Difference between revisions of "JD"

From wiki.pengtools.com
Jump to: navigation, search
(Oil)
(Oil)
Line 12: Line 12:
 
:<math> {J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} </math>
 
:<math> {J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} </math>
  
:<math> {q} = \frac{kh}{141.2 B \mu} \frac{\bar{P} - P_{wf}}{JD} </math>
+
:<math> {q} = \frac{kh}{141.2 B \mu} \frac{\bar{P} - P_{wf}}{J_D} </math>
  
 
===Gas===
 
===Gas===

Revision as of 15:09, 25 April 2020

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}}
 {q} = \frac{kh}{141.2 B \mu} \frac{\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

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.