H:._E:2:3:25;:.__:__§_E._, :1. in. u ‘1 2...... U «Nu m0 a o b 'I U n. J 9 v‘v ' O I .9 L I 1 .~ - r‘ t ..: a \ _-I ~ LIB-RA I Michi sa’n l) -l“. Q 411:“ I.-. Until. IlllYl‘vl. II III v. u l a , . . u. . . Inc-l ‘Illll II I in . . -I I t . \ I I n O \ | Ix! . If u ~ ~ I l . . . l O I \ I 1 i . I . . . . \ l . . \ \ .1 I x \ \ v I \0 .. I ‘ I h . .. ‘ I V I . p ‘ . I \ - \ - . , I l v ’ I. I u I ‘. \ a . . \ o .. . uh n I . . . . . I . . . ‘ h 4. I l l .. \ s! . u v . n . . . I I ‘ I: I ‘ u - I ‘ \ . . - . . t - , ; p\ ‘ I J - , . it \ . a . - . v a . a r . . o \ l . I . . I l l\ I r . ‘ . ‘ . . x u I t I . l 0 V‘ . . l O V ‘l ‘ . u s I -‘l'la'lllv \/ AUTOEEATIC CILCULA’IILEE 01" DISTIl-lu’i'l‘ (1E! TCW‘ER DESIGH By REESE-TH LEM! TURBIN A TEHZSIS Submitted to the School of Graduate Studies of Eichigan State College of Agriculture and applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1951 .‘tr ~ n ' —‘4- ’1. K 1-?“ )9 n . ""f"',‘f“.h I x \7' Lain!“ u.“ {IL-Ulla. l.) \ Title Fage Table of contents ficknoaledgomentn Introduction Derivation of Equations fiomenclatxne Calculation 2.313 thod Cparational $rinciplaa of the IBM Calculating Funch, Type 602-a Adaptation of thc Calculations to the Calculating 2351 china Setailcd Pracednre for performing the Calculation kppendixt Sample problem L181”. of Iitemtum Cited 11C: 3'] E ELEM-$41723 The author is deeply indebted to Professor J.F. fionnell for his constant advice and encoun- agommnt. Sincere thanks aru also due oombors of tho Lansing office of the 123 Corporation for literaturo and assistance, and to Oldsmobile Liv— ision General Peter Corporation and Vohlert Corpo oration for tho use of 13% machines. I. II’QZ‘RODo CTR)” Bcccucc tho calculations required in tho design of distillation column for mlticomponcnt mixtures are tedious and tin. consuming, it would b- to the advantage of tho cinnical engineer to haw available a cyctcn for automatically performing these calculations. Tho dcnlopmnt of nah a system was mdcrtakcn, and the rcaultc arc herewith present-d. It vac docircd to use a computational method that could be carried out without the exorcise of engineering Judgacnt after a preliminary tablc of data had been prepared. Thor. our. two altornativc methods of approach to this problem the first ran to adapt one of the calculation method: presented by othcr authors to automatic calculating machines; tho second can to develop, it possible, a calculation method particularly suited to automtic mlculc- ticn. 0f tho former, probably the root widely used is the Lewis and hathcccn mthod (1). It was believed that 1: this method were used, considerable trouble would arise in attempting to perform automatically tho catching of comositicns above and below the food tray, particularly if thorc were several diatributod components. Oplcr and Holt: (2) have made use of the 113:; 602 Calculating Punch for performing the tray to tray calculationo of the Louis and Ecthcaon hotbed. may report the solution of four caraponont cyotamc with col. ' fractions cclculatcd to four decimal places. To avoid the troublesome batching of concentrations at the feed tray, it no decided to use the method of determining the separation that could be obtained from e given number of trays, food composition and condition, teed trey loation, and reflux ratio. This method might seem to be less flexible than the determination of the number of trays required to effect c given separation with e given reflux. This objection is not valid, hceever, it this rigorous calculation in used in oonJunction with e quiet, epproxinete method for determining the relation between the number of plates and the reflux ratio. Such e correlation has been given in e meant article by Donnell and Cooper (3) in ehich they nuke use of Underwood'e (1.) method for obtaining linin- ”£1113. By fixing the number of trays and the feed tray location, it is also possible to mks a reliable determination of the best food trey position by taking e series of calculations with the feed entering on different in!" among the calculation methods based on a fixed number of plates, and I fixed reflux ratio are those that have been presented by Thiele and Oeddee (5), 11ml (6), and Ednister (7). Of these, the huml method employs a graphical presentation of K or e reference component plotted against the master of plates as a basis for amputations. This would obviously be mfiuitable for automatic calculation. In the Thiele and Geddos method, tray by tray calculations are based on on assumed temperature for each tray. The results from the enriching and exhausting sections are meshed at the feed tray, and the composition 15 found for each tray. Using these compositixms, tho assumed teapemturoo are checked and reassured if in error. The method proposed by Edmieter makes use of overall equations for both eectione of :1 column. These equations are booed on the use of absorp- tion and stripping factors, LAN and KV/L. After these equations an oval.- noted the results not be meshed at the feed trey. The major drawbacks to the use of either the Thiele end Geddel method or the Water method an that both require feed trey meshing after the initial celeuletione, end that both fail to provide e ample, mtentic procedure to follow for the solution of the problem. It Inc decided to uee e method by which automatic calculation could more easily be performed. The eeewwtione of oonetant colel overflow and negligible heat lose to the surroundings are trade. The first port of the derivation which follows is similar to that given by Edoieter in the reference cited, except that in this once 0. total Camden”? 18 used instead of a partial condeneor. The outstanding rectum of the derivation is eqwation (42) much relates the composition of the distillate to the quantity of dietillate, the number of trays in the col- “, the equilibrim oonditione on each trey in the column, the position 0! we feed trey, the food composition end theme-:1 condition, and the" ro- flux ratio. than the distillate cont-position bee boon obtained, troy by troy col- culetione ere mode down the tower to the still. The calculating machine chosen for this work wee the 1132-5 Calculating Punch, Typo 6024. This machine Hus ol‘zoson bocuuoo it 18 one of the mech- incl, along with the Type 6.92 machine, commonly found in accounting depart- manta. It has {greater store-go capacity than the 632 machine, and its programming is more flexible. With the present wiring of the control panels, a problem having up to twelve componente can be calculated, with mole fractions computed to five decimals. It is planned to alter the wiring to give mole fraction: to seven or eight decimal places since this procedure requiree en occurete value for the concentration of vanishing components in the distillate and bottoms product. II. DEILIVATIGE 0F ELL 1' V'\l .LUJH v-a oi By s material balance for any component at the top of the tower Vm‘ 1-:- re + D to 0’ Rearranging end introducing “1 3'1 =- 31le +2.14. (2) '1 V1 +13 :1: 3,625.15.) . (3) By s mteriel balance around the top of the tower and between the first and second trays V232 = LIX]. + Dxd (A) Roerremging and introducing K2 .134. .3 (5) x1=(.3.3.12 - 351. (6) 32‘2 Combining equations (3) and (6) 3213-3..flexdg<&i£)(7) V131 2 K2 V11:132‘32 1.2: +1., .131... 2.21... V ”1132: :.:y e mtoxiel balance around the top of the tower and be tween the second and third trays and lntroflucing K3 Y3: =. Lgxz +D "d (9) 12:333—13 (10) Io 12 Combining equations (8) and (10) 3.332319% +E§_+‘d_fl_+_u. (11) L2 Io We 71K132K2 new 3‘31“}? (333%) (:31) (3:3 3 (3333 (i3 333 33332) HOME and substituting I. for L/KV and I for K313 Rewriting in general for- ”flu,” g 3d[n(‘llzo o ‘An+ A93.» 0 oAn'h cos +‘n+1)+IIr(A1A20 o Z£§)] For convenience, these two functions of A are decimated as follows! {1(1) 3 A1 ‘20 o oAn'P A2 ‘30 o oAn+o e o +‘n'1'1 (15) 12(A) 9'- 11 A2. 0 o All (16) Equation (14) in then written (mm = 1,, [1: 11(1) + 1, 22(1)] (17) By a eaterial balance for any component at the bottom of the tower to =1 = w. + B 1a. ‘18) :1: .1331" + .4” x (19) 1 By a material balance around the bottom of the column and between the first and second trays 3171 = L2X2 ' Bx; (2°) 10 Introducing [(1 “L212 V1K1 V1K1 (21) Combining equations (19) and (21) fl=fi+1ia+£h (22) Wt V1K1 L1 L1 §=Ea+naun+m (23) L2 1-112 11172 By e material balance around the bottom of the column and between the eecond and third traye L313 :. V2 ’2 + B :ca (21.) Beerrenging and introducing x2 x2 .—. £1331 _. 3.59. (25) v2": “2‘2 Combining equations (23) and (25) .11.}. :15 4.3+ lelvaia+ VIKIB 5. (26) ‘72 K2 V2 K2 12' 1-112 We Multiplying by VZKZ and aubatituting Rex, for y.I ana +2fiasx+mm + 451V)_V_g§3)3x3 (27) Reamnging and eubetituting s for “/1. 1.32:3: x3 B ($152+ 82 + 1) + vsKs(SlSZ)] (28) Rewritten in general form (L3)m+1: I.[B(512 S e 0 es ”+52 3. e esm+e e 0+Sm+1)+vsxs(slsze 0 SD)] (29) 11 The two functions of S are designated as follows: {1(3) = 3182. . .sm+ $233. . .sn+. . dam-+1 (30) {2(3) = 5132. . '3: (31) Equation (29) can then be written (mm: 1,,[3 t1(s) + vex, 12(8)] (32) Since L: = Vy/S, equation (32) can be rewritten (mm .._ 5m x. [13 11(3) + V“ xa 12(3)] _ (33) If the nth tray is immediately above the feed tray, and the nth tray is immediately below the feed tray, the expressions n+1 and M1 will both designate the feed tray, and equations (17) and (33) lay be equated. ' 1d [9 {1(a)+ L1. ram] = 514.1} {1(S)+V‘K. {2(5)} (31.) The number of variablee in equation (34) can be reduced by use of the following identities! Ln/Vn a n/n+1 (35) 1.1.: Ln = RD (36) Va ..-. D(R+ 1) (37) B = 1 «- D ' (38) v” -.-. 0 Va (39) Equation (34) may now be written 1d D £1(A)+RD f2“‘_’] = 3pr [(1 - D) £1(s)+cn(a+1) x, r2(si] (40) Substituting for xi by the use of the equation I r.“ (1+1) 8 1-D 12 and solving for 1d; equation (1.0) becomes rd: ‘ (3H (n+1)cx s t2(s) - 3: :l(s)z n 21(A)+Rf2(1)+3ff1(8) 1>+Ea+1)cxflsr r2(s) . {1(5).Rf2(‘).5t:1(33) "'92 (42) To simplify equation (1.2) substitute the following terms: e = £1“) (43) b = n :2“) ' (41.) o = 3r 11(3) (45) d = (M1)“. at 12(5) (1.6) For this calculation take as a basis I = l. Mutation (1.2) becomes x(1 = (A?) For further simplification males the following substitutions: e =1, e (48) f = If (6 - c) (49) =. a+b+e (50) h = d - (a+b+c) (51) Equation (1.7) can now be Iritten xd = 3% (52) For the more volatile components the determination of x. by equa- tion (1.1) in not advisable due to the small difference between F :1, and D x . For this reason an equation derived from equation (1.0) is used. 11 =-.. x D (n+b) 53 time ‘ ’ 13 The following series of equations obtained from material balances give the quantity of any component in the liquid stream leaving a plate in the upper section, the feed plate, and a plate in the lower section respectively. Upper sections (L101 = 11 D and (3+ 1) (54) (1.2:); = A2 [(1.201 + D :3 ' (55) . (1.x)3 = A3 [(u)2+ D ‘4] ' (55.) (can: ‘n [can _1 + D and] (55b) Feed plates ‘ (L1): = 1/3: [(Lfln + D ad] . (56) where n is the plate above the feed plate. Lower section: ’ (L3). = 1/3“ [(1a)r - 13:5] (57) (1.x)2 = .1/32 [(1.1)3 - ax“) (57a) (1.x):l ; i/s1 [(1.102 .. Ema] * (57b) The composition of the liquid leaving each plate can be readily obtained when the quantity of each component present has been obtained. For a component 'e“ on the nth tray (La) :3! 3 a,“ (58) n ETTLX n l4 homncleture L : mole of liquid leaving a plate Y : mole of vapor leaving a plate F : mole of feed D : 113018 of distillate B .- mole of bottom product a: _— Incl fraction of any component in liquid phase y = mol fraction of any component in vapor phase B : Reflux ratio U!) K : y]: A z W s _- Va = 167/1. 0 = vn/vn C is defined by the thermal condition of the feed. pngpr nix! / 0:1 when feed is a liquid at its boiling point. Subscripta: "I. r = reflux d = distillate s : still :1 : tray numbar in enriching section numbered from condenser to feed tray n = tray numb-er in exhausting section numbered from still to feed tray 1" = feed 1' : feed tray 15 III. CALCULATION METHOD Briefly, this calculation is based on a series of successive approximations of conditions in the tower, with the results of one calculation being used as the basis for the succeeding calculation. In any trial, if the assumed conditions are correct, they will be identical to the conditions calculated in that trial. The first step is to make a preliminary estimate of the quantity and analysis of distillate and residue by assuming that nothing heavier than the heavy’hqy (specified permissible percentage of high boiling compound allowed in distillate) will be contained in the distillate or nothing ' * lighter than the light key will exist in the residue. When an estimate of top and bottom compositions has been made, the approximate temperatures of the top and bottom of the column are obtained as the do! and boiling points. 'The first estimate of tray temperatures is then obtained by assuming an even temperature gradient from tray to , tray; Hiring previously set the refluz.ratic, the ratio of liquid to vapor /'\¢ ~~»‘ f) ”"1"?“ above the feed tray is given by equation (35); halos the feed tray hy the M'- = W <59) From K data for the pressure of the tower, the values of K are found equation for each.component, for the various tray temperatures. The absorption factors are then calculated for each component on each tray in the upper 16 section of the tower, and the stripping factors are calculated for each component on each tray in the lower section. The functions of A and 3 are calculated for each component and the constants c, t, g, and h are determined for each component. i r A value of D is found which, when substituted in equation (52) will give ’ , 2 and = 1 . (60) The composition of the residue is calculated by equation (53). The quantity of each component in the liquid stream leaving each plate is calculated using equations (51.) to (57b), and the composition of the liquid on each tray is obtained from equation (58). Since the l iquid on each tray is at its boiling point, a new esti~ mate of tray temperatures is obtained by determining the boiling points of mixtures of the calculated compositions. A new Zaiue for Lu/Vh is calculated using the new value for D in equation (59). The entire calculation is repeated, using the new tray temperatures and the new value of Lm/Vm, until in any trial the tray temperatures and I the value of D that are calculated are identical to those assumed. 17 IV. OPERATIUI‘EAL PRII-LCI?LZ“S 0F l'liE IUTTIIWA3I'IOI-liaL BUSIZJESS nicnxnms CALCULATING PUNCH, TYPE 602g: (8) The IBM Calculating Punch, Type 602ne, performs the fundamental E arithmetic computations, addition, subtraction, multiplication and divi—1\~z sion, either singly or in any combination selected by the operator. The factors are read into the machine from punched cards and the results are punched in the cards by the machine. The standard machine has six storage units; the first will accommo- date ten digits and the remaining five will each hold twelve. When a number is entered in a storage unit, any number already in the unit‘till automatically be cleared. The machine also has six counters which also hold numbers. Counters differ from storage units in that a number which is read into a counter may be added to or subtracted from a number previously entered in the counter. Products and quotients from multiplications and divisions are also develoPed in the counters. The Operation of the machine is determined by a control panel which. 2 must be wired for each specific problem. Before the control panel is : wired the problem is set up on a planning chart which shows in which storage unit each factor is to be entered, in shich counters the results are obtained, and the sequence of the individual Operations. Each problem is performed by the machine in steps or programs, each program being represented by a line in the planning chart. The first 18 step is always the read cycle, in which the factors are read from the cards into the machine. In each subsequent step a calculation is made, cr'nnmbsrs are transferred from one unit to another. Electrical impulses are available at the program exit terminals, or hubs, as they are called, on each program cycle. These impulses control the operation of the units to which. they are wired. If, for snap)... on program 3, it is desired to transfer a number from storage unit 6 to center 1, wires from two of the program 3 exits would be run to read-out storage 6 and to plus counter l. The numbers transfer from one unit to another as electrical impulses. Circuits between the units involred in such a transfer must he completed on the control panel. The major por- tion of the hubs on the right side of the panel are for this purpose. The cards used in the IBM system contain eighty columns, each column baring twelve positions in any of which a hole may be punched. Ten of the twelve positions correspond to zero and the nine digits snd.the other" on positims are called I and I. The X punch is used to actuate controls; the I'is not used in this problem. The numbers are read from the cards as they'feed into the machine by'e bank of reading brushes, one for each col- umn, and are transmitted to the reading hubs on the contro1.panel. The reading hubs are wired either through counter entry to a counter, or through storage entry to a storage unit, where the numbers will be avail- able when needed. I The electrical impulses which control the operation of the machine may be aired through the pilot selector hubs in the upper left portion of the control panel. The pilot selectors are actually double throw relays. 19 then an impulse is wired to the com-on hub it is available at the normal hub when the pilot selector is in its normal position. The immloe is availnhle at the transferred huh when the pilot selector has been "picked up.‘ I! there are control impulses sired through pilot selectors the cp- erations performed by the machine will he different for the cards which pick up the pilot selectors than for the reminder of the cards. '11» pilot selectors are picked up by an impulse to one of the following: hubs! X or balance pick up, digit pick up, or immdiote pick up. The last of those transfers the pilot selector only for the duration of the cycle in which it is picked up, while the first too canoe the pilot selector to latch in the transferred position until it is drop-pod out by an impulse to the drop-out hub. If the drop-out hub is wired from punch drop-cut inpulsc, the pilot selector will he dropped out after the card is pmchcd. If drop-cut is wired from rend creep-out lawless, the pilot selector will be dropped out after the following cord is read. Thor. are twenty control brushes in the macidne located ahead of the eighty reading brushes. Tiny are placed to road in clay twenty of the eighty columns in the card. "en X punched in one of these columns will be read to a control hmsh, and will be available at the corresponding control leading hub. 11' a pilot collector is to he used to coz‘xta‘OI incul- ses Iran read cycles, it sr‘xould he picked up from control reading brushes. 1: it is to he used to control impulses from promo exits, the pilot selector is picked up from the reading banshee. If, in performing a series of calculations, one of the factors re- mains constant for each calculation, that foot-3r may be entered from the 20 first card only, into one of the storage units. The number will remain in the storage unit and can be read out repeatedly until the storage unit is cleared by an impulse from read cycles to the storage read in hub. To prevent the inpulse tron reaching storage read in for all cards in a ser- ies except the first one, a wire is run from read cycles to the common but of e pilot selector, and from the transferred hub of the some pilot _ selector to the read in hub of the storage unit. The pilot selector ie picbd up by an I read from the card by one of the control reading brush- es. The first card in the series is therefore punched with on X which will pick up the pilot selector, and cause the group factor to be read into the storage unit. Since X's are not punched in subsequent cards in the series the group factor will remain in the storage unit until the first card in the next series is read in. In this type of calculation the first card is called the 1 card and the remainder are called RX cards. (Bo-selectors are similar to the pilot selectors and may be used in conjunction with then or independently. They are picked up by an impulse to the eta-selector pick up. If this impulse comes from a pilot selector couple exit, the co-selector will be transferred for the same length of ties on the pilot selector. If the impulse comes from a program exit the co-selector will be transferred only through that program. The circuits through which the numbers pass in moving from one unit to another in e certain program nay introduce back circuits in another progral. If this occurs the circuits are wired through the transferred side of a oo-eelector which is picked up for that program only. 21 The details of wiring a control panel for a specific calculation till be explained by the use of an example -control panel number 2 for this problem. Using this board the machine will perform any of the follmaing calculations! (n+3) c .. A' (AH-BUG - A. (A—B) c = a' (A-BVG = A' The result obtained in each of these calculations may, if desired, be left in the mchine and used as the term A of the following colonic- tion. The selection of addition or subtraction, and multiplication or division is made by control punches in the card. This will be explained in detail later. The description of this control panel will be sith reference to the planning chart and the wiring diagram. The explanation will take the program steps in the order they appear on the chart and orplain the wir- ing associated with each. The encircled numbers on the wiring diagram indicate the programs in which numbers are transmitted through the desig- nated.wirea. X Card . W A is need from columns 31 . 39 of the X can! into storage unit 6. The first control reading hub is wired to the X or balance pick up for pilot selector 1, which is picked up by on X punched in the 1 card in the first control reading positlcn. CALCULATING PUNCH TYPE 602A PLANNING CHART S W N U E G A R O T S C. X (A :8) ; PROBLEM APPLICATION .35 I<¢UO~E ... R 7 PUNCH UNITS COUNTER DIVIDEND DIVR.—MULT. STORAGE UNIT OPERATION $5. I