Difference between revisions of "Productivity index"

Revision as of 10:36, 14 June 2023

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

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:

{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}}

Thus, rate could be calculated as:

{q} = {J}(\bar{P} - P_{wf})

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

\mu

= viscosity, cp

@@ Line 14: / Line 14: @@
 == Nomenclature  ==
 :<math> B </math> = formation volume factor, bbl/stb
+:<math> J </math> = productivity index, stb/psia
 :<math> J_D </math> = dimensionless productivity index, dimensionless
 :<math> kh</math> = permeability times thickness, md*ft