1536
Ind. Eng. Chem. Res. 2009, 48, 1536–1542
SEPARATIONS Role of Initial Still Charge on Batch Distillation Xuemei Zhang,*,† Chungui Jian,‡ and Sufei Zhang† School of Chemical Engineering and Technology, Tianjin UniVersity, Tianjin 300072, China, and Tianjin UniVtech Co. Ltd., Tianjin 300072, China
Batch distillation is widely used in chemical industries, but the role of initial still charge on batch distillation has not been well understood and is still the focus of debate among researchers. A constant molar holdup model for batch distillation was built in this work in order to study the role of initial still charge. The degree of separation difficulty q was used to correlate the design and operating parameters in batch distillation. And yield was selected as the criterion of evaluating the performance of batch distillation under different initial still charge. The simulation results show that an optimum initial charge occurs in batch distillation at q e 0.6 for ideal mixtures. Moreover, the yield keeps constant if the column holdup and initial still charge increase and drop in the same scale with the other operating parameters being fixed. Experiments were made to check the optimum charge with an iso-propanol-n-propanol-n-butanol system, which agreed well with the simulation results. The investigations make it possible to achieve a profitable operation by choosing an optimal amount of charge. 1. Introduction Batch distillation is widely used in chemical industries, especially in the production of high-value-added, low-volume specialty chemicals. It is characterized by outstanding features such as flexibility in operation and the ability of obtaining many different products with a single batch column. Because batch distillation is an inherently unsteady-state process, there are so many operating parameters affecting the process that it is hard to understand the process well so far. A numbers of researchers have been concentrating on seeking for the optimal strategies in batch distillation. Converse,1 Corward,2 Robinson,3 Mayur,4 and Kerkhof5 studied optimal reflux ratio policies in batch distillation. Keith,6 Hansen,7 and Yang8 worked with vapor rate. Yang9 presented the varying pressure policy in batch distillation. Li and Woany,10 Frattini et al.,11 and Barolo and Dal Cengio12 used different strategies to optimize batch distillation. However, Diwekar13 and Noda et al.14 concluded that optimal reflux ratio is, for most cases, close to the constant reflux ratio. In addition, most of the other proposed optimal policies are infeasible in practice because of the difficulties in operation. So, it is of great importance to develop a feasible and convenient operating policy. Among the design and operating parameters in batch distillation, initial still charge is an important one. Up to now, only a few literatures concerning the effect of initial still charge on the performance of batch distillation are available. Luyben15 studied various design and operating policies for binary batch distillation columns with the objective of achieving a maximum production rate. It is shown that initial still charge can significantly affect batch distillation cycle time or capacity. Li16 considered the effect of various operating parameters on the optimal initial still charge for binary batch distillation. However, these results are restricted to binary systems by far. And no systematic study of the effects of initial still charge on batch * To whom correspondence should be addressed. E-mail:
[email protected]. † School of Chemical Engineering and Technology. ‡ Tianjin Univtech Co. Ltd.
distillation is done to correlate the facts observed. Hence, a systematic study was done in this work to investigate the effects of initial still charge quantitatively. In this work, a mathematical mode based on constant molar holdup was developed to make a systematic investigation on the role of initial still charge on the performance of batch distillation for binary and ternary ideal systems. The measure of “the degree of difficulty of separation” first proposed by Kerkhof17 was used to correlate the design and operating parameters in batch distillation. Moreover, the modeling results were experimentally validated with a typical ideal ternary system. 2. Mathematical Model The schematic representation of a typical batch distillation column is given in Figure 1. The mathematical model of batch distillation in this work is developed on the following basic assumptions: (a) constant molar flow for the liquid and the vapor, (b) negligible vapor holdup, (c) total condensation with no subcooling, (d) constant molar holdup on the plates and in the condenser, (e) constant relative volatilities of the mixtures, and (f) adiabatic column and theoretical trays. Because distillation time is affected by many factors in experiments, the accumulated amount of vapor is selected as
Figure 1. Schematic representation of a batch distillation column.
10.1021/ie8003607 CCC: $40.75 2009 American Chemical Society Published on Web 12/24/2008
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1537
the differential variable to reduce the differences between simulation results and the experimental ones. Mass balance of component j for the condenser: H1
dx1,j ) K3,jx3,j - x1,j dV
(1)
Mass balance of component j for the reflux drum: H2
dx2,j ) x1,j - x2,j dV
(2)
important to develop a method of characterizing batch columns and separation tasks. In this work, the measure of “the degree of difficulty of separation” was selected to correlate the design and operating parameters in batch distillation. For a binary mixture, given the number of plates (NT) of a batch column, the type of mixture to be handled (R), an initial charge composition (x0B), and specified product purity (xP/), Kerkhof proposed a measure q, the degree of difficulty of separation to characterize the separation task which is expressed as:
Mass balance of component j on tray i (i ) 3, 4,..., NT + 2): dxi,j ) Wxi-1,j - (Ki,j + W)xi,j + Ki+1,jxi+1,j Hi dV
q) (3)
dV
x0B(1 - x/p)(RNT+1 - 1)
(9a)
From Fenske’s equation, Kerkhof’s equation can be expressed as below:
Mass balance of component j for the rebolier: d(HNT+3xNT+3,j)
x/p - x0B
RNm+1 - 1 RNT+1 - 1 0
) WxNT+2,j - KNT+3,jxNT+3,j
q)
(4)
Overall mass balance around the column: RNm+1 )
x/p
1 - x0B
1 - x/p
x0B
0
dHNT+3 dV
)W-1
(5)
Vapor-liquid equilibrium on tray i: yi,j ) Ki,jxi,j
(6)
Wherein, W) Ki,j )
R R+1 Rj
q)
k i,k
k)1
In this work, a single cut batch operation is considered, whereby one distillate and one bottom residue are produced. The column is operated with constant vapor load to the 0 as condenser and constant reflux ratio. We define H0B and xBj the total amount of initial charge and its composition. At time t ) 0, a part of this total charge is assumed to be distributed along the column to provide the holdup on the plates and in the condenser, the remaining fraction giving the initial reboiler holdup. Thus, the following boundary conditions: NT+2
HN0 T+3 ) H0B -
∑H
i
(7)
i)1
x0ij ) x0Bj
(8)
There are two types of stop criterion in batch distillation: (1) the instantaneous composition of key component approaching the specified purity from above and (2) the averaged composition of the accumulated distillate approaching the specified purity from above. In this work, the later is used. The model has been implemented in Fortran language. The mathematical model is a group of stiff differential equations and has been solved with the Gear method. 3. Characterization of the Separation A difficulty in the study on the effect of initial still charge on batch distillation is that there are many parameters affecting the performance of batch distillation. Moreover, the ranges of some parameters, such as the number of plates (NT), reflux ratio (R), and relative volatility (R), are wide. Accordingly, it is very
(9c)
Kerkhof’s expression can only reflect the degree of difficulty of separation at the initial time. It cannot denote the degree of difficulty for the whole process of the separation task. What’s more, its value is greatly affected by the type of mixture and its range is too large (as seen in Table 1). So, it is hard to use this expression to compare the degree of difficulty of separation for different mixtures. Christensen and Jorgensen18 proposed the following expression:
NC
∑R x
(9b)
∫
xB0
xBF
j
(Nm + 1) dxB 0 (xB - xFB)(NT + 1)
(10)
Where xFB, xB are the final and intermediate composition in the j m is the minimum necessary number of plates reboiler, N averaged over the bottom composition under total reflux. Christensen and Jorgensen assumed a constant relative j m using the Fenske equation: volatility R and evaluated N
(
ln jm + 1 ) N
x/p 1 - xB 1 - x/ xB p
)
(11) ln R Christensen and Jorgensen’s expression is based upon the j m) ratio of the average minimum necessary number of plates (N to the actual number of plates (NT). It reflects the average degree of difficulty of separation of the separation task. But it assumes that the distillate composition is constant. In practice, the operation modes of batch distillation consist of constant distillate composition operation and constant reflux ratio operation. In constant distillate composition operation, the content of light key component in the reboiler drops gradually with the process. Thus, the minimum necessary number of plates at the end of the operation is the most. In constant reflux ratio operation, both the content of light key component in the reboiler and that in the distillate drop gradually with the process. The minimum necessary number of plates changes during the process, among which the most one is the minimum necessary number of plates for the process. So, both Kerkhof’s and Christensen and Jorgensen’s equations cannot reflect the actual degree of difficulty of separation. To overcome the disadvantages of the above expressions, the following expression is proposed in this work.
1538 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 1. Comparison between Different Expressions Of q Kerkhof’s expression case
x0B
R
x/p
E/p
NT
0 Nm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.5,0.5 0.5,0.5 0.5,0.5 0.5,0.5 0.5,0.5 0.5,0.5 0.5,0.5 0.5,0.5 0.2,0.8 0.8,0.2 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.3,0.4,0.3 0.2,0.2,0.6 0.6,0.2,0.2
1.79,1 1.79,1 1.79,1 1.79,1 1.79,1 1.79,1 1.79,1 1.6,1 1.2,1 1.8,1 4.03,2.25,1 4.03,2.25,1 4.03,2.25,1 4.03,2.25,1 4.03,2.25,1 4.03,2.25,1 4.03,2.25,1 3.2,2,1 3.6,2,1 2.4,2,1
0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.995 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.99
0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.9
40 30 22 17 14 12 10 30 80 20 40 31 23 18 15 13 11 30 20 60
6.89 6.89 6.89 6.89 6.89 6.89 6.89 8.78 27.95 5.65 8.35 8.35 8.35 8.35 8.35 8.35 8.35 10.58 7.98 21.98
Nm + 1 NT + 1
q)
q0 4.20e-9 1.42e-6 1.50e-4 2.75e-3 1.58e-2 0.05 0.1622 4.61e-5 7.52e-5 2.13e-4 9.89e-9 1.87e-6 1.97e-4 3.61e-3 0.021 0.066 0.213 1.08e-4 8.50e-4 9.61e-4
(12)
Where Nm is the minimum necessary number of plates for the process under total reflux. It can be determined as follows. From the mass balance in the batch distillation column, HB ) (HB - dHB) + D
HBxBj ) (HB - dHB)(xBj - dxBj) + DxDj
dxBj dHB ) HB xDj - xBj
(15)
For binary systems, the instant composition of light component in the distillate can be deduced from Fenske equation: R 1 + (R
From eqs 15 and 16, ln
HFB H0B
)
Nm+1
1 RNm+1 - 1
xB
( ( ))
ln
(16)
- 1)xB
1 - x0B xFB
1 - xFB x0B
+ ln
1 - x0B 1 - xFB
(17)
Where HFB is the final holdup in the reboiler. For a binary mixture, given the initial charge composition (x0B), the initial charge in the still (H0B), the specified product purity (xp/), and the specified yield (Ep/), the final composition in the reboiler (xFB) and the final holdup in the reboiler (HFB) can be expressed as follows: HFB ) H0B xFB )
H0Bx0BE/p xp
H0Bx0B(1 - E/p) HFB
(18)
(19)
expression in this work
0.22 0.29 0.40 0.51 0.61 0.70 0.83 0.37 0.39 0.39 0.26 0.33 0.44 0.55 0.66 0.75 0.87 0.42 0.47 0.47
Nm
q
8.09 8.09 8.09 8.09 8.09 8.09 8.09 10.26 30.92 6.82 8.59 8.59 8.59 8.59 8.59 8.59 8.59 10.89 6.57 23.31
0.22 0.29 0.40 0.51 0.61 0.70 0.83 0.36 0.39 0.37 0.23 0.30 0.40 0.50 0.60 0.69 0.80 0.38 0.36 0.40
Thus,Nmcan be solved from eqs 17-19. For multicomponent systems, the final composition in the reboiler (xFB) and the final holdup in the reboiler (HFB) cannot be expressed in analytical equations. They are determined by the numerical method described as follows. From the Fenske equation: xDj ) RNj m+1
xBj x xBNC DNC
(20)
Summation equation NC
∑x
(14)
Where xBj, xDj are the instantaneous composition of component j in the reboiler and the distillate. From eqs 13 and 14,
xD )
8.14 8.14 8.14 8.14 8.14 8.14 8.14 10.32 30.76 7.10 9.49 9.49 9.49 9.49 9.49 9.49 9.49 11.97 8.85 27.52
(13)
Where HB is the instantaneous holdup in the reboiler and D is the amount of accumulated distillate. From the mass balance of component j in the batch distillation column,
Nm+1
Christensen and Jorgensen’s expression jm N qj
Dj ) 1
(21)
j)1
From eqs 19 and 20 xDNC )
NC
∑ j)1
(
1 RNj m+1
xBj xBNC
)
(22)
For a multicomponent mixture, the instantaneous distillate composition (xDj) can be determined by eqs 20 and 21. Given 0 ), the number of plates (NT), the initial charge composition (xBj 0 the initial charge in the still (HB), and the specified product purity (xp/), eq 15 is solved with Fourth order Runge-Kutta method. Dichotomizing method is used to work out the minimum necessary number of plates which meets the specified yield (E/p). Dichotomizing method is one dimension searching method. The basic idea of the dichotomizing method is the following: Supposing there is a solution in the interval [a, b] for the equation f(x) )0. a1 is set as a and b1 as a1 + ∆Nm. If f(a1) ) 0 (or f(b1) ) 0), then a1 (or b1) is the solution for f(x) ) 0 and the searching procedure stops. If f(a1)f(b1) > 0, there is no solution in the interval [a1, b1]. Then, a1 is set as b1 and b1 as a1 + ∆Nm. If f(a1)f(b1) < 0, there is a solution in the interval [a1, b1]. Then, the interval [a1, b1] is divided into two halves by a0 ) 1/2(a1 + b1).The procedure is repeated with a series of intervals: [a1, b1], [a2, b2],..., [ak, bk]... The length of [ak, bk] is bk - ak ) [1/(2k-1)](b - a). The solution is worked out when |bn - an| < ε (ε is the specified accuracy error). The outstanding advantage of the dichotomizing method is simplicity. The calculation procedure is summarized in Figure 2.
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1539 Table 2. Input Data in the Investigations xB0
mixture iso-propanol-n-propanol n-hexane-cyclohexane benzene-toluene iso-propanol-n-propanol-n-butanol n-hexane-cyclohexane-n-heptane benzene-toluene-o-xylene
0.5, 0.6, 0.3, 0.3, 0.4, 0.2,
x/p
E/p
0.5 0.99 0.8 0.4 0.99 0.8 0.7 0.99 0.8 0.4, 0.3 0.99 0.8 0.4, 0.2 0.99 0.8 0.5, 0.3 0.99 0.75
holdup on plate (h) 0.025 0.025 0.025 0.025 0.025 0.025
(1) relative volatility (Rj), (2) number of column plates (NT), (3) the initial amount of still charge (H0B) and its composition (x0Bj), and (4) the specified product purity (x/p) and specified yield (E/p). The unknown variables are the following: reflux ratio (R), the final compositions on the trays (xi,j), the final holdup in the reboiler (HFB), the composition of the accumulated distillate (xpj), and the yield Ep. For a mixture consisting of NC components, the number of the unknown variables is (NT + 4)NC + 3. The mass balance in a batch distillation column with negligible holdup can be expressed in eqs 1-5 with Hi ) 0. Mass balance for the receiver: dP )1-W dV Mass balance of component j for the receiver:
(23)
d(Pxpj) ) (1 - W)x2j (24) dV Where P and xpj are the amount of accumulate distillate and its composition individually. Stop criterion: Ep ) E/p
(25)
The number of the constraints expressed in eqs 1-5 and eqs 23-25 is (NT + 4)NC + 3. Then, the degrees of freedom is the following:
Figure 2. Flowchart of calculation procedure of Nm.
Comparisons between different expressions of q are illustrated in Table 1. The degree of difficulty of separation q expressed in eq 12 correlates the number of column plates (NT), the type of mixture (R), the initial charge composition (x0Bj), the specified product purity (xp/), and specified yield (Ep/). It can reflect not only the degree of difficulty of the given separation task but also the degree of the number of plates of a given column in excess of the minimum. The value q increases with decreasing relative volatility, increasing specified product purity and decreasing number of plates in excess of the minimum. Its value is independent of the amount of initial charge. It ranges from 0 (infinite number of stages) to 1 (minimum number of stages). To make the investigation on a firm well-defined basis, the value of the reflux ratio in the studied cases is determined on the following basis: (1) the same (or close) q (Because the value of NT is an integer, q for the compared cases may have tiny differences.); (2) the same yield with negligible holdup on the plates (corresponding to infinite initial charge). For a given batch distillation column with negligible holdup and a given separation task, the following parameters are known:
f ) number of unknown variables number of the constraints ) 0 For a given batch distillation column with negligible holdup and a given separation task, the reflux ratio is unique. It can be worked out by dichotomizing search method. For an assumed reflux ratio, the group of differential equations composed of eqs 1-5 and eqs 23-25 is solved with the Gear method. This is repeated until eq 25 is satisfied. Thus, the value of the reflux ratio in the compared cases is determined. 4. Results and Discussions Three typical binary mixtures and three typical ternary mixtures are used in the investigations. The binary mixtures are the following: iso-propanol-n-propanol, n-hexane-cyclohexane, and benzene-toluene. The ternary mixtures are the following: iso-propanol-n-propanol-n-butanol, n-hexane-cyclohexane-n-heptane, and benzene-toluene-o-xylene. The input data are listed in Table 2. Effects of the amount of initial still charge on the yield of batch distillation at different q are shown in Figure 3. Figure 3 shows that the effect of the amount of initial still charge on the yield is discrepant at different q. For q > 0.6, the yield increases with increasing amount of initial charge, and the increasing tendency becomes mild with amount of initial charge increases. For q e 0.6, there is an optimal amount of initial charge, at which the yield reaches the maximum. The yields at different amount of initial charge for the mixtures in Table 2 are investigated under the following
1540 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009
Figure 3. Effect of the amount of initial still charge at different q values.
conditions: NT ) 25, R ) 6, the ratio of the column holdup HT (the sum of holdup on all plates, the holdup in the condenser, and the holdup in the reflux drum) to initial charge to the reboiler (H0B) is set to 0.05. Results are shown in Figure 4. It is shown in Figure 4 that the yield keeps constant if the column holdup HT and the initial still charge H0B increase and drop in the same scale with the other parameters being fixed. In principle, the effect of initial charge on batch distillation is caused by column holdup. Holdup in a batch column (plates,
reflux drum and condenser) acts as an accumulator. It plays two roles: On one hand, it gives slower dynamic response in the concentration profile. Thus, holdup makes the change of the content of light key component in the distillate lag behind that in the reboiler, which is the “flying wheel effect” proposed by Pigford.19 On the other hand, it accumulates the light component and thus depletes the light component in the reboiler. For q > 0.6, the plates available in the column are relatively little, the ratio of holdup in condenser and reflux drum to the
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1541
Figure 4. Effect of initial charge on yield under the same ratio of HT to HB0.
holdup in the column is relatively large. Because the holdup in condenser and reflux drum is detrimental to the performance of batch distillation,20 the effect of holdup’s depleting the light component in the reboiler (effect 1) exceeds the effect of keeping the concentration of light key component (effect 2). With little amount of initial charge to the reboiler, the holdup in the column depletes the light component in the reboiler quickly, resulting in a quick drop of the instantaneous concentration of light component in the distillate and thus low yield. With slightly larger amount of initial charge in the reboiler, the ratio of column holdup to the charge in the reboiler becomes less, effect 2 becomes gradually weaker, and thus the yield increases. Finally, when the amount of initial charge reaches a certain value, the effect of holdup is negligible, and thus, the yield keeps constant. For q e 0.6, the plates available in the column are more than those for q > 0.6, and the ratio of holdup in condenser and reflux drum to the holdup in the column is relatively little. Both the effects of holdup affect the performance of batch distillation. When the initial charge to the reboiler is very little, the distillation proceeds very quickly. Although both effects are very strong, effect 1 dominates. Column holdup depletes the light component in the reboiler quickly, resulting in a quick drop of the instantaneous concentration of light component in the distillate and thus a low yield. With the amount of initial charge to the reboiler increases, the process becomes slower and the ratio of column holdup to the charge in the reboiler becomes less. Both effects become weaker, and effect 2 becomes weaker than effect 1. So, the yield increases. When the amount of initial charge reaches a certain value, effect 1 is negligible, and thus, the yield drops. 5. Experimental Validation A laboratory scale batch distillation column as shown in Figure 5 was built to validate experimentally the simulation results. The column is made of glass with a heated insulation jacket to reduce heat losses. It consists of a reboiler, a holdup collector, a column section, and a total condenser. The column section is 1000 mm long and 45 mm in diameter. It is packed with 3 × 3 mm Dixon rings made from stainless steel. A reflux splitter controlled by an electromagnet is installed at the top of the column. The boilup rate is adjusted by varying the voltage of the heater. A thermometer is placed at the top of the column and in the reboiler respectively. The differential pressure is measured by the U-form tube differential manometer. A holdup collector is installed between the reboiler and the column section to measure the column holdup. Distillate flowrate is measured by weighting the distillate for a fixed period of time.
Figure 5. Scheme of experiment apparatus for batch distillation: (1) condenser, (2) reflux splitter, (3) electromagnetic coil, (4) distillate receiver, (5) holdup collector, (6) holdup outlet, (7) reboiler, (8) pressure manometer, (9 and 12) thermometer, (10) packing, (11) electric heating jacket.
Figure 6. Comparison of experimental and simulation profiles for instantaneous distillate and residue composition (F ) 1500 mL). Table 3. Summary of Column Data and Experimental Conditions mixture
isopropanol-n-propanol-n-butanol
NT ) 25; xB0 ) (0.30, 0.42, 0 0.28); R ) 5; x/p ) 0.99; q ) 0.37 experimental condition Holdup in the condenser and reflux drum is 12.5 mL. Holdup in the packing is 156.3 mL. The distillate rate is 1.5 mL/min. The differential pressure between the condenser and the reboiler is 150 Pa.
The column data and experimental condition are summarized in Table 3. The comparisons of experimental results with the simulation results are illustrated in Figures 6 and 7. The results in Figures 6 and 7 indicate that the simulation results agree well with the experimental results. So, the model built in this work simulate the behavior of batch distillation satisfactorily. It can be seen from Figure 7 that the yield initially increases with the initial charge until the appearance of a peak. Then the yield gradually drops with the initial charge. Accordingly, the experimental results presented in Figure 7 validate the presence of an optimum initial charge. 6. Conclusions The mathematical model for batch distillation based on the assumption of constant molar holdup was built in this work. The role of initial charge on batch distillation for ideal mixtures was investigated systematically with the measure of the degree
1542 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 P ) amount of accumulate distillate, mol/h R ) reflux ratio xBj ) instantaneous reboiler composition xDj ) instantaneous composition of distillate 0 xBj ) initial composition of still charge xi,j ) liquid composition of component j on the ith plate xp/ ) specified product purity xpj ) composition of accumulated distillate Rj ) relative volatility of component j to component NC Superscripts and Subscripts i ) plate number (1, NT) j ) component number (1, NC)
Literature Cited Figure 7. Comparison of experimental and simulation results under different initial charge values.
of difficulty of separation. And, the results show that initial charge plays an important role on the performance of a batch column indeed. For q > 0.6, the yield initially increases with amount of initial charge, and keeps constant ultimately. For q e 0.6, there is an optimal amount of initial charge. In principle, the difference in performance is caused by holdup in the batch column. For a given column, the yield keeps constant if the column holdup HT and the initial still charge H0B increase and drop in the same scale with the other parameters being fixed. A mixture of isopropanol-n-propanol-n-butanol was employed to validate experimentally the simulation results. And the simulation results agree well with the experimental results. In brief, the investigations presented in this work identify the occurrence of an optimum ratio of column holdup to the amount of initial still charge (HT/H0B) for ideal mixtures. In practice, the amount of column holdup is fixed for an existing batch distillation column and is usually dictated by the separation task. Thus it is always possible to achieve a profitable operation by choosing an optimal amount of charge. It is more convenient and more feasible than any other optimum modes of operation. Nevertheless, the conclusions drawn in this work presents a direction for design of a batch distillation column. Effects of initial still charge in the rebioler should be taken into account in designing the geometry of reboiler. Notation Ep ) yield Ep/ ) specified yield HB ) the instantaneous holdup in the reboiler, mol or h HB0 ) amount of initial still charge, mol/h HBF ) final holdup in the reboiler, mol/h Hi ) holdup on the ith plate, mol/h Ki,j ) vapor-liquid equilibrium constant for component j on the ith plate L,V ) accumulated amount of liquid or vapor, mol NC ) the number of components in mixtures NT ) number of column plates
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ReceiVed for reView March 4, 2008 ReVised manuscript receiVed September 1, 2008 Accepted October 27, 2008 IE8003607
