The document discusses inflow performance relationships (IPRs), which represent the relationship between flow rate from a reservoir to a wellbore and bottomhole pressure. It covers IPRs for single-phase, two-phase, and three-phase flow. For single-phase flow, the IPR shows a linear relationship between flow rate and pressure. For two-phase and three-phase flow, the presence of additional phases like gas causes the IPR curve to deviate from linear. The document also discusses methods for predicting future IPR curves based on changes in parameters like reservoir pressure and productivity index over time.

1. INFLOW PERFORMANCE
RELATIONSHIP
The flow performance of reservoir fluid from the reservoir
to the wellbore
1

2. Inflow Performance Relationship
□ Representing the flow
rate from the reservoir
to the bottom of the
well
□ The production
performance shows the
relationship between
flow rate to the bottom
hole pressure
□ Its is assumed that the
reservoir fluid flow
follows single well radial
model
2
Porous Media
(porosity, permeability,
rock compressibility,
etc)
Near Wellbore Condition
Open hole, Perforation,
Damage Zone, Fracturing
and Azidizing
Pr
Pwf
Pr
Reservoir Fluids:
Gas, Oil and Water Number of Phases
Reservoir
Boundary
Wellbore
Flow
direction

3. Fluid Flow Modelling in a Single Well
3
Porous Media
(porosity,
permeability, rock
compressibility, etc)
Near Wellbore Condition
Open hole, Perforation,
Damage Zone,
Fracturing and Azidizing
Pr
Pwf
Pr
Reservoir Fluids:
Gas, Oil and
Water Number of Phases

4. Mathematical Representation
Fluid Flow to the Wellbore
□ Basic partial differential equation
for fluid flow in a radial porous
media,
□ The equation is considered as non-
linear, since the implicit pressure
dependence of density,
compressibility, and viscosity.
□ The solution of the PDE can be
obtained after imposing the
boundary equation.
□ The boundary condition is
□ Steady state condition, so dp/dt = 0
Or
□ Semi steady state condition, so dp/dt = C
□ Both boundary conditions yield
different solution.
□ The solutions are shown on the next
slide.
4
 = f(P)
= f(P)
c = f(P)

5. Solution for Single Phase (Oil) Flow
5
Note :
• Pe is pressure at the boundary
• P bar is average reservoir pressure
•Q is production rate
• r is distance from the well
• re is distance of reservoir boundary
• rw is wellbore radius
Note :
•  is viscosity
• k is reservoir permeability
• h is thickness of reservoir
• S is skin factor, that show the condition
near the wellbore

6. Drainage Area Shape Factors
6

7. Inflow Performance Relationship
□ For single phase (oil) semi steady state solution,
based on average reservoir pressure
7
• The inflow performance relationship shows
the relation between pressure at the
wellbore (Pwf) and production rate (q)
• At a certain time, the rest of variables are
constant

8. Inflow Performance Relationship
□ IPR could also be represented by
Productivity Index, i.e.:
□ The ability of reservoir to produce oil
(bbl/day) for one psi drawdown
8
• PI : productivity Index, bbl/d/psi
• Drawdown is (Pe – Pwf)

9. The Well Productivity Using IPR
□ The slope of graph represent
the productivity index (PI)
□ At Pwf = Pr, the production rate
is zero
□ At Pwf = 0, the production rate
is maximum
□ Using the IPR curve, for certain
flowing bottom hole pressure
the corresponding rate could
be obtained, vise versa
□ The IPR is very important to
determine the ability of well to
produce
9
0
500
1000
1500
2000
2500
3000
0 1000 2000 3000 4000 5000 6000
Laju produksi, stb/d
Tekanan
Alir
dasar
Sumur,
psi
Slope is PI
Pr
qmax

10. Class Problem - IPR
□ The pressure build up test data
obtained the following data:
□ The average reservoir
pressure is 1542 psi
□ The corresponding
production rate to the
flowing bottom hole
pressure is 255 bbl/d to 1109
psi
□ The bubble point pressure is
low, about 50 psi
□ Water cut is considered very
low
□ Construct the IPR Curve
□ Determine the
maximum flow rate
□ Calculate the flow rate
at Pwf = 980 psi
10

11. The Limitations of Oil IPR
□ In real conditions, most of the
well produced two or three
phase of reservoir fluid.
□ Two phase IPR represents gas
and oil flow in the reservoir
□ Three phase IPR represents gas,
oil, and water flow in the reservoir
□ In multiphase flow in reservoir, the
following phenomenons are
occurred:
□ When the pressures at the reservoir fall
below the bubble point pressure, then
the gas coming out from the solution,
and flows in the porous medium
□ Gas and oil flow is determined by the
relative permeability of gas and oil
□ At this condition the single phase
(oil) IPR does not valid
11
0
500
1000
1500
2000
2500
3000
0 1000 2000 3000 4000 5000 6000
Laju produksi, stb/d
Tekanan
Alir
dasar
Sumur,
psi

12. Two Phase Flow Conditions in the Reservoir
12
Oil Phase Pr
Oil Phase Pr
Pwf
Pwf
P(r) > Pb
P(r) < Pb
P(rx) = Pb
Gas + Oil Oil Phase Pr
Pwf
P(r > rx) > Pb
P(r < rx) > Pb
rx
Skin

13. Two Phase (gas & oil) IPR
□ In a oil system , the gas is dissolved in oil
phase, when the reservoir pressure
above the bubble point pressure.
□ When the pressure below the bubble
point pressure, gas will out from the
solution, become free gas. This situation
will cause the oil viscosity increases.
□ The free gas fill rock pores, it will
increase the gas saturation and
decreasing the oil saturation
□ If gas saturation increases, the value of
gas relative permeability increases. On
the other hands, the oil relative
permeability decreases due to oil
saturation decreases.
□ Therefore, the relationship between
production rate to the bottom hole
flowing pressure is not linear.
13

14. Two-Phase Flow Equation
14
□ Two-Phase Flow (Oil + Gas) in Porous
Medium

15. Two Phase (Oil & Gas) IPR
□ Refer to reservoir condition, where
Pr > Pb,
□ This makes the IPR curve
deviating from the linear trend
below bubble-point pressure
□ The lower the pressure, the larger
the deviation. If the reservoir
pressure is below the initial
bubble-point pressure, oil and gas
two phase flow exists in the whole
reservoir domain and the reservoir
is referred as a ‘‘two-phase
reservoir.’’
15
Pb
Linear section
Non-Linear section

16. Vogel’s Dimensionless IPR (no-skin factor)
16
2
r
wf
r
wf
max
o
P
P
8
.
0
P
P
2
.
0
0
.
1
Q
q














=
Two-Phase IPR Curve could be constructed by applying pressure build
up test data, that are reservoir pressure, and oil production with
corresponding flowing bottom hole pressure.
2
)
(
)
(
)
(
)
(
)
(
max
8
.
0
2
.
0
0
.
1






















=
test
r
test
wf
test
r
test
wf
test
o
P
P
P
P
q
Q






















=
2
max 8
.
0
2
.
0
0
.
1
r
wf
r
wf
o
P
P
P
P
Q
q
IPR curve Equation:

17. Two Phase IPR with Skin
3
2
max
)
(
42
.
0
)
(
44
.
0
)
(
14
.
0
1
r
wf
r
wf
r
wf
o
P
P
P
P
P
P
Q
Q



=
Sukarno & Jurgantono (Tugas Akhir):
- 4 < Faktor Skin > 10
2
Pr
Pwf
1.0446
-
Pr
Pwf
0.0446
1
Qmax
Qo













=

18. Mathematical Modelling for 3-Phase IPR
18
□ Model Pengembangan IPR 3 – fasa
□ Sukarno (Disertation) and Wiggins (SPE 124041)
Gas, Oil and Water
Sumur Gas, oil, and water flow simultaneously
Sw = 1 – So - Sg
Method of Calculation IMPES

19. Wiggins’ Three Phase Dimensionless IPR
2
r
wf
r
wf
max
o,
o
)
P
P
0.481092(
)
P
P
0.519167(
1
q
q


=
0
500
1000
1500
2000
2500
3000
0 1000 2000 3000 4000 5000
Laju Produksi, stb/d
Tekanan
Dasar
Sumur,
psi
qo
qw
qt
2
r
wf
r
wf
max
w,
w
)
P
P
0.284777(
)
P
P
0.722235(
1
q
q


=
Oil Dimensionless IPR
Water Dimensionless IPR

20. FUTURE IPR CURVES
Predicting future production rate of a well is very important,
especially for designing artificial lift equipment specification,
production allocation for each well, and to estimate the
production rate or flowing bottom hole pressure.
20

21. Two-Phase Production Rate Equation
21
As a function of pressure
Kro as function of
Oil saturation
So = f(P)
Changing to time

22. Future Two-Phase IPR
□ The changing of two-phase IPR curve is
represented by the changing of slope of the
curve, that means the productivity index, J.
□ For two-phase IPR, the productivity index
could be represented by dq/dPwf = J
□ This statement could be applied to predict
the future two-phase IPR
22

23. The Changing of Productivity Index (1)
23

24. The Changing of Productivity Index (2)
□ Muskat stated that the ratio
of Productivity Index at two
consequtive time could be
represented by the mobility
ratio
□ Productivity Index is defined
of the slope of IPR curve wf
dP
dq
J =
24

25. The Changing of Productivity Index (3)
25
 
r
max
o
*
p
P
Q
8
.
1
J =
Based on Vogel’s Equation, the Productivity Index, (dq/dPwf)
could be represented by
Subscript “p” represent at present time
Therefore , the ratio of future
and present J could be
represented by the ratio of
Mobility at the future and
present.

26. Fetkovich Formulation
□ Assuming that kro/oBo
is linear to pressure,
therefore kro/oBo ratio
of mobility at two
different pressure is
equal to the pressure
ratio.
□ Therefore the
productivity index ratio
is equal to the reservoir
pressure ratio.
2
r
1
r
2
1
P
P
J
J
=
26
ri
r
P
o
o
ro
P
o
o
ro
P
P
B
k
B
k
ri
r
=



















27. Persamaan Fetkovich
rf
ri
Pr
Pr
P
P
J
J
f
i
=
 n
2
wf
2
rf
Pr
o P
P
J
q f

=
 n
2
wf
2
rf
ri
rf
i
Pr
o P
P
P
P
J
q 
=
ri
rf
Pr
Pr
P
P
J
J i
f
=
27
The value of J and n are
obtained from isochronal
test
Using Fetkovich’s Equation, and by
assuming J and n are constants thru time

28. Eckmeir’s Equation to Predict IPR
□ Assuming “n” equal to 1.0, the ratio of maximum flow rate of
two reservoir pressure could be represented as follows:
3
1
r
2
r
1
max
o
2
max
o
P
P
Q
Q








=
3
ri
rf
i
max
o
f
max
o
P
P
Q
Q 







=
28

29. Future IPR Curve - Sukarno
   
 
wf
r
w
e
3
o P
m
P
m
S
5
.
0
r
r
ln
kh
10
08
.
7
q 











=

29
 
r
w
e
3
max
o P
m
S
5
.
0
r
r
ln
kh
10
08
.
7
Q











=

 
 
ri
rf
i
max
o
f
max
o
P
m
P
m
Q
Q
=
For Pwf = 0 then Qo,max:
The Qmax ratio is equal to

30. Future IPR Curve - Sukarno
 
  







=
ri
rf
ri
rf
P
P
429922
.
3
exp
033210
.
0
P
m
P
m
 
  







=
ri
rf
ri
rf
P
P
152343
.
4
exp
015215
.
0
P
m
P
m
 
 
ri
rf
i
max
o
f
max
o
P
m
P
m
Q
Q =
30
API > 40
API < 40
2
Pr
Pwf
1.0446
-
Pr
Pwf
0.0446
1
Qmax
Qo













=

31. The Changing of IPR Curve Due to The
Changing of Reservoir Pressure
31
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1000 2000 3000 4000 5000 6000
Laju Produksi, stb/d
Tekanan
Alir
dasar
Sumur,
psi
Awal
Np= 8601
Np=17202
Np=25804
Np=34405
Np=43006
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 10000 20000 30000 40000 50000
Produksi Kumulatif, stb
Tekanan
Reservoir,
psi

32. Persamaan peramalan kurva ipr
32
3
ri
rf
i
max
o
f
max
o
P
P
Q
Q 







=
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1000 2000 3000 4000 5000 6000
Laju Produksi, stb/d
Tekanan
Alir
dasar
Sumur,
psi
Awal
Np= 8601
Np=17202
Np=25804
Np=34405
Np=43006
Q-max-f Q-max-i
Pr-i
Pr-f

33. The Valid Assumption in the Application of Future
IPR
□ The well producing from solution gas drive reservoir
□ The well have not changed the producing formation
□ The well had never been stimulated (acidizing or fracturing)
33

34. END OF MEETING
34