Characteristic mixed volume element for compressible two-phase displacement in porous media

Abstract

Numerical simulation of a two-phase compressible displacement problem is considered in this paper, modelled by a nonlinear system of PDEs. Considering the characters of mathematical model, we present an efficient combination algorithm of the method of characteristics (MOC) and mixed finite volume element (MFVE). The MFVE is used for computing the pressure, Darcy velocity and the saturation. Furthermore, the saturation equation is convection-dominated. MOC eliminates numerical dispersion and nonphysical oscillation, and computes the values at the sharp fronts well. An MFVE-MOC is formed for the saturation. An optimal error estimates in l2 norm is concluded. Finally, numerical examples are given to show the effectiveness and practicability. The composite scheme possibly solves this actual problem well.

KEYWORDS:

• Compressible miscible displacement
• characteristic mixed finite volume element (CMFVE)
• local conservation of mass
• error estimates
• numerical examples

2010 Mathematics Subject Classifications:

• 65N12
• 65N30

Acknowledgements

The authors would like to thank the reviewers for their helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11871312] and Natural Science Foundation of Shandong Province (grant number ZR2016AM08).