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:
 
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>
Thus, rate could be calculated as:
 
:<math> {q} = {J}(\bar{P} - P_{wf})</math>
 
  
 
== 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

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