Effective drainage radius for numerical well-reservoir contact model: where
{\bf D} = \{ D_{\perp 1}, D_{\perp 2} \} – dimensions of the grid cell around well in transversal plane to the well axis. Strictly speaking, the above formula is only valid in case well penetrates through the whole length of grid cell
\bf D perpendicular to the cell faces. There are many modifications and generalization of the Peaceman formula but in the most practical cases it works very well when sufficiently fine LGR is applied.
(1)
r_e = 0.28 \ \frac{ \sqrt{
\Big( \frac{k_{\perp 2}}{k_{\perp 1}} \Big)^{1/2} D_{\perp 1} ^2
+
\Big( \frac{k_{\perp 1}}{k_{\perp 2}} \Big)^{1/2} D_{\perp 2} ^2
} }
{ \Big( \frac{k_{\perp 2}}{k_{\perp 1}} \Big)^{1/4} + \Big( \frac{k_{\perp 1}}{k_{\perp 2}} \Big)^{1/4}}
In particular case of isotropic permeability k_{\perp 1} = k_{\perp 2} the Peaceman effecxtive radius is given by:
| (2) | r_e = 0.28 \ \sqrt{D_{\perp 1} ^2+ D_{\perp 2} ^2} |
and in case of a square grid cell D_{\perp 1} = D_{\perp 2} = D_{\perp}:
| (3) | r_e = 0.4 \ D_{\perp} |
Obviously, there is a natural limit to the degree of LGR for Peaceman approach.
The formula
(3) assumes that external boundary of drainage area is greater than well radius which introduces a natural limitation to applicability of the Peaceman formula for pressure calculations in near-reservoir zone with
D_{\perp} < 2.5 \, r_w.
This is, for example, the case in SPT where time lag between pressure response to the flow variation is so small (seconds) that it dictates very small grid size around wellbore and Peaceman approximation can not be properly applied.