Punched Card Devices for Distillation Calculations ARTHUR ROSE AND THEODORE J. WILLIAMS The Pennsylziania State College, State College, Pa.
Punched card computers were used successfully for plate-to-plate calculations of binary and ternary steadystate continuous distillations when simplifying assumptions are applicable, and for stepwise plate-to-plate calculations with appreciable holdup. Methods are described for extending the procedures to cases where simplifying assumptions are not applicable. The use of the computers greatly speeds up calculation and reduces the labor and chances of error in complex calculations.
STEADY-STATE CALCULATIONS FOR BlNARY MIXTURES
When the molal overflow and relative volatility may be assumed constant, the problem of calculating plate compositions from distillate composition is simple. Even this becomes laborious with graph paper, slide rule, and desk calculator if m m y plates are involved, or if numerous trials of different reflux ratios or distillate compositions are required. A digital computer can obtain values of 21, yt-1, ~ 1 - 1 , yt--2, .rt--2, etc., quickly (Figure 4) by alternate use of the well lmown equations
A
GREAT deal of progress has been made in recent years in -xn = (1) the use of distillation as a means of purifying and analyzing ?/n CY( 1 - grz) complex mixtures. I n some cases progress in theory or design and has been restricted because of the number of variable factors, the .complexity of the relations between these, and the difficult or I1 Yn-1 = .; r n I. I” laborious nature of the computations involved. The value of modern computing machinery as an aid in such situations has or by the equation resulting from combining Equations 1 and 2, been ‘ pointed out frequently, and applications in ballistics, with taking successive values t , t - 1, t - 2, etc., where tis the numnucleonics, and physics are well known. ber of plates or stages in the column. The relative volatility, CY, The present paper describes the use of certain types of punched and the rates, L and V , and the reflux ratio RD,are constant for card digital computers as an aid in obtaining numerical values reany one calculation in consequence of the simplifying assumpquired for the solution of problems in distillation. The comtions. The values of these quantities and Z D are determined by puters used and suggested are those developed b y the Interthe circumstances for which the calculation is to be made. national Business Machines Corporation from punched card deA detailed description of a specific example of these steady-state vices originally used solely for bookkeeping and similar operacalculations is given in a following portion of this paper. tions. Two varieties of recently developed units are parThe preceding equations apply only t o the section of a fracticularly important-namely, Type 604 electronic calculating tionating column above where the feed enters-i.e., the enriching punch and the more recent card programmed electronic calculasection. Similar equations that apply to the lower section are tor (Figure 1). These machines use electronic devices to pernot discussed herein. form operatiom of addition, subtraction, multiplication, and It requires little more time and trouble to get plate composidivision. Properly guided sequences and repetitions of these tions.for 100 different reflux ratios and/or distillate compositions, basic operations make possible a great variety of mathematical than for a single ease. I n fact, it is not worthwhile to do these operations. simple binary calculations on a computer unless many answers Guidance for the electronic mechanisms and the introduction are required. Their simplicity makes them suitable for ai1 exof the original numbers used in the calculations is provided by planation of the method of using the computers. special properly punched cards (Fijpre 2 ) and detachable wired There are many practical situations in which the preceding control panels (Figure 3). Answers are automatically punched equations are of little value because the simplifying assumptions on the same or other cards or, in the case of the card programnied are not justified. I n such cases, computers are even more useful, calculator, can be printed directly in the form of tables. Auxiliary devices are required for the original punching of the cards used to initiate the calculations, t o sort the final answer cards and, in the cwe of the Type 604 calculating punch, for the printing of answers or preparation of cards for further calculations. In some cases, the auxiliary tabulating and printing device, known as the Type 402 tabulator, may also be used to graph results of calculations automatically. T h e original applications in this laboratory were in connection with the complex calculations of batch distillation theory, but other examples relate to conventional continuous distillation theory including multicomponent mixtures. This paper indicates possible approaches for some of these, together with some details and examples. Extension to calculations for related separation Figure P. T.R.M. Card Programmed Electronic Calculator processes is immediately obvious.
+
+
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Figure 2. Us=lnu.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1950
hours of machine time on the Type 604 computer and 4.7 hours on other auxiliary equipment. The numerical answers appeared first on the punched cards from the computer and were then automatically typed in convenient rows and columns by a Type 402 tabulator so that particular values might be located easily. This group of values probably constitutes all that will ever be needed for this particular set of distillation conditions, since answers for intermediate values of RD and X D can be obtained by interpolation. Similar calculations will soon be made for other values of a. It is intended that these will be made generally available, together with methods of interpolation. When this is clone, it will not be necessary for anyone who has the tables to do McCabe-Thiele or Smoker equation calculations for cases where simplify+g assumptions including constant relative volatility are applicable. Some further details of the actual computations are described since the procedure is basic for the more complex distillation calculations. The actual computations were made to four significant figures using the Type 604 unit. This is composed of a Type 604 electronic calculating unit and a Type 521 gang summary punch. The control panels for each of these were first wired in accordance with the diotates of the operating equation. I n this case, this is a combination of Equations 1 and 2 as follows:
Punch Cards
d h o w . Standard I.B.M. punch rard Card punched for binary steady-state plate-to-plate calculation
n hcri necessary basic data for calculations are available. kiquatioiis and computation methods follow for cases in which the vapor-liquid equilibrium docs not correspond to Equation 1, for cases of unequal heats of vaporization of the components for nonadiabatic operation, and for plate efficiencies other than 100%. For thr vapor-liquid equilibrium case, use is made of the relation
x
= ay
+ b y 2 + cy3 + dy4 + . . . .
(3)
instead of Equation 1, the values of a, b, c , etc., being chosen to obtain agreement with experimental vapor-liquid equilibrium data for the mixture. One w t ~ l lestablished procedure for hand calculations in cases of unequal heats of vaporization is to use fictitious molecular weights chosen so as to give equal heats of vaporization. The effect of this is to modify the vapor-liquid equilibrium curve. With a computer this modification merely requires changes in the constants of Equation 3. If the column is not adiabatic, the actual values of V and L for any plate can be estimated from those a t the top of the column by simple equations such as
+ kVg = (1 + k)Vi L"-* = V f - l + k V l = V f + 2kVt, etc. Vt-1 = Vt
Following the wiring, a card was manually prepunched for each separate combination of RD and X D . For the example considered here there were 575 different cards required since there were 23 separate values of RD and 25 of X D . Each card was punched for the proper values of RD,( R D 1) a,a- 1, zti+ and .rn since these are the basic values of this particular calculation. In addition, the cards were numbered consecutively, and punched accordingly. This i. qecessary for ease of sorting later. These data were punched in columns 1 to 24 of the card and nrranged as follows for card number 1 (Figure 2):
+
Colunm 1 = card idcntification number = 1 Colunms 2-5 = RD = 100, punched as 0100 Columns 6-13 = '(RD l ) a = 108.474, punched as 01081740 Cmlumns 14-16 = a - 1 = 0.074, punched as 074 Columns 17-20 = S D = 0.9500, punched as 950 Columns 21-24 = z,,+~ = 0.9500, punched as 950
+
The distillate composition appeared twice on all these original manually punched cards in order to maintain symmetry with succeeding steps in the calculation since ZD = zn+l for the top plate but not for others. The entire group of cards were placed in the hopper of the Type 521 punch, and from here were automatically and rapidly passed through the machine one by one. The calculator proceeded to calculate zt for each of the 575 cases and punched the answers in the next four spaces (25 to 28) of
(4)
where k is a fraction related to the magnitude of heat leak. For computations involving plate efficiency (in terms of liquid composition) Equation 1 niust be replaced by E
-
TABLE I. TIONS OF
VALUES USED I N CALCULATIONS O F PLATE COMPOSI-
~OO-PLATE COLUMNWITH VARIOUSREFLUXRATIOS AND PRODUCT COMPOSITIONS A.
-
Values of Reflux Ratio ( R L/D) 1 40 150
3 5
DETAILeD PROCEDURE FOR COMPUTqTION
An example of the steady-state binary calculations for the enriching section, when simplifying assumptions are applicab!e, is the computation of values from zlw to for a mixture with = 1.074 (methylcyclohexane-n-heptane)for all the combinations of distillate compositions and reflux ratios of Table I. These were of interest in connection with the comparison of certain theoretical and experimental work. By the use of the Type 604 I.B.M. computer, a total of 57,500 values of x were obtained in 16.5
10 ~. 15 20
25 30
50 60 70 ..
200
80
400
90 100
500 1000
250
4nn _._
125
B. Values of Distillate Composition
(ZD)
0,5000 0.4500
0.4000
0.3500 0.3000 0.2500 0.2000 0 . 150.0 0.1000
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Vol. 42. No. 12
For computer us
= f ( Y A Y", zic, u*m nac,
.CP).
(8)
E m h 01 them w x e tlicn used with the coriespondirig opeiating
(10)
Tiwsc equations m e w in thrces, but only two need be used since tho three niale fractions must always add ta unity. For the top plate zAn= zdi,, zB. = q8", if B total eondcnser is used. 'Thus for the top plate calculation for any particular mixture and reflux ratio, specific numerical values were available for dl the quantities on the right side of ICquation 10. These were supplied to the eornputer, which then computes zm-,, ZB*-,, as.?, ma-, etc., at the rate of approximately 50 calculations per minute. Other series of computations followxi for different distillate compositions and reflux ratios.
Figure 3.
Control Panel of the tilectronir: CalculstinCr
Punch
Fiyore
4.
Upper Seetiou of Fractional Distiltation Coliimn
The o m with which u computer givrs plate coinpositions lor a large group of distillate compositions and reflux ratios is advantageous wben trial and error ewleulations are required. If the range of distillate compositions and reflux ratios can be chosen so it9 to include those giving the desired answer, this can be obtained by inlerpolation after a single series of computations. Similar ealculntions can be made for mixtures of four or more components n,ith no complications other than inereax in the volurnc of work roughly proportions] to the number of compo nents. Equations and methods for variable relative volatility, unequal heats of vaporization, non:idiabatic operation, and plate
December 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
efficiencies other than 100% are more complex, but can be developed for many cases by analogy with the corresponding binary equations. USSTEADY-STATE. BATCH DISTILLATION OF BINARY MIXTURES
The preceding portions of this paper discussed the use of com puters for performance of the frequently encountered steady-state calculations of continuous distillation. The greater complexity of the unsteady-state calculations of batch distillation is well known, and the following portions of this paper give a brief consideration of the use of computers for these more difficult calculations. The calculations for negligible holdup are relatively simple by conventional methods, so that it would not be necessary to use computers unless a large number of curves were to be calculated. When holdup is not negligible, which is probably the usual cme, an entirely different and more complex procedure must be used ( I ) . The basic equations already described were modified for use with the computer to give the following:
A . For the liquid leaving the top plate:
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entire sequence of cards, and repeats the process as often as the group of cards is passed through the machine. This procedure makes possible the calculation of such batch distillation curves with relative ease and speed, whereas manual method8 required almost prohibitive amounts of time. The same procedure applies to batch distillation of multicomponent mixtures except that there is tt group of the above equations (11, 12, and 13) for all but the reference component. CONCLUSION
Digital computers of the I.B.M. type have been used successfully for plate-to-plate cnlculations of binary and ternary steadystate continuous distillation when simplifying assumptions are applicable, and for stepwise plate-to-plate calculations of batch distillation with appreciable holdup. The reduction in labor is enormous compared with conventional methods. The use of the computers greatly speeds up calculation and reduces the labor and the chances for ermr in the more complex calculations. However, the machines do not think, and in practical problems it is not always immediately obvious how a computer may be used to advantage. There is still a great need and an opportunity for chemical engineers and chemists to exercise their training and ingenuity in working out efficient solutions to cnlculation problems by use of computation devices. NOMENCLATURE
etc. = constants based on experimental vapor-liquid equilibrium data distillate rate, moles per interval of time Murphree plate efficiency total holdup per plats, moles fraction related to heat leak in nonadiabatic columri liquid rate, moles per interval of time reflux ratio L/D total moles in still in batch distillation vapor rate, moles per interval of time mole fraction more volatile component in liquid mole fraction more volatile component in vapor relative volatility
a, b, c,
H.
For the liquid leaving all other plates:
D
=
E
= =
H k
=
L = RD =
Lx,, C.
v
[
1 f (a
1)
- 1)Xn;
IS (12)
For the liquid in the still:
Y
n==1
The computation is started by supplying the computer with the values of all the quantities on the right-hand side of theae equations. Those are determined by the mixture under consideration, the quantity and composition of the charge, the holdup, the distillate rate, and the reflux ratio. The compositions $ti and znifor the start of the calculation are ztoand zn,-i.e., the plate compositions after steady state has been reached, but before distillate removal has commenced. When the control panels have been wired to correspond to the equations, and the numerical values are punched on cards and supplied to the computer, values of xtl, znl, and xx, are computed automatically and punched into the cards. These are then ready for computation of a,, xn,, and X X ~ . Repetition produces additional numerical values as desired. Efficient use of the computer requires need for and performance of a considerable group of calculations. Thus, the first use of this procedure was to make calculations for a group of 25 different batch distillations. These varied in charge composition, holdup to charge ratio, reflux ratio, and method of startup. The cards for all of these are prepared and supplied to the computer. This then calculates and punches proper values of xt,, etc., on the
V z y CY
= = = = =
Subscripts A , B, C = components A , H , C in ternary mixture c = charge in batch distillation D = distillate 0 , 1, i = time during batch distillation n = any platen S = still t = top plate t - 1 = plate just below top plate LITERATURE CITED
(1) Rose, Johnson, and Williams, IND.ENG.CHEM.,42, 2145 (1950).
RECEIVED February 17, 1950. Presented before the Division of Physical and Inorganic Chemistry at t h e 117th Meeting of the AMERICANCHEMICAL SOCIETY, Detroit, Mich.
Correction I n the paper on “Nitration of Nitro-p-xylene” [IND.ENQ. CHEM.,42, 356-8 (1950)], an error appears in Figure 4. Above a wave length of 285 mp the upper curve is the 2,3- isomer and the lower curve is the 2,6- isomer.. Below 285 mp the upper curve is the 2,6- isomer and the lower curve is the 2,3- isomer. KENNETH A. KOBE T. BROCKETT HUDSON
