Hybrid mixed discontinuous Galerkin finite element method for incompressible wormhole propagation problem

TL;DR

This paper introduces a hybrid mixed discontinuous Galerkin finite element method tailored for simulating incompressible wormhole propagation in oil reservoirs, ensuring local mass balance and bounded porosity with proven convergence.

Contribution

A novel combined hybrid mixed finite element and discontinuous Galerkin method for wormhole modeling, with convergence analysis and optimal error estimates.

Findings

Method maintains local mass balance.

Porosity remains bounded during simulation.

Numerical examples confirm theoretical accuracy.

Abstract

Wormhole propagation plays a very important role in the product enhancement of oil and gas reservoir. A new combined hybrid mixed finite element method is proposed to solve incompressible wormhole propagation problem with discontinuous Galerkin finite element procedure, in which, the new hybrid mixed finite element algorithm is established for pressure equation, while the discontinuous Galerkin finite element method is considered for concentration equation, and then the porosity function is computed straightly by the approximate value of the concentration. This new combined method can keep local mass balance, meantime it also keeps the boundedness of the porosity. The convergence of the proposed method is analyzed and the optimal error estimate is derived. Finally, numerical examples are presented to verify the validity of the algorithm and the correctness of the theoretical results.