Selective Adsorption Computations with Digital Computers ARTHUR ROSE, R. J. LOMBARDO, AND THEODORE J. WILLIAMS The Pennsylvania State College, State College, Pa.
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URING ('he oper.ation Existing methods for predicting compositions during In making the calculations selective adsorption processes are exceedingly complex for it isaaaumed that the adsorbof batch a d s o r p t i o n C O ~ U ~ the ~ S concenpractical multicomponent and nonideal cases. ent column is divided into tration of a component in A stepwise, stagewise method of calculation is suggested discrete unit sections. These either the adsorbed or liquid for such calculations, and the application of readily were arbitrarily taken as 1 Phase a t mY time and Place available IBM computers to simple cases is illustrated. P a m in the PreliminarS caiThe basis for extension to more complex cases is indicated. CulationS. It Was then asin the column is determined by the phase equilibria, the sumed that the following disrate of flow of fluid through Crete proceases occurred. the column, and the previous column concentrations. The tlif1. Liquid mixture of volume ( H D H s ) and of feed composition X D entered the to gram of adsorbent and equilibrium was ierential eguations for this process are complex, and their sohestablished between atsorbed and unadsorbed phmes, giving new tion poses a formidable problem. This paper demonstrates a compositions xl(1) and yl(1). The material balance relation bestepwise, stagewise method of calculation which it is believed tweenthese various quantities is: will predict the ideal or maximum separation possible with a ( H n H s =~H D X I W Hsy,cl, (1) .given adsorbent and binary mixture. The authors also discuss the application of readily available International Business 31%2. Liquid feed mixture of volume H D entered the top gram of chines (IBM)computers to the solution of this problem, and gel and an equal volume of mixture of composition xl(l) passed into the second gram of gel. A new equilibrium was established which may be taken to predict compositio,ls indicate further in the first gram: .during adwrption of more complex mixtures. H,syi(i) H D X O= H D X I W H s ~ r 2 ) (2) BASlS FOR CALCULATIONS 3. Liquid feed mixture of volume Ha entered the top gram and dis laced an equal volume of composition an) into the second The total qurr,nt,ityof liquid mixture passing through an adram orgel, thus loading it with a total of H D H s milliliters of %sorptioncolumn may be divided into two categories: !quid. The new equilibrium in the first gram of gel is governed 1. The dynamic holdup-Le., the unadsorbed liquid between by .the interstices of the gel that is free to flow through these inter( H D - H s ) . T ~ ( ? ) HSXO H s , Y I ( ~=) HDZIG) HSYl(3) (3) etices. 2. The etatic holtfup-i.e., the liquid that is actually adsorbed 4. Successive discrete portions of feed nlixture of volume .on the gel. and Hs alternately entered the top gram, and displaced corresponding volumes into the second gram, and established new I t has been demondrakd (6) that the volume of liquid of compositions governed by material l)alance equations of the on unit quantity of silica gel is normal density forms: constant for a variet,y of volatile liquids of widely differing physiHsyl(i) 4- HDXO= HDXici+u Hsyl(i+l) (2%) cal properties, Preliminary experiments in the course of the present investigation indicate the same relation is valid for other H ~ ~ , (+~ H~~~ + ~ ,+ ( H ~ H ~ ) ~ =~H ~ ~~ ~++~H ,~~ ~ + , ( ~~ + ~, , adsorbents. For this reason the dynamic holdup and the static (38) holdup are expressed in terms of volume of liquid mixture (at in which is an odd integer* Z O O C.) per gram of adsorbent. For this same reason, compositioris are expressed &s volume fractions. Reasoning similar to the above gives the following equations The relation between the compositions a t equilibrium Of the for the successive material balances in the second gram of gel: dynamic and the stat.ic holdup-i.e., of unadsorbed and adsorbed H D X I W Hsxitz) HDWO H a m ) (1b) liquid m i x t u r e m a y be expressed as an x-y diagram analogous to vapor-liquid equilibrium curves. In this paper the ?/ values HDX~~JH ) s y w ) = HDXP:P) H a v m (2b) represent volume fraction of the most strongly adsorbed com( H D - Hs).Q(z) Hszicr) HSVW = Hmi(s) Hs~izcs) (3b) ponent in the adsorbed phase, and x values represent the equilibH D X I ( ~ + Z )H s u ~ ( = ~ ) HDTZ(
