  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.
