Well index in reservoir simulation for slanted and slightly curved wells in 3D grids

A new, accurate method for computing the well index (WI) for a well that is oriented in an arbitrary direction in a 3D grid is presented. The method is simple and seminumerical and takes well direction and neighboring gridblocks into account. It is assumed that the medium is homogeneous. The method can be applied for any grid or discretization. However, only Cartesian grids with a seven-point stencil are used here. Properties of the seminumerical WI are investigated for both synthetic and field examples. The investigated properties are convergence rate and dependency on well direction, well location, grid geometry, and anisotropy. The new method shows the importance of taking the neighboring gridblocks into account.