Carbon 41 (2003) 2533–2545

A dsorption of propane and propylene onto carbon molecularsieve

a a b a ,*´Carlos A. Grande , Viviana M.T.M. Silva , Carlos Gigola , Alırio E. RodriguesaLaboratory of Separation and Reaction Engineering(LSRE), Department of Chemical Engineering, Faculty of Engineering,

University of Porto, Rua Dr. Roberto Frias s/n 4200-465, Porto, Portugalb ´PLAPIQUI, Camino La Carrindanga, Km. 7, Bahıa Blanca(8000), Argentina

Received 13 March 2003; accepted 28 June 2003

Abstract

Equilibrium data for propane and propylene adsorption on a carbon molecular sieve (CMS) 4A from Takeda are presentedin the temperature range 343–423 K and 0–300 kPa pressure. The pellet adsorption loading is 0.9 mol /kg for propane and1.2 mol /kg for propylene at 100 kPa and 373 K. The equilibrium selectivity for propylene in the low-pressure range are 2.3(343 K) and 1.7 (423 K). Experimental data were fitted with the Toth and Dubinin models. Zero length column (ZLC)technique has been used to determine the controlling mechanism and estimate the diffusivity parameters. Transport of bothhydrocarbons in the pellets is controlled by micropore diffusion. Breakthrough curves were measured in the sametemperature range and atmospheric pressure, at the low partial pressure of adsorbate (linear region of the isotherm). Simplemodels have been used in the simulation of breakthrough curves. 2003 Elsevier Ltd. All rights reserved.

Keywords: A. Molecular sieves; D. Adsorption properties; Diffusion

1 . Introduction be produced from many different organic sources: bitumin-ous coal, bones, coconut shell, etc. The final micropore

Adsorption techniques have been explored in the last size depends on the pyrolysis and activation steps in theyears to carry out olefin/paraffin separations as an alter- manufacturing process[2,3]. The micropore size is gener-native to the traditional processes. Propane/propylene ally assumed as uniform. The main use of CMS adsorbentseparation is the most intensive separation carried out in has been the nitrogen production from air[4,5] by meanspetrochemical industry; the polymer-grade propylene re- of a kinetic separation where both components are nearlyquires a purity .99.5% which can be obtained in a equally adsorbed but diffusion of oxygen is much fasterdistillation column with over 200 theoretical plates and being preferentially adsorbed and the CO /CH separation2 4

high reflux ratios. Adsorptive methods or hybrid adsorp- [6,7].tion–distillation methods should increase the separation Pure propane and propylene adsorption equilibrium isfactor, resulting in a less energy demanding process[1]. particularly well documented for CMS 5A[8–11] and forThe search for an adequate adsorbent is still an important other home-prepared carbon molecular sieves[12,13],primary research activity. although data for CMS 4A is very scarce. Recent in-

For the modeling of adsorptive processes such as PSA vestigations in CMS 4A (Bergbau–Forschung with pore˚(pressure swing adsorption) or VSA (vacuum swing ad- size ranging from 3 to 5 A) showed that both molecules

sorption) equilibrium and kinetic data are needed to solve were totally excluded[14].material and energy balances. The objective of this work is to report pure propane and

Carbon molecular sieves (CMS) are adsorbents that can propylene equilibrium isotherms at 343, 373 and 423 Kover CMS 4A (Takeda Chem. Ind. Lda., Japan) performedin a manometric device. A complete physicochemical*Corresponding author. Tel.:1351-22-508-1671; fax:1351-characterization of the adsorbent has been performed. Zero22-508-1674.

E-mail address: arodrig@fe.up.pt(A.E. Rodrigues). length column (ZLC) technique was used to determine the

0008-6223/03/$ – see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0008-6223(03)00304-X

2534 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

controlling mechanism of diffusion as well as the diffusivi-ty values. Breakthrough curve measurements at very lowconcentrations were performed to confirm/determine theequilibrium capacity obtained manometrically and thekinetics parameters obtained by zero length column tech-nique.

Equilibrium data was analyzed in terms of the theory ofvolume filling of micropores, TVFM, with the Dubinin–Radushkevich model[15] and also with the Toth model[16].

2 . Experimental

All the equilibrium measurements were made in amanometric–chromatographic equipment operated inclosed system. The pressure transducer used for total Fig. 2. ZLC configuration.amount adsorbed measurements is Lucas Schaevitz 9000series from 0 to 500 kPa with an error of60.5 kPa. Thescheme of the equipment is shown inFig. 1. The system ZLC is shown inFig. 2. All connections after the valvewas called manometric and not volumetric because the real were 1/160 and therefore dead volume effects werevariable measured is the pressure[17]. completely minimized. To activate the samples, a flow of

27 3The activation of the samples was made in vacuum at helium of 2.0310 m /s at 523 K (1 K heating ramp)523 K for periods of at least 16 h. For all the equilibrium was used overnight (16 h at least).experiments reported in this paper, we assume that the Breakthrough curves were measured in a similar schemeinitial calibration procedure with helium is valid and that (using a Carlo Erba gas chromatograph) changing the ZLChelium is not adsorbed on CMS 4A at ambient temperature cell by a column filled with the adsorbent in a GC oven.

27and low pressures[18]. The results of the calibration at To activate the samples, a flow of helium of 3.333103higher temperatures (343, 373 and 423 K) are consistent m /s at 523 K (1 K heating ramp) was used overnight (16

with this assumption, at least within the error of the h at least). Experimental details of ZLC and breakthroughequilibrium and pressure measurements. experiments are listed inTable 1.

Zero length column measurements were carried out Air Liquide provided all gases used in this report:using a Perkin-Elmer AutoSystem XL Gas Chromatograph propane N35, propylene N24 and helium N50 (purityoven to heat the cell and the flame ionization detector greater than 99.95, 99.4 and 99.999%, respectively). The(FID) detector for concentration measurements. The CMS 4A, extrudates of 1/160 diameter, was kindlyswitching valve (helium and helium–hydrocarbon streams) provided by Takeda (Lot. No. M965).was inside the GC where gases are preheated before The macroporosity of the sample was measured byentering the cell. The complete system description of the mercury intrusion. This analysis was performed in a

Poresizer 9320 (Micromeritics) in a range of pressuresbetween 0.5 and 30 000 psia (pore determination between

˚360 mm and 60 A).For microporosity determination, carbon dioxide ad-

sorption equilibrium at 297 K was determined in aRubotherm microbalance (Bochum, Germany). Each pointof equilibrium was measured only after 1 h; i.e., the timeneeded to ensure constant weight (equilibrium). The tem-perature was controlled with an electric oven with60.5 K.The isotherm presented here has been measured twice withreproducible results and was completely reversible. Activa-tion of the sample was performed at 523 K for 4 h and invacuum.

To complete the physicochemical characterization, scan-ning electron microscopy (SEM) was used to observe theFig. 1. Manometric–chromatographic equipment used for adsorp-micropore structure. We will call ‘crystal’, in analogy withtion equilibrium measurements. A thermocouple (T) was insertedzeolites, all the agglomeration of crystalline parts of thein the middle of the adsorbent chamber (AC) to measure tempera-

ture variations with adsorption. sample where the main amount of micropores is located.

C.A. Grande et al. / Carbon 41 (2003) 2533–2545 2535

T able 1ZLC and breakthrough curves experimental conditions

C H and C H conc., C (%, v/v) 1.10 and 1.053 6 3 8 o23Pellet radius,R (m) 1.1310 mp

Zero length column Breakthrough curves3 27 23C H flow rate,Q (m /s) 5.0310 Mass of adsorbent (kg) 7.22973103 8 p3 27 3 27C H flow rate,Q (m /s) 4.5–5.2310 ; Flow rate (m /s) 1.043103 6 p

276.2–6.8310 (100 kPa, 300 K)3 27Cell volume,V (m ) 2.8310 C concentration 1.05–1.10%c 3

(v /v)23 25Extrudate length,H (m) 2.3310 Column volume and 1.12310

3 23(small extrudates); size (m ) (9.3310 [3235.0310 0.165 m)

(large extrudates);3 28Extrudate volume,V (m ) 6.1310 Bed porosity 0.283s

(small extrudates);285.7310

(large extrudates)

3 . Theoretical data interpretation[16]. Here, for high-pressure data, thepressure has to be replaced by the fugacity. This model has

Exponential description of adsorption was extensively been extensively used for gas adsorption on microporousapplied in the correlation of adsorption equilibria. All the adsorbents[23] and specifically for propane–propyleneexponential equations grouped in the theory of volume adsorption on zeolites[24]. It is Langmuir reducible whenfilling of micropores (TVFM) assume that the adsorption the heterogeneity parameter,n, is unity (homogeneoustakes place volumetrically[19]. The fundamental postulate adsorbent). The other three parameters have the sameis the temperature invariance of the amount adsorbed as a physical meaning as in the Langmuir isotherm: heat offunction of the adsorption potential, defined as the negative adsorption (DH ), maximum adsorbed phase concentration

odifferential free energy of adsorption[20]. (q ) and infinite adsorption constant (K ). The Toth modelm

The generalized Dubinin model is expressed as is expressed by

o d 1 /nP q K Ps dm eq]RT ln ]]]]q 5 (2a)nP 1 /nF S D G 11K P]]]q 5 q exp 2 (1) s deqm Eo

DHo ]K 5K expS2 D (2b)where P is the gas pressure,q and q are the adsorbed eqm RTconcentration (actual loading) and maximum adsorbedconcentration (maximum loading), respectively,E is the Zero length column (ZLC) technique is a powerfulo

characteristic energy of adsorption andd is the third fitting technique for diffusivity measurement of pure gases onconstant of the equation which is a measure of the porous solids[25]. The procedure is to saturate a smallheterogeneity of the system and assumes a small integer amount of adsorbent with a diluted mixture of the adsor-value, generally between 3 and 6 for molecular sieves[21]. bate till equilibrium in the adsorbed phase is reached. ThenFor high pressures, fugacity should be used instead of the inlet is switched to an inert stream to clean thepressure. The Dubinin–Radushkevich equation assumes adsorbent. From this desorption curve the diffusivity andthat the pore size distribution is Gaussian (d52) and is equilibrium parameters are extracted. It has been exten-generally used for activated carbons. These equations are sively used for diffusivity measurements in zeolites[26–extensively used for adsorption on activated carbons and 28]. Combined macro–micropore control in bidisperseCMS, respectively[15] and the fitting of only two parame- adsorbents were also considered in literature[29].ters makes them very interesting for engineering purposes, In fact, there are techniques that are similar to ZLC,even when its low-pressure thermodynamic limit (Henry namely the shallow bed to measure film mass transfer andlaw zone) is incorrect. DAB (differential adsorption bed) to measure intraparticle

The main problem of the exponential models is its diffusion. The shallow bed technique has been used toincorrect behavior in the low-pressure zone where all the measure film mass transfer coefficients in liquid phaseexponential isotherms fail to fit the Henry constant[22]. [30]. Combined measurements of mass transfer coefficientTo overcome this difficulty for the breakthrough modeling, and internal diffusion were also performed using thisa four-parameter equation, the Toth model was used for technique[31,32]. DAB technique was used to measure

2536 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

pure and multicomponent gas diffusion[15,33]. An open dispersed plug flow. Additionally to the macropore–micro-microbalance system was used to measure ethane kinetics pore resistances we have included the possibility of a filmin zeolite 4A [34]. resistance in the external surface of the pellets. The mass

For the mathematical modeling of the ZLC it is consid- balance in a differential element of the column can beered that the adsorbent is homogeneous and the Fick’s law described as[37]of diffusion can be applied to the kinetic measurements of

2 Ca sorbate in an extrudate by ZLC. The mass transfer K Lip≠ C ≠C ≠C 12´i i i c]] ] ] ]] ]]control is limited by micropore diffusion and sorbate D 2 v 5 1 ´S Dax p2 ≠z ≠t ´ ≠t≠z cconcentrations used are low enough to describe adsorption

equilibrium by the Henry law (linear isotherm). ]≠ qK Li12´cWith these assumptions, solutions for infinite slabs, ]] ]]1 r (5)S D p´ ≠tinfinite cylinders and spheres were obtained[24,35]. c

2 2 with initial condition:` exp 2D b t /Xs dC c j] ]]]]]5 2L O (3)2 C 5 0 (6)C i 0,zs db 1 L L 1 12 So S51 s dj

and Danckwerts boundary conditions:where S50, 1 and 2 for slabs, cylinders and spheres,

≠Crespectively,C andC are the instantaneous and initial gas io ]D 5 v C 2C (7)s dUax i iophase concentration, respectively,D is the crystal or ≠z t,0s dc

micropore diffusivity andK is the equilibrium constant,X≠Ciis the crystal representative spatial dimension (radius for ] 50 (8)U≠z t,Ls dinfinite cylinder and sphere and half length for infinite

slab) andL is the ZLC parameter. where D is the axial dispersion coefficient,́ is theax c

porosity of the column,́ is the pellet porosity,C is the2 p ioF Xp feed concentration of componenti entering the column,]]]]L 5 (4)(S 1 1)KV D ]s c q is the pellet averaged amount adsorbed per gram ofK Li

where F is the purge flow-rate andV is the volume of particle,C is the gas phase concentration of componenti,p s i

adsorbent in the cell. The rootsb for the differentj C is the pellet averaged concentration of componentiK Lipgeometries are given inTable 2, where J and J are0 1in the macropores of the pellet,r is the density of thepBessel functions of first kind of order zero and one,pellet andn is the interstitial gas velocity.respectively.

In these equations we have considered that the amountIf macropore resistance controls the diffusion process allof gas adsorbed is very small compared to the total flowthe equations have the same form, but the micropore orentering the bed and thus the velocity is constant in thecrystal diffusivity has to be replaced by the apparententire column. In accordance to the ‘trace system’ assump-diffusivity, D 5´ D / [´ 1 (12´ )K] and the repre-ap p p p ption, the process has also assumed to be isothermal.sentative spatial dimension is referred to the pellet radius

The mass balance in a volume element of the pellet isor half-length.represented by:Parameter determination for equilibrium models

](Dubinin–Radushkevich and Toth) and diffusivity from ≠C ≠C≠q 1 ≠ip ipi SF G]] ] ]] ]]ZLC experiments was performed in MATLAB 5.0 (The ´ 1r 5 ´ D R (9)p solid p pS≠t ≠t ≠r ≠RRMathworks) using the Nelder Mead Simplex method ofdirect search. We used the SOR (square of residuals) errorwith initial condition:function [36] for equilibrium parameter optimization and

C 50 (10)ip 0,Rs dthe ARE (average of residuals) for kinetic parameters fromZLC experiments[28]. and boundary conditions:

For the analysis of the breakthrough curves we will≠Cipconsider the case of a bed filled with a bidisperse ad- ]]´ D 5 k C 2C (11)U t,Rus dp p f i ip ps dt,R≠R s dpsorbent where the flow can be considered as an axially

T able 2Transcendental equations of ZLC model for different geometries

Slabs Cylinder Spheres

b tan b 2 L 5 0 b J b 2LJ b 5 0 b cot b 1 L 2 15 0s d s d s ds dj j n 1 n 0 n k k

C.A. Grande et al. / Carbon 41 (2003) 2533–2545 2537

≠Cip]] 5 0 (12)U≠R t,0s d

where D is the pore diffusion coefficient,C is the gasp ip]concentration of componenti in the macropores,q is thei

average amount adsorbed in the crystals,R is the pelletp

radius andk is the film mass transfer resistance in thef

external surface of the pellet. The sub-indexS denotes thegeometry of the pellet and has the values of 0, 1 and 2 forinfinite slab, infinite cylinder and spheres, respectively.

The mass balance in the micropores is described by:

≠q ≠q1 ≠i iS] ]] ]5 FD r G (13) Fig. 3. Macropore determination by mercury intrusion.cS≠t ≠r ≠rr

with initial condition: elements for the pellet and for the crystal, with two internalcollocation points in each domain.

q 5 0 (14)0,rs d

and boundary conditions: 4 . Adsorbent characterization

q 5 q 5H C (15) For a correct interpretation of the equilibrium andt,r s ips dckinetic data, some basic aspects of the adsorbent have to bepreviously known; i.e., microporosity, macroporosity,≠q

] 5 0 (16)U structure of the micropore agglomerations, etc. To de-≠r t,0s d

termine the macropores existing in the sample, a mercuryintrusion analysis was performed. The result, shownwhereD is the crystal or micropore diffusivity andr isc cgraphically inFig. 3, indicates that the average macropor-the crystal radius. The adsorption equilibrium law givesosity size is 0.3mm. This value is typical for carbonthe boundary condition in the crystal limit. In this work,molecular sieves, although when compared with otherwe used the linear isotherm to describe adsorption equilib-CMS samples it looks relatively narrow[2,38].rium because the hydrocarbon partial pressures were very

The method used to determine the microporosity waslow and no difference was observed between introducingcarbon dioxide adsorption at ambient temperature[39],the Toth model or the linear model, except that with thewhich is better than nitrogen adsorption at 77 K, becauselinear model, the computation time was much faster.the nitrogen molecule is practically excluded (or very slowIn the equations presented above, average variablesdiffusion rate at 77 K). The isotherm obtained at 297 K upwhere mentioned and are defined by:to pressures of 3000 kPa is presented inFig. 4. Buoyancy

Rp

2 S]]C 5 E C R dR (17)K Lip ipS11s d Rp 0

Rp

2 S] ]]q 5 E q R dR (18)K Li iS11s dRp 0

rc

2 S] ]]q 5 Eq r dr (19)i iS11s drc 0

All the equations presented here were solved simul-taneously in gPROMS (PSE enterprise). The orthogonalcollocation method on finite elements (OCFE) was usedwith 20 finite elements and two interior collocation points Fig. 4. Carbon dioxide adsorption on CMS 4A Takeda at 297 K.in each element of the adsorption bed, and seven finite Solid line represents the generalized Dubinin model.

2538 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

Fig. 6. Adsorption equilibrium of propane at 343, 373 and 423 Kon CMS 4A Takeda. Solid lines are the Toth model and dottedFig. 5. Scanning electron micrographs of the adsorbent.lines the Dubinin–Radushkevich model.

corrections at high pressures have been made accordingly5 . Adsorption equilibriumto the procedure indicated in previous literature[40]. Forpressures up to 1000 kPa the typical plateau was almost Adsorption equilibrium isotherms of propane and pro-reached in a value around to 3.5 mol /kg. Data are in pylene at 343, 373 and 423 in the 0–300 kPa pressureagreement with other works published using a CMS range are shown inFigs. 6 and 7,respectively. Solid linesTakeda 4A adsorbent[41]. The isotherm was fitted (solid in figures correspond to the Toth model fitting while dottedline in Fig. 4) with the generalized Dubinin equation using: lines are the Dubinin–Radushkevich model. At the lowerq 53.6976 mol /kg,E 513.6 kJ/mol andn52.46. The temperature measured, the saturation plateau is reachedm o

parameters are also in reasonable agreement with pub- around 200–250 kPa for both gases. Clearly, the selectivitylished parameters for carbon dioxide in CMS 5A[42]. As of the material towards propylene is not high: in thesuggested in other works, when the value ofn cannot be low-pressure range the Henry constant relation (H /C3H6

fitted correctly to a value of 2 or 3 this corresponds to a H ) are 2.3 (343 K) and 1.7 (423 K). The fittingC3H8˚mixture of very fine micropores (in this case around 4 A) parameters of both models are shown inTable 4. Pro-

˚and some other larger micropores[41]. The value of 6 A as pylene data at 343 K is comparable with previous reportsaverage pore size has been attributed to this sample by at 323 K on CMS 5A[11].other independent researchers involved in the propane/ Note that for the fitting of both adsorption isotherms, thepropylene CYTED project that deals with this adsorbent Dubinin–Radushkevich model has been used instead of the[43]. Dubinin–Astakhov model. The Dubinin–Astakhov model

The morphology of the sample was observed by SEM(scanning electron microscopy) and can be seen inFig. 5.

Two images were recorded and shown that an average‘crystal’ size is difficult to specify for the case wheremicropore controls the diffusion process, so the parameter

2D /r will be reported. Also the shape is not very wellc c

defined, reason why we will use the sphere model formicropore diffusion, as a first approximation. InTable 3we present the physical properties of the adsorbent.

T able 3Physical properties of CMS Takeda 4A

3Particle density,r (kg/m ) 900p

Pellet porosity,́ (–) 0.315p

Average macropore diameter (mm) 0.303 24Macropore volume (m /kg) 3.1310

24Micropore volume by CO adsorption 1.73102 Fig. 7. Adsorption equilibrium of propylene at 343, 373 and 4233(m /kg)K on CMS 4A Takeda. Solid lines are the Toth model and dotted23Extrudate radius,R (m) 1.1310p lines the Dubinin–Radushkevich model.

C.A. Grande et al. / Carbon 41 (2003) 2533–2545 2539

T able 4Propane and propylene adsorption equilibrium parameters

Sorbate q (mol /kg) E (kJ /mol) d (–)m o

Dubinin–RadushkevichC H 1.367 18.23 23 8

C H 1.669 21.23 23 6

oSorbate q (mol /kg) K (mol /kg.kPa) DH (kJ /mol) n (–)m eq

Toth22C H 1.757 1.81310 11.46 0.3563 822C H 1.927 1.32310 14.35 0.3253 6

T able 5does not fit the data correctly always giving steepestPropane diffusion parameters obtained by ZLC

isotherms. This is another indication of a wide micropore2Temp. Flow-rate K (–) K (–) D /Rsize distribution, like in activated carbons. The Toth c c

3 21(K) (m /s) integration (s )model, although having four parameters to fit, describes27 25the data with higher accuracy, particularly in the low- 343 5.02310 67.2 269.8 2.031027 25pressure range, which is fundamental for binary adsorption 373 5.02310 59.9 155.2 6.031027 24423 5.07310 58.6 85.5 1.9310equilibrium predictions[44].

6 . Zero length column technique

Zero length column (ZLC) experiments were performedat the same temperatures of equilibrium measurements(343, 373 and 423 K). The equilibration period was at least1 h. All the runs were duplicated. The experiments forpropane desorption are reported inFig. 8. A flow around

27 35310 m /s was used (see details inTable 5). A veryweak dependence with temperature was observed.

The dead volumes of the equipment were highly mini-mized and the adsorption rate was not extremely fast, sothe adsorption step previous to desorption was also mea-sured. As an example, inFig. 9 we present the adsorption/desorption steps at 343 K, both in normal scale (Fig. 9a) aswell as in semi-logarithmic scale using the transformation

Fig. 8. Zero length column (ZLC) desorption curves of propane in27 3CMS 4A using 5310 m /s of helium as purge at 343, 373 and Fig. 9. Comparison between adsorption and desorption curves of

423 K. Solid lines are the complete solution of Eq. (3) using 150 propane in CMS 4A at 343 K obtained by ZLC. (a) Normal scale.terms. (b) Semi-log scale.

2540 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

of 12C /C for the adsorption curve (Fig. 9b). The error in this case we have variable-sized micropores in a dis-o

the adsorption curve in the final tail of the curve is higher tribution of crystals of non-uniform shape, a problem thatthan in the desorption step due to the lower sensitivity of will require much information concerning the structure ofthe FID detector at higher concentrations. The equilibrium the pellet. For this reason a simplification was adopted.and kinetic parameters for the fitting of both curves were If we look atFig. 8 trying to define a slope and interceptthe same. As both curves are symmetrical, we can con- needed for the long time response approach[35], we seeclude that we are working in the linear zone of the that the slope is very difficult to establish. This was alsoisotherm. At the three temperatures the amounts adsorbed reported in non-uniform crystal structure adsorbents[47].in adsorption and desorption steps (obtained by integration For this case, we use the complete solution of Eq. (3)of the curve) was the same although only poor agreement instead of the long time response solution.is obtained with the manometric data. These large differ- The values of the equilibrium constants and the crystalences are due to an incomplete integration (the area below diffusivities for propane are presented inTable 5. TheC /C that is not accounted for in some cases should even long-term behavior is reached for very large values ofo

be higher than the integrated area). In all the cases the time. Only using a minimum of 10 terms in the series thedifferences are higher at lower temperatures. higher-term values of the summation can be neglected. In

The effect of partial activation[35] is shown inFig. 10 this work we used at least 100 terms to fit the data.for desorption curves at 343 K. If the saturation step is The micropore model has an exponential dependence

operformed for only 250 s (equilibrium in the gas phase was with temperature in the formD 5D exp(2E /RT ) wherec c aoapparently reached), the desorption curve has almost theD is the limiting diffusivity at high temperatures andE isc a

same final slope but the amount adsorbed is clearly not the the activation energy. From the experiments for propanesame giving an underestimate value of the equilibrium diffusion reported inTable 5the activation energy of 33.7constant. kJ /mol has been calculated which is higher than the value

As the kinetic diameter of propane is very close to the of 29 kJ/mol reported for CMS 5A[9]. This indicates that˚nominal value of the adsorbent (higher than 3.8 A, which even with a wide micropore distribution, the smaller

seems to be the demarcation limit between propane and micropores impose a higher resistance controlling thepropylene molecules[45]), micropore resistance was as- diffusion step.sumed to control the diffusion process. Propylene desorption analysis were performed with a

27 3A spherical shape was assumed for micropores as a first flow-rate of helium of 4.5–5.2310 m /s (see details insimplification for data interpretation. We also have to keep Table 6) and the results are shown inFig. 11.To confirmin mind that whatever the shape we choose to describe the the absence of external resistances another set of experi-crystal structure, we are making a gross oversimplification ments were performed using a higher flow rate between 6.2

27 3by saying that the radius is uniform in all the structure and 6.8310 m /s (seeFig. 12). The final slopes in awhen it really has large variations as can be seen inFig. 5. semi-logarithmic plot are coincident supporting the as-Only few studies in the literature deal with ZLC experi- sumption of no film transfer resistances. These experi-

23ments with samples with a crystal distribution[46,47]. If a ments were performed using extrudates ofR 51.1310p23distribution of crystals and/or micropores is present and m andL55.10 m that can be considered as infinite

not considered, the ZLC measured diffusivity will repre- cylinders for macropore diffusion[48].sent only the larger crystals with a higher value ofr . In In previous reports of propylene diffusion in CMSc

Takeda 5A, the micropore resistance controls the diffusionprocess[9]. No data were found for the diffusivity of

propylene on CMS 4A and in general data with propylene

T able 6Propylene diffusion parameters obtained by ZLC

2Temp. Flow rate K (–) D /Rc c3 21(K) (m /s) (s )

27 24Large 343 4.63310 708.6 1.231027 24extrudates 373 4.85310 497.5 2.031027 24423 5.30310 196.6 9.531027 24343 6.33310 593.0 1.431027 24373 6.88310 402.4 2.831027 24423 6.75310 155.6 9.731027 24Small 343 6.33310 572.4 1.431027 24extrudates 373 6.88310 468.3 2.8310

Fig. 10. Partial activation effect in ZLC desorption curves of 27 23423 6.75310 133.3 1.131027 3propane at 343 K.Q 55310 m /s.He

C.A. Grande et al. / Carbon 41 (2003) 2533–2545 2541

Fig. 11. ZLC desorption curves of propylene in CMS 4A Takeda Fig. 13. ZLC desorption curves of propylene in CMS 4A Takedaat 343, 373, 423 and 448 K measured in the ‘large extrudates’. at 343, 373 and 423 measured in the ‘small extrudates’. The

27 3 27 3The helium flow rate used was around 4.5310 m /s (seeTable helium flow rate used was around 6.67310 m /s (seeTable 6).6).

roots of Eq. (3) are different, a different value of apparenton CMS was found only for the case of wider micropores diffusivity should be obtained). If diffusion in micropores[12] and for the case of membrane permeation[49]. Of is the controlling step, no difference should be observed incourse if the controlling step is diffusion in the micropores the curves (within the accuracy of the measurements).of CMS 5A, we should expect the same tendency in this Desorption curves obtained with these ‘small extrudates’adsorbent. are shown inFig. 13. The flow-rate used was also 6.2–

27 3As the pellets are extrudates we could not vary the pellet 6.8310 m /s, a flow-rate where no film mass transferradius because is constant in all of them. In order to was observed in the larger extrudates. The slope of theconfirm the micropore control, experiments with almost desorption curves is similar indicating that no variationthe same mass of adsorbent but with cylinders of different occurs when we change the external geometry of the pellet,

23 23length (2.3310 m) and the same radius (R 51.1310p confirming the micropore control of the propylene diffu-m) were performed. A reasonable assumption to analyze sion in this CMS sample.the data is to perform all the calculations assuming the The equilibrium constant and the micropore diffusivityshape of the adsorbent as spheres. In these ‘small extru-parameters for propylene diffusion in CMS 4A obtained indates’ a sphere of equivalent volume can describe the all the experiments are shown inTable 6.geometry to perform the calculations. If the control step is From the experiments reported inTable 6the activationin the macropores, some differences in the slope will be energy of 30.8 kJ/mol has been calculated which is a littleobserved (in fact to keep the same pore diffusivity, as the higher than the 29 kJ/mol reported for CMS 5A[9], but is

clearly within the error of the measurements. In the case ofCMS 5A no distinction between propane and propylene

were noticed in the energy of activation, but in this case,with narrow micropores, some difference was detected(propane has more difficulty to penetrate the narrowermicropores).

7 . Breakthrough curve measurements

The manometric–chromatographic equipment is apowerful method to determine pure component and binaryadsorption equilibrium. In this equipment there is acompromise between the pressure range and the pressureaccuracy in the low-pressure range. The Henry constant isobtained asH 5 q /P. In the measurement of the pressurewe have an error of 0.5 kPa, which in measurements ofFig. 12. ZLC desorption curves of propylene in CMS 4A Takedapressures around 2 kPa translates an error of 75% in theat 343, 373 and 423 measured in the ‘large extrudates’. The

27 3helium flow rate used was around 6.67310 m /s (seeTable 6). estimation of the Henry constant. To avoid a poor extrapo-

2542 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

lation of the Henry constant from the manometric data,breakthrough curves were measured using a 1% con-centration of hydrocarbon, which can be considered in thelinear zone of the isotherm and gives a reliable value of theHenry constant needed to predict the binary equilibriumwith confidence[44].

After obtaining the experimental data, the first thing todo is to calculate the stoichiometric time to compare withthe capacity obtained by the dynamic method with themanometric one (even knowing that large differences may

]occur). The calculation of the stoichiometric time,t, hasmade by[37]:

`

12´L Cc]] ]] ]t 5 11 H 5E 12 dt (20)F S D G S Du ´ Ci c o

0 Fig. 14. Propane breakthrough curves at 343, 373 and 423 K.Solid lines represent the bidisperse model of Eqs. (5)–(19).whereV is the volume of the column,u is the interstitiali

gas velocity,H is the Henry constant and́ is the porosityc To calculate the film mass transfer coefficient, theof the column. Note that we have used the linear isotherm correlation proposed by Wakao and Funazkri has been usedexpression for the calculation of the stoichiometric time, [37]:due to the very low pressure of hydrocarbon used. The

1 / 3 0.6comparison between the Henry constant obtained from the Sh5 2.011.1Sc Re (22)breakthrough curve (stoichiometric time) and the man-

with the dimensionless numbers, defined by:ometric value is performed inTable 7 for propane andpropylene. Note that in the manometric constant there is

r nd m 2R kgas p gas p fnot a specific value but a range of values, which includes ]] ]] ]]Re5 Sc5 Sh5 (23)m r D Dgas gas mthe error associated with each measurement. In the case of

propylene, all the values determined from the breakthroughAlthough the ZLC experiments indicate a micropore-curves are inside the range determined in the manometric

controlled diffusion a general model, including macropore,equipment. In the case of propane the difference betweenmicropore and film resistances was developed and tested inthe two Henry values increase with the temperature. This isthis system. This model was selected because in the searchbecause the first manometric measurements at 373 and 423of a proper adsorbent for the propane/propylene sepa-K were only at 6 and 8 kPa, a point out of the linear zoneration, some adsorbents studied have macropore resis-of equilibrium with a small slope than the Henry constant.tances [28,50] while others, like this adsorbent haveOnce the equilibrium has been verified and calculatedmicropore control. In order to fill the parameters of thefrom dynamic experiments, the kinetic parameters de-bidisperse model, a pore diffusivity has to be given. To dotermined by ZLC will be compared with those needed to fitthis, we assume a tortuosity factor of 6 and the porethe breakthrough curves. In order to use the bidispersediffusivity D has been calculated as a function of thepmodel described in Eqs. (9)–(23), we need to calculate theKnudsen (D ) and molecular (D ) diffusion coefficients:k maxial dispersion coefficient and the film mass transfer

resistance. The axial diffusion coefficient has been calcu- 1 1 1] ] ]5t 1 (24)lated by[37]: S DpD D Dp m k

D 5 0.451 0.55́ D 1g 2R v (21)s dax c m 2 pThe experimental breakthrough curves measured are

where g is constant with value of 0.5 andD is the shown inFigs. 14 and 15for propane and propylene,2 m

molecular diffusion coefficient. respectively. The experimental conditions of measurement

T able 7Henry constant comparison between manometric and dynamic (breakthrough) methods

]Temp. t(s) H (mol /kg?kPa) C H H (mol /kg?kPa) C H3 8 3 6

(K) [C H ]–[C H ]3 8 3 6 Dynamic Manometric Dynamic Manometric

343 5478.3–12716.6 0.277 0.16–0.27 0.643 0.77–0.40373 3337.2–7750.3 0.167 0.10–0.14 0.392 0.47–0.23423 1622.0–2687.1 0.082 0.03–0.04 0.136 0.15–0.11

C.A. Grande et al. / Carbon 41 (2003) 2533–2545 2543

30 kJ/mol for propane and propylene were calculated andfrom dynamic experiments values of 23–16 kJ/mol.Clearly the ZLC experiments are indicating a majordifficulty of the molecules to adsorb and also the differ-ence between the gases is smaller than the values calcu-lated from breakthrough curves. With those considerations,we can consider that the diffusivity values obtained fromthe breakthrough curves are more representative and willbe used in further experiments with this adsorbent.

Using the Dubinin–Raduschkevich fitting of the equilib-rium data, the isosteric heat of adsorption for both hydro-carbons was calculated with the Clausius–Clapeyron equa-tion obtaining a heat of adsorption that depends on theamount adsorbed. This dependence is a decreasing func-tion, which ranges from almost 40 to 10 kJ/mol in the case

Fig. 15. Propylene breakthrough curves at 343, 373 and 423 K. of propylene and from 35 to 10 kJ/mol for propane. Also,Solid lines represent the bidisperse model of Eqs. (5)–(19). from the Henry constant determined by the dynamic

method (breakthrough curves) via a Van’t Hoff relation wedetermined the isosteric heat of adsorption at zero cover-

of these curves are detailed inTable 1. The solid lines age. The values obtained from these experiments are 18.4represent the fit with the bidisperse model. and 23.7 kJ/mol for propane and propylene, respectively.

The crystal diffusivity parameters used for the fitting of The values obtained from the dynamic experiments areboth gases are listed inTable 8.In all the cases we have much smaller than the reported values on CMS 5A[9],verified that the mass transfer coefficient calculated from which can be comparable only with the initial values,Eq. (22) is too large and we can consider that film mass determined by the Clausius–Clapeyron equation using thetransfer resistance is negligible. Also, the macropore Dubinin–Radushkevich model.diffusion was changed (simulating a tortuosity factor up to12) and no variations were observed. So we confirm thatthe control of the diffusion mechanism is really in the 8 . Conclusionsmicropores for both gases.

Note that the diffusivity parameters obtained from the Propane and propylene adsorption equilibrium andZLC and the dynamic methods have large deviation kinetics onto a carbon molecular sieve Takeda 4A has beenbetween them, i.e., a factor of 2–4 for propane and 15–50 investigated using manometric, ZLC and chromatographicfor propylene. As we marked in the adsorbent characteriza- techniques. The selectivity of the material towards pro-tion, the adsorbent has a distribution of ‘crystal’ sizes pylene at low pressures is around 2 and decreases at higherwhich is better detected in the breakthrough curves than in pressures. Micropore diffusion controls the adsorptionthe ZLC experiments, where the largest particles are kinetics of both hydrocarbons. Amounts adsorbed at veryresponsible for the final response of the desorption curves. low pressures from manometric and dynamic experimentsTo that, we have to add the micropore size distribution, are coincident allowing a correct estimation of the Henryalready mentioned in the equilibrium section and that in law constant of both gases. The micropore diffusivitythis case of molecular sieving may affect more one of the coefficients determined by zero length column techniquegases, in this case propylene. This distribution can be and the ones determined from the breakthrough model arereflected in the calculation of the activation energy of clearly not coincident and this fact can be explained by thediffusion. From the ZLC experiments, values from 33 to non-uniform size of the micropore structure. Diffusion

parameters of propane and propylene determined byT able 8 breakthrough curves have a difference of two orders ofDiffusion parameters and energy of activation determined from

magnitude. Looking at the equilibrium and kinetic databreakthrough curvespresented in this paper, we can see that this adsorbent can

2 21Gas Temp. D /r (s ) Ec c a be used in a pressure swing adsorption unit with a kinetic(K) (kJ/mol) separation scheme and not equilibrium one.

25C H 343 8.4310 23.393 824373 2.231024423 4.0310 A cknowledgements23C H 343 6.0310 16.573 622373 1.1310 The authors would like to thank financial support from22423 1.6310 Foundation for Science and Technology (FCT) by project

2544 C.A. Grande et al. / Carbon 41 (2003) 2533–2545

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