### Abstract

The simulation of multiphase flow presents several difficulties, including (1) the occurrence of sharp moving fronts when convection is dominating, (2) the need for a good approximation of velocities to calculate the convective terms of the equation, and (3) flow singularities around wells. To handle the first difficulty, we propose a Godunov-type higher-order scheme based on a piecewise linear approximation of the saturation associated with a multidimensional slope limiter. With respect to the second, the pressure equation is approximated by means of a mixed-hybrid formulation equivalent to the classic mixed formulation but yielding a positive-definite linear system. To solve the third difficulty, we introduce macroelements around wells. Numerical experiments illustrate the capabilities of the method.

Original language | English |
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Pages (from-to) | 567-575 |

Number of pages | 9 |

Journal | SPE Reservoir Engineering (Society of Petroleum Engineers) |

Volume | 5 |

Issue number | 4 |

Publication status | Published - Nov 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Process Chemistry and Technology

### Cite this

*SPE Reservoir Engineering (Society of Petroleum Engineers)*,

*5*(4), 567-575.