## Abstract

We present a spatial renormalization group algorithm to handle immiscible two-phase flow in heterogeneous porous media. We call this algorithm FRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithm for Correlated Transport in Anisotropic Media, and the R stands for relative permeability. Originally, FRACTAM was an approximate iterative process that replaces the L x L lattice of grid blocks, representing the reservoir, by a (L/2) x (L/2) one. In fact, FRACTAM replaces the original L x L lattice by a hierarchical (fractal) lattice, in such a way that finding the solution of the two-phase flow equations becomes trivial. This triviality translates in practice into computer efficiency. For N = L x L grid blocks we find that the computer time necessary to calculate fractional flow F(t) and pressure P(t) as a function of time scales as τ ∼ N^{1.7} for FRACTAM-R. This should be contrasted with the computational time of a conventional grid simulator τ ∼ N^{2.3}. The solution we find in this way is an acurate approximation to the direct solution of the original problem.

Original language | English |
---|---|

Pages (from-to) | 247-279 |

Number of pages | 33 |

Journal | Transport in Porous Media |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 1997 |

Externally published | Yes |

## Keywords

- Effective properties
- Heterogeneity
- Relative permeability
- Renormalization numerical algorithm
- Simulation

## ASJC Scopus subject areas

- Catalysis
- General Chemical Engineering