November 1951
INDUSTRIAL A N D ENGINEERING CHEMISTRY
d
the column. Secondsubscript in parentheses) refers to time during the process, a n to the total number of discrete portions of charge that have entered the column = first e uilibrium coin osition (unadsorbed li uid) calculated for top (grst) unit quantity of g a = second equilibrium cornposition (unadsorbed liquid) calculated for top unit quantity of el = ith equilibrium composition (unadsorbef liquid) calculated for top unit quantity of gel. z is arbitrarily dcsignated as an odd integer so as to dietinguish between calculations by Equations 2 on the one hand and Equations 3 on the other hand = first e uilibrium composition (unadsorbed liquid) calcuyated for second unit quantity of gel = first e uilihrium compmition (unadsorbed liquid) calcu?ated for nth unit quantity of gel = volume fraction of more strongly adsorbed component in adsorbed phase. Subscript8 have same meaning as for x = equilibrium composition in adsorbed phase when composition of unadsorbed li uid is zl(,) = equilibrium composition in a8sorbed phase when composition of unadsorbed liquid is zn(i) = separation factor ( 6 ) in ternary phase equilibrium equations
quantities of adsorbent were assumed in the calculations. A method of programing for ternary development calculations is suggested,
ACKNOWLEDGMENT
h
Grateful acknowledgment is made to the Research Corp. for financial assistance with the computations, including especially the rental oharges on the IBM autornatio computers. Acknowledgment is also made to Patricia Peters and Jerome Sekerke for their careful and painRtaking work during the early tedious phme of the calculations.
NOMENCLATURE = arbitrary constants used for convenience add simplicity in writing Equations Id, 2d, 3d. When used with prime mark-Le., A’, R’,et?.these refer to values applicable for x < 0.226; otherwise for x > 0.226 = ae subscripts to designate components in a ternary mixture = empirical constants in phase equilibrium equatioii (Equation 4)when x > 0.226 = same as g h when x < 0.226 = dynamic holdup (unabsorbed liquid), ml./unit weight of adsorbent = static holdup (adsorbed liquid), ml./unit weight of adsorbent = total volumetric holdup = HD Hs, ml./unit weight of adsorbent = volume fraction of more strongly adsorbed component in feed t o the top of the column = volume fraction of more stron ly adsorbed component in unadsorbed phase. fiirst subscript (not in parentheses) refers to location in column-i.e., these subscripts correspond to the various unit quantitieu of gel into which the column is divided for urpoees of calculation. Numbering is down from tKe top of
A , B, a, b, e, d, e
A, B g, h
g‘, h’
HD Hs HT xo
T
+
2459
LITERATURE CITED (1) Bhkley, 6. R., Wagner, G. L., and Smith, R. W., private
communication.
(2) Eagle, S., and Soott, J. W., IND.ENG.CHEM., 42, 1289 (1960). (3) Ibid., pp. 1291-92. (4) Lombardo, R. J., unpublished data. (5) Mair, B. J., Westhaver, J., and Roasini, F. D., IND. ENQ.CHEY., 42,1282 (1960). (6)IM., p. 1284. (7) Ibid., p. 1286. (8) Whittaker, E.,and Robinson, G., “The Calculus of Obeervations,” p. 266, New York, D. Van Ncxrtrand Co., 1948. R E O ~ I V EApril D 4, 1961.
Stepwise Plate-to-Plate Computation of Batch Distillation Curves When Simplifying Assumptions A r e Not Applicable ARTHUR ROSE, R. CURTIS JOHNSON, A N D THEODORE J. WILLIAMS The Pennsylvania State College, Stale College, Pa. Prediction of the course of a batch fractional distillation under practical operating conditions involves complex and laborious calculations. The present paper describes the use of readily available IBM computers for predicting industrially important batch distillation operations for cases of appreciable holdup, variable relative volatility, variable molal overflow, and plate efficiency other than 100%. The derivation of the necemary equations is given and the programing is described in detail. The agreement between calculated and experimental curves makes the procedures useful for releetion of advantageous operating conditions for practical batch distillation operations.
ARLIER papers from this laboratory ( 1 4 ) described a method of predicting the course of a batch distillation with appreciable holdup when simplifying assumptions, such as equal molal overflow and 100% plate efficiency, were applicable. These papers indicated the general approach to such calculations by means of the previously described stepwiee plate-to-plate procedure and automatic punched card computers. The present paper gives the detailed computational procedures for certain nonideal batch distillation calculations in which it is not possible to make all the simplifying aesumptions. The cam of greatest interest has been the one involving plate efficiency of 74% (chosen to correspond with a particular set of experimental results) instead of 100%. This wm apparently the only factor that caused major discrepancies between experimental resulta and those calculated with all the simplifying m m p t i o n s previously listed.
E
INDUSTRIAL AND ENGINEERING CHEMISTRY
2460
Figure 1.
Page 1 of Planning Chart for Batch Distillation Calculation
BASIC EQUATIONS The equations for the 74% plate efficiency calculations are only slightly different from those given in the previous papers, but are repeated here for ready reference.
For change in top plate liquid composition due to removal of a small quantity, D moles, of distillate during one L‘interval”of time:
For corresponding change in liquid composition from other plates :
(2)
For corresponding change in composition of liquid in still pot: (3) For values of vapor coniposition: yn = eyX
Vol. 43, No. 11
+ (1 - e)y,-,
(4)
where y * = f b q ( z ) . In the present work
For vapor composition from t,he stsillpot:
Thk method of calculation requires knowledge of the initial liquid and vapor compositions for a batch column operating with a specific mixture specified number of plates, reflux ratio, holdup, and vapor rate. For a total reflux startup these may be calculated by methods previously described. The first three q u a tions then serve for calculation of new plate and still (liquid) compositions after removal of a small quantity of distillate D. When these new values are obtained, they are used with Equations 4 and 5 to obtain the corresponding equilibrium y * values, and then the actual y values corresponding to 74% plate efficiency. Then the first three equations may again be used to obtain new
liquid composition values after the removal of a second small quantity of distillate. Additional x values are obtained by repetition of the procedure. The process of computation is lengthened further by the necessity for making a material balance check after each new set of 2 and g values is obtained, and by the necessity of averaging or correcting the x values first obtained. The correction is carried out by means of the equation
The material balance check is necessary to eliminate arithmetic errors, and the averaging reduces a truncation error to negligible size.
CARD-PROGRAMED ELECTRONIC CALCULATOR The card-programed calculator performs the required calculations automatically by use of a deck of 155 punched cards (for the particular conditions used in this study). Each card suppliee certain numerical values such as the starting compositions, or it directs the machine to perform a particular arithmetic operation and the related transfers of various numbers from one storage register to another, etc. The process of planning the punching patterns on these cards, and the related planning of the wiring of control panels, are referred to as programing. The order in which the various calculations are made on the computer is not the same as the order in which the equations are listed in the previous discussion. Rearrangement allows more effective use of the computer. The steps in the actual procees of calculation are as follotvs: Card 1. Enters the numerical valucs of starting liquid coiiipositions and the value of efficiency. Card 2. Causes a transfer of e from one storage position to another, in order to clear the first position for other factors. Cards 3 to 8. Calculate and store zm/4 values to be used later in averaging calculations (Equation i , . Cards 9 to 14. Calculate ycT0)valueb from Equation 5. Cards 15 and 16. Clear two counter groups for other uses. Cards 17 to 33. Calculate y/1(0)through YS(O) by Equation 4. Cards 34 to 63. Calculate preliminary z(,) values a t end of interval 1 by Equations 1, 2, and 3. Cards 64 to 75. Calculate 2(,)/2 valuvs which are added to z(0)/4values for later use in E uation 7. Cards 76 to 129. Reycat %e above piocess of obtaining y *
INDUSTRIAL AND ENGINEERING CHEMISTRY
November 1951
2461
1 ~~0OO00OOOOOOOOOOOOOOQOOOOOOOOOOOOOOOOOO0000~00~~000000000~0000~0000000~00000000 I 2 3 1 5 I 1 8 a IO 11 iz 13 14 IS II 11 18 11 a0 zi zz za Y I Sa n o n1031 ~l JI II r SI JI m 1041 u u u u u nu ce ISI u uw s Y S Y~n 10 81 u w w IB b i w a i o 11 IZ 13 14 1 18 n 18 B Y 11~111111111111111111111111111111111111111111111111~111111111111~111~~1111111111 22222222222222222222222222222222222222222222222222222222222222222122221212222222
33333333333333333333333333333333333333333333333333333333333331333311333333333333 444444444444444144444441444444444444~44444444441444444414444414444444444444444444 5555555555555555555555555555555555555555555555555555555151515~555555155555555555 666666666666S6666666666666666666666666666666666666~66~66666666~66666666666666666
I
1 1 71 1 7 1 1 1 1 1177 11 7 1 1 1 1 11 1 11 11 11177 1 11111 1 1 111 7 1 7 1711 117 1117 1 71 11 11 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1
99999999999999999999999999999999999999999999999999999989899999999999999999999999 I I a 4 s 8 t 8 * IO 11 11 13 14 IS 18 11 II IO m n a ai4 a a n a n Y 31 ut)H 1s JI 31 m a441u u u ~ u 4 u 1 49% 31 u u w IY a s Y 10 81 (Ia w r) u iiGII( n 11 n 13 14 7s 18 n 11 IS 10 IBM 8001
~~o~~oooeo~ooooooooooooooooooooooooooooooooooooooooo~ooooooooooooooooooooooooooo I I z 4 5 E I 6 B IO 11 IZ 13 14 IS 18 11 18 1810 ZI n n H n a n a n Y 31 as5 JI 1s J $731 m 1041 u u u e u 41 u u IO SI u u w Is ST s IO w 81 u w w IM F u ~ ta 10 11 12 13 74 n i o n n i s 10 tllll~l~~lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll~lllllllllll
2212222222222222222222222222 2222222222222222222222222222222222222222222222222222
3333333333333333333333~333333333333333333333333333333333333333333333333333333333 4144444444444444444444~444444444444444444444444444444444444444444444444444444444
555555555555555555555555555555555555555~5555555555555555555555555555555555555555 606666666666166666666666666606666666666666660666666666666666666666666666666S6666
111111111~7111111111111111111111111111111111111111111111111111171111111111111111 000080~000000000000000000000000000~00%08000000000000~008000~0000000060~0080U0006 9999999999999999999999Y999999999999999999999999999999999999999999999999999999999 I t a 4 s 8 1 8 o ID 11 it 13 14 IS 18 11 11 IO m ZI zz n H I S n n a a I ai az t)JI I Y ai SJI u 11 u u u u u e uce I81 x u w IY II s n 10 II K N w t5 w a w w i u 71 12 73 14 15 i s 11 IP n 10 IBH 5081
Figure 2. Punched Cards in Batch Distillation Calculation Upper. Card I
Lower. Card 2
and y at end of interval 1-i.e., effectiveduring interval L a n d the preliminary values of 2 a t end of interval 2. Cards 130 to 141. Calculate x2)/4 and add to previously stored factors to obtain averaged vaiues of x at the end of interval 1, using Equation 7. Cards 142 to 151. Material balanw Calculation on corrected z values. Cards 152 to 155. cards to allow time for storage ; %m : previous group of cards. and transfer of last kn:% The result of the passage of the deck of cardr through the machine is that the original xo composition va ues are replaced values corresponding to compositions after the reby new ql) moval of D moles of distillate. If desired, these and any intermediate values of interest may be printed as the calculation is proceeding. The calculation of a set of za) (corrected) values is achieved by passing cards 3 through 155 through the process a second time. The first two cards are not necessary after the first passage, aa their only function is to introduce original numerical values. The continuation of the calculation is mere repetition of the passage of cards 3 through 155 through the machine, As the computer operates a t the rate of 150 cards per minute, the com-
putation proceeds a t the rate of approximately D moles of distillate removed for each minute of computer time. The general sequence of calculation is
1. Preliminmy value of xi+ Preliminary value of z,+ 3. Averaging of corrected xi with preliminary to obtain corrected x , + ~ 4. Material balance check 2.
~
iand +
x,+) ~
DETAILS OF PROGRAMING The detailed description of the programing is rather complex, and is summarized by a planning chart. A portion of the planning chart for the calculation under consideration is shown in Figure 1; an explanation of the first few lines will indicate the meaning of the symbols, the general nature of the problems of programing, and the solution of these problems. (The remainder of the planning chart and wiring diagrams for this calculation may be obtained by application to the senior author.) The various column headings on the planning chart are explained as they are encountered. “Operation” indicates the
2462
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
Vd. 43, No. 11
The punching 3 in the operation column (column 6) signifies multiplication of the factor 2500 by the value of ZNO) which is simultaneously read into electronic storage B EM the result of punchings 72 in card columns ’7 and 8. The punching 7 results in the ~ ~ ( value 0 ) remaining in the counter group 2 &e well aa being transferred to electronic storage B. This punching 7 in column 7 always results in retention of the number in the counter group as well as transfer to electronic storage, whereas an 8 punching in column 7 always results in clearing the counter group after the transfer. The result of the punchings in columns 1 through 8 in card 3 is that the product of 2500 and zs(o)appears in the electronic counter, C. The 11 punching in Channel C columns indicates transfer of this product to auxiliary storage 11. Adjustment of the decimal point (if necessary) is done a t SA later s t q e in the process. Cards 4 through 8 perform multiplication and storage operations similar to card 3, as indicated by the code and aymbols on the planning chart. Cards 9 through 14. The only symbol requiring explanation here is the 6 punching in the operation column. This, through special wiring arrangements, causes calculation of y * values from 5 values by Equation 5. Cards 15 and 16 are merely transfers to clear counbr groups 2 and 3, so they may be used in succeeding operations. Card 1. The punching of the No. 1 card shown in Figure 2 Card 17. The symbol 2 in the operation column signifies that is different from all the others because it is used to enter the initial the value of e coming into electronic storage B is to be subtracted li uid plate compositions, the still pot composition, and the plate from the value unity read from the card entry oolumns into clecegciency for the particular example that is being calculated. tronic storage A . The additional 7 punching in the operation This card has punchings of 07400 in columns 45 through 49 to column indicates that the resulting 1-e value appearing in the introduce the plate efficiency, e, and a series of punchings in colcounter is to be transferred into electronic storage A umns 50 through 73 for the several numerical values of za(~) electronic as well as into counter group 2,as directed by the 72 punching in z1(0), etc. I t also has an z (or 11)punch in column 13 which actuChannel C columns. The transfer into electronic storage A ates the mechanisni of the various computer arts to enter the allows use of l-e in the calculation made in the next card cycle. 1 throug! 7 as indicated on values of e and z into counter groups . Accordingly, card 18 has no punchings whatever in columns 4 the planning chart. and 5. These counter groups, and also the electronic and auxiliary storage registers, are merely devices where particular numbers The detailed punching of the remaining cards (18 through may be stored until they are needed later in the calculations. 155)is similar to that already discussed. The entry of B ~ in D auxiliary storage register 22 does not correThe programing of the calculations for a five-plate column with spond to a card punching, but is merely to indicate that this storage register is reserved for ~ Z in D later steps in the computation the same assumptions as included above can be modified very Card 2. This card is unched with the number pattern 002-00easily for different values of charge composition, efficiency, 1-81-17-0in columns 1 tLough 11 (see picture of card in Figure 2 relative volatility, reflux ratio, holdup, and charge size, In all and corresponding line on planning chart in Figure 1). The card these cases the only cards in the deck which must be changed are number appears in the first three columns. The over-all purpose of this card is to transfer the plate efficiency, e, from storage in the first card (when a change in one of the variables affects the counter group 1 to auxiliary storage register 17. Direct transfer initial conditions), and any cards where any of these variables, of e from card 1 to auxiliary storage 17 is not possible. or quantities dependent on them, are introduced into the calculaThe path that is always followed in any transfer from one auxiltion. It is thus possible to simulate a given distillation column iary storage unit or counter group to another involves passage of the number through the electronic counter, C. by the computer, and to study a range of vatirablm just as one The double zero in columns 4 and 5 signals the mechanism to would investigate them experimentally. transfer the value punched in card columns 13 through 23 into electronic storage A . These card columns are headed “Card Entry into Channel A,” Electronic storage A automatically RESULTS OF CALCULATIONS clears itself of numbers present from previous operations before Repeated passage of the deck of cards through the computer receiving a new number as indicated above. As in this specific results in accumulation of values such as those in Table I. Each case there are no punchings in columns 13 through 23, the number entered in electronic storage A is zero successive column of numbers (except the first) resulte from an The number 1 in column 6 indicates that the operation called additional passage of the deck through the machine. For the for is addition of the number entered in electronic storage A to purpose of plotting a conventional distillation curve of inthe number simultaneously entered into electronic storage B as stantaneous distillate composition us. per cent of charge distilled, the result of punches in columns 7 and 8. The 81 punching in these columns (labeled Channel B) signals the mechanism to only the XD values are required. transfer the number e in counter group 1 into electronic storage Comparison of Calculated and Experimental Distillation B,and also causes the counter group 1 to be cleared of this numCurves. The results of eight calculations of the type just deber e. The result of the operations to this point is that the quanscribed are given in Figures 3, 4,and 5. These figures also show tity e (added to zero) ap ears in the electronic counter, C. The punching 17 in co&mns 9 and 10 (labeled Channel C)indicorresponding experimental curves. In addition, Figure 5 cates that the number e is to be transferred from electronic counter shows the calculated curve for one comparable case where 100% C into auxiliary storage 17. The zero punching in column 11 plate efficiency waa used in the calculations. indicates that no shift of the decimal point is involved in this last transfer. The symbol e appears on card line 3 in the electronic counter PROGRAMING FOR OTHER NONIDEAL CONDITIONS column and on card line 4 in the auxiliary storage register 17. The results of the above work indicated that most of the The former is to indicate that e will be printed by the printing part of the mechanism during the time that card 3 is passing discrepancy between experimental and calculated curvw was due through the mechanism-i.e., during card cycle 3. The latter to plate efficiency; consequently, no detailed calculations were indicates that e does not a pear in stora e register 17 until card made for other types of nonideality. The following sections, cycle 4, and cannot be furtKer transferrefor used in a calculation however, discuss the general approach to programing such caluntil card cycle 5. Card 3. The funotion of this card is to calculate z.(o /4 from culations. Z.(O), and to store the value for later use. The punchngs in The performance of a column can deviate from ideal behavior columns 1 through 5 of this card have the same significance as on because of numerous factors. Among these are nonadiabaticity, card 2, except that in this case the 2500 punchings in card colline holdup, varying heats of vaporization of the components, umns 20 through 23 are read into electronic storage A .
operation being performed or the quantity being calculated as the result of the pasmge of the particular card through the machine. The number appearing in the column headed “Card hTo.” indicates the number of the card in the deck, so that each line of the planning chart corresponds to a siligle card arid the associated operations and calculations. The first three columns on each card are punched to indicate the proper card number. In order to be concrete and specific the succeeding discussion deals with the programing for the batch distillation of a charge of 284.8318 moles of a binary mkture with constant relative volatility (alpha) of 2.23 (ethylene dichloride-toluene), charge composition zc = 0.254,in a column with five plates of 74% efficiency, and a still pot, considered as a perfect plate. The holdup is 35.1% of the charge, and the reflux ratio is 9 to 1. The quantity of distillate removed during one time interval is 1 mole, so that L = 9and V = 10. However, the programing is so general that the computation for a different plate efficiency or starting composition would require only the substitution of a differently punched No. 1 card.
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
November 1951
heab of mixing of the components, varying plate holdup, and varying relative volatility. Some, but not all, of these may be easily handled by simple modification or extension of the procedure already described. The general approach for these cases has been indicated in a previous paper, but some further details are made available here. Calculations Involving Varying Relative Volatility. The method for thia common case haa been indicated by Rose and Williama (3)and a solution of a typical problem in continuous column design has been presented by Rose, Williams, and Dye (9). If y* can be expressed as a fairly simple explicit function of zsuchasy. ( I I : bra +ma . or
+
+ .. y* = x / ( a + bx)
W
2 -I
d
c
v,
0
IO
20
30
40
50
60
% OF CHARGE DISTILLED
Figure 3. Raaulta of Calculationa
-
1. Experimental. R
-
-
2/1, ze = 0.504, holdup 34 2 7 2. Caicdated R 2/l, 20 P 0.604, e 0.74, holdup 36% 3. Experimental. R p 2/1, 5 0 0.2S4, holdup 40 17 4. CiIcuPated. R 2/1,20 = 0.264,e 0.74, holdup
-
-
45
0
5. Calcup(ated. R * 2/1,zc 0.101,6 0.74, holdup 43% 6. Experimental. R e 2/1, 50 0.101, holdup 36.9% p
-
XD XI 24
vf 21
za xa
% distilledb
8V
1.
2. 3. 4. 5. 6.
Sample Summary of Calculated Composition Values during Batch Distillation Charge. 284.8318molee Holdup. 35.1% of charge Reflux ratio. 9 to 1 Relative volatility. 2.23 Plate efficiency. -0.74 Time
21 21
the procedure deacribed in this paper need merely be modified by substituting the above equations for the usual relative volatility equation. If the substitute equation is more complex, a few more cards may need to be added to the deck. Nonadiabaticity. If the degree of nonadiabaticity in 8 column can be expressed mathematically or assumed constant during a distillation, the size of the liquid and vapor stream may be adjuste? aocordingly. The equations already presented may be used, except that each 2! and y value must be multiplied by the proper L or V vdue correspondingto the stream under consideration. Theae values would be introduced at the proper times from the punched btruction cards or, in the w e of the m a t h e matical expression for nonadiabaticity, can be calculated as needed.
0
Table 1.
2463
b
Before' removal of distillate 0,8471 0.7617 0.6457 0.5054 0.3601 0.2335 0.1202 0
After
Afar
After
removii of D moles of dbtillate 0.8438 0.7572 0.6397 0,4983 0.3527 0.2276 0.1196 0.36
r e i o v i l of 2 D molw of distillate 0,8405 0.7525 0,6335 0.4912 0.3462 0.2232 0.1187 0.70
SD moles of distillate 0.8371 0.7477 0,6274 0.4844 0,3402 0.2195 0.1178 1,05
r e m G d of
But after column is at steady state at total reflux Mole % of charge distilled.
Varying Plate Holdup, If the amount of holdup is constant during a distillation, but the amounts held up on the various plates are different, the equations m presented above may be used. Proper H valups can be introduced from cards when needed. No method of computation has been developed a t this time to take into account varying holdup during a distillation. Heat Effects. If the heats of vaporization of the components of the mixture are different, it may be possible to take this into account by using the Peters method of a fictitious molecular weight for one of the components. In this c u e the vapor-liquid equilibrium relationship must be modified ac cor ding1 y , Heat effwts due to mixing of the components introduce an additional degree of complication that requires a different type of progmming that is beyond the scope of the present diacussion. Condenser Holdup. The effect of condenser holdup is to augment depletion of the still pot, and thus to lower all the starting comp o s i t i o n s . I t also causes a time lag in ZR, and the quantity of material held up in the oondenser must be taken i n t o a c c o u n t in the material balance calculations. in actuality, there are several different " kinds of holdup assqci0 10 20 30 40 50 60 a t e d w i t h t h e con% OF CHARGE DISTILLED denser. Thew may be d e s i g n a t e d a s conFigure 4. Reaults of Calculations denser holdup proper, Ex rimental R 4/1,zc 0.604,holdup 34.490 condenser line holdup Carhed. 4/l,ze = 0.504, 6 0.74,holdup 36% (in the line between Ex erimental. R 4/1. zc 0.254,holdup 30.9% C a h r t e d . R = 4/1, = 0.254,6 0.74,holdup = the condenser exit and a5 CaEulated. R = 4/1,l i c = 0.101, e 0.74,holdup = the take-off line), and reflux line holdup (in %Enmental. R = 4/1,zo = 0.101,holdup 36 7%
-
- -- -
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2464
the line between the take-off line and the point where reflux enters the top plate). In the succeeding discussion it is considered that only the last is appreciable, that the other two categories are negligible, and it is assumed that longitudinal mixing is negligible in the reflux line.
If HR = LR-i.e., if the contents of the reflux line flow out onto the top plate durin the time D moles of distillate are removedZRI = zn(i-,). I n %is caRe the latter must be stored in the computer until needed in the subsequent calculations. If HR = ~ L Rthen , ZR(~= ) ~ ~ ( i - 2 and ) storage must be provided for both z ~ ( i - 2and ) Z D + ~ )until they are needed. 1.0
I
I I
I
I
I
VoL 43, No. 11
those involving a larger number of plates, multicomponent cabulations, those involving change of holdup as the distillation progresses, and those involving consideration of heats of mixing. The first two categories can be dealt with by a less elegant computation procedure involving parallel computation for a considerable number of different values of the factors involved. This type of computation has been indicated by Rose and Williams ( a ) and described in detail by Williams ( 4 ) . The limitations as to plates and components, for the programing d e scribed in this paper, arise from exhaustion of the storage capacity of the available computer. Addition of more storage units is a partial solution which has not been thoroughly investigated. The programing for categories 3 and 4 has not been investigated beyond determining that considerable complexities are involved.
I
CONCLUSIONS The card-programed electronic calculator has been successfully used to calculate batch distillation curves for a column with five plates with a constant alpha mixture when holdup was appreciable and plate efficiency was different from 100%. The same programing can be used with a change in only a fey of the instruction cards to calculate curves for different values of charge, charge composition, per cent holdup, reflux ratio, relative volatility, and efficiency. By changing the programing slightly, nonadiabaticity, different heats of vaporization of the components, varying relative volatility, line holdup, and different plate holdups can be studied. The programing for multicomponent mixtures, more plates, heats of mixing, and varying holdup are more difficult and may not be suitable for calculation by means of this machine.
0*7L 0.6
ACKNOWLEDGMENT Grateful acknowledgment is made for financial aid from the Research Corp. of New York. Joan A. Schilk and Harry A. Kahn aided in the study of the IBM programing.
NOMENCLATURE
20
10
30
40
50
60
D = product removed, mole8 per interval
% O f CHARGE DISTILLED
Figure 5. Results of Calculations 1.
2.
-- -
-
e
-
Calculated. R = 9/1.%c 0.250, e = 1,holdup = 28.8% Calculated. R = Q/l, z c 0.254,e 0.74,holdup 35%
3. Ex erimental. R = 9/1,zc = 0.254,holdup = 30 6 9 4. Cakulated. R Q/l, z c 0.101,e = 0.74,h o l d u c 3
.5.
43 %
Experimental R
=
S/l,zc
a, 6, e = constants
0.101,holdup = 36.6%
If HR < LE,the material flowing onto the top plate during an interval consists partly of material condensed during the previous interval IUS a certain amount condensed during the current interval. this case, it is still necessary t o provide storage for Z D ( { - ] ) and in addition t o provide for calculation of the correct average composition of the material entering t,he top plate.
%I
CALCULATIONS FOR A COMBINATION OF NONIDEAL CONDITIONS In order to test further the ideas indicated above, the detailed programing waa worked out for a case involving nonadiabaticity, condenser line holdup, and different holdup on the different plates, as well as efficiency other than 100%. Other usual simplifying assumptions were made. The experience gained n the earlier simpler calculations described in this paper and additional study since the earlier programing waa done led to a program deck of only 117 cards for the above calculation LIMITATIONS AND EXTENSION
= Murphree y-efficiency, defined by e = yn - “”-:
y: - Y 9 r - 1 = equilibrium relationship, defined by y * = f.,,(r) H = holdup, moles per plate L = liquid downflow, moles per interval 8 = total moles in still pot V = vapor flow, moles per interval z = mole fraction more volatile component in liquid y = mole fraction more volatile component in vapor a = relative volatility I: = summation
fe12
Subscripts C = char e D = distiaate (o), (I)$ . . , . i = interval number 1, 2, . , . n, , . t = platenumber 1 , 2 , , R = reflux s = still pot
. . . .
LITERATURE CITED (1) . , Rose. Arthur, Johnson, R. C., and Williams, T. J., IND. ENQ. CHEM.,42, 2145 (1950). (2) Rose, Arthur, and Williams, T. J., Ibid., 42,2494 (1950) (3) Rose, Arthur, Williams, T. J., and Dye, W. S., 111, “Continuous
Distillation Design Calculations with the Card Programei Calculator-Solution of Trial and Error Type Problems, International Business Machines Seminar on Industrial Computation, Endicott, N. Y.,September 1950. (4) Williams, T. J., M.S. thesis, The Pennsylvania State College, 1950.
The general procedure outlined in this paper encounters difficulties for the following types of batch distillation calculations:
. . . n, , . . . t o p plate
RECEIVED April 4, 19-51.
