JD

Brief

JD - dimensionless productivity index, inverse of dimensionless pressure (based on average pressure) which contains the type of flow regime, boundary condition, drainage shape and stimulation .

Math & Physics

${J_D} = \frac{1}{\bar{P}_D}$

From the Darcy's law for an unfractured well located in the center of a circular drainage area, the JD is:

Pseudo-steady state:

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

Steady state:

${J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{1}{2}+S}}$

${J_D}$	Well in circular drainage area	Well in the drainage area with the shape factor ${C_A}$	Workover Potential (WOP)
Gas	Flowing	Calculated with Nodal Analysis using the PQplot by setting the flowing wellhead pressure (FWHP) equal to the current flowing line pressure (FLP) at the well head. Use the current value of JD.	Calculated with Nodal Analysis using the PQplot by using the largest tubing practical that will fit in the current well bore with a FWHP equal to the current FLP. The largest tubing size is approximately the casing drift diameter minus the tubing coupling diameter > 0.5 inches for clearance (see Pipe Catalog). Use JD=0.13.
Oil	Flowing	Calculated the same way as for the Gas Flowing case	Calculated as absolute open flow (AOF). Use JD=1.27.
Oil	Artificial Lift (ESP, Rod Pump, PCP)	Calculated by setting the flowing bottomhole pressure (Pwf) equal to the fluid level at the pump depth. Use the current value of JD.	Calculated as absolute open flow (AOF). Use JD=1.27. Note: If WOP > all lift capacities thats good, must engineer a higher performance system.

Oil

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

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

Gas

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

Maximum $J_D$

The undamaged unstimulated vertical well potential in a pseudo steady radial flow is:

${J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.13$

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

$J$ = productivity index, stb/psia

$J_D$ = dimensionless productivity index, dimensionless

$kh$ = permeability times thickness, md*ft

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

$\bar{P}_D$ = dimensionless pressure (based on average pressure), dimensionless

$P_{\bar{P}}$ = 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

See Also

• Darcy's law
• JD
• J
• Production Potential