Drawdown = PR - Pwf .

Inflow Performance Relationship (IPR)

1. Straight-line IPR • qo= C(P2

R – P2wf)n

• qo= J(PR – Pwf)

Open-flow potential

IPR Calculation Methods

Concepts

Productivity Index, J

2. non-linear IPR

• Vogel’s Method

IPR Calculation Methods

3. Fetkovich’s

qo

qo(max)

1 - Pwf

PR

=2 n

For case of n =1,

based on field observations for saturated oil wells.

normalization

qo

qo(max)

1 - Pwf

PR

=2

qo= C(P2R – P2

wf)n

Developed from:

Observations of the American Bureau of Mines

consider the effect of high velocity (non-Darcy, turbulent flow)

slightly different from Vogel’s, somewhat more conservative

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.

1. Calculate the productivity index, J based on the lowest four flow rates. Find qmax based on the straight IPR.

2. 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.

3. Repeat step 2 using Fetkovich’s method.

4. Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find qmax.

Point Pwf (psia) q o (stb/day)

1 166 24352 183 24603 351 23524 534 22605 787 19656 867 18957 996 17658 1066 16259 1194 147010 1267 126011 1342 104512 1470 72013 1476 61014 1497 56515 1558 23516 1600 0

Table Q1

Solution

q

Pr - Pwf

• Productivity Index = J = stb/d.psi

q Lowest P wf J (stb/day/psi)

235 1558 5.60565 1497 5.49610 1476 4.92720 1470 5.54

Average 5.38

qmax (based the straight IPR)

J =q

Pr - Pwf

0

qmax = J Pr

qmax = (1600 psi) (5.38 stb/d.psi) = 8608 stb/d

1. Calculate the productivity index, J based on the lowest four flow rates. Find qmax based the straight IPR.

2435 stb/d @ 166 psi=

2. 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

qmax = 3706 stb/d

Production data

0

200

400

600

800

1000

1200

1400

1600

1800

0 500 1000 1500 2000 2500 3000

q o (stb/d)

Pw

f (p

si)

Plot of observed rates vs. Pwf

@ Point 10, q = 1260 psi

Pwf = 1267 psi

2435 stb/d @ 166 psi

=

Point Pwf (psia)

Field Vogel's1 166 2435 35972 183 2460 35823 351 2352 34014 534 2260 31285 787 1965 26246 867 1895 24347 996 1765 20968 1066 1625 18969 1194 1470 150210 1267 1260 126011 1342 1045 99912 1470 720 52213 1476 610 49914 1497 565 41715 1558 235 17316 1600 0 0

qo (stb/d)

Production data

0

200

400

600

800

1000

1200

1400

1600

1800

0 1000 2000 3000 4000

q o (stb/d)

Pw

f (p

si)

Plot of observed & Vogel’s rates vs. Pwf

Vogel’s

Observed

Field Data vs. Vogel’s

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

qmax = 3378.6 stb/d

@ Point 10, q = 1260 psi, Pwf = 1267 psi

Point Pwf (psia)

Field Back-Pressure1 166 2435 33422 183 2460 33343 351 2352 32164 534 2260 30025 787 1965 25616 867 1895 23877 996 1765 20698 1066 1625 18799 1194 1470 149710 1267 1260 126011 1342 1045 100212 1470 720 52713 1476 610 50314 1497 565 42115 1558 235 17516 1600 0 0

qo (stb/d)

Field Data vs. Fetkovich

Production data

0

200

400

600

800

1000

1200

1400

1600

1800

0 1000 2000 3000 4000

q o (stb/d)

Pw

f (p

si)

Observed

Backpressure

4. Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find qmax.

n & C ?

Backpressure Equation qo= C(P2R – P2

wf)n

Log-Log PLot

100000

1000000

10000000

100 1000 10000

qo

Pr2

- P

wf2

q0 (stb/d) Pwf (psia) Pr 2 - Pwf 2

2435 166 25324442460 183 25265112352 351 24367992260 534 22748441965 787 19406311895 867 18083111765 996 15679841625 1066 14236441470 1194 11343641260 1267 9547111045 1342 759036720 1470 399100610 1476 381424565 1497 318991235 1558 1326360 1600 0

C = 0.08 (plugging a value on the line into)

n = 1/slope = ~0.7

qo= C(P2R – P2

wf)n

Field Data vs. Backpressure

Point Pwf (psia)

Field Backpressure1 166 2435 24942 183 2460 24903 351 2352 24284 534 2260 23145 787 1965 20706 867 1895 19707 996 1765 17838 1066 1625 16679 1194 1470 142210 1267 1260 126011 1342 1045 107312 1470 720 68413 1476 610 66314 1497 565 58515 1558 235 31616 1600 0 0

qo (stb/d)

Production data

0

200

400

600

800

1000

1200

1400

1600

1800

0 500 1000 1500 2000 2500 3000

q o (stb/d)

Pw

f (p

si)

Backpressure

Observed

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

Point Pwf (psia) Field Vogel's Back-Pressure (n=1) Back-Pressure (n=0.7)1 166 2435 3597 3342 24942 183 2460 3583 3334 24903 351 2352 3401 3216 24284 534 2260 3129 3002 23145 787 1965 2624 2561 20706 867 1895 2434 2387 19707 996 1765 2096 2069 17838 1066 1625 1896 1879 16679 1194 1470 1502 1497 142210 1267 1260 1260 1260 126011 1342 1045 999 1002 107312 1470 720 522 527 68413 1476 610 499 503 66314 1497 565 417 421 58515 1558 235 173 175 31616 1600 0 0 0 0

qo (stb/day)

Many oil wells produce from reservoirs with pressure above Pb but with Pwf below Pb

qo= J(PR – Pwf)Pb Pwf Pr

IPR curve is characteristic of reservoirs with a solution gas drive

qo= J(PR – Pwf) + (P 2b – P 2

wf)J

2Pb

Pwf Pb Pr

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.

i. Calculate the productivity index, J if flowing bottomhole pressure is greater than bubble point pressure.

ii. Calculate the production rate if bottomhole flowing pressure is held at the bubble-point pressure to avoid the blockage in the near wellbore region.

iii. Calculate the maximum production rate that can be expected from the well.

iv. Plot the IPR curve for the entire range of wellbore flowing pressures, both above and below the bubble point.

Solution

i. J = 0.066 stb/d/psia.

ii. qob = 118.5 stb/d/psia.

iii. qmax = 178.7 stb/d/psia. (Pwf = 0)