5548
Ind. Eng. Chem. Res. 2006, 45, 5548-5560
Semicontinuous Distillation with Chemical Reaction in a Middle Vessel Thomas A. Adams II and Warren D. Seider* Department of Chemical and Biomolecular Engineering, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6393
Semicontinuous distillation with chemical reaction in a middle vessel (SDRMV) has been studied as a feasible means of combining separation and reaction unit operations using forced cyclic methods. A chemical process producing 2,4-dimethyl-1,3-dioxolane (24DMD) and water from the exothermic, reversible reaction of acetaldehyde and propylene glycol has been designed using the SDRMV method. Processes producing equivalent amounts and purities of 24DMD using traditional batch and continuous methods have also been designed. Rigorous simulations and detailed economic analyses over a range of production rates for the three processes show that SDRMV is the most economically optimal method for a broad range of intermediate production rates. The great potential of forced cyclic methods, using continuous distillation with a fed-batch reactor, a holding tank, and a supervisory control system, for the production of fine and specialty chemicals is demonstrated. Introduction The demand for specialty chemicals is rising, particularly in East Asian countries.1,2 This increased demand is pushing production rates for these chemicals into intermediate capacities, up from the low capacities typically obtained by batch distillation. Since batch systems are designed to operate with relatively low production rates, they are not economically suitable for intermediate and higher rates. Conversely, continuous production systems are most efficient at high production rates and lose their economy-of-scale benefits as those rates decrease. Therefore, a novel method called semicontinuous distillation (SD) has recently been developed to provide a costeffective means of separating chemicals at intermediate production rates. SD is based on a forced cyclic technique using a distillation column interacting with one or more middle vessels. Using this technique, SD is capable of separating threecomponent mixtures using only one column.3-6 Additionally, semicontinuous methods have been developed for azeotropic distillation7 and extractive distillation.8 Semicontinuous distillation with chemical reaction in a middle vessel (SDRMV) has recently been introduced by Adams and Seider9 as a novel, feasible design strategy for performing separations and reactions together in a semicontinuous manner. This process builds upon the forced cyclic principles of SD and tightly integrates the reaction step with the distillation process as in reactive distillation (RD). The controlled, periodic interaction of a reaction in an auxiliary vessel with distillation allows multipurpose usage of the column during alternating phases of the cyclic campaign. This is accomplished without the startup, shutdown, or cleaning stages in batch processes, saving both time and energy. Additionally, the semicontinuous method requires fewer columns when compared to continuous systems and operates at lower production rates that are often less profitable in continuous processes. Thus, SDRMV can be the preferred choice for operations at intermediate production rates, having its greatest potential in the fine and specialty chemical industries. While conventional RD has been shown in recent years to be a cost-effective way of integrating reactions and separations, * To whom correspondence should be addressed. E-mail: seider@ seas.upenn.edu.
it is not suitable for all systems. Loading catalyst on the trays may require many trays to have large liquid holdups to complete the reaction, and it also limits the temperature and kinetics to the thermodynamic equilibrium conditions of the column. Shoenmakers and Buehler10 proposed performing the reaction in a series of tightly integrated reaction vessels outside of the column. Later, Kaymak and Luyben11 showed that performing the reaction in integrated side vessels is economically preferable to regular RD for certain exothermic A + B h C + D reactions. Consequently, a reaction of this type has been chosen for use in a case study of SDRMV. Case Study A reaction system involves the following exothermic, reversible reaction:
It is used in a case study to compare the economics of the three design strategies (continuous, semicontinuous, and batch). The two products form a low-boiling azeotrope (83 °C at 1 bar), with the products and azeotrope having intermediate boiling points. The two products are also close boilers, with normal boiling points of 93 and 100 °C for 2,4-dimethyl-1,3-dioxolane (24DMD) and water, respectively. The normal boiling points of acetaldehyde (A) and propylene glycol (P) are 21 and 181 °C, respectively. As shown in Figure 1, a three-component azeotrope between acetaldehyde, water, and 24DMD is formed at pressures above 2.1 bar. This sets an upper bound on the pressure used in the separations process. The kinetic rate equation of Broekhuis12 was used for simulation purposes, equilibrium data were taken from the work of Dhale,13 and UNIQUAC constants describing the VLLE behavior were taken from the work of Chopade et al.14 Chopade et al. showed that two liquid phases form when 24DMD and water are subcooled. However, there is only one liquid phase at temperatures near or above the bubble point of the mixtures at pressures from 1.0 to 1.8 bar, and consequently, only one
10.1021/ie051139r CCC: $33.50 © 2006 American Chemical Society Published on Web 03/10/2006
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5549
Figure 1. UNIQUAC-predicted residue curves for the acetaldehyde, water, and 24DMD system at two pressures. The azeotrope between 24DMD and water moves into the three-component region at pressures above 2.1 bar. The presence of propylene glycol does not affect the nature of the azeotrope.
Figure 2. Continuous process. A ) acetaldehyde, P ) propylene glycol, D ) 24DMD, and W ) water.
liquid phase appears in our studies. Also, note that the rate equation as described by Broekhuis is missing a term, which has been included herein:
(
)
C DC W dND ) WKcw0e-E/RT CACP dt Keq
(1)
where ND is the amount of 24DMD generated by reaction (kmol), W is the total weight of solution in the reactor (kg), Kc is the rate constant (9.037 × 1018 kgsoln2/(kgcat kmol min)), w0 is the catalyst to solution weight ratio, E is the activation energy (102 GJ/kmol), Keq is the temperature-dependent equilibrium constant, and Ci is the concentration of species i (kmol/kgsoln). The objective of the case study is to create an equimolar 24DMD and water product, with a maximum of 2.0 mol % of acetaldehyde and propylene glycol. Beyond 2.0%, the cost of removing the impurities becomes exceedingly expensive, requiring high reflux ratios and a large number of column trays. The binary product is sent downstream to another process. Unreacted acetaldehyde and/or propylene glycol are recovered and recycled. Continuous Process. A continuous process was simulated using ASPEN PLUS 2004. Note that traditional reactive distillation is unattractive for integrating the reaction and
separation steps for several reasons. First, because the two reaction products have intermediate boiling points and the reaction is highly reversible, it is difficult to recover the product in a sidedraw. Second, because one of the reagents leaves in the distillate (acetaldehyde) and one leaves in the bottoms product (propylene glycol), the reaction is shifted to the left. To counter this effect, a large excess of one reagent can be used, with high recirculation costs. Third, in reactive distillation, the temperatures in the column are thermodynamically related to the pressure, which cannot exceed 2.1 bar for the case study. Hence, temperature cannot be adjusted to control the rate and extent of the reaction. The continuous system in this study employs a continuous stirred-tank reactor (CSTR) and two distillation columns, as shown in Figure 2. Equimolar acetaldehyde and propylene glycol are fed to the CSTR. The reactor effluent, at 89 °C and in chemical equilibrium (approximately 73% products, 27% reagents by moles), is fed to the acetaldehyde removal distillation column. Acetaldehyde in the distillate is recycled to the CSTR. The remaining three species exit in the bottoms product, which is sent to the second distillation column, the propylene glycol removal unit. Here, the propylene glycol is recovered in the bottoms product and recycled to the CSTR. Equimolar 24DMD and water are recovered in the distillate.
5550
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Figure 3. Batch recipe. A ) acetaldehyde, P ) propylene glycol, D ) 24DMD, and W ) water.
1 and the inlet streams to the FBR (feed, acetaldehyde recycle, and still contents from the previous batch) are
(
)
C DC W dNi ) νiWKcw0e-E/RT CACP + xD,iFD + xF,iFF + dt Keq xS,iFS (2)
Figure 4. Simulation model for the FBR.
The process was simulated over a range of fresh feed flow rates varying from 0.5 to 64 kmol/h. The CSTR, columns, condensers, and reboilers scale with the production rate. The reflux ratios, boilup ratios, column pressures, reactor temperature, feed stages, and feed qualities were adjusted to minimize the annualized cost. Batch Process. In the batch process shown in Figure 3, a fed-batch reactor (FBR) receives equimolar acetaldehyde and propylene glycol and produces a 24DMD and water product at 48 °C in chemical equilibrium, which is transferred to the empty distillation still. After a warmup period, as acetaldehyde appears in the distillate, it is recycled to the FBR. When the acetaldehyde has been removed from the column, the distillate becomes rich in 24DMD and water and is collected in a receiver tank. When nearly all of the water has been removed from the still, the heater stops and the liquid propylene glycol left in the column drains into the still. The still contents, which are rich in propylene glycol, are sent to the distillate receiver and subsequently recycled to the FBR. The column is purged with nitrogen to remove unwanted water vapors and to cool the tower for the next batch. For the FBR, shown in Figure 4, the dynamic mass balance equations involving the modified kinetic rate expression in eq
where Ni, W, Kc, w0, E, Keq, and Ci are defined in eq 1; the stoichiometric coefficients are νi ) -1 (i ) A or P), νi ) 1 (i ) D or W); FD, FF, and FS are the molar flow rates in the distillate return stream, fresh charge stream, and still return stream, respectively (herein, FF and FS are specified and FD is the time-varying distillate rate determined using a BATCHSEP simulation); and xD,i, xF,i, and xS,i are the mole fractions of species i in the distillate return stream, fresh charge stream, and still return stream, respectively. Equation 2 was integrated and the temperature of the FBR was fixed (48 °C) to give the maximum yield of product within the time available for reaction. This simulation was performed for batch charges between 5 and 150 kmol of feed. The batch distillation process was simulated, assuming equilibrium stages, using ASPEN BATCHSEP 2004. The distillation column contained 20 trays spaced 18 in. apart. A range of batch charges were simulated between 5 and 150 kmol of reactor effluent. The column had a 1.0 ft inner diameter except for charges greater than 100 kmol, where a 1.5 ft diameter was more cost-effective. The cooldown process was modeled by integration of the dynamic energy balance governing conduction in the steel wall and convection between the wall and nitrogen, as shown in Figure 5. Nitrogen enters the bottom of the column at 20 °C and 200 Nm3/h. The column is assumed to be adiabatic, and the rounded header and footer sections are ignored. For simplicity, it is assumed that the volumetric flow rate of the nitrogen does not vary with temperature. Hence, the rate of heat transfer between the wall and nitrogen is slightly underestimated
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5551
Figure 5. Schematic of column cooldown at the end of the batch cycle.
and the cooling times are slightly overestimated, giving conservative estimates. The column was divided into segments of about ∆L ) 0.1 in. The integration time-step was the residence time of nitrogen in segment ∆L and was on the order of a fraction of a second. The liquid temperature profile at the end of the batch cycle was used to initialize the wall and gas temperatures inside the column. The thermal conductivity of 304 stainless steel is 8.09 Btu/(h ft °F), and the heat-transfer coefficient was estimated using the simplified equation for heat transfer to common gases inside tubes with large L/D ratios:15
ho ) 0.0144CpG0.8/D0.2
(3)
where Cp is the heat capacity (Btu/(lb °F)), G is the mass velocity of nitrogen (lb/(h ft2)), D is the diameter of the column (ft), and h0 is the heat-transfer coefficient, approximately 0.37 Btu/(ft2 h °F). To check the accuracy of this result, an alternative method of estimating ho is to approximate it as 1/200th of the heat-transfer coefficient of steam,16 which is estimated at 100 Btu/(ft2 h °F).17 This gives 0.5 Btu/(ft2 h °F), in close agreement with eq 3. Semicontinuous Distillation with Chemical Reaction in a Middle Vessel. The SDRMV process uses one 30-tray column, one FBR, and one auxiliary tank (Tank 2), as shown in Figure 6. Both the tank and the FBR act as middle vessels and interact semicontinuously with the column. There is no down time between cycles, and consequently, the process is in continuous operation. A cycle consists of two major phases of operation, with three modes in each phase. In the first mode of the first phase (Mode 1), the FBR begins with the reaction mixture near chemical equilibrium at 99 °C (approximately 35 mol % 24DMD and water each and 15 mol % acetaldehyde and propylene glycol each). The FBR interacts semicontinuously with the distillation column, feeding it the mixture of four species. The column removes acetaldehyde in the distillate and recycles it to the FBR, creating more product during this mode by providing an excess of acetaldehyde. The
bottoms stream from the column, consisting of the other three species, is collected in Tank 2. When the FBR is nearly empty, Mode 2 begins. In this mode, the FBR effluent valve is closed. The acetaldehyde remaining in the column is transferred to the distillate stream, which is sent to the FBR. This ensures that there is negligible acetaldehyde in the column before the next phase begins. The FBR also receives a fresh charge of equimolar acetaldehyde and propylene glycol, and the reaction begins to take place. Following this purge step, transitional Mode 3 begins. The contents of auxiliary tank 2 are fed to the column, the distillate stream is returned to the auxiliary tank, and no product is removed at the bottom of the column. This shifts the column profile such that the bottoms contains nearly pure propylene glycol while the condenser is nearly devoid of propylene glycol. After this profile is achieved, the second phase of operation begins. In the first mode of the second phase (Mode 4), the auxiliary tank continues to feed the column, but bottoms product, consisting of nearly pure propylene glycol, is sent to the FBR. The distillate, which is devoid of propylene glycol, returns to Tank 2. Thus, the propylene glycol is removed from Tank 2, leaving only 24DMD and water at the end of Mode 4. Another purge step (Mode 5) follows, where residual water and 24DMD in the column are recovered and sent to Tank 2. Similar to Mode 2, there is no bottoms product or feed during Mode 5; only distillate is withdrawn. When trace amounts of propylene glycol appear in the distillate, Mode 5 is terminated. The cycle terminates with transitional Mode 6, which prepares the column for the first mode of the next cycle. The FBR contents, which have approached chemical equilibrium, are fed to the column. Distillate is collected and returned to the FBR, with no bottoms product taken from the column. During this mode, the composition profile in the column becomes acetaldehyde rich near the top, with the other three species concentrating near the bottom. After the products 24DMD and water are drained from Tank 2, the next cycle begins with Mode 1. Note that the full cycle is summarized in Table 1. Also, an animated video of the SDRMV process is available.18
5552
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Figure 6. SDRMV design strategy. FCs (flow controllers) and CCs (composition controllers) are used, with FTs (flow transmitters) and CTs (composition transmitters). The annotated numbers indicate the modes during which the devices are active. The behavior and functionality of each controller changes throughout the cycle. Table 1. Summary of the Modes of Operation of the SDRMV Processa mode 1 2 3 4 5 6
feed to column
species in feed
distillate destination
FBR
A, D, W, P
Tank 2 Tank 2
D, W, P D, W, P
FBR
A, D, W, P
FBR FBR Tank 2 Tank 2 Tank 2 FBR
distillate species A A D, W D, W D, W A
bottoms destination
bottoms species
run time
Tank 2
D, W, P
FBR
P
36% 3% 12% 31% 4% 14%
A ) acetaldehyde, D ) 2,4-dimethyl-1,3-dioxolane, W ) water, and P ) propylene glycol. The run time is expressed as a fraction of the total cycle time. This number is approximate and varies depending on the system scale and production rate. a
The supervisory control system is complex, and consequently, it is summarized here for brevity. Each mode requires a different control scheme with different tuning parameters and triggers. The first modes in each phase (Modes 1 and 4) have column feeds that change widely in composition, while the desired purities of the outlet streams remain approximately constant. Therefore, a model-based, feed-forward scheme is effective for controlling the column during these modes, coupled with a standard P or PI feedback controller. To determine the feedforward law, simulations were performed using a RadFrac block in ASPEN PLUS for a variety of reflux ratios and possible feed compositions. For each of these, the Design Spec/Vary function was utilized to determine the boilup ratio necessary to achieve the specified purity in the bottoms. From these data, equations were determined that calculate the desired boilup ratio as a function of the mole fraction of the key component in the feed, which is used as the feed-forward law. These laws create an ideal dynamic control trajectory for the boilup ratio during these modes. However, the simulations begin from some initial state and require many cycles before the system approaches an unchanging behavioral cycle. Therefore, the feed-forward laws may not be totally adequate for maintaining the bottoms purity, and so, an additional feedback control scheme is applied.
During the purge modes (2 and 5) and the transition modes (3 and 6), the controllers need only to hold a constant reflux ratio and adjust the feed or distillate flow rates to regulate the column internal flow rates within tight bounds. The control system is summarized in Table 2. Note that, for simulations, either distillate rates or boilup ratios are specified, with steam duties and flow rates calculated. In practice, the controller would adjust the steam flow rate, as shown in Figure 6. Note that the focus of this design study was on selecting the design variables rather than on achieving optimal control solutions. Set-points were not altered and disturbances were not rejected using regulatory control. This issue will be studied in future work by the authors. The simulation of the SDRMV process was achieved by integration of the dynamic MESH equations describing the column,19 together with the mass balance equations for the FBR and the mass balance equations for Tank 2. The equations were integrated using the first-order implicit-Euler method for rigorous dynamic distillation presented in ref 19 (p703), with a stepsize adjustment algorithm by Michelsen.20 The method of Seader and Henley19 was selected because of its rigor and its ability to be adapted for both batch and continuous modes of operation. The step-size adjustment algorithm was used to minimize the
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5553 Table 2. Controller Summary phase
I
mode
1
2
type law
specified maintain cnst RR ) 2.25
type
model-based FF with P-FB control RB adjusted so xA,bot does not exceed limit
law
II 3
4
Distillate Controllers specified specified maintain cnst maintain cnst distillate rate RR ) 0.6 and RR ) 1.0
specified maintain cnst distillate rate and RR ) 4.0
5
6
PI control maintain cnst RR ) 20; regulate distillate rate to keep internal liquid flow rates balanced
specified maintain cnst distillate rate and RR ) 8
xP,dist > small value, or sump volume < specified value
sump volume > large value, all product in T2 has been emptied, and xD,bot > small value
Bottoms Controllers model-based FF with PI-FB control RB adjusted to ensure xP,bot stays close to unity Feed Controllers
type law
P control feed rate adjusted to keep internal liquid flow rates balanced
triggers
xD,FBR < small value, or NFBR < small value, or xA,bot > small value
Stopping Trigger xW,sump < xP,T2 < small value small value
xA,dist < small value, or sump volume < specified value
numerical errors of integration. Several explicit-Euler integration steps are used immediately after a mode switch because the Jacobian matrices are near-singular immediately following a discrete variable change. Chemical properties such as vaporliquid equilibria, mixture molar volumes, mixture enthalpies, and bubble-point temperatures are modeled using the UNIQUAC equation and through function calls to the ASPEN PROPERTIES 2004 engine. The simplified dimensionless equations that describe the total molar holdup for each species in the FBR and Tank 2 are
dθFBR,i dτ
)
νiDAR
∑i
(
θFBR,AθFBR,P -
)
θFBR,DθFBR,W
µiθFBR,i
Keq
xFBR,iφFBR_OUT +
∑
-
xs,iφs (4)
s)inlet streams
dθT2,i dτ
) -xT2,iφT2_OUT - xT2,iφT2_DRAIN +
∑
s)inlet streams
xs,iφs (5)
where θX,i is the dimensionless molar holdup in unit X for species i, τ is the dimensionless time, νi is the stoichiometric coefficient (νi ) -1 for i ) A or P, νi ) 1 for i ) D or W), DAR is the dimensionless rate constant, µi is the dimensionless molecular weight of species i, Keq is the reaction equilibrium constant, xX,i is the liquid mole fraction of species i in unit or stream X, and φX is the dimensionless molar flow rate from unit X or in stream X. Note that definitions for the dimensionless variables are in the Nomenclature section. The simplified dynamic equations for the liquid mole fractions of each species in the column, including the condenser and reboiler, are
[] [ ]
dx1,i Γ2 Γ2K2,i )x1,i + x2,i dτ θ1 θ1
[
(6)
]
ΓjKj,i + Γj+1 - Γj + Λj-1 + φF,j dxj,i Λj-1 xj-1,i xj,i + ) dτ θj θj φF,jxF,j Γj+1Kj+1,i xj+1,i + j ) 2, ..., N - 1 (7) θj θj
[
]
ΓNKN,i - ΓN + ΛN-1 - ΛN dxN,i ΛN-1 xj-1,i + xN,i ) dτ θN θN
(8)
where xj,i is the liquid mole fraction of species i on stage j, xF,j,i is the liquid mole fraction of species i in the feed to stage j, Γj is the dimensionless vapor flow rate leaving stage j, θj is the dimensionless total molar holdup on stage j, Kj,i is the vaporliquid equilibrium constant of species i on stage j, Λj is the dimensionless liquid flow rate leaving stage j, and φF,j is the dimensionless total molar flow rate of the feed stream to stage j. The simplified dynamic equations for the total molar holdup in the condenser, on the column trays, and in the reboiler are
(
)
dθ1 1 ) Γ2 - 1 + Λ dτ RR 1
(9)
dθj ) Γj+1 - Γj + Λj-1 - Λj + φF,j j ) 2, ..., N - 1 dτ (10) dθN ) ΛN-1 - (1 + RB)ΛN dτ
(11)
where RR and RB are the reflux and boilup ratios, respectively. The simplified dynamic energy balances on the column stages,
5554
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
including the condenser and reboiler, are
θ1 θj
dηL,1 ) Γ2ηV,2 - Γ2ηL,1 - ΨC dτ
(12)
dηL,j ) Γj+1(ηV,j+1 - ηL,j+1) - Γj(ηV,j - ηL,j) + dτ Λj-1(ηL,j-1 - ηL,j) + φF,j(ηL,Fj - ηL,j) j ) 2, ..., N - 1 (13)
dηL,N ) ΛN-1(ηL,N-1 - ηL,N) + ΛN-1RB(ηV,N - ηL,N) + θN dτ ΨR (14) where ΨC and ΨR are the dimensionless heat duties for the condenser and reboiler, respectively, ηL,j and ηV,j are the dimensionless molar enthalpies for the liquid and vapor on stage j, and ηL,Fj and ηV,Fj are the dimensionless molar enthalpies for the liquid and vapor in the feed streams to stage j. The reflux ratio is related to the distillate flow rate, the liquid rate leaving the condenser, and the vapor rate leaving tray 2 by
Γ2 , φDist ) Λ1/RR Λ1 ) 1 + 1/RR
(15)
where φDist is the dimensionless molar flow rate of the distillate. The boilup ratio is related to the bottoms flow rate, the vapor leaving the reboiler, the vapor leaving the bottom stage, and the liquid leaving the reboiler as follows:
ΛN )
ΛN-1 ) φBot, ΓN ) ΛNRB 1 + RB
(16)
where φBot is the dimensionless molar flow rate of the distillate. The vapor-liquid equilibria are described by
yj,i ) Kj,ixj,i j ) 1, ..., N; i ) 1, ..., C
(17)
where yj,i is the vapor mole fraction of species i on stage j and the K-values for each species on each stage account for nonideality in the liquid phase. The integration algorithm for this system is summarized: (1) After each time-step, the controllers record measurements and modify the reflux ratio, the feed rate to the column, and either the distillate rate or boilup ratio, as appropriate. The controllers also determine when a mode switch occurs based on the trigger criteria in Table 2. (2) The equations for the two tanks (eqs 4 and 5) are integrated using an implicit predictor-corrector method, assuming that the compositions, temperatures, pressures, and flow rates of the effluent streams from the distillation column are fixed at the end of the previous time-step. Then, the mole fractions, molar holdups, enthalpies, volumes, and duties of the two tanks are updated. (3) Initial values of the column vapor mole fractions, liquid mole fractions, temperatures, flow rates, K-values, and volumes are fixed at the end of the previous time-step. (4) The liquid mole fractions on the column stages are computed by implicit predictor-corrector integration of eqs 6-8, which form a tridiagonal matrix for each chemical species:
dxi ) Zixi + qi dτ
(18)
where xi is the vector of liquid mole fractions of species i in the column and xj,i are the liquid mole fractions of species i on
stage j. The vector qi has the elements, qi(j) ) -(φF,jxFj,i)/θj, which are computed from values at the end of the previous timestep. The matrix, Z, is tridiagonal, with the following elements:
Zi(j,j) ) -
Kj,iΓj + Γj+1 - Γj + Λj-1 + φF,j θj
Zi(j + 1,j) )
Zi(j - 1,j) )
Λj j ) 1, ..., N - 2 (subdiagonal) θj+1
Kj,iΓj j ) 2, ..., N - 1 (superdiagonal) θj-1
Zi(1,1) )
Zi(N,N) ) -
j ) 2, ..., N - 1
-Γ2 (condenser) θ1
KN,iΓN - ΓN + ΛN-1 - ΛN (reboiler) θN
These elements are computed using the flow rate and holdup profiles at the end of the last time-stepsa good assumption when using small step sizes. Note that in batch operation, ΛN ) 0, and when no feed is sent to the column, the q vector is also zero. (5) The liquid mole fractions on each stage are normalized. Then, the temperatures, K-values, and vapor mole fractions on each stage are determined simultaneously, using steps 5a-d in the algorithm below, which continues in steps 5e and f to determine the stage holdups and vapor and liquid traffic. In this case study, ASPEN PROPERTIES 2004 was used to compute the K-values, using the UNIQUAC equation with interaction coefficients from ref 14. (5a) The temperatures on each stage are initialized. (5b) The K-values at each temperature and composition are determined. (5c) The vapor mole fractions on each stage are determined using eq 17. (5d) When the sum of the mole fractions on each stage is unequal to unity, new temperatures are estimated, and control returns to step 5b. Otherwise, the next step is executed. (5e) The column holdups are determined by calculating the molar volume on each stage (using ASPEN PROPERTIES 2004) and multiplying by the specified stage volume. (5f) Equations 9-14 are solved to determine the liquid and vapor flow rates on each stage, with the left-hand-side derivatives calculated using a backwardsdifference estimationsa good approximation at small time-steps. With this approximation, the energy and mole balance equations around the condenser and reboiler (eqs 9, 11, 12, and 14) are linear in the unknown flow rates. In continuous operation, the reflux and boilup ratios are defined and ΛN is nonzero. Therefore, substituting eqs 9 and 11 into eq 10 and similarly substituting eqs 12 and 14 into eq 13, the mass and energy balances on the stages (excluding stages 1 and N for the condenser and reboiler) become
AΓ + BΛ + f ) 0 CΓ + DΛ + g ) 0
(19)
where Γ is the vector of dimensionless vapor flow rates (Γ2, ..., ΓN-1) , Λ is the vector of dimensionless liquid flow rates
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5555
(Λ2, ..., ΛN-1), f(k) is a vector with elements f(k) ) φk+1 dθk+1/dτ, g(k) is a vector with elements g(k) ) ηL,F,k+1φk+1 d(θk+1ηL,k+1)/dτ, and A, B, C, and D are di-diagonal matrices:
[ [
( )
A)
RR -1 1 1 + RR -1 1 -1 1 ... ... -1
-1 1 -1 1 -1 B) ... ...
[
ηL,2
C)
[
D)
1
( )
RB -1 1 + RB
( )
] ]
Figure 7. Optimization as the temperature varies in the CSTR of the continuous process. The total costs include the utilities for the heat exchangers and the CSTR jacket and installation of the heat exchangers.
RR - ηV,2 ηV,3 1 + RR -ηV,3 ηV,4 -ηV,4 ηV,5 ... ... -ηV,N-1
-ηL,2 ηL,2 -ηL,3 ηL,3 -ηL,4 ... ... ηL,N-2 ηV,N-1
( )
]
RB - ηL,N-1 1 + RB
]
The coefficients of these matrices are computed using specifications or values at the end of step 5d. For any positive RR and RB, eqs 19 are solved directly:
Λ ) (-CA-1B + D)-1(-g + CA-1f) Γ ) A-1(-f - BΛ)
(20)
In batch operation, because the boilup ratio is undefined, eqs 20 cannot be used to solve for the liquid and vapor flow rates. Instead, the distillate flow rate, φDist, is specified by the controller, and Λ1 is directly calculated using eq 15. This allows the direct calculation of Γ2, in eq 9, and in turn Γ3, Γ4, ..., down the column. In either the batch or continuous modes, the reboiler and condenser heat duties are determined after the liquid and vapor flow rates have been calculated. (5g) The next time-step is begun at step 1. Results For each design, a range of production rates was simulated. Using detailed cost analyses, the annualized cost was optimized for the three designs at each production rate. Steam costs were taken from ref 17 to be $5.5, $8.8, and $12.1 per 1000 kg of low-, medium-, and high-pressure steam, respectively. Cooling water was assumed to cost 1.3¢ per cubic meter, with chilled water at $3.30 per gigajoule of cooling load. The ASPEN ICARUS PROCESS EVALUATOR 2004 was used to determine both the equipment costs and the total direct materials and labor costs for installation (including foundations, platforms,
piping, instrumentation, electrical connections, insulation, and painting). All relevant hardware (columns, condensers, reboilers, tanks, reactors, and batch sumps) were costed. Pumps were not considered because they have relatively low purchase costs and small operating costs. The cost of the supervisory control system (SCS) was also neglected because it has an insignificant impact on the optimal design for a given production rate. Note that, at low production rates, the cost of the SCS for batch and SDRMV designs should be approximately equal because both involve complex, hybrid systems. Furthermore, while the control system for the continuous design is less expensive than for the SDRMV design, at high production rates, the cost of the control system is small compared to the other costs of production and can be ignored. For each design, the total capital investment was computed, including the cost of land, site preparation, and working capital, and the cost of manufacturing was computed, including utilities, labor, maintenance, benefits, overhead, operations, taxes, and depreciation. Considering the rapid turnover of many fine and specialty chemicals, the lifetime of the process was set at three years. As the annual production rate of 24DMD was varied, the annualized costs of the three designs were compared using a three-year lifetime; that is, an effective interest rate of 33%. For the batch and semicontinuous designs, each batch is assumed to follow immediately after the previous batch with no downtime. Comparisons of the annualized costs for the three designs are presented at the end of this section. Continuous Process. For the continuous design base case, each column was specified to have 20 trays. The reflux and boilup ratios for each column were adjusted to minimize the total duty of the two reboilers, with the total impurities (acetaldehyde and propylene glycol) in the distillate of the second column constrained to be less than 2.0 mol %. This was repeated for different numbers of stages. Fewer than 20 stages required significantly higher reflux ratios, while more than 20 stages had little effect on the reflux ratios, and consequently, 20 stages were selected for the base-case design. Then, the feed location in each column, feed quality, column pressure, CSTR temperature, and CSTR volume were adjusted to minimize selected objective functions. Figure 7 shows the effect of the CSTR temperature on the total energy costs over three years plus the heat exchanger installation costs, with the optimal design at 89 °C. Figure 8 shows the effect of the quality of the feed to the second column. Using a saturated liquid feed required the smallest energy consumption for the entire process, and therefore, the bottoms product from Column 1 is fed directly to Column 2 without heating or cooling. A similar study found that it is not cost-effective to heat or cool the CSTR effluent before feeding the first distillation column. Similarly, as shown in Figure 9, it is not necessary or costeffective to reheat or subcool the acetaldehyde recycle stream.
5556
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Figure 8. Optimization of total energy duty, for the heat exchangers and CSTR jacket, by varying the quality of the feed to the second distillation column of the continuous process.
Figure 9. Effect on the total energy cost as a function of the acetaldehyde recycle stream temperature in the continuous process.
Figure 10. Total energy costs, over three years, and heat exchanger installation costs as a function of Column 1 condenser pressure and cooling water temperature difference for the continuous process.
This is because the total energy consumption is a minimum when the stream is a saturated liquid. This cool stream absorbs the heat of reaction in the CSTR, reducing the cooling water load. Note that any heat added to this stream increases the cooling water load. By a similar analysis, the propylene glycol recycle stream is not cooled. The energy costs of the continuous process are also affected by the column pressures, with bubble points and the ease of separation altered. For this case study, increased pressure moves the water-24DMD azeotrope toward being equimolar, which simplifies their recovery, as they are produced in a 1:1 molar ratio. However, as shown in Figure 1b, a ternary azeotrope involving water, 24DMD, and acetaldehyde appears at pressures above 2.1 bar, complicating the recovery of acetaldehyde. Consequently, because all four species are present in Column 1, the upper bound on pressure is 2.1 bar. Figure 10 shows the total cost of utilities, over three years, plus the heat exchanger installation costs as a function of the pressure in Column 1. The parameter is the difference between the outlet and inlet temperatures of the cooling water. The near-optimal pressure is 1.8 bar, with a cold-side temperature difference of 6 °C,
selected because the cost is consistently low over a wide pressure range. Note that the sharp increase at high pressures arises from the difficulty in achieving the specified purities due to the ternary azeotrope. Batch Process. To obtain a base-case design, the column diameter, coolant flow rate, reflux ratio, controller set-points, and stopping criteria for each of the steps during the batch operation were varied to minimize the batch time. Low-pressure steam was chosen as the heating medium until the acetaldehyde collection was completed. After this, high-pressure steam was utilized to heat the still. Because the column diameter had little effect on performance, a 1.0 ft diameter was chosen to minimize capital costs. However, for batch charges of 150 kmol or greater, the column diameter was set at 1.5 ft because the resulting batch times were considerably smaller. The number of stages was selected at 20, based on the results of the continuous analyses. The final batch recipe chosen is described in Table 3. The batch size was varied from 5 to 150 kmol, which in turn increased the cycle time and production rate (see Figure 11). As expected, larger batches were energetically more efficient, requiring less energy to produce each kilogram of 24DMD (see Figure 12). The detailed cost analysis results are summarized at the end of this section. SDRMV Process. Because the SDRMV process includes many parameters that can be tuned and tweaked and a simulation cycle takes a long time to complete on a modern desktop computer, formal optimization is not practical. Instead, the controllers, flow rates, triggers, and set-points were tuned through an educated trial-and-error approach for a base case such that the desirable purities, internal flow rates, and performance were achieved. The reflux ratios were determined mode by mode, depending on the constraints for distillate purity in each mode. As shown in Table 2, modes which recycle distillate to the feeding tank (Modes 1, 3, and 4) do not require high purity in the distillate, and consequently, reflux ratios are permitted to remain low. During purge modes (Modes 2 and 5), impurities are undesirable and, consequently, a high reflux ratio is required. Mode 6 requires a relatively high reflux ratio to ensure that the desired concentration profile in the column is achieved in a timely manner. During continuous operation (Modes 1 and 4), the boilup ratios are regulated by controllers as described in Table 2. During batch operation (Modes 2, 3, 5, and 6), distillate flow rates are either specified or regulated by a controller. The boilup ratio and distillate flow rate vary widely from mode to mode, as shown in Figure 13. Note the low boilup ratios at the beginning of Modes 1 (τ ) 0) and 4 (τ ) 41) and the high boilup ratios at the end of these modes (τ ) 31, 66). This is because the feed stream at the beginning of the mode is rich initially in the heavy species which decreases in concentration as the mode progresses. However, this is acceptable, because widely varying distillate and bottoms flow rates are common in batch operation. Furthermore, the reflux and boilup rates experience small variations throughout the cycle, as shown in Figure 14, ensuring that the column is feasible to operate. To avoid weeping and flooding throughout the cycle, the column diameter and tray spacing were adjusted to ensure that the internal flow rates are well-balanced. The Fair correlation21 was used to determine the minimum column diameter to prevent flooding at each time-step in the cycle for tray spacings of 18 and 24 in. Then, the column diameter for each tray spacing was selected as the maximum of the values calculated, rounded up to the nearest half-foot increment. When the minimum column diameters remain approximately constant (within a one-
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5557 Table 3. Optimized Batch Recipe step
description
1
charge still
2
column startup
3
collect acetaldehyde
4
collect 24DMD and water
5
collect PG
6
purge and cooldown
actions
stopping criteria
(a) charge still with FBR effluent (b) turn distillate controller to manual mode with no reflux (a) begin heating still with low-pressure steam (b) set reflux ratio to 10 (controller is still in manual mode) (c) recycle the small amount of acetaldehyde in the distillate to the FBR (a) set the coolant flow rate to 6000 kg/h (b) turn distillate controller on; controller uses a PI algorithm to keep top tray liquid temperature at set-point (36°C) (c) recycle the distillate to the FBR (a) use high-pressure steam to heat the still (b) change the controller set-point to 110°C (c) begin collecting 24DMD and water in the distillate receiver (a) stop heating the still (b) stop collecting distillate (c) allow liquid on the trays to drain into the still (d) send distillate receiver contents downstream (a) blow cool nitrogen through column to purge vapors from system and cool the steel wall
Figure 11. Batch times and production rates for various batch charges. A 1.0 ft diameter column was used for batch charges 100 kmol or less, and a 1.5 ft diameter was used for charges greater than 100 kmol. This is partially responsible for the sharp change in slope between 100 and 150 kmol.
the still has been charged completely the top tray temperature reaches 36°C
the mole fraction of acetaldehyde in the still drops to 0.1 mol %
the water in the distillate receiver reaches 49.8 mol % distillate receiver is empty and the liquid in the column has drained into the still 100 min
Figure 13. (a) Boilup ratio and (b) distillate rate for the SDRMV design.
Figure 14. (a) Reflux rate and (b) boilup rate for the SDRMV design. Figure 12. Energy consumed per kilogram of 24DMD produced using the batch process as the batch charge is varied. Due to economies of scale, larger batch sizes are more energy efficient, except with very small charges.
half-foot interval), then the column is well-sized and the internal flow rates are balanced sufficiently well to avoid both flooding and weeping. As an example, Figure 15 shows the minimum column diameter to avoid flooding, based upon the conditions on the top and bottom trays for a tray spacing of 18 in. During several time cycles, the minimum column diameters rarely move outside the half-foot interval from 1 to 1.5 ft. The tray spacing and column diameter combination that had the lowest direct capital cost was chosen as the final design specification for the column; that is, a 1.5 ft inner diameter with an 18 in. tray spacing. The number of column trays is also an important consideration. Increasing the number of trays requires taller columns
but lower reflux ratios. This, in turn, reduces internal column flow rates and column diameters. To select the number of trays, the methods above for controller tuning and column sizing were used for 10-, 20-, and 30-tray columns. The 10-tray column required very high reflux ratios and a large diameter, while a small diameter was sufficient for the 30-tray column, resulting in the lowest capital cost. Because the minimum column diameters did not decrease significantly beyond 30 trays and columns with more than 30 trays are more costly, 30 trays were selected for the base-case design. Having selected a base-case SDRMV design, the batch size and the rate at which each batch is processed (expressed as the ratio of the FBR effluent rate to that for the base case; that is, the dimensionless flow parameter) were varied. Several simulations were performed over a range of these two parameters. As Figures 16 and 17 show, the cycle time is inversely proportional
5558
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Figure 15. Minimum column diameter to avoid flooding for a tray spacing of 18 in. Figure 18. Annualized cost as a function of the rate of production for three batch sizes, with the dimensionless flow parameter annotated.
Figure 16. Inverse cycle time as a function of the dimensionless flow parameter for three batch sizes.
Figure 19. Molar holdup trajectories for three cycles in (a) the FBR and (b) Tank 2. A ) acetaldehyde, P ) propylene glycol, D ) 24DMD, and W ) water. In part a, D and W have nearly identical trajectories.
Figure 17. Annual production rate of 24DMD as a function of the dimensionless flow parameter, for three batch sizes.
to and the rate of 24DMD production is directly proportional to the dimensionless flow parameter. In general, unlike the batch process, as the batch size in the SDRMV process decreases, it becomes more economically efficient, as shown in Figure 18. However, for a very high flow rate to batch size ratio, the residence times are impractically small. Therefore, cycle times less than 30 min were rejected as infeasible. As a result, larger batch sizes are required with larger flow rates. Using a strategy in which the amount of feed charged to the FBR each cycle equals the amount collected as product in the previous cycle, the semicontinuous design showed no instabilities over several cycles. Figure 19 illustrates the molar holdup
trajectories for three cycles in the FBR and Tank 2. The molar profiles in the FBR are nearly identical from cycle to cycle. In Tank 2, the final product composition at the end of the first cycle initially ends with more 24DMD than water; however, a greater proportion of water is collected in T2 in later cycles. Eventually, the same amount of 24DMD and water is removed from T2 at the end of each cycle. Note that this transient behavior in achieving limit cycles is due to the arbitrary initial loading of the trays in the column. For a more in-depth understanding of the cyclic campaign, the reader is encouraged to view an animated video clip of the process.18 Economic Comparisons. The SDRMV process has significantly lower capital costs than the continuous design for the entire range of production rates examined, as shown in Figure 20. This is expected, since the SDRMV process requires only one distillation column. Additionally, the SDRMV process requires smaller tanks than the batch design and, therefore, requires less capital for production rates above 1.0 MM kg/yr of 24DMD. The annual manufacturing costs for the batch and
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5559
Figure 20. Total capital investment for continuous, batch, and SDRMV processes.
To obtain the local optimum for the batch and continuous configurations, several iterations of a univariate search procedure are implemented until convergence criteria are satisfied. While no proof of convergence is possible, the design parameters for the continuous system were perturbed over a wide range around the vicinity of the optimum. No significant improvements were observed, with the best case reduction in the production cost reaching only 0.3%. Note that only one local optimum in the annualized cost space for the batch and continuous processes was observed. A more thorough search in the more complex space for the SDRMV process might lead to an improved global optimum, rendering the SDRMV process even more attractive. Conclusions
Figure 21. Annual cost of manufacturing for continuous, batch, and SDRMV processes.
A semicontinuous distillation with chemical reaction in a middle vessel (SDRMV) design should be considered for processes that benefit from the integration of separation and reaction operations, where conventional reactive distillation is infeasible and where intermediate flow rates are required. The SDRMV process studied herein is economically optimal compared with equivalent batch or continuous processes over a large range of production rates. Because growth in the fine and specialty chemicals industries is causing an increased demand for processes that operate at intermediate production rates, the SDRMV concept emerges as a novel and useful design strategy. Acknowledgment This study was made possible by a National Science Foundation Graduate Fellowship. Helpful conversations with Leonard A. Fabiano are gratefully acknowledged. Nomenclature
Figure 22. Economic comparison of the three designs. The annualized cost includes all cumulative utility costs, capital costs, labor, engineering, land, taxes, and amortization and uses an effective interest rate of 33%.
SDRMV processes are approximately equivalent, as shown in Figure 21. The continuous process requires the least annual expense at production rates above 2.0 MM kg/yr due to higher energy efficiencies and economies of scale. The annualized costs of the three processes for a range of production rates are shown in Figure 22. For the SDRMV process, the results for the batch charge of 5 kmol were chosen for dimensionless flow parameters of 2.0 or less. For systems with dimensionless flow parameters greater than 2.0, the 10 kmol batch charge was required. When comparing the optimal designs of the three processes, the batch process is optimal for production rates less than 1.0 MM kg/yr of 24DMD. The SDRMV design is optimal for rates between 1.0 and about 4.5 MM kg/yr, and the continuous design is optimal for rates greater that 4.5 MM kg/yr. While some variations in the results can be anticipated due to inaccuracies, the large optimal region gives reason to seriously consider SDRMV at intermediate production rates. Note that the batch and continuous lines intersect at approximately 2.0 MM kg/yr, which compares well to the results of Gorsek and Glavic,22 who report that their multipurpose batch process is equivalent to a continuous process at 1.8 MM kg/yr.
A ) contact or surface area (ft2) A, B, C, D ) (N - 2) × (N - 2) matrices defined in eq 19 Ci ) concentration of species i in the reactor (kmol/kgsoln) Cp ) heat capacity (Btu/(lb °F)) D ) column diameter (ft) DAR ) dimensionless rate constant ) Kcw0e-E/RTN0τ0W0-1 E ) activation energy (GJ/kmol) f, g ) (N - 2) × 1 vectors defined in eq 19 FX ) molar flow rate from unit X or into stream X (kmol/min) G ) mass velocity (lb/(h ft2)) h0 ) heat-transfer coefficient (Btu/(ft2 h °F)) H0 ) enthalpy scaling factor (GJ/kmol) hL,j ) liquid molar enthalpy on stage j (GJ/kmol) hV,j ) vapor molar enthalpy on stage j (GJ/kmol) k ) thermal conductivity (Btu/(ft h °F)) Kc ) reaction rate constant (kgsoln2/(kgcat kmol min)) Keq ) reaction equilibrium constant KX,i ) vapor-liquid equilibrium constant of species i on stage j L ) column height (ft) Lj ) liquid flow rate leaving stage j (kmol/min) MW0 ) initial average molecular weight in the FBR (kgsoln/ kmol) N ) number of stages in the column (including condenser and reboiler) Nj ) liquid molar holdup on stage j N0 ) amount of liquid in the FBR at the start of the cycle (kmol) ND ) amount of liquid 24DMD in the FBR (kmol) Nj,i ) liquid holdup of species i on stage j qi ) N x 1 vector for species i defined in eq 18 Qj ) heat duty on stage j (GJ/min)
5560
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
R ) universal gas constant (GJ/(kmol K)) RB ) boilup ratio RR ) reflux ratio t ) time (min) t0 ) residence time of liquid on a tray in the column (min) T ) reactor temperature (K) Vj ) vapor flow rate leaving stage j (kmol/min) w0 ) catalyst weight to solution weight ratio (kgcat/kgsoln) W0 ) initial weight in the FBR at the start of the cycle (kg) W ) weight of liquid in the reactor (kg) xj,i ) liquid mole fraction of species i on stage j yj,i ) vapor mole fraction of species i on stage j Zi ) N × N matrix for species i defined in eq 18 Greek Symbols Γj ) dimensionless vapor flow rate leaving stage j ) Vjt0/N0 Γ ) (N - 2) × 1 vector defined in eq 19 ηL,j ) dimensionless liquid molar enthalpy on stage j ) hL,j/H0 ηV,j ) dimensionless vapor molar enthalpy on stage j ) hV,j/H0 θj,i ) dimensionless molar holdup of species i on stage j ) Nj,i/N0 θj ) dimensionless total molar holdup on stage j ) Nj/N0 Λj ) dimensionless liquid flow rate leaving stage j ) Ljt0/N0 Λ ) (N - 2) × 1 vector defined in eq 19 µi ) dimensionless molecular weight of component i ) MWi/ MW0 νi ) stoichiometric coefficient ) -1 for i ) A, P and +1 for i ) 24DMD,W τ ) dimensionless time ) t/t0 φX ) dimensionless molar flow rate from unit X or in stream X ) FX/(t0/N0) Ψj ) dimensionless heat duty in stage j ) Qj/H0 Subscripts A ) acetaldehyde B ) bottoms product Bot ) bottoms D ) 24DMD; distillate Dist ) distillate F ) feed i ) species counter j ) stage counter P ) propylene glycol S ) sump; inlet stream counter T2 ) Tank 2 W ) water Acronyms and AbbreViations A ) acetaldehyde CC ) concentration controller CT ) composition transmitter CSTR ) continuous stirred-tank reactor 24DMD ) 2,4-dimethyl-1,3-dioxolane FBR ) fed-batch reactor FC ) flow controller FT ) flow transmitter P ) propylene glycol; proportional (controller) PI ) proportional-integral (controller) SD ) semicontinuous distillation
SDRMV ) semicontinuous distillation with chemical reaction in a middle vessel TC ) temperature controller W ) water Literature Cited (1) Savage, E. v. Demand for Gases Rising in Specialty Markets and Asia. Chem. Market Rep. 2004, 265 (3), 14. (2) Chang, J. Specialties Hitting Sweet Spot. Chem. Market Rep. 2005, 267 (25), 10. (3) Monroy-Loperena, R.; Alvarez-Ramirez, J. Some Aspects of the Operation of Semi-Continuous, Middle-Vessel Distillation Columns. Chem. Eng. Commun. 2004, 191 (11), 1437-1455. (4) Phimister, J. R.; Seider, W. D. Bridge the Gap with Semicontinuous Distillation. Chem. Eng. Prog. 2001, 97 (8), 72-78. (5) Phimister, J. R.; Seider, W. D. Semicontinuous, Middle-Vessel Distillation of Ternary Mixtures. AIChE J. 2000, 46 (8), 1508-1520. (6) Phimister, J. R.; Seider, W. D. Distillate-Bottoms Control of MiddleVessel Distillation Columns. Ind. Eng. Chem. Res. 2000, 39 (6), 18401849. (7) Phimister, J. R.; Seider, W. D. Semicontinuous, Pressure-Swing Distillation. Ind. Eng. Chem. Res. 2000, 39 (1), 122-130. (8) Phimister, J. R.; Seider, W. D. Semicontinuous, Middle-Vessel, Extractive Distillation. Comput. Chem. Eng. 2000, 24 (2-7), 879-885. (9) Adams, T. A.; Seider, W. D. In A NoVel Concept: Semicontinuous ReactiVe Distillation, Proceedings of the 2005 AIChE Spring National Meeting, Atlanta, GA, Apr 10-14, 2005; p 1735. (10) Shoenmakers, H. G.; Buehler, W. K. Distillation Column with External Reactorssan Alternative to the Reaction Column. Ger. Chem. Eng. 1982, 5, 292-296. (11) Kaymak, D. B.; Luyben, W. L. Design of Distillation Columns with External Side Reactors. Ind. Eng. Chem. Res. 2004, 43 (25), 80498056. (12) Broekhuis, R. R.; Lynn, S.; King, C. J. Recovery of Propylene Glycol from Dilute Aqueous Solutions Via Reversible Reaction with Aldehydes. Ind. Eng. Chem. Res. 1994, 33 (12), 3230-3237. (13) Dhale, A. D.; Myrant, L. K.; Chopade, S. P.; Jackson, J. E.; Miller, D. J. Propylene Glycol and Ethylene Glycol Recovery from Aqueous Solution Via Reactive Distillation. Chem. Eng. Sci. 2004, 59 (14), 28812890. (14) Chopade, S. P.; Dhale, A. D.; Clark, A. M.; Kiesling, C. W.; Myrant, L. K.; Jackson, J. E.; Miller, D. J. Vapor-Liquid-Liquid Equilibrium (VLLE) and Vapor Pressure Data for the Systems 2-Methyl-1,3-dioxolane (2MD) + Water and 2,4-Dimethyl-1,3-dioxolane (24DMD) + Water. J. Chem. Eng. Data 2003, 48 (1), 44-47. (15) McAdams, W. H. Heat Transmission, 3rd ed.; McGraw-Hill: New York, 1954; p 532. (16) McCabe, W. L.; Smith, J. C.; Harriott, P. Unit Operations of Chemical Engineering, 5th ed.; McGraw-Hill: New York, 1993; p 1130. (17) Seider, W. D.; Seader, J. D.; Lewin, D. R. Product and Process Design Principles: Synthesis, Analysis, and EValuation, 2nd ed.; Wiley: New York, 2004; p 802. (18) Adams, T. A. Animation of Semicontinuous Reactive Distillation Case Study, Case 280. http://www.seas.upenn.edu/∼adamsta/case280.avi (accessed 2005). (19) Seader, J. D.; Henley, E. J. Separation Process Principles; Wiley: New York, 1998; Chapter 13. (20) Michelsen, M. L. Efficient General Purpose Method for Integration of Stiff Ordinary Differential Equations. AIChE J. 1976, 22 (3), 594-597. (21) Wankat, P. C. Equilibrium Staged Separations: Separations in Chemical Engineering; Elsevier: New York, 1988; p 707. (22) Gorsek, A.; Glavic, P. Design of Batch Versus Continuous Processes Part 2: Multi-Purpose Equipment. Chem. Eng. Res. Des. 1997, 75 (A7), 718-723.
ReceiVed for reView October 12, 2005 ReVised manuscript receiVed January 23, 2006 Accepted January 31, 2006 IE051139R
