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New linear driving force correlation spanning long and short cycle time pressure swing adsorption processes

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Abstract

A simple, semi-empirical, generalized expression was developed for the LDF mass transfer coefficient k as a function of the half cycle time θ c that encompasses and transitions between the well-known regions governed by the long cycle time constant Glueckauf k and the short cycle time dependent k. This new expression can be used to estimate k = f(θ c ) for any system, irrespective of the loading and irrespective of θ c , no matter if k is in the cycle time dependent region or not. A three times wider transition region between the Glueckauf k and the cycle time dependent k was also established, with the Glueckauf LDF limit now valid for θ c  > 0.3 and the short cycle time limit now valid for θ c  < 0.01. When evaluating this region for several adsorbate-adsorbent systems, the minimum Glueckauf θ c spanned three orders of magnitude from thousands of seconds to just a few seconds, indicating a cycle time dependent k is not necessarily limited to what is normally considered a short cycle time. For virtually any θ c less than this minimum Glueckauf θ c , this new first-of-its-kind expression can be used to readily provide an accurate value of k = f(θ c ). Since the widely accepted half cycle time concept does not apply to the actual simulation of a multi-step, unequal step time, pressure swing adsorption process, the value of k = f(θ c ) from this new expression can be based on either the shortest cycle step in the cycle or a different value of k = f(θ c ) for each cycle step time in the cycle, with validity confirmed either by experiment or by process simulation using the exact solution to the pore diffusion equation.

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Abbreviations

a(q):

Function of the amount adsorbed in the particle that depends on the type of diffusion process and defined by Eq. (5) or (7)

b(q):

Function of the amount adsorbed in the particle that depends on the type of diffusion process and defined by Eq. (6) or (8)

b :

Affinity parameter in the Langmuir adsorption isotherm, kPa−1

D :

Diffusivity, m2 s−1

D M,g :

Macropore diffusivity, m2 s−1

D m,s :

Micropore diffusivity, m2 s−1

K :

Extracted LDF mass transfer coefficient, s−1

k′:

Glueckauf LDF mass transfer coefficient, s−1

k″:

Alpay and Scott LDF mass transfer coefficient, s−1

P :

Partial pressure of the adsorbate, kPa

P o :

Partial pressure of the adsorbate outside the pellet or crystal, kPa

P o,i :

Initial partial pressure of the adsorbate outside the pellet or crystal, kPa

Q :

Amount adsorbed in the particle, mol kg−1

\(\bar{q}\) :

Volume average amount adsorbed in the particle, mol kg−1

q i :

Initial amount adsorbed in the particle, mol kg−1

q * :

Amount adsorbed in the particle in equilibrium with P o , mol kg−1

q s :

Saturation capacity parameter in the Langmuir adsorption isotherm, mol kg−1

r :

Distance from the center of the particle (pellet or crystal), m

R :

Radius of spherical particle, m

R g :

Ideal gas constant, 8.314 J mol−1 K−1

R p :

Radius of spherical pellet, m

R c :

Radius of spherical crystal, m

t :

Time, s

t c :

Half cycle time, s

T :

Temperature of the particle, K

∆P :

Amplitude of the pressure perturbation, kPa

ε p :

Pellet porosity

ρ p :

Pellet density, kg m−3

θ c :

Dimensionless half cycle time

ϑ(q):

Function that represents dependency of diffusivity on the amount adsorbed in the particle and equal to b(q)/a(q)

\(\psi \left( {\sqrt {\theta_{c} } } \right)\) :

Correction factor as a function of dimensionless half cycle time, defined by Eq. (26)

\(\phi \left( {\sqrt {\theta_{c} } } \right)\) :

Fermi–Dirac function defined by Eq. (27)

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Funding

The authors gratefully acknowledge financial support provided in part by the DOE National Energy Technology Laboratory, DOE Award Number DE-FE0007639, in part by the SAGE Center at the University of South Carolina, and in part by the Process Science and Technology Center, a consortium composed of the University of Texas at Austin, the University of South Carolina, and the Texas A&M University.

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Authors and Affiliations

  1. Department of Chemical Engineering, University of South Carolina, Columbia, SC, 29208, USA

    Mohammad I. Hossain, Armin D. Ebner & James A. Ritter

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  1. Mohammad I. Hossain
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  2. Armin D. Ebner
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  3. James A. Ritter
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Correspondence to James A. Ritter.

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Hossain, M.I., Ebner, A.D. & Ritter, J.A. New linear driving force correlation spanning long and short cycle time pressure swing adsorption processes. Adsorption 22, 939–950 (2016). https://doi.org/10.1007/s10450-016-9801-1

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  • DOI: https://doi.org/10.1007/s10450-016-9801-1

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