Mechanisms by Which and 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 in a fixed bed of silica gel shows transfer coefficient with concentration of the that constant length mass transfer zones form, the adsorbed . 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. 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 : 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 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 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. 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. An equation is avail­ studied: 10, 22 and 45 ft/min based on the total able in the literaturel8, 19 which describes transient cross-section area of the tower. These velocities change for a favorably curved isotherm (7 < 1): were calculated from the gas flow rate for each run assuming ideal gas behavior for convenience x = of calculating. Pertinent tower and silica gel data are given in Table 2.

EXPERWENTAL RESULTS

When 7 = 1, this equation reduces to the form of The effluent relative concentrations CICO were Eq. 4 which is for Model A. Eq. 7 reduces to Eq. 8 plotted vs time to give effluent curves similar to which represents a constant length transfer zone that shown in Fig. 3. These effluent curves were when 7 is less than one, and N R is large: used to calculate the amount of component adsorbed 1 x during a run and to calculate mass transfer rate In - = NR(Z - 1) •..••. (8) lor 1- x coefficients. Fig. 3 also shows that constant length adsorption zones were obtained for hexane Eq. 8 gives a symmetrical curve about midpoint. its at a velocity of 11 ft/min. Since this equation is based on reaction kinetics, The effluent curves for bed depths of 43 and 89 it does not show the effect of diffusion upon the in. are shown. The effluent curve for the longer bed effluent curve shape. Nevertheless, Eqs. 7 and 8 depth is shifted back 32.3 minutes to show how can be used to correct a transient effluent curve well both curves match. Since one bed length is slope at a particular point to what the slope would about twice that of the other, this shows that a be when the constant length zone is reached. This constant length transfer zone was obtained. procedure will be described in the section on data Analysis of all hexane data showed that constant analysis. length transfer zones formed in the 14.65-ft tower at all velocities tested. The effluent data on all EXPERWENTAL PROGRAM experimental runs are available. ll Figs. 4 and 5 Adsorption runs were made by adding either show the amount of pentane and hexane adsorbed pentane or hexane to a dry natural gas and flowing in each run. These same data give curved isotherms this enriched gas through a silica gel bed. when plotted on coordinate paper. This curvature City gas (Table 1) was compressed and scrubbed is common to preferentially adsorbed hydrocarbon 9 through activated beds. Liquid hydrocarbon in binary mixrures. Comparison of this equilibrium was metered into the flowing gas which bypassed data with curves plotted according to Eq. 1 gave 7 the adsorption tower. When a constant component values of 2/3 and 2/5 for pentane and hexane, concentration was obtained, the enriched gas was respectively. These values were used in all data turned through the tower. The effluent concentration analyses. from the tower exit was analyzed with a chromatograph

TABLE 2 - ADSORPTION TOWER AND SILICA GEL DATA Tower Data Silica Gel Data

Packed tower length 14.65 ft Mesh size 3 to 8 Tower diameter 2.90 in. Average particle diameter, dp 0.00909 ft Tower cross-section area 0.0459 sq ft Effective transfer area, ap 284 sq ft/ft Bulk dens ity of packed bed: Adsorption surface area 750 to 800 sq m/gm Pore volume 0.43 cc/gm Runs 56 to 81 50.69 Ib/cu ft Sil ica density (no porosity) 137 Ib/cu ft Runs 82 to 90 52.75 Ib/cu ft Calculated average pore size 22 Angstrom

168 SOCIETY OF PETROLEUM ENGINEERS JOURNAl. DATA ANALYSIS plotted on probability paper, and the mid-point slope for each curve was determined graphically. With Effluent curves were replotted in dimensionless these values Fig. 6 was prepared. To use this form for the calculation of mass transfer coefficients. curve, find the dimensionless mid-point slope for In our first analysis the hexane effluent curves a given run which is designated the transient showed an asymmetric shape which matched that of slope. Read the asymptotic or limiting slope off Eq. 6 where particle diffusion controls mass transfer Fig. 6 using either the pentane or hexane line. The rate. Our tests showed that a stable zone length limiting slope, which is a corrected slope, is used formed during hexane adsorption, and Marks et al. 10 to calculate the combined transfer coefficient showed that a constant length zone could form kkinCo' during pentane adsorption. Because of these findings The correlation of Wilke and Hougen20 was used constant zone lengths were assumed for all runs at to obtain the fluid phase mass transfer coefficient: first. Experimental effluent curves were then compared with curves calculated from Eq. 6. Under k = 1.82{P:9 -0.5~6) -0.67.. (10) this assumption the calculated mass transfer f p) coefficients for pentane adsorption were a strong Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 function of velocity. This indicated transient With the combined transfer coefficient kk' C zone growth. At this point the transient effluent tn 0 curves were corrected by the use of Eqs. 7 and 8. calculated from the effluent curve slopes and with The final analysis was made using the following the fluid phase transfer coefficient kjap calculated procedure. from the Wilke and Hougen correlation, the particle mass transfer coefficient can then be calculated from Eq. (Tables and CALCULATION OF MASS 9 3 4). TRANSFER COEFFICIENTS GAS PHASE DIFFUSIVITY Diffusion through the gas to the surface of an adsorbent particle and diffusion inside the particle The gas phase diffusivities for both pentane and gives a series resistance which can be expressed hexane in natural gas were obtained from the by: b I .HIGH VELOCITY .MEDIUM VELOCITY TLOW VELOCITY •...• (9) k a .20 PP ... ~ For a linear isotherm (r = 1), parameter b is also ~ .15 1/ C equal to one. For nonlinear isotherms where r is u ::::i less than one, b is some value greater than one. lit .~r Using the method of Hiester et al. 6 the parameter b .10 •... i.o'" for pentane and hexane was found to be 1.2 and "­ .09 ...... 01 z ~ ..... 1.43, respectively. The combined transfer coefficient .07 kkinCo was calculated from the slope of the :! ~ 'II' z .06 dimensionless effluent curves at x = 0.5 after the ~ / .... slope was corrected to its limiting value by the •... .05 I following procedure. ... .04 / - . ...- To correct the mid-point slopes of the effluent )( f curves, Eqs. 7 and 8 were used. Dimensionless .03 1.5 2.0 3.0 effluent cutves for four dimensionless bed lengths .3 .4 .5 .6 .7.8.91.0 NR were calculated. These effluent curves were Co - MOLE PERCENT PENTANE

• RUN 118 SHIFTED 32.3 MINUTES FIG. 4 - ADSORPTION EQUILIBRIA (PENTANE). • RUN 117 ... RUN 118 • HIGH VelOCITY • MEDIUM VELOCITY '" LOW VELOCITY Co - .853% C6 Co - .885% C6 TB - 94 0 F TB - 93 0 F .30 PB - 800 psig PB - 80S psig .... w y vt/J - 11.4fpm vt/J - 10.4 'pm Cl LENGTH BED - 43 IN. LENGTH BED - 89 IN. ~ ------1.0 ..---'=':';"'::"';~~-"",--=-"~_-r----r""'~""'r-"] .20 ~ ::; ./ in r~ .15 f----- ~ .8 ~ ...... \;;" V ~f- u(J z .6 « X ~- II )( .10 ...... l! - f-- - )( :i: .09 .4 II) .08 ..... "" .... ./ .07 0- .2 x .06 .05 .2 2.5 .3 .4 .5 .6 .7 .8.9 1.0 1.5 2.0 o 70 80 90 Co - MOLE PERCENT HEXANE

FIG. 3 - STABILIZED ZONE RUN (HEXANE). FIG. 5 - ADSORPTION EQUILIBRIA (HEXANE).

JUNE, 1966 169 TABLE 3 - CALCULATED TRANSFER TABLE 4 - CALCULATED TRANSFER COEFFICIENTS (HEXANE) COEFFICIENTS (PENTANE) X Co T X (Ib hexane·lb U( kfap/D kp~ Co T Run (mole kfap/D kpa Number per cent) silica gel) (ft-min) (min-I) (min-I) Run (mole (I b pentane-I b U( p Number per cent) silica gel) (ftomin) (min-I) (min-I) 71 0.61 0.158 10.49 1.08 0.195 72 1.20 0.197 10.67 1.72 0.372 58 1.46 0.124 10.83 3.16 0.397 0.410 73 0.47 0.131 11.10 1.02 0.129 59 1.69 0.146 11.18 3.12 74 1.00 0.204 11.28 1.37 0.303 60 0.66 0.069 10.59 2.58 0.329 69 0.50 0.133 24.61 1.57 0.230 61 2.04 0.157 10.83 3.44 0.576 70 0.93 0.182 23.45 2.12 0.430 62 1.49 0.139 10.74 2.86 0.392 76 1.37 0.201 21.12 2.69 0.453 63 0.56 0.058 11.07 2.60 0.282 22.42 0.382 77 0.94 0.178 19.80 2.07 0.324 56 1.02 0.101 3.83 21.70 3.45 0.362 78 0.48 0.123 20.95 1.52 0.166 57·A 0.51 0.056 79 0.43 0.104 42.67 2.26 0.223 57-B 0.60 0.068 22.24 3.34 0.312 80 0.37 0.106 44.08 1.97 0.176 64 1.52 0.124 22.96 4.64 0.517 0.427 81 0.76 0.151 38.97 2.64 0.244 65 1.14 0.112 23.55 3.97 82 1.22 0.159 44.76 4.18 0.694 66 1.55 0.130 22.96 4.62 0.541 23.40 0.316 83 1.31 0.211 45.66 3.40 0.926 68 0.54 0.064 3.27 84 1.23 0.134 45.66 4.76 0.554 86 0.38 0.048 45.01 4.06 0.431 Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 0.160 44.48 5.18 0.448 Hirschfelder et al. equation14 using the Stiel and 87 1.62 88 0.47 0.060 44.90 4.11 0.272 Thodos 17 modification. These diffusivities were 89 0.99 0.111 44.03 4.60 0.526 corrected for high using the charts of 90 1.60 0.168 45.46 5.02 0.575 Slattery and Bird. 1S These values were then used in Eq. 10 to obtain the fluid-phase, mass-transfer plot of kpa vs Q; therefore l/D was used as the coefficient. p adsorbate concentration parameter. These high pressure gas diffusitivities were also used to estimate the contribution of pore Fig. 7 shows that veloeiry somewhat affects the diffusion to total mass transfer in the particle. Pore transfer coefficient of pentane but not as much as diffusion contributed a maximum of 30 to SO per before the effluent curves were corrected for transient cent at the lowest concentration of pentane and change. The influence of velocity that remains is hexane and much less at higher concentrations.ll further explained. Eq. 7 which was used to correct for transient BEHAVIOR OF THE PARTICAL MASS conditions assumes a constant transfer coefficient TRANSFER COEFFICIENT for all adsorbate concentrations. At early zone Figs. 7 and 8 show the variation of particle transfer times a high concentration gradient exists mass transfer coefficient with the inverse of D within the particle. A larger particle mass transfer which increases as Q and C increase. Variation of coefficient results because of the high adsorbate bed adsorbate capacity caused more scatter in the concentration in the outer radius of the particle. The mass transfer coefficient at tre beginning of the run will be higher than when the zone reaches a CALCULATED POINTS • PENTANE • HEXANE • HIGH GAS VELOCITY • MEDIUM GAS VELOCITY • LOW GAS VELOCITY 3.0 ....-----r-----,.---- 10 r---....----,--.....,....--,------r-----,

.8 1------1- 2.0 I-----____+___ I" z ~ .6

l1. 0 1.0 ~------.j~~ l1. .4 ~

o 1.0 2.0 ) 3.0 o"---_---'-__.L..-_.....l..._--L__~_...... 5 6 7 8 9 10 11 Coq, 3 (~~) --(10) t QoPB

FIG. 6 _ CORRECTION OF TRANSIENT MID-POINT FIG. 7 - PARTICLE TRANSFER COEFFICIENT VS A SLOPES. FUNCTION OF CONCENTRATION (PENTANE).

170 SOCIETY OF PETROLEUM ENGINEERS JOURNAL constant length. This, in effect, slows the rate of The effluent curves for the hexane runs were transient zone growth. As a result the correction either stabilized or very near their final constant for transient change using Fig. 6 may be too small length. In contrast, calculations showed that the for the higher velocities. This effect is not corrected, pentane adsorption zones had not reached a and some influence of velocity remains. constant length for any of the velocities and Fig. 8 for hexane shows no effect of velocity at conditions of these runs. all and a strong dependence upon the adsorbate For a small value of r, the controlling mechanism concentration. The greater curvature of the hexane may be distinguished by the characteristic shape of adsorption isotherm causes the hexane transfer the effluent curve (Fig. 2). As r becomes smaller, zone to stabilize faster than the pentane transfer the initial slopes of the predicted effluent curves zone. The first analysis of the hexane data for fluid phase diffusion controlling and particle assumed a constant zone length and gave results diffusion become quite different. As r approaches very close to those in Fig. 8. 1, the effluent curve shape for particle diffusion controlling approaches the shape of the curve for SIGNIFICANCE OF RESULTS flui~ phase diffusion controlling. Since the value

of r for pentane is about 0.7, the controlling transfer Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 The transfer coefficient behavior and the mechanism is more difficult to distinguish. effluent curve shape show that particle diffusion controlled the adsorption rate of pentane and SURFACE DIFFUSION hexane on silica gel in this study. This particle diffusion is about 85 per cent or more of the total The particle transfer coefficient kpap increases diffusional resistance and consists primarily of with adsorbate concentration. This shows that the diffusion of molecules along the solid surface of diffusion inside the particle is along the surface of the silica gel pores. Gas phase diffusion to the the pores and not in the gas phase. This finding is 2 3 outer surface of the silica gel particle is 15 per supported by the basic work of Carman • who cent or less of the total resistance. The transfer showed that surface diffusion was an increasing mechanism of hexane onto silica gel in this study function of adsorbate concentration. He reported a was initially by the shape of the figure for the surface diffusion coefficient of Freon distinguished 5 effluen t curve. The characteristic shape of the on silica gel to be 10- sq cm/sec at a concentration of one monolayer adsorbed. This is the order of effluent curve and the stability of the transfer magnitude of the diffusion coefficients for hexane zone are caused by the curvature of the equilibrium adsorption isotherm. and pentane in silica gel in this study, At the lowest concentrations of pentane and INFLUENCE OF ISOTHERM CURVATURE hexane, pore diffusion in the gas phase may have contributed a maximum of 30 to 50 per cent of the As the curvature factor r of the isotherm transfer rate. We believe that the actual contribution decreases, a smaller bed length is required for a of the fluid phase pore diffusion to the transfer of stabilized zone to form. The value for hexane pen tane or hexane is negligible. Surface diffusion (r = 0.4) causes fast stabilization of the hexane generally tends to dominate over pore diffusion for transfer zones, and the stabilized zone length is adsorbent particle porosities less than 0.6 and much shorter than that for pentane where r = 2/3. particularly for larger and heavier molecules which • HIGH GAS VELOCITY are usually more easily condensed. 2 The calculated • MEDIUM GAS VELOCITY A LOW GAS VELOCITY pore diffusion rate in this study was only as high as one-half of the surface diffusion rate. As the 1.0 amount of adsorbed phase increases, the paths open • to pore diffusion decrease even more. Furthermore, .8 these paths are probably filled with counter-diffusing or other light molecules. Carman showed that surface diffusion was divided -I • z .6 - ---- into three ranges: (1) when the concentration of :E the adsorbed phase is less than one monolayer; / (2) when one or more adsorbed layers exist; and Q. / r-----• ~ .4 • , A (3) when capillary condensation exists. .... Kiselev8 showed that pentane on silica gel began ~• capillary condensation at PIPs = 0.3 and reached .... ---~ ---~------.2 adsorption capacity at PIPs = 0.6 for an average l'(i pore size of 25 Angstrom units (P represents partial pressure of the pentane and P s represents o saturated of the pentane). In other 4 5 6 7 8 3 words the pores may be completely filled with the Coq, (10)3 condensed liquid even before the vapor phase is QoPB saturated. FIG. 8 - PARTICLE TRANSFER COEFFICIENT VS A The diffusion of pentane and hexane in this study FUNCTION OF CONCENTRATION (HEXANE). probably encompasses all three of these diffusion

JUNE, 1966 171 ranges. Just two molecular layers fill the average CONCLUSIONS pore size of the silica gel used, and the second These conclusions are based on experimental layer is only a fraction of that in the first layer. data for a small pore silica gel. Since mid-point slopes from the effluent curves 1. The equilibrium adsorption isotherms for were used in the evaluation of the particle mass pentane and hexane are curves, not straight lines. transfer coefficients, the average diffusion rate is 2. The hexane transfer zone stabilizes faster, in a partial monolayer. or reaches a constant length sooner, than the pentane Smith and Metzner16 show surface diffusivity to transfer zone because the hexane isotherm curvature be a function of both the slope of the adsorption is greater. isotherm and the square of the adsorbed phase 3. As the isotherm curvature increases, the concentration. This increase with concentration effluent curve becomes more asymmetric around the below the full monolayer is attributed to surface mid-point and makes it easier to distinguish the heterogeneity. 1 As the more active or tenaceous controlling diffusion mechanism. sites are filled, additional molecules move faster along the surface with lower aCtlvatlOn° 0 en~rgle~.• 3 4. Particle diffusion controls the transfer rate of Temperature increases the surface dlffuslOn hexane and pentane, making up about 85 per cent coefficient but decreases the adsorbed phase of the total transfer resistance. This particle content more so that the net effect is to decrease diffusion is mainly diffusion of the adsorbed the adsorption rate. 16 molecules along the pore surfaces inside the Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 dessicant particle. 5. The equation of Glueckauf and CoatesS,19 TRANSFER ZONE STABILITY (Eq. 6) matches the effluent data very well. If the constant zone length model is used to 6. Accurate adsorption equilibria are more analyze adsorption data in a short fixed bed - too important than accurate mass transfer coefficients short for the transfer zone to stabilize - the mass in the design of fixed-bed adsorbers. transfer coefficient will be an apparent function of velocity. This procedure will lead to the wrong conclusion that fluid phase diffusion controls the NOMENCLATURE adsorption rate even though particle or surface diffusion actually controls the transfer rate. For CONCENTRATION NOMENCLATURE short bed lengths the effluent curves must be C = moles solute per cubic feet of gas, or corrected to give the correct particle mass transfer mole per cent when indicated coefficients. Eqs. 7 and 8 can be used to correct c* = solute concentration at gas-solid inter­ these curves; nevertheless, the calculated coeffi­ face cients may still be somewhat in error because the Co = inlet concentration of solute in gas particle diffusion coefficient is not constant as Eq. 7 demands, but it is a function of the adsorbed Q = moles solute per pound of dessicant, phase within the particle. Because of this adsorbed phase dependence on adsorbate concentration the transfer Q* solute concentration at gas-solid inter- zone will take a longer time to stabilize at high face adsorbate feed rates. Where this is the case, longer Qo solute capacity of dessicant at Co bed lengths should be used to obtain experimental X T dessicant capacity at Co, lb solute/lb data. silica gel C TRANSFER COEFFICIENT VS x =--= dimensionless concentration of solute BED ADSORPTION CAPACITY Co in gas o Effluent curves were predicted by using: (1) the y ="""""'-- = dimensionless concentration of solid particle transfer coefficient correlations in Figs. Qo dessicant 7 and 8; (2) Eqs. 9 and 10 in conjunction with Fig. T equilibrium parameter to express rela­ 6; and (3) Eq. 6. Equation 6 gives an excellent tionship between x and y (Eq. 1) fit with the experimental effluent curve data. In the prediction of effluent curves the dynamic adsorption COLUMN AND FLOW PARAMETERS capacity of the bed was more important than the mass transfer coefficient. Dynamic adsorption V = column volume, cu ft = hA capacity fixes the mid-point time of the effluent h = height of tower, ft curve for a given bed length. The mass transfer A = superficial cross section area, cu ft coefficient fixes the relative slope of the effluent ¢ = bulk porosity of packed bed curve. For predicting break-out times or cut-off V¢ = effective fluid volume of tower, cu ft times for natural gas adsorption in a fixed bed,an error in the dynamic adsorption capacity causes a q = volumetric flowrate of gas, cu ft/min ~ greater error in the predicted time than does the = resI°dence tIme. for gas, mIn° same per cent error in the mass transfer coeffi­ q ll cient. v = 1¢ = linear flowrate, ft/min

172 SOCIETY OF PETROLEUM ENGINEERS JOURNAL G total volume of gas that has entered e ZN = dimensionless time column at time t, cu ft/min G-V¢ total volume of gas that has passed ACKNOWLEDGMENTS out of column at time t, cu ft The authors wish to thank the Davison Chemical pB = bulk density of dessicant in column, Co. for their support of this research and the Dowell lb/cu ft Division of the Dow Chemical Co. for their help QoPB V stoichiometric capacity of column, lb in preparing this manuscript. moles solute D distribution ratio -a limiting saturation REFERENCES QoPB value for tower D = 1. Basmadjian, D.: "The Separation of H 2 and D by Co ¢ Moving Bed Adsorption: Corroboration of Adso~ber Design Equations", Canadian Jour. of Chem. Eng. TRANSFER RATE PARAMETERS (Dec., 1963) 269. 2. Carman, P. C. and Malherbe, P. L. R.: "Diffusion kfap = gas phase mass transfer coefficient, min-1 and Flow of Gases and Vapors through Micropores, Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021 IT. Surface Flow", Proc., Royal Society (1950) Vol. kpap = partical mass transfer coefficient, 203A, 165. 1 min- 3. Carman, P. C. and Raal, F. A.: "Diffusion and Flow kkinCo = combined mass transfer coefficient, of Gases and Vapors through Micropores, ITI. Surface min- 1 Diffusion Coefficients and Activation Energies", Proc., Royal Society (1951) Vol. 209A, 38. = ordinary gas phase diffusivity, sq ft/hr 4. Dale, G. H., Haskell, D. M., Keeling, H. E. and = adsorbate surface diffusivity in parti­ Worael, L. A.: "Dynamic Adsorption of cle, sq ft/hr and Isopentane on Silica Gel", Chem. Eng. Prog. = effective pore diffusivity, sq ft/hr Symp. Ser. (1961) Vol. 57, 42. effluent curve slope for constant 5. Glueckauf, E. and Coates, J: 1.: "Theory of Chroma­ length transfer zone tograph, IV. The Influence of Incomplete Equilibrium on the First Boundary of Chromatograms and on the (dx/dZ)t effluent curve slope for transient Effectiveness of Separation", Jour. Chem. Soc. (1947) growth of transfer zone Vol. 150, 1315. b equilibrium and concentration gradient 6. Hiester, N. K., Radding, S. B., Nelson, R. L., Jr. parameter for combination of gas and Vermuelen, T.: "Interpretation and Correlation phase and solid phase transfer of Ion Exchange Column Performance under Non­ Linear Equilibria", AIChE Jour. (Sept., 1956) 404. coefficient (Eq. 9) time of flow through tower, mm 7. Hougen, O. A. and Marshall, W. R.: "Adsorption from a Fluid Stream Flowing Through a Stationary particle diameter, ft Granular Bed", Chem. Eng. Prog. (1947) Vol. 43, = particle transfer area, sq ft/cu ft 197. = porosity inside adsorbent particle 8. Kiselev, A. V. and Eltekov, Y. A.: "Effect of Nature of Adsorbent and Pore Size on Shape of BET = superficial velocity, ft/hr or ft/min Vapour Adsorption Isotherm", Proc., Second Inter­ gas density, lb/cu ft national Congress of Surface Activity, Vol. II; Solid-Gas Interface, Academic Press, New York, = gas , lb/ft hr N. Y. (1957) 228.

DIMENSIONLESS TIME AND 9. Lewis, W. K., Gilliland, E. R., Chertow, R. and DISTANCE PARAMETERS Cadogan, W. P.: "Adsorption Equilibria, 1. Hydro­ carbon Gas Mixtures", 1319-1325, II. Pure Gas N = number of transfer units-dimensionless Isotherms", Ind. Eng. Chem. (July, 1950) 1326. distance 10. Marks, E. E., Robinson, R. ]., Arnold, C. W. and For external diffusion: Hoffman, A. E.: "Dynamic Behavior of Fixed-Bed Adsorbers", Jour. Pet. Tech (April, 1963) 443. Nf = kfpV¢/q F or internal particle diffusion: 11. McLeod, H. O. Jr.: "A Study of the Mechanisms by which Pentane and Hexane are Adsorbed on Silica N = kpapD V¢/q p Gel," PhD Dissertation, The U. of Oklahoma, For combined diffusion: Norman, Okla. (June, 1965). NR = kkinCoD V¢/q 12. Michaels, A. S.: "Simplified Method of Interpreting Z = throughput ratio-this value reaches Kinetic Data in Fixed-Bed Ion Exchange", Ind. Eng. unity when the volume of feed which Chem. (1952) Vol. 44, 1922. has passed through the column 13. Needham, R. B., Campbell, J. M. and McLeod, contained an amount of the component H. 0.: "A Critical Evaluation of the Mathematical Models Used for Dynamic Adsorption of Hydrocar­ adsorbed numerically equivalent· to bons," Presented at AIChE Adsorption Symposium, the adsorption capacity of the column Memphis, Tenn. (1964)

Z = G-V¢ Co(G-V¢) G-V¢ 14. Reid, R. C. and Sherwood, T. K.: "The Properties of Gases and Liquids. VIII. Diffusion Coefficients", Gstoic QoPBV DV¢ McGraw-Hill Book Co., New York, N.Y. (1958).

JUNE. 1966 173 15. Slattery, J. C. and Bird, R. B.: "Calculation of the Vol. 66, 1664. Diffusion Coefficient of Dilute Gases and of the 19. Vermuelen, T.: "Separation by Adsorption Methods", Self-Diffusion Coefficient of Dense Gases", AIChE Advances in Chemical Engineering, Academic Press, jour. (June, 1958) 137. Inc., New York, N.Y. (1958) Vol. 2, 147. 16. Smith, R. K. and Metzner, A. B.: "Rates of Surface 20. Wilke, C. R. and Hougen, D. A.: "Mass Transfer in Migration of Physically Adsorbed Gases", jour. the Flow of Gases· through Granular Solids Extended Phys. Chem. (Oct., 1964) 2741. to Low Modified Reynolds Numbers", AIChE Trans. 17. Stiel L. 1. and Thodos, G.: "Lennard-Jones Force (1945) Vol. 41, 445. Con~tants Predicted from Critical Properties", jour. 21. Wilke, C. R. and Lee, C. Y.: "Estimation of Chem. and Eng. Data (April, 1962) 234. Diffusion Coefficients for Gases and Vapors", Ind. 18. Thomas, H. C.: "Heterogeneous Ion Exchange in a and Eng. Chem. (June, 1955) 1253. Flowing System", jour. American Chem. Soc. (1944) *** Downloaded from http://onepetro.org/spejournal/article-pdf/6/02/166/2152748/spe-1248-pa.pdf/1 by guest on 24 September 2021

17.•· SOCIETY OF PETROLEUM ENGINEERS JOURNAL