1262
Znd. Eng. Chem. Res. 1991, 30, 1262-1270
GENERAL RESEARCH Measurement of the Single-Component Adsorption Kinetics of Ethane, Butane, and Pentane onto Activated Carbon 'IJsing a Differential Adsorption Bed P. L. J. Mayfield and D. D. Do* Department of Chemical Engineering, University of Queensland, St. Lucia QLD 4072, Australia
The transient uptake of three paraffins onto a commercially available activated carbon has been studied by using the differential adsorption bed (DAB) technique, first reported by Carlson and Dranoff (1985),and a gravimetric method. A model describing adsorption in a single bimodal adsorbent particle was developed to analyze the experimental uptake data. The model accounts for the effects of macropore, solid, and micropore diffusion. The controlling mechanisms for the observed global uptake were identified by using experimental data measured for a wide range of conditions, and particle geometries and the appropriate parameters extracted. Diffusivities were determined at temperatures between 10 and 60 "C. A macropore tortuosity factor of 8 waa measured for the activated carbon used. For adsorption of ethane using commercially available l/lein. extrudate pellets, the mechanisms of pore, solid, and micropore diffusion were identified as important. Similar mechanisms were observed for n-butane and n-pentane adsorption. Good agreement between model predictions and experimental data was found over the broad range of conditions studied.
Introduction Optimal design and operation of any fixed-bed adsorption unit requires detailed knowledge of both the thermodynamic and kinetic characteristics of the gas-solid system of interest. This requirement emphasises the importance of methods that can be used to measure or even predict these properties. To correctly measure the kinetic properties, it is first necessary to select a suitable experimental method. This is used to measure the global adsorption rate. Second, these experimental adsorption rate measurements must be correctly interpreted to identify and quantify the contributing physical processes. Hence, a rational understanding of the mechanistic processes involved is required. This understanding is applied in the derivation of suitable mathematical models that are used in the analysis of the experimental data. Experimental Methods A wide variety of experimental methods are currently available for the measurement of global adsorption uptake rates. Included in these are gravimetric measurement, pulse chromatography (Schneider and Smith, 1968a), fixed-bed breakthrough (Masamune and Smith, 1965), and the Wicke-Kallenbach diffusion cell (Wicke and Kallenbach, 1941),which have been used extensively to determine single-component uptake rates. Pulse chromatography and fixed-bed breakthrough suffer from the drawback that the "bed processes" must be accounted for in the analysis of the results. This increases the complexity of the mathematical analysis significantly and may lead to erroneous results. It is also noted the pulse chromatography analysis is applicable only to linear regions of the isotherm. The simpler geometries of the gravimetric and diffusion cell methods avoid the
complications of the bed methods mentioned previously. However, the diffusion cell method requires a specially formed pellet of the adsorbent of interest. Obtaining a pellet representative of the original adsorbent is very difficult, and flawed data may result. In addition to this, any difference in pressure across the pellet will create a convective contribution to the diffusion measurement. Ultimately, these methods share one significant disadvantage in that they cannot be extended to analyze multicomponent systems. Carlson and Dranoff (1985, 1986) recently reported a new method called the differential adsorption bed (DAB) technique, which can be readily applied to both single and multicomponent systm" As the name suggests, the experiments are carried out under differential conditions. This allows simplification of the associated mathematical modeling analysis to that for a single particle. They applied their technique to measure the uptake of ethane onto 4A zeolite. Equilibrium data were also evaluated. Agreement was found with earlier work by Kondis and Dranoff (1971) and Yucel and Ruthven (1980) on the same adsorbentjadsorbate system, confirming the applicability of the technique to the 4A zeolite system. The noticeable lack of multicomponent data in the literature coupled with the fact that most systems of commerical importance are multicomponent highlights the importance of this experimental technique for future work.
Adsorption Modeling As mentioned previously, a suitable mathematical model is required for interpretation of the experimental kinetic data. A majority of' diffusion models in the literature are devoted to the description of catalyst supports, such as y-alumina and zeolitic molecular sieves. The more complex structure of activated carbon, which is generally
0888-5885/91/2630-1262$02.50/0 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30,No. 6, 1991 1263 centration. (iv) On the basis of experimentally measured equilibria the Langmuir isotherm applies. (v) Adsorption at the microsphere surface follows Langmuir kinetics (surface barrier). (vi) The particle is assumed to be isothermal. The mass balances for the particles above may be written as
'6
3 V
0.20 .
W
W
W (r
0
a O oo,O
I 100
1000
Pore Diameter
10000
(A)
100000
Figure 1. Pore size distribution of Ajax activated carbon from mercury porosimetry (A) and nitrogen adsorption (B).
thought to exhibit a wider range of pore sizes, has posed a variety of difficulties in the formulation of suitable models. Indeed, many researchers have resorted to using single lumped parameter models with minimal success. Of the few models proposed the branched pore model of Peel et al. (1981) for liquid systems probably best describes adsorption within activated carbon. However, for applications in gas-phase adsorption it is limited in its capabilities to describe mechanisms such as adsorbed-phase diffusion radially into the particle in parallel with macropore diffusion (solid diffusion). Hence, to analyze the experimental results, a mathematical model describing the mass-transfer mechanisms present within a single particle of activated carbon has been derived. The formulation of this model is described in the following section. In this paper the DAB method has been applied to the measurement of adsorption kinetics in an activated carbon adsorbent. Initially, single-component experiments dealing with the uptake of ethane, n-butane, and n-pentane onto a commercially available activated carbon (Ajax type 976) have been performed. The proposed model has been used to identify the dominant processes and evaluate the relevant transport parameters.
Model Formulation To model the activated carbon adsorbent, as realistic a physical picture of the solid as possible must be adopted. This picture reflects the conflict between the complex structure of the actual solid and the difficulties and limitations associated with solving the mathematical model. For our work we have assumed the carbon exhibits a bimodal pore distribution. This assumption is supported by the measured pore size distribution. The PSD was determined by both mercury porosimetry and nitrogen adsorption (Figure 1). As detailed by Gray and Do (1989) this assumption is one of mathematical convenience and is used commonly in the literature. The high gas velocities required to attain differential conditions during adsorption means that film resistance to heat and mass transfer is minimal. Consequently, in terms of heat transfer the particle may be considered isothermal. On the basis of this description a comprehensive single-particle model was formulated that included the effects of external film resistance, macropore diffusional resistance,solid diffusion, finite adsorption rate (surface barrier), and micropore diffusional resistance. Consider a particle of arbitrary shape (sphere, cylinder, slab) with a bimodal pore size distribution. For the analysis the following assumptions are made: (i) The microparticles are spherical. (ii) Solid diffusion occurs in parallel with macropore diffusion. (iii) The macropore, solid, and micropore diffusivities are independent of con-
with
r, = o r =o
ac,/ar, = o
(14
ac/ar = aC,/ar = o
(Id)
r = R,
D, aC,/ar,$
=
- c,h) - kdCplR,
(le)
r=R fmDpac/arlR + (1- eM)D,ae,,/dr(R = kM(Co - CIR) (If) where C is the adsorbate concentration in the macropore (mol/cm3 macrovoid), C, is the adsorbate cqncentration in the microsphere (mol/cm3microsphere), C, is the volume-averaged microsphere concentration, eM is the macropore porosity, Dp is the macropore diffusivity based on void area (cm2/s),D, is the solid diffusivity (cm2/s), D, is the micropore diffusivity (cm2/s),R, is the microsphere radius, R is the particle radius, SMA is the particle shape factor (for a spherical particle SMA = 21, It, is the intrinsic adsorption rate constant, Itd is the desorption rate constant, kMis the film mass-transfer coefficient, and Cois the adsorbate concentration in the bulk phase. By defining the following nondimensional variables and parameters in eqs 2
1264 Ind. Eng. Chem. Res., Vol. 30, No. 6,1991 Table I. Physical Properties of Ajax Activated Carbon bulk density pp 0.733g/cm3 micropore porosity tp 0.59 total porosity 0.71 av macropore d i m 0.8 pm macropore 0.31 nitrogen surface area 1200 m2/g porosity t~ (rp > 5.0 nm)
as a function of time for direct comparison with experimental uptake curves.
It is important to note the physical significance of each of the nondimensional parameters. The parameters u1 and u2 are closely related with ul,representing the fraction of adsorption capacity in the macropore voids, and u2 represents the complementary capacity in the micropores. The "shape" or nonlinearity of the isotherm is indicated by the parameter A. The shape varies from linear (A > 1. ul,u2, and X characterize the equilibrium, and the remaining parameters are categorised as rate parameters. The Biot number (Bi) is the ratio of the time scale of macropore diffusion to that for diffusion across the stagnant film around the particle. Large values (Bi> 100) indicate minimal resistance in the external film. Parameter 5 quantifies the contribution of solid diffusion with respect to pore diffusion, and the effect of finite adsorption kinetics at the micropore pore mouth is measured by the parameter B. Large values of B indicate that diffusion into the micropores occurs more slowly than adsorption at the pore mouth. "he final parameter y measures the ratio of the time scale of macropore adsorption control to that of micropore diffusion controlled adsorption. Hence, it follows that when y >> 1macropore diffusion is a controlling mechanism, and conversely when y > 1; 5 1. (ii) Macropore diffusion control-nonlinear isotherm: y >> 1; 5 > 1. (iii) Combined macroporesurface diffusion control: y >> 1; 5 = O(1). (iv) Solid diffusion control: y >> 1; E >> 1. (v) Combined macropore-micropore diffusion control: y 1 O(1); 5 > 1. (vi) Micropore diffusion control: y > 1. (vii) Combined macropore-surface-micropore diffusion control: y = O(1); [ 9 O(1); B >> 1. Model equations (3) were reduced to a set of ordinary differential equations by using orthogonal collocation (Villadsen and Michelsen, 1978) and then numerically integrated by using Gears method. The DGEAR routine from the IMSL library was employed. The model was tested over a wide range of parameter combinations against well-known solutions of degenerate models. Modeling results were presented in terms of the fractional uptake
Experimental Section Adsorbent/Gases. Activated carbon Type 976 (Ajax Chemical Co., Australia) supplied as l / ,-in.-diameter cylindrical extrudateg was used. The structural properties of the adsorbent were evaluated by using a combination of nitrogen adsorption (Micromeritics ASAP 2000) and mercury porosimetry (Micromeritics Model 9200). These are summarized in Table I. The measured pore size distribution is shown in Figure 1. Three particle geometries were prepared for use in kinetic measurements. Particles of spherical geometry were obtained by crushing and sieving. Cylindrical particles were prepared by taking long sections of extrudate and carefully trimming the end faces. Epoxy resin was then painted over these faces, leading only the cylindrical surface of the extrudate exposed to the adsorbate. Slab particles were made in a similar fashion. However, in this case the extrudate was trimmed to a specific length and the cylindrical surface painted with epoxy, thus leaving only the circular end faces exposed to the adsorbate. The carbon was degassed at 300 OC under vacuum. Particles coated with epoxy were restricted to degas temperatures below 150 "C to ensure integrity of the coating. An adsorption run performed by using a pellet painted on all surfaces confirmed the ability of the epoxy covering to prevent adsorbate entering the adsorbent. All experiments were performed using high-purity (oxygen-free nitrogen, O.F.N.) nitrogen (supplied by Commonwealth Industrial Gas Ltd.(C.I.G.)) as the inert carrier. Ethane and n-butane were supplied in chemically pure grade by Matheson gases. Premixed cylinders of 10.3 and 29.4 mol 9a C& were supplied by C.I.G. Analytical reagent grade n-pentane was obtained from Ajax Chemicals. Adsorbate gases were mixed by using a bank of Porter rotameters. Pentane mixtures were produced by bubbling nitrogen through two temperature-controlled saturators connected in series. Dynamic measurements were made by using the differential adsorption bed technique and a standard gravimetric method. Details of both are given below. DAB. Apparatus. Both equilibrium and transient uptake measurements were performed using the DAB apparatus. This comprised four major components. These were the gas mixing system, adsorption bed, desorption bomb, and the GC for sample analysis. The apparatus is shown schematically in Figure 2. Two adsorber designs were used. The first was used for equilibrium measurements where a large amount of sample was necessary. It was constructed from 3/8-in. stainless steel tube. The adsorbent was supported on a 100-pm stainless steel mesh. A 1/8-in. type K thermocouple was located axially within the bed to measure the adsorbent temperature. The second adsorber was used for kinetic measurements. It consisted of a 3/8-in.stainless steel Cajon plug with the interior machined out to house the adsorbent. This was sealed with the corresponding cap fitting by using a stainless steel gasket. The bed was enclosed within a 100-pm mesh screen. The significant feature of this adsorber was the minimal dead volume between the
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1266 ISOTHERMAL
)'err
I
GAS BUBBLERS
GAS MWNG
Krm: wclc
w - 3
w-1
PR-2
w-3
I
PR-5
I
I
PR-K
GAS ANALYSIS NI"
WSOEBRTE SAQS
SECTION
Figure 2. Schematic diagram of DAB apparatus.
gas inlet and outlet at the four-way valve. The adsorber temperature was controlled by either a water bath or furnace depending on the magnitude of the desired temperature. With the four-way valve the bed could be isolated from the gas mixing system during desorption. A desorption bomb (of calibrated volume 120 cm3) was connected to the bed via a three-way valve. Special inserts was used to adjust the bomb volume to as little as 30 cm3 for certain applications. The bomb could be independently evacuated, or a vacuum could be applied to the bed via the bomb. The bomb was fully instrumented (P,T,V, C) to allow complete analysis of the desorbed gas. Pressure was measured by using a Barksdale Series 302 pressure transducer and temperature was determined with a K type thermocouple. Adsorbate concentration in the bomb was measured by an FID GC (Shimadzu Type GC-8APF) fitted with either a Durapak or Chemipak-C18 separation column depending on the gases to be analyzed. Sampling was carried out by flushing a portion of the bomb inventory through a Valco sample valve via a line. A small liquid trap was used to ensure a constant sample-loop pressure for each injection. The GC was calibrated at least daily by using calibration gases. Procedure. The bed was initially degassed overnight by purging the heated bed with a small flow of O.F.N. grade nitrogen. A bed temperature of between 150 and 280 "C was used depending on the nature of the sample. Once degassed, the bed was brought to the adsorption temperature by using a water bath. The adsorbate mixture concentration was then checked by GC analysis before being flushed through the system with the adsorber isolated. Flow rates of the order 1200 sccm/min were used. Concurrently, the bomb pressure transducer calibration
was checked, and the bomb evacuated. Next, the sorbent was exposed to the adsorbent stream for a predetermined adsorption time before once again being isolated. With the bed isolated, the evacuated bomb was connected to desorb the adsorbed gas at a reduced total pressure. The desorption was assessed by heating the bed to sample degas temperature for between 40 and 60 min depending on the adsorbate. On completion of desorption, nitrogen was flushed through the adsorber to carry the desorption products into the adjoining bomb, which was sealed at the designated pressure. The pressure and temperature of the bomb were then measured and recorded before the amount of adsorbate present was established by GC analysis of the gas. This amount was then corrected to remove the contribution of the adsorbate trapped in the voids of the adsorbers at isolation. By repeating this procedure for a series of exposure times, an uptake rate curve could be generated for the chosen experimental conditions. With sufficiently long adsorption times the equilibrium loading could be determined. As mentioned previously a larger amount of adsorbent was used in this case. TGA. Apparatus. Gravimetric measurements were made using a modified Stanton Redcroft STA 780 microbalance (Gray and Do, 1989). Adsorbate gases were mixed in the same manner as for the DAB apparatus. Typically a flow rate of 400 sccm/min was used. The cylindrical adsorbent particles were suspended from one side of the microbalance inside a 5-mm4.d. ceramic tube located within the furnace. The pellets were suspended such that the '/,&.-diameter circular cross section of the particles occupied 10% of the tube cross-sectional area. During adsorption, adsorbate gas passed downward through this tube and exited at the base of the furnace.
1266 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 E 03
-0
1
P
. i
000-y
A
Growmetric d a t a
1
400 500 800 ADSORSATE P R i S j U R E ( k p c )
1000
200
Figure 3. Isotherms for ethane adsorption onto Ajax activated carbon measured a t 10,30, and 60 "C by using DAB apparatus compared to Langmuir isotherm predictions using parameters of Table 11.
Table 11. Langmuir Isotherm Parametem for Ethane, n -Butane, and n -Pentane on Ajax Activated Carbon at 10-200 O C (Mayfield and Do, 1989) temp, "C species 10 30 60 150 200 units ethane 5.54 4.74 3.31 2.02 1.24 mol/cma X 12.35 9.168 6.830 2.917 2.144 cm3/mol X 0.986 0.969 0.929 0.909 R2 (-AH) 10.20 kJ/mol n-butane 5.49 4.92 4.31 3.13 mol/cma x 8.444 8.358 5.192 2.019 cm3/mol x R2 0.999 0.999 0.998 0.984 (-AH) 12.56 kJ/mol n-pentane 4.52 4.23 3.81 2.71 mol/cms x 7.671 6.189 3.065 0.646 cms/mol x R2 0.999 0.999 0.998 0.989 (-AH) 18.24 kJ/mol
F
108
?
108 104
F
108
lo-'
104
1
cr,
200
400
800
600
ADSORBATE PRESSURE (kPc)
Figure 4. Isotherms for butane adsorption onto Ajax activated carbon measured at 10, 30,60,and apparatus 0 - 150 "C using DAB . compared to Langmuir isotherm predictions using parameters of Table 11. z
60Ci
I
0 ^
coo
G4
'0 0 A:S?RBATE
20 0
^
I
I
30 0
PRESSJRE (kPa)
Figure 5. Isotherms for pentane adsorption onto Ajax activated carbon measured at 10, 30, 60, and 150 "C using DAB apparatus compared to Langmuir isotherm predictions using parameters of Table 11.
This arrangement created better gas-solid contact at higher gas velocities, conditions necessary to achieve differential operation of the apparatus. Procedure. The adsorbent particles were initially degassed in a pure nitrogen environment at 150 OC. This was continued until constant sample mass was achieved. After degassing, the furnace was cooled and maintained at the adsorption temperature. The adsorbate gas was mixed and the composition verified by FID GC analysis. The run was started by passing the adsorbate mixture through the ceramic tube. The sample weight change was monitored until constant mass was achieved again. The uptake cullreg were corrected for drag and buoyancy effects. Results and Discussion Equilibrium Adsorption Capacities. Isotherms measured by the DAB method for each of the gas species can be seen in Figures 3-5. Independent capacity measurements were made for ethane adsorption on the same carbon using a Stanton Redcroft microbalance (Mayfield and Do, 1988). These capacities, shown in Figure 3,confirm the suitability of the DAB method for this type of work. A comparison with results for other carbons (of
0 0
5000
1 OOOO
15000
TIME ( s e c s )
Figure 6. Experimentally measured versus model uptake curvea for adsorption of 10% ethane in helium onto 1/8-in.-diameter 4A molecular sieve extrudates.
approximately the same surface area) in the literature (Kuro-Oka et al., 19W,Payne et al., 1968)shows our data to exhibit similar isotherm shape and capacity. Ethane exhibited a moderately nonlinear isotherm, whereas the isotherms for butane and pentane could be better described as approaching rectangular. The isotherm data were fitted to a simple Langmuir isotherm expression (Mayfield and Do, 1989): c, = C,bC/(l+ bC) (4) Good results were obtained. The model parameters, C and b, are reported for a range of conditions in Table along with the correlation coefficients of the parameter fits. It should be noted that eq 4 has been fitted empirically, and hence the parameters cannot be strictly regarded as physical constants. Adsorption Kinetics. An initial experiment was performed to reproduce the results of Carlson and Dranoff (1985). A mixture of 10 mol 90CzHs in helium was adsorbed onto 'I8-in. Linde 4A molecular sieve extrudates at 25 "C. Evaluation of the parameter y (y = 0.01 using a macropore tortuosity of 8) confirmed that the l/s-in. pellets, like the lll6-in. extrudates used by Carlson and Dranoff, were under micropore diffusion control. The extracted micropore diffusion coefficient of 3.5 X lo6 s-l compares well with the other authors' value of 4.13 X lo6 s-l. The experimental data and micropore diffusion model prediction are compared in Figure 6. The variation between the values of diffusivity can be easily explained by the virtue of minor differences between lIl6-in. and '/&I. extrudates. This result was interpreted as proof of correct experimental procedure and analysis. Evaluation of Adsorbent Tortuosity. Gas-phase diffusion in the macropores is normally by combination of molecular and Knudsen diffusion mechanisms. The
fi
Ind. Eng. Chem. Res., Vol. 30,No. 6, 1991 1267 I
I
:pot a
! 2oL G O0
0
1oc
A
60C
-
50
100
150
200
250
10
0
TEMPERATURE
Model
(C)
Figure 7. Plot of the apparent tortuosity versus adsorption temperature illustrating the effect of surface diffusion on the variation of tortuosity.
diffusion coefficients may be calculated by using correlations such as the Chapman-Enskog equation and the Knudsen equation. To take into account the random orientation and geometry of the macropores, the empirical concept of tortuosity factor has been adopted. With this model the effective macrospore diffusivity, De, is defined as 4=~ W T M (5) where D,is the combined Knudsen-molecular diffusivity (defined in the Nomenclature section) and rMis the macropore tortuosity factor. Before analysis of the kinetic data can be performed, it is first necessary to determine the value of the tortuosity for Ajax activated carbon. This is done by measuring the adsorption rate for conditions where gas-phase macropore diffusion is the controlling mechanism, that is, in the absence of solid diffusion. With the approach of Schneider and Smith (1968a,b) the presence of a solid diffusion contribution to the total adsorption flux was identified by measuring adsorption rates at increasing temperatures. Experiments were performed using ethane as the adsorbate and 2-mm slab particles of Ajax activated carbon. In this procedure, the experimental data were analyzed by using a macropore diffusion control model (submodel ii). The effective diffusivities obtained were then compared to the calculated value of combined diffusivity, D,,and the apparent tortuosity evaluated by using eq 5. The values of apparent tortuosity were found to rise with increasing adsorption temperature to an asymptotic value of approximately 8 at temperatures of 150 O C and above. The initially low values of tortuosity indicate the presence of solid diffusion flux in parallel with the gas diffusion flux. As the temperature increases, the solid diffusion flux reduces as a consequence of the decreasing adsorbed phase concentration until its contribution to the overall flux is insignificant. This is evidenced by the final region of the constant apparent tortuosity in Figure 7. The measured macropore tortuosity value of eight is used in all subsequent analysis and is considered an adsorbent property independent of adsorbate species. Ethane Adsorption. Micropore Diffusion. Previous work (Mayfield and Do, 1988) at small particle sizes (dp = 512 ccm) showed micropore diffusion to control uptake. The kinetics were characterized by the micropore diffusion time constant D,/R,2, and good agreement between experiment and simulation was found. M i d uptake curves are displayed in Figure 8 for ethane uptake at 10 and 60 "C. Values of the time constant obtained were typically of the order of 1W2s-l. This indicates the much greater rate of adsorption onto carbon when compared to similar values for 4A zeolite which are typically of the order lo6 s-l. The time constant was observed to be essentially independent of the bulk phase concentration, thus ruling out the
30
20
40
TIME (secs)
Figure 8. Experimental versus predicted uptake curves for adsorption of 29.4%ethane in nitrogen onto 512-rm-diameterspherical Ajax activated carbon particles at 10 and 60 "C. w y
2 a
10
3
1
Q
$ 05 to
?i
GO GO
o A
Extrudate ( y = 2 4, ( = I l m m Slab (y-3 8)
1/16
500 0
1000 0
78)
1500 0
TIME (secs)
Figure 9. Effect of particle size and geometry on the adsorption of 29.4% ethane at 30 OC. Table 111. Diffusional Time Constants (8-l) for Ethane Uptake on Ajax Activated Carbon (Mayfield and Do, 1988) C2He concn, mol % 11.0
10
20.7
29.4
1.20 X
temp, "C 30 1.45 X 1.5 X 1.6 X
60
2.3 X lo-*
presence of any surface barrier and supporting the assumption of micropore diffusion control at these conditions. The temperature dependence of the time constant was found to be activated as expected. An Arrhenius plot produced a value of activation energy of 10.1 kJ/mol. Independent determination of the diffusion time constant by gravimetric uptake was performed at 30 O C and 29.4% ethane. The extracted value of 1.6 X 5-l compared favorably with the values obtained by the DAB method. The time constants, measured by DAB, characterizing micropore diffusion of ethane in Ajax activated carbon are summarized in Table 111. Macropore Diffusion. Investigation of the macropore diffusion mechanisms was performed using slab geometry particles because of their long diffusion path length. For particles of 2 and 4 mm the parameter y (defined eq 2) is calculated as 15.2and 60.8, respectively. These values confiim the dominance of macropore diffusion resistance. With data for a range of particle sizes and geometries the value of surface diffusivity for 29.4% ethane was found to be 7.5 X lo6 cm2/s. The fitted data are shown in Figure 9. The wide range of fits using the same diffusion parameters indicates negligible anisotropic effects. A ratio of the solid diffusion flux to the pore diffusion flux (5) of 1.78 was found for the runs plotted in Figure 9. This is an indication of the importance of the solid diffusion mechanism. The solid diffusivity was found to decrease with decreasing adsorbed-phase concentration. This is consistent with observations made by other workers (Higashi, 1963;Yang, 1973). It is noted that the model used to evaluate the solid diffusivity assumes the diffusitivity to be independent of concentration; hence, the
1268 Ind. Eng. Chem. Res., Vol. 30,No. 6, 1991 Table IV. Physical Constants Characterizing Ethane Adsorption onto Ajax Active Carbon temp, "C Dhw const 10 30 60 150 D,, cm2/s 1.31 X lo-' 1.48 x lo-' 1.76 x lo-' 2.44 x 10-1 De, cm2/s 5.07 x 10-3 5.74 x 10-3 6.84 X 9.46 x 10-3 D,, cm2/s 30% 7.40 x 10-5 7.55 x 10-5 7.50 X loa 20% 6.0 X 10" 10% 4.0 x 10-5 1.20 x 10-2 1.60 X 2.30 X 5.04 X lo-' D,/R2, l/s C,, mol/cma 5.54 x 10-8 4.74 x 10-3 3.31 x 10-3 2.02 x 10-8 b, cm3/mol 1.235 X lo6 9.166 X 10' 2.917 X 10' 6.835 X 10' W
200 2.89 X lo-' 1.12 x 10-2
6.85 X 1.24 x 10-3 2.144 X 10'
W
y 10
2 a 3
d Q
0
29 4% E i h o n e (7=2 4 t = l 78)
A
19 5% Ethane ( y = 2 92 ( = 1 73)
E ! Io 4
50 0 TIME (secs)
100 0
Figure 10. Experimental versus predicted uptake curvea for ethane adsorption onto 1/16-in.-diameterAjax activated carbon cylindrical extrudates at 30 "C-effect of concentration.
Y
E
"-Butane 60 C, 21.4% (y=7 55. ( = 2 43)
0
30 C: 20 6% (7=9.2: (=2 99)
G
00 00
gc
A
Y i
LL
-
05
0.5
r/
/ 0 I m m Slob ( y = 9 . 2 , (=2 99) A 2 m m Slob (7=368.( = 2 99)
Y/
o OK
GO
2000
4000 6000 TIME (secs)
I
8000
Figure 11. Experimental versus predicted uptake curves for adsorption of 20% butane at 30 "C onto 1- and 2-mm-long Ajax activated carbon slabs.
functional form of any dependence between the two must be viewed with caution. Adsorption onto 1/16-in. cylindrical extrudatea was found to fall into an intermediate region described by all three diffusion mechanisms. Using the parameters determined at the extremes of macropore and micropore resistance (Table IV), the general model provided good fits at different temperatures and concentrations. The effect of adsorbate concentration is shown in Figure 10. n -Butane Adsorption. An approach similar to that used for ethane was used in the analysis of n-butane adsorption. The mechanisms of micropore diffusion, pore diffusion, and solid diffusion were found to be present. Analysis of experiments in the macropore diffusion control region realized a value of solid diffusivity of 3.325 X lo-&cm2/s for adsorption at 30 "C. This is compared to a literature value of 1.6 X 10+ cm2/s for n-butane diffusion on Spheron 6 carbon black at 30 O C (Rossand Good, 1956). The pore diffusivity was calculated by using the tortuosity value of 8 determined previously. A value of 5 of 3.43 for 20% n-butane adsorption at 30 "C is evidence of the dominant contribution of solid diffusion flux to the overall uptake. Model fits for two slab particle lengths are shown in Figure 11. Variation of the solid diffusion coefficient showed the same trends as observed for ethane adsorption. The effect of temperature on adsorption in 1-mm slabs is shown in Figure 12.
I
00
300 0
100 0 200 0 TIME (secs)
Figure 12. Temperature dependence of n-butane adsorption under the conditions of macropore diffusion control (1-mm slab particles, 20% n-butane). Table V. Physical Constants Characterizing Butane Adsorption onto Ajax Active Carbon temp, "C phys const 10 30 60 150 Do, cm2/s 8.72 X loT2 9.91 X 1.18 X lo-' 1.63 X lo-' De, cm2/s 3.38 X lo4 3.84 X 4.58 X 6.33 X lo4 D,, cmz/s 4.0 X lo* 30% 20% 3.00 X lo* 3.25 X lo* 3.70 X lo* 4.10 X lod 10% 2.5 X lo6 1.15 X 1.54 X D,/R2, l/s 0.90 X 10" 1.00 X 4.92 X C, mol/cm3 5.49 X 4.31 X 3.13 X lo4 b, cmg/mol 8.444 X le 8.358 X le 5.192 X le 2.019 X le Table VI. Physical Constants Characterizing Pentane Adsorption onto Ajax Active Carbon temD. "C phys const 10 30 60 150 D,, cmz/s 7.54 X 10" 8.58 X 1.02 X lo-' 1.44 X lo-' De, cmz/s 2.92 X 3.33 X 3.97 X 5.58 X D,, cm2/s 13% 2.2 x 10-6 1.80 X 2.10 X lod 2.90 X lo* 8% 1.65 X 1.46 X lo-? D,/R2, l/s 0.80 X 10" 0.90 X 10-2 1.05 X 4.23 X C, mol/cm3 4.52 X 3.81 X 2.71 X b, cm3/mol 7.671 X l@ 6.189 X lo6 3.065 X lo6 0.646 X l@ ~~
~~
~~
For very small particles (dp 512 rm) micropore diffusion was found to be dominant. Taking into account the strong solid diffusion flux,the calculated value of y of 0.50 confirms micropore diffusion to be the dominant mechanism at these conditions. Once again all three major mechanisms are important for adsorption in 1/16-in.cylindrical particles. The extracted kinetic parameters are summarized in Table V. n -Pentane Adsorption. Adsorption of n-pentane was found to be characterized by the same mechanisms and trends aa those observed for both ethane and n-butane adsorption. The relevant transport parameters are summarized in Table VI. The effect of particle size and geometry can be observed in Figure 13. Good fits are obtained over the range of conditions. The value of the parameter [ of 4.5 shows the influence of solid diffusion to be strong even at relatively
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1269 W
y 1.0
; I a
' 3
n
0.5
/
1/16" Extrudotes (y-14 4. (=457)
0
l m m Slob ( y = 2 2 3, ( = 4 47) 2mm Slab (y=91 4 , ( = 4 57)
V
!
1100 pm Spheres (7=4 37; (=2.89)
A
1000 0 TIME (secs)
2000 0
Figure 13. The effect of particle size and geometry on the adsorption of 8.4% n-pentane at 30 O C . W
I
I
y 1.0
2 a $ -
Nomenclature A = nondimensional adsorbate concentration in macropore = c/c, A, = nondimensional adsorbate concentration in micropore = C,/C,O A, -= average nondimensional micropore concentration =
C,/ qL0 Bi = Blot number (defined in eq 2)
3
2
Acknowledgment Support from Australian Research Council and UQ/ CSIRO collaborative grants is gratefully acknowledged.
LL
00 00
tration. Similar mechanisms were observed for n-butane and n-pentane adsorption. Good agreement between model predictions and experimental data was found over the broad range of conditions studied.
0.5
L
nn " -
00
50 0 100 0 TIME (secs)
150 0
Fwre 14. Influence of temperature on adsorption kinetics of 8.4% n-pentane into l/le-in.-diameterextrudate pellets of Ajax activated carbon.
lower gas-phase concentrations of 8.4%. This is a consequence of the highly nonlinear rectangular isotherm observed for n-pentane, which ensures large adsorbed-phase concentrations even at low gas-phase concentrations. The effect of temperature on adsorption in 1/16-in. cylindrical particles is shown in Figure 14. It is interesting that at 150 OC the global adsorption rate is slower than a t 60 OC. This is an example of the influence of adsorbed-phase concentration on the solid diffusion flux. In this case the decrease in adsorbed concentration dominates any increase in solid diffusivity leading to a slower overall uptake rate. Conclusions A bimodal particle model incorporating the mechanisms of macropore diffusion, solid diffusion, micropore diffusion, and finite intrinsic adsorption rate was derived and used to identify mechanisms present for the adsorption of ethane, butane, and pentane onto the commercially available activated carbon Ajax 976. Experimental data were obtained by using a gravimetric method and the new DAB method. The DAB method was shown to be appropriate for kinetic measurements in activated carbon. Its importance in future multicomponent work was noted. Controlling mass-transfer mechanisms were identified by fitting model predictions to experimental data. An initial experiment to reproduce the results of Carlson and Dranoff (1985) proved the equipment and procedure used to be suitable for the measurement of adsorption kinetics. A macropore tortuosity factor of 8 was determined from ethane adsorption experiments performed a t a number of higher temperatures up to 200 "C. The importance of using a data set covering a wide range of experimental conditions such as temperature, concentration and particle size and geometry was clearly demonstrated. For adsorption of ethane using commercially available l / extrudate pellets the mechanisms of solid, pore, and micropore diffusion were identified as important. The solid diffusion coefficient was found to be concentration dependent and increased with increasing adsorbate concen-
b = Langmuir isotherm parameter (cm3/mol) C = adsorbate concentration in the macropores (mol/cm3of macrovoid) Co = bulk adsorbate concentration (mol/cm3 of gas) C, = adsorbed concentration in particle (mol/cms of microsphere) = mean adsorbed concentration within particle (mol/cm3 of microsphere) CrO= mean equilibrium particle concentration (mol/cm3of microsphere) C, = Langmuir isotherm parameter (mol/cm3of microsphere) D, = combined straight pore diffusivity = (l/D,o~ + l/D&' (Cm2/s) De = effective macropore diffusivity (D, = CMDJTM) (cmz/s) Dk = Knudsen diffusitivity (cm2/s) DMOL = molecular diffusivity (cm2/s) Dp = pore diffusivity based on void area (Dp = D e / e ~(cm2/s) ) D, = solid diffusivity (cmz/s) D, = micropore diffusion coefficient (cm2/s) k , = intrinsic adsorption rate constant (cm3/mol e) kd = intrinsic desorption rate constant (8-l) kM = external film diffusion mass-transfer coefficient (cm/s) qst = isosteric heat of adsorption (kcal/mol K) r = radial coordinate within macropores (cm) r, = radial coordinate with micropores (cm) R = effective macropore path length (cm) R, = effective micropore path length (cm) R, = universal gas constant (kcal/mol K) S, = specific surface area (m2/g) t = time (s) T = absolute temperature (K) x = nondimensional radial coordinate in macropores = r / R x, = nondimensional radial coordinate in micropores = r,,/Rfi
e,
Greek Symbols y = model parameter defined in eq 2 5 = model parameter defined in eq 2 CM =
macropore porosity = micropore porosity B = model parameter defined in eq 2 X = model parameter defined in eq 2 9 = model parameter defined in eq 2 pp = particle density (g/cm3 of particle) ps = true solid density (g/cm3 of solid) u1 = model parameter defined in eq 2 uz = model parameter defined in eq 2 T = nondimensional time defined in eq 2 rM= macropore tortuosity 6,
Literature Cited Carlson, N. W.; Dranoff, J. S. On the Adsorption of Ethane on 4A Zeolite Pellets. Znd. Eng. Chem. Process Des. Deu. 1985,!24,1300. Carlson, N. W.; Dranoff, J. S. Competitive Adsorption of Methane and Ethane on 4A Zeolite. h o c . Second Eng. Found. Conf. on
Znd. Eng. Chem. Res. 1991,30, 1270-1280
1270
Fundamentals of Adsorption; Santa Barbara, CA, May 4-9,1986. Gray, P. G.; Do, D, D. Adsorption and Desorption of Gaseous Sorbates on a Bidisparsed Particle with Freundlich Isotherm-Part II. Experimental Study of Sulphur Dioxide Sorption on Activated Carbon Particles of Various Geometries. Gas Sep. Purif. 1989,3, 210. Higashi, K.; Ito, H.; Oishi, J. Surface Diffusion Phenomena in Gaseous Diffusion (I). Surface Diffusion of Pure Gas. J. At. Energy SOC.Jpn. 1963,5, 846. Kondis, E. F.; Dranoff, J. S. Kinetics of Isothermal Sorption of Ethane on 4A Molecular Sieve Pellets Znd. Eng. Chem. Process Des. Dev. 1971, 10, 108. Kuro-oka, M.; Suzuki, M.; Nitta, T.; Katayama, T. Adsorption Isotherms of Hydrocarbons and C02on Activated Carbon Fibre. J. Chem. Eng. Jpn. 1984, 17, 588. Masamune, S.; Smith, J. M. Adsorption of Ethyl Alcohol on Silica Gel. AZChE J. 1966, 11, 41. Mayfeld, P. L. J.; Do, D. D. Adsorption of Methane and Ethane onto Activated Carbon using a Differential Adsorption Bed. Proc. Chemeca '88; Sydney, Aug 1988. Mayfield, P. L. J.; Do, D. D. Adsorption of Ethane, Butane and Pentane onto Activated Carbon using a Differential Adsorption
Bed. Znt. Symp. Gas Sep. Technol.; Antwerp, Sept 10-15,1989. Pame. H. K.: Studervant. G. A.: Leland. T. W..Znd. EM. - Chem. Fundam. 1968, 7, 363. Peel. R. G.: Benedek. A.: Crowe. C. M. A Branched Pore Kinetic Model for Activated Carbon Adsorption. AZChE J . 1981,27,26. Ross,J. W.; Good,R. J. Adsorption and Surface Diffusion of n-Butane on Spheron 6 (2700 "C) Carbon Black. J. Phys. Chem. 1966, 60, 1167. Schneider, P.; Smith, J. M. Adsorption Rate Constanta from Chromatography. AZChE J. 1968a, 14,762. Schneider, P.; Smith, J. M. Chromatographic Study of Surface Diffusion. AZChE J. 196813, 14,886. Villadsen, J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation; Prentice-Hall, NJ, 1978. Wicke, E.; Kallenbach, R. Kolloid 2. 1941, 97, 135. Yang, R. T.; Fenn, J. B.; Haller, G. L. Modification to the Higashi Model for Surface Diffusion. AZChE. J. 1973, 19, 1052. Yucel, H.; Ruthven, D. M. Diffusion in 4A Zeolite. J. Chem. SOC., Faraday Trans. 1980, 76,60. '
Received for review January 4, 1990 Accepted January 21,1991
Liquid Distribution in Trickle Beds. An Experimental Study Using Computer-Assisted Tomography Pierre G. Lutran and Ka M. Ng* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003
Edward P. Delikat Mobil Research and Development Corporation, P.O. Box 1026, Princeton, New Jersey 08540
Liquid distribution in trickle beds with a quiescent gaseous phase was visualized by using computer-assisted tomography (CAT). The model system was made up of a column packed with uniform, nonporous glass spheres, distilled water, or a mixture of water and ethanol for a lower surface tension. Flow patterns at the bed scale were recorded as a function of various parameters-liquid flow rate, the size of the particles, the type of liquid inlet distributor used, and surface tension. The flow pattern was shown to depend strongly on whether the bed had been prewetted by flooding the column with liquid or was initially dry. Furthermore, the flow pattern a t a given liquid flow rate depended on whether it was obtained by decreasing or increasing the liquid flow rate to the present state.
Introduction Trickle beds can be defined as a fixed bed of catalyst particles, contacted by a gas-liquid, two-phase flow. The flow can be cocurrent (downflow or upflow) or countercurrent. Because of the absence of flooding, cocurrent downflow is the most common mode of operation in industry. Trickle-bed reactors are used primarily in the petroleum industry for hydrocracking, hydrodesulfurization, and hydrodenitrogenation. It is estimated that a significant fraction of the petroleum processed in a refinery passes through a trickle bed in one way or another. In view of its commercial significance, many studies have been performed to understand the performance of trickle beds. Of special interest is a better understanding of the distribution of the gaseous and liquid phases, for it controls other transport processes and thus the overall reactor performance. Phase distribution at the reactor scale is expressed in the form of various flow regimes-trickling, pulsing, bubble, and spray flows (Weekman and Myers, 1964; Sato et al., 1973; Charpentier and Favier, 1975; Ng, 1986; Ng and Chu, 1987). Most common in practice is trickling flow that occurs at moderate liquid and gas flow rates. In this regime, the liquid flows down the bed from particle to particle on the surfaces of the packings while the gas travels in the interstitial void space. The trickling regime can be further divided into two regimes. At suf0888-588519112630- 1270$02.50/0
ficiently low liquid flow rates, a fraction of the packings remain unwetted. This is the partial wetting trickling regime. If the liquid flow rate is increased, the partial wetting regime changes to complete wetting trickling regime in which the packings are totally wetted by liquid. In the trickling regime, some interesting flow features at the particle scale can he identified. The liquid holdup comprises films, rivulets, pendular structures, liquid pockets, and filaments (Figure 1). Films and rivulets are associated with a single particle, while other flow features involve two or more particles. A rivulet is a liquid stream flowing over the surface of a particle and can result from the splitting of a liquid film on the surface of a catalytic particle. The presence of liquid pockets and pendular structures is due to capillary force. While a liquid pocket extends over several pore chambers, a pendular structure resides at the contact point of two pellets. The shape of a liquid pocket is random and depends on the configuration of the packings at a given location within the bed. Filaments are liquid streams that flow down the bed in the channels between the particles. The lateral width of a filament can extend over more than one pore chamber. A filament can be viewed as a continuous string of liquid pockets. The relative amounts of these features are expected to vary with the gas and liquid flow rates, surface tension, wettability, the gas and liquid inlet distributors used,and the size and shape of the packings, among other 0 1991 American Chemical Society
