This document summarizes key topics in reservoir engineering related to gas well performance and driving mechanisms. It covers turbulent gas flow models including the laminar-inertial-turbulent approach and pseudopressure method. It also discusses calculating inflow performance relationships, predicting future IPRs, modeling horizontal gas wells, and the primary recovery mechanisms of depletion drive, gas cap drive, water drive, and combination drive.

1. Reservoir Engineering 1 Course (1st Ed.)

2. 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.)

3. 1. Turbulent Flow in Gas Wells: LIT Approach
(Case C)
2. Comparison of Different IPR Calculation
Methods
3. Future IPR for Gas Wells
4. Horizontal Gas Well Performance
5. Primary Recovery Mechanisms
6. Basic Driving Mechanisms

5. Case C.
Pseudopressure Quadratic Approach
Pseudopressure Equation can be written as:
Where
The term (a2 Qg) represents the pseudopressure
drop due to laminar flow while the term (b2 Qg2)
accounts for the pseudopressure drop due to
inertial-turbulent flow effects.
The Equation can be linearized by dividing both
sides of the equation by Qg to yield:
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6. Case C. Graph of Real Gas PseudoPressure Data
The above
expression
suggests that a
plot of versus
Qg on a
Cartesian scale
should yield a
straight line
with a slope of
b2 and
intercept of a2
as shown in
Figure.
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7. Case C. Gas Flow Rate Calculation
Given the values of a2 and b2, the gas flow rate at
any pwf is calculated from:
It should be pointed out that the pseudopressure
approach is more rigorous than either the pressuresquared or pressure-approximation method and is
applicable to all ranges of pressure.
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9. The Back-Pressure Test
Rawlins and
Schellhardt (1936)
proposed a method for
testing gas wells by
gauging the ability of
the well to flow against
various back pressures.
This type of flow test is
commonly referred to
as the conventional
deliverability test.
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10. IPR for Different Methods
Figure
compares
graphically
the
performance
of each
method with
that of ψapproach.
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11. IPR for All Methods (Cont.)
Since the pseudo-pressure analysis is considered more
accurate and rigorous than the other three methods,
the accuracy of each of the methods in predicting the
IPR data is compared with that of the ψ-approach.
Results indicate that the pressure-squared equation
generated the IPR data with an absolute average error
of 5.4% as compared with 6% and 11% for the backpressure equation and the pressure approximation
method, respectively.
It should be noted that the pressure-approximation method is
limited to applications for pressures greater than 3000 psi.
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13. Future
Inflow Performance Relationships
Once a well has been tested and the appropriate
deliverability or inflow performance equation
established,
It is essential to predict the IPR data as a function of
average reservoir pressure.
The gas viscosity μg and gas compressibility z-factor
are considered the parameters that are subject to
the greatest change as reservoir pressure p–r
changes.
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14. Future IPR Methodology
Assume that the current average reservoir pressure is
p–r, with gas viscosity of μg1 and a compressibility
factor of z1. At a selected future average reservoir
pressure p–r2, μg2 and z2 represent the corresponding
gas properties.
To approximate the effect of reservoir pressure
changes, i.e. from p–r1 to p–r2, on the coefficients of
the deliverability equation, the following methodology
is recommended:
Back-Pressure Equation
LIT Methods
Pressure-Squared Method
Pressure-Approximation Method
Pseudopressure Approach
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15. Future IPR: Back-Pressure Equation
The performance coefficient C is considered a pressuredependent parameter and adjusted with each change of
the reservoir pressure according to the following
expression:
The value of n is considered essentially constant.
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16. Future IPR: LIT Methods
The laminar flow coefficient a and the inertial-turbulent
flow coefficient b of any of the previous LIT methods, are
modified according to the following simple relationships:
Pressure-Squared Method
• The coefficients a and b of pressure-squared are modified to
account for the change of the reservoir pressure from p–r1 to p–
r2 by adjusting the coefficients as follows:
• (the subscripts 1 and 2 represent conditions at reservoir pressure
p–r1 to p–r2, respectively.)
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17. Future IPR: LIT Methods (Cont.)
Pressure-Approximation Method
Pseudopressure Approach
• The coefficients a and b of the pseudo-pressure approach are
essentially independent of the reservoir pressure and they can be
treated as constants.
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18. Current and Future IPR Comparison
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20. Horizontal Gas Well
Many low permeability gas reservoirs are
historically considered to be noncommercial due to
low production rates.
Most vertical wells drilled in tight gas reservoirs are
stimulated using hydraulic fracturing and/or acidizing
treatments to attain economical flow rates.
In addition, to deplete a tight gas reservoir, vertical
wells must be drilled at close spacing to efficiently
drain the reservoir.
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21. Horizontal Gas Well (Cont.)
This would require a large number of vertical wells.
In such reservoirs, horizontal wells provide an attractive
alternative to effectively deplete tight gas reservoirs and
attain high flow rates.
Joshi (1991) points out those horizontal wells are
applicable in both low-permeability reservoirs as
well as in high-permeability reservoirs.
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22. Effective Wellbore Radius
in Horizontal Gas Well
 In calculating the gas
flow rate from a
horizontal well, Joshi
introduced the concept
of the effective
wellbore radius r′w into
the gas flow equation.
The effective wellbore
radius is given by:
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Where
L = length of the
horizontal well, ft
h = thickness, ft
rw = wellbore radius, ft
reh = horizontal well
drainage radius, ft
a = half the major axis of
drainage ellipse, ft
A = drainage area, acres
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23. Qg Calculation
from a Horizontal Gas Well
Methods of calculating the horizontal well drainage area A are
presented in previous lecture.
For a pseudosteady-state flow, Joshi expressed Darcy’s equation
of a laminar flow in the following two familiar forms:
Pressure-Squared Form
Where Qg = gas flow rate, Mscf/day
s = skin factor
k = permeability, md
T = temperature, °R
Pseudo-Pressure Form
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24. IPR Curve for Horizontal Gas Well
For turbulent flow, Darcy’s equation must be
modified to account for the additional pressure
caused by the non-Darcy flow by including the ratedependent skin factor DQg.
In practice, the back-pressure equation and the LIT
approach are used to calculate the flow rate and
construct the IPR curve for the horizontal well.
Multirate tests, i.e., deliverability tests, must be
performed on the horizontal well to determine the
coefficients of the selected flow equation.
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27. Reservoir Classification
Each reservoir is composed of a unique
combination of geometric form, geological rock
properties, fluid characteristics, and primary drive
mechanism.
Although no two reservoirs are identical in all
aspects, they can be grouped according to the
primary recovery mechanism by which they
produce.
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28. Driving Mechanisms Characteristics
It has been observed that each drive mechanism has
certain typical performance characteristics in terms of:
Ultimate recovery factor
Pressure decline rate
Gas-oil ratio
Water production
The recovery of oil by any of the natural drive
mechanisms is called primary recovery.
The term refers to the production of hydrocarbons from a
reservoir without the use of any process (such as fluid
injection) to supplement the natural energy of the reservoir.
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29. Primary Recovery Mechanisms
For a proper understanding of reservoir behavior
and predicting future performance, it is necessary
to have knowledge of the driving mechanisms that
control the behavior of fluids within reservoirs.
The overall performance of oil reservoirs is largely
determined by the nature of the energy, i.e., driving
mechanism, available for moving the oil to the
wellbore.
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30. Driving Mechanisms
There are basically six driving mechanisms that
provide the natural energy necessary for oil
recovery:
Rock and liquid expansion drive
Depletion drive
Gas cap drive
Water drive
Gravity drainage drive
Combination drive
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32. Rock and Liquid Expansion
At pressures above the bubble-point pressure, crude oil
(in undersaturated reservoirs), connate water, and rock
are the only materials present. As the reservoir
pressure declines, the rock and fluids expand due to
their individual compressibilities.
As the expansion of the fluids and reduction in the pore
volume occur with decreasing reservoir pressure, the
crude oil and water will be forced out of the pore space
to the wellbore.
This driving mechanism is considered the least efficient
driving force and usually results in the recovery of only
a small percentage of the total oil in place.
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33. The Depletion Drive Mechanism
This driving form may also be referred to by the
following various terms:
Solution gas drive
Dissolved gas drive
Internal gas drive
In this type of reservoir, the principal source of
energy is a result of gas liberation from the crude
oil and the subsequent expansion of the solution
gas as the reservoir pressure is reduced.
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34. Production Data
of a Solution-Gas-Drive Reservoir
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35. Gas Cap Drive
Gas-cap-drive reservoirs can be identified by the
presence of a gas cap with little or no water drive.
Due to the ability of the gas cap to expand, these
reservoirs are characterized by a slow decline in the
reservoir pressure. The natural energy available to
produce the crude oil comes from the following two
sources:
Expansion of the gas-cap gas
Expansion of the solution gas as it is liberated
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36. Production Data for a Gas-Cap-Drive
Reservoir
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37. The Water-Drive Mechanism
Many reservoirs are bounded on a portion or all of
their peripheries by water bearing rocks called
aquifers.
The aquifers may be so large compared to the
reservoir they adjoin as to appear infinite for all
practical purposes, and they may range down to
those as small as to be negligible in their effects on
the reservoir performance.
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38. Types of Aquifers
The aquifer itself may be entirely bounded by
impermeable rock so that the reservoir and aquifer
together form a closed (volumetric) unit.
On the other hand, the reservoir may be
outcropped at one or more places where it may be
replenished by surface water.
Regardless of the source of water, the water drive is
the result of water moving into the pore spaces
originally occupied by oil, replacing the oil and
displacing it to the producing wells.
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39. Reservoir Having Artesian Water Drive
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40. Aquifer Geometries
It is common to speak
of edge water or
bottom water in
discussing water influx
into a reservoir.
Bottom water occurs
directly beneath the oil
and edge water occurs
off the flanks of the
structure at the edge of
the oil
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41. Production Data
for a Water-Drive Reservoir
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42. The Gravity-Drainage-Drive
Mechanism
The
mechanism of
gravity
drainage
occurs in
petroleum
reservoirs as a
result of
differences in
densities of
the reservoir
fluids.
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43. The Combination-Drive Mechanism
The driving mechanism most commonly
encountered is one in which both water and free
gas are available in some degree to displace the oil
toward the producing wells.
Two combinations of driving forces can be present
in combination drive reservoirs. These are
(1) Depletion drive and a weak water drive and;
(2) Depletion drive with a small gas cap and a weak
water drive.
Then, of course, gravity segregation can play an
important role in any of the aforementioned drives.
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44. Combination-Drive Reservoir
The most
common type
of drive
encountered,
therefore, is a
combinationdrive
mechanism as
illustrated in
Figure.
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45. 1. Ahmed, T. (2006). Reservoir engineering
handbook (Gulf Professional Publishing). Ch8
& 11