Difference between revisions of "JD"

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==Maximum <math>J_D</math>==
 
==Maximum <math>J_D</math>==
  
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The unstimulated vertical well potential in a pseudo steady radial flow is:
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The undamaged unstimulated vertical well potential in a pseudo steady radial flow is:
  
 
:<math> {J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.13</math>
 
:<math> {J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.13</math>

Revision as of 15:08, 9 July 2023

Brief

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

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}}

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
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

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. 
  2. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named DW
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