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JD - dimensionless productivity index[1], inverse of dimensionless pressure (based on average pressure) which contains the type of flow regime, boundary condition, drainage shape and stimulation [2].

Math & Physics

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

From the Darcy's law for the unfractured well the JD is:

Well in circular drainage area Well in a drainage area with the shape factor  {C_A}[2]
Steady state  {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{1}{2}+S}} {J_D} = \frac{1}{\frac{1}{2}ln{\frac{4.5A}{C_A{r_w}^2}+S}}
Pseudo steady state  {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} {J_D} = \frac{1}{\frac{1}{2}ln{\frac{2.25A}{C_A{r_w}^2}+S}}

Some typical  {C_A} values: circle 31.6, square 30.88 [3].


 {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


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 in a circular drainage area:

 {J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.1287

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


 B = formation volume factor, bbl/stb
 C_A = Dietz shape factor, dimensionless
 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


  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. 
  2. 2.0 2.1 Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
  3. Dietz, D.N. (1965). "Determination of Average Reservoir Pressure From Build-Up Surveys"Free registration required (SPE-1156-PA). J Pet Technol. 
By Mikhail Tuzovskiy on 20230712123204