Difference between revisions of "Productivity index"

Revision as of 10:23, 14 June 2023

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

From the Darcy's law the J in pseudo-steady state is as follows:

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

{J} = \frac{kh}{141.2 B \mu} {J_D}

{q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) 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

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

\mu

= viscosity, cp

@@ Line 1: / Line 1: @@
 ==Brief==
-[[Productivity index|J]] - well productivity index characterizes how much oil, gas or water the well can produce per unit of pressure drop.
+[[Productivity index|J]] - well productivity index characterizes how much oil or water the well can produce per unit of pressure drop.
 ==Math & Physics==
@@ Line 8: / Line 8: @@
 :<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
-===Oil===
 :<math> {J} = \frac{kh}{141.2 B \mu} {J_D} </math>
 :<math> {q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D </math>
-===Gas===
-:<math>J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}</math>
 ==Maximum <math>J_D</math>==
@@ Line 58: / Line 54: @@
 |titlemode= replace
 |keywords=well productivity index, well deliverability
-|description=Productivity index for oil, gas and water wells
+|description=Productivity index for oil or water wells
 }}