## Summary

In this paper, we present a new analytical expression and a simple numerical procedure for the equivalent wellblock radius and well index for nonuniform grids for homogeneous anisotropic reservoirs or completely heterogeneous reservoirs for a partially penetrating vertical well.

Equivalent wellblock radius is obtained analytically for the homogeneous and anisotropic reservoirs with nonsquare grids. The new equation has the same structure as Peaceman's equation (Peaceman 1983) with one additional parameter accounting for the partial penetration and vertical-flow effects. The new formula reduces to Peaceman's formula when the well is fully penetrating.

For heterogeneous reservoirs with nonsquare grids, the equivalent wellblock radius is computed from the solution of a 1D linear ordinary-differential equation.

A field simulation study with complete reservoir heterogeneity showed that well index calculated by using Peaceman's method underpredicts the well-production rate by 20%. The new method presented in this paper reduces this error to 1%. Similarly, a model problem with a nonsquare grid shows approximately 30% rate error with Peaceman's method, while the new method reduces the error to less than 3%.