Well flow models for various numerical methods.

*(English)*Zbl 1158.76393Summary: Numerical simulation of fluid flow and transport processes in the subsurface must account for the presence of wells. The pressure at a gridblock that contains a well is different from the average pressure in that block and different from the flowing bottom hole pressure for the well. Various finite difference well models have been developed to account for the difference. This paper presents a systematical derivation of well models for other numerical methods such as standard finite element, control volume finite element, and mixed finite element methods. Numerical results for a simple well example illustrating local grid refinement effects are given to validate these well models. The well models have particular applications to groundwater hydrology and petroleum reservoirs.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

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