### Abstract

The simulation of multiphase flow presents several difficulties, among which are the following three which we would like to address: i) sharp moving fronts can occur when convection is dominating, ii) a good approximation of velocities is necessary to calculate the convective terms of the equation, iii) the flow presents singularities around wells. Concerning i), we propose a discontinuous piecewise polynomial approximation of the saturation which allows us to design a higher order scheme. Inside each cell, the water conservation equation is multiplied by test functions and integrated by parts. With respect to ii), the pressure equation is approximated by means of a mixed-hybrid formulation which is equivalent to the classical mixed formulation. Finally, concerning iii), we introduce macro-elements around wells.

Original language | English |
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Title of host publication | Society of Petroleum Engineers of AIME, (Paper) SPE |

Publisher | Soc of Petroleum Engineers of AIME, USA SPE 16018 |

Pages | 259-270 |

Number of pages | 12 |

Publication status | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Society of Petroleum Engineers of AIME, (Paper) SPE*(pp. 259-270). Soc of Petroleum Engineers of AIME, USA SPE 16018.