Adsorption dynamics of carbon dioxide on a carbon molecular sieve 5A

PERGAMON Carbon 38 (2000) 1339–1350

Adsorption dynamics of carbon dioxide on a carbon molecularsieve 5A

*S.W. Rutherford, D.D. DoDepartment of Chemical Engineering, The University of Queensland, St. Lucia, Queensland 4072, Australia

Received 5 August 1999; accepted 24 November 1999

Abstract

Measurement of batch adsorption of carbon dioxide with a carbon molecular sieve (commercially manufactured Takeda5A) indicates no molecular sieving action but instead, micropore diffusion is shown to be rate limiting the adsorptiondynamics. Permeation measurement through the same pellets is also performed and steady state analysis indicates there isnegligible adsorbed phase transport along the pellet and that the gas phase diffusion process is a combined Knudsen andviscous mechanism. Batch adsorption and permeation methods are critically compared for their utility in determining whichmass transfer processes are relevant and the conditions under which each technique is most useful are given. 2000Elsevier Science Ltd. All rights reserved.

Keywords: C. Adsorption; D. Adsorption properties, Diffusion, Transport properties

1. Introduction gas diffusion in larger pores, or viscous flow in largepores if a pressure drop is applied.

The study of mass transport in porous adsorbent materi- 2. adsorption into the grains via an adsorbed phaseals is important for its practical application in separation diffusion mechanism.and purification technology. Whether the application in- 3. mass action mechanism for adsorbate to enter the grainvolves chromatographic purification, separation via cyclic as a result of pore mouth restriction sometimes gener-circulation through an adsorbent bed, or membrane sepa- ated through treatment of the micrograin. The massration, information concerning the nature of adsorption and action mechanism is useful in some molecular sievingstructure of the adsorbent material is required for design materials which are produced especially to create apurposes. The established view of the structure of many barrier resisting the adsorption of large molecules andadsorbent materials manufactured in pellet form is that preferentially allow smaller molecules to adsorb. Inthey are composed of crystalline or semi-crystalline grains these materials, it can often be this barrier that is ratein the order of micron size. These grains are surrounded by limiting the adsorption process [2,3].voids which allow fluid phase transport through the pellet[1]. The difficulty in the analysis of many dynamic ad-

When studying the transport of adsorbate through the sorption processes lies in the determination of the role ofpellet, it is necessary to identify the physical processes the adsorption process itself. Ultimately it must be de-involved and relate such processes to the porous structure. termined whether adsorption is fast or slow in comparisonThese processes may include: to the gas phase transport. This requires analysis of the

timescales involved in the pellet scale diffusion andmicropore diffusion processes. Generally, for species with

1. gas phase transport via Knudsen diffusion at low high affinity diffusing through pellets of large macroscopicpressures in small pores, molecular diffusion for mixed length, macropore diffusion controls the mass transfer

process. This gives rise to analysis by the macroporediffusion control model, conveniently presented by Rut-*Corresponding author. Tel.: 161-7-3365-4154; fax: 161-7-hven [1]. Alternatively, mass transfer of species of lesser3365-2789.

E-mail address: [email protected] (D.D. Do). affinity diffusing through pellets of small macroscopic

0008-6223/00/$ – see front matter 2000 Elsevier Science Ltd. All rights reserved.PI I : S0008-6223( 99 )00269-9

1340 S.W. Rutherford, D.D. Do / Carbon 38 (2000) 1339 –1350

NomenclatureA Cross-sectional area of mediumB Viscous flow parametero

b Parameter of isotherm equationC Concentration of diffusing speciesC Upstream concentration0

C Saturation capacityms

D DiffusivityD Pore diffusivityP

D Adsorbed phase diffusivitym

D Effective diffusivitye

D Adsorbed phase diffusivity at zero loadingm0

F Fractional uptakeJ FluxL Length of the pelletm Amount uptakent

m Shape factor for particleP PressureR Radius of microparticlem

S Steady state slopeT Absolute temperaturet TimeV Volume of vessel in which measurement takes place

length is rate limited by the micropore diffusion process. cally or volumetrically, with a carrier gas or single gasFor this case, analysis by the micropore diffusion control adsorption. Possibly the simplest method is to measuremodel may be applicable [1]. A more general scenario may single gas batch adsorption by volumetric method as weinvolve a combination of processes, a situation in which a have performed in this investigation. The procedure andmore complex description is necessary for analysis of apparatus have been described elsewhere [5] for differen-dynamics. tial operation of the batch adsorber. In this investigation

For purposes of experimental determination, it is useful the experiment is performed over a large initial pressureto isolate each process and evaluate its contribution to the drop, making it an ‘integral’ procedure and nonlinearmass transfer process independently. This proves a more effects result in an averaged measurement being taken.accurate means than evaluating parameters from optimi- Although the analysis of data obtained by this method issation when several processes are involved. Naturally, this more complex, it is useful when only a small total amountis a more experimentally intensive path, but by this means is uptaken by the sample resulting in a small pressureit is possible to determine which of the possible mecha- change. For each of our measurements conducted in thisnisms are relevant to the transport process under inspec- fashion, the sample was prepared by outgassing for around

26tion. In this investigation, we employ batch adsorption and 60 h at 10 Torr.permeation methods to determine which of the processes The material under analysis is a commercial carbonare significant in the adsorption of carbon dioxide in a molecular sieve from the Takeda chemical companycommercially supplied carbon molecular sieve. Analysis of termed 5A, because it is capable of selectively adsorbingdynamics is presented and discussed with the aim of species of molecular size less than 5 Angstrom andfurther determining the conditions under which each excluding molecules of size greater than 5 Angstrom [6].technique is most useful. The sample under analysis is supplied in extruded pellet

format of cylindrical shape with properties shown in Table1.

2. Experimental Electron microscopy analysis of the material shows thatthe pellet is composed of an agglomeration of discrete

There are many established techniques for investigatingdynamics of adsorption. Some are critically reviewed by

Table 1Bulow and Micke [4] with discussion of their relativeProperties of material used in batch adsorption experimentmerits. Of these techniques, batch adsorption is well

employed as it is used to simultaneously obtain dynamic Sample Weight Diameter Lengthinformation and the amount adsorbed at equilibrium. The

Takeda 5A 1.25 g 0.3 cm 0.3 cmbatch adsorption experiment can be conducted gravimetri-

S.W. Rutherford, D.D. Do / Carbon 38 (2000) 1339 –1350 1341

Table 2microparticles of the order of micron size [6]. InterstitialProperties of material used in permeation experimentvoids and microparticle porosity give the pellet its porous

structure which has been probed using mercury intrusion Sample Length Diameteron a Micromeritics Poresizer 9320. The pore size dis-

Takeda 5A 0.6 cm 0.3 cmtribution is shown in Fig. 1, the average size (diameter)being calculated at 0.5 mm. The total macroporosity ismeasured at 0.28.

It is useful to couple the information obtained from parameters as discussed in Ruthven [1]. The two parame-batch adsorption with that obtained from a steady state ters are defined astechnique such as permeation. For this reason, we have

2Rha malso measured permeation through a Takeda 5A pellet of]]a 5 (1a)C Ddimensions shown in Table 2. The procedure and ap- s m

paratus for the permeation setup has been described≠Celsewhere [7]. DH mS D] ]b 5 (1b)

pC ≠Ts

2.1. Consideration of heat transfer For a ‘worst case’ calculation, the following correlation isvalid under stagnant heat transfer conditions [8]:

Because adsorption is an exothermic process, the dy-knamics of mass transfer can be affected by temperature f]h 5 (1c)build up within the particle. With a coupling of heat and R

mass transfer, it is necessary toFor carbon dioxide at low pressures (k 50.015 W/m/K)f

we estimate a heat transfer coefficient in the order of 102W/m /K. Typical values for heat capacity for coal can be

1. account for simultaneous heat and mass transfer, or obtained from [9] C 51306 J /kgK and density 1400p32. limit the pressure increment taken such that the maxi- kg/m . Later it is shown that for micropore diffusion of

2mum temperature rise is so small that the process is carbon dioxide the mobility is in the order of: D /R 523m m23 21considered to be isothermal. 10 s . Furthermore, a typical value for heat of ad-

sorption for carbon dioxide is around 20 kJ /mol [10] andBecause the mass transfer is of primary interest, it is in all experiments a maximum change in the adsorbed

advantageous to ensure that the process is isothermal. This phase concentration of 0.45 mmol /ml is not exceeded.requires an estimate of the maximum allowable pressure Under these conditions we have a ¯6 and b ¯0.1. Accord-increment undertaken by comparing mass and heat transfer ing to Ruthven [1], this makes the adsorption process

Fig. 1. Pore size evaluation by Mercury Intrusion.


clearly isothermal and coupled analysis of heat transfer is nisms are coupled, an accurate means of determining thenot warranted. gas phase diffusion is vital for an accurate measurement of

the adsorbed phase mobility. This is an important point tonote because many methods of measuring the adsorbedphase flux simply rely on an estimate of the gas phase flux3. Steady state permeation and evaluation of gasand hence the resulting accuracy of the adsorbed phasephase processesdiffusivity can be heavily dependent upon this estimate. Abetter means for determining the gas phase contribution isBecause it provides a direct means for measurement ofby separate and independent measurement. Helium per-mass transfer, the permeation experiment provides anmeation is utilised for this process in many porouseffective means for characterisation for many types ofadsorbents. Transport within the macropores dominates theporous materials. Measurement can be performed bytransport process for helium and the magnitude of theadsorbed phase flux is much less than that of the gas phase.

The gas phase diffusion process has been studied(i) forcing liquid through the porous material under aintensively and in the simplest case (single gas permeation)hydrostatic head [11],there are two mechanisms which dominate, Knudsen(ii) allowing diffusion of a species within a ‘carrier gas’diffusion at low pressures and viscous permeation at higherthrough the material utilising the concentration gradientpressures. For this case the diffusivity is described by[12] or

(iii) forcing gas through the material subject to a´Boconstant pressure drop (which we consider in this ]D 5 P 1 ´D (3)e Pminvestigation).

where B is the viscous flow parameter, m the viscosity ofoIn most instances the boundary conditions of the experi-the penetrating gas, ´ is the volume fraction of the materialment can be maintained constant with respect to time, inthat is contributing to the flow and D is the porePwhich case a steady state of permeation is ultimatelydiffusivity which is inversely proportional to the squarereached. A steady flow out of the material can be mea-root of molecular weight of the penetrating gas. It issured, the rate being proportional to the flux. By thisobvious from Eq. (3) that a plot of effective diffusivity vs.means we are measuring the flux directly. If a constantpressure will be linear with gradient: ´B /m and intercept:opressure drop is used to drive the gas phase transport´D . If such a plot is linear, this does not exclude thepprocess (usually maintained by ensuring that the supplypresence of adsorbed phase diffusion accompanying gasand receiving volumes are very large) then the pressurephase transport. However, if the gradient of two differingwill rise linearly in the receiving volume with time. Thespecies is inversely proportional to viscosity and theslope of this linear rise (S) is evaluated from the data andintercept inversely proportional to the square root ofthe flux is given bymolecular weight, this ensures that gas phase flow domi-

SV nates that of the adsorbed phase because the adsorbed]]J 5 (2a) phase flux has a more complex dependence on molecularAR Tg

properties of the diffusing species than a simple pro-where A is the cross-sectional area of the media. After portionality [13].evaluating the flux directly, the diffusivity is often used to With the pellets described earlier in the experimentalcharacterise the mobility of the transport process. Using section, we have measured the steady state slope forFick’s law we obtain the diffusivity as a function of the carbon dioxide, helium, argon, oxygen and nitrogen per-measured slope and pressure drop (DP) meation at 208C for a range of pressures. The permeation

process with helium, argon, oxygen and nitrogen reachesSVL]]D 5 (2b) steady state very quickly and there is no measurablee A DP

transient permeation phase. For carbon dioxide this is notwhere D represents the combined effective diffusivity the case and the dynamics can be monitored on a measur-e

which will be the sum of all transport processes occurring able timescale. This is due to the intrusion of adsorptionin parallel along the direction of transport. For macro / dynamics in the permeation process which we discuss in amicroporous or bidispersed solids this may include a later section. Of interest is the steady state slope which wemacroporous diffusion (Knudsen, viscous or molecular obtain from linear regression of the data at large times. Thediffusion depending on the conditions) and possibly a steady state slope for helium, oxygen, argon and nitrogencoupled adsorbed phase diffusion process. The presence of measurement is also obtained by linear regression. Thethe adsorbed phase diffusion increases the observed correlation coefficient is high for all data sets, the lowest

2mobility beyond that which would be expected from the value of which is R 50.98. When plotted against pressure,gas phase diffusion alone. Because both diffusion mecha- the effective diffusivity, obtained from the steady state


pressure rise using Eq. (2b), appears to be linearly related obtain: t 54.2 and t 55.8. Approximately the sameK V

to pressure as is shown in Fig. 2. Linear regression shows value for the diffusive tortuosity was obtained for diffusionthat such a correlation is valid. For helium, argon, oxygen within Ajax activated carbon [15] and similar values areand nitrogen permeation at steady state we have deter- reported by Ruthven [1]. The viscous tortuosity is alsomined the following relationships: close to this value indicating that the pore network presents

the same magnitude of resistance to both diffusionalHe 2 25D (cm /s)7.0 3 10 P(Torr) 1 0.12 (4a)e motion at low pressures and viscous transport at higherpressures.O 2 252D (cm /s) 5 6.0 3 10 P(Torr) 1 0.046 (4b)e

N 2 252D (cm /s) 5 7.3 3 10 P(Torr) 1 0.048 (4c)e4. Adsorption isotherm from batch measurement

Ar 2 25D (cm /s) 5 5.5 3 10 P(Torr) 1 0.041 (4d)e The amount of carbon dioxide adsorbed at equilibriumFor carbon dioxide permeation at steady state we have: by Takeda 5A pellets at 208C has been determined by

volumetric batch adsorption as discussed in the experimen-CO 2 252D (cm /s) 5 8.4 3 10 P(Torr) 1 0.042 (4e)e tal section. Fig. 3 provides the isotherm graphically. It canbe seen that the slope of the isotherm is larger at low

The viscous flow parameter (´B ) and corrected pore0] pressure than it is at higher pressures typical of manyŒdiffusivity (D M) are determined by equating thesep isotherms of type 1. For comparative purposes, we haveexperimentally determined relationships with Eq. (3) for

included isotherm data for other adsorbent materials,all five gases considered. These values are plotted against

including an activated carbon fibre and a commerciallymolecular weight and viscosity in Fig. 2f and 2g. The

available activated carbon extrudate which have similarfigures show that within 65% error, the viscous flow

adsorption properties to the Takeda 5A sample. This is aparameter for all gases is independent of viscosity and the

result of the fact that all samples share a generally relatedcorrected pore diffusivity independent of molecular

carbonaceous structure and therefore have similar affinityweight. We can conclude from this that Knudsen and

for gas adsorption. The comparison illustrated on Fig. 3viscous mechanisms are present within the gas phase flow

verifies that the measured isotherm is within an appropriateand adsorbed phase flow if present, contributes negligibly

range for carbon dioxide adsorption.to the mass transfer. For convenience we have included in

The classic Langmuir isotherm equation is often utilisedTable 3, the viscosity of the gases used.

in the description of gas adsorption at low relativepressures where isotherm relations are generally of type 1.

3.1. Evaluation of TortuosityThe mathematical form for such a relation is represented as

It is well known that the structure of a porous material is C bCms]]C 5 (5a)fundamentally related to gas phase transport processes. A m 1 1 bC

useful summary of early work in this area is given in thewhere b represents the affinity and C represents atext of Carman [14]. For materials with a pore size ms

saturation concentration. We can fit this isotherm equationdistribution it is known that the permeability and Knudsen24to the data and in doing so we obtain C 59.8310diffusivity can be related to the distribution of pore size ms

5mol /ml and b53.3310 ml /mol.through Darcy’s law:

]2r 4.1. Adsorption dynamics]B 5 (4f)o 8tV

The steady state permeation result has proven useful in]2where r is mean square pore size and t is the viscousV identifying the presence and absence of some common

tortuosity factor and through the Knudsen diffusion rela- mass transfer mechanisms. We have shown that there istion: insignificant adsorbed phase flux of carbon dioxide, how-

]] ever consideration must be given to the dynamics of2r 8RT] ]D 5 (4g) adsorption. Depending upon the conditions of measure-P œ3t pMK ment, the processes of macropore diffusion or micropore¯where r is mean pore size and t is the diffusive tortuosity diffusion may dominate [1]. In molecular sieving materialsK

factor. The Takeda 5A sample used in this investigation such as the CMS used in this investigation, it is possiblehas had pore size distribution measured using Mercury that a pore mouth resistance may influence mass transferintrusion and diffusivity has been evaluated from permea- and cause molecular sieving [2,3]. However it has beention measurements. As a result, the tortuosity may be shown that for Takeda 5A CMS, only molecules of size inevaluated from Eq. (4f) and (4g). By this method we the order of cyclohexane experience molecular sieving


Fig. 2. (a) Effective diffusivity for helium at 293 K through Takeda 5A pellets; (b) Effective diffusivity for carbon dioxide at 293 K throughTakeda 5A pellets; (c) Effective diffusivity for nitrogen at 293 K through Takeda 5A pellets; (d) Effective diffusivity for oxygen at 293 Kthrough Takeda 5A pellets; (e) Effective diffusivity for argon at 293 K through Takeda 5A pellets; (f) The viscous flow parameterdetermined from gas permeation plotted against the viscosity; (g) The product of the pore diffusivity times the square root of molecularweight of the permeating gas plotted against the molecular weight.


4.2. Mass balance

The general mass balance for considering single gasadsorption /diffusion process within our pellet must includea Knudsen and viscous flux and exclude any adsorbedphase flux. This can be represented as:

¯≠C ´B≠C 1 ≠ ≠Cm om] ] ]] ] ]´ 1 (1 2 ´) 5 r C 1 ´DF S D Gm P≠t ≠t ≠r m ≠rr

(5b)

¯where C is the gas phase concentration and C is them

volumetric average microparticle concentration. In mostinstances the permeation experiment is conducted with slabporous media implying that the shape factor m, in the massbalance is generally zero (m50).

Fig. 2. (continued) In the usual analysis of permeation data the adsorptionprocess is often fast in comparison to the diffusion alongthe pellet scale. When this is the case, a change in the gas

Table 3 phase concentration makes an instant change in the aver-Viscosity of gases at 293 K and 1 atm age adsorbed phase concentration. Local equilibrium isGas Viscosity (poise) established and this usually results in the ‘pore diffusion’

24 model being invoked to describe permeation dynamics andHelium 1.9531024 as has been useful in describing this situation [8]. HoweverNitrogen 1.7731024 such a model can only be used when the timescale forArgon 2.2231024 macropore diffusion is much greater than the timescale forCarbon Dioxide 1.4631024Oxygen 2.03310 micropore diffusion. This condition has been conveniently

quantified by the parameter g and the condition [8]:

2C R Dm p m]]]g 5 4 1.2CD Re[16]. Therefore we shall consider only micropore /macro- m

pore diffusion in the description of mass transfer of carbonHowever, when micropore diffusion is slow (the mi-dioxide.croparticle is large or D is low in magnitude), the pellet ism

small (R low in magnitude) or the gas phase diffusionp

process is fast (D large in magnitude), there is no locale

equilibrium between the sorbate and the microparticle.Diffusion within the microparticle must be considered andto account for this additional process within the pellet,uptake within the microparticle can be expressed using aparabolic approximation for the concentration profile,resulting in [17]:

¯≠C 15D (C )m m m ¯] ]]]5 C 2 C (5c)s dm m2≠t Rm

where C is the equilibrium adsorbed phase concentrationm

which is related to concentration through the isothermrelation and D is the adsorbed phase diffusivity whichm

normally adopts a dependence upon concentration de-scribed by the Darken relation, which for the Langmuirisotherm is:

Fig. 3. Adsorption equilibrium of carbon dioxide on carbon fibreDm0at 298 K (taken from [22]), on Ajax activated carbon (taken from

]]]D 5 . (5d)m[23]) and on carbon molecular sieve (CMS) (Takeda 5A in this 1 2 C /Cm ms

work) at 293 K. Also included is the fit of the Langmuir isothermEq. (5a). Mathematically this system of equations (under linear


isotherm conditions), is similar to that solved by Good- rate. Hence inspection of the initial rate of pressure riseknight and Fatt [18] who showed that a resistance to mass provides a useful visual identification for determining,transfer perpendicular to the main direction of transport based on the shape of the downstream pressure rise curve,influenced the rate of pressure rise in the outgoing volume. whether there is local equilibrium between gas and ad-It was found that a large resistance caused a faster initial sorbed phases within the pellet.rise than a lower resistance. In terms of the adsorption As indicated earlier, the dynamics of permeation isproblem at hand, this would imply that a slower micropore displayed on a measurable timescale for carbon dioxide butdiffusion would lead to a faster initial rise in the down- not for the other gases. This is due to the influence ofstream pressure. In relation to the condition above, this adsorption processes within the pellet effectively slowingwould further imply that the lower the value of g, the the transient permeation rate on the pellet scale. Fig. 4higher the initial rate of pressure rise. In the case where the show the downstream pressure rise for carbon dioxidemaximum limit was approached when g <1, the down- permeation for a number of upstream pressures and it isstream pressure rise would be dominated simply by the gas obvious that there is a relatively fast initial pressure rise,phase flow and rise at a fast initial rate. In the case where indicative of the fact that the micropore diffusion processthe other limit was approached when g 41 (local equilib- is slow and that the parameter g is not much greater thanrium), the downstream pressure rise could be described by 1. Therefore, the simplified ‘pore diffusion’ descriptionthe ‘pore diffusion ‘ model and rise at an initially slow based on the assumption of local equilibrium is inappro-

Fig. 4. (a) Downstream pressure rise in the permeation experiment of carbon dioxide at 293 K through Takeda 5A pellets at upstreampressure 19.623 Torr; (b) Downstream pressure rise in the permeation experiment of carbon dioxide at 293 K through Takeda 5A pellets atupstream pressure 40.86 Torr; (c) Downstream pressure rise in the permeation experiment of carbon dioxide at 293 K through Takeda 5Apellets at upstream pressure 8.197 Torr; (d) Downstream pressure rise in the permeation experiment of carbon dioxide at 293 K throughTakeda 5A pellets at upstream pressure 65.5 Torr.


Table 4priate here. For this reason we must solve the general massParameter values for solution of Eq. (5)balance of Eq. (5) in order to obtain the parameter

2representing micropore diffusion D /R . Constant Valuem0 m

´ 0.28V 1100 ml4.3. Solution of mass balance

3 2´B /m 1.5310 (ml cm /s /mol)o

2´D 0.04 (cm /s)PIn order to solve this mass balance, boundary conditionsL 0.6 cmare required. The upstream boundary condition for the 2A 0.707 cm

permeation experiment is

C(0,t) 5 C (5e)0 5. Analysis using time lag intercept

and downstream, the continuity of mass implies that theFig. 4 show that the downstream pressure rise ap-

amount entering the downstream volume isproaches a linear asymptote indicating steady state flow.The intercept of this asymptote with the time axis is known≠C ≠C

] ]x 5 L; V 5 ADe as the time lag and has been used as a general means for≠t ≠xcharacterisation of transient permeation processes [20].

In order to simultaneously solve Eq. (5) for the down- The relationship between time lag and the upstreamstream pressure rise, it is necessary to use numerical pressure can reveal information about transport mobilitytechniques, because the isotherm and diffusivity relation- and amount adsorbed. It can be shown by manipulation ofships are non-linear. Here we opt to solve the equations the mass balance of Eq. (5b) according to the method ofsimultaneously using the numerical method of lines. The Frisch [21] that this relationship carries the form:

2kinetic parameter D /R shall be evaluated by simulta-m0 mC C0 0neous fitting of the permeation curves which appear in Fig.

25 for the upstream pressures indicated. Other parameters L E ´C 1 (1 2 ´)C H(u) EH(w) dw duS Ds dm

have been evaluated previously and Table 4 summarises u0]]]]]]]]]]]t 5 (6a)these values. lag C 30

Fig. 4 contains the fit of Eq. (5) represented as continu- EH(u) duous lines to the data which is represented as open circles. 1 20The prediction of the measured pressure rise against time

is reasonable. The result of the optimisation is evaluation where the function H is given as2of the kinetic parameter, the limiting diffusivity, D /R 5m0 m23 211310 s . This value is close to that presented by ´Bo2 24 ]H 5 C 1 ´D (6b)Kapoor and Yang [19] who obtained D /R 59310 Pm0 m m

21s for carbon dioxide adsorption into a molecular sievingcarbon at 298 K. Having evaluated the isotherm relation from batch

adsorption and obtained the time lag from linear regressionof the steady state asymptote, it is possible to solve Eq. (6)by numerical integration and compare with the experimen-tally derived time lag. Fig. 5 shows the time lag for aseries of upstream pressures represented as open circlesand it is evident that the time lag decreases with upstreampressure for two reasons:

1. the slope of the isotherm decreases with increasingpressure

2. the gas phase mobility increases as a result of theintrusion of viscous permeation mechanism.

The solution of Eq. (6) is also shown on Fig. 5 and thefit is reasonable validating the accuracy of the time lagmeasurement and the time lag procedure as a method forFig. 5. The relationship between the measured time lag and the

upstream pressure. characterisation for this case.


5.1. Shape of permeation curve and time lag these measurements using dynamic batch adsorption data.This dynamic data was obtained while monitoring pressure

As we have discussed, the parameter g, representing the change in order to obtain the amount adsorbed at equilib-ratio of the timescales for micropore diffusion and pellet rium (discussed earlier). This experiment was conductedscale diffusion processes, influences the shape of the curve within a large volume (2000 ml) for the purpose ofof downstream pressure rise against time. This is evident in keeping the maximum change in pressure between 5 andFig. 6, which represents permeation of carbon dioxide with 10%. In this manner, the boundary condition can bean upstream pressure of 19 Torr (curve B). The ratio of the considered effectively constant, but the pressure measure-macropore to micropore diffusion timescale, noted as g, is ment is sensitive enough to monitor this relatively smallin the order of 0.4 for permeation through the Takeda 5A transient change. The experiment was also conducted in anpellet. According to Gray and Do [10] this implies that ‘integral’ fashion with outgassed pellets. As a result of theboth macropore and micropore diffusion intrude into the large total change in concentration within the pellet and thepermeation process a situation known as ‘bimodal’ diffu- isotherm being non-linear over this range, the masssion. Also shown on Fig. 6 are two bounds, one being the balance must be solved by numerical means.limit of macropore diffusion control (curve C, g 41), the The batch adsorption experiment was conducted withother being the limit of micropore diffusion control (curve spherical particles of radius R 50.15 cm for the purposep

A, g <1). It can be seen that curve A has a very small of measurement of the adsorption equilibrium isotherm.change in the gradient as time increases. However, all The dynamic pressure change was monitored with respectthree curves should reach the same rate of pressure rise at to time in order to determine when true equilibrium wassteady state and according to Goodknight and Fatt [18], all reached. Under these measurement conditions the parame-three should have the same time lag for the advancing gas ter g is in the order of 0.1 implying that microporeto penetrate the pellet. This would imply that for curve A, diffusion is controlling the mass transfer. For this case, theextrapolation of the linear steady state rise back to the time mass balance will reduce to:axis to obtain the time lag, would result in large error. This

≠C D ≠C1 ≠m m0 m2reinforces the need for other means of characterisation, ] ]] ]]]]5 r (7a)S D2≠t ≠r 1 2 C /C ≠rr m mssuch as batch adsorption, to be undertaken to complimentthe time lag measurement when bimodal diffusion is

subject to the boundary and initial conditions of ourobserved.

‘integral’ experiment:

C bC5.2. Verification by batch dynamic measurement ms 0]]r 5 R ; C 5 (7b)m m 1 1 bC0

Having characterised all the relevant mass transferand to the initial conditionprocesses including gas phase permeation and micropore

diffusion by permeation method, it is possible to verify t 5 0; C 5 0 (7c)m7

and the fractional uptake (F ) is given by

Rm

3 2]1 1 bC E r C drs d0 m31 2Rmm t 0]] ]]]]]]]F 5 5 (7d)m C bCequ ms 0

The 5–10% change in concentration that is measuredduring adsorption will affect the shape of the uptake curvebut to a negligible extent as shown by Ruthven [1].Modification of the boundary condition (Eq. 7b) is there-fore not necessary. Having already evaluated the necessaryparameters, solution of Eq. (7) was undertaken andcompared to the batch dynamic curves as is shown in Fig.7. The continuous lines show the solution of Eq. (7) andthe open circles represent data points. The fit is reasonablefor all curves presented, showing good consistency be-Fig. 6. The predicted downstream pressure rise of carbon dioxidetween the dynamic methods of batch adsorption andwith upstream pressure 19.62 Torr (as shown in Fig. 4a) noted aspermeation.Curve B. Curve A represents the limit of slow adsorption

The batch adsorption experiment has been commonly(micropore diffusion control: g <1) and Curve C represents thelimit of fast adsorption (local equilibrium: g 41). used for determining kinetic data and proves more useful


than the steady state permeation experiment in the respectthat the equilibrium isotherm can be determined simul-taneously with dynamic data. However the flux cannot bedetermined directly in the batch experiment, often makingestimation of the gas phase transport processes necessary, aprocedure which can result in large error. This is aninherent weakness of the batch method. On the other hand,the permeation experiment can measure the flux accuratelyand when the two methods are coupled as we have used inthis investigation, the results provide a valuable means ofcharacterisation.

6. Conclusion

Analysis of equilibrium and kinetics of batch adsorptionhas shown that the micropore diffusion, characterised bythe Darken relation, is rate limiting the dynamics of uptakein small Takeda 5A pellets. The permeation experimentundertaken with larger Takeda 5A pellets shows thatbimodal diffusion control applies to the mass transferprocess. Steady state diffusion measured by permeationexperiment is shown to consist primarily of a combinedKnudsen and viscous mechanism with negligible adsorbedphase flux along the pellet present. It is shown that acombination of both batch adsorption and permeationexperiments prove to be a valuable method of characterisa-tion.

Acknowledgements

This project is supported by the Australian ResearchCouncil.

References

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Adsorption dynamics of carbon dioxide on a carbon molecular sieve 5A