The industry widely uses membrane gas separation as it

presents many advantages over other methods, such as

cryogenic distillation or adsorption [1]. In particular, the

economic efficiency of the method has been proven in natural

gas treatment [2, 3]. The main advantage is that membrane gas

separation does not involve a phase change, leading to less

energy consumption than cryogenic distillation [4]. On the

other hand, cryogenic distillation has about 90 % higher

energy consumption than membrane gas separation processes

The predicted selectivity is used in a countercurrent

model, which is solved with a finite element approach. It is

more efficient than solving differential equations to calculate

permeate mole fraction values than experimentally obtained

values from the literature [16]. Case Study 1 compares an

asymmetric high-flux membrane's values by Pan et al. that

separates helium from methane [17]. The second case study

Abstract: - Gas separation polymeric membranes have gained significant attention in various industries, including gas

processing, petrochemicals, and environmental applications. Accurately predicting the permeance of these membranes is

crucial for optimizing their design and performance. This paper presented a numerical prediction model for the permeance

of a binary gas mixture under various process conditions, using only algebraic equations to minimize the calculation effort.

The model considers input parameters such as feed and permeate flow rates, feed pressure, feed and permeate mole fraction,

and membrane area. It demonstrates the behavior of permeance and selectivity in this study. The study also presented two

case studies that utilize predicted selectivity to model counter-current flow and compare the results with experimental data

from the literature. The first case study involves recovering helium from natural gas using an asymmetric high-flux

membrane. The second case study separates air using nano-porous carbon as the membrane material. The numerical

analysis successfully accurately predicted the permeance of gas separation polymeric membranes. The model accounted

Key-words: - Permeance, Numerical Modeling, Membrane Gas Separation.

Received: March 12, 2024. Revised: August 5, 2024. Accepted: September 8, 2024. Published: October 9, 2024.

1. Introduction

2. Numerical Model

side at the feed inlet and the reject outlet, equations 5 and 6.

On the low-pressure side, partial pressure is required at the

permeate outlet, equation 7.

P2, A's partial pressure at the reject outlet, and P3, A's partial

pressure on the permeate side.

and LF and equations 1 and 2, the reject concentration xR

needed in equation 9, can be calculated via the component

balance. The calculation of the partial pressures of

component B follows the same scheme; since this model

deals only with binary gas mixtures, the concentration of B in

the feed is defined by 1 – xF, and so on for permeate and

WITH THE DEVELOPED MATHEMATICAL MODEL

gas. Helium-rich natural gas consists of up to 4 % Helium

[20]. This case study deals with separating a binary

mixture of helium and methane. The other components of

natural gas are not considered in the simulation. The

selectivity is first predicted and then used as input in a

countercurrent model. The numerically calculated

permeate mole fraction values obtained by the developed

mathematical model are compared with the generated

values from Pan et al. [17]. The developed model predicts

the selectivity with 66.4 and uses these values as input in

kPa because on the permeate side, 1 atmosphere is

data quite well. However, in the end (at low xR values),

the experimental data are slightly higher than those

calculated with the developed mathematical model. A

comparison is shown in Table II.

Fig. 5. The permeance of A and B over feed pressure, with

with xF=0.209, LF=1×106, θ=0.4, Am=6.9×108 cm2, and

The calculation assumes that the feed mole fraction of O2

and N2 are 0.198 and 0.802, respectively. Thus, all other

components usually present in the air are neglected in the

simulation. The experiment is carried out by Merrit et al. at a

3.3 Case Study II: Air separation

Fig. 7. The selectivity is predicted with a stage cut of 0.23,

a permeate mole fraction of 0.986, a pressure ratio of 0.05, and

a feed mole fraction of 0.6. The solid line is the developed

mathematical model's solution, and the triangles are the

reference values [17].

REFERENCE VALUES.

Fig. 8. Results of Case Study II. The triangles refer to the

experimentally obtained permeate mole fractions by Merrit et

al. [18].

The comparison in the Case Studies shows that the

developed model calculates permeate mole fractions

pressure compensates better for the assumption of

and selectivity was investigated by changing the feed flow rate

and pressure. The results show that increasing the feed flow

rate leads to a linear increase in permeance. The ratio between

the two permeances remains constant, which results in a

constant selectivity. This behavior is expected, as selectivity

is assumed to be a material property of the membrane and

should not be influenced by the feed flow rate. A change in

the feed pressure leads to a potential behavior of both

permeances and selectivity. The selectivity decreases with

increasing feed pressure. The examination of equations 13 and

14 shows a 1/∆p relationship that leads to the observed

mixtures. However, dealing with multi-component mixtures

for industrial applications would be interesting because most

gas streams consist of more than two components. Therefore,

extending this model to a multi-component mixture would be

meaningful. Also possible would be a coupling of different

mathematical models, like the thermodynamic model from

Lee and coworkers [12] or the temperature dependency model

of Prabhakar et al. [13], to improve the accuracy and scope of

the mathematical models.