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Mathematical modeling and optimization of gas transport through carbon molecular sieve membrane and determining the model parameters using genetic algorithm

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Abstract

Permeation of N2, CH4, O2 and CO2 molecules through a carbon molecular sieve (CMS) was studied over a wide range of pressures using the transport mechanism. For proper utilization of carbon molecular sieve membrane in gas separation processes, prediction of behavior and recognition of proper gas transport mechanism as well as finding effective permeation parameters are necessary. A mathematical model of the gas transfer through a CMS membrane was developed using genetic algorithm (GA). Numerous types of mechanisms have been proposed so far for gas transport through capillaries, namely: Knudsen, slip and viscous flow. Moreover, surface flow usually occurs in parallel with other transport mechanisms such as Knudsen or viscous flow. The experimental data of gas permeation in CMS membranes and an appropriate genetic algorithm-based optimization method were used to establish the transport parameters. A GA, an optimization procedure based on the theory of evolution, was compared with non-linear regression for the ability of these two algorithms to fit the coefficients of Poultry growth models. It was found that GA approach could be more capable to define the parameters of permeation equation than non-linear regression. The model in most cases showed a good agreement between the predicted and measured values of the permeability.

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Abbreviations

r :

Pore radius

λ :

Mean free path

T :

Temperature in K

R :

Constant of gas

N :

Number of Avogadro

d :

Gas molecules collision diameter in m

\(\overline{p}\) :

Membrane average pressure as \(\overline{p}\) = (p f  − p p )/2

p f :

Feed pressures in Pa

p p :

Permeate pressures in Pa

N su :

Surface flow of membrane

A p :

Pores cross sectional area in m2

ρ app :

Membrane density in kg/m3

τ :

Factor of tortuosity

L :

Pore length in m

CR:

Resistance coefficient in kg/m2.s

S s :

Specific surface area of the solid on which the adsorbed molecules are mobile in m2

x :

Adsorbed amount per unit weight of the membrane in kmol/kg

N(r):

Function of normal pore size distribution in m−1

\(\bar{r}\) :

Mean pore radius in m

n :

Total pores number on a membrane surface

σ :

The standard deviation of pore size distribution in m

q :

Concentration of the adsorbed phase

q s :

Saturation capacity

b :

Affinity coefficient

J total :

Total gas flow

N g :

Flow in the gas phase

N Su :

Surface flow

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Authors and Affiliations

  1. Department of Chemical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Vahid Pirouzfar

  2. Faculty of Chemical Engineering, Tarbiat Modares University, 14115-114, Tehran, Iran

    Mohammad Reza Omidkhah

Authors
  1. Vahid Pirouzfar
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  2. Mohammad Reza Omidkhah
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Correspondence to Vahid Pirouzfar.

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Pirouzfar, V., Omidkhah, M.R. Mathematical modeling and optimization of gas transport through carbon molecular sieve membrane and determining the model parameters using genetic algorithm. Iran Polym J 25, 203–212 (2016). https://doi.org/10.1007/s13726-016-0414-z

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  • DOI: https://doi.org/10.1007/s13726-016-0414-z

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