Difference between revisions of "Productivity index"

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(Math & Physics)
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==Math & Physics==
 
==Math & Physics==
 
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[[Productivity index|J]] is defined as follows:
From the [[Darcy's law]] the [[Productivity index|J]] is:
 
 
:<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
 
:<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
 
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From the [[Darcy's law]] for an unfractured well located in the center of a circular
 +
drainage area, the {J} in pseudo-steady state is as follows:
 
:<math> {J} = \frac{kh}{141.2 B \mu} {J_D} = \frac{kh}{141.2 B \mu} \times \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} </math>
 
:<math> {J} = \frac{kh}{141.2 B \mu} {J_D} = \frac{kh}{141.2 B \mu} \times \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} </math>
  

Revision as of 10:28, 14 June 2023

Brief

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

Math & Physics

J is defined as follows:

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

From the Darcy's law for an unfractured well located in the center of a circular drainage area, the {J} in pseudo-steady state is as follows:

 {J} = \frac{kh}{141.2 B \mu} {J_D} = \frac{kh}{141.2 B \mu} \times \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}}
 {q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D

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

See Also