714
Ind. Eng. Chem. Res. 1999, 38, 714-722
A Novel Distillate Policy for Batch Reactive Distillation with Application to the Production of Butyl Acetate† Ganesh Venimadhavan,‡ Michael F. Malone, and Michael F. Doherty* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-3110
Considering the longstanding importance of batch distillation in chemical production, it is surprising that the utility of manipulating operating policies was not understood until the 1970s. This is partly due to the mathematical difficulty of finding the time-optimal policy. Perhaps the most elegant and effective treatment of this problem is found in the work of Mayur and Jackson (Chem. Eng. J. 1971, 2, 150-163). They used Pontryagin’s maximum principle to find the optimal reflux policy for the batch distillation of ideal multicomponent mixtures. In this paper, motivated by Mayur and Jackson’s classic treatment, we examine a novel distillate policy and a conventional column configuration for batch distillation with chemical reaction. This distillate policy leads to a new explicit reflux policy for the special class of equimolar reactions. For the particular case of butyl acetate production, it is shown that this leads to complete conversion of ingredients and high-purity products, which are unattainable by the traditional approach, in a single operation. Introduction Batch processes have always been used in the chemical industry, especially for development and for seasonal, uncertain, or low-capacity production. Batch reactors and batch distillations are very common. Their combination in reactive distillation is a process alternative that has the potential to lower process costs and reduce environmental emissions, advantages which have been demonstrated in continuous processing.2-6 Batch reactive distillation is often used for equilibrium-limited reactions, but systematic design methods for batch reactive distillation are scarce. Typically, a liquid-phase reaction takes place in the reboiler, and a product is removed using a batch rectifier placed above the still. This configuration has the potential for essentially complete conversion of the limiting reactant. For azeotropic mixtures, however, it may not be possible to reach complete conversion due to the presence of low-boiling azeotropes containing one or more reactants. In such cases, novel operating strategies and/or equipment configurations may be advantageous. This is the case for butyl acetate production, which we use as an example in this work. Butyl acetate is an important solvent in the chemical industry. It is used primarily in coatings, where its solvent power and its low relative volatility make it useful for adjustment of evaporation rate and viscosity. It is particularly useful as a solvent for acrylic polymers, vinyl resins, etc. It is also used as a reaction medium for adhesives, as a solvent for leather dressings, and a process solvent in various applications and in cosmetic formulations. The equilibrium constant favors the pro† This paper is dedicated to Professor Roy Jackson in honor of his many outstanding contributions to the mathematical analysis of chemical engineering systems. * To whom correspondence should be addressed at Department of Chemical Engineering, 154B Goessmann Laboratory, 686 North Pleasant Street, Amherst, MA 01003-3110. Telephone: (413) 577-0132. Fax: (413) 545-1133. E-mail: mdoherty@ ecs.umass.edu. ‡ Present address: UOP LLC, P.O. Box 5017, Des Plains, IL 60017-5017.
Figure 1. Schematic of a batch reactive distillation process.
duction of butyl acetate, but acceptable product purity requires further purification. Earlier work on batch reactive distillation focused on developing detailed models, e.g., Cuille and Reklaitis7 or on optimizing operations, e.g., Mayur and Jackson,1 Egly et al.8 and Quintero-Marmol and Luyben.9 We are interested in developing a simplified model to capture the essence of the process and to provide insight for exploring process alternatives. With such a model, we show how a novel operating strategy can lead to a simplified process with higher productivity than that of a conventional strategy. Simplified Batch Reactive Distillation Model The schematic of a batch reactive distillation system is given in Figure 1. We develop a simplified model with the following assumptions:
10.1021/ie9804273 CCC: $18.00 © 1999 American Chemical Society Published on Web 02/04/1999
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 715
(1) The liquid-phase reaction takes place in the still alone. (2) The column provides N theoretical stages which are in a quasi-steady-state. (3) The vapor and liquid flow rates are constant from stage to stage (constant molar overflow (CMO)). (4) A total condenser produces a saturated liquid product. (5) The operating reflux is large and can be approximated as total reflux for the purpose of calculating column profiles. (6) The holdup on the stages and in the condenser is negligible compared to that in the still. We consider a single reaction of the form c
νiAi ) 0 ∑ i)1
(1)
where νi is the stoichiometric coefficient of component i in the reaction, Ai indicates component i, and c is the total number of components. Extending the model to systems with multiple reactions is straightforward. Mass Balances Material balances for the column shown in Figure 1 give
dHS ) - D + νTHSr dt
(2)
and
dHSxS,i ) -DxD,i + νiHSr dt
i ) 1, ..., c - 1
(3)
where HS is the molar liquid holdup in the still, D is the distillate flow rate, xS,i is the liquid-phase mole fraction of component i in the still, xD,i is the mole fraction of component i in the distillate, νT is the sum c νi), and r is of the stoichiometric coefficients (νT ) ∑i)1 the reaction rate per mole of mixture and has units of inverse time. Using a dimensionless “warped” time defined by
dξ )
D dt HS
(4)
we can rearrange eqs 2 and 3 to find
HS dxS,i ) (xS,i - xD,i) + (ν - νTxS,i)r dξ D i
HS,0/D0 1/kf,ref
dxS,i r ) (xS,i - xD,i) + Da(νi - νTxS,i) dξ kf,ref i ) 1, ..., c - 1
(5)
(6)
where HS,0 is the initial molar holdup in the still, D0 is the initial distillate flow rate, and kf,ref is the forward reaction rate constant evaluated at a reference temperature, Tref. Equation 5 can be rewritten as
HS D0 dxS,i r ) (xS,i - xD,i) + Da (ν - νTxS,i) (7) dξ HS,0 D i kf,ref
(8)
This distillate policy is intended to keep the instantaneous Damko¨hler number approximately constant. That is, the rate of product removal is kept roughly comparable to the rate of production. For a discussion of a similar policy for simple reactive distillation, see Venimadhavan et al.10 Equation 8 describes the rate of change of the liquid mole fractions in the still. The pseudo-steady-state material balances for the column are
yn-1,i )
R 1 x + x R + 1 n,i R + 1 D,i
(n ) 1, ..., N; i ) 1, ..., c)
(9)
where y0 is the composition of vapor in phase equilibrium with xS. The total condenser leads to the relationship
xD,i ) yN,i
(10)
For mixtures that phase separate on condensation, eq 10 needs to be modified according to the reflux policy selected (i.e., we can reflux either one of the phases alone or a mixture of both). The vapor phase in equilibrium with the liquid in the still and on each stage can be calculated using a phase equilibrium model:
yn,i ) f(xn,i,P)
(11)
For vapor-liquid-liquid equilibrium, we use a rigorous global stability test (Wasylkiewicz et al.11) at each state point in the still and on every stage, at every time step. Degrees of Freedom Because we neglect the holdup on the stages and in the condenser, the initial composition in the still corresponds to the feed composition
xS ) xS,0
The Damko¨hler number, Da, is the ratio of a characteristic residence time to a characteristic reaction time and is defined as
Da )
If we choose a novel decreasing distillate rate policy such that D/D0 ) HS/HS,0, eq 7 reduces to
(12)
To solve eq 8 with the initial condition (12), we need to relate the distillate composition to the still composition at each instant of time. Once the column pressure is specified, such a relation corresponds to the solution of a set of algebraic equations made up of the operating relationships in eq 9, the total condenser in eq 10, and the phase equilibrium relationships in eq 11. There are N(c - 1) independent equations from eq 9, c - 1 from eq 10, and (N + 1)(c - 1) from eq 11; the total number of equations is (2N + 2)(c - 1). There are c - 1 variables for yS, c - 1 variables for xD, 2N(c - 1) variables for yi and xi, and one each for the number of stages, the reflux ratio, and Da. The total number of variables is (2N + 2)(c - 1) + 3, and there are (2N + 2)(c - 1) equations, resulting in 3 degrees of freedom. Thus, once values are chosen for three of the unknown variables, eq 8 can be integrated. In this paper, we study the performance
716
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
Table 1. Thermodynamic Data for the Butyl Acetate System Antoine Parameters and the Area and Volume Parameters for the UNIQUAC Equation component water (1) butanol (2) acetic acid (3) butyl acetate (4)
A
B
C
r
q
23.2256 21.9783 22.1001 21.07637
-3835.18 -3080.66 -3654.62 -3151.09
-45.343 -96.150 -45.392 -69.150
0.92 3.4543 2.2024 4.8274
1.4 3.052 2.072 4.196
Binary Interaction Parameters for the UNIQUAC Equation (cal/mol)a U11 ) 0.0 U12 ) 581.1471 (a) U13 ) 527.9269 (b) U14 ) 461.4747 (c)
U21 ) 68.0083 (a) U22 ) 0.0 U23 ) 148.2833 (d) U24 ) 82.5336 (e)
U31 ) -343.593 (b) U32 ) -131.7686 (d) U33 ) 0.0 U34 ) -298.4344 (f)
U41 ) 685.71 (c) U42 ) 24.6386 (e) U43 ) 712.2349 (f) U44 ) 0.0
Antoine Equation ln(Psat) ) A +
B , T+C
Psat [Pa], T [K]
UNIQUAC Equationb ln γi ) ln γCi + ln γRi ln γCi ) ln
φi
[
xi
+
z 2
qi ln
φi
+ li -
m
ln γRi ) qi 1 - ln(
li )
ϑi
∑
φi xi
∑x l
j j
j
m
ϑj τji) -
j)1
∑ j)1
ϑjτij m
∑ϑ τ
]
k kj
k)1
z (r - qi) - (ri - 1) 2 i
z ) 10
a All interaction parameters, U , are taken from the Vapor-Liquid Equilibrium Data Collection of the DECHEMA Chemistry Data ij Series edited by J. Gmehling and U. Onken. The volume and page numbers are as follows: (a) Vol. 1, Part 1b, p 254; (b) Vol. 1, Part 1, p 106; (c) Vol. 1, Part 1b, p 338; (d) Vol. 1, Part 2d, p 157; (e) Vol. 1, Part 2b, p 197; (f) Vol. 1, Part 5, p 147. b z is the coordination number; τji ) exp[- (uji - uii)/RT], τii ) τjj ) 1; φi is the dimensionless volume fraction of component i defined as rixi/∑jrjxj; and ϑi is the dimensionless area fraction of component i defined as qixi/∑jqjxj.
aspects of the system by specifying the number of stages, N, the reflux ratio, R, and the Damko¨hler number, Da. The simplified model considers the case R ) ∞, in which case eq 9 reduces to yn-1 ) xn. Reaction Kinetics We study the esterification of acetic acid with butanol to produce butyl acetate.
HOAc + n-BuOH S n-BuOAc + H2O
(13)
Kinetic data for a sulfuric acid catalyst were obtained from Leyes and Othmer.12 They report concentration vs time data at various temperatures and catalyst concentrations. They also gave values for the apparent (concentration-based) equilibrium constant at different temperatures (this quantity is also a function of composition for nonideal liquid mixtures). Using a UNIQUAC model to estimate the activity coefficients (see Table 1 for the thermodynamic data), we calculated the thermodynamic equilibrium constant Keq at each temperature. We found that the equilibrium constant did not vary strongly with temperature (it varied from 15.1 to 11.3 over a temperature range of 100-120 °C). Because there is a lot of scatter in the values of Keq between the values of 11.3 e Keq e 15.1 (Venimadhavan13), we used a mean value of 12.57 for all further calculations. This corresponds to a Gibbs free energy of reaction ∆G0 ) -1.87 kcal/ mol, which is reasonable for esterification reactions. The kinetic data were regressed to get the forward reaction
rate constant for the activity-based homogeneous rate expression
(
r ) kf aHOAcaBuOH -
)
aBuOAcaH2O Keq
(14)
where r is the reaction rate per mole of mixture, kf is the forward reaction rate constant, and ai are the liquidphase activities. Both r and kf have units of reciprocal hours. Figure 2 shows a typical fit of the experimental data and the prediction of eq 14. Figure 3 shows the logarithm of the forward reaction rate constant as a function of reciprocal temperature. A least-squares fit of the points in Figure 3 gives the following Arrhenius expression:
(
kf ) exp 22.17 -
6873.9 T
)
(15)
where kf is the forward reaction rate constant with units of reciprocal hours and T is in kelvin. The activation energy based on this rate expression is 13.66 kcal/mol. Vapor-Liquid-Liquid Equilibrium In the reaction mixture, there are three minimumboiling binary azeotropes (butanol and butyl acetate, water and butanol, water and butyl acetate) and one ternary azeotrope (water, butanol, and butyl acetate). While the azeotrope between butanol and butyl acetate
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 717 Table 2. Mole Fractions of the Two Heterogeneous Azeotropes Containing Water and Butyl Acetate component
overall composition
aqueous phase
organic phase
water BuOH BuOAc
Ternary Azeotrope 0.712 0.995 0.085 0.004 0.203 0.001
0.232 0.206 0.562
water BuOAc
Binary Azeotrope 0.7228 0.9988 0.2772 0.0012
0.1694 0.8309
Table 3. Boiling Points and Stabilities of All of the Pure Components and Azeotropes in a Ternary Mixture of Water, Butanol, and Butyl Acetate at 1 atm Pressure
Figure 2. Comparison of the model prediction vs experimental data from Leyes and Othmer12 for butyl acetate kinetics; data from experimental run O (T ) 110 °C, catalyst concentration ) 0.0322 wt % H2SO4).
Figure 3. Forward reaction rate constant vs reciprocal temperature for the butyl acetate reaction.
is homogeneous, the others are heterogeneous. There is some uncertainty about the relative boiling temperature of the two lightest azeotropes. Some sources report that the lightest boiler is the heterogeneous ternary azeotrope between water, butanol, and butyl acetate (McKetta14), while others report that the heterogeneous binary azeotrope between water and butyl acetate is the lightest (Karpilovskiy et al.15). Experimental values of the normal boiling points of these azeotropes vary over an interval of ∼2 °C and overlap (pp 1194 and 1693 in Gmehling et al.16). The boiling point of the ternary azeotrope ranges from 89.40 to 90.60 °C, while the boiling point of the water-butyl acetate azeotrope ranges from 90.20 to 91.04 °C. It is critical to know which is actually the lightest boiler because even though
pure components and azeotropes
normal boiling temperature (°C)
stabilitya
water-butanol-butyl acetate water-butyl acetate water-BuOH water butanol-butyl acetate butanol butyl acetate
89.40-90.60 90.20-91.04 92.83 100.0 116.94 117.74 125.95
UN or SA? SA or UN? SA SN SA SN SN
a UN indicates unstable node, SN indicates stable node, and SA indicates saddle.
their boiling points are quite close their compositions are not (see Table 2). If the binary azeotrope is the lightest boiler (which comes off as the overhead vapor to the condenser), then the design would be quite easy. Because this is an azeotrope between the reaction products, its removal allows for complete conversion of the limiting reactant in the still. In addition, the overhead product separates in the condenser/decanter into two liquid phases: an aqueous phase of nearly pure water and an organic phase which contains ∼83 mol % butyl acetate and ∼17 mol % water. The water phase is removed from the process, and butyl acetate is purified in a stripper (the overhead vapor from the stripper can be recycled to the decanter). On the other hand, if the ternary azeotrope is the lightest boiler, the second liquid phase in the condenser/decanter has a composition of ∼56 mol % butyl acetate, ∼23 mol % water, and ∼20 mol % butanol. In this case, the design would be very different. Because there is no acetic acid in either of these azeotropes, our uncertainty is confined to a ternary mixture containing water, butanol, and butyl acetate. For ternary systems, Doherty and Perkins17 and Doherty18 developed rules for the structure of residue curve maps based on topology. The global result is expressed in terms of a relationship between the different types of singular points in the system:
2N3 - 2S3 + N2 - S2 + N1 ) 2
(16)
where N denotes a node (stable or unstable), S denotes a saddle, and the subscripts represent the number of components in that singular point (i.e., 1 indicates a pure component, 2 indicates a binary azeotrope, and 3 indicates a ternary azeotrope). In addition to the two azeotropes in question, there are five other singular points in this ternary mixture. These are the three pure components (water, butanol, and butyl acetate; all stable nodes) and the two binary azeotropes (one between water and butanol and the other between butanol and butyl acetate; both of which are saddles). (See Table 3 for the boiling points and stabilities.) The stabilities of
718
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
Figure 4. Nonreactive residue curve map for a mixture of water, butanol, and butyl acetate. The diagram also shows the liquidliquid-phase boundary.
these five singular points can be resolved by rules given by Doherty.18 The only scenario that satisfies eq 16 demands that the ternary azeotrope containing water, butanol, and butyl acetate is the unstable node while the binary azeotrope between water and butyl acetate is a saddle. Therefore, we conclude that the ternary azeotrope is the lightest boiler and the overhead vapor entering the condenser/decanter has a composition close to this azeotrope. The phase equilibrium was modeled using the UNIQUAC equation (Table 1) with parameters from data sets that are consistent with the above result. Figure 4 is the residue curve map for a mixture of water, butanol, and butyl acetate calculated by the model in Table 1.
Figure 5. Batch reactive distillation of butyl acetate at infinite reflux and an aqueous reflux policy, N ) 7, and an initial molar ratio of BuOH:HOAc ) 1:1. The composition of HOAc in the distillate is not shown because it is nearly zero.
Column Configuration The overhead vapor condenses into a water-rich phase and an organic-rich phase that contains ∼56 mol % butyl acetate, the rest being a mixture of water and butanol. Now we need to pick the phase that we will remove as distillate. The amount of that phase removed as distillate and the amount that is refluxed to the column is determined by the reflux ratio. Intuitively, we would like to remove the main product as the distillate. This implies a configuration that removes the organic phase as the distillate and returns the aqueous phase to the column as reflux. Figure 5 shows the model results for this configuration with Da ) 1, N ) 7, and an initial molar ratio of butanol to acetic acid of 1:1. These results show that this distillate policy is poor. First, the composition of the desired product in the distillate is never greater than ∼56 mol %. Therefore, we need to purify the product further and recover butanol for recycle. Second, we are returning a stream rich in the unwanted product (water) back to the column as reflux. The removal of one of the reactants (butanol) in the distillate and the buildup of water in the still (Figure 5a) will lead to an increase in the rate of backreaction, leading to an increase in the overall batch time.
A second and more common strategy is to remove the aqueous stream as distillate and return the organic phase with the desired product back to the column as reflux, e.g., Keyes,19 Leyes and Othmer,12 and Zhicai et al.20 Figure 6 shows the still and distillate compositions for this configuration with Da ) 1, N ) 7, and an initial molar ratio of 1:1 butanol to acetic acid. The still gets progressively richer in butyl acetate while the distillate consists of nearly pure water. The advantages of this distillate policy are (1) continuous removal of a nearly pure (unwanted) product from the system and (2) a higher purity of the desired product at the end of the run. The end of the reaction in the still can be detected from a sharp decrease in the water concentration in the distillate. At this point, butyl acetate can be removed as the distillate to separate it from the trace amounts of the other components in the system. Figure 7 shows the still and distillate compositions for this second phase of the operation, which is a nonreactive purification step (note that the warped time has been reset to zero in the figures). At the beginning of this step, a mixture of butanol, acetic acid, and butyl acetate is produced as a distillate. After the butanol and acetic acid have been
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 719
Figure 6. Batch reactive distillation of butyl acetate at infinite reflux and an organic reflux policy, N ) 7, and an initial molar ratio of BuOH:HOAc ) 1:1. The compositions of BuOAC and HOAc in the distillate are not shown as they fall rapidly to values below the composition of BuOH.
distilled, there is a pure butyl acetate cut. The intermediate “slop” cut is typically collected and recycled. A difficulty is that there is a long tail of contaminated product (Figure 7b). One of the reasons for this is that the separation of acetic acid and butyl acetate is very difficult because of a tangent pinch between those components in the vicinity of pure butyl acetate. There are also very stringent purity requirements on butyl acetate (e.g., less than 50 ppm acetic acid). This means that a significant acetic acid concentration in the still at the end of the reaction will lead to unacceptable product purity. One solution is to charge the still with a small excess of butanol to compensate for the slightly higher loss in the distillate. Acetic acid is now the limiting reactant and is eliminated. The final mixture in the still consists only of butyl acetate and a small amount of butanol. Figure 8 shows the still and distillate compositions for Da ) 1, N ) 7, and an initial charge that contains 49 mol % acetic acid and 51 mol % butanol. At the end of the reaction, the still has ∼95 mol % butyl acetate, 5 mol % butanol, and only trace amounts of the other components. Butanol and butyl acetate form a binary azeotrope with a composition of ∼79 mol % butanol and 21 mol %
Figure 7. Purification of the butyl acetate in the still at an infinite reflux, and N ) 7 for the case in Figure 6. The composition of water in the distillate is not shown because it is nearly zero.
butyl acetate. Once the reaction reaches completion, the water composition in the distillate drops sharply and the distillate composition reaches a composition close to the azeotrope until all of the butanol in the system is removed. Pure butyl acetate then starts coming off the top the column (Figure 9b). The intermediate cut with the azeotropic composition may be recycled to a fresh batch. It can be seen that the amount of sloppy cut under these conditions is much less than that in Figure 7b. To study the effect of the number of stages, we increased the number of stages in the column to 20. The results of this simulation (Venimadhavan13) show no qualitative difference from Figure 6. The only difference is that, because a larger number of stages improves the separation, the cuts are slightly sharper. A More Rigorous Model The major advantage of a simplified model is that it gives a quick estimate of the behavior of the system. To access the accuracy of the simplified model, we developed a more rigorous model in which we relaxed some of the simplifying assumptions. These included the infinite reflux and the quasi-steady-state assumptions. When these assumptions are removed, the system is
720
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
Figure 8. Batch reactive distillation of butyl acetate at infinite reflux and an organic reflux policy, N ) 7, and an initial molar ratio of BuOH:HOAc ) 51:49. The compositions of HOAc and BuOAc in the distillate are not shown because they are nearly zero.
modeled by a set of (N + 1)(c - 1) differential equations (c-1 equations for the still and c - 1 equations for each of the N stages). Without the quasi-steady-state assumption, a steady-state material balance cannot be written for the envelope in Figure 1 and, hence, the still equation is modified to
dHSxS,i ) -VyS,i + Lx1,i + νiHSr dt
(17)
where yS,i is the vapor phase mole fraction of component i leaving the still, x1,i is the liquid-phase mole fraction of component i on stage 1, V is the vapor flow rate, and L is the liquid flow rate. With the introduction of the Damko¨hler number and with use of the decreasing distillate rate policy D/D0 ) (HS/HS,0), eq 17 can be reduced to a form similar to eq 8.
dxS,i ) (R + 1)(xS,i - yS,i) + R(x1,i - xS,i) + dξ r Da(νi - νTxS,i) i ) 1, ..., c - 1 (18) kf,ref In this equation, R represents the reflux ratio, L/D.
Figure 9. Purification of the butyl acetate in the still at infinite reflux and N ) 7, beginning with a feed composition produced as the still composition at the end of the distillation shown in Figure 8.
For any stage n, if we assume that the holdup (H) on the stage is a constant (but not negligible), material balance yields (stage numbering increases up the column)
H
dxj,i ) L(xj+1,i - xj,i) + V(yj-1,i - yj,i) dt i ) 1, ..., c - 1
(19)
This equation is rearranged to give
dxj,i HS ) [R(xj+1,i - xj,i) + (R + 1)(yj-1,i - yj,i)] dξ H i ) 1, ..., c - 1
(20)
The condenser balance (eq 10) remains the same as that for the simplified model. This formulation introduces two new variables, the reflux ratio, R, and the ratio of the holdup in the still to the holdup on a stage. For our calculations, we set R ) 10 and the holdup in the still to be 50 times the holdup on a stage (in other words, around 12% of the total system holdup is on the stages). The number of stages N was set to seven as before, and we removed the aqueous phase as distillate. Figure 10 gives the still
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 721
ξ)
( )
D0 t HS,0
(21)
Therefore,
HS(t) ) HS,0e-(D0/HS,0)t
(22)
D(t) ) D0e-(D0/HS,0)t
(23)
The value of D0 is set by the initial and final sizes of the batch HS,0 and HS,F, respectively, and a choice of the total time for distillation, tbatch, according to D0 ) (HS,0/tbatch) ln(HS,0/HF,0). Normally, the vapor rate is maintained at a constant value near the maximum for flooding. In this case, a material balance for the condenser leads to
V ) (r(t) + 1)D(t)
(24)
Substituting for D(t) and rearranging give the explicit reflux policy
r(t) ) (r0 + 1)e -(D0/HS,0)t - 1
(25)
where r0 is the initial reflux ratio. The value of r0 is set by the vapor rate (equipment) and D0 according to r0 ) V/D0 - 1. This policy suggests that occasional measurements of the still holdup and comparison to the distillate flow can be used to update the distillate and reflux rates to maintain D/H approximately constant at its set point. Conclusions
and distillate compositions as a function of the dimensionless time with results similar to Figure 6. The main difference is that the response of the rigorous model is a little slower because of the stage dynamics. This gives us confidence that we can use the simplified model to get a good understanding of the system behavior. This is desirable because the more detailed calculations are extremely slow compared to the simplified model. This is due to the rigorous phase stability test followed by vapor-liquid equilibrium or vaporliquid-liquid equilibrium calculations for the still, and each stage and a liquid-liquid flash calculation in the condenser for each time step. A typical run time for the simplified model is on the order of 2-3 h on a DEC 3000 AXP while that for the more detailed model is ∼2 weeks. Although the simplified model and the detailed calculation at large reflux agree well, it is also useful to have an explicit policy for the reflux to implement the results.
We have developed a simplified model for batch reactive distillation and used it to study alternative operating strategies for the production of butyl acetate. In this mixture, there is some uncertainty in the literature about the identity of the light boiler. Using a relationship based on topology, we have proved conclusively that the heterogeneous ternary azeotrope between water, butanol, and butyl acetate is the lightest boiler and hence the composition of the overhead vapor must be close to this azeotrope. The azeotrope phase-separates on condensation into an aqueous phase which is predominantly water (99.5 mol % water) and an organic phase which is a mixture of water, butanol, and butyl acetate. We also describe a novel operating policy in which the distillate flow rate is decreased in proportion to the still holdup. We have studied a column configuration in which the aqueous phase is removed as distillate and the organic phase is returned to the column as reflux. This constantly removes one of the products from the reaction, thus forcing the reaction forward, and this accumulates the desired product (butyl acetate) in the still. Once the reaction is complete, butyl acetate is collected as a high-purity distillate. An intermediate slop cut, which is a mixture of butanol and butyl acetate (with water as a trace component and an immeasurable amount of acetic acid), is first collected and recycled to a fresh batch. Thus, we can produce high-purity butyl acetate without any additional separation steps.
Distillate and Reflux Policies
Acknowledgment
For the special case of νT ) 0, the decreasing distillate rate policy, D/D0 ) HS/HS,0, leads to an explicit relationship between ξ and t (see eq 2) as follows:
We are grateful to the sponsors of the Process Design and Control Center, University of Massachusetts, Amherst, and especially for helpful comments from BASF,
Figure 10. Batch reactive distillation of butyl acetate at a reflux ratio R ) 10, Hstill/Hstage ) 50, an organic reflux policy, N ) 7, and an initial molar ratio of BuOH:HOAc ) 1:1.
722
Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
AG, and Eastman Chemical Co. Financial support was provided by the NSF (Grant CTS-9613489). Notation ai ) liquid-phase activity of component i Ai ) component i D ) distillate flow rate (mol/time) D0 ) initial distillate flow rate (mol/time) Da ) Damko¨hler number, defined as HS,0kf,ref/D0 ∆G0 ) Gibbs free energy of reaction (kcal/mol) H ) liquid holdup on a stage (mol) HS ) liquid holdup in the still (mol) HS,0 ) initial liquid holdup in the still (mol) Keq ) reaction equilibrium constant kf ) forward reaction rate constant (1/time) kf,ref ) forward reaction rate constant at reference temperature (1/time) L ) liquid flow rate (mol/time) N ) number of stages in the column r ) reaction rate (1/time) R ) reflux ratio t ) clock time V ) vapor flow rate (mol/time) xD,i ) liquid-phase mole fraction of component i in the distillate xn,i ) liquid-phase mole fraction of component i on stage n xS ) vector of mole fractions in the still xS,0 ) vector of initial mole fractions in the still xS,i ) liquid mole fraction of component i in the still yn,i ) vapor phase mole fraction of component i on stage n Greek Symbols νi ) stoichiometric coefficient of component i νT ) sum of the stoichiometric coefficients ξ ) “warped” time variable Subscripts 0 ) initial D ) distillate i ) component i 1, n - 1, n, N ) stage numbers S ) still
Literature Cited (1) Mayur, D. N.; Jackson, R. Time-Optimal Problems in Batch Distillation for Multicomponent Mixtures and for Columns with Holdup. Chem. Eng. J. 1971, 2, 150-163. (2) Agreda, V. H.; Partin, L. R. Reactive Distillation Process for the Production of Methyl Acetate. U.S. Patent 4,435,595, Mar 6, 1984.
(3) Agreda, V. H.; Partin, L. R.; Heise, W. H. High Purity Methyl Acetate via Reactive Distillation. Chem. Eng. Prog. 1990, 86 (2), 40. (4) Grosser, J. H.; Doherty, M. F.; Malone, M. F. Modeling of Reactive Distillation Systems. Ind. Eng. Chem. Res. 1987, 26, 983. (5) Smith, L. A. Catalytic Distillation Process. U.S. Patent 4,307,254, Dec 22, 1981. (6) Smith, L. A. Method for the preparation of methyl tertiary butyl ether. U.S. Patent 4,978,807, Dec 18, 1990. (7) Cuille, P. E.; Reklaitis, G. V. Dynamic Simulation of Multicomponent Batch Rectification with Chemical Reaction. Comput. Chem. Eng. 1986, 10 (4), 389-398. (8) Egly, H.; Ruby, V.; Seid, B. Optimum Design and Operation of Batch Rectification Accompanied by Chemical Reaction. Comput. Chem. Eng. 1979, 3, 169-174. (9) Quintero-Marmol, E.; Luyben, W. L. Inferential ModelBased Control of Multicomponent Batch Distillation. Chem. Eng. Sci. 1992, 47 (4), 887-898. (10) Venimadhavan, G.; Doherty, M. F.; Malone, M. F. Effects of Kinetics on Residue Curve Maps for Reactive Distillation. AIChE J. 1994, 11, 1814-1824. Correction: AIChE J. 1995, 12, 2613. (11) Wasylkiewicz, S. K.; Sridhar, L. N.; Doherty, M. F.; Malone, M. F. Global Stability Analysis and Calculation of Liquid-Liquid Equilibrium in Multicomponent Mixtures. Ind. Eng. Chem. Res. 1996, 35, 1395-1408. (12) Leyes, C. E.; Othmer, D. F. Esterification of Butanol and Acetic Acid. Ind. Eng. Chem. 1945, 37, 968-977. (13) Venimadhavan, G. Effects of Kinetics on Reactive Distillation. Ph.D. Dissertation, University of Massachusetts, Amherst, MA, 1998. (14) McKetta, J. J., Ed., Encyclopedia of Chemical Processing and Design; Marcel Dekker: New York, 1983, Vol. 19, pp 381402. (15) Karpilovskiy, O. L.; Pisarenko, Yu. A.; Serafimov, L. A. Multiple Solutions in Single-Product Reactive Distillation. Distill. Adsorpt. ‘97 1997, 2, 685-694. (16) Gmehling, J.; Menke, J.; Krafczyk, J.; Fischer, K. Azeotropic Data. Parts I & II; VCH: Weinheim, Germany, 1997. (17) Doherty, M. F.; Perkins, J. D. On Dynamics of Distillation Processes. III. The Topological Structure of Ternary Residue Curve Maps. Chem. Eng. Sci. 1979, 34, 1401-1414. (18) Doherty, M. F. The Presynthesis Problem for Homogeneous Azeotropic Distillation has a Unique Explicit Solution. Chem. Eng. Sci. 1985, 40, 1885-1889. (19) Keyes, D. B. Esterification Processes and Equipment. Ind. Eng. Chem. 1932, 24, 1096-1103. (20) Zhicai, Y.; Xianbao, C.; Jing, G. Esterification-Distillation of Butanol and Acetic Acid. Chem. Eng. Sci. 1998, 53, 2081-2088.
Received for review July 3, 1998 Revised manuscript received November 5, 1998 Accepted November 5, 1998 IE9804273
