Feasibility of Reactive Distillation for Ternary Systems with Azeotropic

Ind. Eng. Chem. Res. 2011, 50, 1305–1320

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Feasibility of Reactive Distillation for Ternary Systems with Azeotropic Mixtures: Decomposition Reaction† Chin-Shih Chen, Jeffrey D. Ward,* and Cheng-Ching Yu Deptartment of Chemical Engineering, National Taiwan UniVersity, Taipei 106-17, Taiwan

Systematic research on feasibility analysis for reactive distillation for ternary azeotropic systems has been conducted by Guo et al. [Guo, Z.; Chin, J.; Lee, J. W.; Feasibility of continuous reactive distillation with azeotropic mixtures. Ind. Eng. Chem. Res. 2004, 43, 3758-3769]. The analytical method they used was tray-by-tray calculations with difference point. There are two feasibility criteria, which are positive reaction extent is required on all trays and products can be reached by distillation or reactive distillation. In this work, we find that the feasibility analysis of reactive distillation using this method can be augmented by admitting the reverse reaction which can be compensated for by excess positive reaction on other trays. Two concepts that can accelerate the feasibility analysis are also shown. The first one is that the analysis of VLE vectors at the equilibrium line and the tray-by-tray calculation method with difference point are equivalent for determining the feasibility. Furthermore, the pinch point in the tray-by-tray calculation under chemical equilibrium and infinite reflux ratio is equivalent to a reactive azeotrope. The number of possibly feasible cases is increased by 21 from 27 to 48 out of all 113 possible ternary configurations. Nine of the 21 new cases are feasible regardless of the value of the equilibrium constant, and twelve cases may be feasible if the equilibrium constant is high enough. The result compares well with reactive distillation column simulations. 1. Introduction Reactive distillation (RD) columns combine distillation and chemical reaction into a single unit. Reactive distillation is attractive because it may reduce capital and energy costs and can break azeotropes.1 However, this process is notorious for being difficult to design. The engineer must spend a lot of time on trial-and-error, make a guess at a series of design variables, carry out simulation, and try to reach the product specifications. Feasibility analysis allows the designer to determine whether a process is feasible or not. By eliminating inherently infeasible processes, engineers can save time and increase the design efficiency. Short-cut design accompanied by feasibility analysis can also provide a reasonable starting point for further detailed design. Short-cut design using the reaction difference point,2 a virtual point outside the real composition, is a simple and reliable method for feasibility analysis. Feasibility analysis of three component systems can be performed by applying stage calculations using the reaction difference point.3 The main advantages of this method are as follows: (a) The interaction between chemical reaction and vapor-liquid equilibrium can be clearly shown on the composition map. (b) The method is simple and does not require complex calculation. The only required information is the residue curve map (RCM) and the stoichiometry and kinetics of the reaction. Guo et al.4 analyzed the feasibility of an azeotropic threecomponent system and determined that a single reactive distillation column is infeasible for 2IKSLK+HK (an intermediate key reactant reacts to form light key and heavy key products) when there is an azeotrope between LK and HK. In this work, we find that this infeasible case becomes feasible if the restrictions are modified to allow the reverse reaction in part of the reactive section (the loss can be balanced by an excess * To whom correspondence should be addressed. E-mail: jeffward@ ntu.edu.tw. † C. S. Chen and J. D. Ward dedicate this paper to C. C. Yu, who was the principal investigator on this project.

extent of reaction on other reactive trays). Out of 113 possible azeotropic configurations,5 the number of possibly feasible cases is increased from 27 to 48. These feasible RCMs can be classified into four groups (see Figure 1): (A) One product is a stable node, and the other is an unstable node. (B) One product is a saddle, and there is no azeotrope between the two products. (C) There is an azeotrope between products but no node between the reactant and either product. (D) There is an azeotrope between the products and one or more nodes on the RCM edge next to the saddle product. Cases A and B were confirmed by

Figure 1. Feasible RCMs can be classified into four groups: (A) Products are UN and SN; there is no azeotrope between P1 and P2. (B) At least one product is a saddle point, but there are still no azeotropes between P1 and P2. (C) One product is a saddle, and there is a node or saddle between the two products but no azeotropes between the reactant and either product. (D) There is an azeotrope between products and on at least one edge between the reactant and a product.

10.1021/ie1006118  2011 American Chemical Society Published on Web 12/15/2010

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Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011

For the reactive rectifying section (Figure 2B), analogous operations can be performed to give Ln D br δ bx + Ln + D n Ln + D R,n

(7)

br ) bx + 2(ξ /D)(C bR - C bP) δ R,n D n

(8)

byn-1 )

Figure 2. Two different control volumes are needed for reaction difference point analysis: (A) A control volume in the striping section (ξm is the total extent of reaction on all of the trays from tray 1 to m, including column base). (B) A control volume in the rectifying section (ξn is the total extent of reaction on all the trays from tray n to the top).

Guo et al4 and are further confirmed in this work. Cases C and D are discovered in this work. 2. Feasibility Analysis 2.1. Graphical Stage Calculation. Graphical stage calculation2,3 is based on material balance. Consider the control volume of the stripping section shown in Figure 2A. There are two streams leaving the system (vapor flow rate Vm and bottoms flow rate B) and one liquid flow entering the system (Lm+1). ξm is the accumulated extent of reaction on all of the trays from the bottom to tray m, including the column base. The variables ym, xB, and xm+1 are the composition vectors of Vm, B, and Lm+1, respectively, and ν is the chemical stoichiometry vector, i.e., ) (νP1, νP2, νR) ) (+1, +1, -2) for the reaction 2R f P1 + P2. The overall and component mole balances can be expressed as Lm+1 ) Vm + B

(1)

Lm+1b xm+1 ) Vmb ym + Bx bB + ξmb ν

(2)

Equation 2 can be rearranged by defining the normalized bR ) reactant and product stoichiometry coefficient vectors,4 C b (0,0,1)and CP ) (0.5, 0.5, 0) to form bR - C bP)) Lm+1bxm+1 ) Vmbym + B(xbB + 2(ξm /B)(C

(3)

The cascade difference point4 is defined as bs ) bx + 2(ξ /B)(C bR - C bP) δ R,m B m

(4)

Substitution of the cascade difference point into eq 3 gives bs Lm+1bxm+1 ) Vmbym + Bδ R,m

(5)

Combination of eq 1 and eq 5 gives bxm+1 )

Vm B bs δ by + Vm + B m Vm + B R,m

(6)

Equation 6 is the lever-arm rule, which can be used to perform tray-by-tray calculation graphically in the feasibility analysis for the reactive striping section.

where ξn is the accumulated extent of reaction from tray n to the top of the column. The algorithm for stage calculation is shown below. RCM430 of group B is chosen to illustrate how the tray-by-tray calculations are performed. The corresponding graphs are shown in Figure 3A. We assume that the product purity is specified. (We take 0.99 mol % as the purity requirement in this work.) (1) Start with the residue curve map and reaction information. (2) Draw the reaction equilibrium line on the RCM. (3) Generate the vapor phase composition line corresponding to the reaction equilibrium line. (4) Estimate a proper feed tray location. (5) Evaluate the cascade difference point line. (6) Solve the material balance using the lever arm rule, and make sure that the reaction is in the forward direction (both ξm and ξn are positive). (7) Find the composition of the other phase by vapor-liquid equilibrium. (8) Repeat steps 5 and 6 until the product composition is reached. (9) Check whether the other product can be reached by distillation (the product is a node in its distillation region) or by reactive distillation (repeat steps 4, 5, and 6). Figure 3B shows how the stage calculation is performed using the lever arm rule (eq 6). Figure 3C indicates how the amounts of reaction are determined (using the proportional relation in eq 4). The steps given above are developed by Lee and coworkers.3 However the algorithm does not always correctly predict the feasibility of azeotropic systems when there is an azeotrope between products. Take RCM-001 of group C as an example, and the azeotropes shown in Figure 4A. There is a minimum boiling azeotrope on the P1-P2 edge. If the analysis is limited to forward reaction conditions only, as shown in Figure 4B, vapor composition above tray n + 1 moves away from product P1 (LK). A high-purity product cannot be reached by reactive distillation. This system is infeasible with a limitation to forward reaction only.4 But when we perform a simulation, as shown in Figure 5A and B, RCM-001 is feasible under certain conditions. What causes the incorrect prediction? The operating line is based on material balance and could not be wrong. We need to check the other assumptions. 2.2. Reverse Reaction. The criterion of forward reaction only seems to be reasonable because product is consumed, not created, from the reverse reaction. But we can allow the reverse reaction on some of the column trays and use excess forward reaction on other reactive trays to make up this loss. Such a technique is practical in reality and should be considered in a feasibility analysis. Therefore, in this work, we relax this constraint. We allow the reverse reaction in the reactive rectifying or stripping section. Step 6 is rewritten as (6) Solve the material balance using the lever arm rule. The reaction can be in the forward or reverse direction, which means ξm (ξn) can be positive or negative. Also, two additional steps are added:


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s Figure 3. Tray-by-tray calculations with difference point. (A) Steps in graphical stage calculation. (B) Lever relation among yNF-1, xNF, and δR,NF (eq 6). (C) Proportional relation between B and 2ξNF (eq 4).

(10) Check whether the overall reaction extent is positive and matches the demand of the process. If the criteria are met, the process is feasible. (11) If neither reactive distillation nor distillation can achieve a product with the desired purity or if the desired production rate cannot be achieved, then this case is infeasible. Product P1 (LK) of RCM-001 (group C) is a saddle, and therefore pure P1 cannot be obtained using an ordinary rectifying section. According to step 9, we can try reactive distillation when distillation fails to achieve a pure product. This means we have an RD column with catalyst on the top stages. Figure 4C gives an illustration of this amendment. Unlike the graphical

stage calculation in Figure 4B, the compositions in a reactive rectifying section approach the light key product, and high-purity light key product can be obtained. Note that the cascade difference point for this section is located in the region of reverse reaction (ξn < 0). This means that reverse reaction occurs in the reactive rectifying section. But if there is sufficient forward reaction in the reactive zone below the feed tray, it can compensate for the reverse reaction. Using eqs 4 and 8, we can determine the amount of reaction in each section from Figure 4C: 2ξNF ) 3.86B, 2ξNF-1 ) -1.86D. The amount of overall reaction (2ξNF + 2ξNF-1) is equal to 2B (by assuming B ) D), so the production requirement is met. A single RD column

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Figure 4. (A) RCM-001. (B) Tray-by tray calculation with only forward reaction (the line segments of δrn - P1(LK) indicate the extent of reaction). (C) Tray-by-tray calculations which allow the reverse reaction to reach the specifications. (Let B ) D, 2ξNF + 2ξNF-1 ) 2B; the overall extent of the reaction can meet the requirement).

configuration is feasible for RCM-001. In this case, the reverse reaction is not a harmful situation that must be prevented. Rather, it is a necessary condition that helps to achieve the desired product specifications. With the two additional steps, RCM-001 in group C would be determined to be a feasible case. Systems that need reverse reaction to reach specifications would not be recognized as infeasible cases. By taking reverse reaction into consideration, feasibility analysis can give more correct predictions. 2.3. Vapor Liquid Equilibrium Vector. Graphical methods are useful for visualizing a design with a specific reflux ratio and boil-up rate. But there are some properties that are inherent in a chemical system itself that can be investigated before such graphical analysis is conducted. A system may be feasible under certain conditions but infeasible for others, or it may be infeasible under all conditions. Next, we discuss a method that can be used to determine if a process is inherently infeasible before tray-by-tray calculations are performed. This method is attractive because it may accelerate the analysis. When a system

is inherently infeasible, it will be infeasible for any specific column design, so there is no need to apply tray-by-tray calculations. We take RCM-430 of group B as an example. High-purity products can be reached by tray-by-tray calculations at a large chemical equilibrium constant (Keq) in this system. But the compositions are limited to low purity at small Keq’s, as shown in Figure 6A and B. So the RCM-430 is feasible at large Keq’s and infeasible at small Keq’s. This phenomenon has been discussed by Guo et al.4 Can this result be obtained directly without tray-by-tray calculations? Notice that in step 7, which was mentioned in previous sections, that the composition of the other phase is calculated by vapor-liquid equilibrium. Visualize this step by using a vector, xnfyn, which represents the VLE, as shown in Figure 6A. If xn approaches xn+1, the compositions would encounter a pinch point just like Figure 6B. This happens when the slope of the VLE vectors approaches the slope of the material balance lines. So we can obtain the feasibility of any system by graphing


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Figure 7. Analysis of vapor liquid equilibrium vectors for RCM-430: (A) The vectors do not invert on the equilibrium line until high product purity is reached when Keq is high. (B) The vectors invert on the equilibrium line at low purity for low Keq. This means RCM-430 is only feasible when the system has high Keq.

Figure 5. Result of simulation for RCM-001 (group C). (A) Configuration of single RD column with 30 reactive rectifying trays, 20 nonreactive stripping trays, and feed at the 30th tray. (B) Composition profile. The composition approaches pure product slowly in the reactive rectifying section, so high purity product can be obtained. A single RD column is feasible for RCM-001.

Figure 8. Stage calculation with infinite boil-up rate (infinite reflux ratio). The pinch point obstructs the reactive stripping, and the product purity specification cannot be met (xP1(HK) ) 0.99).

Figure 6. Tray-by-tray calculation for RCM-430: (A) The specification can be reached by reactive distillation at large Keq (the bold arrow is the VLE vector). (B) The composition encounters a pinch point and cannot reach the specifications regardless of the number of reactive trays when the systems has small Keq.

all VLE vectors along the equilibrium line and checking if there is an inversion, as shown in Figure 7 (in this work, inversion is defined as a change in the direction of the vectors such that the included angle between the vectors and the x axis changes from less than 45° to more than 45° or from more than 45° to less than 45°). If the vectors on the equilibrium line do not invert before reaching the desired product purity (Figure 7A), reactive distillation (with forward or reverse reaction) can achieve the desired purity, and the process is feasible. If the vectors invert before reaching the specifications (Figure 7B), then step 7 will lead the composition in the wrong direction, away from the products, and the process is infeasible. The inversion of VLE vectors corresponds directly to the failure of the tray-by-tray calculations. VLE vector analysis gives the same prediction as tray-by-tray calculations, but with a simpler procedure. The primary conclusions of feasibility analysis can be obtained easily by graphing the VLE vectors. This method can be applied to all possibly feasible RCMs and gives a necessary and sufficient

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Figure 9. Transformed composition analysis: (A) projecting xL and xH onto the L-H edge as YH. (B) Projecting corresponding vapor composition onto the L-H edge as YH. (C) XH ) YH indicating reactive azeotrope. (D) Reactive azeotrope in T-X-Y diagram. Table 1. Antoine Constants and Normal Boiling Points for the for LK, IK, HK Systema

component

normal boiling point, °C

relative volatility

AVP

BVP

CVP

LK IK HK

39.6 59.1 79.2

4 2 1

12.34 11.45 10.96

3862 3862 3862

0 0 0

a

Table 2. Binary Interaction Parameters for the Wilson Equationa for LK, IK, HK (1, 2, 3) RCM-311s

coefficient

Λ12 ) 2.7183 Λ22 ) 1.0000 Λ32 ) 0.3012

Λ11 ) 1.0000 Λ21 ) 1.0000 Λ31 ) 1.0000

Λ12 ) 1.0000 Λ22 ) 1.0000 Λ32 ) 0.3012

BVP,j T + CVP,j

Λ13 ) 1.0000 Λ23 ) 0.3012 Λ33 ) 1.0000

RCM-430

with T in K and Pjsat in bars.

criterion to determine if the design is actually feasible (assuming that reaction equilibrium is achieved at each stage). 2.4. Reactive Azeotrope. Is there any physical significance to a design being inherently infeasible? What causes a design to be “infeasible” according to stage-by-stage calculations? To answer these questions, we study an infeasible condition: a small chemical equilibrium constant and RCM-430. This case is shown in Figure 7B. This process encounters a pinch point which prevents the purity from reaching the specification. As the boilup ratio is increased, as shown in Figure 8, the maximum achievable product purity increases. However, even if the process is operated under its physical limit, an infinite boil-up ratio, the pinch point still exists. The pinch point under the total boil-up ratio is exactly the “reactive azeotrope”, which was discovered by Doherty and Malone and discussed in the book by the same authors.1 Doherty and Malone use a mathematical approach to analyze reactive azeotropes, and the framework for the analysis is based on “transformed composition,” which is invariant under reaction.2 Consider reaction 2, IKSLK+HK. The transformed composition can be expressed as XHK ) xHK + 1/2xIK

Λ13 ) 1.0000 Λ23 ) 0.3012 Λ33 ) 1.0000

RCM-020

The Antoine equation is ln Pjsat ) AVP,j -

Λ11 ) 1.000 Λ21 ) 2.7183 Λ31 ) 1.0000

(9)

Λ11 ) 1.0000 Λ21 ) 2.7183 Λ31 ) 1.0000

Λ12 ) 2.7183 Λ22 ) 1.0000 Λ32 ) 2.7183

Λ13 ) 1.0000 Λ23 ) 2.7183 Λ33 ) 1.0000

RCM-001 Λ11 ) 1.0000 Λ21 ) 1.0000 Λ31 ) 0.1353

Λ12 ) 1.0000 Λ22 ) 1.0000 Λ32 ) 1.0000

Λ13 ) 0.1353 Λ23 ) 1.0000 Λ33 ) 1.0000

Λ11 ) 1.0000 Λ21 ) 1.0000 Λ31 ) 0.4066

RCM-021 Λ12 ) 1.0000 Λ22 ) 1.0000 Λ32 ) 0.2231

Λ13 ) 0.4066 Λ23 ) 0.2231 Λ33 ) 1.0000

RCM-031 Λ11 ) 1.0000 Λ21 ) 1.0000 Λ31 ) 0.1353 a

Λ12 ) 1.0000 Λ22 ) 1.0000 Λ32 ) 2.7183

Λ13 ) 0.1353 Λ23 ) 2.7183 Λ33 ) 1.0000

The Wilson equation is ln γi ) 1 - ln[

∑Λ x] - ∑ ij j

j

Λjixj

∑Λ x

jk k

k

where Λi,j is assume to be independent of the temperature.

YHK ) yHK + 1/2yIK

(10)

where xIK and xHK are liquid mole fractions and yIK and yHK are vapor mole fractions of the IK and HK components. Because

Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011 Table 3. Physical Properties for the Simulation Case activation energy (cal/mol) specific reaction rate at 332 K (s-1) heat of reaction (cal/mol) heat of vaporization (cal/mol) relative volatilities (LK/IK/HK)

forward (EF) backward (ER) forward (kF) ∆Hrxn ∆Hv

12 000 12 500 0.08 5000 6944 4/2/1

mole fractions add up to unity (yLK + yIK + yHK ) 1), eq 10 can be rewritten as

YHK ) yHK + 1/2(1 - yLK - yHK) )

YHK )

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(1 - yLK) + yHK 2 (11)

(1 - yLK) + yHK (1 - yLK) + yHK + (1 - yHK) + yLK

(12)

It is clear that XHK falls between zero and one (1 g XHK g 0). When xHK ) 1, we have unity for the transformed variable, XHK ) 1, and similarly, xLK ) 1 gives XHK ) 0. Consider the

Figure 10. 2IKSLK+HK. Summary of feasible single-feed reactive distillation column RCMs. (A) Feasible when the chemical equilibrium line only passes through distillation regions that touch a product. (B) Feasible with large chemical equilibrium constant. (C) Feasible at small chemical equilibrium constant. (D) Feasible at intermediate chemical equilibrium constant.

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Figure 11. Groups A, B, C, and D for the reaction 2HKSLK+IK.

ternary space in Figure 9A where the solid line represents the chemical equilibrium line and the dashed line is the corresponding vapor line (in vapor-liquid equilibrium with liquid composition in the chemical equilibrium line). Project the numerator and the denominator of the right-hand side of eq 12 from a composition in the two-dimensional space onto the L-H edge along the direction of V, the direction of the reaction (the reactant converting to the two products). YH is the ratio of these two projections. So eq 10 describes a transformation that projects the composition onto the L-H edge. YHK is a transformed composition based on the composition (yLK, yHK). Projection XHK can be obtained in the same way, as shown in Figure 9B. When the composition approaches the reactive azeotrope, the difference between the projected compositions becomes smaller and is equal to zero for a reactive azeotrope, as shown in Figure

9C. When XHK is equal to YHK, the transformed composition behaves like an azeotrope, as in the T-X-Y diagram shown in Figure 9D. In Figure 9C, a reactive azeotrope occurs when the projection of the vapor-liquid equilibrium vector is parallel with the direction of the reaction (slope ) 1). Returning to the stage calculations in Figure 8, the material balance line for Vf∞ is parallel to the VLE vectors and the direction of the reaction (slope ) 1). The pinch point under an infinite boil-up ratio is identical to the reactive azeotrope such that the physical limitation is exactly the reactive azeotrope. We can obtain the maximum achievable product purity of the reactive distillation column by locating the reactive azeotrope for systems with zerosum stoichiometry. The same phenomenon also occurs in


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are simulated to demonstrate the result of the feasibility analysis. The component balances for the column are expressed as Condenser: d(MDxD,j) ) VNTyNT,j - LDxD,j - DxD,j + νjRD dt

(13)

Middle trays: Mi

d(xi,j) ) Li+1xi+1,j + Vi-1yi-1,j - Viyi,j - Lixi,j + νjRi + FixF,j dt

(14) Figure 12. For RCM-311S (group A). (A) VLE vectors do not invert along the entire chemical equilibrium line. (B) VLE vectors invert at two locations when the chemical equilibrium line intersects the boundary of gray region.

systems with non-zero-sum stoichiometry; however the analysis is somewhat more complicated.6 2.5. Simulation. This feasibility analysis method is based on the assumption of chemical equilibrium on reactive trays. Therefore, it is most applicable to real systems which operate with a large Da number. Single hybrid reactive distillation columns7 (with reactive and nonreactive sections, and with a condenser and reboiler that may also be packed with catalyst)

Reboiler: d(MBxB,j) ) L1x1,j - VByB,j - BxB,j + νjRB dt

(15)

Here, xi,j and yi,j denote liquid and vapor mole fractions of component j of the ith tray, with Li and Vi representing liquid and vapor flow rates for the ith tray. Since equal molar overflow is assumed, the vapor and liquid flow rates are constant throughout the stripping and rectifying sections, except for the reactive zone, as a result of an exothermic reaction. The heat

Figure 13. For RCM-020 (group B). (A) When Keq ) 10, VLE vectors do not invert along the entire chemical equilibrium line. (B) When Keq ) 0.033, VLE vectors invert at two location,s but the process is still feasible for a single reactive distillation column using a reactive stripping and nonreactive rectifying section. (C) Composition profiles and normalized extent of reaction (Keq ) 0.033). Even with a small chemical equilibrium constant, this system still can still reach high purity products using a single reactive distillation column.

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Figure 14. For RCM-430 (group B). (A) Tracking of the reactive azeotrope with increasing chemical equilibrium constant in the RCM. (B) The feasible region for RCM-430 can be found by analyzing the reactive azeotrope. In this case, purities reaches 0.99 when Keq is larger than 16.01. (C) Composition profiles and normalized extent of reaction (Keq ) 30). Reverse reaction is observed in the reactive rectifying section. This is the key to the design of a feasible single reactive distillation column.

of reaction vaporizes some liquid on each tray in this section. Therefore, the vapor flow rate increases going up through the reactive zone, while the liquid flow rate decreases going up through the reaction zone: Vi ) Vi-1 -

∆Hrxn R ∆Hv i

(16)

Li ) Li+1 +

∆Hrxn R ∆Hv i

(17)

3. Classification of Feasible RCMs

where ∆Hrxn is the heat of reaction (-5000 cal/mol) and ∆Hv is the latent heat of vaporization (6944 cal/mol). The vapor-liquid equilibrium is assumed to be nonideal and is described by the Wilson equation. A bubble point temperature calculation is used to find the tray temperature. (See Table 1 for the vapor pressure data of the pure components, Table 2 for the coefficients of Wilson’s equation, and Table 3 for physical properties for the simulation case.) P)

∑γ

S i,jxi,jPj

Total pressure P and vapor pressure Ps are in bars. The column pressure is fixed at 1.0 bar. Equations describing the material balances were programmed in C code, and all simulations were carried out on a Pentium PC. Simulations were performed using a dynamic program that is integrated until temperatures and compositions converge. Saturated liquid feeds were assumed, and the feed flow rate was 0.0252 kmol/s of pure IK. The product purities of LK and HK were specified to be 99%.

(18)

The total number of possible ternary RCMs has been verified to be 113.5 In the reaction 2RSP1+P2, feasible RCMs can be classified into four groups, which we label A, B, C, and D (Figure 1). With the intermediate key as the reactant (2IKS LK+HK), the number of feasible cases in each group is 9, 15, 14, and 10, respectively (Figure 10). We can also perform the same analysis for 2HKSLK+IK. The RCM for this type of volatility ranking is exactly identical to a geometric rotation of the previous case. The number of feasible cases is 5, 18, 5, and 8, respectively (Figure 11). The case of 2LKSHK+IK is very


Figure 15. For RCM-001 (group C). Feasibility analysis using VLE vectors for RCM-001. (A) At low chemical equilibrium, VLE vectors do not invert, so high purity products can be obtained by tray-by-tray calculation. (B) VLE vectors invert, so this process is infeasible at high chemical equilibrium constant. (C) In this case, the process is feasible when Keq is less than 3.08.

uncommon in practice. Also, for all of these cases, a slight difference in the stoichiometry, i.e., RSP1+P2 or 2RS2P1+P2, does not change the qualitative result and only affects the critical valves of the chemical equilibrium constant. The change results from the slight change in the direction of the reaction vector. Take RSP1+P2 for example. The reaction vectors change from being parallel to the direction of (1,1) to converging to the point (1,1). 3.1. Group A. In the RCMs of group A, both products are nodes: one is a stable node, and the other is an unstable node. This system is feasible when all of the distillation regions through which the chemical equilibrium line passes touch a

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product. On the other hand, the system is infeasible if the chemical equilibrium line passes through a distillation region that does not touch a product. This result can also be found by analyzing the VLE vectors. Take RCM-311S of group A as an example. There are four different distillation regions in RCM-311S, as shown in Figure 12A. If the reaction equilibrium line does not pass through the gray region, VLE vectors will not invert at any point along the chemical equilibrium line. High-purity product can be reached by tray-by-tray calculation. Simulation confirms this. But in Figure 12B, the gray region causes the VLE vectors to invert at two points, where the chemical equilibrium line intersects the distillation boundaries of the gray region. This causes the tray-by-tray calculation (reactive section) to get stuck at these two points. Furthermore, because there is no product in the gray region, nonreactive distillation cannot be used to overcome this problem. So a single reactive distillation column, hybrid or nonhybrid, is not feasible. In RCM-020 of group A, there is no infeasible region like that of RCM-311S. The two distillation regions both contain product ends. Is this case always feasible? In Figure 13A, for a Keq equal to 10, there is no inverse VLE vector along the whole chemical equilibrium line. So it is feasible under this condition. Also there is a reactive azeotrope when Keq is equal to 0.033 (Figure 13B), the VLE vectors invert when the chemical equilibrium line come close to the intermediate boiling component. Reactive separation will be inhibited by the presence of the azeotrope.8 A nonhybrid RD column is infeasible. However, unlike RCM-311S, a high-purity light product can be obtained from the top of the column because there is a product in the distillation region, so a nonreactive section can be used. On the right side of the diagram, we can keep away from this pinch point by taking advantage of the chemical equilibrium line. We need additional reactive stages to keep our composition trajectory away from the azeotrope. This means more reactive stripping trays are required, as shown in Figure 13C. The feed is at the 66th tray (the reboiler being tray one), and there are 46 reactive striping trays. Most of the reaction occurs in the reactive striping section. For group A, even if there is a reactive azeotrope which lies in the path of the product, we can still obtain high-purity products by using a nonreactive distillation section. 3.2. Group B. Group B includes RCMs without an azeotrope between two products but where at least one product is a saddle point. This process is only feasible at a large chemical equilibrium constant.2 We can explain this phenomenon by tracking the reactive azeotrope. The method of tracking the reactive azeotrope was developed by Okasinski and Doherty.8 With a known set of starting points, arc-length continuation can be used to track azeotropes as a function of the reaction equilibrium constant. Figure 14A shows the location of the reactive azeotrope on a ternary composition diagram as Keq changes from zero to infinity. At Keq ) 0, the reactive azeotrope occurs at a heavy product composition of 0.65. As Keq increases, the location of the azeotrope moves to a higher product composition. Figure 14B shows the heavy product composition of the azeotrope versus Keq. If Keq is greater than 16.01, the heavy product composition is great than 0.99, and the process is feasible. A simulation was performed to confirm the result of the feasibility analysis (Keq ) 30). A nonreactive rectifying section and reactive stripping section were used to get high-purity light and heavy products. The reboil drum was packed with 10 times the amount of the catalyst on each tray to keep the composition

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Figure 17. For RCM-021 (group D). (A) VLE vectors do not invert along the entire chemical equilibrium line for intermediate chemical equilibrium constants. (B) VLE vectors invert when approaching the node (IK). In this case, in contrast with the RCM-020 (group A), single column reactive distillation is infeasible. This is because we cannot rely on distillation or reactive distillation to reach P1 (LK).

Figure 16. For RCM-001 (group C, Keq ) 0.5). Composition profiles and normalized extent of reaction. Catalyst is packed in the reflux drum, and there is a reactive rectifying section where the reverse reaction occurs. This is the key to a feasible single reactive distillation column design.

profile on the chemical equilibrium line. As shown in Figure 14C, the product specifications can be achieved. Note that the thermodynamic behavior of the reactive azeotrope in RCM-430 of 2IKSLK+HK is similar to that of RCM-000 of 2HKSLK+IK, which was explored by Okasinski and Doherty.8 Thus, in some cases, RCMs of one type of volatility ranking can be analyzed as a geometric rotation of another for the purposes of feasibility analysis. 3.3. Group C. RCMs of group C all have an azeotrope between the two products but no node between the reactant and either product. This system was reported to be infeasible for a single reactive distillation column.1 For a large chemical equilibrium constant, this result is true, as shown in Figure 15B. The VLE vectors invert when the chemical equilibrium line approaches the azeotrope on the LK-HK edge. But after modifying the constraints to allow a negative extent of reaction, the process becomes feasible at a low chemical equilibrium constant. The tray-by-tray calculations are shown in Figure 4. Since there is no node (UN or SN) on the edge of either product, the VLE vectors remain in the correct direction toward the light product (Figure 15A). The composition profile does not get stuck at the edge of the RCM. The process is feasible for a low chemical equilibrium constant. The feasible region is found by tracking the reactive azeotrope near the light product, as shown in Figure 15C. The process is feasible when Keq is smaller than 3.08. A simulation confirmed this result. The configuration of the reactive distillation column has the catalyst packed in the reflux drum and a reactive rectifying section (Figure 16A). The profile of the reactive rectifying section is fixed near the chemical equilibrium line by reaction. The purity of the light product is raised little by little through the reverse reaction, as shown in Figure 16. 3.4. Group D. RCM-021 is somewhat similar to the cases of group C. There is an azeotrope between the two products, and this group is infeasible for a large Keq. The azeotrope can

Figure 18. We can find feasible regions in RCM-031 (group D) by analyzing the reactive azeotrope. (A) VLE vectors do not inverse at intermediate Keq. (B) In this case, the process is feasible when Keq is between 0.68 and 6.78.

also be overcome in some cases by applying reactive distillation, as in RCM-001 of group C. But there is also a significant difference: There is an additional azeotrope between the reactant and one of the products, and the reactant is a saddle point. If the chemical equilibrium line comes near the intermediate key, the VLE vectors will invert, and the process will be infeasible. As shown in Figure 17, the VLE vectors do not invert when the chemical equilibrium constant is equal to 10 (Figure 17A) but do invert at a Keq equal to 0.2 (Figure 17B). This means that this case is not feasible at a low chemical equilibrium constant.


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Figure 19. For RCM-031. (A) Feasible design of single RD column. (B) Composition profile in RCM. (C) Composition profile and extent of reaction.

Recall RCM-020 of group A. Even though this RCM also has the intermediate boiling reactant as a stable node and a distillation boundary, it is still feasible at all values of Keq. Why are the results so different? The answer is that both products of RCM-020 are nodes. We do not need a reactive stripping or rectifying section. When a reactive azeotrope is encountered, distillation can be used to replace reactive distillation. A single hybrid column (with both reactive and nonreactive sections in the same device) is feasible at a low chemical equilibrium constant. As for RCM-021, with one saddle product and an azeotrope between two products, a reactive stripping section is needed for breaking through the azeotrope between products.

If liberated from the constraint of chemical equilibrium, the top product would soon approach the lightest boiling azeotrope. This is the reason why RCM-020 is feasible at low chemical equilibrium constant but RCM-021 is not. This is also why group D differs from group C. Take RCM031 as an example to explain the feasibility condition. There are two azeotropes, one is the lightest azeotrope between two products and another is located on the edge of the heavy product, which is a saddle. The two products are both saddle points. This means we need a reactive section at both ends of the column. The VLE vectors invert for both low and high Keq’s (because of the heavy azeotrope, similar to the RCM-430, and

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Figure 20. (A) Two column configuration with one reactive distillation column and one distillation column. The region in the dashed boundary is the control volume for feasibility analysis. (B) Feasibility analysis for the reactive distillation column. All compositions in the reactive sections are located near the chemical equilibrium line.

the light azeotrope, similar to RCM-001). But at intermediate Keq’s, there is no inversion of VLE vectors at the light boiling end of the chemical equilibrium line, and the vectors point to the direction of high purity at the heavy boiling end (Figure 18A). Reactive distillation can produce high-purity products. We can also analyze this problem using a bifurcation diagram (Figure 18B). The composition trajectory will always converge to a stable node at the top of the column and an unstable note at the bottom of the column. However, the two products are both saddle points in RCM-031. By applying the reaction, we make a node at the bottom of the column. The composition of the node varies with Keq and can reach the specification when Keq > 0.68. At the top of the column, two nodes exist when the reaction is applied. One node never reaches the specifications at any Keq. From the bifurcation analysis, the two nodes coalesce and disappear when Keq < 6.78 (this is a turning-point bifurcation when the solution is tracked as a function of Keq). Then, P1(LK) becomes a reachable product (see also the VLE vectors in Figure 18A). The feasible region is when Keq is between 0.68 and 6.78 (Figure 18B). A steady state design for a feasible condition, Keq equal to 1.0, is shown in Figure 19A. The composition trajectory for

reactive distillation at the top and bottom of the column is maintained near the reaction equilibrium line and approaches the specifications gradually (Figure 19B). Composition profiles are shown in Figure 19C. There is a small amount of reverse reaction in the reactive rectifying section, similar to the feasible configurations for RCM-001. The purity of the light product increases gradually and reaches the desired specifications. Notice also the distillation boundary in RCM-021 (Figure 17A). Such a boundary always obstructs distillation. It divides the RCM into two parts (right and left regions). Composition trajectories located in the right region can never reach P1(LK). When the feed composition is located in the left region of the RCM, R(IK) is the light product rather than P2(HK). Since the chemical equilibrium line intersects the boundary, the obstruction can be overcome by reactive distillation. When there are suitable reaction conditions (see Figure 17A, checking the VLE vectors along the whole chemical reaction equilibrium line), the composition trajectory can cross the distillation boundary. High-purity products can be obtained. RCM-021 is a good example of how a distillation boundary can be overcome by reactive distillation.


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Figure 21. RCM-430 (group B, Keq ) 0.25). This is infeasible using a single column for small chemical equilibrium constant, but it is feasible with two columns. (A) Steady state configuration. (B) Composition profile in RCM for the reactive distillation column.

3.5. Strategy for Infeasible Condition in Group B. Some strategies for infeasible cases were discussed by Guo et al.4 Groups C and D were handled by using an entertainer. In this work, a two-column configuration, which includes one reactive distillation column and one nonreactive distillation column but no entertainer, is designed to deal with the infeasible cases in group B. The conceptual configuration is shown in Figure 20A. Since there is no azeotrope between the two products, one product is a saddle point. Our design concept is to consume the intermediate boiling reactant as much as possible in the reactive distillation column and to produce a distillate stream with both products. Then, a conventional distillation column can separate them. The key point is whether high conversion can be achieved in the reactive distillation column. Take RCM-430 for example. A single reactive column has been shown to be infeasible at low Keq’s. Is the two-column configuration feasible for this case, especially for a low Keq? We start with a material balance on the control volume in Figure 20A. The result is the same as eqs 9 and 10. Then, we set specifications for the top product stream. From a mole balance, the compositions of L and H at the top of the column must be equal to each other. Regardless of the conversion in the column, the output composition should be located on the line between S (Figure 20B). The specifications cannot be reached xD and δR,B using only reactive distillation since xD is far from the chemical equilibrium line, and consequently they must be achieved by distillation. So we plot the bubble point temperature versus composition of the light product and heavy product along at the 45° line. The lowest temperature is located at a composition of xLK ) xHK ) 0.5, i.e., no reactant. For an equimolar reaction,

this point is the favorable product at the top. So we can achieve a high purity of LK and HK. Only a small number of reactive S and x1 trays is needed (Figure 20B). yB is located between δR,1 where the reaction is in the forward direction. Then, the stage calculations satisfy material balance. Additional stages above the reactive stages are rectifying distillation stages that raise the purity of the top product to xD. The slight amount of residue IK does not interfere with separation in the distillation column. This configuration is also validated by simulation, as shown in Figure 21A. The composition trajectory is close to the prediction of the feasibility analysis (Figure 20B). High-purity products cannot be produced by a single reactive distillation column for RCM-430 of group B with a low chemical equilibrium constant. But two-column systems (one reactive distillation and one distillation column) are feasible for this type of RCM. Feasibility analysis and simulation both confirm this. 4. Conclusion Feasibility analysis for reactive distillation is extended by allowing the reverse reaction. In this case, a system with the reaction 2IKS LK+HK and an azeotrope between two products becomes feasible in some cases. The number of possibly feasible cases is increased from 27 to 48 out of 113 possible ternary configurations. Feasibility analysis can be accelerated by using vapor-liquid equilibrium vectors. The reactive azeotrope was shown to be identical to the pinch point of tray-by-tray calculations. Using these two useful tools, feasible RCMs can be quickly classified into four groups, which are as follows: (A) Two products are

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nodes, feasible when the chemical equilibrium line only passes through distillation regions with products. (B) One product is a saddle point, and no azeotrope is present between two products, feasible for a large chemical equilibrium constant. (C) There is an azeotrope between two products but no nodes between the reactant and either product. This group is feasible for a small chemical equilibrium constant. (D) There is an azeotrope between the two products and one or more nodes on the RCM edge next to the saddle product; this group is feasible at an intermediate chemical equilibrium constant. For group B, which is infeasible at a low chemical equilibrium constant, a twocolumn configurations is shown to be able to produce highpurity products. Nomenclature AVP ) Antoine vapor pressure coefficient B ) bottom molar flow rate [mol/time] BVP ) Antoine vapor pressure coefficient CR ) reactant stoichiometric coefficient vector CP ) product stoichiometric coefficient vector CVP ) Antoine vapor pressure coefficient D ) distillate molar flow rate [mol/time] Da ) Damkohler number EF ) activation energy of forward reaction ER ) activation energy of reverse reaction F ) feed flow rate [mol/time] Keq ) reaction equilibrium constant kF ) specific reaction rate of the forward reaction L ) liquid flow rate [mol/time] M ) liquid holdup NR ) tray number of rectifying section Nrxn ) tray number of reactive section NS ) tray number of stripping section P ) total pressure of column Ps ) vapor pressure R ) amount of reaction [mol/time] T ) temperature t ) time V ) vapor flow rate [mol/time] X ) transformed composition in liquid phase x ) liquid composition Y ) transformed composition in vapor phase y ) vapor composition Greek Letters γ ) activity coefficient δR ) raction difference point r δR,n ) reactive cascade difference points for the rectifying section at tray n s δR,m ) reactive cascade difference points for the stripping section at tray m

∆Hrxn ) heat of reaction ∆Hv ) heat of vaporization Λji ) Wilson binary coefficient V ) chemical stoichiometry ξn ) accumulated molar reaction extent from the top to stage n ξm ) accumulated molar reaction extent from the bottom to stage m Subscripts B ) bottoms D ) distillate F ) feed HK ) heavy key component i ) ith tray IK ) intermediate key component j ) jth component LK ) light key component m ) tray index of rectifying section n ) tray index of stripping section NT ) total tray number of reactive distillation column NF ) feed tray P1 ) product 1 P2 ) product 2 R ) reactant

Literature Cited (1) Doherty, M. F. Malone, M. F. Conceptual Design of Distillation Systems; McGraw-Hill: New York, 2001. (2) Hauan, S.; Ciric, A. R.; Westerberg, A. W.; Lien, K. M. Difference points in extractive and reactive cascades: I-basic properties and analysis. Chem. Eng. Sci. 2000, 55, 3145–3159. (3) Lee, J. W.; Hauan, S.; Westerberg, A. W. Feasibility of a reactive distillation column with ternary mixtures. Ind. Eng. Chem. Res. 2001, 40, 2714–2728. (4) Guo, Z.; Chin, J.; Lee, J. W. Feasibility of continuous reactive distillation with azeotropic mixtures. Ind. Eng. Chem. Res. 2004, 43, 3758– 3769. (5) Matsuyama, H.; Nishimura, H. Topological and thermodynamic classification of ternary vapor-liquid equilibria. J. Chem. Eng. Jpn. 1977, 10, 181–187. (6) Chen, C. S.; Yu, C. C. Effects of Relative Volatility Ranking on Design and Control of Reactive Distillation Systems with Ternary Decomposition Reactions. Ind. Eng. Chem. Res. 2008, 47, 4830–4844. (7) Kaymak, D. B.; Luyben, W. L. Effect of the chemical equilibrium constant on the design of reactive distillation columns. Ind. Eng. Chem. Res. 2004(b) , 43, 3666–3671. (8) Okasinski, M. J.; Doherty, M. F. Thermodynamic Behavior of Reactive Azeotropes. AIChE J. 1997, 43, 2227–2238.

ReceiVed for reView March 14, 2010 ReVised manuscript receiVed November 2, 2010 Accepted November 15, 2010 IE1006118

Feasibility of Reactive Distillation for Ternary Systems with Azeotropic

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