3 Phase IPR

Three-phase Inflow Performance Relationship

3 Phase IPR Curve

3 Phase IPR is an IPR curve calculated on the basis of total barrels of produced fluid, including gas.

3 Phase IPR curve is used in Pump Design software for pump sizing.

Math and Physics

The volume of 1 stb of liquid plus associated gas at any pressure and temperature is given by:

$VF=WCUT\ B_w + (1-WCUT)\ B_o + (GLR\ - (1-WCUT)R_s - WCUT\ R_{sw})B_g$

The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:

$V=q_{t_{sc}} \times VF$

$q_{t_{sc}}$ is calculated as usual using:

• Vogel's IPR equation
• Composite IPR equation

3 Phase IPR calculation example

Figure.1 3 Phase IPR calculation example

Following the well #1 example given by Brownon Figure 5.8, page 191:

Given:

$P_r$ = 2550 psi

$P_b$ = 2100 psi

Test data:

$P_{wf}$ = 2300 psi

$q_t$ = 500 b/d

Calculate:

Determine the 3 Phase IPR curves for F_w=0, 0.25, 0.5, 0.75, and 1.

Solution:

The problem was run through PQplot software for different values of watercut.

Result 3 Phase IPR curves are shown on Fig.1. Points indicate results obtained by Brown .

The PQplot model from this example is available online by the following link: 3 Phase IPR calculation example

Nomenclature

$A, B, C, D, tan(\beta), CD, CG$ = calculation variables

$F_o$ = oil fraction, fraction

$F_w$ = water fraction, fraction

$J$ = productivity index, stb/d/psia

$P$ = pressure, psia

$q$ = flowing rate, stb/d

Subscripts

b = at bubble point

max = maximum

o = oil

r = reservoir

t = total

wf = well flowing bottomhole pressure

wfG = well flowing bottomhole pressure at point G

See also

IPR

Vogel's IPR

Composite IPR

Darcy's law