Selectivity Engineering with Simple and Complex Hybrid Reactive

Article pubs.acs.org/IECR

Selectivity Engineering with Simple and Complex Hybrid Reactive Distillation Columns Shabih Ul Hasan,† Ranjan Malik, and Sanjay Mahajani* Department of Chemical Engineering, IIT-Bombay, Powai, Mumbai-400 076, India S Supporting Information *

ABSTRACT: A new synthesis and design method is developed for simple and complex hybrid reactive distillation columns, to achieve desired selectivity in case of multireaction schemes involving multicomponent mixtures wherein, reactant is a saddle in the corresponding residue curve map. The developed methodology makes use of attainable region approach as well as combined graphical-simulation approach. We determine the surface of reactive stage compositions (SRSC) such that if the reaction takes place at any of the compositions that belongs to SRSC then the desired selectivity is ensured. Design guidelines have been formulated based on the number of compositions of the reactive species that appear in the equation of the SRSC, to identify appropriate hybrid RD configurations for the reaction scheme of interest. The method is illustrated using an industrially relevant example of intramolecular aldol condensation of cyclohexanone to achieve the desired selectivity toward 2-cyclohexylidene cyclohexanone. The results provide good initialization for rigorous simulation. The algorithm presented here can be applied to any number of components and can be directly applied to even multiazeotropic systems as well but is restricted to single reactant (i.e., single feed configurations) multireaction schemes with multiple products undergoing side reactions.

1. INTRODUCTION Reactive distillation can be advantageously used to improve selectivity of the desired product by favorably manipulating the composition profiles with the aid of distillation attributes to suppress side reactions. The development of a systematic design procedure for reactive distillation (RD) columns to obtain higher or desired selectivity in case of simple and complex reaction schemes has been the theme of our work published in the recent past.1−7 Hasan et al.6 have proposed a conceptual design algorithm for single feed hybrid reactive distillation columns to achieve desired selectivity in case of single reactant multireaction schemes. It was also shown that hybrid RD columns are particularly useful when the reactant is intermediate boiling or saddle in the residue curve map of the given mixture. Their algorithm is restricted to pseudo-ternary mixture and to the cases wherein only one product undergoes further side reaction. The objective of the present work is to remove these restrictions and develop an algorithm that would encompass broader range of reaction schemes. It requires inclusion of complex hybrid RD configurations in the available design options. Complex configurations are those that involve multiple feeds and side streams. In this work, we restrict ourselves to a single reactant schemes and hence consider only the configurations with single feed but one or more side stream(s). There has been considerable work on the design of either multicomponent reactive distillation columns or nonreactive side draw columns. However, for the complex columns with both the attributes, that is, reactive distillation column with side-draw, no conceptual design methods have reported to the best of our knowledge. Though the design of hybrid RD columns has been investigated well in the past,8−18 the work was restricted to a single reaction systems and the objective was to obtain the desired conversion instead of selectivity. There © 2014 American Chemical Society

have been limited number of studies that cover multireaction systems in which RD can be used to improve the selectivity of the intermediate product(s).19−25 However, the analysis was restricted to the specific scheme of interest and objective was not to develop a generic design method. With regard to the design of nonreactive side draw columns, there have been few attempts to develop robust and alternative approaches. For example, Gllnos and Malone26 proposed a shortcut procedure to design side stream distillation column for ideal mixtures. Their method is based on certain assumptions of purities of key components in bottom, distillate, and side streams. Wasylkiewicz et al.27 designed ternary distillation column with side draw using extended BVM. Since the side stream composition is not known a priori, its purity constraint limits the feasible design specifications. Recently, Beneke et al.18 also reported the problems they faced while designing a side draw column for ternary mixture using column profile maps. According to them, if the liquid side-stream is below the feed then the stripping section profile starting from the bottom composition has to run through the side stream composition. However, it is impractical to specify all the products a priori, since the profile running from the bottom composition may be nowhere near the specification we would like to achieve for the side stream. Moreover, the bottom and side stream compositions are closely linked to each other, and the location of the side stream is affected by the reboil ratio used. In short, the extension of BVM for the design of hybrid RD columns with side draw, giving a desired selectivity, is not straightforward because the column profile in the 3D space is required to Received: Revised: Accepted: Published: 18526

May 14, October October October

2014 2, 2014 16, 2014 16, 2014

dx.doi.org/10.1021/ie501961x | Ind. Eng. Chem. Res. 2014, 53, 18526−18538

Industrial & Engineering Chemistry Research

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pass not only through a feasible side stream composition but also through the fixed selected stage composition at which reaction takes place in the column to give the desired selectivity. Moreover, it is hard to specify all the product purities in a multicomponent system, a priori, since the spec in the present problem is on selectivity and not on product purities. In view of this, we adopt a new approach that combines the advantages of both graphical and simulation methods. The visual information provided by geometric methods allows one to get a better understanding of the thermodynamic behavior and the constraints on possible separation. Without visualization in composition space, the number of possible alternatives that could be simulated is large, and individual runs may be expensive. Simulation based approach, on the other hand, brings in convenience, as it does not require product compositions to be specified unlike that in BVM, and hence, it is easily extensible to systems with any number of components. To sum up, the combined graphical-simulation approach is less iterative, easy to implement, and has an ability to hit the exact solution, as against the BVM for multicomponent mixtures. The proposed algorithm is based on the visualization of the locus of liquid feed stage compositions (LFSCs) and its intersection with a surface in composition space such that if the reaction takes place at any of the compositions on this surface then the desired selectivity is achieved. In this work, we restrict ourselves to single reactant single-feed hybrid RD configurations with or without side draw and consider both zeotropic as well as multiazeotropic mixtures. The article is organized as follows: we start with the geometric interpretation of CSTR and complex hybrid RD column. Then, we introduce the reader to the concept of surface of reactive stage compositions (SRSC), which forms a basis for the proposed design algorithm. A stepwise design algorithm is presented by considering two hypothetical examples of complex van de Vusse type reaction scheme involving zeotropic and multiazeotropic mixtures. The developed algorithm for the conceptual design is then extended to an industrially important reaction of self-aldol condensation of cyclohexanone. Finally, few guidelines are provided to identify appropriate hybrid RD configurations for the reaction scheme of interest.

Figure 2. Analogy between arbitrary reactor (R) and complex hybrid RD Column.

reaction takes place at product composition hence the rate vector at that point is collinear with the mixing vector of feed and product streams (Figure 1a). In any other reactor, the composition at which the reaction takes place is different than the product composition, and hence, the colinearity condition is no longer valid (Figure 1b). One can cleverly manipulate this composition by introducing separation attributes as is done in the case of reactive distillation. As shown in Figure 2, let us consider a complex distillation column with single reactive stage. In this case, the reaction does not take place at a composition corresponding to the product stream (P), which is the overall composition obtained by virtually mixing the overhead, side draw, and bottom streams. The composition of the reactive stage depends on the distillation attributes such as reflux ratio, side draw to feed ratio, feed location, number of stages, etc. Therefore, the next exercise is to know which are the points in the composition space that can be the potential reactive stage composition(s) giving the desired selectivity corresponding to the point to be attained? The following section determines the surface of such feasible reactive stage compositions.

3. SURFACE OF REACTIVE STAGE COMPOSITIONS (SRSC) Now, consider an equimolar van de Vusse type reaction scheme (eq 1) with only one reacting component A. We select this

2. GEOMETRIC INTERPRETATION OF CSTR AND COMPLEX HYBRID RD COLUMN In our earlier work,6 we presented geometrical interpretation of reactors and concluded that the composition at which reaction takes place, depends on the type of the reactor. In CSTR, the

Figure 3. SRSC for reaction scheme represented by eq 2.

scheme for the present analysis because it is well-known that the reactor choice becomes difficult when both series and higher order parallel reactions occur simultaneously. Hence, the general guidelines of conventional steady state reactor(s) selection do not apply to this system. Thus, these schemes represent the class of complex schemes, which may need reactor networking. Application of simple and complex hybrid

Figure 1. Graphical representation of (a) CSTR, (b) arbitrary reactor (R). (Adapted with permission from ref 6. Copyright 2013, Elsevier.) 18527



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RD columns for such reaction is not studied before and is the main subject of this paper. All the reactions in this reaction scheme are irreversible, except B to C, with first, second and third reactions are of first order while the fourth reaction is of second order. One can notice here that more than one product (i.e., B and C) undergo further side reaction(s). The feed is pure reactant A and the kinetic rate constants are given by [k1 k2 k3 k4] = [1 1 1 3]. It may be noted that we consider B to C reaction to be reversible, as we want to extend the analysis further for the single reactant multireaction schemes in which more than one product undergo further side reactions. ⎫ undesired(k4) A ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ D , ⎪ ⎪ ⎪ 2 * * * * [rArBrCrD] = [− k1xA − k4xA , − k 2xB + k1xA ⎬ ⎪ + k 3xC*, k 2xB* ⎪ ⎪ − k 3xC*, k4xA*2] ⎭

desired(k1)

undesired(k 2)

A ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ B XoooooooooooooY C desired(k 3)

and

Figure 5. SRSC for reaction scheme represented by eq 3. (1)

By using material balances for the components A and B on any arbitrary reactor, we get xB , P − xB ,0 xA , P − xA ,0

=

k x* − k 2xB* + k 3xC* rB = 1A rA −k1xA* − k4xA*2

(2)

where xi,p is the product composition of component i, xi,0 is the inlet composition of component i and x* denotes the compositions at which the reaction takes place in the reactor. The LHS of eq 2 is the slope of line joining points A (xA0, xB0) and P (xAP, xBP) and can be calculated once the position P is fixed. It should be noted that point P is on x−y plane (Figure 3) and since eq 2 is independent of xC,P, its value is not required for plotting the surface of reactive stage compositions (SRSC). Hence, for any desired point P in the composition space, eq 2 gives a relation between xA*, xB* and xC*, which represents the SRSC as shown in Figure 3. Furthermore, it should be noted that once we choose point P, which is not the part of the SRSC, it implies fixed desired selectivity, and hence, if the reaction occurs at any of the compositions on the SRSC then the desired selectivity is ensured.

Figure 6. Selected reactive composition X* on the projection of the SRSC.

4. DESIGN PROCEDURE For convenience, we spilt the reaction and distillation attributes of the complex hybrid reactive distillation column (Figure 4a)

Figure 7. Curves for a range of reflux ratios at different values of reboil ratios representing LFSCs. Figure 4. (a) Complex hybrid (RD) column and (b) reactor separator system (non-RD).

However, it is different from CSTR in the sense that the reactor composition and that of the product stream are not same. We impose a constraint on the reactor composition such that reaction occurs at a rate that gives the desired performance in terms of conversion and selectivity.6 The composition of the product stream from this reactor can thus be determined by material balance that accounts for the extent of reaction. The product is then sent to a non-RD column which separates the given mixture into the product streams having compositions

as shown in Figure 4b. The new configuration consists of a hypothetical well-mixed reactor followed by a nonreactive distillation column (non-RD), that gives the same performance as that of a complex hybrid RD column (Figure 4a). We call the reactor in Figure 4b a hypothetical well-mixed reactor because similar to CSTR, it is a perfectly mixed reactor and can be represented as a point in composition space. 18528



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Figure 8. (a) Identical column profiles in triangular diagram. (b) Column profiles along the length of column. The close overlap indicates that the design is feasible.

Table 1. Design Specifications for Simple Hybrid RD Column column configuration

non-RD

no. of components, NC volatility [A B C D] no. of stages, N feed location, Nfl feed flow rate, F feed composition, Xf no. of reactive stages, Nr location of reactive stage, Nrl Damkohler number/catalyst loading reflux ratio, R reboil ratio, S end compositions after mixing the distillate and bottom streams

4 [3 5 2 1] 12 6th stage 1 (0.3 0.175 0.0553)

4 [3 5 2 1] 12 6th stage 1 (1, 0, 0) 1 6th stage 0.3386

RD

22.26 6.35 (0.3 0.175 0.0553)

22.26 6.35 (0.3 0.175 0.0553)

Figure 10. Family of curves (FOC) for a range of reflux and reboil ratios representing LFSCs.

Figure 11. Feasible condition that satisfies our requirements.

Figure 9. Selected reactive stage composition X* on the curve of the SRSC.

reaction and separation allows us to determine the parameters such as Damkohler number, reflux/reboil ratios, number of stages of the RD column giving the desired performance. This would be illustrated by considering the following examples. Example 1: van de Vusse Scheme with the SRSC as a function of only two compositions and zeotropic mixtures. Consider an equimolar van de Vusse type reaction scheme (see eq 3), with only one reacting component A. All the reactions are irreversible; the first and second reactions are first

same as that of the end compositions of the RD column. If the feed stage in the RD column is the reactive stage then the column profiles of non-RD column and RD column coincide for the same distillation attributes (Hasan et al.;6 Appendix A). In other words, irrespective of whether the reaction is carried out inside the column or outside, the column profiles of both complex hybrid RD column (Figure 4a) and nonreactive column (non-RD; Figure 4b) remain similar. This isolation of 18529



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Figure 12. (a) Identical column profiles in triangular diagram. (b) Column profiles along the length of column. The close overlap indicates that the design is feasible.

Figure 13. (a) SRSC. (b) Selected reactive stage composition X* on the curve of SRSC.

Figure 14. (a) FOC for a range of reflux and reboil ratios representing LFSCs. (b) Feasible condition that satisfies our requirements.

⎫ undesired(k 3) A ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ D ⎪ ⎪ ⎬ [rArBrCrD] = [− k1xA* − k 3xA*2 , − k 2xB* + k1xA*, k 2xB* ⎪ 2 ⎪ , k 3xA* ] ⎭

order, and the third reaction is second order. The kinetic rate constants and volatilities are [k1 k2 k3] = [1 1 3] and [αA αB αC αD] = [3 5 2 1], respectively. We mention here that hybrid RD columns are especially useful when the reactant is of intermediate volatility. Therefore, the relative volatilities chosen here are such that the reactant should be of intermediate volatility. One can take any order of volatalities for other components present in the system. The feed is pure reactant A.

desired(k1)

undesired(k 2)

A ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ B ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ C

and

(3)

The equation of the SRSC for the above reaction scheme is given by eq 4 and plotted in composition space as shown in Figure 5. 18530



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Figure 15. Column profiles in (a) 3D composition space (b) along the height of the column. The close overlap indicates that the design is feasible.

xA , P − xA ,0 xB , P − xB ,0

=

−k1xA* − k 3xA*2 k1xA* − k 2xB*

We determine Da by applying material balance for either component A (eq 6) or component B (eq 7), for any arbitrary reactor in which reaction takes place at the selected composition X*. Further, by writing material balance for component C (eq 8), one can find the composition of C in the reactor outlet or in the feed to the distillation column (Figure 6a, Hasan et al.6).

(4)

In the examples considered in our previous work,6 we assign the same volatilities to C and D and consider the mixture as pseudo-ternary mixture for a more convenient graphical representation in 2D. Since it is an overconstrained problem, the design procedure developed in our previous work6 does not work in the present case wherein C and D have different volatilties. We therefore use a 3D space to visualize the profiles. Now, for the present example, since the equation of SRSC (see eq 4) contains reactive compositions of only two reactants, we can use simple hybrid RD column having two adjustable parameters, that is, reflux ratio and reboil ratio. These parameters will be manipulated in order to obtain the required composition on the reactive stage. In the following part of this section, we illustrate the steps of the design procedure for the reaction scheme given by eq 3, to obtain desired selectivity using simple hybrid RD column. Step 1: Select point P (Figure 5) in the composition space according to the desired selectivity. This point represents the overall output composition of simple hybrid RD column (Figure 6b, Hasan et al.6), obtained by virtually mixing distillate (D) and bottoms (B) streams. Hence, it can be considered as the feed to non-RD column in Figure 6a (Hasan et al.6). Step 2: Join point P (0.3, 0.175) and A (1, 0) to calculate the slope of line AP, and hence obtain the surface of reactive stage compositions (SRSC) using eq 4 as shown in Figure 5. Step 3: Select any reactive stage composition, X*, on the projection of the SRSC in 2D according to the choice of energy saving or catalyst loading (see Figure 19, Hasan et al.6) as shown in Figure 6. For the present example, let X* = [x*B x*A ] = [0.68, 0.1632]. It should be noted here that since we need to fix only two reactive compositions xA* and xB* on the feed stage of non-RD column we can work in 2D composition space. Step 4: Find the composition of all the components including C and D in the feed that is sent to the distillation column (Figure 4a). The concentration of C is related to the extent to which individual reactions take place, which in turn depends on the Damkohler number (Da), that is, the ratio of characteristic liquid residence time to the characteristic reaction time (eq 5). ⎛W k ⎞ Da = ⎜ cat ref ⎟ ⎝ F ⎠

⎛ −k x* − k x*2 ⎞ 3 A ⎟=0 xA ,0 − xA , P + Da⎜ 1 A k ref ⎝ ⎠

(6)

⎛ k x* − k x * ⎞ 2 B ⎟=0 xB ,0 − xB , P + Da⎜ 1 A k ref ⎠ ⎝

(7)

⎛ k x* ⎞ xC ,0 − xC , P + Da⎜ 2 B ⎟ = 0 ⎝ k ref ⎠

(8)

The composition of component D can be calculated from the summation constraint and hence the feed to non-RD column gets fully specified. Step 5: For the simulation of non-RD column, along with the feed composition, we also have to specify the number of stages, feed location, and operating parameters such as reflux and reboil ratios. For optimum design, the number of stages can be chosen on the basis of capital and operating costs, which is out of the scope of the present work. For illustration purpose, we consider N = 12 with reboiler as the first stage. Since reactant A in our case is saddle in the residue curve map, one can choose the feed location anywhere near the middle of the column (Nfl = sixth stage). Step 6: Find the operating parameters such that the feed stage composition of the non-RD column coincides with the selected reactive composition, X*. To obtain this intersection, we draw curves representing locus of liquid feed stage compositions (LFSCs) obtained for a range of reflux ratios (1-to-500) and at different values of reboil ratios, as shown in Figure 7. The LFSCs is defined as the locus of all liquid feed stage compositions for a range of reflux ratios obtained for any fixed value of the reboil ratio. The range over which reflux ratio can be varied may be decided by visualizing the curves of LFSCs, that is, whether or not they cross the projection of SRSC containing selected reactive stage composition, X*. It can be clearly seen in (Figure 7) that the reactive composition, X*, of interest lies in the vicinity of the curve obtained for S = 6.

(5) 18531



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hybrid RD column with side draw in the present example to introduce a new continuous adjustable parameter viz. side draw to feed ratio, SD. With the help of this parameter one can adjust the composition of component C on the feed stage of non-RD column to make it equal to the one selected on the SRSC. The design procedure to obtain the desired selectivity using complex hybrid RD columns is given as follows. Step 1: Select any point P (Figure 3) according to the desired selectivity of intermediate product, B in the composition space. This point now represents the overall output composition of complex hybrid RD column (Figure 4b), obtained by virtually mixing distillate (D), side draw (SD), and bottoms (B) streams. Hence, it can be considered as the feed to non-RD column in Figure 4a. Step 2: Join point P (0.3, 0.175) with A (1, 0) to calculate the slope of line AP, and hence obtain the SRSC using eq 2, as shown in Figure 3. Step 3: Select any reactive stage composition, X*, on the curve of the SRSC as shown in Figure 9. For the present example let X* = [x*A x*B x*C ] = [0.61, 0.2584, 0.08]. It should be noted that from clarity point of view, we draw the curve of SRSC for a constant value of xC* (i.e., xA* and xB* vary but xC* = 0.08). For full surface of reactive stage compositions refer Figure 3. Also, only those compositions are plotted which lie within the 3D composition space. Step 4: Find the composition of all the components in the hypothetical feed that is sent to the non-RD distillation column (Figure 4b) by using the material balances given by eqs 9, 10, and 11. Note that eq 11 suggests a new constraint along with xA* > 0, xB* > 0, xC* > 0 in selecting the reactive stage composition X* on the SRSC; that is, xB* > xC*; otherwise, we may end up in negative hypothetical feed composition of component C.

Step 7: The next step is to consider the values of reboil ratio, near S = 6 and narrow down the range of reflux ratios. The values of two operating parameters viz. S and R, at the exact intersection of feed stage of non-RD column with the selected reactive stage composition, X*, are found to be 6.35 and 22.26, respectively. The column profile for non-RD column (Figure 6a, Hasan et al.6) in 3D composition space is then plotted as shown in Figure 8. Step 8: Obtain the column profile for RD, with the feed as pure A and the feed stage as the reactive stage, using same design and operating parameters as used for the non-RD case. The profiles coincide (Figure 8) to indicate that the design is feasible. Hence, the desired selectivity for the given complex reaction scheme is attainable through simple hybrid RD column with design specifications given in Table 1. The feasible design giving the desired selectivity obtained above assumes constant molar overflows. Nonequimolar multireaction schemes can be dealt with in a similar way as that discussed in our earlier work (Hasan et al.;6 example 2, section 5). The Da value for a single reactive stage, determined in the above exercise, in some cases, may turn out to be relatively high and hence impractical at times. In such cases, the option of distribution of the catalyst over multiple stages, without affecting the desired selectivity, may be explored. To keep the concentration uniform in the reactive section, feed can also be distributed equally over all these catalytic stages. A solved example may be found elsewhere (Hasan et al.6 Appendix SB of Supporting Information). Even after distribution, if the catalyst requirement is exorbitantly high then cost considerations would eliminate this option. Depending on the specification of number of stages, feed location, and side draw location, the above algorithm generates multiple feasible designs which can be evaluated and compared in terms of capital cost, energy saving and catalyst loading to determine a good/optimal design for the given set of design goals. Example 2: van de Vusse type Scheme with the SRSC as a function of three compositions and zeotropic mixtures. Let us consider another example of equimolar van de Vusse type scheme with only one reacting component (A), for which the SRSC is a function of compositions of three components involved in the scheme (see eq 1). The SRSC for this reaction scheme is given by eq 2 and is shown in Figure 3. All the reactions are irreversible, except B to C, with first, second and third reactions being first order, while the fourth being a second order reaction. The kinetic rate constants and volatilities are [k1 k2 k3 k4] = [1 1 1 3] and [αA αB αC αD] = [3 5 2 1], respectively. Note that A is the saddle in the residue curve map. In the present example, one can notice that the SRSC is now the function of the composition of the third component (xC*) as well. As a result, we need to fix all the three reactive compositions viz. xA*, xB*, and xC* on the feed stage of the nonRD column. This is because now the calculation of Damkohler number (i.e., catalyst loading required for a given conversion) also depends on xC* (see eq 10) unlike the example 1 (see eqs 6 and 7). Therefore, if we use simple hybrid RD column with only two adjustable parameters for the present example then the composition of C (x*C ) on the feed stage is dictated by the relative volatilities of the components involved. Therefore, the composition of C on the feed stage of non-RD column (Figure 4b) need not be same as the one selected on the SRSC for any combination of reflux and reboil ratios. The design problem is thus overconstrained and leads to a mismatch in the column profiles of RD and non-RD columns. Hence, one must use

⎛ −k x* − k x*2 ⎞ 4 A ⎟=0 xA ,0 − xA , P + Da⎜ 1 A k ref ⎝ ⎠

(9)

⎛ k x* − k x * + k x * ⎞ 2 B 3 C ⎟=0 xB ,0 − xB , P + Da⎜ 1 A k ref ⎝ ⎠

(10)

⎛ k x* − k x * ⎞ 3 C ⎟=0 xC ,0 − xC , P + Da⎜ 2 B k ref ⎠ ⎝

(11)

Step 5: Specify the number of stages, feed location, side draw location and operating parameters (say N = 12, Nfl = 7th stage). Side draw location depends on the volatility of that product whose composition is required to be adjusted through side draw to obtain the desired selectivity; in the present case it is component C. Hence, if the volatility of component C is less than the volatility of the reactant A then the side draw location is below the feed location (Sdl = 6th stage). Step 6: Find the operating parameters such that the feed stage composition of the non-RD column coincides with the selected reactive stage composition, X*. To obtain this intersection, draw the family of curves representing LFSCs obtained for a range of reflux and reboil ratios by choosing initially some arbitrary value of side draw to feed ratio (say SD = 0.2). It should be noted that there is one curve that corresponds to the range of reflux ratios at a given value of SD and reboil ratio. Now if one considers the range of reboil ratios, too, then a family of curves can be plotted. Figure 10 shows 18532



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three such families for a range of reflux (5-to-500) and reboil ratios (5-to-500) at three different values of SD. The bounds on the range of reflux ratio can be decided by visualizing one curve of LFSCs, that is, whether or not it crosses the curve of the SRSC containing selected reactive stage composition, X*, while the reboil ratio can start from any small value until the performance becomes insensitive at higher values of reboil ratios. It can be clearly seen in Figure 10 that the reactive composition, X*, of interest lies in the vicinity of curves obtained for SD = 0.4. Step 7: Next step is to consider the range of side draw to feed ratio, near the value SD = 0.4 and narrow down the ranges of reflux and reboil ratios based on the results shown in Figure 10. The exact intersection of feed stage of non-RD column with the selected reactive stage composition, X*, is shown in Figure 11. The values of three operating parameters viz. SD, S, and R at this intersection are found to be 0.4283, 51.75, and 180, respectively. The column profile for non-RD side draw column in 3D composition space is then plotted as shown in Figure 12. Step 8: Obtain the column profile for RD, with the feed as pure A and the feed stage as the reactive stage, using the same design and operating parameters as used for the non-RD case. The profiles coincide (Figure 12) to indicate that the design is feasible. Hence, the desired selectivity for the given complex reaction scheme is attainable through complex hybrid RD column having N = 12, Nfl = Nrl = 7th stage, Sdl = 6th stage, Da = 0.4055, R = 180, S = 51.75, and SD = 0.4283. The detail design specifications can be seen in Table S1 in the Supporting Information. From the foregoing examples, it may be concluded that the nature of the given reaction scheme has strong impact on the configuration to be used to obtain the desired selectivity. If multiple components undergo side reactions then one can increase the number of side draw streams to attain the desired compositions on the reactive stage and hence the desired selectivity. Example 3: van de Vusse type scheme with the SRSC as a function of three compositions and multiazeotropic mixtures. Consider the same simplified equimolar van de Vusse scheme (eq 1) with rate constants, [k1 k2 k3 k4] = [1 1 1 3] and volatilities as B > A > C > D. A hypothetical multicomponent azeotropic mixture28 consisting of three minimum boiling binary azeotropes is chosen to show that the design procedure described above for multicomponent zeotropic mixtures is also applicable to the mixtures involving multiple azeotropes. The distillation boundary shown by the shaded surface in Figure 13b, divides the space into two distillation regions. Figures 13, 14, and 15 show the results obtained by following the procedure described for example 2. It can be clearly seen that the developed methodology can be successfully applied to even multiazeotropic systems to obtain one of the promising designs of desired selectivity for the reaction scheme given by eq 1 using a side draw hybrid RD column having N = 12, Nfl = Nrl = 6th stage, Sdl = 5th stage, Da = 0.7375, R = 638, S = 159, and SD = 0.435. The detail design specifications can be seen in Table S2 in the Supporting Information.

Figure 16. RCM for cyclohexanone−water−aldol system (Pressure: 1 atm. Themodynamic model: Wilson).

Figure 17. SRSC for reaction scheme represented by eq 13. Note: SRSC is not coinciding with the ACD plane.

Figure 18. Selected reactive stage composition X* on the curve of the SRSC.

products.29 The reaction scheme and rate equations are given in Appendix A. Thermodynamics is modeled using WILSON equation and the kinetic data is taken from Mahajan et al.29 The residue curve map (RCM) for the cyclohexanone−water−aldol system is shown in Figure 16. It depicts minimum boiling azeotrope between cyclohexanone and water. The kinetic parameters and binary interaction are given in Tables S3 and Table S4, respectively, in the Supporting Information. This reaction scheme falls in the category of single reactant series parallel reactions and is given by eq 12; the equation of the SRSC of which is given by eq 13.

5. CASE STUDY: SELF-ALDOL CONDENSATION OF CYCLOHEXANONE Intramolecular or self-aldol condensation of cyclohexanone yields an isomeric mixture of corresponding aldols, which has important industrial applications. This reaction suffers from selectivity loss due to formation of various undesired side18533



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Although the self-aldol condensation is an example of series parallel reaction scheme, due to the complex reaction kinetics (see Appendix A), it poses a challenge in achieving the desired selectivity. The activity coefficients present in eq 13 are temperature and composition dependent. As the reaction kinetics is valid for the temperature range 353−373 K (Mahajan et al.29), we find the rate constants at temperature 373 K. It may be noted here that in this work, we have restricted ourselves to only conceptual design for which a design algorithm is proposed to obtain one of the feasible designs of desired selectivity, and hence, we used temperature independent kinetics. Once the feasible design specifications are obtained from the conceptual design algorithm, one can do rigorous simulations using ASPEN PLUS, which uses temperature dependent kinetics. A comparison of the conceptual design with the rigorous design is discussed later at the end of this section. Because of the presence of activity coefficients in eq 13, the equation of the SRSC includes three reactive compositions viz. xA*, xB*, and xC*. Therefore, as discussed before, we need to fix three compositions, viz. xA*, xB*, and xC*, on the feed stage of the non-RD column which requires three adjustable parameters and hence, one must use hybrid RD column, with side draw, to achieve the desired selectivity. It should be noted here that by using WILSON model, eq 13 can be converted into a nonlinear equation in which the only variables are xA*, xB*, and xC*; xD* can be calculated by summation equation. This nonlinear equation can be solved in MATLAB using ‘fsolve’ solver to obtain the values of x*B over a geometrically rectangular grid formed by x*A and x*C . Hence, the SRSC can be plotted using eq 13 and is shown in Figure 17. The design procedure to obtain the desired selectivity using hybrid RD column with side draw for cyclohexanone system is given as follows. Step 1: Select any point P (Figure 17) according to the desired selectivity of intermediate product, B in the composition space. Step 2: Join point P (0.33, 0.33) with A (1, 0) to calculate the slope of line AP, and hence obtain the SRSC using eq 13, as shown in Figure 17. Step 3: Select any reactive stage composition X* on the curve of the SRSC as shown in Figure 18. For the present example let X* = [x*A x*B x*C ] = [0.98, 0.0146, 0.005]. Since the

Figure 19. Family of curves (FOC) for a range of reflux and reboil ratios representing LFSCs.

Figure 20. Feasible condition that satisfies our requirements. desired(k1)

2A ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ B + C undesired(k 2)

A + B ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ D + C

xB , P − xB ,0 xA , P − xA ,0

=

k1γA2xA*2 − k 2xA*γAxB*γB −2k1γA2xA*2 − k 2xA*γAxB*γB

(12)

(13)

Figure 21. (a) Identical column profiles in triangular diagram. (b) Column profiles along the length of column. The close overlap indicates that the design is feasible. 18534



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Table 2. Design Specifications of Complex Hybrid RD Column for Cyclohexanone System column configuration no. of components, NC volatility order, C > A > B > D no. of stages, N feed location, Nfl feed flow rate, F feed composition, Xf feed stage composition, X* side draw location, Sdl no. of reactive stages, Nr location of reactive stage, Nrl Damkohler number/catalyst loading reflux ratio, R reboil ratio, S side draw to feed ratio, SD end compositions after mixing the distillate, side draw and bottom streams

non-RD 4 water > cyclohexanone > 2-cyclohexylidenecyclohexanone > 2,6-dicyclohexylidenecyclohexanone 12 6th stage 1 (0.33 0.33 0.3367) (0.98, 0.0146, 0.005) 8th stage

72.5 46.7 0.215 (0.33 0.33 0.3367)

in the present case it is cyclohexanone (A). From Figure 16 it can be clearly seen that cyclohexanone forms a minimum boiling azeotrope with water due to which cyclohexanone is mainly present in the rectifying section. As a result, to adjust its composition through side draw, we need to consider the side draw location above the feed location (Sdl = 8th stage). Moreover, aldol (B) being much heavier than cyclohexanone (A), exits from the bottom along with other heavy boilers (D), and hence, its composition is adjusted through reboil ratio. On the other hand, water (C) is the most volatile component and hence its composition is adjusted through reflux ratio. Step 6: Draw the family of curves representing LFSCs obtained for a range of reflux and reboil ratios by choosing initially some arbitrary value of side draw to feed ratio (say SD = 0.2). Figure 19 shows three such families for a range of reflux (5-to-200) and reboil ratios (5-to-100) at three different values of SD. It can be clearly seen in Figure 19 that the reactive composition, X*, of interest lies in the vicinity of the curves obtained for SD = 0.2. Step 7: Next step is to take the range of side draw to feed ratio, near the value SD = 0.2 and narrow down the ranges of reflux and reboil ratios based on the results shown in Figure 19. The exact intersection of feed stage of non-RD column with the selected reactive stage composition, X*, is shown in Figure 20. The values of three operating parameters viz. SD, S, and R at this intersection are found to be 0.215, 46.7, and 72.5, respectively. The column profile for non-RD side draw column in 3D composition space is then plotted as shown in Figure 21. Step 8: Obtain the column profile for RD, with the feed as pure A and the feed stage as the reactive stage, using the same design and operating parameters as used for the non-RD case. The profiles coincide (Figure 21) to indicate that the design is feasible. Hence, the desired selectivity for the given complex reaction scheme is attainable through hybrid RD column with side draw design specifications given in Table 2. The conceptual design methodology proposed in this paper is used to design a hybrid RD column with side draw for the self-aldol condensation of cyclohexanone. Figure 22 shows that the results of the conceptual design algorithm are found to be in good agreement with those obtained by rigorous simulation using ASPEN PLUS simulator. It should be noted that the composition profiles shown in Figure 22 are obtained for the

Figure 22. Comparison between conceptual and rigorous (ASPEN based) design for intramolecular aldol condensation of cyclohexanone.

reaction scheme of interest is a series parallel reaction, X*, for aldol (B) is as small as possible so that the side reaction is suppressed. Moreover, since the presence of water (C) as a reaction product inhibits the reaction rate, a low concentration of water is also favorable on the reactive stage. Step 4: Find the composition of all the components in the hypothetical feed that is sent to the non-RD column (Figure 4b) by using the material balances given by eqs 14, 15, and 16. (xA ,0 − xA , P) + Da

( −2k1xA*2γA2 − k 2xA*γAxB*γB) =0 1 + k wxC*2γ 2

(14)

(k1xA*2γA2 − k 2xA*γAxB*γB) =0 1 + k wxC*2γ 2

(15)

(k1xA*2γA2 + k 2xA*γAxB*γB) =0 1 + k wxC*2γ 2

(16)

C

(xB ,0 − xB , P) + Da

C

(xC ,0 − xC , P) + Da

C

RD 4 water > cyclohexanone > 2-cyclohexylidenecyclohexanone > 2,6-dicyclohexylidenecyclohexanone 12 6th stage 1 (1, 0, 0) (0.98, 0.0146, 0.005) 8th stage 1 6th stage 429 72.5 46.7 0.215 (0.33 0.33 0.3367)

Step 5: Specify the number of stages, feed location, side draw location (say N = 12, Nfl = 6th stage, reboiler = 1st stage) and the operating parameters. Side draw location depends on the volatility of that component whose composition is required to be adjusted through side draw to obtain the desired selectivity; 18535



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achieve one of the reactive stage compositions that belongs to SRSC on the feed stage of non-RD with help of separation attributes. It should be noted that not all reactive compositions on the SRSC are attainable by varying the distillation attributes. Figure 24 shows that in spite of using the whole set of operating parameters we are not able to achieve the desired X* by using simple (Figure 24a) and complex (Figure 24b) columns, and hence, we need to select some other X* on the SRSC.

same design specifications of RD column given in Table 2. The quantitative difference in the composition profiles of conceptual design and rigorous design is mainly due to the fact that in the conceptual design, constant molar overflow assumption is used.

6. PRACTICALLY UNATTAINABLE POINTS IN THE COMPOSITION SPACE AND FEASIBLE REACTIVE STAGE COMPOSITIONS ON THE SRSC Figure 23 shows the variation of the SRSC with the selected point P (xAP, xBP) in ABD plane for a desired selectivity. The

7. CONCLUSIONS The work proves the potential of simple and complex hybrid reactive distillation columns to obtain the desired selectivity in case of single reactant multireaction schemes for the cases wherein, reactant is saddle. The design method for simple and complex hybrid RD columns developed here can be applied to mixture with any number of components and can be directly applicable to even multiazeotropic mixtures as well. The methodology developed here is more generalized as compared to our earlier work (Hasan et al.6), which was restricted to pseudo ternary mixture and to the cases where only one product undergoes further side reaction. The number of side draws required in this configuration depends on the number of components undergoing the reaction in the given scheme. Further, the methodology is also illustrated with the help of industrially relevant example of intramolecular aldol condensation of cyclohexanone to achieve the desired selectivity toward 2-cyclohexylidene cyclohexanone. The results obtained from the design procedure provided very good initialization for rigorous simulations. The applicability of the proposed algorithm is restricted to single reactant multireaction schemes involving multicomponent systems and to the cases wherein, maximum of three reactive compositions of reactants are present in the equation of SRSC. It requires further work to extend the methodology for multireactant multireaction schemes involving multicomponent systems leading to double feed RD configurations. Also, it would be interesting to investigate the presence of inerts in the feed stream by using the proposed algorithm.

Figure 23. Variation of the SRSC with the desired selectivity at the selected point P.

SRSC (eq 2) are plotted for the reaction scheme given by eq 1. The SRSC are plotted by including the constraints viz. (x*A > 0, xB* > 0, xC* > 0 and xB* > xC*). The last constraint is induced by material balance of component C given by eq 11. It is clear from Figure 23 that as one wants to achieve higher desired selectivities, the available space of potential reactive stage compositions contracts. Even if we are able to achieve the desired selectivity by selecting point Pn (0.05, 0.9), the design may not be feasible practically because of the requirement of high amount of catalyst loading. It is worth mentioning here that the required amount of catalyst is higher for lower concentrations of reactant A present on the reactive stage. Thus, the desired selectivity is attainable if we are able to

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APPENDIX A Reaction Scheme (Mahajan et al.29):

Figure 24. (a) Infeasible X* for example 1 and (b) infeasible X* for example 2. 18536



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(i) Cyclohexanone (2A) → 2-cyclohexylidenecyclohexanone (B) + water (C) r1 =

k1aA2 1 + K CaC2

where

KC = KC 0

and

Subscripts

A, B, C, D = components involved in reaction i = ith component ref = reference component

⎛ −E ⎞ k1 = k10 exp⎜ 1 ⎟ ⎝ RT ⎠

⎛ −HC ⎞ ⎟ exp⎜ ⎝ RT ⎠

Abbreviations (A.1)

(ii) 2-cyclohexylidenecyclohexanone (B) + cyclohexanone (A) → 2,6 dicyclohexylidenecyclohexanone (D) + water (C) r2 =

k 2aAaB 1+

and

■

KCaC2

where

⎛ −E ⎞ k 2 = k 20 exp⎜ 2 ⎟ ⎝ RT ⎠

⎛ −HC ⎞ ⎟ KC = KC 0 exp⎜ ⎝ RT ⎠

■

(A.2)

REFERENCES

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where aA, aB, and aC are activities of cycohexanone, aldol, and water, KC is adsorption coefficient for water, k1 and k2 are rate constants for reaction (mol/h·gm·cat), r1 and r2 are rates of reaction (mol/h).

ASSOCIATED CONTENT

S Supporting Information *

Design specifications of complex hybrid RD columns for example 2 and 3 in Tables S1 and S2, respectively. The kinetic and binary interaction parameters for the case study of selfaldol condensation of cyclohexanone in Tables S3 and S4, respectively. This material is available free of charge via the Internet at http://pubs.acs.org.

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BVM = boundary value method CSTR = continuous stirred tank reactor Da = Damkohler number FOC = family of curves LFSCs = locus of liquid feed stage compositions non-RD = nonreactive distillation column RD = reactive distillation column SRSC = surface of reactive stage compositions

AUTHOR INFORMATION

Corresponding Author

*Tel.: +91-22-2576 7246, 2578 2545. Fax: +91 22 2572 6895. E-mail: [email protected]. Present Address †

Motilal Nehru National Institute of Technology, Allahabad211004, India. Notes

The authors declare no competing financial interest.

■

NOTATION F = feed flow rate (mol/sec) k = rate constant N = total number of stages NC = number of components Nfl = feed stage location Nr = total number of reactive stages Nrl = reactive stage location rk = reaction rate for kth reaction, mol/(time × mass of catalyst) Wcat = mass of catalyst xi* = reactive stage composition of ith component Xf = feed composition X* = reactive stage composition R = reflux ratio S = reboil ratio Sdl = side-draw location SD = side-draw to feed ratio

Greek Letters

α = relative volatility 18537



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(18) Beneke, D.; Peters, M.; Glasser, D.; Hildebrandt, D. Understanding Distillation using Column Profile Maps, 1st ed.; John Wiley and Sons; New York, 2012; pp 157−205. (19) Thotla, S.; Agarwal, V.; Mahajani, S. M. Aldol condensation of acetone with reactive distillation using water as a selectivity enhancer. Ind. Eng. Chem. Res. 2007, 46, 8371−8379. (20) Talwalkar, S.; Mankar, S.; Katariya, A.; Aghalayam, P.; Ivanova, M.; Sundmacher, K.; Mahajani, S. Selectivity engineering with reactive distillation for dimerization of C4 olefins: Experimental and theoretical studies. Ind. Eng. Chem. Res. 2007, 46, 3024−3034. (21) Thotla, S.; Mahajani, S. M. Conceptual design of reactive distillation for selectivity improvement in multiple reactant systems. Chem. Eng. Res. Des. 2009a, 87, 61−82. (22) Thotla, S.; Mahajani, S. M. Reactive distillation with side draw. Chem. Eng. Proc. 2009b, 48, 927−937. (23) Hasabnis, A.; Mahajani, S. Entrainer-based reactive distillation for esterification of glycerol with acetic acid. Ind. Eng. Chem. Res. 2010, 49, 9058−9067. (24) Orjuela, A.; Kolah, A.; Hong, X.; Lira, C. T.; Miller, D. J. Diethyl succinate synthesis by reactive distillation. Sep. Purif. Technol. 2011, 88, 151−162. (25) Keller, T.; Dreisewerd, B.; Górak, A. Reactive distillation for multiple-reaction systems: Optimization study using an evolutionary algorithm. Chem. Proc. Eng. 2012, 34 (1), 17−38. (26) Gllnos, N. K.; Malone, M. F. Design of side stream distillation column. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 822−828. (27) Wasylkiewicz, S. K.; Kobylka, L. C.; Castillo, F. J. L. Optimal design of complex azeotropic distillation columns. Chem. Eng. J. 2000, 79, 219−227. (28) Rooks, R. E.; Julka, V.; Doherty, M. F.; Malone, M. F. Structure of distillation regions for multicomponent azeotropic mixtures. AIChE J. 1998, 44 (6), 1382−1391. (29) Mahajan, Y. S.; Kamath, R. S.; Kumbhar, P. S.; Mahajani, S. M. Self condensation of cyclohexanone over ion exchange resin catalysts: Kinetics and selectivity aspects. Ind. Eng. Chem. Res. 2008, 47, 25−33. (30) Mahajan, Y. S. Process development studies in reactive distillation. Ph.D. Thesis, IIT Bombay, India, 2007.

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Selectivity Engineering with Simple and Complex Hybrid Reactive

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