Simulating wormhole propagation during reactive dissolution of carbonates is often significantly challenging, because of the high nonlinearity of the governing equations with complex fluid physics. High resolution grids are often required to represent the complex geological heterogeneity, which demands massively parallel computers with a large number of processors. Herein, we present a parallel and scalable simulator on parallel computers for the fully implicit solution of the wormhole propagation model. Our approach is based on a family of mixed finite element methods for the spatial discretization and the implicit Backward Euler scheme for the temporal integration, to handle the combination of complicated flow physics and high resolution grids in their full complexity. Moreover, the active-set reduced-space method, as a class of bound-preserving inexact Newton algorithms, is proposed for the resultant nonlinear system of equations, to guarantee the nonlinear consistency of the fully implicit discretization in a monolithic way and to ensure the boundedness requirement of the solution. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed simulator for a set of heterogeneous medium problems. Large-scale results are provided to show the scalability for reservoir simulation with hundreds of millions of unknowns by using several thousand processors.
Bibliographical noteKAUST Repository Item: Exported on 2021-08-05
Acknowledged KAUST grant number(s): BAS/1/1351-01, URF/1/3769-01, URF/1/4074-01
Acknowledgements: This work is partially supported by the National Natural Science Foundation of China (No. 11971006), the Hunan Province Natural Science Foundation, China (No. 2020JJ2002), and the PetroChina Innovation Foundation, China (No. 2019D-5007-0213). This work is also partially supported by King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01, URF/1/4074-01, and URF/1/3769-01.
ASJC Scopus subject areas
- Geotechnical Engineering and Engineering Geology
- Computer Science Applications