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Rate and equilibrium sorption parameters for nitrogen and methane on carbon molecular sieve
Rate and equilibrium sorption parameters for nitrogen and methane on carbon molecular sieve* K. F. Loughlin,
M. M. Hassan,
A. I. Fatehi
and M. Zahur
Depa~ment of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia Sorption parameters for nitrogen and methane on carbon molecular sieve (CMS) have been obtained using chromatographic, volumetric and gravimetric techniques. The equilibrium parameters - Henry constants, heats of adsorption and Langmuir constants -are consistent with reported literature values. Measurements of adsorption rates using a volumetric apparatus give results inconsistent with the diffusion hypothesis. The phenomena can be explained by the presence of a barrier resistance along with a diffusion mechanism. Analysis of results shows that the resistance measured by the chromatographic method is consistent with the resistance of the combined barrier resistanc~iffusion model. The latter two resistances can only be obtained from the volumetric results. The general equation for additivi~ of resistances of Haynes and Sarma (AIChE J (1973) 19 1043) for breakthrough curves on a chromatogram is modified to account for the barrier resistance. Keywords: carbon molecular sieves; methane; nitrogen; rates of adsorption; overall mass transfer coefficients; barrier resistance; diffusional time constants
Nomenclature Surface area of crystallite (cm’) :p Surface area of macroporous particle (cm*) UP Surface area of crystallite per unit volume of particle (cm-‘) Langmuir constant (cm3 mmol-‘) b Gas-phase concentration (mmol cm-‘) C Crystallite diffusivity (cm* s-‘) D, Dispersion coefficient (cm2 s-‘) DL Macropore diffusivity (cm2 s-‘) Particle diameter (cm) ? Activation energy (kcal mol-‘) .8 Roots of eigencondition (Equation (20)) &I First root of eigencondition -&I0 Limiting heat of adsorption (kcal mol-‘) Barrier mass transfer coefficient (cm s-‘) kr, Chromatographic mass transfer rate (s-‘) k, Film mass transfer coefficient (cm s-‘) kr Equilibrium constant (dimensionless) 4 K,.,, Pre-exponential factor in the vant Hoff equation (dimensionless) Overall mass transfer coefficient (cm s-‘) k, Mass transfer coefficient (s-l) Volumetric slope (Equation (11)) (s-‘) I
L
Chromatographic column length (cm)
N
Molar flux (mol cm-2 s-‘) Number of particles Number of crystallites per particle Sorbate concentration in particle (mmol cm-3) Sorbate concentration in crystallite (mm01 cmm3) Particle equilibrium surface concentration (mm01 cmW3) Saturated sorbate concentration in particle (mm01 cme3) Crystallite surface concentration in equilibrium with gas phase (mmol cmv3) Interfacial crystallite concentration (mm01 cmp3) Radial coordinate (cm) Radius of crystallite (cm) Gas constant Outer radius of particle (cm) Temperature (K) Time (s) Total fractional uptake (Equation (21)) Internal heat of adsorption (kcal mol-‘) Free volume of gas phase (cell) (cm3) Volume of crystallite (cm”)
4 hr, 4
Q 4* 4s
Q* Qi r ; Rr T t
u -AU, V v,
cont. *Based on a paper presented at the Annual Meeting of the AIChE, Miami Beach, Florida, USA, November 2-6, 1992. 09#-4214/93/040264-10 @ 1993 Butterworth- Heinemann Ltd
264
Gas Separation & Purification 1993 Vol 7 No 4
Sorption parameters for N2 and CH, on C&E: VP Volume of particle (cm’) V, Total volume of solid phase (cm’) V Interstitial velocity in packed beds (cm s-‘) Greek letters a cp L 5 CL D
WV&) Particle voidage Column voidage rckBID, First moment of chromatogram Second moment of chromatogram
Subscripts B
Barrier resistance
K.F. Lough/in et at.
Chromatographic Crystallite Film f Initial L Longitudinal n th term in series ;1 Zero coverage, time zero Overall pre-exponential OS PYPO Particle S Saturation Solid phase S S OveraIl V Volumetric 1 First 03 Infinite time
C C
Introduction
Theory
The design of adsorption columns or pressure swing adsorption (PSA) processes requires a priori knowledge of the equilibrium and kinetic data for each sorbatesorbent system. In column design, the most frequent isotherm emptoyed is the Langmuir isotherm because of its simplicity. The parameters for this isotherm are the Henry constant and the saturation loading; frequently, the constants have to be adjusted from the ‘intrinsic’ values to fit the experimental data. The kinetic data required are the column dispersion characteristics and the rate of particle uptake, the latter being commonly characterized by film, macropore or micropore diffusion or combinations of these. With these data available, the design of adsorption columns or PSA processes can be implemented providing the appropriate model is employed. In this study, adsorption data for nitrogen and methane on carbon molecular sieve (CMS) are reported. Unlike zeolites, which tend to be somewhat reproducible, different batches of CMS tend to have different adsorption parameters, particularly kinetic. Equilibrium data for the adsorption of nitrogen and methane on CMS are limitedId. Kinetic data on CMS particles must account for the complex nature of the particles. They are generally considered to be composed of microporous particles within a macroporous matrix, with the size of the microporous particles indeterminate at present. Consequently, transport through the macropores must occur before any significant micropore transport arises. This dual transport problem was first solved by Ruckenstein et al.’ for the constant pressure system and simplified by Lee6 who also derived the constant volume solution (see also Karger and Ruthven7). The uptake of nitrogen and oxygen on CMS particles was measured by Ruthven et al.‘, and they observed an initial significant rapid equilibrium adsorption on the macropores. They expanded Lee’s solution to allow for this sudden initial uptake of 15 to 20%, characteristic of rapid adsorption on the macropore walls followed by slow diffusion in the micropores. Dominguez et al* measured the rate of adsorption of oxygen and nitrogen mixtures on CMS and reported that the uptake did not follow a diffusion law but rather a mass action rate law based on Langmuir kinetics. This paper reports expe~mental results for the rates of sorption of methane and nitrogen on CMS, which are significantly different from those reported above.
Chromatographic and volumetric methods were used to obtain the equilibrium and rate data, and a gravimetric method was used to obtain equilibrium data only. The equilibrium constant Kp is derived from the first moment expression
(1) and correlated by vant EIof?‘s equation Kp = Kpoexp( -AU,/RT)
(2)
where AU, is related to the limiting heat of sorption AH0 by AU, = AH, + RT
(3)
Vol~etrically and gravimet~cally, small incremental steps were made initially into a clean CMS sample to measure the equilib~um parameters &, . Subsequently, the adsorption isotherms at 298 K were measured volumetrically to a pressure of I MPa and correlated using Langmuir’s isotherm: bC 4 -_=_ l+bC 45
(4)
In the limit as C tends to zero, $ should equal bq,, but this is only true if the isotherm 1s truly Langmuir. Chromatographically, the rate constants are obtained from the second moment equation
(5) where kcis the desired rate parameter. It does not indicate the sorption mechanism, but is frequently related to the film, micropore or macropore regime using appropriate experimental and/or theoretical calculation techniques. The intrinsic mechanism can be deduced from volumetric or gravimetric experiments involving small step changes provided an appropriate model is used. Experimental volumetric measurements, when plotted as uptake versus time on a semi-logarithmic basis, proved linear for the initial 90% uptake, curved in the intermediate region, and became linear again at longer times.
Gas Separation
& Purification
1993 Vol 7 No 4
265
Sorption
parameters 10
References Ruthven, D.M., Raghavan, N.S. and Hassan, M.M. Adsorption and diffusion of N, and 0, in carbon molecular sieve Chem Eng Sci (1986) 41 132551332 Ackley, M. and Yang, R.T. Kinetic separation by pressure swing adsorption: method of characteristics AIChE J (1990) 36 1229-1238 Kapour, A. and Yang, R.T. Kinetic separation of methane-carbon dioxide mixtures by adsorption on molecular sieve carbon Chem Eng Sci (1989) 44 1723-1733 Chihara, K., Suzuki, M. and Kawazoe, K. Adsorption rate on molecular sieving carbon by chromatography AIChE J (1978) 24 237-246 Ruckenstein, E., Vaidyanathan, A.S. and Youngquist, G.R. Sorption by solids with bidisperse pore structures Chem Eng Sci (1971)
26 1305-1318 Lee, L.K. Kinetics of sorption in biporous adsorbent particles AIChE J (1978) 24 531-533 Karger, J. and Ruthven, D.M. Diffusion in Zeolites Wiley, New
York, USA (1992) Dominguez, J.A., Psaras, D. and LaCava, A.I. Langmuir kinetics
as an accurate simulation of the rate of adsorption of oxygen -_ and nitrogen molecules on non-Fickian carbon molecular sieves AZChE Symp Ser (1988) 84 (264) 73-82 Crank, J. The Mathematics of Diffusion
London, UK (1956)
Oxford University, Press,
for N2 and CH, on CMS:
K.F. Loughlin
et al.
J. and Caro, J.J. Interpretation and correlation of zeolitic diffusivities obtained from nuclear magnetic resonance and sorption experiments J Chem Sot Faraday Trans 1(1977) 73
Karger,
1363-1376
11 Karger, J. and Pfeifer, H Nuclear magnetic resonance measurement of mass transfer in molecular sieve crystallites J Chem Sot Faraday Truns I(l991)
87 (13) 1989-1996
12 Huang, T. and Li, K. Ion-exchange kinetics for calcium radiotracer in a batch system Ind Eng Chem Fundam (1973) 12 (1) 50-55 13 Zahur M. Air separation on carbon molecular sieves, 4A and 5A zeolites by pressure swing adsorption MS Thesis KFUPM, Dhahran (1991) 14 Abdul-Rehman, H.B. Equilibrium adsorption of light alkanes and their mixtures at high pressure on 5A, 13X and SR-115 adsorbents MS Thesis KFUPM, Dhahran (1988) 15 Lmghlin, K.F. Diffusion in 5A zeolites PhD Thesis UNB Fredericton, NB (1970) 16 Fatehi, A& Laughlin, K.F. and Hassan, M.M. Separation of methane-nitrogen mixtures using carbon molecular sieve by pressure swing adsorption Gas Sep Purif (to be submitted) 17 Haynes, H.W. and Sarma, P.N. A model for the application of gas chromatography to measurements of diffusion inbidisperse St&ture catalvst AIChE J (1973) 19 1043-1046 18 Ruthven 6.M. Principle‘s of Adsorption and Adsorption Processes Wiley, New York, USA (1984) 19 Breck, D.W. Zeolite Molecular Sieves Wiley, New York, USA (1974)
Gas Separation & Purification 1993 Vol 7 No 4 273
M. M. Hassan,
A. I. Fatehi
and M. Zahur
Depa~ment of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia Sorption parameters for nitrogen and methane on carbon molecular sieve (CMS) have been obtained using chromatographic, volumetric and gravimetric techniques. The equilibrium parameters - Henry constants, heats of adsorption and Langmuir constants -are consistent with reported literature values. Measurements of adsorption rates using a volumetric apparatus give results inconsistent with the diffusion hypothesis. The phenomena can be explained by the presence of a barrier resistance along with a diffusion mechanism. Analysis of results shows that the resistance measured by the chromatographic method is consistent with the resistance of the combined barrier resistanc~iffusion model. The latter two resistances can only be obtained from the volumetric results. The general equation for additivi~ of resistances of Haynes and Sarma (AIChE J (1973) 19 1043) for breakthrough curves on a chromatogram is modified to account for the barrier resistance. Keywords: carbon molecular sieves; methane; nitrogen; rates of adsorption; overall mass transfer coefficients; barrier resistance; diffusional time constants
Nomenclature Surface area of crystallite (cm’) :p Surface area of macroporous particle (cm*) UP Surface area of crystallite per unit volume of particle (cm-‘) Langmuir constant (cm3 mmol-‘) b Gas-phase concentration (mmol cm-‘) C Crystallite diffusivity (cm* s-‘) D, Dispersion coefficient (cm2 s-‘) DL Macropore diffusivity (cm2 s-‘) Particle diameter (cm) ? Activation energy (kcal mol-‘) .8 Roots of eigencondition (Equation (20)) &I First root of eigencondition -&I0 Limiting heat of adsorption (kcal mol-‘) Barrier mass transfer coefficient (cm s-‘) kr, Chromatographic mass transfer rate (s-‘) k, Film mass transfer coefficient (cm s-‘) kr Equilibrium constant (dimensionless) 4 K,.,, Pre-exponential factor in the vant Hoff equation (dimensionless) Overall mass transfer coefficient (cm s-‘) k, Mass transfer coefficient (s-l) Volumetric slope (Equation (11)) (s-‘) I
L
Chromatographic column length (cm)
N
Molar flux (mol cm-2 s-‘) Number of particles Number of crystallites per particle Sorbate concentration in particle (mmol cm-3) Sorbate concentration in crystallite (mm01 cmm3) Particle equilibrium surface concentration (mm01 cmW3) Saturated sorbate concentration in particle (mm01 cme3) Crystallite surface concentration in equilibrium with gas phase (mmol cmv3) Interfacial crystallite concentration (mm01 cmp3) Radial coordinate (cm) Radius of crystallite (cm) Gas constant Outer radius of particle (cm) Temperature (K) Time (s) Total fractional uptake (Equation (21)) Internal heat of adsorption (kcal mol-‘) Free volume of gas phase (cell) (cm3) Volume of crystallite (cm”)
4 hr, 4
Q 4* 4s
Q* Qi r ; Rr T t
u -AU, V v,
cont. *Based on a paper presented at the Annual Meeting of the AIChE, Miami Beach, Florida, USA, November 2-6, 1992. 09#-4214/93/040264-10 @ 1993 Butterworth- Heinemann Ltd
264
Gas Separation & Purification 1993 Vol 7 No 4
Sorption parameters for N2 and CH, on C&E: VP Volume of particle (cm’) V, Total volume of solid phase (cm’) V Interstitial velocity in packed beds (cm s-‘) Greek letters a cp L 5 CL D
WV&) Particle voidage Column voidage rckBID, First moment of chromatogram Second moment of chromatogram
Subscripts B
Barrier resistance
K.F. Lough/in et at.
Chromatographic Crystallite Film f Initial L Longitudinal n th term in series ;1 Zero coverage, time zero Overall pre-exponential OS PYPO Particle S Saturation Solid phase S S OveraIl V Volumetric 1 First 03 Infinite time
C C
Introduction
Theory
The design of adsorption columns or pressure swing adsorption (PSA) processes requires a priori knowledge of the equilibrium and kinetic data for each sorbatesorbent system. In column design, the most frequent isotherm emptoyed is the Langmuir isotherm because of its simplicity. The parameters for this isotherm are the Henry constant and the saturation loading; frequently, the constants have to be adjusted from the ‘intrinsic’ values to fit the experimental data. The kinetic data required are the column dispersion characteristics and the rate of particle uptake, the latter being commonly characterized by film, macropore or micropore diffusion or combinations of these. With these data available, the design of adsorption columns or PSA processes can be implemented providing the appropriate model is employed. In this study, adsorption data for nitrogen and methane on carbon molecular sieve (CMS) are reported. Unlike zeolites, which tend to be somewhat reproducible, different batches of CMS tend to have different adsorption parameters, particularly kinetic. Equilibrium data for the adsorption of nitrogen and methane on CMS are limitedId. Kinetic data on CMS particles must account for the complex nature of the particles. They are generally considered to be composed of microporous particles within a macroporous matrix, with the size of the microporous particles indeterminate at present. Consequently, transport through the macropores must occur before any significant micropore transport arises. This dual transport problem was first solved by Ruckenstein et al.’ for the constant pressure system and simplified by Lee6 who also derived the constant volume solution (see also Karger and Ruthven7). The uptake of nitrogen and oxygen on CMS particles was measured by Ruthven et al.‘, and they observed an initial significant rapid equilibrium adsorption on the macropores. They expanded Lee’s solution to allow for this sudden initial uptake of 15 to 20%, characteristic of rapid adsorption on the macropore walls followed by slow diffusion in the micropores. Dominguez et al* measured the rate of adsorption of oxygen and nitrogen mixtures on CMS and reported that the uptake did not follow a diffusion law but rather a mass action rate law based on Langmuir kinetics. This paper reports expe~mental results for the rates of sorption of methane and nitrogen on CMS, which are significantly different from those reported above.
Chromatographic and volumetric methods were used to obtain the equilibrium and rate data, and a gravimetric method was used to obtain equilibrium data only. The equilibrium constant Kp is derived from the first moment expression
(1) and correlated by vant EIof?‘s equation Kp = Kpoexp( -AU,/RT)
(2)
where AU, is related to the limiting heat of sorption AH0 by AU, = AH, + RT
(3)
Vol~etrically and gravimet~cally, small incremental steps were made initially into a clean CMS sample to measure the equilib~um parameters &, . Subsequently, the adsorption isotherms at 298 K were measured volumetrically to a pressure of I MPa and correlated using Langmuir’s isotherm: bC 4 -_=_ l+bC 45
(4)
In the limit as C tends to zero, $ should equal bq,, but this is only true if the isotherm 1s truly Langmuir. Chromatographically, the rate constants are obtained from the second moment equation
(5) where kcis the desired rate parameter. It does not indicate the sorption mechanism, but is frequently related to the film, micropore or macropore regime using appropriate experimental and/or theoretical calculation techniques. The intrinsic mechanism can be deduced from volumetric or gravimetric experiments involving small step changes provided an appropriate model is used. Experimental volumetric measurements, when plotted as uptake versus time on a semi-logarithmic basis, proved linear for the initial 90% uptake, curved in the intermediate region, and became linear again at longer times.
Gas Separation
& Purification
1993 Vol 7 No 4
265
Sorption
parameters 10
References Ruthven, D.M., Raghavan, N.S. and Hassan, M.M. Adsorption and diffusion of N, and 0, in carbon molecular sieve Chem Eng Sci (1986) 41 132551332 Ackley, M. and Yang, R.T. Kinetic separation by pressure swing adsorption: method of characteristics AIChE J (1990) 36 1229-1238 Kapour, A. and Yang, R.T. Kinetic separation of methane-carbon dioxide mixtures by adsorption on molecular sieve carbon Chem Eng Sci (1989) 44 1723-1733 Chihara, K., Suzuki, M. and Kawazoe, K. Adsorption rate on molecular sieving carbon by chromatography AIChE J (1978) 24 237-246 Ruckenstein, E., Vaidyanathan, A.S. and Youngquist, G.R. Sorption by solids with bidisperse pore structures Chem Eng Sci (1971)
26 1305-1318 Lee, L.K. Kinetics of sorption in biporous adsorbent particles AIChE J (1978) 24 531-533 Karger, J. and Ruthven, D.M. Diffusion in Zeolites Wiley, New
York, USA (1992) Dominguez, J.A., Psaras, D. and LaCava, A.I. Langmuir kinetics
as an accurate simulation of the rate of adsorption of oxygen -_ and nitrogen molecules on non-Fickian carbon molecular sieves AZChE Symp Ser (1988) 84 (264) 73-82 Crank, J. The Mathematics of Diffusion
London, UK (1956)
Oxford University, Press,
for N2 and CH, on CMS:
K.F. Loughlin
et al.
J. and Caro, J.J. Interpretation and correlation of zeolitic diffusivities obtained from nuclear magnetic resonance and sorption experiments J Chem Sot Faraday Trans 1(1977) 73
Karger,
1363-1376
11 Karger, J. and Pfeifer, H Nuclear magnetic resonance measurement of mass transfer in molecular sieve crystallites J Chem Sot Faraday Truns I(l991)
87 (13) 1989-1996
12 Huang, T. and Li, K. Ion-exchange kinetics for calcium radiotracer in a batch system Ind Eng Chem Fundam (1973) 12 (1) 50-55 13 Zahur M. Air separation on carbon molecular sieves, 4A and 5A zeolites by pressure swing adsorption MS Thesis KFUPM, Dhahran (1991) 14 Abdul-Rehman, H.B. Equilibrium adsorption of light alkanes and their mixtures at high pressure on 5A, 13X and SR-115 adsorbents MS Thesis KFUPM, Dhahran (1988) 15 Lmghlin, K.F. Diffusion in 5A zeolites PhD Thesis UNB Fredericton, NB (1970) 16 Fatehi, A& Laughlin, K.F. and Hassan, M.M. Separation of methane-nitrogen mixtures using carbon molecular sieve by pressure swing adsorption Gas Sep Purif (to be submitted) 17 Haynes, H.W. and Sarma, P.N. A model for the application of gas chromatography to measurements of diffusion inbidisperse St&ture catalvst AIChE J (1973) 19 1043-1046 18 Ruthven 6.M. Principle‘s of Adsorption and Adsorption Processes Wiley, New York, USA (1984) 19 Breck, D.W. Zeolite Molecular Sieves Wiley, New York, USA (1974)
Gas Separation & Purification 1993 Vol 7 No 4 273