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Ind. Eng. Chem. Res. 2001, 40, 1686-1693
SEPARATIONS Adsorption Equilibria and Kinetics of Propane and Propylene in Silica Gel Carlos A. Grande† and Alı´rio E. Rodrigues* Laboratory of Separation and Reaction Engineering (LSRE), Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal
Adsorption equilibrium isotherms for propane and propylene on narrow pore silica gel (NSG) and wide pore silica gel (WSG) were measured by gravimetry in the temperature range 303343 K and at pressures up to 101 kPa. The isotherms were correlated by the generalized Dubinin isotherm and Polanyi’s theory. Both adsorbents have a higher affinity for propylene. The loading at 100 kPa of propylene is 2 and 0.7 mmol/g on NSG and WSG, respectively. These loadings are 1.5 higher than those for propane with both adsorbents. The heat of adsorption estimated by the Clausius-Clapeyron equation decreases with the degree of coverage. Adsorption kinetics in the same temperature range was studied by the zero-length column method using the long time response. The diffusion of propane and propylene in both silicas is controlled by Knudsen diffusion. The pore diffusivities determined in the temperature range 303-343 K are 2.4 × 10-32.8 × 10-3 and 1.7 × 10-3-2.4 × 10-3 cm2/s for propane and propylene on NSG, respectively. For WSG these values are 6.4 × 10-3-9.9 × 10-3 cm2/s for propane and 6.6 × 10-3-12.1 × 10-3 cm2/s for propylene. Average tortuosity factors of 2.5 for NSG and 2.0 for WSG were obtained. 1. Introduction The propane-propylene separation is the most energyconsuming separation of the petrochemical industry. In the traditional separation, distillation, the separation factor is in the range 1.05-1.12. Adsorptive methods or hybrid adsorption-distillation methods1 should increase the separation factor, resulting in a less energydemanding process. For the modeling of adsorptive processes such as pressure swing adsorption (PSA) or vacuum swing adsorption (VSA), equilibrium and kinetic data are needed to solve the material and energy balances. Silica gel was tested as the adsorbent for the propanepropylene separation half a century ago.2 The equilibrium data reported suggest a separation factor of around 4 in the range of pressure and temperature studied (270-370 K and 0-1 atm). All pure-component isotherms have type I behavior and could be correlated by Polanyi’s theory of pore filling.3 Recent reports with silica gel with a surface area of over 600 m2/g show excellent agreement with the data of Lewis et al.1,4-6 Kinetic data indicate pore diffusivities 4 times lower than those in activated carbon7 and more than 1 order of magnitude less than those in zeolite 13X.8 The objective of this work is to report equilibrium and kinetic data of propane and propylene over two samples of silica gel: one with a high superficial area and a * To whom correspondence should be addressed: Phone: +351 22 508 1671. Fax: +351 22 508 1674. E-mail: arodrig@ fe.up.pt. † On leave from UNS-PLAPIQUI, Camino La Carrindanga Km. 7, Bahı´a Blanca 8000, Argentina.
narrow pore diameter (NSG) and the other with a low superficial area and wider pores (WSG). The temperature range studied was between 303 and 343 K. Equilibrium data are presented in the 0-100 kPa range performed by a gravimetric method, and kinetic data were obtained at atmospheric pressure via zerolength column (ZLC) equipment.9 Equilibrium data were analyzed in terms of the theory of volume filling of micropores (TVFM), namely, the Dubinin generalized isotherm model (or general model of the Dubinin-Astakhov equation) and Polanyi’s theory.10 The kinetic data were treated using the long time response (LTR) of the desorption curve of the ZLC experiences.11 2. Experimental Section: Materials and Methodology Adsorption equilibrium measurements were carried out in a closed system microbalance (CI, Robal, U.K.) connected to a large gas reservoir to ensure constant pressure in each step of adsorption. Approximately 100 mg of sample was used for each run. Before each experiment, the sample was outgassed until 100 Pa, and then the regeneration procedure began: heating to 423 K with a heating rate of 1 K/min and leaving at this temperature for a period of 12 h. The temperature is controlled with an electric oven with (1 K. Regeneration temperatures over 473 K may damage the sample. No weight variations were observed after this period. Isotherm measurements started by introducing gas until the desired equilibrium pressure; when no weight variations were recorded, more gas was entered into the system by incrementing the pressure. When atmos-
10.1021/ie000901g CCC: $20.00 © 2001 American Chemical Society Published on Web 03/13/2001
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1687 Table 1. Experimental Conditions for ZLC Runs adsorbent
NSG
WSG
cell height (cm) cell volume (cm3) pellet porosity, p pellet radius, Rp (cm) cell porosity, b
1.70 0.27 0.40 0.11-0.13a 0.73
1.70 0.27 0.58 0.19 0.68
a Variations are due to the noncompletely spherical shape of the particles.
Table 2. Physical Properties of Grace Davison NSG and WSG Pellets adsorbent
NSG
WSG
surface area (m2/g) average pore diameter (Å) average pellet porosity bulk density (g/cm3) particle density (g/cm3) solid density (g/cm3) water adsorption (wt %, 50% RH)
780 44 0.4 0.72 1.26 2.10 30
340 120 0.58 0.40 0.92 2.18 13
pheric pressure was reached, the desorption run was also recorded. With that procedure, isotherms of propane and propylene at 303, 323, and 343 K were obtained. Kinetic measurements were carried out on ZLC equipment already existing in our laboratory.12 The ZLC was placed in a gas chromatograph oven (Carlo Erba 6000, Milan, Italy) which is also used to analyze the exit of the cell by a flame ionization detector (FID). The scheme for the ZLC cell is similar to the one used by Da Silva for pellets larger than 1/16 in.13 The activation of the adsorbent was carried out by heating the sample up to 423 K (heating rate of 1 K/min) and keeping it there for 5 h with a helium flux of 23 cm3/min. Helium was also used as an inert purge gas in all of the experiments. Internal lines connecting the elements of the equipment were 1/16 in. stainless steel tubes trying to minimize the dead-volume effects. The inlet concentration of hydrocarbon in the saturation step was never superior to 3% in volume. Diffusivity measurements were carried out at 303, 323, and 343 K with two flow rates of purge gas; 29.3 and 65.0 cm3/min. Experimental conditions for the ZLC runs are detailed in Table 1. All gases used in this paper were provided by Air Liquide: propane N35, propylene N24, and helium 50 (purity greater than 99.95, 99.4, and 99.999%, respectively). The samples of NSG and WSG were kindly provided by Grace Davison (Barcelona, Spain). The properties of both adsorbents are presented in Table 2. The fitting of the model equations to experimental data was done with MATLAB 5.0 (The Mathworks, Inc.) using in all cases the square of residuals (SOR) defined by14
SOR (%) )
∑(qexptl - qcalcd)2
100 2
the characteristic curve is determined. The characteristic curve qVs vs f(A/Vs) is the locus of all of the isotherms for a particular adsorbate-adsorbent system, where q is the adsorbed-phase concentration (expressed in mmol/g) and Vs is the volume of the adsorbate considered as a saturated liquid. Dubinin relates the adsorption potential to the differential molar work of adsorption, -∆G3. The fundamental postulate is that the degree of filling θ ) q/qs is a function of the adsorption potential A, such that θ ) f(A/E0). The generalized Dubinin equation is15
[(
q ) qs exp -
The fundamental parameter of TVFM is the adsorption potential A ) RT ln(Po/P) where Po is the saturated vapor pressure. Polanyi’s theory and the Dubinin equation are based on the invariance of the adsorption potential with temperature. This was experimentally confirmed for microporous adsorbents but not completely satisfactory for large-pore and nonporous adsorbents. Polanyi’s theory is very powerful for the prediction of adsorption below the critical temperature, once
d
(2)
where qs is the maximum loading, E0 is the characteristic energy of adsorption, and d is the third fitting constant of the equation. The constant d was initially supposed to be an integer. Its physical meaning has been attributed to the number of degrees of freedom that the adsorbed molecules lost,16 being 1 or nearly 1 for hydrocarbons adsorbed on silica gel. The Dubinin-Radushkevich equation assumes that the pore size distribution is Gaussian (d ) 2). It has to be pointed out that the generalized Dubinin model is not thermodynamically correct, predicting a Henry slope of zero. This problem is presented by all of the exponential isotherms,17 but the prediction of multicomponent adsorption is good enough if the isotherm fits well the experimental data.18 The ZLC is probably the easiest way to determine intracrystalline diffusivities in zeolite crystals.19-21 Zeolite pellets where macropore control is the dominant mechanism were also considered.8,22,23 The same concept can be used for microporous adsorbents without a bidisperse structure, like activated carbon, CMS (Carbon Molecular Sieve), and silica gel as examples. The procedure for ZLC experiments starts with the activation of the adsorbent, then saturation with a low concentration of sorbate in order to describe the adsorption equilibrium by Henry’s law, and finally the measurement of the desorption curve, purging with an inert gas. Higher concentrations of sorbate can be used, resulting in other modeling equations.24 At long times, both models give the same slope because the concentration inside the particle will fall to low values, where the adsorption equilibrium becomes linear. The mathematical description of the ZLC was detailed elsewhere.8,11 The LTR for spherical pellets assuming linear equilibrium model is
() (
)
β12Dapt C 2L = ln 2 ln C0 β1 + L(L - 1) Rp2
(3)
β1 cot(β1) + L - 1 ) 0
(4)
(1)
3. Theoretical Section
)]
RT ln(Po/P) E0
L)
bQpRp2 3(1 - b)[p + (1 - p)K]VcDap
(5)
where β1 is the root of fundamental equation (4), Dap is the apparent diffusivity, Rp is the radius of the pellet, b is the porosity of the ZLC cell, p is the porosity of the pellet, Qp is the purge flow rate, Vc is the volume of the cell, and K is the equilibrium constant. For large values of the parameter L, the approximation β1 ) π is valid although the ratio C/C0 is still a
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function of L, which includes the purge flow rate.24 Equation 3 indicates that for sufficiently high flow rates, under kinetic control, the effective diffusivity is independent of the purge flow rate. When eq 3 is plotted as ln(C/C0) vs t and is fit to the long time desorption data, the slope is -β12Dap/Rp2. Because we are working in the Henry’s law region (linear isotherm), the apparent diffusivity (Dap) is related to the pore diffusivity (Dp) by
Dap )
pDp p + (1 - p)K
(6)
where Dp is the pore diffusivity. This parameter is related to molecular, Knudsen, and surface diffusion by7
τp 1 1 ) + Dp Dm Dk 1 - p qFp Ds + τp p C τs
(7)
where Dm is the molecular diffusivity, Dk is the Knudsen diffusivity, q is the adsorbed-phase concentration, C is the gas-phase concentration, Fp is the density of the particle, and τp and τs are the pore and superficial tortuosities. If there is no better approximation, τs can be assumed to be equal to τp. The Knudsen diffusivity is calculated by
Dk ) 9700rpxT/M
(8)
where rp is the pore radius (cm) and M is the molecular weight of the adsorbate. In the following calculations, the mean pore radius was used. The molecular diffusivity is usually calculated by the Chapman-Enskog equation. Surface diffusion occurs in parallel with the other mechanisms and is an activated process. Surface diffusion is important in hydrocarbon adsorption on activated carbon7 and in adsorption of low molecular weight hydrocarbons (C1-C3) on silica gel at low pressures; in that case another set of data using another carrier gas would be needed. 4. Results and Discussion 4.1. Adsorption Equilibrium Isotherms. When new experimental data of a previously investigated system is obtained, the first thing to do is to confront it with other published data. The Polanyi potential is a very useful tool for this purpose; for the same adsorbateadsorbent, all of the experimental data should fall in the same characteristic curve. The procedure used for representing the experimental points was described previously.25 Fugacities were approximated with partial pressures because data at low pressure were represented. Polanyi plots are presented in Figure 1a for NSG and Figure 1b for WSG. Excellent agreement was observed when NSG was compared with previous data.5,26 The adsorbed-phase concentration was also expressed as q′ in mmol/m2 to normalize the data of both adsorbents (NSG and WSG; Figure 1b). Minor differences were observed between both materials, indicating the same kind of physical interaction for propane and propylene. Comparison of WSG with other published data was not possible because no other data of previous works with C3 hydrocarbon adsorption on a low superficial area silica gel were found.
Figure 1. Polanyi’s characteristic curves, qVs vs A/Vs, of propane and propylene: (a) C3H6 and C3H8 on NSG; (b) C3H6 and C3H8 on WSG; (c) normalized characteristic curves, q′Vs vs A/Vs, of C3H6 and C3H8 on NSG and WSG (q′ is represented in mmol/m2). Symbols in a: 9, this work, 303 K; [, this work, 323 K; b, this work, 343 K; ×, Lewis et al.,3 278 K; +, Lewis et al.,3 293 K; *, Lewis et al.,3 343 K; 2, Malek and Farooq.5 Symbols in b: empty points, data of WSG; full points, data of NSG; 0, 9, this work, 303 K; ], [, this work, 323 K; O, b, this work.
Figure 2 shows the data obtained for propane (a) and for propylene (b) on NSG, while Figure 3 shows corresponding data on WSG. Experimental values for data storage are presented in the appendix. The values fitted with the Dubinin model (eq 2) are represented as solid lines in these figures. For the calculation of the degree of filling, the adsorbed-phase concentration, q, was used instead of the most commonly used volume of the pores. As shown in the figures, the fitting is very good in the temperature and pressure ranges studied. One can expect, however, higher deviations at very low pressures, where the Dubinin model is thermodynamically inconsistent. Table 3 shows the parameters of the Dubinin equation for both systems NSG and WSG. The value of the constant d is near 1, showing that the adsorbate (propane and propylene) loses 1 degree of freedom when adsorbed in silica gel, as is expected for hydrocarbons with molecular sizes at least 5 times smaller than the pore size.16 In NSG the characteristic energy of adsorption of propylene is 7.09 kJ/mol, 2 kJ/mol higher than propane (5.05 kJ/mol). For WSG this parameter is nearly the same for both gases (4.66 and 4.78 kJ/mol for propane and propylene, respectively). It can be seen from the experimental isotherms that the interactions of both gases are not the same. It can be concluded that, in the WSG-hydrocarbon systems, the parameters of
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1689
Figure 2. Adsorption equilibrium isotherms at 303, 323, and 343 K over NSG: (a) propane; (b) propylene. Solid lines are the generalized Dubinin model.
Figure 3. Adsorption equilibrium isotherms at 303, 323, and 343 K over WSG: (a) propane; (b) propylene. Solid lines are the generalized Dubinin model.
Table 3. Fitting Parameters of the Generalized Dubinin Model Applied to Experimental Data at 303, 323, and 343 K system
qs
E0 (J/mol)
d
SOR %
C3H8-NSG C3H6-NSG C3H8-WSG C3H6-WSG
4.680 4.925 2.045 2.646
5047 7089 4667 4781
1.153 1.262 1.158 0.993
0.284 0.713 0.187 0.036
the Dubinin model have no physical meaning, even when the fitting of experimental results is very accurate. This can be due to problems of the model when dealing with mesoporous adsorbents.15 The heats of adsorption for all systems were estimated with the Clausius-Clapeyron relation and are presented in Figure 4. The isosteric heat decreases with the degree of coverage, with a logarithmic decay. Predictions of the isosteric heats with the Dubinin equation lead always to a logarithmic decay expression.The decay in the isosteric heat can be explained by the heterogeneity of the adsorbent (at low coverage, the molecules adsorb in the more active sites, blocking them and leaving the less active sites for higher coverages.27 In NSG, for coverages higher than 0.4 mmol/g, the difference in the heats of adsorption of propene and propane correspond to the differences in the energies of adsorption (E0). The isosteric heat of adsorption was also calculated from other data.26 The same behavior was observed with differences of (3 kJ/mol when compared with the NSG adsorbent. A decrease in the isosteric heat of adsorption was also reported for higher alkanes adsorbed on silica gel.28 The heats of adsorption
Figure 4. Isosteric heat of adsorption calculated by the ClausiusClapeyron equation at 303 K as a function of the adsorbed-phase concentration.
at high coverage were approximately twice the value of the heat of vaporization. 4.2. Kinetics of Adsorption. ZLC desorption curves of propane and propylene in NSG with purge flow rates of 29.3 and 65.0 cm3/min of helium taken at 303, 323, and 343 K are presented in Figure 5. Similar plots for propane and propylene in WSG are presented in Figure 6. The reason for using the LTR is because the kinetic curves are very fast, and if the complete solution is modeled, many errors due to the washing of the cell and due to dead volume effects may hide the real diffusivity values. The plots in semilog scale allow direct calculation of the slope of the long time asymptote that has the information of the pore diffusivity. Figure 5a also
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Figure 5. Experimental desorption curves for C3H6 and C3H8 in NSG at 303, 323, and 343 K: (a) C3H8 using 29.3 cm3/min of He as the purge; (b) C3H8 using 65.0 cm3/min of He as the purge; (c) C3H6 using 29.3 cm3/min of He as the purge; (d) C3H6 using 65.0 cm3/min of He as the purge. Full lines in part a are complete ZLC model results using parameters from LTR.
Figure 6. Experimental desorption curves for C3H6 and C3H8 in WSG at 303, 323, and 343 K: (a) C3H8 using 29.3 cm3/min of He as the purge; (b) C3H8 using 65.0 cm3/min of He as the purge; (c) C3H6 using 29.3 cm3/min of He as the purge; (d) C3H6 using 65.0 cm3/min of He as the purge.
shows results from simulations with the complete ZLC model using parameters from the LTR. The slopes of the curves (eq 3) with both flow rates are the same, confirming kinetic control in both cases. However, the intercept value is different and depends on the purge flow rate. The effect of the different purge flow rates is not very strong because the species are not strongly adsorbed. The slopes of the curves have been calculated
with at least five points in the linear asymptote; thiswas an important point in the analysis of the results. Desorption curves, using nitrogen as the purge gas, were measured to assess the importance of surface diffusivity. For both gases in the two samples studied, no surface diffusivity was detected. This was investigated because some references indicated the importance of surface diffusivity of propane.4,29 The apparent diffusivity Dp obtained using eqs 3-5 is presented in Table 4. It has to be pointed out that the model for spherical pellets has been used for the NSG pellets, but the pellets used were not exactly spherical. The pore diffusivity was calculated using eq 6, with the value of K obtained from the fit of eq 3. Values are presented also in Table 4. The equilibrium constants extracted from the ZLC experiments were comparable to the constants taken from gravimetric measurements when fitted with a thermodynamically correct isotherm in the low-pressure region. The Dubinin equation is not able to fit very low pressure data because of its incorrect value of Henry’s constant. The values of the adsorption constant K ) FpHRT where H is Henry’s constant were obtained by fitting the Langmuir equation to the isotherms. In NSG pellets, the pores are narrow (mean pore diameter: 44 Å), so the transport flux should be controlled by Knudsen diffusion or by surface diffusion. Previous experiments with another purge gas, nitrogen, exhibit very different slopes at long times, indicating that surface diffusion is not dominant. Knudsen diffusion, Dk, was calculated using eq 8, and values are presented in Table 4. From eq 7, without molecular and surface diffusion, the pore diffusivity should be well represented by the Knudsen diffusivity. A plot of Dk/Dp for the different experiments should be indicative of the tortuosity factor; see Figure 7a. This plot can also indicate the presence of surface diffusion.7 The pore diffusivities determined in the temperature range 303343 K are 2.4 × 10-3-2.8 × 10-3 and 1.7 × 10-3-2.4 × 10-3 cm2/s for propane and propylene. Average tortuosity values ranging from 2 to 6 were reported for silica gel.29 An average tortuosity value of 2.5 can be estimated from all of the experiments made. In this way, additional confirmation of the absence of surface diffusion was obtained. In WSG pellets, the mean pore diameter is larger than that in NSG (120 Å), and the diffusion can be controlled by a combination of mechanisms (molecular and Knudsen). Molecular diffusion, Dm, was calculated using the Chapman-Enskog equation and is shown in Table 4. Pore diffusivities, Dp, were calculated from eq 7 without molecular diffusion, being 6.4 × 10-3-9.9 × 10-3 cm2/s for propane and 6.6 × 10-3-12.1 × 10-3 cm2/s for propylene. The values are very close to Knudsen diffusion, and for tortuosity calculations, the molecular diffusivity has a minor effect. A plot of Dk/Dp for WSG is presented in Figure 7b. The tortuosity has an average value of 2.0 estimated from the complete set of experiments for WSG. In both materials, Knudsen diffusion was the dominant mechanism for mass transfer. These results are consistent with data previously published.7 The effects of surface diffusion for both propane and propylene were not detected in all of the experiments made using helium or nitrogen as the purge gas. The main problem in measuring diffusivities from the desorption curves of these materials is that the response
Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1691 Table 4. Pore Diffusivities from ZLC Experiments temp (K)
slope
intercept
Dap × 105 (cm2/s)
K
Dp(calcd) (cm2/s)
Dk(estd) (cm2/s)
Dm(estd) (cm2/s)
τ(calcd)
303 323 343
0.011 0.017 0.025
0.069 0.080 0.087
1.9 3.1 4.7
C3H8-NSG (Qp ) 29.3 of He/min) 81.1 0.00236 58.5 0.00273 41.6 0.00296
0.0056 0.0058 0.0060
0.390 0.433 0.480
2.7 2.4 2.3
303 323 343
0.014 0.017 0.031
0.081 0.074 0.088
2.6 3.2 5.8
C3H8-NSG (Qp ) 65 cm3 of He/min) 76.7 0.0026 57.7 0.0024 37.9 0.0028
0.0056 0.0058 0.0060
0.390 0.433 0.480
2.1 2.4 2.1
303 323 343
0.005 0.009 0.014
0.084 0.079 0.079
1.0 1.6 2.6
C3H6-NSG (Qp ) 29.3 cm3 of He/min) 189.9 0.0024 109.6 0.0023 68.4 0.0023
0.0057 0.0059 0.0061
0.429 0.478 0.529
2.3 2.6 2.6
303 323 343
0.005 0.008 0.014
0.068 0.061 0.055
0.99 1.5 2.5
C3H6-NSG (Qp ) 65 cm3 of He/min) 172.1 0.0022 100.9 0.0020 55.2 0.0018
0.0057 0.0059 0.0061
0.429 0.478 0.529
2.6 3.0 3.4
303 323 343
0.040 0.044 0.048
0.193 0.174 0.166
17.6 19.1 20.6
C3H8-WSG (Qp ) 29.3 cm3 of He/min) 56.4 0.0074 46.5 0.00667 40.8 0.0064
0.0153 0.0158 0.0162
0.390 0.433 0.480
2.0 2.3 2.5
303 323 343
0.053 0.057 0.061
0.117 0.087 0.077
21.5 22.7 24.1
C3H8-WSG (Qp ) 65 cm3 of He/min) 61.5 0.0099 43.0 0.0074 35.7 0.0065
0.0153 0.0158 0.0162
0.390 0.433 0.480
1.5 2.1 2.4
303 323 343
0.036 0.049 0.050
0.225 0.205 0.170
16.4 22.0 21.7
C3H6-WSG (Qp ) 29.3 cm3 of He/min) 73.5 0.0089 49.2 0.0080 40.8 0.0066
0.0156 0.0161 0.0166
0.429 0.478 0.529
1.7 2.0 2.4
303 323 343
0.040 0.056 0.064
0.140 0.110 0.084
17.0 23.0 25.4
C3H6-WSG (Qp ) 65 cm3 of He/min) 96.5 0.0121 55.7 0.0095 38.2 0.0073
0.0156 0.0161 0.0166
0.429 0.478 0.529
1.2 1.6 2.2
cm3
coefficients with temperature (expected in the temperature range of 303-343 K for Knudsen diffusion control) were within experimental error and the technique used gave us only qualitative information about the diffusion mechanism. The larger differences of the pore diffusivities determined from the curves at 65.0 cm3/min of purge gas when compared with those determined using 29.3 cm3/ min can be because the response of the desorption curve is so fast that it makes us work in limit conditions where dead volumes and cell washing effects are important. This effect is particularly noticeable in WSG. 5. Conclusions
Figure 7. Tortuosity of silica gel determined by the ZLC method: (a) NSG; (b) WSG.
is very fast and the amount adsorbed is not high, so the reproducibility of the results, particularly for the wide silica samples, was around 20%. The other source of error is how many points are considered to be in the “LTR”. Large differences in the value of the intercept can be due to this fact. Values reported in Table 4 are indicative that variations of less than 10% of diffusion
The adsorption equilibriums of propane and propylene onto two commercial silica gel pellets (Grace Davison) were carried out to test both adsorbents for possible PSA utilization. The loading of propylene on the NSG is always 1.5 times the corresponding value of propane. The low amounts of hydrocarbons adsorbed by the WSG at the temperatures studied (303-343 K) confirmed the poor behavior of this adsorbent for C3 separation by PSA. The TVFM correlates the data with high accuracy and very little computational effort. Equilibrium data for NSG were consistent with previous values reported in the literature.2,3,5 The ZLC method was used for the determination of diffusivities of propane and propylene in silica gel. Surface diffusivity was not present in both samples analyzed. The diffusion in both samples was well described by Knudsen diffusion, although they have different mean pore diameters. This is consistent with other data.7 The pore diffusivities determined in the temperature range 303-343 K are 2.4 × 10-3-2.8 × 10-3 and 1.7 ×
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Table 5. Experimental Data of Propane and Propylene on NSG and WSG T ) 303 K
T ) 323 K
T ) 343 K
P (kPa) q (mmol/g) P (kPa) q (mmol/g) P (kPa) q (mmol/g) Adsorption Isotherms on NSG 0 2.31 7.02 15.62 21.95 30.60 43.15 52.94 67.32 81.52 98.02
0 0.125 0.255 0.417 0.521 0.652 0.808 0.926 1.088 1.240 1.391
0 2.32 7.44 14.80 22.53 31.16 39.54 49.45 61.48 73.01 84.80 97.52
0 0.340 0.610 0.867 1.032 1.194 1.342 1.497 1.651 1.777 1.903 2.016
Propane 0 0 2.01 0.059 6.19 0.129 10.51 0.198 16.26 0.277 20.38 0.323 25.83 0.392 31.92 0.455 38.45 0.515 48.08 0.594 55.99 0.653 64.19 0.706 68.26 0.739 71.55 0.772 77.60 0.805 81.08 0.834 86.58 0.868 96.75 0.920 Propylene 0 0 2.65 0.181 8.10 0.376 15.32 0.548 21.95 0.687 31.04 0.811 40.12 0.962 49.45 1.046 61.53 1.158 73.61 1.276 84.56 1.371 97.82 1.477
0 1.72 6.04 10.42 16.21 22.70 28.70 33.90 38.87 43.78 49.48 53.56 63.48 70.07 76.11 85.89 89.08 92.62 99.25
0 0.026 0.073 0.109 0.162 0.214 0.254 0.287 0.327 0.350 0.393 0.409 0.465 0.501 0.531 0.581 0.597 0.620 0.650
0 2.36 7.62 15.13 22.01 30.37 39.11 47.46 61.52 76.11 84.76 96.40
0 0.091 0.219 0.360 0.466 0.577 0.679 0.758 0.878 0.977 1.032 1.099
Adsorption Isotherms on WSG 0 1.97 6.60 12.25 18.95 25.29 31.69 39.02 47.19 57.38 64.76 73.71 81.44 97.68
0 0.036 0.090 0.141 0.192 0.233 0.269 0.305 0.341 0.383 0.416 0.449 0.476 0.524
0 2.51 8.12 14.66 23.03 30.12 39.42 49.36 61.12 73.02 83.56 98.37
0 0.106 0.195 0.263 0.324 0.372 0.427 0.482 0.529 0.581 0.629 0.687
Propane 0 0 7.39 0.047 14.92 0.084 22.65 0.117 33.69 0.158 46.34 0.194 55.11 0.217 64.61 0.244 77.32 0.274 97.71 0.324
Propylene 0 0 2.90 0.072 7.97 0.126 15.06 0.181 23.03 0.222 31.30 0.260 41.14 0.301 50.14 0.338 62.99 0.379 75.93 0.424 85.13 0.461 98.96 0.499
ments with two different purge flow rates and propane and propylene desorption.
0 2.01 7.57 13.46 23.98 34.74 45.40 56.11 65.20 73.60 79.06 91.24 98.37
0 0.008 0.026 0.043 0.070 0.092 0.119 0.142 0.162 0.178 0.188 0.206 0.218
0 3.00 8.32 14.71 22.19 29.87 39.47 50.54 60.58 72.48 83.56 97.04
0 0.041 0.079 0.113 0.143 0.171 0.201 0.231 0.260 0.290 0.314 0.345
10-3-2.4 × 10-3 cm2/s for propane and propylene on NSG, respectively. For WSG these values are 6.4 × 10-3-9.9 × 10-3 cm2/s for propane and 6.6 × 10-3-12.1 × 10-3 cm2/s for propylene. Average tortuosity values of 2.5 and 2.0 for NSG and WSG, respectively, were estimated from ZLC experi-
Acknowledgment Financial support from ALFA-NSPnet Project ALR/ B7-3011.94.04-6.0018.9. C.A.G. acknowledges D. C. S. Azevedo and J. M. V. Prior for technical support. Appendix See Table 5. Notation A ) adsorption potential, kJ/mol C ) molar concentration of the sorbate in the gas phase, mol/m3 C0 ) initial molar concentration of sorbate in the ZLC cell, mol/m3 d ) parameter of the generalized Dubinin model Dap ) apparent diffusivity parameter, cm2/s Dk ) Knudsen diffusivity, cm2/s Dm ) molecular diffusivity, cm2/s Dp ) pore diffusivity, cm2/s Ds ) Surface diffusivity, cm2/s E0 ) characteristic adsorption energy, kJ/mol H ) Henry’s constant, mmol/(g kPa) K ) equilibrium constant L ) ZLC parameter defined by eq 5 M ) molecular weight, mol/g P ) pressure, kPa Po ) pressure of the saturated gas, kPa q ) adsorbed phase concentration, mmol/g q′ ) adsorbed phase concentration, mmol/m2 qs ) maximum adsorbed phase concentration, mmol/g Qp ) purge gas flow rate, cm3/min R ) ideal gas constant, 8.314 kJ/mol‚K Rp ) pellet radius, cm rp ) pore radii, Å T ) temperature, K W ) volume of the micropores per gram of adsorbent, mm3/g W0 ) maximum volume of the micropores per gram of adsorbent, mm3/g Greek Letters b ) ZLC cell void fraction p ) porosity of the pellet β1 ) root of elemental eq 4 τp ) pore tortuosity τs ) surface tortuosity Fp ) density of the particle, g/cm3 Fs ) density of the solid, g/cm3
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Received for review October 16, 2000 Revised manuscript received January 29, 2001 Accepted February 6, 2001 IE000901G
