# Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification

## Abstract

The paper deals with the numerical solution of a compositional model describing compressible two-phase flow of a mixture composed of several components in porous media with species transfer between the phases. The mathematical model is formulated by means of the extended Darcy's laws for all phases, components continuity equations, constitutive relations, and appropriate initial and boundary conditions. The splitting of components among the phases is described using a new formulation of the local thermodynamic equilibrium which uses volume, temperature, and moles as specification variables. The problem is solved numerically using a combination of the mixed-hybrid finite element method for the total flux discretization and the finite volume method for the discretization of transport equations. A new approach to numerical flux approximation is proposed, which does not require the phase identification and determination of correspondence between the phases on adjacent elements. The time discretization is carried out by the backward Euler method. The resulting large system of nonlinear algebraic equations is solved by the Newton–Raphson iterative method. We provide eight examples of different complexity to show reliability and robustness of our approach.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22314895

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 272; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOUNDARY CONDITIONS; COMPUTERIZED SIMULATION; CONTINUITY EQUATIONS; FINITE ELEMENT METHOD; ITERATIVE METHODS; LTE; MATHEMATICAL MODELS; NONLINEAR PROBLEMS; POROUS MATERIALS; TRANSPORT THEORY; TWO-PHASE FLOW

### Citation Formats

```
Polívka, Ondřej, E-mail: ondrej.polivka@fjfi.cvut.cz, and Mikyška, Jiří, E-mail: jiri.mikyska@fjfi.cvut.cz.
```*Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.04.029.

```
Polívka, Ondřej, E-mail: ondrej.polivka@fjfi.cvut.cz, & Mikyška, Jiří, E-mail: jiri.mikyska@fjfi.cvut.cz.
```*Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification*. United States. doi:10.1016/J.JCP.2014.04.029.

```
Polívka, Ondřej, E-mail: ondrej.polivka@fjfi.cvut.cz, and Mikyška, Jiří, E-mail: jiri.mikyska@fjfi.cvut.cz. Mon .
"Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification". United States.
doi:10.1016/J.JCP.2014.04.029.
```

```
@article{osti_22314895,
```

title = {Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification},

author = {Polívka, Ondřej, E-mail: ondrej.polivka@fjfi.cvut.cz and Mikyška, Jiří, E-mail: jiri.mikyska@fjfi.cvut.cz},

abstractNote = {The paper deals with the numerical solution of a compositional model describing compressible two-phase flow of a mixture composed of several components in porous media with species transfer between the phases. The mathematical model is formulated by means of the extended Darcy's laws for all phases, components continuity equations, constitutive relations, and appropriate initial and boundary conditions. The splitting of components among the phases is described using a new formulation of the local thermodynamic equilibrium which uses volume, temperature, and moles as specification variables. The problem is solved numerically using a combination of the mixed-hybrid finite element method for the total flux discretization and the finite volume method for the discretization of transport equations. A new approach to numerical flux approximation is proposed, which does not require the phase identification and determination of correspondence between the phases on adjacent elements. The time discretization is carried out by the backward Euler method. The resulting large system of nonlinear algebraic equations is solved by the Newton–Raphson iterative method. We provide eight examples of different complexity to show reliability and robustness of our approach.},

doi = {10.1016/J.JCP.2014.04.029},

journal = {Journal of Computational Physics},

number = ,

volume = 272,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}