The Well in the Simulator

A Well Inside a Grid Block

A wellbore is a fraction of a foot across; a grid block is tens of feet. The simulator cannot resolve the steep radial pressure funnel around the well, so the block-center pressure is not the wellbore pressure.

The Equivalent Radius

Peaceman showed that the block pressure equals the true flowing pressure at an equivalent radius $r_o \approx 0.2,\Delta x$, about a fifth of the block. The well couples to the block there, not at the wellbore where the grid cannot see.

The Well Index

The well index $WI = \dfrac{2\pi k h}{\ln(r_o/r_w) + s}$ converts the block-to-well pressure difference into a rate, $q = WI,(P_{block} - P_{wf})$. It is the simulator's counterpart of the productivity index, built on the equivalent radius rather than the drainage radius.