Difference between revisions of "Productivity index"

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==Brief==
 
==Brief==
  
[[Productivity index|J]] - well productivity index characterizes how much oil or water the well can produce per unit of pressure drop.
+
[[Productivity index|J]] - well productivity index characterizes how much oil or water a well can produce per unit of the pressure drop.
  
 
==Math & Physics==
 
==Math & Physics==
 
[[Productivity index|J]] is defined as follows:
 
[[Productivity index|J]] is defined as follows:
 
:<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
 
:<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
 +
Thus, rate could be calculated as:
 +
:<math> {q} = {J}(\bar{P} - P_{wf})</math>
 
From the [[Darcy's law]] for an unfractured well located in the center of a circular
 
From the [[Darcy's law]] for an unfractured well located in the center of a circular
drainage area, the [[Productivity index|J]] in pseudo-steady state is as follows:
+
drainage area, the [[Productivity index|J]] in pseudo-steady state is:
 
:<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>
 
:<math> {q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D</math>
 
 
==Maximum <math>J_D</math>==
 
 
The maximum possible stimulated well potential for pseudo steady linear flow is:
 
 
<math>{J_D}_{max}= \frac{6}{\pi} \approx 1.91 </math> , see [[6/π stimulated well potential]]
 
 
The maximum possible stimulated well potential for steady state linear flow is:
 
 
<math>{J_D}_{max}= \frac{4}{\pi} \approx 1.27 </math> , see [[4/π stimulated well potential]]
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==
 
:<math> B </math> = formation volume factor, bbl/stb
 
:<math> B </math> = formation volume factor, bbl/stb
 +
:<math> J </math> = productivity index, stb/psia
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> kh</math> = permeability times thickness, md*ft
 
:<math> kh</math> = permeability times thickness, md*ft
 
:<math> \bar{P} </math> = average reservoir pressure, psia
 
:<math> \bar{P} </math> = average reservoir pressure, psia
:<math> P_{\bar{P}} </math> = average reservoir pseudopressure, psia<sup>2</sup>/cP
 
 
:<math> P_{wf} </math> = well flowing pressure, psia
 
:<math> P_{wf} </math> = well flowing pressure, psia
:<math> P_{P_{wf}} </math> = average well flowing pseudopressure, psia<sup>2</sup>/cP
 
 
:<math> q </math> = flowing rate, stb/d
 
:<math> q </math> = flowing rate, stb/d
:<math> q_g </math> = gas rate, MMscfd
 
 
:<math> r_w </math> = wellbore radius, ft
 
:<math> r_w </math> = wellbore radius, ft
 
:<math> r_e </math> = drainage radius, ft
 
:<math> r_e </math> = drainage radius, ft
 
:<math> S </math> = skin factor, dimensionless
 
:<math> S </math> = skin factor, dimensionless
:<math> T </math> = temperature, °R
 
  
 
===Greek symbols===
 
===Greek symbols===

Latest revision as of 11:07, 14 June 2023

Brief

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

Math & Physics

J is defined as follows:

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

Thus, rate could be calculated as:

 {q} = {J}(\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:

 {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}}

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_{wf} = well flowing pressure, psia
 q = flowing rate, stb/d
 r_w = wellbore radius, ft
 r_e = drainage radius, ft
 S = skin factor, dimensionless

Greek symbols

 \mu = viscosity, cp

See Also