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Semicontinuous, middle-vessel, extractive distillation
ELSEVIER
Computers &Chemical Engineering
Computers and Chemical Engineering 24 (2000) 879-885
www.elsevier.com/locate/compchemeng
Semicontinuous, middle-vessel, extractive distillation James R. Phimister, Warren D. Seider * Department of Chemical Engineering, University of Pennsylvania, Towne Building, Philadelphia, PA 19104/6393 USA
Abstract
A decentralized control configuration is proposed for the semicontinuous, extractive distillation of a low-boiling azeotropic mixture of acetone and methanol. The separation is performed in a middle-vessel column (MVC), having a large external middle vessel, from which the column is fed, and to which a full-liquid sidedraw from the stage above the feed tray is sent. The extractive agent, water, feeds the column on a scheduled basis to facilitate the separation. Based upon the simplicity of a decentralized configuration and the desire to avoid controller overrides, a DB-control configuration is selected. This configuration, in which the distillate flow rate is manipulated to control the composition of the distillate, and the bottoms flow rate is manipulated to control the composition of the bottoms product, has been widely labeled as inoperable. Herein, the configuration is shown to perform satisfactorily when a middle vessel with a full-liquid sidedraw is utilized. A cyclic campaign is simulated showing the satisfactory performance of the D B - M V C control configuration. The advantages of the control configuration are discussed and design specifics are provided. An analysis of the campaign, highlighting the problems overcome, is given. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Middle-vesselcolumn; Decentralizedcontrol; Dual-compositioncontrol
1. Introduction
Within the last decade, novel strategies have been proposed for the batch and semicontinuous distillation of nonideal mixtures (e.g. Safrit, Westerberg, Diwekar & Wahnschafft, 1995; Phimister & Seider, 2000a). With the advent of these strategies, new control methodologies must be considered. In this paper, it is shown that a decentralized control strategy, utilizing the uncommon DB-control configuration (in which the distillate flow rate is manipulated to control the composition of the distillate, and the bottoms flow rate is manipulated to control the composition of the bottoms product) performs effectively in the semicontinuous extractive separation of acetone and methanol, using water as the extractive agent. Fig. 1 shows the residue-curve map for this ternary system. For the extractive distillation of the low-boiling azeotropic mixture, acetone and methanol, Safrit and Westerberg (1997) provide a policy for the batch operation of a middle-vessel column (MVC). The MVC, in Fig. 2, is a column with a large internal or external vessel connected to the middle trays. The extractive * Corresponding author.
distillation policy begins when the middle vessel is charged with the process feed. Initially, the extractive agent is fed to one of the top trays while the column receives the middle-vessel feed. This allows for the removal of acetone in the distillate. Then, the flow of the extractive agent is discontinued and water is removed in the bottoms stream, with a near-azeotropic mixture removed in the distillate, and methanol concentrated in the middle vessel. Phimister and Seider (1999) propose operating the MVC semicontinuously in a process that maintains water in the sump throughout the campaign, with cycling between the removal of acetone in the distillate and the concentration and discharge of methanol from the middle vessel. The motivation for semicontinuous operation is the flexibility gained through the use of a single column, complemented by the benefits of automation in continuous operation; that is, a continuously fed column, continuous operation of the reboiler and condenser, and avoidance of column dumping and recharging. These benefits of automation reduce the labor-intensive operations commonly associated with batch processing. The proposed configuration is shown in Fig. 3.
0098-1354/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S0098-1354(00)00344-6
J.R. Phimister, W.D. Seider/ Computers and Chemical Engineering 24 (2000) 879-885
880
2. Policy The process cycles through three modes. 2.1. Mode I - - charging and methanol production
0.1
0.2 0.3 0.4 0.5 0.6 0.7 Molefrac M E T H A N O L
0.8
Stream $3, consisting of an equimolar mixture, recharges tank T1 (with 50 m 3 of the acetone-methanol mixture) when it is nearly empty. Methanol concentrates in the middle vessel, as the distillate, which approaches the low-boiling azeotrope of methanol and acetone (0.23 and 0.77 mole fractions at 55.4°C), is fed to tank T2, and water in the bottoms product is collected in tank T3 (loaded initially with 50 m 3 of water). When the methanol purity (0.98 mole fraction) is achieved in tank T1, its contents are dumped into product tank T4.
0.9
Fig. 1. Residue-curve map for acetone-methanol-water.
Middle
vessel Middle tray
2.2. Mode 2 - - extraction
After tank T1 is nearly emptied, the contents of tank T2 are dumped into tank T1, and hence, the feed to the column is near the azeotropic composition. Water, the extractive agent, is fed near the top of the column in stream $8 at a fixed flow rate (2 m3/h), the set point of composition controller C-102 is adjusted to 0.02 mole
Fig. 2. Middle-vessel column.
J
~
P
I
T1
I
C-101
1
N
¢,-1~1
" t>,0
LI
Fig. 3. Configuration for the separation of methanol and acetone.
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
fraction methanol (assuming the mole fraction of methanol impurity in the distillate can be measured accurately and instantaneously), and an acetone-water distillate is collected in product tank T5. As extractive agent is added, water and methanol concentrate in the middle vessel, the mole fraction of water in the sump meets its specification (0.98), and water in the bottoms product is sent to tank T3. 2.3. M o d e 3 - -
water recovery
After sufficient acetone is collected in tank T5, the cycling of water is discontinued. The set point of C102 is retumed to near the azeotropic composition (0.75 mole fraction of acetone), and the nearazeotropic distillate is sent to tank T2 in stream $5. Water, still present in the middle vessel, continues to be removed in the bottoms product until the water mole fraction in the sump falls below 0.96, after which valve C-104 is closed. When the concentration of methanol is sufficiently high in tank T1, the contents of tank T1 are collected in tank T4, tank T1 is recharged with the equimolar feed, and the process returns to mode 1. Note that this policy differs from the batch policy of Safrit and Westerberg (1997) in that the extractive portion of the campaign is performed using the previously-collected azeotropic charge, rather than the equimolar feed stream.
3. Control configuration selection Since there are mole fraction specifications for both the distillate and bottoms product, to achieve successful operation of the proposed policy, a dual-composition control strategy is required. However, because the valves on the distillate and/or bottoms streams are closed from time-to-time during a cycle, common control configurations for continuous distillation towers are ineffective for the duration of a cycle. These include the L VB-control configuration (in which the reflux rate controls the distillate composition and the boilup rate controls the composition of the bottoms product), the D VB-control configuration and the L / D , VB/B (reflux-reboil ratio) control configuration. For example, when the flow rate of the bottoms product is zero, the inventory in the sump must be controlled using VB, which consequently cannot be used for composition control. Note that this drawback is circumvented with the less common on-demand control configuration, in which the sump level is controlled by adjusting the feed flow rate. In contrast, the DB-control configuration does not require any overrides during the semicontinuous campaign, as inventory control is maintained by the boilup
881
and reflux flow rates throughout the campaign. With the exception of a few industrial examples (Finco, Luyben & Polleck, 1989), this configuration is used rarely in practice. Phimister and Seider (2000b) contend that the primary reasons for not implementing a DB-control configuration are due to adverse interactions between the level controllers. For a column that is fed continuously and does not have a full-liquid sidedraw, when either of the product compositions are below specification, the column inventory builds (as the product removal rate is less than the feed rate), and the sump or reflux drum overflows. However, for the D B - M V C control configuration, with a full-liquid sidedraw, the sump and reflux drum do not overflow when the product compositions are off-specification.
4. Process design The process feed (to the middle vessel) is a saturated liquid at 1 atm comprised of an equimolar mixture of methanol and acetone. The column has 31 stages, including a condenser and a reboiler, with a l-m diameter. The feed to the column, from the middle vessel, is to tray 21, counting from the top of the column. The feed is held constant at 5 m3/h under flow control for the duration of the campaign. During extraction mode 2, the flow rate of water in stream $8 is held constant at 2 m3/h. A full-liquid sidedraw from tray 20 is fed to the middle vessel. The sump and reflux drum have capacities of 10 m 3 with set points for the holdup volume at 5 m 3. All tanks have capacities of 100 m 3 and the middle vessel, after being charged with the process feed, contains 50 m 3. Tank T3 is filled initially with 50 m 3 of water. The set point for the water mole fraction in the bottoms product is 0.98. As noted previously, the set points for the distillate shift between a methanol mole fraction of 0.02 and an acetone mole fraction of 0.75. The measurements of all controlled variables are assumed to be accurate and instantaneous.
5. Dynamic model The column model is comprised of the MESH (Material balance, Equilibrium, Sum of mole fractions, and Heat balance) equations. The heat balance is formulated using the pseudo-steady-state assumption (Seader & Henley, 1998, p. 695). Vapor-liquid equilibria are calculated using the Wilson equation for the liquidphase activity coefficient with interaction parameters provided by Safrit et al. (1995). The MESH equations are integrated using an implicit integrator with stepsize control, implemented in FORTRAN 90.
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
882 Table 1 C o n t r o l l e r specifications C-101
C-102
C-102"*
C-103
C-104
x sp
5 m3/h
0.75 +
xu xL z* zu zL
-
0.77 + 0.73 + 1.25 m 3 / h 2.5 m 3 / h 0.0 m 3 / h
Kc
-
-62.5
0.02 +
5 m3
0.98 ×
5 m3
0.04 + 0.001 + 1.25 m 3 / h 2.5 m 3 / h 0.0 m 3 / h
8 m3 2 m3 5.5 m3/h 8 m3/h 2.5 m 3 / h
0.999 × 0.96 × 2.5 m 3 / h 1.25 m 3 / h 0.0 m 3 / h
2 m3 8 m3 1.21 M W r 1.71 M W r 0.71 M W ~"
-64.1
0.92
64.1
C-105
0.17
** O p e r a t i o n in m o d e 2; + , m o l e f r a c t i o n o f a c e t o n e ; x , m o l e f r a c t i o n o f w a t e r ; V, r e b o i l e r h e a t d u t y .
6. Valve sizing and controller tuning The valve sizes and controller gains are shown in Table 1. Note that all of the controllers are proportional only, with the manipulated variable, z, set to: z = z* + Kc(x -
x sp)
(1)
where z* is the bias, Kc is the controller gain, x is the measured value of the controlled variable, and x sp is its set point. Because the composition set points are switched from mode-to-mode, and the water mole fraction in the bottoms product is below specification through much of the campaign, the use of integral action is problematic. Even when the integrals are reset during mode switchover, the integral action can saturate the valves as the initial product mole fractions may not be sufficiently close to the new set point. The controller gains are calculated by: zU -- 2 L
K¢
xU _ xL
(2)
such that the valves are closed, at the prespecified lower bound of the measured variable, x L, or fully open, at x u, as the controlled variable moves over its permissible range, z U - z L. For example, for controller C-104, when the mole fraction of water in the bottoms product is at its lower bound, 0.96, its valve is closed (at its lower bound). Likewise, when the water mole fraction is 0.999, the valve is fully open (at its upper bound), providing 2.5 m3/h. Note that the set point and the manipulated variable midpoint are the average of their upper and lower bounds. Valve sizes must be selected carefully for the semicontinuous extractive column because the flow rates vary appreciably from mode-to-mode. For the purposes of this discussion, a constant molar overflow (CMO) model is assumed. Specifically, the side draw flow rate, S, must equal the liquid flow to the top tray plus the extractive flow rate (Lmv-1 = L0 + E), the vapor flow rate off the top tray equals the boilup rate (Vl = VB), and the liquid flow rate leaving the bottom tray equals the feed flow rate (LN = F). At different stages of the campaign, the column operates either at total reflux
and reboil, or with just one product being withdrawn, or with both the distillate and bottoms products being withdrawn. Furthermore, the upper bounds on the product flow rates are selected to ensure adequate production, but must be sufficiently low to avoid large swings in the internal column flow rates during the campaign. Similarly, the maximum and minimum reflux and reboil rates must be selected to ensure satisfactory column operation; that is, to avoid entrainment and weeping. Consider first the distillate and bottoms flow rates. The lower bounds are zero (when the composition reaches its lower or upper bound). The upper bounds are 0.5F, where F is fixed under flow control. For a CMO model, this corresponds to a reboil ratio of 1.0 and a reflux ratio of zero. Hence, to maintain liquid on the trays in the rectifying section, the column cannot operate indefinitely with distillate and bottoms streams at their upper bounds. The upper bounds can be reduced, but the time for each cycle would increase. To keep the sump from being drained, the lower bound of the boilup rate is constrained such that: V~ < F - B u
(3)
Note that at larger boilup rates, VL, with the flow rate of the bottoms product at B U (under composition control), the sump empties. Also, to prevent sump overflow: VU > F
(4)
This constraint prevents overflow as the bottoms flow rate is reduced toward zero. For a continuous column, a turndown ratio (reduction of the boilup rate from the nominal value at steady state) of 50% is generally permissible for sieve trays, and a turn-up ratio of 20% is permissible. Higher turndown ratios are possible for bubble-cap and valve trays. For semicontinuous extractive distillation, since a steady-state does not exist, an alternate upper bound on the boilup rate is needed. An effective bound is found to be: VU < (1.2/0.5)V L
(5)
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
The upper and lower bounds on the reflux flow rates must ensure that the reflux drum does not overflow or drain. To prevent the reflux drum from draining: L L < VL
-
DU
(6)
Furthermore, to prevent the reflux drum from overflowing as the distillate flow rate approaches zero: YoU> V~
(7)
Note that it is desirable to reduce the flow rate of the extractive agent. When E>>F, noting that F > B u, the duration of mode 3 must be extended to remove the extractive agent. An extractive agent should be selected such that small quantities are needed.
7. Results
Trajectories for the streams and tanks over the 240-h (10-day) campaign are shown in Fig. 4A-G, and profi-
O' "0
......... 100
150
200
50
100
150
200
I
I
200
"
50
"'~
'
-
"
- -
= 10
r-.---. 0 '~
0
50
11111
150
50
100
150
,
,
,
I 50
100
' 150
' 200
i
t
I
I
-.,.~-40f/D =0 150
,
~ lOOJ- E
i
On .0 UI
/
E5 0/
I
I
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I.
0
150.
50 ,
100 ,
150 ,
200 ,
,
,'-
0
5O
IO0
150
200
,
I
I
time(hr) Fig. 4. Stream and tank trajectories. (A) Tank holdups. Line styles: ***, T1; - . - , T2; ..., T3, - - , T4; - - , T5. (B) Middle-vessel mole fractions. (C) Distillate mole fractions. Line styles (for B and C): "", acetone; - -, methanol; - - , water. (D) Distillate flow rate. (E) Bottoms flow rate (stream $6). (F) Sump and reflux d r u m holdups. Line styles: - - , sump; - - , reflux drum. (G) Internal column flow rates. Line styles: - - , boilup rate; - - , reflux flow rate.
883
les of the mole fractions in the column, at 20, 79, 81, and 110 h, are shown in the ternary diagrams of Fig. 5A-D. Operation over two cycles is shown, with the second cycle nearing completion after 10 days. The simulation begins in mode 1, after feed stream $3 is added to tank T1 to achieve a 50 m 3 holdup. The holdup in the middle vessel decreases as the azeotropic distillate is removed, as shown in Fig. 4A. Since the distillate is rich in acetone, the middle vessel becomes increasingly concentrated in methanol, as shown in Fig. 4B, and tank T2 fills, as shown in Fig. 4A. The composition controller, C-102 performs satisfactorily, maintaining the distillate near the azeotropic set point (75 mol% acetone) throughout mode 1. The distillate flow rate remains roughly constant during mode 1, as shown in Fig. 4D. Initially, the distillate flow rate is zero until its composition comes on specification. Also, towards the end of mode 1, the concentration of methanol in the column and middle-vessel is high, and hence, it becomes difficult to maintain the distillate composition near the azeotrope, the distillate flow rate is decreased, and the reflux ratio is increased. With most of the water removed in the previous cycle, the bottoms flow rate remains zero for the duration of mode 1, as shown in Fig. 4E. At the start of mode 1, Fig. 4F shows that the holdup in the reflux drum decreases sharply, as the distillate comes on specification. Maintenance of the holdup in the sump is less problematic in mode 1, as the flow rate of the bottoms product is zero. Note that due to the middle vessel and a full-liquid sidedraw, changes in the boilup rate change the holdup in the reflux drum, whereas changes in the reflux flow rate do not similarly affect the sump holdup. Consequently, as expected, the sump holdup leads the holdup in the reflux drum. Due to the direct proportional action of the level controllers, increases in drum and sump levels increase the boilup and reflux rates. Note that the boilup and reflux rates in Fig. 4G are roughly in phase with the holdups in Fig. 4F. Fig. 5A shows the profile of mole fractions on the trays at 20 h. The middle-vessel composition, represented by the large, solid circle, is 44 mol% acetone, 54 mol% methanol, and 2 mol% water. Due to the mass balances, the changes in the middle vessel composition are directed away from the distillate and bottoms product compositions. Gradually, the middle-vessel composition increases in methanol concentration, in the direction of the vector connecting the azeotrope to the middle-vessel composition. When the mole fraction of water in the bottoms product comes on-specification, the middle-vessel composition moves away from the water vertex. The middle vessel is discharged at 78 h, with a transition to mode 2, which occurs between 79 and 101 h (as well as 199 and 237 h). Observe in Fig. 4A the sharp decline in the middle-vessel holdup, as the holdup methanol builds in tank T4.
884
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
B
A
Ao~one ~ . S C
A ~ l o m 56.6 C
j
0.~
(M
O.4
O.6
J 0.11
0.8
0.2 W l * w 100.0 C
o.4
O.a-
o.ff
-
-
-
~.4
-
~
0.8
0.8
M ~ h a r ~ 64.7 C
W a l w 100.0
M~h~lo164.7 C
D
C
AcMofw 50.5 C
Acetone 56.5 C
i!ifi', N ~ -
0.~
Water 100.0 C
0.4
0.8
0.8 Methanol 64.7 C
W a t w 100.0 C
Methanol 64.7 C
Fig. 5. Mole fraction profiles. (A) 20 h (mode 1). (B) 79 h (mode 2). (C) 81 h (mode 2). (D) 110 h (mode 3). Middle-vesselcomposition, solid circle. Tray compositions, small circles. This is followed by a rise in the middle-vessel holdup, at the start of mode 2, as the contents of tank T2 are dropped into tank T1. Also, at this time, water is fed from tank T3 onto the second tray, and the holdup in tank T5 begins to increase as the methanol-water product is removed. During this period, the water holdup in tank T3 decreases. Note that shortly after mode 3 begins, most of the water is recovered. Stream $7 is also available to add fresh water, replacing water lost in the distillate. During mode 2, the middle vessel is increasingly concentrated in water, in a mixture with methanol and acetone, as water is added continuously from tank T3. Gradually, the acetone mole fraction decreases as the acetone-water distillate is removed. Fig. 4C shows that methanol is extracted successfully from the distillate during this period. However, water is added to the distillate, and consequently, an additional separation operation to recover the water is required.
Fig. 4D and E show large flow rates of the distillate and bottoms product during extraction mode 2, which correspond to reductions in the sump and reflux drum holdups and internal flow rates, as shown in Fig. 4F and G. The mole fraction profiles in Fig. 5B, at 79 h (when the distillate composition has not yet reached its specification - - 2 mol% methanol), and in Fig. 5C, at 81 h, show the effect of the extractive agent. The addition of water draws the distillate composition to the acetone-water axis. Through the addition of water, and the removal of the distillate and bottoms product, the middle-vessel composition moves towards the water-methanol axis. Mode 2 terminates when the concentration of acetone in the middle vessel is reduced to 5 mol%. The extractive portion of the campaign (mode 2) is highly nonlinear and requires careful attention. The tray location of the extractive feed, its flow rate, and the distillate flow rate, significantly affect the distillate
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
composition. The proposed configuration, in which the distillate flow rate is manipulated to control its composition, with the flow rate of the extractive feed held constant, is a simple, effective approach to perform the extractive distillation. In applying a proportional controller that manipulates the distillate flow rate to control its composition, it is assumed that the methanol mole fraction is measured accurately and instantaneously. The action of the proportional controller is to reduce the distillate flow rate when the concentration of methanol is too high, and increase its flow rate when more methanol is permissible. If the controlled variable were the acetone mole fraction, a decrease in the distillate flow rate would not necessarily increase the acetone mole fraction in the distillate, since its water mole fraction could increase. Higher mole fractions of acetone in the distillate, without a significant concentration of water, are possible. Safrit et al. (1995) attain distillate products that contain 96 mol% acetone. Our simulations, using the Wilson equation with the same interaction coefficients, provide similar results when the extractive feed is moved to a lower tray. However, most of remaining 4 mol% in the distillate is comprised of methanol, which is deemed unacceptable. The cycle is completed in mode 3, which begins at 101 h (and 237 h). As mode 3 begins, the set point of the distillate is returned to 75 mol% acetone. Initially, a small amount of the acetone-methanol azeotrope is returned to tank T2, although the distillate flow rate is zero for most of the period. The extractive agent is removed in the bottoms product during most of mode 3. As shown in Fig. 4A and E, the level of tank T3 increases as the flow rate of the bottoms product diminishes. Fig. 5D shows a typical mole fraction profile, at 110 h, during mode 3. During this period, the middle-vessel composition is directed away from the water vertex. Once the middle-vessel becomes concentrated in methanol, the cycle is repeated.
885
8. Conclusions It is concluded that: 1. The DB-control configuration, with simple P controllers, operates effectively in the semicontinuous separation of acetone and methanol with water as the extractive agent. 2. The extractive mode is carried out effectively through the manipulation of the distillate flow rate to control its composition, with the flow rate of the feed to the middle vessel held constant. 3. For valve sizing, the bounds on the distillate, bottoms, reflux, and boilup rates introduced herein, provide effective operation of the semicontinuous cycle.
Acknowledgements Partial support for this research was provided by NSF grant CTS96-32992 and is gratefully acknowledged.
References Finco, M. V., Luyben, W. L., & Polleck, R. E. (1989). Control of distillation columns with low relative volatilities. Industrial Engineering & Chemical Research, 28, 75-83. Phimister, J.R., & Seider, W.D. (1999). Semicontinuous, middle-vessel distillation. Foundations of Computer Aided, Process Design, in press. Phimister, J. R., & Seider, W. D. (2000a). Semicontinuous, pressureswing distillation. Industrial Engineering & Chemical Research, 39(1), 122-130. Phimister, J.R., & Seider, W.D. (2000b). Dual composition control in a semicontinuous distillation column. Industrial Engineering & Chemical Research, in press. Seader, J. D., & Henley, E. J. (1998). Separation process principles. NewYork: Wiley. Safrit, B. T., Westerberg, A. W., Diwekar, U., & Wahnschafft, O. M. (1995). Extending continuous conventional and extractive distillation feasibility insights to batch distillation. Industrial Engineering & Chemical Research, 34, 3257-3264. Safrit, B. T., & Westerberg, A. W. (1997). Improved operational policies for batch extractive distillation columns. Industrial Engineering & Chemical Research, 36, 436-443.
Computers &Chemical Engineering
Computers and Chemical Engineering 24 (2000) 879-885
www.elsevier.com/locate/compchemeng
Semicontinuous, middle-vessel, extractive distillation James R. Phimister, Warren D. Seider * Department of Chemical Engineering, University of Pennsylvania, Towne Building, Philadelphia, PA 19104/6393 USA
Abstract
A decentralized control configuration is proposed for the semicontinuous, extractive distillation of a low-boiling azeotropic mixture of acetone and methanol. The separation is performed in a middle-vessel column (MVC), having a large external middle vessel, from which the column is fed, and to which a full-liquid sidedraw from the stage above the feed tray is sent. The extractive agent, water, feeds the column on a scheduled basis to facilitate the separation. Based upon the simplicity of a decentralized configuration and the desire to avoid controller overrides, a DB-control configuration is selected. This configuration, in which the distillate flow rate is manipulated to control the composition of the distillate, and the bottoms flow rate is manipulated to control the composition of the bottoms product, has been widely labeled as inoperable. Herein, the configuration is shown to perform satisfactorily when a middle vessel with a full-liquid sidedraw is utilized. A cyclic campaign is simulated showing the satisfactory performance of the D B - M V C control configuration. The advantages of the control configuration are discussed and design specifics are provided. An analysis of the campaign, highlighting the problems overcome, is given. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Middle-vesselcolumn; Decentralizedcontrol; Dual-compositioncontrol
1. Introduction
Within the last decade, novel strategies have been proposed for the batch and semicontinuous distillation of nonideal mixtures (e.g. Safrit, Westerberg, Diwekar & Wahnschafft, 1995; Phimister & Seider, 2000a). With the advent of these strategies, new control methodologies must be considered. In this paper, it is shown that a decentralized control strategy, utilizing the uncommon DB-control configuration (in which the distillate flow rate is manipulated to control the composition of the distillate, and the bottoms flow rate is manipulated to control the composition of the bottoms product) performs effectively in the semicontinuous extractive separation of acetone and methanol, using water as the extractive agent. Fig. 1 shows the residue-curve map for this ternary system. For the extractive distillation of the low-boiling azeotropic mixture, acetone and methanol, Safrit and Westerberg (1997) provide a policy for the batch operation of a middle-vessel column (MVC). The MVC, in Fig. 2, is a column with a large internal or external vessel connected to the middle trays. The extractive * Corresponding author.
distillation policy begins when the middle vessel is charged with the process feed. Initially, the extractive agent is fed to one of the top trays while the column receives the middle-vessel feed. This allows for the removal of acetone in the distillate. Then, the flow of the extractive agent is discontinued and water is removed in the bottoms stream, with a near-azeotropic mixture removed in the distillate, and methanol concentrated in the middle vessel. Phimister and Seider (1999) propose operating the MVC semicontinuously in a process that maintains water in the sump throughout the campaign, with cycling between the removal of acetone in the distillate and the concentration and discharge of methanol from the middle vessel. The motivation for semicontinuous operation is the flexibility gained through the use of a single column, complemented by the benefits of automation in continuous operation; that is, a continuously fed column, continuous operation of the reboiler and condenser, and avoidance of column dumping and recharging. These benefits of automation reduce the labor-intensive operations commonly associated with batch processing. The proposed configuration is shown in Fig. 3.
0098-1354/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S0098-1354(00)00344-6
J.R. Phimister, W.D. Seider/ Computers and Chemical Engineering 24 (2000) 879-885
880
2. Policy The process cycles through three modes. 2.1. Mode I - - charging and methanol production
0.1
0.2 0.3 0.4 0.5 0.6 0.7 Molefrac M E T H A N O L
0.8
Stream $3, consisting of an equimolar mixture, recharges tank T1 (with 50 m 3 of the acetone-methanol mixture) when it is nearly empty. Methanol concentrates in the middle vessel, as the distillate, which approaches the low-boiling azeotrope of methanol and acetone (0.23 and 0.77 mole fractions at 55.4°C), is fed to tank T2, and water in the bottoms product is collected in tank T3 (loaded initially with 50 m 3 of water). When the methanol purity (0.98 mole fraction) is achieved in tank T1, its contents are dumped into product tank T4.
0.9
Fig. 1. Residue-curve map for acetone-methanol-water.
Middle
vessel Middle tray
2.2. Mode 2 - - extraction
After tank T1 is nearly emptied, the contents of tank T2 are dumped into tank T1, and hence, the feed to the column is near the azeotropic composition. Water, the extractive agent, is fed near the top of the column in stream $8 at a fixed flow rate (2 m3/h), the set point of composition controller C-102 is adjusted to 0.02 mole
Fig. 2. Middle-vessel column.
J
~
P
I
T1
I
C-101
1
N
¢,-1~1
" t>,0
LI
Fig. 3. Configuration for the separation of methanol and acetone.
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
fraction methanol (assuming the mole fraction of methanol impurity in the distillate can be measured accurately and instantaneously), and an acetone-water distillate is collected in product tank T5. As extractive agent is added, water and methanol concentrate in the middle vessel, the mole fraction of water in the sump meets its specification (0.98), and water in the bottoms product is sent to tank T3. 2.3. M o d e 3 - -
water recovery
After sufficient acetone is collected in tank T5, the cycling of water is discontinued. The set point of C102 is retumed to near the azeotropic composition (0.75 mole fraction of acetone), and the nearazeotropic distillate is sent to tank T2 in stream $5. Water, still present in the middle vessel, continues to be removed in the bottoms product until the water mole fraction in the sump falls below 0.96, after which valve C-104 is closed. When the concentration of methanol is sufficiently high in tank T1, the contents of tank T1 are collected in tank T4, tank T1 is recharged with the equimolar feed, and the process returns to mode 1. Note that this policy differs from the batch policy of Safrit and Westerberg (1997) in that the extractive portion of the campaign is performed using the previously-collected azeotropic charge, rather than the equimolar feed stream.
3. Control configuration selection Since there are mole fraction specifications for both the distillate and bottoms product, to achieve successful operation of the proposed policy, a dual-composition control strategy is required. However, because the valves on the distillate and/or bottoms streams are closed from time-to-time during a cycle, common control configurations for continuous distillation towers are ineffective for the duration of a cycle. These include the L VB-control configuration (in which the reflux rate controls the distillate composition and the boilup rate controls the composition of the bottoms product), the D VB-control configuration and the L / D , VB/B (reflux-reboil ratio) control configuration. For example, when the flow rate of the bottoms product is zero, the inventory in the sump must be controlled using VB, which consequently cannot be used for composition control. Note that this drawback is circumvented with the less common on-demand control configuration, in which the sump level is controlled by adjusting the feed flow rate. In contrast, the DB-control configuration does not require any overrides during the semicontinuous campaign, as inventory control is maintained by the boilup
881
and reflux flow rates throughout the campaign. With the exception of a few industrial examples (Finco, Luyben & Polleck, 1989), this configuration is used rarely in practice. Phimister and Seider (2000b) contend that the primary reasons for not implementing a DB-control configuration are due to adverse interactions between the level controllers. For a column that is fed continuously and does not have a full-liquid sidedraw, when either of the product compositions are below specification, the column inventory builds (as the product removal rate is less than the feed rate), and the sump or reflux drum overflows. However, for the D B - M V C control configuration, with a full-liquid sidedraw, the sump and reflux drum do not overflow when the product compositions are off-specification.
4. Process design The process feed (to the middle vessel) is a saturated liquid at 1 atm comprised of an equimolar mixture of methanol and acetone. The column has 31 stages, including a condenser and a reboiler, with a l-m diameter. The feed to the column, from the middle vessel, is to tray 21, counting from the top of the column. The feed is held constant at 5 m3/h under flow control for the duration of the campaign. During extraction mode 2, the flow rate of water in stream $8 is held constant at 2 m3/h. A full-liquid sidedraw from tray 20 is fed to the middle vessel. The sump and reflux drum have capacities of 10 m 3 with set points for the holdup volume at 5 m 3. All tanks have capacities of 100 m 3 and the middle vessel, after being charged with the process feed, contains 50 m 3. Tank T3 is filled initially with 50 m 3 of water. The set point for the water mole fraction in the bottoms product is 0.98. As noted previously, the set points for the distillate shift between a methanol mole fraction of 0.02 and an acetone mole fraction of 0.75. The measurements of all controlled variables are assumed to be accurate and instantaneous.
5. Dynamic model The column model is comprised of the MESH (Material balance, Equilibrium, Sum of mole fractions, and Heat balance) equations. The heat balance is formulated using the pseudo-steady-state assumption (Seader & Henley, 1998, p. 695). Vapor-liquid equilibria are calculated using the Wilson equation for the liquidphase activity coefficient with interaction parameters provided by Safrit et al. (1995). The MESH equations are integrated using an implicit integrator with stepsize control, implemented in FORTRAN 90.
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
882 Table 1 C o n t r o l l e r specifications C-101
C-102
C-102"*
C-103
C-104
x sp
5 m3/h
0.75 +
xu xL z* zu zL
-
0.77 + 0.73 + 1.25 m 3 / h 2.5 m 3 / h 0.0 m 3 / h
Kc
-
-62.5
0.02 +
5 m3
0.98 ×
5 m3
0.04 + 0.001 + 1.25 m 3 / h 2.5 m 3 / h 0.0 m 3 / h
8 m3 2 m3 5.5 m3/h 8 m3/h 2.5 m 3 / h
0.999 × 0.96 × 2.5 m 3 / h 1.25 m 3 / h 0.0 m 3 / h
2 m3 8 m3 1.21 M W r 1.71 M W r 0.71 M W ~"
-64.1
0.92
64.1
C-105
0.17
** O p e r a t i o n in m o d e 2; + , m o l e f r a c t i o n o f a c e t o n e ; x , m o l e f r a c t i o n o f w a t e r ; V, r e b o i l e r h e a t d u t y .
6. Valve sizing and controller tuning The valve sizes and controller gains are shown in Table 1. Note that all of the controllers are proportional only, with the manipulated variable, z, set to: z = z* + Kc(x -
x sp)
(1)
where z* is the bias, Kc is the controller gain, x is the measured value of the controlled variable, and x sp is its set point. Because the composition set points are switched from mode-to-mode, and the water mole fraction in the bottoms product is below specification through much of the campaign, the use of integral action is problematic. Even when the integrals are reset during mode switchover, the integral action can saturate the valves as the initial product mole fractions may not be sufficiently close to the new set point. The controller gains are calculated by: zU -- 2 L
K¢
xU _ xL
(2)
such that the valves are closed, at the prespecified lower bound of the measured variable, x L, or fully open, at x u, as the controlled variable moves over its permissible range, z U - z L. For example, for controller C-104, when the mole fraction of water in the bottoms product is at its lower bound, 0.96, its valve is closed (at its lower bound). Likewise, when the water mole fraction is 0.999, the valve is fully open (at its upper bound), providing 2.5 m3/h. Note that the set point and the manipulated variable midpoint are the average of their upper and lower bounds. Valve sizes must be selected carefully for the semicontinuous extractive column because the flow rates vary appreciably from mode-to-mode. For the purposes of this discussion, a constant molar overflow (CMO) model is assumed. Specifically, the side draw flow rate, S, must equal the liquid flow to the top tray plus the extractive flow rate (Lmv-1 = L0 + E), the vapor flow rate off the top tray equals the boilup rate (Vl = VB), and the liquid flow rate leaving the bottom tray equals the feed flow rate (LN = F). At different stages of the campaign, the column operates either at total reflux
and reboil, or with just one product being withdrawn, or with both the distillate and bottoms products being withdrawn. Furthermore, the upper bounds on the product flow rates are selected to ensure adequate production, but must be sufficiently low to avoid large swings in the internal column flow rates during the campaign. Similarly, the maximum and minimum reflux and reboil rates must be selected to ensure satisfactory column operation; that is, to avoid entrainment and weeping. Consider first the distillate and bottoms flow rates. The lower bounds are zero (when the composition reaches its lower or upper bound). The upper bounds are 0.5F, where F is fixed under flow control. For a CMO model, this corresponds to a reboil ratio of 1.0 and a reflux ratio of zero. Hence, to maintain liquid on the trays in the rectifying section, the column cannot operate indefinitely with distillate and bottoms streams at their upper bounds. The upper bounds can be reduced, but the time for each cycle would increase. To keep the sump from being drained, the lower bound of the boilup rate is constrained such that: V~ < F - B u
(3)
Note that at larger boilup rates, VL, with the flow rate of the bottoms product at B U (under composition control), the sump empties. Also, to prevent sump overflow: VU > F
(4)
This constraint prevents overflow as the bottoms flow rate is reduced toward zero. For a continuous column, a turndown ratio (reduction of the boilup rate from the nominal value at steady state) of 50% is generally permissible for sieve trays, and a turn-up ratio of 20% is permissible. Higher turndown ratios are possible for bubble-cap and valve trays. For semicontinuous extractive distillation, since a steady-state does not exist, an alternate upper bound on the boilup rate is needed. An effective bound is found to be: VU < (1.2/0.5)V L
(5)
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
The upper and lower bounds on the reflux flow rates must ensure that the reflux drum does not overflow or drain. To prevent the reflux drum from draining: L L < VL
-
DU
(6)
Furthermore, to prevent the reflux drum from overflowing as the distillate flow rate approaches zero: YoU> V~
(7)
Note that it is desirable to reduce the flow rate of the extractive agent. When E>>F, noting that F > B u, the duration of mode 3 must be extended to remove the extractive agent. An extractive agent should be selected such that small quantities are needed.
7. Results
Trajectories for the streams and tanks over the 240-h (10-day) campaign are shown in Fig. 4A-G, and profi-
O' "0
......... 100
150
200
50
100
150
200
I
I
200
"
50
"'~
'
-
"
- -
= 10
r-.---. 0 '~
0
50
11111
150
50
100
150
,
,
,
I 50
100
' 150
' 200
i
t
I
I
-.,.~-40f/D =0 150
,
~ lOOJ- E
i
On .0 UI
/
E5 0/
I
I
I
I.
0
150.
50 ,
100 ,
150 ,
200 ,
,
,'-
0
5O
IO0
150
200
,
I
I
time(hr) Fig. 4. Stream and tank trajectories. (A) Tank holdups. Line styles: ***, T1; - . - , T2; ..., T3, - - , T4; - - , T5. (B) Middle-vessel mole fractions. (C) Distillate mole fractions. Line styles (for B and C): "", acetone; - -, methanol; - - , water. (D) Distillate flow rate. (E) Bottoms flow rate (stream $6). (F) Sump and reflux d r u m holdups. Line styles: - - , sump; - - , reflux drum. (G) Internal column flow rates. Line styles: - - , boilup rate; - - , reflux flow rate.
883
les of the mole fractions in the column, at 20, 79, 81, and 110 h, are shown in the ternary diagrams of Fig. 5A-D. Operation over two cycles is shown, with the second cycle nearing completion after 10 days. The simulation begins in mode 1, after feed stream $3 is added to tank T1 to achieve a 50 m 3 holdup. The holdup in the middle vessel decreases as the azeotropic distillate is removed, as shown in Fig. 4A. Since the distillate is rich in acetone, the middle vessel becomes increasingly concentrated in methanol, as shown in Fig. 4B, and tank T2 fills, as shown in Fig. 4A. The composition controller, C-102 performs satisfactorily, maintaining the distillate near the azeotropic set point (75 mol% acetone) throughout mode 1. The distillate flow rate remains roughly constant during mode 1, as shown in Fig. 4D. Initially, the distillate flow rate is zero until its composition comes on specification. Also, towards the end of mode 1, the concentration of methanol in the column and middle-vessel is high, and hence, it becomes difficult to maintain the distillate composition near the azeotrope, the distillate flow rate is decreased, and the reflux ratio is increased. With most of the water removed in the previous cycle, the bottoms flow rate remains zero for the duration of mode 1, as shown in Fig. 4E. At the start of mode 1, Fig. 4F shows that the holdup in the reflux drum decreases sharply, as the distillate comes on specification. Maintenance of the holdup in the sump is less problematic in mode 1, as the flow rate of the bottoms product is zero. Note that due to the middle vessel and a full-liquid sidedraw, changes in the boilup rate change the holdup in the reflux drum, whereas changes in the reflux flow rate do not similarly affect the sump holdup. Consequently, as expected, the sump holdup leads the holdup in the reflux drum. Due to the direct proportional action of the level controllers, increases in drum and sump levels increase the boilup and reflux rates. Note that the boilup and reflux rates in Fig. 4G are roughly in phase with the holdups in Fig. 4F. Fig. 5A shows the profile of mole fractions on the trays at 20 h. The middle-vessel composition, represented by the large, solid circle, is 44 mol% acetone, 54 mol% methanol, and 2 mol% water. Due to the mass balances, the changes in the middle vessel composition are directed away from the distillate and bottoms product compositions. Gradually, the middle-vessel composition increases in methanol concentration, in the direction of the vector connecting the azeotrope to the middle-vessel composition. When the mole fraction of water in the bottoms product comes on-specification, the middle-vessel composition moves away from the water vertex. The middle vessel is discharged at 78 h, with a transition to mode 2, which occurs between 79 and 101 h (as well as 199 and 237 h). Observe in Fig. 4A the sharp decline in the middle-vessel holdup, as the holdup methanol builds in tank T4.
884
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
B
A
Ao~one ~ . S C
A ~ l o m 56.6 C
j
0.~
(M
O.4
O.6
J 0.11
0.8
0.2 W l * w 100.0 C
o.4
O.a-
o.ff
-
-
-
~.4
-
~
0.8
0.8
M ~ h a r ~ 64.7 C
W a l w 100.0
M~h~lo164.7 C
D
C
AcMofw 50.5 C
Acetone 56.5 C
i!ifi', N ~ -
0.~
Water 100.0 C
0.4
0.8
0.8 Methanol 64.7 C
W a t w 100.0 C
Methanol 64.7 C
Fig. 5. Mole fraction profiles. (A) 20 h (mode 1). (B) 79 h (mode 2). (C) 81 h (mode 2). (D) 110 h (mode 3). Middle-vesselcomposition, solid circle. Tray compositions, small circles. This is followed by a rise in the middle-vessel holdup, at the start of mode 2, as the contents of tank T2 are dropped into tank T1. Also, at this time, water is fed from tank T3 onto the second tray, and the holdup in tank T5 begins to increase as the methanol-water product is removed. During this period, the water holdup in tank T3 decreases. Note that shortly after mode 3 begins, most of the water is recovered. Stream $7 is also available to add fresh water, replacing water lost in the distillate. During mode 2, the middle vessel is increasingly concentrated in water, in a mixture with methanol and acetone, as water is added continuously from tank T3. Gradually, the acetone mole fraction decreases as the acetone-water distillate is removed. Fig. 4C shows that methanol is extracted successfully from the distillate during this period. However, water is added to the distillate, and consequently, an additional separation operation to recover the water is required.
Fig. 4D and E show large flow rates of the distillate and bottoms product during extraction mode 2, which correspond to reductions in the sump and reflux drum holdups and internal flow rates, as shown in Fig. 4F and G. The mole fraction profiles in Fig. 5B, at 79 h (when the distillate composition has not yet reached its specification - - 2 mol% methanol), and in Fig. 5C, at 81 h, show the effect of the extractive agent. The addition of water draws the distillate composition to the acetone-water axis. Through the addition of water, and the removal of the distillate and bottoms product, the middle-vessel composition moves towards the water-methanol axis. Mode 2 terminates when the concentration of acetone in the middle vessel is reduced to 5 mol%. The extractive portion of the campaign (mode 2) is highly nonlinear and requires careful attention. The tray location of the extractive feed, its flow rate, and the distillate flow rate, significantly affect the distillate
J.R. Phimister, W.D. Seider / Computers and Chemical Engineering 24 (2000) 879-885
composition. The proposed configuration, in which the distillate flow rate is manipulated to control its composition, with the flow rate of the extractive feed held constant, is a simple, effective approach to perform the extractive distillation. In applying a proportional controller that manipulates the distillate flow rate to control its composition, it is assumed that the methanol mole fraction is measured accurately and instantaneously. The action of the proportional controller is to reduce the distillate flow rate when the concentration of methanol is too high, and increase its flow rate when more methanol is permissible. If the controlled variable were the acetone mole fraction, a decrease in the distillate flow rate would not necessarily increase the acetone mole fraction in the distillate, since its water mole fraction could increase. Higher mole fractions of acetone in the distillate, without a significant concentration of water, are possible. Safrit et al. (1995) attain distillate products that contain 96 mol% acetone. Our simulations, using the Wilson equation with the same interaction coefficients, provide similar results when the extractive feed is moved to a lower tray. However, most of remaining 4 mol% in the distillate is comprised of methanol, which is deemed unacceptable. The cycle is completed in mode 3, which begins at 101 h (and 237 h). As mode 3 begins, the set point of the distillate is returned to 75 mol% acetone. Initially, a small amount of the acetone-methanol azeotrope is returned to tank T2, although the distillate flow rate is zero for most of the period. The extractive agent is removed in the bottoms product during most of mode 3. As shown in Fig. 4A and E, the level of tank T3 increases as the flow rate of the bottoms product diminishes. Fig. 5D shows a typical mole fraction profile, at 110 h, during mode 3. During this period, the middle-vessel composition is directed away from the water vertex. Once the middle-vessel becomes concentrated in methanol, the cycle is repeated.
885
8. Conclusions It is concluded that: 1. The DB-control configuration, with simple P controllers, operates effectively in the semicontinuous separation of acetone and methanol with water as the extractive agent. 2. The extractive mode is carried out effectively through the manipulation of the distillate flow rate to control its composition, with the flow rate of the feed to the middle vessel held constant. 3. For valve sizing, the bounds on the distillate, bottoms, reflux, and boilup rates introduced herein, provide effective operation of the semicontinuous cycle.
Acknowledgements Partial support for this research was provided by NSF grant CTS96-32992 and is gratefully acknowledged.
References Finco, M. V., Luyben, W. L., & Polleck, R. E. (1989). Control of distillation columns with low relative volatilities. Industrial Engineering & Chemical Research, 28, 75-83. Phimister, J.R., & Seider, W.D. (1999). Semicontinuous, middle-vessel distillation. Foundations of Computer Aided, Process Design, in press. Phimister, J. R., & Seider, W. D. (2000a). Semicontinuous, pressureswing distillation. Industrial Engineering & Chemical Research, 39(1), 122-130. Phimister, J.R., & Seider, W.D. (2000b). Dual composition control in a semicontinuous distillation column. Industrial Engineering & Chemical Research, in press. Seader, J. D., & Henley, E. J. (1998). Separation process principles. NewYork: Wiley. Safrit, B. T., Westerberg, A. W., Diwekar, U., & Wahnschafft, O. M. (1995). Extending continuous conventional and extractive distillation feasibility insights to batch distillation. Industrial Engineering & Chemical Research, 34, 3257-3264. Safrit, B. T., & Westerberg, A. W. (1997). Improved operational policies for batch extractive distillation columns. Industrial Engineering & Chemical Research, 36, 436-443.