The well index in a numerical reservoir simulator relates the flow rate to the difference between well flowing pressure and simulator gridblock pressure. The standard method for computing well index, Peaceman's formula (Peaceman 1978), requires an equivalent wellblock radius at which the gridblock pressure is equal to the pressure from an analytical solution for steady-state single-phase flow. Although Peaceman's formula is accurate for fully penetrating vertical wells, it fails to account for the effect of vertical flow in partially penetrating wells.
In this paper, we present a new analytical expression for the equivalent wellblock radius in a homogeneous, anisotropic reservoir with a uniform square grid around the well path. The new equation has the same structure as Peaceman's equation but adds one new parameter to account for partial penetration and for vertical flow. The new formula reduces to Peaceman's formula when the well is fully penetrating. Model simulation study showed that the new method reduced the error in the calculated flow rates from 30% to less than 1% at minimal cost.