Productivity index

Brief

J - well productivity index characterize how much oil, gas or water the well can produce per unit of pressure drop.

Math & Physics

From the Darcy's law the J in pseudo-steady state is as follows:

${J} = \frac{q}{\bar{P} - P_{wf}}$

Oil

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

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

Gas

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

Maximum $J_D$

The maximum possible stimulated well potential for pseudo steady linear flow is:

${J_D}_{max}= \frac{6}{\pi} \approx 1.91$ , see 6/π stimulated well potential

The maximum possible stimulated well potential for steady state linear flow is:

${J_D}_{max}= \frac{4}{\pi} \approx 1.27$ , see 4/π stimulated well potential

Nomenclature

$B$ = formation volume factor, bbl/stb

$J_D$ = dimensionless productivity index, dimensionless

$kh$ = permeability times thickness, md*ft

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

$P_{\bar{P}}$ = average reservoir pseudopressure, psia²/cP

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

$P_{P_{wf}}$ = average well flowing pseudopressure, psia²/cP

$q$ = flowing rate, stb/d

$q_g$ = gas rate, MMscfd

$r_w$ = wellbore radius, ft

$r_e$ = drainage radius, ft

$S$ = skin factor, dimensionless

$T$ = temperature, °R

Greek symbols

$\mu$ = viscosity, cp