Mechanisms by Which Pentane and Hexane Adsorb on Silica Gel DOWELL DIV., DOW CHEMICAL CO. H. O. McLEOD, JR. TULSA, OKLA. J.M.CAMPBELL THE U. OF OKLAHOMA MEMBERS AIME NORMAN, OKLA. Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 ABSTRACT of pentane and hexane. This mechanism is indicated by the effluent curve shape for a constant length Data analysis of pentane and hexane adsorption transfer zone and by the variation of the mass from natural gas in a fixed bed of silica gel shows transfer coefficient with concentration of the that constant length mass transfer zones form, the adsorbed hydrocarbon. curvature of the adsorption isotherm controls the growth of the mass transfer zone and surface THEORY AND DEFINITIONS­ diffusion of molecules inside the silica gel particle MA THEMATICAL MODELS controls the mass transfer rate. Curvature of the hexane isotherm is more than the curvature of the Mathematical solutions for the isothermal adsorp­ pentane isotherm. Because of this curvature the tion of a trace component from a carrier gas are hexane adsorption zones reached a constant length. derived from three relationships: the mass balance Tn contrast, the pentane adsorption zones were or continuity equation, the equilibrium relationship always increasing in length during each run. between the gas and solid phases, and a mass A procedure was developed to obtain correct mass transfer rate equation. The transfer rate is transfer coefficients using effluent curve slopes. proportional to the adsorbate concentration gradient These transfer coefficients increase with the amount within either the gas or solid phase. Mathematical of hydrocarbon adsorbed on the silica gel particle. solutions of these equations usually give the The characteristic shape of the hexane effluent adsorbate concentration as a function of time and curves also show that molecular diffusion inside distance from the bed inlet. That part of the bed in the silica gel particle controls the adsorption rate which the adsorbate concentration changes from a of pentane and hexane. maximum to a minimum value is called the transfer zone. This transfer zone is directly related to a INTRODUCTION plot of the effluent concentration vs time which has a characteristic S-shape. This general shape is The purpose of this study was to detennine the detennined by the continuity equation and occurs mechanisms that control the dynamic adsorption of in many processes of diffusional transfer. hydrocarbons from a natural gas onto silica gel. Before one can deal effectively with multicomponent EQUILIBRIUM ADSORPTION ISOTHERMS adsorption, the transfer mechanisms by which a Different mathematical models of fixed bed single hydrocarbon component is adsorbed from the adsorption occur mainly because different equilib­ gas stream must be defined. Two principal investi­ 4 rium adsorption isothenns are assumed. Eq. 1 gations of this system have been published ,10 and describes the amount of hydrocarbon adsorbed as a indicate that diffusion through the gas around the function of the amount of hydrocarbon in the gas particle controls the adsorption rate. Some of the phase at a constant temperature: 19 experimental observations in each study either do not support this transfer mechanism or are x ;x inconsistent with the mathematical model used in y r + (l-r) x analysis. (1) In this study surface diffusion of molecules inside the particle controls the mass transfer rate There are two main models which describe the separation of a trace component in a fixed bed. Model A assumes a linear isotherm (r = 1); Model B Original manuscript received in Society of Petroleum E~gineers office Aug. 4, 1965. Revised manuscript of SPE 1248 received assumes a favorably curved isotherm (r is less April 6. 1966. Paper was presented at SPE Annual Fall Meeting than 1). held in Denver, Colo., Oct. 3-6, 1965. 4References given at end of paper. SOCIETY OF PETROLEUM ENGINEERS JOURNAL 166 TRANSFER RATE EQUATIONS diffusion controls (Fig. 2). As the parameter r of Both models use the same differential transfer Eq. 1 decreases, the controlling mechanism is more rate equations: easily distinguished. It must be remembered that Eqs. 5 and 6 apply only after the transfer zone has dQ k a (C-C*) f p 1> . (2) reached a constant length. Whichever model is used, the transfer coefficient dt PB obtained from data analysis must meet certain theoretical requirements. The fluid phase mass dQ kpa p (Q* - Q). (3) transfer coefficient kf af1- must vary approximately dt with the square root of gas velocity, and it is independent of adsorbate concentration for trace Eq. 2 describes the transfer rate through a components. The particle mass transfer coefficient hypothetical gas film surrounding the dessicant kpap is a function of adsorbate concentration and particle. Eq. 3 describes the transfer rate through is mdependent of velocity. Both Models A and B a hypothetical transfer zone inside the particle. have been used in previous work to analyze the Adsorption transfer rate may be controlled by either adsorption of hydrocarbons in a fixed bed. Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 or both of these mechanisms. When one transfer Marks et al. 10 used Model A to analyze data resistance is much greater, the transfer is sai1:i to even though they obtained constant length be controlled by either fluid phase diffusion or adsorption zones. Model A requires that the zone particle diffusion. length continually increase with the square root of its depth in the bed. TWO BASIC ADSORPTION MODELS Dale et al. 4 used Model B (constant length zone) Eq. 4 below is the solution for Model A.7 Eqs. 5 to analyze hydrocarbon adsorption data for butane and 6 are the solutions for Model B with fluid phase and pentane on silica gel. The bed depth used in diffusion and particle diffusion controlling, respec­ the study was fairly short and did not allow constant tively. The assumptions involved in these solutions length zones to form. Results of the analysis and others have been previously discussed. 13 apparently showed that fluid phase diffusion x = J(N,ZN) --- PENTANE:r=2/3 - HEXANE:r=0.4 N p =10 1.0 1/I.-' .~- .9 - I _faNe -ZN-~ 1 (2y'ZNn d~ " (4) '/ .. 0 .8 V .7 '" o u .6 I. '" ._. ..... / x (I-xl) + In l-x2 U .5 r-- - In 2 II ,f X .4 f-- . l-r xl (l-x2) I-xl / .3 - f--. ." r In x (I-xl) .2 1/ - 2 .. I x I l-r xl (I- 2) .-~-- I....... o .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 l.l 1.2 1.3 1.4 1.5 1.6 1.7 1.8 The effluent curves predicted by these mathe­ Z matical models differ in two important ways. First, the transfer zone of Model A increases in length FIG. I-EFFECT OF r PARAMETER ON ZONE LENGTH. proportional to the square root of its distance from CONTROLLING MECHANISM: the bed inlet. 7 The transfer zone of Model B ultimately reaches a constant length at a rate - PARTICLE DIFFUSION --- FLUID PHASE DIFFUSION depending on the curvature of the isotherm (Fig. 1). N = 10 Eqs. 5 and 6 describe the Model B effluent curve 1.0 ~10- .9 - - after the transfer zone has reached a constant ~ - length. Second, an important difference between .8 - - .0'-- .7 VI Model A and Model B is in the shape of the o I effluent curve. The effluent curve of Model A has ......u .6 U I the same S-shape regardless of which diffusion 1\ .5 resistance controls the transfer rate. Contrary to )( .4 I this, the effluent curve shape of Model B depends .3 '/ ., upon which mechanism controls the transfer rate, .2 .. l .JI particle diffusion or fluid phase diffusion. .1 ........ Eq. 5 describes the effluent curve for fluid phase . ~ ~ '- -~.7 ~ ~1~lJl~1~lA151~1.71~ diffusion controlling,12 and Eq. 6 describes the o J A 5 effluent curve for particle diffusion controlling. 5 Z These equations are similar; however the initial FIG. 2 - EFFECT OF DIFFUSION MECHANISMS ON slope of the effluent curve is steeper when particle EFFLUENT CURVE SHAPE. JUNE. 1966 167 controls the adsorption rate. Remember that Model TABL E 1-TYPICAL SUPPLY GAS ANAL YSIS B should only be used to analyze data where a Mole constant length transfer zone has been reached. Component (per cent) We found that if Model B is used to analyze C, 88.37 effluent curves which have not stabilized, the C 9.85 calculated particle mass transfer coefficient will 2 C 1.70 vary with velocity. This variation indicates transfer 3 i-C 0.01 control by fluid phase diffusion - even when the 4 n.C 0.003 curve shape shows particle diffusion to be the 4 controlling mechanism. One must make sure that a i-Cs 0.06 constant length zone has been reached, or else the effluent data must be corrected for the transient and recorded along with other pertinent data. change taking place. Pressure and temperature for all the runs were about 800 psig and 90F. Concentration of pentane in the TRANSIENT CHANGE OF THE ADSORPTION ZONE natural gas varied from 0.4 to 2.2 mole per cent. Adsorption which results in a constant length Concentration of hexane varied from about 0.3 to 1.4 mole per cent. Three gas velocity ranges were transfer zone still undergoes a transient period of Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 zone growth at the beginning.