# Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves

## Abstract

In the given article, the main thermodynamic aspects of the issue of modeling diffusion transfer in molecular sieves have been formulated. Dissipation function is used as a basic notion. The differential equation, connecting volume flow with the change of the concentration of catchable component has been derived. As a result, the expression for changing the concentration of the catchable component and the coefficient of membrane detecting has been received. As well, the system approach to describing the process of gases separation in ultra porous membranes has been realized and micro and meso-levels of mathematical modeling have been distinguished. The non-ideality of the shared system is primarily taken into consideration at the micro-level and the departure from the diffusion law of Fick has been taken into account. The calculation method of selectivity considering fractal structure of membranes has been developed at the meso level. The calculation algorithm and its software implementation have been suggested.

- Authors:

- South Kazakhstan State University, 5, Tauke Khan Avenue, 160012 Shymkent (Kazakhstan)

- Publication Date:

- OSTI Identifier:
- 22391666

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1660; Journal Issue: 1; Conference: ICoMEIA 2014: International Conference on Mathematics, Engineering and Industrial Applications 2014, Penang (Malaysia), 28-30 May 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABUNDANCE; ALGORITHMS; CALCULATION METHODS; COMPUTER CODES; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; DIFFERENTIAL EQUATIONS; DIFFUSION; FRACTALS; MATHEMATICAL MODELS; MEMBRANES; MIXTURES; MOLECULAR SIEVES; POROUS MATERIALS; SEPARATION PROCESSES

### Citation Formats

```
Umarova, Zhanat, Botayeva, Saule, Yegenova, Aliya, and Usenova, Aisaule.
```*Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves*. United States: N. p., 2015.
Web. doi:10.1063/1.4915753.

```
Umarova, Zhanat, Botayeva, Saule, Yegenova, Aliya, & Usenova, Aisaule.
```*Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves*. United States. doi:10.1063/1.4915753.

```
Umarova, Zhanat, Botayeva, Saule, Yegenova, Aliya, and Usenova, Aisaule. Fri .
"Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves". United States. doi:10.1063/1.4915753.
```

```
@article{osti_22391666,
```

title = {Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves},

author = {Umarova, Zhanat and Botayeva, Saule and Yegenova, Aliya and Usenova, Aisaule},

abstractNote = {In the given article, the main thermodynamic aspects of the issue of modeling diffusion transfer in molecular sieves have been formulated. Dissipation function is used as a basic notion. The differential equation, connecting volume flow with the change of the concentration of catchable component has been derived. As a result, the expression for changing the concentration of the catchable component and the coefficient of membrane detecting has been received. As well, the system approach to describing the process of gases separation in ultra porous membranes has been realized and micro and meso-levels of mathematical modeling have been distinguished. The non-ideality of the shared system is primarily taken into consideration at the micro-level and the departure from the diffusion law of Fick has been taken into account. The calculation method of selectivity considering fractal structure of membranes has been developed at the meso level. The calculation algorithm and its software implementation have been suggested.},

doi = {10.1063/1.4915753},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1660,

place = {United States},

year = {2015},

month = {5}

}