen, the reaction takes place unevenly through the reactive section. When the operating pressure is 2 bar, there is a peak on stage 12, indicating the maximum reaction heat released on this stage. As the operating pressure increases to 5 bar, the peak moves to stage 11 with its shape to a certain extent broadened. When the operating pressure is 9 bar, there appear two peaks around the feed locations of reactants A and B respectively, namely stages 9 and 14. Because the rectifying/stripping section gives off/takes in heat in operation, the thermal heat released at the bottom part of the reactive section works more favorably for the separation operation than that released at the top part of the reactive section. Based on this interpretation, one can readily understand why the thermodynamic efficiency of the ideal reactive distillation column is higher when the operating pressure is 2 bar than those when the operating pressure is 5 or 9 bar. This comparison signifies the strong effect of operating pressure on internal heat integration between the reaction operation and the separation operation involved. Figure 4 presents the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the ideal reactive distillation column with operating pressure of 2, 5, and 9 bar, respectively. It is readily seen that a low operating pressure leads to relatively small liquid and vapor flow rates (cf. Figure 4b). With the decrease of the operating pressure, increasingly less unconverted reactants A and B leave the top and the bottom of the reactive section, respectively, reducing the burden of the separation operation involved (cf. Figure 4c). This phenomenon signifies the strong effect of operating pressure on internal mass integration between the reaction operation and the separation operation involved. In the case of the operating pressure determined through the minimization of TAC, if the operating pressure corresponding to the minimum capital investment differs from the one corresponding to the minimum operating cost, the resultant operating pressure must lie and move between these two values in the face of changes in utility cost, representing a certain tradeoff between capital investment and operating cost. Figure 5 displays such a detailed tendency. Here, the capital investment

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Figure 6. Hypothetical ternary A + B ) C (∆HR < 0) reactive distillation column. Table 2. Physical Properties and Operating Conditions of A + B ) C (∆HR < 0) System parameter

Figure 4. Steady-state profiles of A + B ) C + D (∆HR < 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

Figure 5. Operating pressure of the minimum TAC with differing utility cost in A + B ) C + D (∆HR < 0) reactive distillation column.

is estimated with the formulas by Kaymak and Luyben,10 and a payback time of 3 years is employed. Cooling water (at 298.15 K) and steam (at 473.15 K) are used as cold and hot utilities, respectively. With the increase of utility cost, the suppression of operating cost becomes increasingly important in process synthesis and design, and this problem can be partly tackled through the reinforcement of process intensification with the abatement of operating pressure. This is why utility cost and operating pressure take a hyperbolic shape in this case.

value

specific equilibrium constant at 366 K heat of reaction (kJ kmol-1) vapor pressure constants A B C relative volatility A:B:C latent heat of vaporization (kJ kmol-1) molecular weights A/B/C (g mol-1) number of stages rectifying section reactive section stripping section feed flow rate of reactant A (kmol s-1) feed flow rate of reactant B (kmol s-1) feed location of reactant A feed location of reactant B thermal condition of FA thermal condition of FB bottom product composition (C, mol %)

20 -41 840 Avp 12.3463 11.6531 10.9600 4:2:1 29 053.7 50/50/100

Bvp 3862 3862 3862

0 9 5 0.012 63 0.012 82 10 2 1.0 1.0 98

3.2. Ternary Reactive Distillation System with Two Light Reactants and One Heavy Product. 3.2.1. Process Description. This hypothetical ideal reactive distillation system is also adapted from Luyben with the assumption that the reaction is in chemical equilibrium on each reactive stage.9,18 As shown in Figure 6, it has a configuration, 0/9/5, with a reactive section above the stripping section. The process operates in a total reflux mode with all the overhead vapor condensed and returned as reflux, and two pure reactant feeds, FA and FB, are fed onto the bottom and top of the reactive section, respectively. The specification of the bottom product is set at 98 mol %, and Table 2 tabulates the physicochemical properties and nominal steady-state operating conditions. The hypothetical reversible reaction occurring on the reactive stages is A+B)C

(8)

The component composition on stage j in the reactive section is in chemical equilibrium and is constrained by Keq,j )

xC,j xA,jxB,j

(9)


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Figure 7. Effect of operating pressure on heat duties in A + B ) C (∆HR < 0) reactive distillation column.

Figure 9. Steady-state profiles of A + B ) C (∆HR < 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition. Figure 8. Net reaction rate profiles of A + B ) C (∆HR < 0) reactive distillation column.

As the reaction is exothermic and reduces the molecular number (∑νi ) -1), the mass balance equations in the reactive section become Vj ) Vj+1 - rj,C∆HR /∆Hv

(10)

Lj ) Lj-1 + rj,C∆HR /∆Hv - rj,C

(11)

3.2.2. Impact of Operating Pressure. The effect of operating pressure on the system performance is depicted in Figure 7. Again, the heat duties of condenser and reboiler decrease monotonically with the decrease of operating pressure, demonstrating that a relatively low operating pressure is favorable to process intensification in a reactive distillation column involving an exothermic reaction. Figure 8 presents the profiles of net reaction rates in the reactive section when the operating pressure is set to be 1, 5, and 8 bar, respectively. As can be seen, when the operating pressure is 5 or 8 bar, there are two peaks on stages 2 and 10, respectively. While the one on stage 2 is fairly high, the one on stage 10 is fairly low, implying the reaction occurs mainly at the top of the reactive section. With the operating pressure set at 1 bar, only does a large and flat peak locate on stage 9, implying the reaction occurs mainly at the bottom of the reactive section. Since the involved reaction is exothermic, the thermal heat of reaction should be released to the bottom part of the

reactive section. Of the three cases examined, setting the operating pressure at 1 bar is certainly the best option because it favors mostly internal heat integration between the reaction operation and the separation operation involved. Figure 9 presents the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the ideal reactive distillation column with the operating pressure set at 1, 5, and 8 bar, respectively. Again, it is noted that a low operating pressure leads to relatively small vapor and liquid flow rates (cf. Figure 9b). With the decrease of operating pressure, less unconverted reactant B leaves the bottom of the reactive section, implying an increasing enhancement of internal mass integration between the reaction operation and the separation operation involved (cf. Figure 9c). In case of the operating pressure determined through the minimization of TAC, the relationship between operating pressure and utility cost is displayed in Figure 10. The operating pressure appears to be independent of utility cost in this case, because both the minimum capital investment and the minimum operating cost locate at 1 bar in the operating pressure. 3.3. Ternary Reactive Distillation System with a Heavy Reactant and Two Light Products. 3.3.1. Process Description. The process is adapted from Chen and Yu with the assumption that the reaction is in chemical equilibrium on each reactive stage.19 As shown in Figure 11, the process has a configuration, 9/10/7, with a total condenser at the top and a partial reboiler at the bottom. The fresh reactant A is fed onto the top of the reactive section, and the specifications are set at 98 mol % for the top product B and the bottom product C,

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A(h) ) B + C

(12)

where reactant A(h) indicates that reactant A is the heaviest among all the reacting components. The component composition on stage j in the reactive section is in chemical equilibrium and is constrained by Keq,j )

xB,jxC,j xA,j

(13)

As the reaction is endothermic (∆HR > 0) and increases the molecular number (∑νi ) 1), the mass balance equations in the reactive section become

Figure 10. Operating pressure of the minimum TAC with differing utility cost in A + B ) C (∆HR < 0) reactive distillation column.

Figure 11. Hypothetical ternary A(h) ) B + C (∆HR > 0) reactive distillation column. Table 3. Physical Properties and Operating Conditions of A(h) ) B + C (∆HR > 0) Decomposition System parameters specific equilibrium constant at 366 K heat of reaction (kJ kmol-1) vapor pressure constants A B C relative volatility A:B:C latent heat of vaporization (kJ kmol-1) molecular weights A/B/C (g mol-1) number of stages rectifying section reactive section stripping section feed flow rate of reactant A (kmol s-1) feed location of reactant A thermal condition of FA overhead product composition (B, mol %) bottom product composition (C, mol %)

value 20 41 840 Avp 10.9600 12.3463 11. 6531 1:4:2 29 053.7 100/50/50

Bvp 3862 3862 3862

9 10 7 0.0126 11 1.0 98 98

respectively. Table 3 lists the physicochemical properties and nominal steady-state operating conditions. The reversible reaction is

Vj ) Vj+1 - rj,C∆HR /∆Hv

(14)

Lj ) Lj-1 + rj,C∆HR /∆Hv + rj,C

(15)

3.3.2. Impact of Operating Pressure. The impact of operating pressure on the system performance is displayed in Figure 12. Contrary to the ideal reactive distillation columns involving exothermic reactions with high thermal effect (i.e., the two previous examples), the heat duties of condenser and reboiler decrease monotonically with the enhancement of operating pressure, indicating that a high operating pressure benefits process intensification in a reactive distillation column involving an endothermic reaction. Figure 13 presents the profiles of net reaction rates in the reactive section of the ideal reactive distillation column when the operating pressure is set to be 6, 9, and 12 bar, respectively. As can be seen, the reaction takes place primarily at the top of the reactive section with a great peak on stage 11. Zooming in the reactive section indicates that there exists also a small and flat peak at stage 20, the bottom of the reactive section. With the enhancement of operating pressure, the peak at the top of the reactive section becomes increasingly high and the one at the bottom of the reactive section increasingly low. Since the reaction is endothermic, the thermal heat of reaction should be supplied from the top part of the reactive section. Through the comparison of the three cases, one can easily find that designating the operating pressure at 12 bar is the best option because it facilitates mostly internal heat integration between the reaction operation and the separation operation involved. Figure 14 presents the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the ideal reactive distillation column with the operating pressure fixed at 6, 9, and 12 bar, respectively. A high operating pressure gives rise to small vapor and liquid flow rates although the reduction magnitudes appear to be marginal (cf. Figure 14b). With the increase of operating pressure, less unconverted reactant A leaves the bottom of the reactive section (although this cannot be clearly identified in Figure 14c), implying an increasing enhancement of internal mass integration between the reaction operation and the separation operation involved. In the case of the operating pressure determined through the minimization of TAC, the operating pressure shows no changes with utility cost due to the fact that both the minimum capital investment and the minimum operating cost exist at 12 bar in the operating pressure. 3.4. Ternary Reactive Distillation System with an Intermediate Reactant and a Lighter and a Heavier Products. 3.4.1. Process Description. The process is illustrated in Figure 15, containing a decomposition reaction in chemical equilibrium on each reactive stage. It accommodates a threezone structure, 8/12/4, and the feed location of reactant A is


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Figure 12. Effect of operating pressure on heat duties in A(h) ) B + C (∆HR > 0) reactive distillation column.

Figure 14. Steady-state profiles of A(h) ) B + C (∆HR > 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

Figure 13. Net reaction rate profiles of A(h) ) B + C (∆HR > 0) reactive distillation column.

arranged at the middle of the reactive section because it is the intermediate substance among all the reacting components. The specifications are set to be 98 mol % for products B and C, respectively, and Table 4 lists the physicochemical properties and nominal steady-state operating conditions. The reversible reaction is A(i) ) B + C

(16)

where reactant A(i) indicates that reactant A is the intermediate boiler among all the reacting components. 3.4.2. Impact of Operating Pressure. The effect of operating pressure on the system performance is illustrated in Figure 16. Again, the heat duties of condenser and reboiler decrease monotonically with the increase of operating pressure, demonstrating that a relatively high operating pressure is favorable to process intensification in a reactive distillation column involving an endothermic reaction. Figure 17 presents the profiles of net reaction rates in the reactive section of the ideal reactive distillation column when the operating pressure is specified at 3, 8, and 12 bar, respectively. The reaction occurs intensively on the feed stage (stage 16) of reactant A with a great peak there. Two other small peaks exist on stages 10 and 21, the top and the bottom of the reactive section, respectively. With the enhancement of operating pressure, the peak on the feed stage is raised and the one on

Figure 15. Hypothetical ternary A(i) ) B + C (∆HR > 0) reactive distillation column.

stage 21 is lowered. Because the one on stage 10 is fairly small, its effect can be ignored. Since the reaction is endothermic, the thermal heat of reaction should be supplied from the top part of the reactive section. In terms of the distribution of the net reaction rates, it is not difficult to understand that choosing the operating pressure at 12 bar is the best option because it helps to strengthen internal heat integration between the reaction operation and the separation operation involved.

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Table 4. Physical Properties and Operating Conditions of A(i) ) B + C (∆HR > 0) Decomposition System parameter specific equilibrium constant at 366 K heat of reaction (kJ kmol-1) vapor pressure constants A B C relative volatility A:B:C latent heat of vaporization (kJ kmol-1) molecular weights A/B/C (g mol-1) number of stages rectifying section reactive section stripping section feed flow rate of reactant A (kmol s-1) feed location of reactant A thermal condition of FA overhead product composition (B, mol %) bottom product composition (C, mol %)

value 2 41 840 Avp 11.6531 12.3463 10.9600 2:4:1 29 053.7 100/50/50

Bvp 3862 3862 3862

8 12 4 0.0126 16 1.0 98 98

Figure 18 presents the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the ideal reactive distillation column with the operating pressure fixed at 3, 8, and 12 bar, respectively. When the operating pressure has been enhanced from 3 to 8 bar, the vapor and liquid flow rates exhibit a great reduction (cf. Figure 18b). However, when

Figure 18. Steady-state profiles of A(i) ) B + C (∆HR > 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

Figure 16. Effect of operating pressure on heat duties in A(i) ) B + C (∆HR > 0) reactive distillation column.

the operating pressure has been enhanced from 8 to 12 bar, they display a fairly small reduction. This phenomenon corresponds closely to the varying tendency observed in Figure 16. With the enhancement of operating pressure, less unconverted reactant A leaves the top and the bottom of the reactive section, implying an increasing enhancement of internal mass integration between the reaction operation and the separation operation involved (cf. Figure 18c). In the case of the operating pressure determined through the minimization of TAC, the relationship between operating pressure and utility cost is displayed in Figure 19. It is readily seen that, with the increase of utility cost, process intensification must be strengthened by a certain degree through the enhancement of operating pressure. 4. Impact of Operating Pressure on Process Intensification in Hypothetical Reactive Distillation Columns Involving Kinetically Controlled Reactions

Figure 17. Net reaction rate profiles of A(i) ) B + C (∆HR > 0) reactive distillation column.

4.1. Quaternary Reactive Distillation System Involving a High Exothermic Reaction. 4.1.1. Process Description. The hypothetical ideal reactive distillation system proposed by Luyben and co-workers is adopted again.13-17 The process has a structure, 7/6/7, and the specification of the top and the bottom products is set at 95 mol %, respectively (cf. Figure 1). For the forward and backward reactions, the specific reaction rates are assumed to be 0.008 and 0.004 kmol s-1 kmol-1, respectively, at 366 K, and the activation energies are 125 520 and 167 360


Figure 19. Operating pressure of the minimum TAC with differing utility cost in A(i) ) B + C (∆HR > 0) reactive distillation column.

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Figure 20. Effect of operating pressure on heat duties in A + B T C + D (∆HR < 0) reactive distillation column.

kJ kmol-1, respectively. The liquid holdup is specified to be 1 kmol per stage. The hypothetical reversible reaction occurring on the reactive stages is A+BTC+D

(17)

where the double-headed arrow indicates that the reaction is a kinetically controlled one. The net reaction rate for component i on stage j in the reactive section is given by ri,j ) ViHj(kf,jxA,jxB,j - kb,jxC,jxD,j)

(18)

where kf,j and kb,j are the forward and backward specific reaction rate constants and given by kf,j ) (kf)366e-(Ef/R)(1/Tj-1/366)

(19.1)

Figure 21. Net reaction rate profiles of A + B T C + D (∆HR < 0) reactive distillation column.

kb,j ) (kb)366e-(Eb/R)(1/Tj-1/366)

(19.2)

the reaction takes place more intensively at the bottom part of the reactive section. Because the involved reaction is exothermic, the thermal heat of reaction should be released to the bottom part of the reactive section. Of the three cases examined, designating the operating pressure at 6 bar appears to be the best option because it reinforces mostly internal heat integration between the reaction operation and the separation operation involved. Although from the aspect of internal heat integration, the ideal reactive distillation column should operate at an operating pressure of 6 bar, the influence of reaction kinetics must be considered because it can pose strong influences on internal mass integration between the reaction operation and the separation operation involved. More specifically, process intensification should be performed through a careful trade-off between these two kinds of process integration. Choosing the operating pressure at 6 bar leads actually to relatively low temperatures and relatively low reacting velocities in the reactive section, restraining the degree of internal mass integration between the reaction operation and the separation operation involved. For the compensation of internal mass integration, the operating pressure must be increased, and this is why Figure 20 shows that the operating pressure at 9 bar (instead of 6 bar) corresponds to the optimum system performance. Figure 22 shows the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the ideal

Here, the liquid holdup Hj is an important design parameter that can reflect the amount of catalyst installed on a reactive stage. A large value represents a design condition that a large amount of catalyst has been installed on a reactive stage, and vice versa. 4.1.2. Impact of Operating Pressure. The effect of operating pressure on the system performance is illustrated in Figure 20. Sharply different from the ideal reactive distillation columns involving equilibrium-limited reactions, there is a sharp drop in the heat duties of condenser and reboiler when the operating pressure is increased from 5 to 6 bar, and this has been caused by the drastic enhancement in the reaction rates for the forward and backward reactions. Further increase of the operating pressure leads to a relatively small reduction in the heat duties of condenser and reboiler. The minimum locates at the operating pressure of 9 bar. Beyond that point, the heat duties of condenser and reboiler turn to increase with a relatively small slope. Figure 21 presents the profiles of net reaction rates in the reactive section when the operating pressure is set at 6, 9, and 12 bar, respectively. The reaction takes place unevenly through the reactive section. When the operating pressure is fixed at 9 and 12 bar, there are two peaks located respectively on stages 9 and 14. When the operating pressure is fixed at 6 bar, there is, however, only one peak located on stage 14, implying that

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Figure 23. Effect of operating pressure on heat duties in A + B T C + D (∆HR > 0) reactive distillation column.

Figure 22. Steady-state profiles of A + B T C + D (∆HR < 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

reactive distillation column with the operating pressure at 6, 9, and 12 bar, respectively. Among the three process designs studied, the one with the operating pressure at 9 bar necessities the least vapor and liquid flow rates (cf. Figure 22b). Moreover, the least amount of unconverted reactants A and B leaves the top and the bottom of the reactive section respectively, reflecting the reinforcement of internal mass integration between the reaction operation and the separation operation involved (cf. Figure 22c). In the case of the operating pressure determined through the minimization of TAC, the operating pressure is not affected by the changes in utility cost because the operating cost has its minimum value at the same operating pressure as does the capital investment. 4.2. Quaternary Reactive Distillation System Involving a High Endothermic Reaction. 4.2.1. Process Description. The hypothetical ideal reactive distillation system proposed by Luyben and co-workers is adopted again,13-17 but modified with the assumption that the reaction is now endothermic. The activation energies of the forward and backward reactions are exchanged with each other. 4.2.2. Impact of Operating Pressure. The effect of operating pressure on the system performance is illustrated in Figure 23. The heat duties of condenser and reboiler decrease monotonically with the increase of operating pressure. More specifically, while the heat duties of condenser and reboiler decrease rather quickly when the operating pressure is below 9 bar, they decrease relatively slowly when the operating pressure is beyond 9 bar. The outcome manifests that a relatively high operating

Figure 24. Net reaction rate profiles of A + B T C + D (∆HR > 0) reactive distillation column.

pressure favors process intensification in a reactive distillation column involving an endothermic reaction. Figure 24 presents the profiles of net reaction rates in the reactive section when the operating pressure is fixed at 6, 9, and 12 bar, respectively. Again, the reaction takes place unevenly throughout the reactive section. While a peak exists in the middle of the reactive section when the operating pressure is set at 9 or 12 bar, an even greater one appears in the bottom of the reactive section when the operating pressure is set at 6 bar. Because the involved reaction is endothermic, the thermal heat of reaction should be supplied from the top part of the reactive section. Of the three cases examined, designating the operating pressure at 12 bar appears to be the best option because it reinforces mostly internal heat integration between the reaction operation and the separation operation involved. Figure 25 shows the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition when the operating pressure is set at 6, 9, and 12 bar, respectively. As can be seen, a high operating pressure leads to relatively small vapor and liquid flow rates (cf. Figure 25b). When the operating pressure is specified at 12 bar, the least unconverted reactant A and B leave the top and bottom of the reactive section respectively, reflecting that a relatively high operating pressure also favors internal mass integration between the reaction operation and the separation operation involved (cf. Figure 25c).


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Figure 27. Reactive distillation column synthesizing MTBE from isobutylene and methanol. Table 5. Physicochemical Properties and Operating Conditions of MeOH + i-But ) MTBE (∆HR < 0) System

Figure 25. Steady-state profiles of A + B T C + D (∆HR > 0) reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

In the case of the operating pressure determined through the minimization of TAC, the relationship between operating pressure and utility cost is displayed in Figure 26. In the case of an increase in utility cost, process intensification must be strengthened by a certain degree through the enhancement of operating pressure.

parameter

value

heat of reaction (kJ kmol-1, 1100 kPa, 298 K) latent heat of MTBE vaporization (kJ kmol-1, 1100 kPa, 380 K) number of stages rectifying section reactive section stripping section feed flow rate of reactant MeOH (kmol s-1) feed flow rate of reactant i-But (kmol s-1) feed flow rate of reactant n-But (kmol s-1) feed location of reactant MeOH feed location of reactant i-But feed thermal condition of MeOH feed thermal condition of i-But overhead product composition (n-But, mol %) bottom product composition (MTBE, mol %)

-37 700 38 020 2 8 5 0.198 0.198 0.350 4 11 1.0 0 94 95

5. Impact of Operating Pressure on Process Intensification in Real Reactive Distillation Systems Two systems are to be studied in this section. One is the synthesis of methyl tert-butyl ether (MTBE) from isobutylene (i-But) and methanol, which is a highly exothermic and equilibrium-limited reaction. The other is the esterification of acetic acid and methanol producing methyl acetate, which is an exothermic and kinetically controlled reaction. 5.1. Reactive Distillation Column Synthesizing MTBE from Isobutylene and Methanol. 5.1.1. Process Description. As shown in Figure 27, the reactive distillation system incorporates a 2/8/5 configuration, and its nominal operating conditions are summarized in Table 5.5,20 The reaction occurring on the reactive stage is MeOH + i-But ) MTBE

(20)

Every reactive stage is assumed to be in chemical equilibrium, and the following equation is used to represent the temperature dependence of the reaction equilibrium constant. ln Keq ) -16.33 + 6820/T

Figure 26. Operating pressure of the minimum TAC with differing utility cost in A + B T C + D (∆HR > 0) reactive distillation column.

(21)

The simulation of the MTBE reactive distillation column is carried out using the commercial ChemCad software, and the liquid phase activities are calculated using the UNIQUAC model

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Figure 28. Effect of operating pressure on heat duties of the MTBE synthesis reactive distillation column.

Figure 30. Steady-state profiles of the MTBE reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

Figure 29. Net reaction rate profiles of the MTBE reactive distillation column.

with the binary interaction parameters given by Rehfinger and Hoffmann.21 5.1.2. Impact of Operating Pressure. The effect of operating pressure on the system performance is illustrated in Figure 28. The heat duties of condenser and reboiler increase monotonically with the increase of operating pressure, demonstrating that a relatively low operating pressure is beneficial to process intensification in the MTBE reactive distillation column. Figure 29 details the profiles of net reaction rates in the reactive section when the operating pressure is chosen as 2, 4, and 6 bar, respectively. As can be seen, the reaction takes place unevenly through the reactive section. When the operating pressure is 2 bar, there are two peaks occurring on stages 4 and 8, and the one on stage 4 is much smaller than the one on stage 8. The distribution indicates that the reaction heat is released mainly at the lower part of the reactive section and this actually favors internal heat integration between the reactive section and the stripping section. As the operating pressure increases to 4 bar, there is left only one peak locating on stage 4. When the operating pressure increases further to 6 bar, apart from the increase in the magnitude of the peak on stage 4, a minor inverse peak appears on stage 11. This phenomenon indicates that the reaction heat is now released and absorbed mainly at the top and bottom parts of the reactive section, representing adverse internal heat integration between the reactive section/rectifying

section and the reactive section/stripping section, respectively. Since MTBE synthesis is highly exothermic, one can readily understand why the thermodynamic efficiency is higher when the operating pressure is 2 bar than it is when the operating pressure is 4 or 6 bar. Figure 30 presents the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the MTBE reactive distillation column with the operating pressure at 2, 4, and 6 bar, respectively. It is readily seen that a low operating pressure leads to relatively small liquid and vapor flow rates (cf. Figure 30b). With the decrease of the operating pressure, increasingly less unconverted reactants isobutylene and methanol leave the top and the bottom of the reactive section, respectively, reducing the burden of the separation operation involved (cf. Figure 30c). This phenomenon signifies the strong effect of operating pressure on internal mass integration between the reaction operation and the separation operation involved. 5.2. Reactive Distillation Column Producing Methyl Acetate from Acetic Acid and Methanol. 5.2.1. Process Description. A reactive distillation system, 2/25/9, is adopted here (cf. Figure 31), and its nominal operating conditions are summarized in Table 6.22 The esterification reaction occurring on the reactive stage is MeOH + HAc T MeAc + H2O

(22)

The net reaction rate is expressed in the pseudohomogeneous model with components represented in terms of activity and catalyst weight based kinetics.


rMeAc ) mcat(kfaHAcaMeOH - kbaMeAcaH2O)

(23)

kf ) (2.961 × 104)e-49190/(RT)

(24)

kb ) (1.348 × 106)e-69230/(RT)

(25)

The process is simulated using the RADFRAC module of the commercial Aspen Plus software, and the UNIQUAC model is used to calculate activity coefficients accounting for the nonideal vapor-liquid equilibrium. 5.2.2. Impact of Operating Pressure. The effect of operating pressure on system performance is illustrated in Figure 32. The heat duties of the condenser and reboiler first decrease with increasing operating pressure and reach their minima when the operating pressure is 1.8 and 1.7 atm, respectively. They begin to increase with the further increase in the operating pressure, demonstrating that the selection of operating pressure is extremely important to process intensification in the methyl acetate reactive distillation column. Figure 33 presents the profiles of net reaction rates in the reactive section when the operating pressure is set at 1.4, 1.7,

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Figure 32. Effect of operating pressure on heat duties in methyl acetate producing reactive distillation column.

Figure 33. Net reaction rate profiles of the methyl acetate reactive distillation column.

Figure 31. Reactive distillation column producing methyl acetate from acetic acid and methanol. Table 6. Physicochemical Properties and Operating Conditions of MeOH + HAc T MeAc + H2O (∆HR < 0) System parameter -1

heat of reaction (kJ kmol , 100 kPa, 330 K) latent heat of H2O vaporization (kJ kmol-1, 100 kPa, 298 K) activation energy (kJ kmol-1) forward backward preexponential factor (kmol s-1 kgcat-1) forward backward liquid holdup (m3) number of stages rectifying section reactive section stripping section feed flow rate of reactant HAc (kmol h-1) feed flow rate of reactant MeOH (kmol h-1) feed location of reactant HAc feed location of reactant MeOH feed thermal condition of HAc feed thermal condition of MeOH overhead product composition (MeAc, mol %) bottom product composition (H2O, mol %)

value -33 566.80 43 868.87 49 190 69 230 29 610 1 348 000 0.037 958 4 2 25 9 50 50 4 28 1.0 1.0 95 95

and 2.0 atm, respectively. There appears a high peak at the bottom of the reactive section, implying that the reaction takes place primarily at the bottom part of the reactive section. With the increase of operating pressure, the peak moves further to the bottom of the reactive section and this is favorable to internal heat integration between the reaction operation and the separation operation involved. Figure 34 shows the steady-state profiles of temperature, vapor and liquid flow rates, and liquid composition of the methyl acetate reactive distillation column with the operating pressure at 1.4, 1.7, and 2.0 atm, respectively. Among the three process designs studied, the one with the operating pressure at 1.7 atm shows the least amount of HAc at the bottom of the reactive section (combined with the fact that that almost no difference can be found in the MEOH composition at the top of the reactive section), and this results actually from the refinement of internal mass integration between the reaction operation and the separation operation involved (cf. Figure 33c). It is now clarified that fixing the operating pressure at 1.4 atm is not the best option for internal mass integration and internal heat integration between the reaction operation and the separation operation involved. Although in terms of internal heat integration the operating pressure should be fixed at 2.0 atm, it leads to internal mass integration that is inferior to the case when the operating pressure is set at 1.7 atm. This is why the

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One may argue that for a reactive distillation column involving a reversible (either equilibrium-limited or kinetically controlled) endothermic reaction, although the operating pressure should be maintained high enough to shift the reaction to the product side (i.e., a favorable effect), it may also present a negative effect on system performance because of the suppression of the relative volatilities of the reacting mixture. The argument is certainly reasonable, and in this situation the net effect of the pressure enhancement should therefore depend on the relative magnitudes of the positive and negative effects. When the reaction involved is characterized by a high thermal effect, the positive effect could overwhelm the negative one and the pressure enhancement is likely to present a favorable impact on system performance. (However, special caution should be exercised in the separation of some highly nonideal reacting mixtures with near-azeotropic compositions.) This is why in the current work we have confined ourselves to the studies of only those reactive distillation columns involving reactions with high thermal effect. 7. Conclusions

Figure 34. Steady-state profiles of the methyl acetate reactive distillation column: (a) temperature, (b) vapor and liquid flow rates, and (c) liquid composition.

methyl acetate reactive distillation column appears to be most thermodynamically efficient when its operating pressure is fixed at 1.7 atm. 6. Discussion It is worth stressing here the fact that both the hypothetical ideal and real systems studied in this work have indicated consistently the impact of operating pressure on process intensification. The purpose of employing the hypothetical ideal reactive distillation columns is to strip away the inherent nonlinearity (i.e., that introduced by the nonideal vapor-liquid equilibrium and the temperature/composition dependence of the thermal heat of vaporization) and demonstrate essentially the impact of operating pressure on process intensification. Although the detailed physicochemical properties of the reacting mixtures separated may compound the impact of operating pressure on process intensification, they are unlikely to distort the essential characteristics for most of the reacting mixtures, especially when they are characterized by high thermal effect. In fact, with the alleviation of the nonlinear behavior, the benefits of process intensification in ideal systems become frequently much smaller than those in real systems because of the relative simplicity of the interplay between the reaction operation and the separation operation involved. Although more practical examples need to be examined in the future, recent outcomes on internal mass integration and internal energy integration in some complicated reactive distillation columns involving reactions with high thermal effect have demonstrated the tendency.2,20,23,24

In this work, the impact of operating pressure on process intensification has been explored for the reactive distillation columns involving reactions with high thermal effect. Three specific situations have been identified and should be dealt with cautiously during process synthesis and design. For the reactive distillation columns involving reversible endothermic reactions, because increasing operating pressure enhances reactant conversion and reaction heat load, process intensification can be reinforced between the reaction operation and the separation operation involved. For the reactive distillation columns involving equilibriumlimited exothermic reactions, because decreasing operating pressure leads to increased reactant conversion and reaction heat load, process intensification can be reinforced between the reaction operation and the separation operation involved. For the reactive distillation columns involving kinetically controlled exothermic reactions, because the appropriate selection of operating pressure could maximize reactant conversion and reaction heat load, process intensification can be reinforced between the reaction operation and the separation operation involved. Six hypothetical ideal and two real systems involving five equilibrium-limited reactions and three kinetically controlled ones respectively are intensively studied. The obtained results indicate that it is reasonable and frequently necessary to strengthen process intensification through a deliberate determination of operating pressure within the feasible region bounded by the given hot and cold utilities. Apart from the reduction of utility consumption, the abatement of fixed investment could also be acquired. This finding is of great importance to the synthesis and design of reactive distillation columns involving reactions with high thermal effect. Acknowledgment The project is financially supported by the National Science Foundation of China under Grant 20776011, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. Appendix A generalized steady-state model of the hypothetical ideal reactive distillation columns involving either equilibrium-limited


reactions or kinetically controlled ones has been developed in terms of the principle of mass and energy balance in conjunction with the given vapor-liquid equilibrium relationship. Owing to the drastic differences in the physicochemical characteristics of the reacting mixtures separated, specific solution philosophies must be devised respectively for the steady-state models of the reactive distillation columns involving equilibrium-limited and kinetically controlled reactions, thereby facilitating the convergence speed and lessening the computational burden. For the former, besides the heat duties of condenser and reboiler and the distribution of liquid compositions in the nonreactive sections, the profiles of net reaction rates and two liquid compositions (preferably one reactant and one product) in the reactive section are chosen as decision variables. For the latter, the heat duties of condenser and reboiler and the distribution of liquid compositions in the reactive and nonreactive sections are chosen as the decision variables. Once the decision variables are determined, other process variables can be calculated in a 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 energy balance equations can be solved to give the vapor and liquid flow rates. The steady-state model is solved using a modified Newton-Raphson method, and the satisfaction of component mass balance equations, i.e., eq A1, as well as the attainment of the product specifications, i.e., eqs A2 and A3, is taken as the convergence criterion. It appears to be quite robust and can approach a solution fairly quickly for the various hypothetical ideal reactive distillation columns. |Lj-1xi,j-1 + Vj+1yi,j+1 - Ljxi,j - Vjyi,j + Fjzi,jδj,m + ri,j | e ε (A1) |xd - xsp d | e ε

(A2)

|xbot - xsp bot | e ε

(A3)

Notation A ) component a ) liquid activity Avp ) vapor pressure constant, Pa B ) component b ) bottom flow rate, kmol s-1 Bvp ) vapor pressure constant, Pa K C ) component D ) component d ) distillate flow rate, kmol s-1 E ) activation energy of a reaction, kJ kmol-1 F ) feed flow rate of reactants, kmol s-1 H ) stage holdup, kmol ∆HR ) heat of a reaction, kJ kmol-1 ∆HV ) heat of vaporization, kJ kmol-1 Keq ) specific chemical equilibrium constant k ) specific reaction rate constant, kmol s-1 kmol-1 L ) liquid flow rate, kmol s-1 mcat ) catalyst weight, kg n ) number of stages P ) pressure, bar Q ) heat duty, kW R ) ideal gas law constant, kJ kmol-1 K-1 r ) net reaction rate, kmol s-1 T ) temperature, K TAC ) total annual cost, $ year-1 V ) vapor flow rate, kmol s-1

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x ) liquid composition y ) vapor composition z ) feed composition Greek Symbols δ ) Kronecker function ε ) error tolerance ν ) stoichiometric coefficients of a reaction Subscripts A ) component index B ) component index b ) backward reaction bot ) bottom product C ) component index d ) distillate D ) component index f ) forward reaction i ) component index j ) stage index m ) feed stage index Superscripts s ) saturation sp ) product specification

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ReceiVed for reView July 3, 2009 ReVised manuscript receiVed March 9, 2010 Accepted March 13, 2010 IE100067Z

Understanding the Impact of Operating Pressure on Process

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