Id.Eng. Chem. Process Des. Dev. 1981, 20,
responds to the depth from the surface. It is obviously seen that the limestone with poor reactivity, Le., inactive limestone, gives high Al/Ca intensity. Observation of Surface of Limestone. Limestones treated by the solutions no. 1,2, and 5 in Table I11 were provided for the electron microscopic observation. Figure 7 shows the electron micrographs. It is clearly seen that the surface of the limestone treated by the solution of no. 2 is covered with a large number of small particles. The diameter of the particle is calculated to be 0.1-0.3 pm. It is supposed that the dissolution of limestone into the absorbing liquid is restrained by the formation of these particles. The pH of the absorbing liquid is lowered due to the restraint of the dissolution, which in turn results in the decrease of SO2 absoring ability of the liquid. The particles formed on the surface of limestone contain Ca, Al, and F and the F/A1 mole ratio is approximately 5. Ando has studied the F removal from waste water using calcium hydroxide. Calcium forms an insoluble compound with F- in the presence of aluminum compound (Ando, 1974). The compound is known as fluoroapatite. It is also known that calcium forms various insoluble fluoroapatite with F- in the presence of phosphate (Ferguson, 1949; Berry, 1967; Prener, 1967; Ravex, 1967; Drehmel, 1972). The small particle is thought to be an apatite such as CaA1F3(0H)2CaF2.
147
147-153
Literature Cited Ando. J. Gypsum Llme(Japan) 1974, No. 133, 4. Ando, J. Kogal To Talsaku 1976, 12(8), 75. Berry, E. E. J . Inorg. Nucl. Chem. 1967, 20, 1585. Bjede, I.; Bergtsson, S.; FarnMst, K. Chem. Eng. Scl. 1972, 27, 1853. Borgwardt, R. H. EPA-050/2-74-1289, U.S. Envkonmental Protection AgenCY, 1974, pp 225-240. Cronkright, W. A.; Leddy, W. J. Envkon. Scl. Technol. 1976, 70, 509. Drehmel, D. C., paper presented at 2nd International Sympodum for Llmel Limestone Wet Scrubbing, New Orleans, La., Nov 8-12, 1971 (Procw& ings issued by EPA, APTD-1101 1 107 (1971); paper presented at 05th Annual Meetlng of APCA, Paper No. 72-105, June 12-18, 1972. Epsteln, M. EPA-000/2-75-050, U.S. Envlronmental Protection Agency, 1975. Ferguson, J. Am. Mlneral. 1949, 34, 385. Hollinden, G. A.; Moore, N. D.; Schultz, J. J., paper presented at 4th Annual Environmental Engineering and Science Conference, Loulsvllk, Ky., Mer 1974. McMichael. W. J.; Fan, L. S.; Wen, C. Y. Ind. Eng. Chem. Process Des. Dev. 1976, 15, 459. Ponder, W. H. Thermal Power Conference, Washignton, D. C., Oct 1974. Prener, J. S. J . E/ectrochem. Scl. 1967, 174(1), 77. Princiotta. F. T. Chem. Eng. prog. 1976, 74(2). 58. Ramachandran, P. A.; Sharma. M. M. Chem. Eng. Scl. 1969, 24, 1681. Ravez, J., Hagenmuiler, P. Buu. Soc. Chem. Fr. 1967, 7067(7), 2545. Rochelle. 0. T.; King, C. J. I d . Eng. Chem. Fundem. lP77, 76(l), 07. Rosenberg, H. S.; Engdahl, R. B.; Oxiey, J. H.; Genco, J. M. Chem. Eng. Frog. 1975, 71(5), 00. Sada,E. et ai.. Prephts fw 41th Annual Meeting of the Society of Chemlcal Engineers, Japan, 1970, p 250. Uchida, S.; Wen, C. Y.; McMichael, W. J. Ind. ‘Eng. Chem. Frocess Des. Dev. 1975, 15, 88. Uchida, S.; KoMe, S.; Shindo, M. Chem. Eng. Scl. 1975, 30. 044.
Receiued for reuiew March 12, 1980 Accepted August 21, 1980
Control of an Energy-Conserving Prefractionator/Sidestream Column Distillation System Nlckos P. Doukas and Wllllam L. Luyben’ Department of Chemical Engineering, Lehlgh University, Bethlehem, Pennsylvanla 180 15
Two alternative control schemes (the “L”-scheme and the ‘ID”-scheme)were studied for a twoGolumn configuration consisting of a prefractionator column and a sidestream column. The system separated a ternary mixture into three moderately pure product streams with four compositions controlled simultaneously. The L-scheme utilized manipulation of the sidestream drawoff tray location to control one of the sidestream compositions. The D-scheme used the overhead distillate product rate from the prefractionator to control one of the sidestream compositions. Simulation results predicted that both schemes give stable and effective control of the system for moderate disturbances. The Dscheme handled large changes in the lightest component in the feed better, while the L-schame handled large changes in the heaviest component better. The D-scheme is probably preferable under most conditions because it is easier to implement.
Introduction Complex distillation systems involving sequences of conventional and sidestream columns are becoming more popular because they reduce energy requirements. However, they are potentially more difficult to operate and control. Luyben (1966) and Buckley (1969) have discussed qualitatively the problem of controlling single sidestream columns. Tyreus and Luyben (1975) have presented simulation and experimental results for the control of a single sidestream column separating a binary mixture into three product streams. Doukas and Luyben (1978a) presented simulation results for the control of a single sidestream column separating a ternary mixture into three product streams. The purpose of this paper is to present results of sim0196-4305/81/1120-0147$01.00/0
ulation studies of a prefractionator/liquid sidestream two-column system separating a ternary mixture. A feed containing 40% benzene, 40% toluene, and 20% o-xylene is fed into the prefractionator, which makes a rough preliminary split and feeds its overhead and bottom products to the sidestream column at two different feed-tray locations. The three product streams coming out of the sidestream column are (1)a benzene distillate with 4.8% toluene impurity, (2) a liquid toluene sidestream with 4.8% benzene and 5% o-xylene impurities, and (3) a xylene bottoms with 5% toluene impurity. This system was chosen because it was shown to be the most eoonomical configuration for this separation (Doukas and Luyben, 1978b). The specific numerical example studied in this paper is the ternary system benzene, toluene, and o-xylene 0 1980 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
I
/
I
\
I
T==F-t-; ;;.IO
xo20)g.o
--
o.;ut
;o0-
120
.O
LS
IO= 190 em
Figure 3. o-Xylene vs. LS under the same conditions as in Figure 2.
XB2(3)..9 5
Figure 1. Steady-state design of the prefractionator/sidestream column (all flow rates in kg-mol/h).
Figure 4. o-Xylene vs. LS for different distillate rates leaving the prefractionator, when XF(1) = XF(2) = 0.30, XF(3) = 0.40, and NS = 20.
LS
Figure 2. Benzene vs. LS for different sidestream tray locations, when X F ( 1 ) = XF(2) = 0.30, X F ( 3 ) = 0.40, and D1 = 156.5 kgmol/h.
(BTX). In addition to being of wide industrial importance in its own right, the BTX system is typical of a broad class of commercially important distillation systems such as petroleum light-ends units and petrochemical feed, product, and recycle purification processes. Based on past experience, the results of this study should be generally applicable to a broad class of distillation separation systems. The relative volatilities, feed compositions, and product purities are fairly typical of many important industrial processes. The alternative control schemes evaluated in this paper should be useful in many industrial systems.
I
a0
8s
IO1
35
115
LS
Figure 5. Benzene vs. LS under the same conditions as in Figure 4.
Description of the System The columns studied are shown in Figure 1. Saturated liquid feed is introduced onto tray 10 of a 19-tray column (prefractionator). Its two product streams are fed as saturated liquids on trays 37 and 16 of a 40-tray sidestream column. A liquid sidestream is withdrawn from tray 20.
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 148 Table I. Controller Settings for thg L-Scheme controlled manipulative final settings: K , rI, min
1
0. CI3S
XB2
XS1
XS3
QB
LS
0.12 30
0.222 30
CC3 R (NS) 0.10 2.0
XD2
34
30
IT I
I56
01
Figure 6. Sidestream composition changes vs. D1 when N S = 20 and LS = 112 kg-mol/h (Line A correspondsto X F ( 1 ) = X F ( 2 ) = 0.40, X F ( 3 ) = 0.20, and line B to X F ( 1 ) = X F ( 2 ) = 0.38, X F ( 3 ) = 0.24 cases.)
Figure 9. L-scheme.
XSISP l o w s i g n a l selector
Figure 7. Control scheme for the liquid sidestream (L-scheme).
XS3SP
.et
.49
INPUT T O
.a4
.6S
FlXEO
GAIN
I.
RELAYS
Figure 8. Fixed gain relays signals (atm).
Both columns operate a t atmospheric pressure. Column pressure drop was neglected. For the first and second column, respectively, we have heat inputs of 2 X loe and 1.7 X lo6 kcal/h, diameters of 200 and 190 cm, tray liquid molar holdups ranging from 1.4 to 1.8 and 1.3 to 1.7 kg-mol,
Figure 10. D-scheme.
I
holdups in the reflux drums of 22.8 and 19.7 kg-mol, holdups in the column base of 23.3 and 19.3 kg-mol, a i d reflux ratios of 0.70 and 1.16. Tray efficiencies of 100%, tray weir heights of 3.8 cm, saturated liquid feed and re-
150
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
Table 11. Controller Settings for t h e D-Scheme controlled manipulative final settings: K , T I ,min
XD2 R
Qg
XS1 LS
XS3 D1
0.12
0.443
30
30
0.18 2 110 34
X32
!-I--= +-I?
*Is----
s
E-
-
?
?
9
I?
-.5 -
-
?
9-
*Ip,
9
s
:9
e
?
0.0
s -1
-73
1.5
2.25
3.0
TIME(HRS) Figure 13. Composition changes vs. time for a composition change of +12.5% benzene in the feed (L-scheme).
? 0.0
-75
1.5
2.25
3.0
TIPIE(HRS1 Figure 11. Composition changes vs. time for a composition change of +50% o-xylene in the feed (L-scheme).
io--" 4 !
+-In
U
7
2
e
;
ID
b
i
:L e
0.0
.75
1.5
2.25
3.0
TIHE(HRS1 Figure 14. Changes of the manipulative variables vs. time for a composition change of +12.5% benzene in the feed (L-scheme).
9 0.0
-75
1.5
2-25
3.0
TIME[HRSl Figure 12. Changes of the manipulative variables vs. time for a composition change of +50% o-xylene in the feed (L-scheme).
flux, total condensers, and partial reboilers are assumed. Top and bottom temperatures are 121 and 157 "C for the first column, and 114 and 175 OC for the second column. System Modeling and Simulation Since there are three components, three continuity equations are required to describe each of the 59 trays (19 + 40), the column bases (2), and the reflux drums (2). A total of 189 (63 X 3) nonlinear ordinary differential equations, plus the nonlinear algebraic equations for vapor-liquid equilibrium, were solved simultaneously via digital simulation. Tray hydraulics were approximated by a linearized form of the Francis weir formula. A Euler
integration algorithm was used with a step size of 2.5 s. A more rigorous energy equation [Doukas and Luyben (1978a),Distefano (1968),and McCune and Gallier (1973)l was used. Steady-State Analysis The possibility of using a control scheme (hereafter called the L-scheme) for the sidestream composition, similar to the one used in previous work [Tyreus and Luyben (1975) and Doukas and Luyben (1978a)],was fmt explored through a steady-state analysis. Liquid sidestream rate was changed as well as the sidestream drawoff location, while the overhead and bottom compositions were held constant by manipulating reflux rate and heat input, respectively. Figures 2 and 3 show results for the case with o-xylene feed concentration increased from 20% to 40% (30% benzene, 30% toluene, and 40% o-xylene). The desired values of benzene and o-xylene in the sidestream are also shown (line C) in both figures. With this feed
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
151
9
-1
*pI,
E!
!2
? 0.0
.76
1.5
2.25
3.0
.75
0.0
TIME[ HRS I
1.6
2. 25
3.0
TIflE(HRS1
Figure 15. Composition changes vs. time for a composition change of +50% o-xylene in the feed (D-scheme).
Figure 17. Composition changes vs. time for a composition change of +12.5% benzene in the feed (D-scheme).
E!
K?
!*
0
J, E!
P
"+ il Q
I
-
V I 1
J ISn
2.26 0.0
.75
3.0
1.6
T IMEL HRS I
Figure 16. Changes of the manipulative variables vs. time for a composition change of 50% o-xylene in the feed (D-scheme).
disturbance the uncontrolled open-loop system with a sidestream flow rate corresponding to its steady-state value (point A in both figures) gives a sidestream composition corresponding to point B. By decreasing the sidestream rate (LS)we can bring benzene composition on specification (LS N 87, Figure 2). Then by drawing the sidestream off at a tray higher in the column and reducing the LS rate a little more we can bring the o-xylene concentration on specification (Figure 3). Hence, this control scheme, which leaves the first column uncontrolled, seems capable of handling fairly big disturbances in feed composition from a steady-state standpoint. The L control scheme considered above was based on holding the distillate rate of the prefractionator constant. Since this distillate rate can be used for control purposes, an alternative control scheme (hereafter called the Dscheme) was evaluated. A steady-state analysis was first made when the distillate rate from the prefractionator was
0.0
I
.75
I
1.5
I
2.25
I 3.0
TIME( HRS I
Figure 18. Changes of the manipulative variables vs. time for a composition change of +12.5% benzene in the feed (D-scheme).
varied. The effect on the sidestream composition of changes of the sidestream rate was also explored. Overhead and bottom compositions of the sidestream column were kept on specification by manipulating reflux rate and heat input in the sidestream column. Reflux rate in the prefractionator is held constant at its base-case value. Figures 4 and 5 show the results for a change in o-xylene feed concentration from 20% to 40% (30% benzene, 30% toluene, and 40% o-xylene). Sidestream drawoff is from tray 20. Points A and B (Figures 4 and 5) correspond to the new steady-state sidestream compositions with no change in sidestream flow rate or sidestream drawoff tray location. The desired sidestream composition lies along line C. By manipulating LS we can bring benzene concentration on specification. However, changing the distillate rate from the prefractionator (Dl) cannot be used to achieve the desired o-xylene concentration in the sidestream, at least for such a big feed composition disturb-
152
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
-
P
d
.l
g
'1
X
c+-. E .?Jc--P
-
M
x v)
9
P
w
-?
x v)
-
*ITl
s
4
01
E-
52
.75
-b
9
?
0.0
'1
1.5
2.25
J5
2.25
3.0
TIME[ HRS I
TItlECHRS I
Figure 19. Composition changes vs. time for a composition change of +25% benzene in the feed (D-scheme).
1 s
0.0
3.0
Figure 21. Composition changes vs. time for a composition change of +loo% o-xylene in the feed (L-scheme).
rs 1
.
E
F 5 1
4
1 I D 1
0.0
T IfiE [ HRS I Figure 20. Changes of the manipulative variables vs. time for a composition change of +25% benzene in the feed (D-scheme).
ance. Figure 6 shows the effect of changing the prefractionator distillate rate on the sidestream composition for constant LS and N S , for smaller changes of feed composition. Because this second control scheme is easier to implement, its rangeability and performance were also explored. Control of the Prefractionator/Sidestream Column The four compositions to be controlled in the three product streams of the sidestream column were (1)toluene impurity in the distillate; (2) benzene impurity in the liquid sidestream; (3) o-xylene impurity in the liquid sidestream; and, (4) toluene impurity in the bottoms. Base level in the first column (prefractionator) was controlled by manipulating bottoms flow rate (Bl). Reflux-drum level in the same column was controlled by manipulating heat input (QBl)to the prefractionator re-
I
.75
I
1.5
I
2.25
I
3.0
TINE( HRS I
Figure 22. Changes of the manipulative variables vs. time for a composition change of +loo% o-xylene in the feed (L-scheme).
boiler. In all cases the prefractionator reflux flow rate (or reflux to feed ratio) was held constant. Base level in the sidestream column was controlled by manipulating bottoms flow rate (B2). Toluene impurity in the sidestream column bottoms was controlled by manipulating heat input to the sidestream column reboiler (QB). &flux-drum level in the sidestream column was controlled by manipulating distillate rate (02). Toluene impurity in the sidestream column distillate was controlled by manipulating reflux flow rate ( R ) to the sidestream column. A. L-Scheme. Impurities of o-xylene and benzene in the sidestream were controlled by manipulating sideatream drawoff location and sidestream flow rate as shown in Figure 7. Liquid was removed from one or two trays at any point in time. To increase o-xylene concentration a valve lower in the column was opened wider, while the valve immediately above it was pinched back. Liquid was removed from one or any two consecutive locations from
lnd. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
trays 18, 19,20, 23, and 26. Figure 8 gives the ranges for the outputs from the fixed gain relays. The controllers in the multi-loop control system, shown in Figure 9, were tuned empirically. Each control loop was tested on the nonlinear model, with the remaining three on manual, for closed-loop stability. The performance of the control scheme, with all the controllers on automatic, was examined on the nonlinear model. Table I gives the final controller settings for the L-scheme. B. D-Scheme. Impurities of benzene and o-xylene in the sidestream were controlled by manipulating sidestream drawoff rate and the prefractionator distillate rate, respectively. Figure 10 shows the actual scheme for this case. The prefractionator distillate rate was pulsed and the transfer function relating D1 and XS(3) was obtained. Starting with the Ziegler-Nichols settings, the controller was retuned to give closed-loop stability with a reasonable phase margin. The settings of the other three controllers were left the same as in the L-scheme. Table I1 shows the final control settings for the D-scheme. Simulation Results for Moderate Disturbances Both control schemes were tested on the nonlinear model. Figures 11-14 give results for the L-scheme. Figures 15-18 give results for the D-scheme. A. L-Scheme. Figures 11and 12 gives results for a feed composition disturbance when at t = 0.0 the feed composition was changed from XF(1) = XF(2) = 0.40 and XF(3) = 0.20 to XF(1) = XF(2) = 0.35 and XF(3) = 0.30. Figures 13 and 14 give results when at t = 0.0 the feed composition was changed from XF(1) = XF(2) = 0.40 and XF(3) = 0.20 to XF(1) = 0.45, XF(2) = 0.35 and XF(3) = 0.20. Stable, effective control was obtained with the L-scheme. Feed flow rate and product composition setpoint disturbances were also tried with good results. B. D-Scheme. Figures 15-18 show the results for the same feed composition disturbances as were imposed on the L-scheme. Again, good control was obtained. Simulation Results for L a r g e r Disturbances For disturbances of the magnitude mentioned above, both control schemes gave satisfactory performance. The steady-state analysis (Figures 2-5) predicted that the L-scheme could handle bigger disturbances in feed composition than the D-scheme. To test the rangeability of both schemes, the following two disturbances were applied in the feed composition. (1) Benzene in the feed was increased from 40% to 50%, while toluene was decreased from 40% to 30%, and o-xylene concentration remained unchanged. (2) Benzene and toluene concentrations in the feed were decreased from 40% each to 30% each, while o-xylene concentration was increased from 20% to 40%. The D-scheme handled the first disturbance (Figures 19 and 20), but went unstable for the second one. The Lscheme went unstable with either disturbance. Therefore, the D-scheme appeared better. However, the possibility of retuning controllers had to be explored before definite conclusions could be drawn. We were unable to find settings that would stabilize the D-scheme for the disturbance with the increased amount of o-xylene in the feed. The L-scheme was stabilized only for the disturbance with the increased amounb of o-xylene in the feed, when the reset time of the composition controller that adjusts the drawoff tray location was changed
153
from 30 min to 110 min. Results are shown in Figures 21 and 22. A combination of the two control schemes was also tested. A split-range controller was used to vary the distillate rate from the prefractionator and, simultaneously, to adjust the drawoff tray location. No improvement in controllability or rangeability was obtained. Conclusions Because it is easier to implement in terms of equipment, the D-scheme is probably to be preferred in most systems. However, the L-scheme should be considered when large changes in o-xylene are expected. Nomenclature B1,BZ = bottoms flow from first and second column, respectively, kg-mol/ h CT = composition transmitter CC1, CC3 = composition controller output for the benzene and xylene concentrations in the sidestream, atm D1, 0 2 = distillate flow from first and second column, respectively, kg-mol/h F = feed rate, kg-mol/h FC = flow controller FT = flow transmitter K , = controller gain LC = level controller LS = liquid sidestream flow rate, kg-mol/h NF = feed tray NF1, NF2 = feed trays for a column with two feeds NS = sidestream tray N?' = total number of trays Q B l , QB = heat input to the first and second column, respectively, kcal/h R1, R = reflux flow of the first and second column, respectively, kg-mol/h SP = controller set point T = temperature, "C X B l ( J ) ,XBB(J) = bottoms composition of component J in first and second column, respectively, mole fraction X B 2 = controlled bottoms composition, mole fraction XBZSP = set point for the bottoms composition controller X D l ( J ) ,XDZ(J) = overhead composition of component J i n first and second column, respectively, mole fraction X D 2 = controlled overhead composition, mole fraction XDZSP = set point for the overhead composition controller X F ( J ) = feed composition of component J for a saturated feed, mole fraction XS(J) = liquid sidestream composition of component J,mole fraction X S 1 , X S 3 = controlled sidestream compositions, mole fraction X S l S P , X S 3 S P = set points for the sidestream controllers T I = controller reset time, min Literature Cited Buckley, P. S. Chem. Eng. Rag. 1089, 65(5),45. Dlstefano, G. P. AIChE J . 1088, 14, 190. Doukas, N. P.; Luyben, W. L. Inst. Tech. 1978a, 25(6), 43. Doukas, N. P.; Luyben, W. L. Ind. Eng. Chem. Process Des. Dev. 1978b. 17, 272. Luyben, W. L. ISA J . 1966, 13(7), 37. McGune, L. C.;Gallier, P. W. ISA Trans. 1073, 12, 193. Tyreus, 0 . ; Luyben. W. L. Ind. Eng. Chem. Process Des. Dev. 1075, 14, 391.
Received f o r review October 22, 1979 Accepted August 19, 1980
