## Abstract

A novel numerical algorithm for computing incompressible, discontinuous, two-phase flows in two-dimensional, inhomogeneous, and isotropic porous media is presented. The algorithm uses Colella et al's. hybrid sequential explicit-implicit approach for both accuracy and speed of the calculations. The explicit part uses a high-order Godunov scheme with a modified Van Leer geometrical slope limiter, similar to those used in shock dynamics. The implicit part is a two-step solver: the first step is a Crank-Nicolson saturation solver and the second one is a Poisson solver for the phase pressure. Both use fast multilevel multigrid solvers with the number of operations of the order of θ[Nlog(N)], where N is the number of grid points. For an implicit simulator, the number of operations is θ(N_{3}) per time step. Two numerically stiff reservoir engineering problems are presented to demonstrate the low numerical dispersion and second-order accuracy of our method.

Original language | English (US) |
---|---|

Title of host publication | Production Operations and Engineering/General |

Pages | 871-884 |

Number of pages | 14 |

Volume | Pi |

State | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 Annual Technical Conference and Exhibition. Part Delta - Denver, CO, USA Duration: Oct 6 1996 → Oct 9 1996 |

### Other

Other | Proceedings of the 1996 Annual Technical Conference and Exhibition. Part Delta |
---|---|

City | Denver, CO, USA |

Period | 10/6/96 → 10/9/96 |

## ASJC Scopus subject areas

- Geology
- Geotechnical Engineering and Engineering Geology