| Full text | |
| Author(s): |
Paz, Stevens
[1]
;
Jaramillo, Alfredo
[1]
;
Guiraldello, Rafael T.
[1]
;
Ausas, Roberto F.
[1]
;
Sousa, Fabricio S.
[1]
;
Pereira, Felipe
[2]
;
Buscaglia, Gustavo C.
[1]
Total Authors: 7
|
| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Paulo - Brazil
[2] Univ Texas Dallas, Dept Math Sci, Richardson, TX 75083 - USA
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Applied Mathematical Modelling; v. 91, p. 1100-1116, MAR 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
Two-phase flows in oil reservoirs can be modeled by a coupled system of elliptic and hyperbolic partial differential equations. The transport velocity of the multiphase fluid system is related to the pressure through Darcy's law and it is coupled to a conservation law for the saturation variable of one of the phases. A time step of the classical IMPES (IMplicit Pressure Explicit Saturation) method consists of first solving the elliptic problem for pressure and Darcy velocity, and then updating the saturation with an explicit numerical scheme for conservation laws. This method is very computationally costly, since the timeconsuming elliptic solver must be invoked at time intervals defined by the stability limit of the hyperbolic solver. A popular variant is not to update the velocity at all hyperbolic time steps, but to skip a fixed number Cof them, with Cdetermined by the user. In this work we propose a more accurate and systematic procedure for time stepping in IMPES codes. The velocity is updated at all transport time steps, though the elliptic solver is only invoked every Csteps. In the time steps at which the elliptic problem is not solved, the velocity is extrapolated from previously computed values with polynomials of high degree. Further, we introduce an error estimator that allows for the number Cto be adaptively determined without user intervention. The algorithm was tested in several relevant benchmark problems. This allowed for the optimization of its parameters and comparisons with previous variants. The results show that the proposed algorithm is very stable, reliable and time-cost effective. It is also easily implemented in pre-existent IMPES codes. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |