Difference between revisions of "Productivity index"

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==Brief==
 
==Brief==
  
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[[Productivity index|J]] - well productivity index characterize how much oil, gas or water the well can produce per unit of pressure drop.
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[[Productivity index|J]] - well productivity index characterizes how much oil, gas or water the well can produce per unit of pressure drop.
  
 
==Math & Physics==
 
==Math & Physics==

Revision as of 10:16, 14 June 2023

Brief

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

Math & Physics

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

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

Oil

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

Gas

J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}

Maximum 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

Nomenclature

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

Greek symbols

\mu = viscosity, cp
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