Inflow Performance

Exercises

Reservoir Capabilities

• Darcy’s Law for radial flow

– Liquid flow in Laminar Flow through

a permeable medium is described by

Darcy’s Law

s75.0r

rlnB

pphk10X08.7q

w

eoo

wf3

(for pseudo-steady state flow conditions)

Productivity Index

• A common indicator of liquid reservoir

behavior is PI or productivity index

–Referred to as “J” in SPE

nomenclature

psi/D/STBpp

qJ

wf

Productivity Index in Terms

of Darcy’s Law

sr

rB

hkJ

w

eoo 75.0ln

00708.0

(for pseudo steady state flow conditions)

Calculating Flowrate

• Using PI, we can calculate flowrate, q,

quickly and easily from

)pp(Jq wf

Exercise 1

• Given reservoir parameters:

k = 30 md

h = 40 ft

o = 0.5 cp

Bo = 1.2 RB/STB

hole size = 8 ½ inches

s = 0

Exercise 1

• Calculate:

– J for re = 1,000 ft

– q for a drawdown ( ) of 750 psi

– q for a drawdown of 1,000 psi

– With = 3,000 psia, calculate q for a

complete drawdown

– Assume pseudo-steady state, radial flow

p

wfpp

Exercise 1

Inflow Performance

Solution

psi/D/STB97.1

075.0354.0

000,1ln2.15.0

403010x08.7

s75.0r

rlnB

kh10x08.7J

3

w

eoo

3

Exercise 1

Inflow Performance

Solution

• For a drawdown of 750 psi

q = J (p - pwf)

= (1.97) (750) = 1,480 STB/D

• For a drawdown of 1,000 psi

q = (1.97) (1,000) = 1,970 STB/D

Exercise 1

Inflow Performance

Solution

• For a complete drawdown

q = J (p - 14.7)

= 1.97 (3,000 - 14.7)

= 5,880 STB/D

Multiphase Flow

• Mathematical model for Vogel’s curve

2

8.02.01p

p

p

p

q

q wfwf

max

Multiphase Flow

• Mathematical relationship between

Vogel (qmax) and reservoir pressure,

productivity index above Pbp

8.1max

pJq

Finding Vogel qmax

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

q/qmax

pw

f/p

r

Exercise 2

• Reservoir parameters:

= 2,350 psia

k = 140 md

h = 35 ft

o = 0.8 cp

Bo = 1.25 rbbl/STB

re = 2,000 ft

rw = 0.411 ft

pb = 3,000 psia

s = 2

p

Exercise 2

• Calculate J

• Calculate qmax

• Construct IPR curve

• Assume pseudo-steady state radial

flow

Exercise 2

Inflow Performance

Solution

D/STB650,4

8.1

350,2562.3

8.1

pJq

psi/D/STB562.3

275.0411.0

000,2ln25.18.0

3514010x08.7

s75.0r

rlnB

kh10x08.7J

max

3

w

eoo

3

Exercise 2

Inflow Performance

Solution

0

500

1,000

1,500

2,000

2,500

0 1,000 2,000 3,000 4,000 5,000 6,000

Pw

f (p

sia

)

q, STB/D

Multiphase Flow

• Generalized Vogel

qmax

J pb

1.8

q O

O

qb

Rate

pwf

pb

Pre

ss

ure

p

Multiphase Flow

• How to find qmax:

2

b

wf

b

wfbmaxbb

wfb

p

p8.0

p

p2.01qqqq:thenqqfor

ppJq:applieslawsDarcy',qqfor

8.1

pJqq b

bmax

Exercise 3

• Reservoir parameters:

= 2,350 psia

k = 140 md

h = 35 ft

o = 0.8 cp

Bo = 1.25 rbbl/STB

re = 1,500 ft

rw = 0.411 ft

pb = 2,000 psia

s = 2

p

Exercise 3

• Calculate J

• Calculate qmax

• Construct IPR curve

• Assume pseudo-steady state radial

flow

Exercise 3

Inflow Performance

Solution

DSTB

pJqq

DSTB

ppJq

psiDSTBJ

bb

bb

/52058.1

2000562.31247

8.1

/1247

20002350562.3

//562.3

max

Exercise 2

Inflow Performance

Solution

0

500

1,000

1,500

2,000

2,500

0 1,000 2,000 3,000 4,000 5,000 6,000

Pw

f (p

sia

)

q, STB/D

24

Exercise:

A closed circular reservoir having pressure of 5651 psia will be put on

production with selected flowing bottom hole pressures. What would be

the production rates from the reservoir if the Pbhf is set to 5651 psia,

5000 psia, 3000 psia and 1000 psia.

The following data are given:

Porosity: 0.19

Permeability 8.2 md

Pay zone thickness: 53 ft

Bubble point pressure: 50 psia

Fluid formation volume factor: 1.1

Fluid viscosity : 1.7 cp

Total compressibility: 12.9 10-6

Drainage area: 640 acres

Wellbore radius 0.328 ft

No wellbore damage or improvement

Consider pseudo-steady state and steady state flow condition.

PETE – 331 Reservoir Deliverability

25

Exercise:

Calculate the productivity index of a well in a closed circular reservoir

having a pressure of 5651 psia and construct its IPR curve.

The following data are given:

Porosity: 0.19

Permeability 8.2 md

Pay zone thickness: 53 ft

Bubble point pressure: 50 psia

Fluid formation volume factor: 1.1

Fluid viscosity : 1.7 cp

Total compressibility: 12.9 10-6

Drainage area: 640 acres

Wellbore radius 0.328 ft

No wellbore damage or improvement

Consider pseudo-steady state flow condition.

PETE – 331 Reservoir Deliverability

26

Exercise:

Calculate the productivity index of a well in a closed circular reservoir

having a pressure of 5651 psia and construct its IPR curve using the

generalized Vogel equation.

The following data are given:

Porosity: 0.19

Permeability 8.2 md

Pay zone thickness: 53 ft

Bubble point pressure: 3000 psia

Fluid formation volume factor: 1.1

Fluid viscosity : 1.7 cp

Total compressibility: 12.9 10-6

Drainage area: 640 acres

Wellbore radius 0.328 ft

No wellbore damage or improvement

Consider pseudo-steady state flow condition.

PETE – 331 Reservoir Deliverability