Ind. Eng. Chem. Res. 2001, 40, 879-884
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Batch Distillation in a Column with a Cold Middle Vessel for Heat-sensitive Compounds Xianbao Cui, Zhicai Yang,* Huaiqi Shao, and Hongmei Qu School of Chemical Engineering, Tianjin University, Tianjin 300072, China
Batch distillation in a column with a cold middle vessel is studied experimentally and simulated by a constant molar holdup model. The experimental results agree well with those simulated. The middle vessel is improved by adding an inside heat exchanger, and the flow rate in the stripping section can be controlled by the pressure in the middle vessel. The liquid temperature in the middle vessel is analyzed by a simple method, and the analysis results show that the liquid temperature in the middle is greatly decreased by the inside heat exchanger. The feasibility of using such a kind of column to separate heat-sensitive compounds is analyzed, and the analysis results show that it is a competitive choice for batch distillation of heat-sensitive compounds. Introduction Batch distillation is an important unit operation frequently used for small-scale production. Batch distillation is preferable to continuous distillation when fine and special chemicals are separated. The most outstanding feature of batch distillation is its flexibility, as a single column can separate many different kinds of components from a multicomponent feed. Thus, batch distillation is widely used in the separation and purification of high-value chemicals. Because many highvalue chemicals are sensitive to heat, the traditional batch distillation process is not suitable for the separation of the heat-sensitive compounds because of the long distillation time. A new type of batch distillation process, which is called batch distillation in a column with a middle vessel (BDMV), is a good choice for such separations. This type of column was first mentioned by Robinson and Gilliland.1 It is a combination and generalization of two conventional types of batch distillation columns: batch rectifier and batch stripper. Bortolini and Guarise,2 Devyatikh et al.,3 Davidyan et al.,4 Meski and Morari,5 and Barolo et al.6 studied the features and behavior of this type of batch distillation column. The mixture to be separated is loaded into the middle vessel, and different products are simultaneously withdrawn from the top and the bottom of the column; therefore, the distillation time in such column is much shorter. Furthermore, an inside exchanger is used to keep the liquid cool in the middle vessel (Figure 1), so most of the mixture to be separated can be stored in a cool state. Thus, the time that the mixture is heated at high temperature can be greatly reduced. Therefore, batch distillation in a column with a cold middle vessel (BDMCV) is suitable for the separation of heat-sensitive mixtures. Experiment The process and apparatus that we used are illustrated in Figure 2. We utilized two sections of a 500mm long, 40-mm diameter packed glass columns with a 2000-mL agitated flask as the middle vessel. Each section is packed with φ3×3 mm Dixon rings. The liquid flow rate in the stripping section of the column is controlled by the pressure in the middle
Figure 1. Column with a middle vessel: 1, inside heat exchanger; 2, middle vessel.
vessel. This is because the column is operated under vacuum conditions, so that, at the beginning of column start-up, the middle vessel must be under vacuum to ensure that the liquid in the rectifying section flows into the middle vessel. Then, the middle vessel is isolated from the vacuum resource, and the liquid in the middle vessel can flow into the striping section by siphon. The pressure in the middle vessel is gradually dropped, with the liquid in the middle vessel decreasing. At this time, some nitrogen gas must be blown into the middle vessel to keep the liquid flowing into the stripping section. The pressure in the middle vessel is controlled to certain value according to the pressure drop in the stripping section, so that the flow rate in stripping section can be kept at a proper value. There is an inside heat exchanger between the rectifying section of the column and the middle vessel, so that the hot liquid from rectifying section can exchange heat with the cold liquid that flows from the middle vessel to the stripping section. Therefore, the liquid in the middle vessel can be stored in a cool state, and the liquid flows into the stripping section can be heated to relatively high temperature.
10.1021/ie000491w CCC: $20.00 © 2001 American Chemical Society Published on Web 01/12/2001
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Figure 2. Column with a cold middle vessel: 1, condenser; 2 and 10, reflux controller; 3, 6, 9, and 11, thermometer; 4 and 13, product receiver; 5 and 8, packed column; 7, inside heat exchanger; 12, reboiler; 14, middle vessel; 15, butler; 16, vacuum pump; 17 and 18, reflux control device.
Comparison of the Experimental and Calculated Results In the experimental column, there are 6 theoretical stages in the rectifying section and 10 theoretical stages in the stripping section, as the stripping section is better wetted. The reflux ratio is 5, and the reboil ratio is 15. The initial volume of the mixture in the middle vessel is 1410 mL, and the holdup in the reboiler is 260 mL. The initial mixture contains 0.41 benzene, 0.50 toluene, and 0.09 o-xylene in terms of mole fraction. The column is operated at 85.3 kPa. The column is simulated by a simple model based on theoretical stages and constant molar holdup (see Appendix). The experimental results and the simulation results are shown in Figure 3. Figure 3 shows that benzene is mainly removed from the top, o-xylene is mainly removed from the bottom, and toluene is concentrated in the middle vessel. The experimental and simulation results show that two products can be obtained simultaneously from the top and bottom of the column, and the third product can be obtained finally in the middle vessel, so the operation time is much shorter than that of the conventional batch distillation process. In addition, the simulation results agree well with the experimental results, so the mathematical model is reliable.
Figure 3. Comparison between experimental data and calculation results.
Analysis of the Temperature in the Middle Vessel The scheme of the inside heat exchanger and middle vessel is illustrated in Figure 4. The energy balance for the inside heat exchanger and middle vessel is
L1h1 ) L2h2 + Qloss
(1)
Qloss ) K2S2(T - T0)
(2)
where L1 is the liquid flow rate entering the inside heat exchanger, L2 is the liquid flow rate leaving the inside heat exchanger, h1 is the enthalpy for L1, h2 is the enthalpy for L2, Qloss is the heat loss, T is the liquid temperature in the middle vessel, T0 is the ambient
Figure 4. Scheme of inside heat exchanger and middle vessel.
temperature, and K2 and S2 are, respectively, the heat transfer coefficient and the heat loss surface for the middle vessel. Equation 1 can be rewritten as
L1cp1T1 ) L2cp2T2 + Qloss
(3)
where cp1 and cp2 are the average heat capacities for L1
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 881
and L2, respectively, and T1 and T2 are the temperatures for L1 and L2, respectively. For the inside heat exchanger
L1(T1 - T3)cp1 ) L2(T2 - T)cp2
(4)
L1(T1 - T3) ) K1S1∆Tm
(5)
(T1 - T2) - (T3 - T) T1 - T2 ln T3 - T
(
∆Tm )
)
(6)
where T3 is the liquid temperature at the bottom of inside heat exchanger and K1 and S1 are, respectively, the heat transfer coefficient and the heat transfer surface for the inside heat exchanger. From the mass balance of the column, we obtain
( )(
L2 ) L1
)
R + 1 RB + 1 R RB
(7)
where R is the reflux ratio and RB is the reboil ratio. If L1, cp1, cp2, T1, K1, K2, S1, S2, R, and RB are known, then T2,T, T3, L2, ∆Tm, and Qloss can be resolved from eqs 2-7 by a numerical method (such as the Newton method). If (T1 - T2)/(T3 - T) < 2, eq 6 can be replaced by
∆Tm )
T1 - T2 + T3 - T 2
(8)
Substitution of eq 8 into eq 5, eq 2 into eq 3, and eq 7 into eqs 3-5 yields
L1cp1T1 )
L1 c T + K2S2(T - T0) A p2 2
(9)
A(T1 - T3)cp1 ) cp2(T2 - T)
(10)
T1 - T2 + T3 - T L1(T1 - T3)cp1 ) K1S1 2
(11)
where
A)
( )(
)
RB R R + 1 RB + 1
(12)
Equations 9-11 are a group of linear equations, so T, T2, and T3 can be resolved directly. Suppose cp1 ) cp2, then
{[
K2S2 1 T ) A L1cp - K1S1(1 - A) T1 + T Lc + 2 L1cp 0 1 p K2S2 1 1 K S (1 + A) L1cp - K1S1A 1 - A + 2 1 1 2 L1cp K2S2 1 + K2S2A (13) K S 1+A 2 1 1 L1cp
]}/{
]
(
(
(
[
)
K2S2 K2S2 T+A T + T1 L1cp L1cp 0
T2 ) -A T3 )
(
)
K2S2 1 K2S2 + TT A L1cp L1cp 0
)
) }
(14) (15)
Figure 5. Effect of heat transfer surface in inside heat exchanger.
Example. If L1 ) 72 mol/h, S1 ) 0.06594 m2, S2 ) 0.03821 m2, cp ) 45 cal/(mol °C), K1 ) 200 kcal/(m2 h °C), K2 ) 5 kcal/(m2 h °C), T1 ) 91 °C, T0 ) 20 °C, R ) 5, and RB ) 10, then T ) 26.54 °C, T2 ) 70.79 °C, T3 ) 34.35 °C, Qloss ) 1.25 × 103 cal/h, and the heat transfer in inside heat exchanger is Q ) 1.85 × 105 cal/h. It can be seen that the temperature in the middle vessel (T) is much less than T1, and the heat loss Qloss is much less than Q. Because the temperature in the middle vessel is low, it is safer for a heat-sensitive compound to be stored in the middle vessel. The liquid temperatures in the middle vessel and the inside heat exchanger are affected by the heat transfer surface in the inside heat exchanger S1, so the heat transfer in the inside heat exchanger Q and the heat loss Qloss are also affected by S1. Different results are calculated according to different values of S1 and are shown in Figure 5. It can be seen from Figure 5 that T and T3 decrease sharply when S1 increases, but T2 increases only a little. The heat transfer Q in the inside heat exchanger increases, and the heat loss decreases, when S1 increase. Therefore, if the heat transfer surface in the inside heat exchanger is large enough, then the liquid temperature in the middle vessel can nearly reach ambient temper-
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Figure 6. Three types of batch distillation columns.
ature T0. Because the heat loss depends on the liquid temperature in the middle vessel, the heat loss can be neglected when S1 is sufficiently large. Evaluation of BDMCV for Heat-Sensitive Compounds The distillation equipment for heat-sensitive compounds can be evaluated by the degradation index Id provided by King.7 The definition of Id is
Id ) log(Psta)
(16)
where Ps is the saturated vapor pressure in kilopascals, t is the heated time in hours, and a is an energy coefficient. The batch distillation column that we used includes three parts: the body of the column, the middle vessel, and the reboiler, so the total Id of the equipment is
Id ) log(10IdB + 10Idp + 10IdM)
(17)
IdB ) log PsB + a log tB
(18)
IdP ) log Psav + a log tP
(19)
IdM ) log PsM + a log tM
(20)
where IdB is the Id for the reboiler; IdP is the Id for the column body; IdM is the Id for the middle vessel; PsB and PsM are the saturated pressures at the temperatures of the reboiler and the middle vessel, respectively; Psav is the saturated pressure at the average temperature of the column body; and tB, tP, and tM are, respectively, the heated times in the reboiler, the column body, and the middle vessel. If the Id of the equipment is small, the amount of reacted heat-sensitive compound is small during the distillation process. Thus, the smaller the Id, the more reliable the equipment. The Ids for three types of batch distillation columns (see Figure 6) are studied for comparison. Column A is the conventional batch distillation column, column B is the conventional batch distillation column with a middle vessel (BDMV), and column C is the batch distillation column with a cold middle vessel (BDMCV). The liquid in the middle vessel of column B is kept at the boiling point, whereas the liquid in the middle vessel of column C is kept at a temperature below the boiling point. For the three types of columns, suppose that
TTA ≈ TTB ) TTC
(21)
Tav ≈ TMB > TMC
(22)
TBA ≈ TBB ) TBC
(23)
where TTA, TTB, and TTC are the temperatures at the top of the columns; TMB and TMC are the temperatures in the middle vessels of column B and C; Tav is the average temperature of the column body of column A; and TBA,TBB, and TBC are the temperatures of the reboilers. o-Xylene is considered as the pseudo-heat-sensitive compound in the following calculation. Suppose that a ) 2.4, Tav ≈ TMB ) 364 K, TBA ) TBB ) TBC ) 415 K, TMC ) 296 K, tBA ) 4.98 h, tBB ) tBC ) 1.34 h, tMB ) tMC ) 3.64 h, and tPA ) tPB ) tPC ) 0.87 h. The Antonie equation is
log Ps ) A -
B (C + T)
(24)
where Ps is the saturated vapor pressure in kilopascals and T is the temperature in Kelvin. The Antonie constants for o-xylene are A ) 16.115, B ) 3395.5, and C ) -59.95. Now, the Ids for the three columns are calculated and listed in Table 1. The total degradation index Id consists three contributions: the contribution of the reboiler 10IdB, the contribution of the middle vessel 10IdM, and the contribution of the column body 10IdP. The three contributions are quite different for the different columns. For the three columns mentioned above, the contributions of the column body are approximately equivalent, whereas the contributions of the reboiler in columns B and C are much less than that in column A because of the added middle vessel. The total contribution of the middle vessel and the reboiler in column B (924 + 190.5 ) 1114.5) is less than that in column A (9446.3), so the total Id of column B is less than that of column A. Because the liquid in the middle vessel of column C is kept at a cool state, the contribution of the middle vessel (17.3) is much less than that in column B (924), and the total Id of column C is much less than that of column B. Therefore, the total Id of column C (BDMCV) is the smallest of the three, and it is the best choice for batch distillation of heat-sensitive compounds. Conclusion (1) Batch distillation in a column with a cold middle vessel (BDMCV) is studied experimentally and simu-
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 883 Table 1. Ids for Columns A, B, and C column A column B column C
Id
10IdB
10IdM
10IdP
3.976 3.057 2.370
9446.3 190.5 190.5
0 924.0 17.3
26.26 26.26 26.26
lated by a constant molar holdup mathematical model, and the experimental results agree well with those simulated. (2) The middle vessel is improved by adding an inside heat exchanger, so that the liquid in the middle vessel can be stored in a cool state, which is beneficial to heatsensitive compounds. The liquid temperature in the middle vessel is analyzed by a simple model. The analysis results show that the liquid temperature in the middle vessel is affected by the heat transfer surface of inside heat exchanger, and it can reach a very low temperature (approximately the ambient temperature) if the heat transfer surface of inside heat exchanger is large enough. (3) The liquid flow rate in the stripping section can be controlled by the pressure in the middle vessel, so a BDMCV is easy to operate. (4) BDMCV is evaluated by Id for heat-sensitive compounds, and the analysis results show that such columns are competitive for the batch distillation of heat-sensitive compounds.
column are equal. (6) The reboiler is also a theoretical stage.
Notation
Mass balance
A, B, C ) Antonie constants a ) energy coefficient cp ) heat capacity h ) liquid enthapy Id ) degradation index K ) heat transfer coefficient L ) liquid flow rate P ) pressure R ) reflux ratio RB ) reboil ratio S ) heat transfer surface t ) heated time
Figure A. Scheme of a batch distillation column with a middle vessel.
U0 Ui
Um
dxm,j ) V(ym+2,j - ym,j) + L1(xm-1,j - xm,j) dt j ) 1, ..., c (3) d(Um+1,jxm+1,j) ) L1xm,j - L2xm+1,j j ) 1, ..., c dt
s ) saturation A ) column A B ) column or reboiler C ) column C M ) middle vessel P ) column body T ) top of the column
Ui
(1)
dxi,j ) V(yi+1,j - yi,j) + L1(xi-1,j - xi,j) dt i ) 1, ..., m - 1; j ) 1, ..., c (2)
Superscripts Subscripts
dx0,j ) Vy1,j - Vx0,j j ) 1, ..., c dt
(4)
dxi,j ) V(yi+1,j - yi,j) + L2(xi-1,j - xi,j) dt i ) m + 2, ..., m + n + 1; j ) 1, ..., c (5)
Um+n+2
dxm+n+2,j ) Vxm+n+1,j - Vym+n+2,j j ) 1, ..., c dt (6)
Phase equilibrium Appendix Mathematical Simulation. Figure A shows a column provided with m theoretical stages in the rectifying section, n theoretical stages in the stripping section, and a middle vessel operating with a mixture consisting of c components. The mathematical model is based on the following assumptions: (1) The molar flow rate is constant. (2) The molar holdups in the liquid phase for each theoretical stage, the top of the column, and the reboiler are constant. (3) The molar holdup in the vapor phase is neglected. (4) Vapor and liquid on any particular theoretical stage are in phase equilibrium. (5) The molar flow rates of the vapor phase in the two sections of the
yi,j ) Ki,jxi,j i ) 1, ..., m + n + 2; j ) 1, ..., c (7) Summation equation c
xi,j - 1 ) 0 ∑ j)1
i ) 1,..., m + n + 2; j ) 1, ..., c
(8)
c
yi,j - 1 ) 0 ∑ j)1
i ) 1, ..., m + n + 2; j ) 1, ..., c (9)
where U is the holdup, V is the vapor flow rate, L is the liquid flow rate, K is the equilibrium constant, x is the liquid composition, and y is the vapor composition.
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The mathematical model is resolved by the two-point implicit method. Literature Cited (1) Robinson, C. S.; Gilliland, E. R. Elements of Fractional Distillation; McGraw-Hill Book Co.: New York, 1950. (2) Bortolini, P.; Guarise, G. B. A New Practice of Batch Distillation. Quad. Ing. Chim. Ital. 1970, 6, 150 (in Italian). (3) Devyatikh, G. G.; Churbanov, M. F. Methods of high purification. Znanie 1976, USSR. (4) Davidyan, A. G.; Kiva, V. N.; Meski, G. A., et al. Batch distillation in a column with a middle vessel. Chem. Eng. Sci. 1994, 49, 3033.
(5) Meski, G. A.; Morari, M. Design and operation of a batch distillation column with a middle vessel. Comput. Chem. Eng. 1995, 19, s597. (6) Barolo, M.; Guarise, G. B.; Rienzi, S. A.; Trotta, A.; Macchietto, S. Running batch distillation in a column with a middle vessel. Ind. Eng. Chem. Res. 1996, 35, 4612. (7) King, R. W. Distillation of Heat Sensitive Materials. Br. Chem. Eng. 1967, 12, 568.
Received for review May 16, 2000 Accepted November 17, 2000 IE000491W
