2. 1. Superposition
A. Multiple Well
B. Multi Rate
C. Reservoir Boundary
2. Productivity Index (PI)
3. Inflow Performance Relationship (IPR)
3. 1. Generating IPR for Oil Wells
A. Vogel’s Method
B. Vogel’s Method (Undersaturated Reservoirs)
a.
Future IPR Approximation
C. Wiggins’ Method
D. Standing’s Method
E. Fetkovich’s Method
4. Vogel’s Method
Vogel (1968) used a computer model to generate
IPRs for several hypothetical saturated-oil reservoirs
that are producing under a wide range of
conditions.
Vogel normalized the calculated IPRs and expressed the
relationships in a dimensionless form. He normalized the
IPRs by introducing the following dimensionless
parameters:
Where (Qo) max is the flow rate at zero wellbore
pressure, i.e., AOF.
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5. Vogel’s IPR
Vogel plotted the dimensionless IPR curves for all the
reservoir cases and arrived at the following relationship
between the above dimensionless parameters:
Where Qo = oil rate at pwf
(Qo) max = maximum oil flow rate at zero wellbore
pressure, i.e., AOF
p–r = current average reservoir pressure, psig
pwf = wellbore pressure, psig
Notice that pwf and p–r must be expressed in psig.
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6. Vogel’s Method for Comingle
Production of Water and Oil
Vogel’s method can be extended to account for
water production by replacing the dimensionless
rate with QL/(QL) max where QL = Qo + Qw.
This has proved to be valid for wells producing at water
cuts as high as 97%.
The method requires the following data:
Current average reservoir pressure p–r
Bubble-point pressure pb
Stabilized flow test data that include Qo at pwf
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7. Vogel’s Methodology Applications
Vogel’s methodology can be used to predict the IPR
curve for the following two types of reservoirs:
Saturated oil reservoirs p–r ≤ pb
Undersaturated oil reservoirs p–r > pb
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8. Vogel’s Method:
Saturated Oil Reservoirs
When the reservoir pressure equals the bubblepoint pressure, the oil reservoir is referred to as a
saturated-oil reservoir.
The computational procedure of applying Vogel’s
method in a saturated oil reservoir to generate the
IPR curve for a well with a stabilized flow data
point, i.e., a recorded Qo value at pwf, is
summarized below:
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9. Vogel’s Method:
Saturated Oil Reservoirs (Cont.)
Step 1. Using the stabilized flow data, i.e., Qo and
pwf, calculate (Qo)max from:
Step 2. Construct the IPR curve by assuming various
values for pwf and calculating the corresponding Qo
from:
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10. Vogel’s Method:
Undersaturated Oil Reservoirs
Beggs (1991) pointed out that in applying Vogel’s
method for undersaturated reservoirs, there are
two possible outcomes to the recorded stabilized
flow test data that must be considered, as shown
schematically in next slide:
The recorded stabilized Pwf is greater than or equal to
the bubble-point pressure, i.e. pwf ≥ pb
The recorded stabilized pwf is less than the bubble-point
pressure pwf < pb
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11. Stabilized flow test data
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12. Vogel’s Method: Undersaturated Oil
Reservoirs (Pwf≥Pb)
Beggs outlined the following procedure for
determining the IPR when the stabilized bottomhole pressure is greater than or equal to the bubble
point pressure:
Step 1. Using the stabilized test data point
(Qo and pwf) calculate the productivity index J:
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13. Vogel’s Method: Undersaturated Oil
Reservoirs (Pwf≥Pb) (Cont.)
Step 2. Calculate the oil flow rate at the bubblepoint pressure:
Where Qob is the oil flow rate at pb
Step 3. Generate the IPR values below the bubblepoint pressure by assuming different values of pwf
< pb and calculating the corresponding oil flow
rates by applying the following relationship:
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14. Vogel’s Method: Undersaturated Oil
Reservoirs (Pwf≥Pb) (Cont.)
The maximum oil flow rate (Qo max or AOF) occurs
when the bottom hole flowing pressure is zero, i.e.
pwf = 0, which can be determined from the above
expression as:
It should be pointed out that when pwf ≥ pb, the
IPR is linear and is described by:
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15. Vogel’s Method: Undersaturated Oil
Reservoirs (Pwf<Pb)
When the recorded pwf from the stabilized flow
test is below the bubble point pressure, the
following procedure for generating the IPR data is
proposed:
Step 1. Using the stabilized well flow test data and
combining above equations, solve for the productivity
index J to give:
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16. Vogel’s Method: Undersaturated Oil
Reservoirs (Pwf<Pb) (Cont.)
Step 2. Calculate Qob by using:
Step 3. Generate the IPR for pwf ≥ pb by assuming
several values for pwf above the bubble point pressure
and calculating the corresponding Qo from:
Step 4. Use below Equation to calculate Qo at various
values of pwf below pb, or:
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17. IPR Prediction
Quite often it is necessary to predict the well’s
inflow performance for future times as the
reservoir pressure declines.
Future well performance calculations require the
development of a relationship that can be used to
predict future maximum oil flow rates.
Several methods are designed to address the
problem of how the IPR might shift as the reservoir
pressure declines.
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18. IPR Prediction (Cont.)
Some of these prediction methods require the
application of the material balance equation to
generate future oil saturation data as a function of
reservoir pressure.
In the absence of such data, there are two simple
approximation methods that can be used in conjunction
with Vogel’s method to predict future IPRs.
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19. IPR Prediction:
1st Approximation Method
This method provides a rough approximation of the
future maximum oil flow rate (Qomax)f at the
specified future average reservoir pressure (pr)f.
This future maximum flow rate (Qomax) f can be used in
Vogel’s equation to predict the future inflow
performance relationships at (p–r)f.
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20. IPR Prediction:
1st Approximation Method (Cont.)
Step 1. Calculate (Qomax)f at (p–r)f from:
Where the subscript f and p represent future and
present conditions, respectively.
Step 2. Using the new calculated value of (Qomax)f
and (p–r)f, generate the IPR by:
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21. IPR Prediction:
2nd Approximation Method
A simple approximation for estimating future
(Qomax)f at (p–r)f is proposed by Fetkovich (1973).
The relationship has the following mathematical
form:
Where the subscripts f and p represent future and
present conditions, respectively.
The above equation is intended only to provide a rough
estimation of future (Qo)max.
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22. Wiggins’ Method
Wiggins (1993) used four sets of relative
permeability and fluid property data as the basic
input for a computer model to develop equations to
predict inflow performance.
The generated relationships are limited by the
assumption that the reservoir initially exists at its
bubble-point pressure.
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23. Wiggins’ Method (Cont.)
Wiggins proposed generalized correlations that are
suitable for predicting the IPR during three-phase
flow.
His proposed expressions are similar to that of
Vogel’s and are expressed as:
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24. Vogel’s vs. Wiggins’ IPR Curves
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25. Standing’s Method
Standing (1970) essentially extended the
application of Vogel’s to predict future inflow
performance relationship of a well as a function of
reservoir pressure.
He noted that Vogel’s equation can be rearranged
as:
Standing introduced the productivity index J as
defined by J=Qo/ ((p–r)-pwf) into above Equation to
yield:
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26. Standing’s
Zero-Drawdown Productivity Index
Standing then defined the present (current) zero
drawdown productivity index as:
Where J*p is Standing’s zero-drawdown
productivity index. The J*p is related to the
productivity index J by:
J=Qo/ ((p–r)-pwf) Equation permits the calculation
of J*p from a measured value of J.
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27. Standing’s Final Expression
for IPR Prediction
To arrive at the final expression for predicting the
desired IPR expression, Standing combines
Equations to eliminate (Qo)max to give:
Where the subscript f refers to future condition.
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28. Standing’s Drawdown
Productivity Index (J*P)
Standing suggested that J*f can be estimated from
the present value of J*p by the following
expression:
Where the subscript p refers to the present
condition.
If the relative permeability data are not available,
J*f can be roughly estimated from:
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29. Summary of Standing’s Method
Standing’s methodology for predicting a future IPR
is summarized in the following steps:
Step 1. Using the current time condition and the
available flow test data, calculate (Qo)max from
Equations below.
Step 2. Calculate J* at the present condition, i.e.,
J*p.
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30. Summary
of Standing’s Method (Cont.)
Step 3. Using fluid property, saturation, and relative
permeability data, calculate both (kro/μoBo)p and
(kro/μoBo)f.
Step 4. Calculate J*f by using below Equation. Use
the other equation if the oil relative permeability
data are not available.
Step 5. Generate the future IPR by applying below
equation.
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31. Disadvantages
of Standing’s Methodology
It should be noted that one of the main
disadvantages of Standing’s methodology is that:
It requires reliable permeability information;
In addition, it also requires material balance calculations
to predict oil saturations at future average reservoir
pressures.
It should be pointed out Fetkovich’s method has
the advantage over Standing’s methodology
In that, it does not require the tedious material balance
calculations to predict oil saturations at future average
reservoir pressures.
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32. Fetkovich’s Method
Muskat and Evinger (1942) attempted to account
for the observed nonlinear flow behavior (i.e., IPR)
of wells
by calculating a theoretical productivity index from the
pseudosteady-state flow equation.
They expressed Darcy’s equation as:
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33. Pressure Function Concept
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34. Fetkovich’s Method: 1st Case
In the application of the straight-line pressure
function, three cases must be considered:
Case 1: p–r and pwf > pb
Where Bo and μo are evaluated at (p–r+ pwf)/2.
Case 2: p–r and pwf < pb
Case 3: p–r > pb and pwf < pb
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35. Fetkovich’s Method:
2nd Case, Present IPR
The term (J/2pb) is commonly referred to as the
performance coefficient C, or:
To account for the possibility of non-Darcy flow (turbulent flow)
in oil wells, Fetkovich introduced the exponent n to yield:
The value of n ranges from 1.000 for a complete laminar flow to
0.5 for highly turbulent flow.
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36. Fetkovich’s Method:
2nd Case, Calculation of C and N
There are two unknowns in the Equation:
The performance coefficient C and the exponent n.
At least two tests are required to evaluate these two
parameters:
A plot of p–2r− p2wf versus Qo on log-log scales will result in a
straight line having a slope of 1/n and an intercept of C at p–2r−
p2wf = 1.
The value of C can also be calculated using any point on the
linear plot once n has been determined to give:
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37. Fetkovich’s Method:
2nd Case, Future IPR
To construct the future IPR when the average
reservoir pressure declines to (p–r)f,
Fetkovich assumes that the performance coefficient C is
a linear function of the average reservoir pressure and,
Therefore, the value of C can be adjusted as:
Fetkovich assumes that the value of the exponent n would not
change as the reservoir pressure declines.
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38. Fetkovich’s Method: Comparison
between Current and Future IPRs
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39. Fetkovich’s Method: 3rd Case
Case 3: p–r > pb and pwf < pb
μo and Bo are evaluated at the bubble-point
pressure pb.
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40. 1. Ahmed, T. (2010). Reservoir engineering
handbook (Gulf Professional Publishing).
Chapter 7
41. 1.
2.
3.
4.
5.
Horizontal Oil Well Performance
Horizontal Well Productivity
Vertical Gas Well Performance
Pressure Application Regions
Turbulent Flow in Gas Wells
A. Simplified Treatment Approach
B. Laminar-Inertial-Turbulent (LIT) Approach
(Cases A. & B.)
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