n
THEODORE J. WILLIAMS Monsanto Chemical Co., St. Louis, Mo.
Instrumentation and Control of Distillation Columns Automation of a continuous distillation column is tricky. Work in the past has either been on experimental columns or involved mathematical theory. Here is information which combines both-and forms the basis for a workable arrangement for controlling distillation columns.
C~SIDERARZE
has been cbritten on distillation as a unit operation and difficulties encountered in column control. Most of the early work was either empirical or devoted to experimental studies of distillation column control (4, 5, 7, 70, 72, 14, 75, 20, 27), but recently several theoretical or mathematical studies have appeared (7,22-24). However, there has been little correlation between these two types of investigations. I n this work such a correlation is attempted by developing, on purely theoretical bases, an optimum control scheme for a distillation column. Basic Factors of Distillation Control
Variables of Distillation Process. For any distillation column, only six independent operating variables are needed to define its operation. External Independent Variables 1. Feed rate 2. Feed composition
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3. Feed temperature or feed quality 4 . Ambient pressure of operation Internal Independent T7ariablee
5,6. Two quantities:
of
the
following
four
Overhead product composition (complete) Bottoms composition (complete) Boil-up rate-feed rate ratio Feed split or distillate bottoms ratio Semi-independent Variables of Column Operation
1. Location of feed tray 2. Column reflux temperature For a binary mixture, the overhead product and bottoms composition is given by the mole fraction of only one component. For a multicomponent mixture of n components, the mole fraction of n - 1 components must be specified. 'This condition is assumed
INDUSTRIAL AND ENGINEERING CHEMISTRY
to prevail in this work, where the overhead or bottoms composition is considered. The semi-independent variables of feed tray location and of reflux temperature can affect distillation column control. However, in distillation theory these are secondary factors usually considered noncritical. For simplification, it is assumed that the optimum feed tray location has been chosen and that the reflux is returned at its boiling point. Thus proper choice of the six main variables will permit determination of all the dependent variables for any given mixture. such as: Dependent Variables Liquid composition. Bottoms, plate. distillate T7apor compositions at each plate or location in the column All unspecified flow rates. Liquid, vapor, distillate take-cff , bottoms take-off Temperatures at each location in column
These dependent variables are, of course, interrelated through the thermodynamic laws governing the vaporliquid equilibria of the mixture and by the material balance requirements of the column itself. The basic problem in distillation control can now be resolved into three parts: determining which two of the four possible internal independent variables should apply, which method is most direct for sensing variations in independent variables specified as constants, and how the displaced variable can be restored to its chosen operating value through adjustment of the controlled system. If the internal variables are to be truly independent, it is absolutely necessary that the boil-up rate be specified as the ratio of the respective stream rate to the feed rate rather than as simply that variable’s rate of flow alone. Classes of Distillation Control. O n the basis of these statements, several schemes for distillatioQ column control may be suggested (Table I and Figure 1). Because of the instrumentation system chosen for each control scheme, certain internal independent variables should be selected. I n Table I, these systems are arranged in order of increasing flexibility to illustrate the development of the optimum system. The scheme of Figure 1, A, requiring a constant feed composition, is the simplest example possible and seems entirely unrealistic in most plant situations. This method has been called inferential or environmental control (9), and succeeds only when it can pre-
Figure 1. Comparison of simple inferential or environmental control with proposed, more sophisticated schemes. Units encircled by arrows show successive stages in control scheme rearrangement required for necessary flexibility of operation A. Original arrangement; 6. This allows far smoother control of heads composition but constant feed still required) C. Ratio of boil up rate to feed rate permits some flexibility;
D.
Composition detection of heads sample allows ultimate degree of control
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a
vent all upsets originating from external sources from reaching the column. Here flow controllers alone are sufficient to maintain steady operation because only boil-up rate and distillate take-off rate need be kept constant. .4 constant feed rate, as required by 1, B, can be attained either if sufficient tankage can be installed between the column and the preceding plant unit or if it is the first element in a processing line. The desire for true flexibility of operation, however, leads to the scheme of C. Here the resetting of the reboilersteam, input-rate control by a cascade
RE LA TI VE VOLA T I L I T Y
3(
Figure 2. Pressure must be closely controlled, if temperature is to b e the primary column variable detected by the sampler
,"
00
10
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20
PROPORTIONAL CONSTANT
30
40
50
60
70
a t
PROPORTIONAL CONSIANT
Figure 3. Diagrams of allowable ranges of controller settings show relations of sampling for five-plate column Relative volatility, cx = 5.0 ( 1 6 )
A.
B.
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
Top plate sampling only Intermediate plate sampling only
DISTILLATION COLUMNS
A TE
7 p,... OUT
The ultimate control scheme for a distillation column embodies results of theoretical studies to give automatic control
This simplifies the control of cooling water, but makes the use of temperature alone as a composition detector impossible. In such a situation some device must be used which measures composition directly or meavures another composition-sensitive but nontemperature-sensitive property, because
controller operating from feed input rate measurements makes it possible to maintain the boil-up rate-feed rate ratio mentioned. I t would then be easily possible to maintain the distillate take-off rate necessary to keep the feed split at that value determined by the instantaneous feed composition as it varies. Thus the feed rate and feed composition can vary independently, as long as the physical limitations of the column, such as flooding rate, are not exceeded. Designation of the boil-up rate-feed rate ratio and the overhead product composition as the specified internal variables allows feed quality to vary along with the feed composition. Slight variations of distillate take-off rate will automatically compensate for the flow variations caused by quality shifts. Thus, the simple constant temperature feed preheat control of Figure 1, A , can be retained throughout. If this temperature can be set to give a feed quality of 1.0 a t the lowest feed composition expected and if the feed mechanism can handle a mixed feed, such an arrangement helps to smooth out column composition fluctuations caused by the change in feed composition itself (24). Figure 1, D, carries the scheme of C one step further and allows the ambient operating pressure to vary also. VOL. 50, NO. 9
SEPTEMBER 1958
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These recommendations should be helpful in considering distillation column control systems.
b
For maximum flexibility, primary column control should maintain boil-up rate-feed rate ratio and overhead composition constant.
b Sampling the top plate will give the best control, if the sampling device is sensitive enough to detect the required range of composition variations.
b
temperature will vary drastically with pressure. Figure 2 relates the boiling pointLe.: tray temperature-variation to the resulting composition variation for various relative volatilities of binary mixtures. I t is therefore necessary to maintain a very close control of pressure, if temperature is to be the primary column variable detected by the sampler for control purposes. Otherwise, another property must be used for satisfactory results. Thus boil-up rate-feed rate ratio and overhead product composition are specified as the optimum internal variables for control. Is this really so? The present situation allows the bottoms take-off rate to be determined by an auxiliary level controller in the reboiler, Thus a constant heat transfer area is maintained in the reboiler and boil-up rate control can be tied directly to steam input rate. Any other scheme would result in level fluctuations with corresponding heat transfer area variations in the reboiler. Thus the steam rate andlor pressure would have to vary in a complex manner to maintain the boil-up rate at its established value. Bottoms composition may be used as an independent variable, but because pot volumes are usually ten or more times greater than plate holdups, bottoms composition can vary only a t a correspondingly slower rate than any plate compositions. Thus a much greater sensitivity can be attained with overhead product composition as the independent variable, even when the bottoms is the desired product.
Problems in Top of Column
Sampling Effect of Dead Space in Samplers. Automatic control theory demands that an error detector be located as close as possible to the point in the system 12 18
When the sampling device has an appreciable dead space error, sampling on a lower plate than the top plate may give a more accurate control. Dead space error should be kept as low as possible.
b
When a composition sampler working on an intermittent
Table I.
Feed rate Fixed
cycle must be used, the sampling cycle should be kept as small as possible-less than one half the mixing time constant of the column plates.
b
The rate control mode or derivative control is ineffective for distillation column control. When top plate sampling can be used, the proportional band mode alone is sufficient. For all other plates reset rate or integral control is necessary for the composition controller. Condenser holdup should be kept small, as it i s destabilizing. Still pot holdup is stabilizing.
Relation of Choice of Independent Internal Variables to Possible Action of External Variables
External Variable Feed Feed composition quality Fixed Fixed
Ambient pressure Fixed
Fixed
Variable
Variable
Fixed
Variable
Variable
Variable
Fixed
Variable
Variable
Variable
Variable
Refer to
Choice of Internal Variable Figure 1 Boil-up rate-feed rate ratio A Distillate rate-bottoms-rate ratio Boil-up rate-feed rate ratio B Overhead composition Boil-up rate-feed rate ratio Overhead composition C Boil-up rate-feed rate ratio Overhead composition D
Table II.
Summary of Recommended Control Scheme Main Control Functions Method of Determining and Regulating Required Variation Designated Independent Internal S'arlable Sampled by dependent variable near top of Overhead product composition column and maintained as constant as possible by resetting reflux rate controller Variations of feed rate detected by flow Boil-up rate-feed rate ratio controller and used to reset steam input rate controller previously set at some intermediate rate for task at hand
Required Subsidiary Controls Subsidiary I'ariable Method of Control Feed preheater on feed line Feed temperature Levei control on reboiler Bottoms take-off rate Variation of condenser cooling water rate Pressure (where necessary for temperature elements) Level control on accumulator Distillate take-off rate
INDUSTRIAL AND ENGINEERING CHEMISTRY
lDlSTlLLATlON COLUMNS where the control correction is applied, so that overcorrections do not cause an oscillatory response of the control system (78). Studies of distillation column responses under automatic control when carried out on analog computers (76,24) show that the top plate of a distillation column can give over ten times as close control as an intermediate plate. This is because fluid flow lags on plates located between the error-detecting and control points allow the oscillations to occur as soon as the controller settings are greater than some given small value. Figure 3 shows this, because it diagrams the allowable range of controlleq settings for each case. The results shown here were obtained
now greater than the expected excursion on the controlled variable. Figure 7, A , and B classifies the cause, of the resulting output error, while Figure 7, C, shows the effect of going still further down the column t o pick the sampling point. The actual choice of the sampling point is thus a compromise between the unavoidable output errors due to control system oscillations and those due to the low sensitivity of the detector. The only solution is to produce a sensitive detector (temperature or otherwise) and locate it as close to the top of the column as possible. Effects of Intermittent Samplers. Another factor which can have a major effect upon the control method chosen is the greatly increased use of samplers which determine composition directly but operate on an intermittent cycle. Mass spectrometers and scanning infrared and ultraviolet analyzers fall into this category (79). Many of these instruments, because of their high cost, are used to determine the output a t several different sampling points through a time-sharing system.
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DEAD SPACE
Figure 6. For a dead space of less than 0.01 5 mole fraction, top plate sampling is best VOL. 50, NO. 9
SEPTEMBER 1958
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c 01
0 02
0 03
0 04
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0 03
0 04
0 05
D E A D SPACE
Figure 8 shows how such a device might operate. This one is a postulated spectrometer used to determine several components in a multicomponent stream. Figure 9 is another diagram of the time sequence of events occurring in such a device; Figure 10 compares the results as determined by the analyzer to the actual stream composition sampled. The response of a computing spectrometer such as this or any of the other intermittent devices mentioned above, ~ v h e nused as part of a control system, has been extensively studied by analog simulation methods (23) (Figure 11). For spectrometers operating on very fast cycles-Le., period of operation less than the basic liquid residence Eime on a plate; time constant, 7, top plate sampling gives much better control; the allowable controller setting is much tighter. For long-period samplers it makes little difference whether
A.
0c5
Sampling on top plate only
-
s 01
0 02 D E A D SPACE
E.
Sampling on Intermediate plate only
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/n DD IiI ONA L c o NT R I 8 u T Io N OF D E A D S P A C E TO OUT
PUT ERROR
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C. Sampling possible on plate two down from top plate
Figure 7. Actual choice of sampling point is a compromise among unavoidable output errors 5-plate column.
1 220
INDUSTRIAL AND ENGINEERING CHEMISTRY
a = 5.0 ( 2 4 )
DISTILLATION COLUMNS
CORRECTION SIGNAL
SAMPLING POINT I N REFLUX LINE OR O N ONE OF COLUMN
1
TO COLUMN CONTROL VALVES
I
SPECTROMETER OBTAINS MASS OR
Semi-independent Variables of Column Operation
ABSORPTION SPECTRUM A N D EVALUATES TO DETERMINE COMPOSITION OF COMPONENTS OF SAMPLE STREAM FINITE TIME PERIOD REQUIRED
LENGTH OF SAMPLING LINE CAUSES FINITE TRUE TIME DELAY
COMPUTING SPECTROMETER
-
I
CONTROLLER
CONTROLLER OPERATES O N COMPOSITION A S DETECTED B Y THE SPECTROMETER AND
ASSOCIATED COMPUTER.COMPARES WITH DESIRED VALUE A N 0 COMPUTES CORRECTIONS TO VALVE SETTINGS
Figure 8.
This is the way such a device might operate
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F I R S T SAMPLE TAI(EN HERE TIME REQUIRED 10
TIME REQUIRED
FIRST SAMPLE TO C O N T R O L I E R HERE PERIOD OF USE
k F O R SAMPLE L I N E - ~ E V A L U A T sPECTIIU&-OF E
FIRST SAJPLE
SECOND SAMPLE
/
SECOND SAMPLE TO
, CONTROLLER HERE
TAKEN HERE
f-
TIME REQUIRED T O
TIME REQUIRED
FOR SAMPLE LINE +tEVALUATE
SPECTRUM?
+PERIOD OF USE OF SECOND SAMPLE
1 THIRD SAMPLE
THIRD SAMPLE
I
TO C0,NlROLLER
T A K E N HERE
FOURTH SAMPLE
the sampler is located on the top plaFe or lower down. The deterioration of sensitivity due to enforced sampling time lags quickly equals that due to fluid flow lags within the column (23).
Optimum Feed Plate Location. One of the semi-independent variables of column operation is feed plate location. If feed composition does not vary greatly, one feed plate location is sufficient. However, for some possible wide variations of feed composition "pinches" and a corresponding reduction in column separating capacity may occur beyond the capacity of the control system to correct. Thus some sort of automatic feed plate changes would be desirable. Figure 12 shows a sample chart of the optimum feed plate locations for a small column. Feed plate location is a function of the feed quality as well as comparison of the actual feed composition to the reference or median feed composition. Such a chart can be developed for any given column and feed mixture. The resulting data can then be used to set a controller which, by means of quick-opening valves, transfers the feed from plate to plate as necessary when the feed composition varies. Effect of Reflux Temperature. In all cases except Figure 1, A , care has been taken to control the amount of reflux fed back to the column rather
a
+
~ ~ t ~ E N R ~ Q Y t R E D
Time,
Figure 9.
t
FOR SAMPLE LINE
of
Time relation of events in operation
intermittent sampling model
V A R I A T I O N OF OUTPUT
A C T U A L V A R f A T l O N OF[
A S USED B Y CONTROLLER
OUTPUT
TIME D E L A Y
2
Figure 10.
1
%
Comparison of real output of process and that used by controller VOL. 50, NO. 9
SEPTEMBER 1958
1221
or other analyzer results has not been recommended. Analog computer simulation indicates that good column control can be achieved without the complexity and expense of a digital computer to determine the operating parameters ( 6 ) . Analog computer simulation has also shown that only proportional and integral control modes can give adequate action in the control of a distillation column. The derivative or rate mode proved completely ineffective for all cases tried. This fact has also been noted by several experimental investigators. I t is therefore recommended that only two mode controllers (proportional and integral or reset) be procured for this purpose.
I TOP PLATE SAMPLINI
A
INTERMEDIATE PLATE SAMPLING
I I
References
IO
IO0
10
S A M P L I N G INTERVAL,
I, IN SECONDS
Figure 1 1. For spectrometers operating on very fast cycles, top plate sampling gives best control
than to control the amount of distillate withdrawn directly. because any fluctuations in condenser vapor rate would be propagated by an accumulator level controller to the reflux stream in the case of 1, A . This must be avoided whenever possible, as such fluctuations can be self-propagating and can lead to sustained control oscillations if a cold reflux is used on the column. By effectively choking off such fluctuations at the accumulator and transferring them to the distillate stream,
the reflux control scheme of Figure 1, B to 1, D, prevents such oscillations from occurring.
Optimum Column Control Scheme The optimum control scheme for the majority of distillation column applications includes the recommendations developed in the previous discussions. Control of the column by any type of automatic computer other than that necessary to evaluate the spectrometer
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REFERENCE FEED C O M P O S I T I O N
09
(1) Bauer, R. L., Orr, C. P., Chem. Eng. PrOgr. 50, 312-18 (1954). (2) Berger, D. E., Campbell, G. G., Ibid., 51, 348-52 (1955,. (3) Berger, D. E., Short, G. R., IND. ENG. CHEM.48. 1027-30 (1956). (4) Boyd, D. M.; Jr., Petrot. Re&r 27, 115-18 (October 1948); 114-17 (Novembpr 1948’1. -, (5) Coulter, K. E., Ibid., 31, 137-8 (December 1951). (6) Engel, H. L., Control Eng. 4, 144-7 (September 1957). (7) Gallagher, G. G., Petrol. Refiner 27, 116-17 (March 1948). (8) Hoyt, P. R., Stanton, B. D., Ibid., 32, 113-19 (October 1953). (9) Kiguchi, S. T., Ridgway, R. L., Ibid., 35, 179-84 (December 1956). (IO) Moore, H. F., Gross, G. W., Petrol. Processing 1948, 441-8 (May 1948). (11) O’Connor. Ward. A.1.Ch.E. Suring ’ Meeting. ” ”, Philadel&ia. Pa.. 1954: (12) Perrv, C. W., ‘Chem. @’ Met. Eng. 52, 108-12 (October 1945). (13) Poffenberger, Xoland, private communication, -.4ugust 1955. (14) Rector, N. K., Petrol. Processing 1949, 525-8 (May 1949). (15) Reynolds, E. H., Troutman, William, Lawn, Gordon, Petrol. Rejner 26, 132-6 (April 1947). (16) Rose, Arthur, Williams, T. J., Ih-D. ENG.CHEM. 47, 2284-9 (1955). (17) SOC. Instrument Technol., ”Plant and Process Dynamic Characteristics,” Butterworth Scientific Publications, London, 1957. (18) Thaler, G. J., Brown, R. G., “Servomechanism Analysis,” McGraw-Hill, New York, 1953. (19) Thomas, B. W., IND. ENG. CHEM. 46, 1371-441 (1954). (20) Tivy, V. V. St. L., Petrol. Refiner 27, 123-8 (Sovember 1948). (21) Uitti, K. D., Ibid., 29, 130-4 (March 1950); Petrol. Processing 1950, 41-4 (January 1950). (22) Williams, T. J., Ph.D. thesis, Pennsylvania State University, 1955. (23) Williams, T. J., Harnett, R. T., Chem. Eng. Progr. 53, 220-5 (1957). (24) Williams, T. J., Harnett, R. T., ROW,Arthur, IND.END.CHEM.48, 100819 (1956). RECEIVED for review J’anuary 29, 1958 ACCEPTED May 19, 1958
‘ 0
Figure 12. Best feed plate location depends on feed quality as well as composition
1222
INDUSTRIAL AND ENGINEERING CHEMISTRY
New Jersey Section, ACS, January 27,
1958.
