### 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 |
---|---|

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.

**Discontinuous and mixed finite elements for two-phase incompressible flow.** / Chavent, Guy; Cohen, Gary; Jaffre, Jerome; Eymard, Robert; Guerillot, Dominique; Weiil, Luce.

Research output: Contribution to journal › Article

*SPE Reservoir Engineering (Society of Petroleum Engineers)*, vol. 5, no. 4, pp. 567-575.

}

TY - JOUR

T1 - Discontinuous and mixed finite elements for two-phase incompressible flow

AU - Chavent, Guy

AU - Cohen, Gary

AU - Jaffre, Jerome

AU - Eymard, Robert

AU - Guerillot, Dominique

AU - Weiil, Luce

PY - 1990/11

Y1 - 1990/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025519540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025519540&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0025519540

VL - 5

SP - 567

EP - 575

JO - SPE Reservoir Engineering

JF - SPE Reservoir Engineering

SN - 0885-9248

IS - 4

ER -