1. IPR Calculation Methods
Concepts
Drawdown = PR - Pwf .
Open-flow potential
Productivity Index, J
Inflow Performance Relationship (IPR)
IPR Calculation Methods
2. non-linear IPR
Straight-line IPR
qo= C(P2R – P2wf)n
qo= J(PR – Pwf)
Vogel’s Method

2. IPR Calculation Methods
3. Fetkovich’s qo
qo(max)
1 -
Pwf PR = 2
For case of n =1,
qo= C(P2R – P2wf)n
Developed from:
Observations of the American Bureau of Mines
normalization qo
qo(max)
1 -
Pwf PR = 2 n
based on field observations for saturated oil wells.
consider the effect of high velocity (non-Darcy, turbulent flow)
slightly different from Vogel’s, somewhat more conservative

3. Exercise: Back Pressure, Vogel’s & Fetkovich’s Methods
Data from a multirate test for a well producing from a pay zone in a field is given in Table Q1.
Table Q1
Calculate the productivity index, J based on the lowest four flow rates. Find qmax based on the straight IPR.
Plot the data in Table Q1 on the Cartesian paper. Use only point 10 to determine qmax with the Vogel’s equation. Plot and tabulate the calculated rates predicted by Vogel’s against corresponding bottomhole flowing pressures given in Table Q1.
Repeat step 2 using Fetkovich’s method.
Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find qmax.

4. Solution
Calculate the productivity index, J based on the lowest four flow rates. Find qmax based the straight IPR. q
Pr - Pwf
Productivity Index = J =
stb/d.psi
qmax (based the straight IPR)
J = q
Pr - Pwf
qmax = J Pr
qmax = (1600 psi) (5.38 stb/d.psi) = 8608 stb/d
psi =

5. = @ Point 10, q = 1260 psi Pwf = 1267 psi qmax = 3706 stb/d
Plot the data on the Cartesian paper. Use only point 10 to determine qmax with the Vogel’s equation. Plot and tabulate the Vogel’s rates corresponding to the bottomhole flowing pressures given in Table Q1.
Vogel’s equation
Plot of observed rates vs. Pwf
@ Point 10, q = 1260 psi
Pwf = 1267 psi
qmax = 3706 stb/d
psi =

6. Field Data vs. Vogel’s Vogel’s Observed
Plot of observed & Vogel’s rates vs. Pwf
Vogel’s
Observed

7. qo qo(max) Pwf PR = qo Pwf PR
3. Repeat step 2 using Fetkovich’s method/ special normalized Back Pressure. qo
qo(max)
1 -
Pwf PR = 2
qo(max) = qo
1 -
Pwf PR 2
@ Point 10, q = 1260 psi, Pwf = 1267 psi
qmax = stb/d

8. Field Data vs. Fetkovich
Observed
Backpressure

9. Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find qmax.
Backpressure Equation
qo= C(P2R – P2wf)n
n & C ?

10. qo= C(P2R – P2wf)n
n = 1/slope = ~0.7
C = 0.08 (plugging a value on the line into)

11. Field Data vs. Backpressure
Observed

12. A plot of the measured data compared with Vogel’s equation, the Backpressure equation & Fetkovich’s equation

14. qo= J(PR – Pwf) + (P 2b – P 2wf)
Many oil wells produce from reservoirs with pressure above Pb but with Pwf below Pb
qo= J(PR – Pwf)
Pb  Pwf  Pr
qo= J(PR – Pwf) (P 2b – P 2wf) J
2Pb
Pwf  Pb  Pr
IPR curve is characteristic of reservoirs with a solution gas drive

15. QUIZ: IPR
A well produces oil at a rate of 108 stb/d with a bottomhole flowing pressure of 1980 psia. The PVT analysis of the core samples and recombined reservoir fluids suggested that the bubble point pressure to be at 1825 psia at a temperature of 195 oF. An initial reservoir pressure of 3620 psia was recorded during the 48-hour buildup following the flow test.
Calculate the productivity index, J if flowing bottomhole pressure is greater than bubble point pressure.
Calculate the production rate if bottomhole flowing pressure is held at the bubble-point pressure to avoid the blockage in the near wellbore region.
Calculate the maximum production rate that can be expected from the well.
Plot the IPR curve for the entire range of wellbore flowing pressures, both above and below the bubble point.

16. iii. qmax = 178.7 stb/d/psia. (Pwf = 0)
Solution
J = stb/d/psia.
ii. qob = stb/d/psia.
iii. qmax = stb/d/psia. (Pwf = 0)