JD

Brief

JD - dimensionless productivity index, inverse of dimensionless pressure (based on average pressure) .

Math & Physics

From the Darcy's law for an unfractured well located in the center of a circular drainage area, the JD in pseudo-steady state is as follows:

${J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}}$

Oil

${J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}}$

Gas

$J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}$

Nomenclature

$B$ = formation volume factor, bbl/stb

$kh$ = permeability times thickness, md*ft

$\bar{P}$ = average reservoir pressure, psia

$P_{wf}$ = well flowing pressure, psia

$r_w$ = wellbore radius, ft

$r_e$ = drainage radius, ft

$S$ = skin factor, dimensionless