Thermodynamically Consistent Darcy-Brinkman-Forchheimer Framework in Matrix Acidization

TL;DR

This paper develops a thermodynamically consistent Darcy-Brinkman-Forchheimer framework for matrix acidization, improving the modeling of porosity changes and incorporating thermal effects, verified through numerical and chemical experiments.

Contribution

It introduces an improved DBF framework with a modified momentum equation that accurately models porosity changes and extends it to include thermal effects, verified by experiments.

Findings

The improved framework satisfies Newton's second law.

Numerical and chemical experiments validate the models.

Parallelization achieves good scalability.

Abstract

Matrix acidization is an important technique to enhance oil production at the tertiary recovery stage, and its numerical simulation is never concluded. From one of the earliest models, i.e. the two-scale model (Darcy framework), the Darcy-Brinkman-Forchheimer (DBF) framework is developed by adding Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is put outside of the time derivation term, which cannot describe the change of porosity well. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton's second law. The modified framework is called improved DBF framework. Furthermore, based on the improved DBF framework, the thermal DBF framework is given by introducing the energy balance equation to the improved DBF framework. Both of the frameworks are verified by the former works through numerical experiments and chemical experiments in labs. Parallelization to the codes of the complicated frameworks is also realized, and good scalability can be achieved.