A decoupled scheme to solve the mass and momentum conservation equations of the improved Darcy–Brinkman–Forchheimer framework in matrix acidization
Type
ArticleKAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2021-12-01Preprint Posting Date
2020-08-07Permanent link to this record
http://hdl.handle.net/10754/673925
Metadata
Show full item recordAbstract
Matrix acidization simulation is a challenging task in the study of flows in porous media due to the changing porosity in the procedure. The improved Darcy–Brinkman–Forchheimer framework is one model to do this simulation. In this framework, the mass and momentum conservation equations are discretized to form a pressure–velocity linear system. However, the coefficient matrix of the linear system has a large condition number, and solving the linear system belongs to the saddle point problem. As a result of that, convergence is hard to achieve when solving it with iterative solvers. It is well known that the scale of the linear systems in matrix acidization simulation is large, and therefore, the usage of iterative solvers is required. Thus, a decoupled scheme is proposed in this work to decouple the pressure–velocity linear system into two independent linear systems: one is to solve for pressure, and the other one is to solve for velocity. It is emphasized that both of the linear systems are discretized from the elliptical partial differential equations, which guarantees fast convergence can be achieved by iterative solvers. A numerical experiment is carried out to demonstrate the correctness of the decoupled scheme and its higher computing efficiency. After that, the decoupled scheme is applied in investigating the factors that cannot change the optimal injected velocity and the dissolution pattern in matrix acidization.Citation
Wu, Y., Kou, J., Wu, Y.-S., Sun, S., & Xia, Y. (2021). A decoupled scheme to solve the mass and momentum conservation equations of the improved Darcy–Brinkman–Forchheimer framework in matrix acidization. AIP Advances, 11(12), 125305. doi:10.1063/5.0067340Sponsors
This work was supported by the Peacock Plan Foundation of Shenzhen (Grant No. 000255) and the General Program of Natural Science Foundation of Shenzhen (Grant No. 20200801100615003)Publisher
AIP PublishingJournal
AIP AdvancesarXiv
2008.03268Additional Links
https://aip.scitation.org/doi/10.1063/5.0067340ae974a485f413a2113503eed53cd6c53
10.1063/5.0067340