Reprinted from

Adsorption Science & Technology2005 Volume 23 Number 10

Multi-Science Publishing Co. Ltd.5 Wates Way, Brentwood, Essex CM15 9TB, United Kingdom

Modelling of Ethane/Ethylene Separation Using

Microporous Carbon

Susana Curbelo and Erich A. Müller

AST 23-10_70 2/5/06 1:37 pm Page 1

855

*Author to whom all correspondence should be addressed. E-mail: e.muller@imperial.ac.uk.

Invited Contribution

Modelling of Ethane/Ethylene Separation Using Microporous Carbon

Susana Curbelo2 and Erich A. Müller1* (1) Department of Chemical Engineering, Imperial College, London

SW7 2AZ, UK. (2) Departamento de Termodinámica y Fenómenos de Transferencia, Universidad Simón Bolívar, Caracas

1080, Venezuela.

(Received 24 August 2005; revised form accepted 30 September 2005)

ABSTRACT: Grand Canonical Monte Carlo simulations of the adsorption of amixture of ethane and ethylene on microporous slit graphite pores are reported.A two-centre Lennard-Jones with point quadrupole potential and a Steele poten-tial with embedded quadrupoles for the carbon were used to model the fluids andsolids, respectively. Under conditions of moderate temperature (260–400 K) andpressure (0.1–1.0 MPa), ethane was preferentially adsorbed over ethylene for thepore widths studied. For micropores less than 2 nm wide, the selectivity towardsethane varied markedly with small changes in the pore structure, whilst for themesopores with widths greater than 2 nm the selectivity was remarkably insen-sitive towards the pore size. The results provide qualitative guidelines for thesynthesis and design of carbons for lower olefin/paraffin separations.

INTRODUCTION

The purification of olefins (unsaturated light hydrocarbons) is essential to their use as precursorsfor the production of polymers. The alkene/alkane (olefin/paraffin) separation between hydro-carbons of the same carbon number is conventionally performed using low-temperature distillation,a difficult process in this case due to the very close boiling points of the components involved. A less energy-intensive option towards obtaining high purity ethylene (and higher alkenes) maywell be an adsorption process.

Alternatives have been sought which exploit chemical complexation (π-complexation), i.e. theformation of reasonably strong bonding between unsaturated bonds in the olefins and cations (e.g. Ni or Cu or Ag salts) grafted onto suitable adsorbents (Yang and Kikkinides 1995). Since thesaturated hydrocarbons will not interact electrostatically with cations, the difference in molecularinteractions promotes extraordinarily high selectivities in the separation processes. In a relatedmanner, recent developments (Nymeijer et al. 2004) point towards the use of polymer membranesin conjunction with liquid–gas adsorption using silver nitrate solutions for olefin/paraffin separa-tions. Whilst the selectivity towards olefins is marked in these processes, the resulting processesare focused on the removal of the olefin from a gaseous stream. In some cases, for example in thestream conditioning prior to a polymerization reactor, although the olefin is a major component ofthe process stream it is the paraffin (which is present in very small quantities) which is of interestin separating. On the other hand, although separation processes based on π-complexation are

AST 23(10)-70-P4 2/5/06 1:07 pm Page 855

fairly selective towards the adsorption of the olefin, it may become energetically prohibitive toregenerate the adsorbents, particularly when such strong interactions are present.

Separations based on the size difference between the molecules, such as carbon sieves, zeolitesor membranes (Ismail and David 2001; Semenova 2004) seem promising, due to the low energycosts of the separation and the high volumes which may be processed. However, the tiny differ-ence between the effective radii of the molecules makes the design of the sieves or membraneschallenging.

It is not yet clear if activated microporous carbons may be used effectively to separate olefin/paraffin mixtures. The adsorption of ethane (Cracknell and Nicholson 1994; Klochko et al. 1999;Do and Do 2004b) and ethylene (Do and Do 2004a) onto activated carbon has been separatelystudied using methods similar to those described here. However, only a recent paper by Do andDo (2005) addresses the competing ethylene/ethane adsorption. The regions of cooperative andcompetitive adsorption are studied, mostly in the sub-monolayer regime. Although the methodologyis similar, the work presented here complements the latter, spanning different temperature andpressure ranges and utilizing slightly different solid and fluid potential functions.

It is an open question as to whether there is a given carbon pore configuration that allows selectiveadsorption towards the paraffin. In general, the olefin is smaller in size (making it easier to entera given micropore) and apparently has a greater affinity towards the carbon surface, particularlyif the carbon is chemically activated and the surface presents polar groups. So, intuitively, onewould expect activated carbons to be selective towards the olefin. The present study attempts toanswer, in a preliminary way, if such a geometry and/or a condition exists which allows paraffinadsorption to be enhanced. The molecular simulations reported here describe in a systematic waythe effects of the variables thought to be important in the physical picture, such as the average porewidth, the mixture composition, the adsorption temperature and the overall pressure.

MOLECULAR MODEL

Recently, Do and Do (2004b) showed how an accurate representation of the VLE properties of eth-ylene by means of a suitable potential model was a pre-requisite for the accurate description ofadsorption onto carbon slit pores. Weitz and Potoff (2005) have optimized parameters for a two-centre Lennard-Jones (LJ) united atom (UA) model of ethylene and compared the results withsome available force fields. Their results indicate that an improvement of the phase behaviour ofthe pure substance is obtained by including point charges to model the quadrupole moment explicitly.

The simulation of point charges in anisotropic and confined volumes is not a simple task since therecourse of truncating the potential and neglecting the long-range interactions may lead to significanterrors. However, for the type of molecules involved, the duality and proximity of the equivalentpoint charges needed to model the charge distribution may be suitably taken into account by meansof a point quadrupole moment (Gray and Gubbins 1984). Point quadrupole moments have anadded advantage in that the potential decays very rapidly with distance so that long-range correc-tions are usually not required.

The fluid intermolecular potential used here is a UA model in which each molecule is modelledas two identical Lennard-Jones spherical sites a distance L apart. An axial point quadrupole momentof strength Q is embedded in the geometrical centre of the molecule. This potential, referred to asthe 2CLJQ model, has been systematically studied by Vrabec et al. (2001) who presented a comprehensive parameter table for simple molecules of industrial interest. The 2CLJQ model is a

856 Susana Curbelo and Erich A. Müller/Adsorption Science & Technology Vol. 23 No. 10 2005

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reasonable compromise between a detailed atomistic description and the simplest possible modelinvolving a single isotropic site. The 2CLJQ potential takes into explicit account the elongatedshape of the molecule and explicitly segregates the multipolar interactions without the need to usepoint charges, which would be difficult to implement in simulations of nano-confined fluids.Performed properly, this explicit account of multipolar forces improves the prediction of mixtureproperties performed using only pure component parameters (Gross 2005).

The fluid–fluid intermolecular potential is described as the sum of the LJ (φLJfluid) and thequadrupolar (φQ–Q) interactions (Gray and Gubbins 1984):

(1)

(2)

where i and j refer to the LJ sites on the molecules, rab refers to the centre–centre distance amongstmolecules where rij is the distance between the centres of molecules i and j, ci = cos θi, cj = cos θj,and c = cos θi cos θj + sin θi sin θj cos φij, where θi and θj are the polar angles of the molecularaxis with respect to a line joining the molecular centres, φij is the difference in the azimuthal anglesand ε0 is the vacuum permittivity (8.85419 × 10−12 C2/(Nm2)).

The parameter values suggested by Vrabec et al. (2001) of σ = 0.34896 nm, ε/k = 136.99 K, L = 0.23762 nm and Q = 0.8277 B have been used for ethane and of σ = 0.37607 nm, ε/k = 76.95 K,L = 0.12695 nm and Q = 4.331 B for ethylene. These parameter values seem to be out of line withsome physical details such as the carbon–carbon bond lengths which are 0.153 nm and 0.133 nmfor ethane and ethylene, respectively. However, it must be borne in mind that L does not representan actual bond length but is rather a fitted parameter. The fact that the trend is correct, e.g. theethane molecule is more elongated than the ethylene molecule and that the dispersion interactions(estimated by the well depth of the LJ potential, ε) are larger for the UA CH3 group found inethane than those corresponding to the UA CH2 group found in ethylene, seems to indicate thatthe parameter set used is internally consistent. On the other hand, the application of the 2CLJQmodel for ethylene involves certain compromises. An inconsistency is readily apparent: the actualmolecule is not axially symmetric but rather planar in nature. This, in turn, induces a non-trivialcharge separation. If one defines an x–y plane which contains the centre of all atoms and a z axisnormal to that plane, the quadrupole moment tensor (Dagg et al. 1982) measured by collision-induced adsorption may be expressed via its three principal components, i.e. Qxx = −3.25 B, Qyy = 1.62 B and Qzz = 1.62 B. If one accepts the definition of an “effective” quadrupole momentas Q2 = 2/3(Q2

xx + Q2yy + Q2

zz), the result (3.25 B) is comparable with the value used in the para-meterization and with literature values (Reed and Gubbins 1973) of a high-temperature angle-average quadrupole (3.9 B). One must take into consideration that this parameterization is aneffective angle-averaging of the actual intermolecular interactions. This angle-averaging hasproved to be very effective in modelling VLE and even LLE (Müller and Gelb 2003). However,care should be taken when interpreting structural properties, especially in the case of ethylenewhere important deviations exist between the model and the actual molecular details.

φπεQ Q

abi j i j i j

Q

rc c c c c c c− = − +( ) − + −( )[ ]3

4 41 5 15 2 5

2

05

2 2 2 2 2

( )

φ εσ σ

LJfluid ijij

ij

ij

ijjir r

=

−

==

∑∑ 4

12 6

1

2

1

2

Modelling of Ethane/Ethylene Separation Using Microporous Carbon 857

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The 2CLJQ potential has been successfully tested (Carrero-Mantilla and Llano-Restrepo 2003) inbulk ethane/ethylene mixtures, showing an excellent prediction of experimental VLE data withoutthe need for binary interaction parameters, thereby suggesting that the model adequately separatesand treats the most important contributions to the intermolecular potentials. Stoll (2004) has suggested an improved fit of VLE data using a cross-parameter of amongst theethane (ii) and ethylene (jj) LJ energy parameters. Recently, Gross (2005) has derived an equationof state for this model with impressive quantitative results.

The solid phase is modelled as a single slit-like pore having two infinite structure-less parallelwalls in the x–y plane separated by a distance H in the z direction. Each of the two walls is takento be the basal plane of a graphite-like surface made up of LJ atoms of diameter σss. Thus, on each plane, the atoms are organized in a hexagonal array with a solid volumetric density of ρss. The LJ potential between one spherical segment of the fluid molecule and each of the moleculesof the solid is integrated over the lateral solid structure. By summing over the planes of moleculesin the surface separated by a distance ∆, the 10–4–3 potential, φLJsolid, is obtained (Steele 1974):

(3)

where the crossed solid–fluid interaction parameters (εsf, σsf) are calculated according to theLorentz –Berthelot rules: σsf = (σss + σff)/2, εsf = (εssεff)

1/2, where the subscript s refers to the solidwhile f refers to the fluid parameters. For a graphite surface (Steele 1974): ρss = 114 nm−3, ∆ = 0.335 nm, εss/k = 28.0 K and σss = 0.340 nm. In this context, H (the pore width) is defined asthe distance separating the planes on each side of the pore, through the centres of the LJ atoms ofthe outermost layer of one wall and the corresponding plane of the opposite wall. Experimentallydetermined pore widths will be smaller, i.e. roughly 0.3–0.38 nm smaller, as a result of subtractingthe effective radius of the carbon atoms at each surface.

It is usually accepted that the electrostatic terms at the graphitic surface are negligible comparedto the van der Waals repulsion–dispersion terms, which are accounted for in the above discussion.However, this may not be so in the case of polar and/or quadrupolar molecules adsorbing onto carbons. It is plausible to assume that the aromatic charge displacement — produced by the fact thatthe carbon atoms in graphite have only three covalent bonds — is somehow similar to those foundin planar aromatic molecules such as benzene, naphthalene and anthracene. Following the suggestionof Vernov and Steele (1992), if the quadrupole moment perpendicular to the molecular plane iscalculated on a per atom basis, a nearly constant value of −1.3 ± 0.2 B is obtained. This suggeststhat explicit accounting of these interactions must be made when strongly polar or quadrupolarmolecules are considered. We have included a quadrupole moment perpendicular to the surfacelocated in the centre of each carbon atom. Although the wall potential [equation (3)] is structure-less,the structure of graphitic carbon is well known and a matrix of quadrupoles may be superimposed.In this study, we have used the experimental value reported by Whitehouse and Buckingham (1993),i.e. Q = −0.91 ± 0.03 B.

In summary, for a given slit pore of width H, the external potential experienced by any moleculein the fluid at z is calculated as the superposition for the two walls [equation (3)] and the sum overall quadrupolar interactions [equation (2)]. We have performed extensive simulations to evaluate theeffect of the addition (or not) of a quadrupole moment to the surface of the carbon. For the particularsystem and conditions studied, we have found that its inclusion had a negligible effect. This is notso in all cases (Müller 2005).

φ πρ ε σσ σ σ

LJsolid ss sf sfsf sf sfz

z z z( ) ( )

( . )=

−

−+

22

5 3 0 612

10 4 4

3∆∆ ∆

ε ε εij ii jj= 1 037.

858 Susana Curbelo and Erich A. Müller/Adsorption Science & Technology Vol. 23 No. 10 2005

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SIMULATION DETAILS

We have used Grand Canonical Monte Carlo simulations (GCMC), as detailed in standard references(Nicholson and Parsonage 1982; Allen and Tildesley 1987; Frenkel and Smit 2002), to obtain theproperties of the inhomogeneous system. In GCMC, the temperature, T, the volume of the pore,V, and the chemical potential of each species, µl, are kept fixed. The number of molecules in thepore is allowed to vary and its average is the relevant quantity of interest. In our simulations, wehave replaced the chemical potential by the more convenient variable: activity, ζi, defined as:

(4)

where Λi is the de Broglie wavelength, which includes contributions from translational and rotationaldegrees of freedom, and k is Boltzmann’s constant. Based on the assumption that the virial equationof state, truncated after the second virial coefficient, is sufficient to describe the pressure–volume–temperature relation for the bulk gas accurately, the pressure may be related to the activity as:

(5)

where B, the second virial coefficient, is available (Daubert and Danner 1994) as a function of temperature for the pure components studied here. For mixtures, an ideal solution is assumed (i.e. the total pressure is the sum of the partial pressures).

The GCMC simulations performed here require three types of moves to be performed randomlyon the system: (i) internal displacement or rotational moves on particles which are already in the confined volume; (ii) moves to attempt to insert molecules within the confined space; and (iii) moves to attempt to delete molecules within the confined space. Each of these moves is attemptedwith a fixed probability, whose ratio in our particular case is equal, i.e. 1:1:1. In the case of binarymixtures, once a type of move has been selected, a random choice of species is made to determineon which particular particle to operate. A new configuration is accepted if exp(−β∆H) > ran, where ran is a random number in the interval [0,1], β = 1/kT and ∆H depends on the type of move.For displacement/rotational moves, ∆H is equal to the difference in configurational energy of thesystem, ∆U; for an insertion attempt it corresponds to:

(6)

and for deletion attempts to:

(7)

where N is the total number of particles present in the confined space. In the case of multi-componentsystems, both the activities, number of particles and pressures referred to in the above equationscorrespond to the values for the particular species.

Potentials were cut off at 2 nm and no long-range corrections were included. Simulations wereperformed in pores with at least 98 nm2 surfaces that typically hold up to a few hundred particlesdepending on the pore width and conditions. The results for larger system sizes showed no system-size dependence. The systems were started up with an empty pore and filled up until an

βζ

β∆ ∆HV

NU=

+ln

βζ

β∆ ∆HN

VU=

+

+ln1

P RT Bi i i i= −ζ ζ( )1

ζµ

ii

i

kT=

exp( / )

Λ3

Modelling of Ethane/Ethylene Separation Using Microporous Carbon 859

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equilibrium condition was attained. Block averages were made after every 100 000 configura-tions. Systems were left to equilibrate for at least 10 million configurations and averages weretaken about the latter 30 million configurations for each run.

RESULTS

Pure component adsorption curves are shown in Figure 1 for a pore of width H = 1 nm at 293.15 K.At low pressures, it is seen that the adsorption of ethane is larger (in terms of µmol/m2) than theadsorption of pure ethylene at the same activity (which is related to the partial pressure). This canbe rationalized by recognizing that since the van der Waals dispersion forces of the ethane mole-cule are larger, its adsorption is enhanced. As the activity (pressure) was increased, both curvesmerge and eventually cross over. At higher pressures, close to the pore filling, it is seen that thepores exhibit a greater capacity towards ethylene.

The general tendencies and the cross-over behaviour of the adsorption curves seen here werealso present in experimental data for ethane/ethylene mixture on activated carbons (Choi et al.2003) and in some older low-pressure data by Kaul (1987) on Kureha beads. However, no directcomparison is possible since no quantitative information was given on the actual pore-size distri-bution of the carbons reported by Choi et al. (although it was mentioned that this was close to themolecular diameter of the adsorbate). In any case, the experimental results show that the crossover of the adsorption curves was achieved at a significantly lower total pressure. It is plausiblethat the carbon used in the afore-mentioned experiments was activated and thus might have possessed polar groups within the pores. The presence of these activated groups would haveenhanced the attraction of the ethylene molecule (due to electrostatic effects), making its adsorptionisotherm closer to that of ethane.

860 Susana Curbelo and Erich A. Müller/Adsorption Science & Technology Vol. 23 No. 10 2005

1

2

3

4

5

6

7

0.001 0.01 0.1 1 10

N (

µmol

/m2 )

ζ (nm−3)

100 kPa 1 MPa

Figure 1. Adsorption of pure substances at 293.15 K for a pore of width H = 1 nm as a function of the activity of the pure gas, ζ. The symbols represent simulation data for ethane (squares) and ethylene (circles). Uncertainties in the data arereflected in the sizes of the symbols. The approximate activities for pressures of 100 kPa and 1 MPa are shown by therespective vertical arrows.

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This effect is compatible with the simulation results shown, which should be understood in thecontext of an idealized limiting scenario. Additionally, the pore-size distribution will have aneffect on the measured isotherms. It must be stressed that no effort was made to adjust the poten-tial parameters in these cases (or to any other experimental sample). Experiments on preciselycharacterized substrates and carbons with narrow pore-size distributions would be necessary toallow a fit of the potential parameters.

We have chosen to study a mixture characteristic of a refinery feedstock, in which 90 mol% ethyl-ene was “contaminated” by 10 mol% ethane. In line with the objective of evaluating the separationprocess, we define the selectivity towards ethane, S, as the ratio of compositions of the binary mixture in the pore with respect to the bulk gas composition:

(8)

where xi refers to the mole fraction of i and 1 and 2 refer to ethane and ethylene, respectively. The variation of the selectivity with pore size is shown in Figure 2 for two total bulk pressures of100 kPa and 1 MPa at 293.15 K. At very small pore widths, i.e. below H = 0.8 nm, a sieving effectoccurs in which the ethylene molecules are excluded sterically from the pore due to their largerLJ diameter. However, this is contrary to what was expected since it would be anticipated that theCH2 group in ethylene would be smaller in size than the UA CH3 group. The Vrabec parameteri-zation shows otherwise and this may be interpreted as a spurious result from the parameter fitting.This particular high selectivity is possibly fictitious. A peak in the selectivity is seen at larger poresizes, with a maximum at ca. 1 nm. Away from the microporous region (H > 2 nm), the selectivityis insensitive to the pore size.

To detail the behaviour at a molecular level, we have plotted in Figure 3 the excess surfaceadsorption Γi of each individual species, corresponding to the adsorption on an individual basis,

. Here, A = 2LxLy is the available simulation cell wall area and is the ensembleNiΓi iN A= /

Sx x

x xpore

bulk

=( )1 2

1 2

/

( / )

Modelling of Ethane/Ethylene Separation Using Microporous Carbon 861

0

1

2

3

4

5

6

0.5 1.0 1.5 2.0 2.5

S

H (nm)

Figure 2. Variation in the selectivity towards ethylene, S, for a bulk ethane/ethylene gas mixture containing 10 mol%ethane as a function of the pore width, H, at 293.15 K. The filled squares correspond to a bulk pressure of 1 MPa whilethe open circles correspond to data for 100 kPa. The dotted curves merely provide a guide to the eye.

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average number of molecules adsorbed in the pore. Figure 3 is complemented with snapshots ofequilibrium configurations at some key conditions (Figure 4). There is clearly more detail in theselectivity curve at higher pressures (1 MPa), which probably arises from a significant increase insteric competition.

Two important competing effects are observed. The ethylene molecules have a smaller overalleffective size, thus they may fit into smaller size pores particularly when only a single monolayeris allowed. In this case, the ethane molecule is hindered both sterically and energetically and thereis a large selectivity towards the ethylene molecule. An example is seen in Figure 4(b). Even forslightly larger pores [Figure 4(c)] in which the ethane (if pure) would fill a monolayer, the highactivity of the ethylene (due to its overwhelming presence in the gas phase — 90%) allows a largeadsorption of ethylene.

Careful detailing allows one to recognize that at these pore widths one monolayer of ethylenefits “loosely” (and there is no space for two). Thus, space is left for a significant amount of ethaneto adsorb and competition for the pore surface is established. This happens for pore widths aroundH = 1 nm [Figure 4(d)]. This point, corresponding to the exact size of a single ethane monolayer,corresponds to the highest selectivity found in this study. The larger dispersion force of ethanewith respect to ethylene accounts for a stronger adsorption as it competes with the ethylene, disrupting the possibility of forming complete monolayers (increasing the entropy of the system).The higher Henry’s constant for ethane (evidenced by a larger zero-coverage slope of the pureisotherm at low pressures) confirms this point. It is in this range of pore sizes that the adsorptionof ethane is maximized with respect to ethylene. For wider pores, two layers of ethylene fit withinthe pore [cf. Figure 4(e) for H = 1.25 nm]. At this point, the energy decrease caused by the formationof a complete additional monolayer causes the ethane selectivity to be at its local minimum. For evenwider pores, the confinement effect — where the molecules can feel the additive attraction of bothwalls — gradually disappears. Thus, due to the relatively low vapour pressure of the gas, no capillarycondensation is expected. Furthermore, the decrease in effective attraction renders the monolayers

862 Susana Curbelo and Erich A. Müller/Adsorption Science & Technology Vol. 23 No. 10 2005

0

2

4

6

8

0.5 1.5 2.5 3.5

Γ (µ

mol

/m2 )

H (nm)

a

b

d

ef

g

c

Figure 3. Surface adsorption per unit area (Γi) for each individual species as a function of the pore width, H, for a bulkethane/ethylene gas mixture containing 10 mol% ethane at 1 MPa and 293.15 K. The circles correspond to ethyleneadsorption while the squares are for ethane adsorption. The letters correspond to the various stages depicted in Figure 4.The dotted curves merely provide a guide to the eye.

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to be more disperse. After ca. H > 2 nm, each wall is independent of each other. It is seen in Figure 3how the adsorption of ethylene actually decreases as the pore width increases from 2 nm to 2.5 nmor greater. From Figure 4(g), it will be seen that a break in the liquid-like film within the poreoccurs at this stage and no further pore-size dependence on the selectivity is detected.

This pattern is not independent of pressure or temperature. Higher pressures tend to favour theselective adsorption of ethylene, most likely through an enhancement of the entropic effects. On theother hand, higher temperatures tend to diminish the energetic differences amongst the moleculesand would thus be detrimental in the separation process. The typical effect of temperature onselectivity is seen in Figure 5, with a marked decline in selectivity as the temperature increases.

The effect of composition on the selectivity is not marked. Figure 6 shows a parity plot betweenthe bulk vapour and the composition of adsorbed ethane in a given ethane/ethylene mixture at a constant total bulk pressure. The regular shape of the curve suggests a rather constant separationfactor regardless of the composition. In all cases, the selectivity towards ethane is larger than unity.

Modelling of Ethane/Ethylene Separation Using Microporous Carbon 863

(a) (b)

(c) (d)

(e)

(g)

(f)

Figure 4. Snapshots of equilibrium configurations corresponding to the system described in Figure 3. The pore width, H,in each case corresponds to the following: (a) 0.7 nm; (b) 0.8 nm ; (c) 0.925 nm; (d) 1.0 nm; (e) 1.25 nm; (f) 1.6 nm; and(g) 2.6 nm. The red spheres depict ethylene molecules while the green spheres correspond to ethane. The sizes of the twotypes of molecules correspond to their LJ diameters.

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CONCLUSIONS

Under the conditions studied, we have shown from a theoretical point of view that there appearsto be a plausible way to separate ethane selectively from ethane/ethylene mixtures. Some of the datacorrespond to selectivities of the order of five or larger. Lower pressures and temperatures lead to an enhancement of the ethane selectivity. Pore widths in the microporous region near H = 1 nm(corresponding to actual pore widths of 0.65 nm) seem to be optimal for such separations. Underthese conditions, small variations in the pore width can lead to large changes in the measured performance. For larger pore widths in excess of 2 nm, the results seem insensitive to variationsin the pore width. Although the selectivity is not large, it should be sufficient however to be used inpressure swing adsorption experiments.

The results should be taken as general directives and not as design-quality results, since someof the assumptions in the model, viz. the effect of surface heterogeneities and the coarse grainingof the model fluid potentials, should be considered further. Separation arises not only as a result of

864 Susana Curbelo and Erich A. Müller/Adsorption Science & Technology Vol. 23 No. 10 2005

2

4

6

8

250 300 350 400

S

Temp. (K)

Figure 5. Effect of temperature on the selectivity of a pore of 1 nm width towards the ethane molecule for an ethane/ethylene gas mixture containing 10 mol% ethane at a bulk pressure of 1 MPa.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

xpore

xbulk

Figure 6. Mole fraction of ethane in the pore, xpore, as a function of the mole fraction of ethane in the bulk gas for a binaryethylene/ethane mixture at 293.15 K and a total pressure of 1 MPa, and for a pore of width H = 1 nm. The symbols depict simulation data while the dashed line provides a guide to the eye.

AST 23(10)-70-P4 2/5/06 1:07 pm Page 864

steric effects but also from differences in dispersion forces. Hence activation, i.e. the addition ofacid or basic groups to the graphite surface, could have a strong negative effect on the overall performance. Most substituents (oxygenated groups, metals, etc.) will have a strong affinity forthe electrons in the ethylene double bond and will contribute to the decrease of ethane selectivity,even possibly inverting it and thereby making the carbon pores more “olefinphilic”.

Such “chemical” activation commonly occurs for industrial-grade carbons. We speculate that“clean” surfaces, such as graphitized carbons, synthetic carbons, carbon fibres or carbon nano-tubes, might be appropriate candidates for the preferential adsorption of alkane molecules overalkene molecules.

ACKNOWLEDGEMENTS

Simulations were performed using the resources of the Laboratorio de Computación de AltoRendimiento (CAR) at USB.

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