with a mean deviation of about 0.03% and a maximum of 0.07% (absolute deviations in relative excess mixing volumes). For the pure components the following densities were used : benzene 0.8790 (American Petroleum Institute Project 44, 1951). 2-propanol 0.7849 (Manufacturing Chemists Association Research Project, 1960), carbon tetrachloride 1.5940 grams per cc. (Manufacturing Chemists .4ssociation Research Project, 1957). Nomenclature
A a b
= cross-sectional area
= absorptivity
c
= beam height = distance from cell wall to detector
D
= absorbance
DAB = diffusivity d
G h
= cell ivall thickness = mass flow rate per unit area = height
J
= mass flux relative to mass-averace mixture velocitv v
L n
p Q q
R s
t u
V ,I
luminous flux number of observations optical path length volumetric flow rate luminous flux per ray luminous flux of composite beam height of slit image diffusion column thickness = velocity = volume of solution = mole fraction = = = = = = = =
GREEKLETTERS p
7
= concentration, mass per unit volume = refractive index = angle
4 SUBSCRIPTS B = benzene
P
w c
= wall = carbon tetrachloride
literature Cited
Aditya, S. K . , doctoral dissertation, Columbia University, New York, N. Y., 1963. .4merican Petroleum Institute Project 44, Selected Values of Physical and Thermodynamic Pro erties of Hydrocarbons and Related Compounds, Table 21a, d t i o n a l Bureau of Standards, Washington, D. C. (1951). Bauer, N., Lewin, S. F., “Determination of Density,” in “Physical Methods of Organic Chemistry,” A . Tl’eissburger, Ed., Vol. I, 3rd ed., Interscience, New York, 1959. Becknian Instrument Co., Fullerton, Calif., “Near-Infrared Spectra of Representative Organic Compounds,” Bull. 726 (1957). Brown, I., Smith, F., Australian J. Chem. 15, 1 (1962). Burchard, J. K., Toor, H . L., J . Phys. Chem. 66, 2015 (1962). Cullinen, H . T., Jr., Cusick, M . R., IND.ENG.CHEM.FUNDAMENTALS 6,72 (1967). Cussler, E. L., Jr., Lightfoot, E. N., A.Z.Ch.E. J . 9,703,783 (1963). Dunlop, P. J., Gosting, L. J., J . Am. Chem. Sac. 77, 5238 (1955). Fujita, H . , J . Phys. Sac. Japan 11, 1018 (1956). Graff, R. A., doctoral dissertation, Columbia University, New York. N. Y.. 1963. Kaye, (V., Spectrochim. Acta 6, 257 (1954). Kaye, \V., Spectrochim. Acta 7, 181 (1955). Lightfoot, E. N., Cussler, E. L., Jr., Chem. Eng. Progr. Symp. Ser. 61, No. 58, 66 (1965). Manufacturing Chemists Association Research Project, “Selected Values of Properties of Chemical Compounds,” Tables 23-2-1(1.1020)-a(1960) and 23-10-2-(4.Oll)-a(l957), Carnegie Institute of Technology, Pittsburgh, Pa. Nyvlt, J., Erdos, E., Collection Czech. Chem. Commun. 26, 500 (1961). Onsager, L., Ann. .V. Y., Acad. Sei.46, 241 (1945). Paraskevopoulos, G. C., Missen, R. LV., Trans. Faraday Sac. 58, 869 (1962). Schotte, IV., doctoral dissertation, Columbia University, New York, N. Y.. 1954. Shuck, F. O., Toor, H. L., J . Phys. Chem. 67, 540 (1963). West, R . F., doctoral dissertation, Columbia University, New York, N. Y., 1951. RECEIVED for review November 28, 1967 ACCEPTED April 12, 1968
= 2-propanol
R A P I D D E T E R M I N A T I O N OF OXYGEN PERMEABILITY OF P O L Y M E R M E M B R A N E S S H U l C H l AIBA, M I N O R U O H A S H I , AND S H I H - Y O W Institute of Applied Microbiology, Uniuersity of Tokyo, Tokyo, Japan
HUANG
The oxygen permeability, ,P, and diffusivity, D ,, of polymer membranes were measured electrochemically b y exposing an electrode covered by the membrane to an atmosphere with a definite partial pressure of oxygen. For membranes with higher oxygen permeability values, such as tetrafluoroethylene, polyethylene, and polypropylene, good agreement was obtained between P, (and D,) determined b y this method and poly(viny1idene measured b y the conventional pressure method. For the less permeable membrane-e.g., chloride)-the agreement was not always satisfactory; this was attributed to the fact that one surface of the membrane in this determination was in contact with an electrolyte solution. The procedure reported permits rapid measurement o f P, and D, values of polymer membranes, eliminating some of the disadvantages associated with determination b y the pressure method. HE usual method of measuring the gas permeability of Tpol) mer membranes requires the measurement of the pressure difference of the gas (Nakagawa, 1965; Tuwiner, 1962) ; the difference is caused by the gas transferred through the membrane from the high pressure side of a specific apparatus to a lower pressure chamber. Although the principle of the measurement is simple, the experimental device must be designed,
in general, to permit a high vacuum operation. T h e measurement for each run requires a long time, particularly when the membrane has a low permeability. These disadvantages, inherent in the measurement of membrane permeability, have caused this kind of apparatus to be used infrequently. T h e purpose of this work was to exploit a rapid method of measuring oxygen permeability of polymer membranes by VOL. 7
NO. 3
AUGUST
1968
497
I
I
Electrolyte Solution
it 1
I
I I
I I
t
0
0
0
-
X Figure 1 . state
to
b
Profile of oxygen partial pressure in the steady
applying the membrane-covered electrode technique (Carritt and Kanwisher, 1959; Clark et al., 1953; Mancy et al., 1962; Sawyer et al., 1959), which is widely used to determine dissolved oxygen in a fermentation broth. The use of oxygen here, originating from the above-mentioned source, does not necessarily restrict this application; the principle can be extended to gases other than oxygen, if due attention is paid to the electrochemical reaction in each case. The oxygen permeability or diffusivity values for a specific polymer membrane may be converted to those for gases other than oxygen, if particular care is taken in the conversion (Stannett and Szwarc, 1955). The permeability and diffusivity values for polymer membranes are of significance in food packaging. The potentiality of this application is one subject of the present study.
qt
1001 Figure 2. Top.
t Determination of D, By integrating i t By defining 0
Boftom.
Measuring Principle and Related Equations
Suppose that the oxygen level in a medium (either gas or liquid) is measured by the membrane-covered electrode technique, and that oxygen consumed a t the electrode surface is supplied from outside the electrode. The reduction of oxygen a t the cathode surface of platinum is assumed as follows (Lingane, 1961) : 0 2
+ 2 H 2 0 + 4e + 4 0 H -
(1)
For a membrane-covered electrode, the flux of oxygen through a series of materials (medium, membrane, and electrolyte solution) can be envisaged eventually in the steady state (Figure 1). If the cathode surface does not degenerate-e.g., excessive formation of platinum oxide is prevented (Lingane, 1961)and if the membrane is tightly attached to the cathode surface, the rate of oxyge'n transfer through the whole series of resistance (Figure 1) is assumed to be controlled by the resistance of the membrane, if other resistances to oxygen transfer are negligible. The electrochemical reaction rate is also assumed not to be a controlling factor in the oxygen transfer. Using these assumptions, several equations regarding the electric current observed in the experimental device are shown below. Steady-State Condition, P, Measurable. T h e observed transient current, if the oxygen concentration or partial pressure is changed stepwise, is as follows (Delahay, 1954) :
it
=
N
F
A
. D, .
(2) x=o
498
I&EC FUNDAMENTALS
( b P m / b ~ ) , ,can ~ be determined by solving Fick's second law: (3) The initial conditions arep, = p, and t = 0. The boundary conditions are p, = p, and x = 0 andp, = p8 a n d x = b. T h e solution is (Jenson and Jeffrey, 1963)
From Equations 4 and 2b and setting the value ofp, = 0,
Since the value of i t becomes indefinite (Equation 5 a t t = 0), thus losing its physical meaning, it was additionally assumed that
($).=, =
The permeability, diffusivity, D,, by
0 att=O
P,, of the membrane is related to the P,
=
D, . S,
where S , is the solubility constant of the membrane.
(7)
O-RING
MEMBRANE-COVERED-ELECTRODE
POLAROGRAPH
AIR-VENT
OUTER
CYLINDRICAL GLASS
PIPE
V-RECORDER
Ag -TUBING ELECTROLYTE SOLUTION ( 0 . 5 N KCL AQ.SOL.)
__
OXYGEN CYLINOER
--NITROGEN FLOW METER
U
U
Figure 4. MEMBRAflE
1-7Pt CATHODE
Figure 3.
Diagram
of electrode
From Equation 5 , the value of i, when t =
i, = N . F . A . p , .f P b
03
is given by (8)
T h e value of P, can be assessed by measuring the values of i, A , b, andp,. Approach to Steady State, Where Relaxation Time Gives D,. If Equation 5 is integrated from t = 0 to a specific time, to, a t which the steady state is attained (Figure 2, top),
i , d t = qm = N . F =
*
A
.
- A)
i, ( t o
6D,
(9)
Then,
Figure 2 (top) shows that the term (imto- qm) is equal to the cross-hatched area, which is easily assessed by using a planimeter. Figure 2 (bottom) illustrates another means of determining D, by the equation (Barrer, 1941)
b2
D, = 68 where 6 is a n intercept of a straight line with the time axis. Figure 2 (bottom) refers to a determination of the equivalent amount of oxygen, q2,diffused through the membrane as a function of time, t. Experimental Procedure
Figure 3 shows the structure of the membrane-covered electrode used in this work. The sensor used was designed originally by one of the authors (Ohashi) for measuring the oxygen tension in a fermentation broth. The electrode is composed of silver tubing as an anode (470 X 10-mm. o.d.), and a platinum disk as cathode (3 to 5 mm. in diameter). The electrodes were sheathed by an outer pipe of polycarbonate resin. An electrolyte solution (0.5N aqueous KCl) was charged into an annular space (Figure 3). The silver tubing was filled with lead granules to ensure favorable contact between the cathode and the membrane
Schematic diagram
of experiment
which is a t the end of the outer pipe (Figure 3). An epoxy resin was used as insulation between the anode and the cathode (Figure 3). The membrane used was changed for each run as described below. Figure 4 is a schematic diagram of the experimental procedure. The membrane-covered electrode was inserted vertically into a glass cylinder through which nitrogen or oxygen gas was passed. A step change of oxygen partial pressure was realized by manipulating a three-way stopcock. The reduction current, i,, was measured polarographically; the value of i, was obtained by dividing the voltage recorded by a millivolt recorder (electric polyrecorder, Model EPR-2T, T O W A Electronics, Ltd., Tokyo) with a value of shunt resistance, R (1 kiloohm in this example). The polarograph used (Type PO-1, Yanagimoto, Kyoto) was operated a t -0.6 volt. With such a shunt resistance, the voltage drop did not affect the magnitude of reduction current, since the oxygen plateau, which appears in the current-potential curve, was wide enough (about 0.6 volt) to cover the voltage drop due to the resistance (Sawyer et al., 1959). The temperature was also varied. The value of permeability as a function of temperature can rarely be found from the conventional pressure method. Prior to each run, the cathode was polished to avoid contamination. This pretreatment was followed by the so-called "warm-up" period (for about 10 minutes), during which the voltage (-0.6 volt) was applied to the electrode and the electrode was exposed to an air or oxygen stream to stabilize the reduction current in each determination of permeability or diff usivity . Results and Discussion
The permeability of polypropylene as determined by substituting the following experimental data into Equation 8 is as follows: For i, = 8.6 pa., b = 0.0042 cm., p s = 76 cm. of Hg, and A = 0.196 sq. cm.
P,
(8.6 x 10-6)(4.2 X (4 X 96,500/22,400) (0.196) (76) cc. a t S.T.P. = 1.4 X 10-10 (20° C.) (cm.) (sec.) (cm. Hg) =
I n the above calculation, the value of N = 4 in Equation 8 was used (cf. Equation 1). This value of P, was in good agreement with the data (1.7 X 10-10 a t 20' C.) obtained by the pressure method. The latter value was determined with the same material by Nakagawa (1967). Effect of Thickness. Permeabilities of several membranes of different thicknesses ranging from 10 to 100 microns were VOL. 7
NO. 3
AUGUST 1968
499
A.
+
I
I
I
I
I
6
58
10
I
0 .
-2 h Y
t
I
2
4
I 12
b x lo3, cm Figure 5. bility
Effect of membrane thickness on permeaPTFE. Polytetrafluoroethylene PE. Polyethylene PP. Polypropylene
$5
4 3
-023
.2
6 2
0s
measured (Figure 5 ) . Most of the membranes showed higher permeability values when the membrane thickness was about 20 microns. I t seems strange that the extension of the membrane caused by the weight of the electrode (total weight 200 grams, Figure 3) apparently resulted in a higher permeability value; however, the mechanical tension which may cause a structural modification is considered to he responsible for this peculiar phenomenon. This phenomenon seems to he worthy of further experimentation and discussion. T o avoid excessive extension, a piece of cotton gauze \vas attached to each membrane. T h e permeability values measured in this situation were constant in the range of 10 to 40 microns (Figure 5). Effect of Temperature. The experimental results obtained so far are shown in Figure 6, in which P, is plotted against 1 / T ; the plot of P, us. 1 / T has no theoretical implication. Clearly, the permeability value increases with increase of temperature. Permeability values measured thus far are shown in Table I. Most of the data are in good agreement \vith those obtained by the pressure method by other workers. The maximum time required for measuring a sample of the lowest permeability value 500
l&EC FUNDAMENTALS
in this work was less than one hour. Therefore, this technique is a rapid and accurate method for determining the oxygen permeability of various polymer membranes. With thin membranes with high values of permeability, the p , value must he carefully selected so that a proportionality between i, andp, can be realized. KO good agreement between the electrode method and the pressure method was observed when elastic membranes such as natural rubber and silicone rubber were used, perhaps because the electrolyte cannot penetrate the space between the cathode and the membrane, which is otherwise guaranteed. The oxygen permeability values for poly(viny1 chloride), poly(viny1 fluoride), and poly(viny1idene chloride) measured by this method (Table I ) are about two to five times larger than those determined by the pressure method. Although the exact nature of this disagreement remains for further discussion and experimentation, it may he attributed to the possibility that these membranes, after being assembled for the specific measurement (Figure 3), exhibited a certain degree of hydrationi.e., a trace amount of water entering the membranes. Various interesting permeability phenomena-for instance, the value of P, being dependent on the time of measurement primarily because of the increase of water content with time of measurement, particularly for hygroscopic membranes (Kunz and Cornwell, 1962)--will he revealed by the membranecovered electrode method reported here. It \vas difficult to measure the permeability of a cellophane membrane by the electrode method, because the cellophane, hygroscopic in nature, was ruptured mechanically when the membrane was fastened on the cathode. The permeability of polyethylene-laminated cellophane which could withstand the mechanical tension was determined as 4 x 10-10 cc. at S.T.P./ (cm.)(sec.)(cm. Hg), when the cellophane side of the film was in contact with the electrolyte. This value is far different from the data for another species of cellophane (No. 20) in Table I. Also, the values of P, measured by the two methods are different in their order of magnitude. These facts are entirely attributable to the hygroscopic nature of the cellophanes examined. Diffusion Coefficient, D,. The determination of oxygen diffusivity through Teflon is exemplified, provided the oxygen partial pressure changes stepwise from 0 to 15.4 cm. of Hg. A set of experimental data was substituted in the right-hand side of Equation 10.
D,
b2
=
(2.5 x -~
. i,
6(i, . to - y.,) 1.50 X lO-’sq. cm./sec.
=
10-312 . (22 x 10-6) 6(1.53 X 10-4)
where to =
150 sec.
i,
22 pa.
=
b = 2.5 X l P c r n .
i,
- to - q,
coulomb (determined by using X a planimeter, Figure 2, top)
= 1.53
On the other hand, the value of D, for the same material determined from Equation 11 is: 13
= 7 sec.
D
= b2 _ =
6e
(2’5
10-3)2 = 1.49 X lo-’ sq. cm./sec. 6x7 (Figure 2, bottom)
Oxygen Permeability of Polymer Membranes as Measured by Two Methods Permeability X 70'O Cc. at S . T . P . / ( C m . ) ( S e c . ) ( C m . H g ) Specification of Membrane Thickness, p Electrode method Pressure method
Table 1.
No. 1 2 3 4 5 6 7 8 9 10 11 12
Silicone rubber Natural rubber Tetrafluoroethylene (Beckman) Tetrafluoroethylene (cast) Tetrafluoroethylene (skived) Tetrafluoroethylene (Du Pont, FEP) Polystyrene Polyethylene, p = 0.920 gram/cc. Polyethylene, p = 0,927 gram/cc. Polypropylene (Mitsui-Noblen) Polypropylene (Mitsubishi-San Orient) Poly(viny1chloride) (heat-shrinkable)
200 200 25 20 50 20 30 20 20 20 9 13
(A)d
Poly(viny1chloride) (heat-shrinkable) (B )* Poly(viny1 chloride) (heat-shrinkable)
13
14
(CY.
15
Poly(viny1chloride) (heat-shrinkable) (A').d
Poly(viny1chloride) (heat-shrinkable) iB')d Poly(biny1chloride) (heat-shrinkable)
16
17
--
65
100
N
N
100
70 40
113 (27.5' C.) 1 5 . 6 (20' C.) 1 0 . 2 (20" C.) 8 . 7 b (20' C.) 5 . 7 (23' C.) 5 . 3 (30' C.) 3 . 1 (30' C.) 3 , 5 (200 C . ) 2 . 1 (20° C.) 1 . 5 (20' C.) 1 . o (200 C.) 0 , 2 2 (200 C.)
431a (20' C.) 9.22" (200 C.) 1Oa
...
3 , 7 =(30" C.) 2.5" (30' C.) 2.1c (200 C.) 1 . 7 a (200 C.)
13
0.42 (20' C.)
13
0 . 8 5 (20'C.)
13
0.35 (25' C . )
0.149'(20° C . ) 0.236 (30' C.) 0.206 (20' C.) 0.455 (30' C . ) 0.467 120* C.'r 0.920 (300 c.j 0.14 (23" C.)
13
0.81 (25" C.)
0.28 (23' C.)
13
1 . 4 (25' C.)
0.57 (23' C.)
30 29 30
0.0795 (20" C . ) 0,0328 (23' C.) 0.069 (23' C.)
0.0825 (20' C.) 0.0165" (20' C.) 0.0004n (20' C . )
13 30
0.0415 (21' C.) 0.0376 (21' C.)
0.008a (20' C . ) 0 . 0 1 2 P (20' C.)
(C'W
18 19 20
R&b& hydrochloride Poly(viny1fluoride) (Tydlar) Cellophane (coated with copolymer of vinylidene chloride and acrylonitrile) Poly(viny1idenechloride) Poly(viny1idenechloride)
21 22
a IMeasured by T . .Vakagawa, Industrial Arts Institute, Agency of Industrial h'cience and Technology. For spec& membranes, of a range of thickness, p , values are arithmetic auerages of seueral samples; unless otherwise noted, p , value w a s determined dejinitely by one run by each method. c T a k e d o and Yamaguchi ( 7 9 5 9 ) . d Specifications of A , B , C, and A ' , B I , C' f o r Poly(vinyl chloride) indicate dlffkrent content of plasticizer i n process of manufacturing membranes, plasticizer content being increased f r o m A to or f r o m A' to Prime implies that date of manufacturing f o r A is different f r o m that f o r A ' , f o r example. e Measured by membrane manufacturer.
c
c'.
Table II. Oxygen Diffusivity of Polymer Membranes as Calculated (Equation 5) or Determined by Electrode Method (Equation 10 or 1 1 ) D,, Sq. C m . / S e c . X lo7 at 20' C. Polymer Membrane Eq. 70 Eq. 7 1 Eq. 5
Teflon (Beckman) Teflon (Du Pont, FEP) Polypropylene Table 111. Item
1.5 1.07 1.62
1.49 1.25 1.37
1.7 1.2 1.6
Comparative Performance of Electrode and Pressure Methods Electrode Method Pressure Method
Speed of measurement Fast (several minutes) Easy Operation Cost of construction Very cheap Membrane to be Generally not suited examined for hygroscopic membranes Applicability to species of gases
Oxygen, primarily
Slow (several hours) Complicated Expensive Applicable even to hygroscopic membranes, in principle Many gases
~
Therefore, the agreement between the two procedures is satisfactory. The value of D, is estimated as 1.7 X lO-'sq. cm. per second from digital computation with Equation 5, excluding a specific region near t = 0, and referring to the experimental data on the transient current, it. Table I1 summarizes the values of D, determined from different angles in the electrode method. T h e agreement of D , between calculation (Equation 5 ) and experimentation (Equation 10 or 11) is also satisfactory. This supports the previous assumption that the resistance of electrolyte to oxygen transfer and the electrochemical reaction rate d o not predominate; the rate of oxygen transfer is con-
trolled by the membrane diffusion as shown by Equation 5 if the membrane is tightly attached to the cathode surface. Advantages and disadvantages associated with the two methods are shown in Table 111. Conclusions
The membrane-covered electrode, which is widely used for measuring the oxygen tension in a fermentation broth, was applied to a rapid determination of the oxygen permeability of various polymer membranes. By measuring the diffusion current in the steady state, values of oxygen permeability through polymer membranes were observed satisfactorily. The time required for the measurement was on the order of a minute to about 1 hour for the higher and the lower values, respectively. The effect of temperature was easily determined. I n addition to the measurement of oxygen permeability, the values of oxygen diffusivity through polymer membranes were studied with reference to an indicia1 response of step change of oxygen partial pressure. Ac knowledgrnent
Thanks are due to T. Nakagawa, Industrial Arts Institute, Agency of Industrial Science and Technology, for his measurement of the permeabilities of many samples by the pressure method, and to companies which supplied the test materials for this specific purpose. Nomenclature
A
= area of cathode, sq. cm.
a
= thickness of electrolyte layer, cm. = thickness of membrane. cm.
b
VOL. 7
NO. 3
AUGUST
1968
501
c,
= oxygen concentration in membrane, grams/cc.
if
= transient current, @a.
Dm = diffusion coefficient in membrane, sq. cm./second F = Faraday’s constant, 96,500 coulombs/gram-equivalent 2,
= steady-state current, pa.
N
= number of electrons per molar unit of reaction
P,
= permeability, cc. at S.T.P./(cm.) (sec.) (cm. of Hg)
lam
= oxygen partial pressure in membrane, cm. of H g
$0
= oxygen partial pressure in sample medium prior to step
change, cm. of H g = oxygen partial pressure in sample medium, cm. of H g
qr
=
&Lt
i,dt,coulombs
R = electrical resistance, ohms
s,
= solubility constant in membrane, cc. a t S.T.P./(cc. of
polymer) (cm. of Hg)
T = absolute temperature, OK. t x
= time, seconds distance along direction of diffusion, cm.
=
GREEKLETTERS = lag time, seconds p = density, gramsjcc.
e
literature Cited
Barrer, R. M., “Diffusion in and through Solids,” p. 19, Cambridge University Press, London, 1941. Carritt, D. E., Kanwisher, J. W., Anal. Chem. 31, 5 (1959). Clark, L. C., Jr., Wold, R., Granger, D., Taylor, F., J . Appl. Physiol. 6 , 189 (1953). Delahay, P., “New Instrumental Methods in Electrochemistry,” p. 217, Interscience, New York, 1954. Jenson, V. G., Jeffrey, G. V., “Mathematical Methods in Chemical Engineering,” p. 284, Academic Press, New York, 1963. Kunz, W. B., Cornwell, R. T. K., Tappi 45, 585 (1962). Lingane, J. J., J . Electroanal. Chem. 2, 296 (1961). Mancy, K. H., Okun, D. A,, Reilley, C. N., J . Electroanal. Chem. 4, 65 (1962). Nakagawa, T., Industrial Arts Institute, Agency of Industrial Science and Technology, Tokyo, unpublished data, 1967. Nakagawa, T., Kogyo-gz’jutsu 6, 20 (1965). Sawyer, D. T., George, R. S., Rhodes, R. C., Anal. Chem. 31, 2 (1959). Stannett, V., Szwarc, M. J., Polymer Sci. 36, 89 (1955). Takeda, B., Yamaguchi, B., J . Chem. Soc. J a p a n , Znd. Chem. Sect. 62, 1897 (1959). Tuwiner, S. B., “Diffusion and Membrane Technology,” p. 232, Reinhold, New York, 1962. RECEIVED for review August 7, 1967 ACCEPTEDFebruary 29, 1968
CO M MU N ICATIO NS
FEED PLATE MANIPULATION IN DISTILLATION COLUMN FEEDFORWARD CONTROL Feedforward control schemes for distillation columns have traditionally used only refliix and/or vapor boilup as manipulative variables. This communication suggests an alternative technique that may have significant advantage: in Tome systems. Its basic idea is to change feed tray location to compensate for feed composition disturbances. Steady-state and dynamic feedforward controller synthesis techniques are presented, Effectiveness of control is demonstrated b y digital simulation of a 20-tray column.
HE
development and application of feedforward control
T to distillation columns have been among the most active and successful areas in chemical engineering process dynamics and control in recent years. The large time constants and dead times and the multivariable, distributed nature of distillation columns often make them difficult to control with conventional feedback techniques. Consequently they are natural candidates for feedforward control. Early theoretical work in the area (Luyben and Gerster, 1964; Rippin and Lamb, 1960) was quickly applied on industrial columns (Lupfer and Parsons, 1962 ; MacMullen and Shinskey, 1964). Linear techniques based on theoretical or empirical column dynamic models have been used in most instances. Recent theoretical work has considered multicomponent systems (Cadman et al., 1967) and some nonlinear effects (DiStefano et al., 1967; Luyben, 1965). Both the academic and the industrial work have been limited to simple systems. Reflux and vapor boilup have been 502
l&EC FUNDAMENTALS
the only manipulative variables discussed in the literature, Disturbances in feed composition and feed rate have been considered with the control objective of maintaining constant product purities. Thus feedforward controller synthesis consists of determining four transfer functions that relate the two manipulative variables (reflux and vapor boilup) to the two disturbances (feed composition and feed rate). One of the most promising alternative schemes is the use of feed tray location as a manipulative feedforward control variable. Such a scheme would intuitively seem desirable for changes in feed composition, particularly where pinch regions form a t the feed tray. Allowing feed plate location to be variable provides an additional degree of freedom. Therefore one product composition could, in theory, be controlled. If feed plate location and one other variable can be manipulatede.g., reflux-two product compositions could be controlled. The effectiveness of such control schemes would be expected to be limited to a certain range of feed compositions because
