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Reservoir Engineering 1 Course (1st Ed.)

1. Productivity Index (PI)
2. Inflow Performance Relationship (IPR)
3. Generating IPR
A. Vogel’s Method
B. Vogel’s Method (Undersaturated Reservoirs)

1. Future IPR Approximation
2. Generating IPR for Oil Wells
A. Wiggins’ Method
B. Standing’s Method
C. Fetkovich’s Method

3. Horizontal Oil Well Performance
4. Horizontal Well Productivity

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.

2013 H. AlamiNia

Reservoir Engineering 1 Course: IPR Methods for Vertical Oil Wells / Horizontal Well

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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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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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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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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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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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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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Vogel’s vs. Wiggins’ IPR Curves

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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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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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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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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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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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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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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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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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Pressure Function Concept

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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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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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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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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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Fetkovich’s Method: Comparison
between Current and Future IPRs

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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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Advantages of Horizontal Oil Well
Since 1980, horizontal wells began capturing an
ever-increasing share of hydrocarbon production.
Horizontal wells offer the following advantages
over those of vertical wells:
Large volume of the reservoir can be drained by each
horizontal well.
Higher productions from thin pay zones.

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Advantages
of Horizontal Oil Well (Cont.)
Horizontal wells minimize water and gas zoning
problems.
In high permeability reservoirs, where near-wellbore gas
velocities are high in vertical wells, horizontal wells can
be used to reduce near-wellbore velocities and
turbulence.
In secondary and enhanced oil recovery applications,
long horizontal injection wells provide higher injectivity
rates.
The length of the horizontal well can provide contact
with multiple fractures and greatly improve productivity.

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Horizontal Oil Well vs. Vertical Oil Well
The actual production mechanism and reservoir
flow regimes around the horizontal well are
considered more complicated than those for the
vertical well, especially if the horizontal section of
the well is of a considerable length.
Some combination of both linear and radial flow actually
exists, and the well may behave in a manner similar to
that of a well that has been extensively fractured.

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IPRs for Horizontal Wells
Several authors reported that the shape of
measured IPRs for horizontal wells is similar to
those predicted by the Vogel or Fetkovich methods.
The authors pointed out that the productivity gain from
drilling 1,500-foot (460m) long horizontal wells is two to
four times that of vertical wells.

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Horizontal Well Illustration
Figure shows the
drainage area of a
horizontal well of length L
in a reservoir with a pay
zone thickness of h.
Each end of the
horizontal well would
drain a half-circular area
of radius b, with a
rectangular drainage
shape of the horizontal
well.
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Horizontal Well Drainage Area
A horizontal well can be looked upon as a number
of vertical wells drilling next to each other and
completed in a limited pay zone thickness.
Assuming that each end of the horizontal well is
represented by a vertical well that drains an area of
a half circle with a radius of b, Joshi (1991)
proposed the following two methods for calculating
the drainage area of a horizontal well.
Joshi noted that the two methods give different
values for the drainage area A and suggested
assigning the average value for the drainage of the
horizontal well.
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Joshi Method I
Joshi proposed that the drainage area is
represented by two half circles of radius b
(equivalent to a radius of a vertical well rev) at each
end and a rectangle, of dimensions L(2b), in the
center.
The drainage area of the horizontal well is given then by:
Where
A = drainage area, acres
L = length of the horizontal well, ft
b = half minor axis of an ellipse, ft
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Joshi Method II
Joshi assumed that the horizontal well drainage area is
an ellipse and given by:
Where a is the half major axis of an ellipse.

Most of the production rate equations require the
value of the drainage radius of the horizontal well,
which is given by:

Where

reh = drainage radius of the horizontal well, ft
A = drainage area of the horizontal well, acres

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IPR Calculations for Horizontal Wells
From a practical standpoint, inflow performance
calculations for horizontal wells are presented here
under the following two flowing conditions:
Steady-state single-phase flow
Pseudosteady-state two-phase flow

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Horizontal Well Productivity
under SS Flow
The steady-state analytical solution is the simplest
solution to various horizontal well problems.
The steady-state solution requires that the
pressure at any point in the reservoir does not
change with time.
The flow rate equation in a steady-state condition
is represented by:
Where
Qoh = horizontal well flow rate, STB/day
Δp = pressure drop from the drainage boundary to wellbore, psi
Jh = productivity index of the horizontal well, STB/day/psi
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Productivity Index
of the Horizontal Well
The productivity index of the horizontal well Jh can
be always obtained by dividing the flow rate Qoh by
the pressure drop Δp, or:
Several methods are designed to predict the
productivity index from the fluid and reservoir
properties. Some of these methods include:
Borisov’s Method
The Giger-Reiss-Jourdan Method
Joshi’s Method
The Renard-Dupuy Method
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Horizontal Well Productivity
under PSS Regime
The complex flow regime existing around a
horizontal wellbore probably precludes using a
method as simple as that of Vogel to construct the
IPR of a horizontal well in solution gas drive
reservoirs.
If at least two stabilized flow tests are available,
however, the parameters J and n in the Fetkovich
equation could be determined and used to
construct the IPR of the horizontal well.
In this case, the values of J and n would not only account
for effects of turbulence and gas saturation around the
wellbore, but also for the effects of nonradial flow
regime existing in the reservoir.
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1. Ahmed, T. (2006). Reservoir engineering
handbook (Gulf Professional Publishing). Ch7

1. Vertical Gas Well Performance
2. Pressure Application Regions
3. Turbulent Flow in Gas Wells
A. Simplified Treatment Approach
B. Laminar-Inertial-Turbulent (LIT) Approach (Cases A.
& B.)

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