JD

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Brief

JD - dimensionless productivity index, inverse of dimensionless pressure (based on average pressure) [1].

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

References

  1. Rueda, J.I.; Mach, J.; Wolcott, D. (2004). "Pushing Fracturing Limits to Maximize Producibility in Turbidite Formations in Russia"Free registration required (SPE-91760-MS). Society of Petroleum Engineers.