Productivity index

Brief

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

Math & Physics

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:

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

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

$P_{wf}$ = 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

• Darcy's law
• JD
• J