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**On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs.**
*(English)*
Zbl 0963.76549

Summary: We present a new, naturally parallelizable, numerical method for the solution of transport-dominated diffusion processes in heterogeneous porous media. For the discretization in time of one of the governing partial differential equations, we introduce a new characteristics-based procedure which is mass conservative, the modified method of characteristics with adjusted advection. Hybridized mixed finite elements are used for the spatial discretization of the equations, and a new strip-based domain decomposition procedure is applied towards the solution of the resulting algebraic problems.

We consider as a model problem the two-phase immiscible displacement in petroleum reservoirs. A detailed description of the numerical method is presented. Following that, numerical experiments are presented illustrating the important features of the new method and comparing computed results with ones derived from previous, related techniques.

We consider as a model problem the two-phase immiscible displacement in petroleum reservoirs. A detailed description of the numerical method is presented. Following that, numerical experiments are presented illustrating the important features of the new method and comparing computed results with ones derived from previous, related techniques.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

86A05 | Hydrology, hydrography, oceanography |

65Y05 | Parallel numerical computation |