Regular Article

Thermodynamically consistent Darcy–Brinkman–Forchheimer framework in matrix acidization^★

¹ College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong 518048, PR China
² School of Civil Engineering, Shaoxing University, Shaoxing, Zhejiang 312000, PR China
³ School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, PR China
⁴ Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
⁵ Department of Petroleum Engineering, Colorado School of Mines, 1600 Arapahoe Street, Golden, CO 80401, USA

^* Corresponding author: shuyu.sun@kaust.edu.sa

Received: 29 May 2020
Accepted: 17 November 2020

Abstract

Matrix acidization is an important technique used to enhance oil production at the tertiary recovery stage, but its numerical simulation has never been verified. From one of the earliest models, i.e., the two-scale model (Darcy framework), the Darcy–Brinkman–Forchheimer (DBF) framework is developed by adding the Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is placed outside of the time derivation term, which prevents a good description of the change in porosity. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton’s second law. This modified framework is called the improved DBF framework. Furthermore, based on the improved DBF framework, a thermal DBF framework is given by introducing an energy balance equation to the improved DBF framework. Both of these frameworks are verified by former works through numerical experiments and chemical experiments in labs. Parallelization to the complicated framework codes is also realized, and good scalability can be achieved.