R. Ewing, R. Lazarov, S.L. Lyons, D.V. Papavassiliou, J. Pasciak and G.X. Qin Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. The pressure of a grid cell containing a well is different from the average pressure in that cell and different from the bottomhole pressure for the well (Peaceman-78}). This paper presents a study of grid pressures obtained from the simulation of single phase flow through an isotropic porous medium using different numerical methods. Well equations are proposed for Darcy flow with Galerkin finite elements and mixed finite elements. Furthermore, high velocity (non-Darcy) flow well equations are developed for cell-centered finite difference, Galerkin finite element and mixed finite element techniques.