Difference between revisions of "Productivity index"

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

@@ 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 a well can produce per unit of the pressure drop.
 ==Math & Physics==
+[[Productivity index|J]] is defined as follows:
-From the [[Darcy's law]] the [[Productivity index|J]] in pseudo-steady state is as follows:
 :<math> {J} = \frac{q}{\bar{P} - P_{wf}} </math>
+Thus, rate could be calculated as:
-===Oil===
+:<math> {q} = {J}(\bar{P} - P_{wf})</math>
-:<math> {J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} </math>
+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:
-:<math> {q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D </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>
-===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>==
-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  ==
 :<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
 :<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_{P_{wf}} </math> = average well flowing pseudopressure, psia<sup>2</sup>/cP
 :<math> q </math> = flowing rate, stb/d
-:<math> q_g </math> = gas rate, MMscfd
 :<math> r_w </math> = wellbore radius, ft
 :<math> r_e </math> = drainage radius, ft
 :<math> S </math> = skin factor, dimensionless
-:<math> T </math> = temperature, °R
 ===Greek symbols===
 :<math> \mu </math> = viscosity, cp
+==See Also==
+* [[Darcy's law]]
+* [[JD]]
+* [[Productivity index|J]]
 [[Category:PQplot]]
@@ Line 52: / Line 41: @@
 |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
 }}

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