Q921 re1 lec2 v1

Reservoir Engineering 1 Course (2nd Ed.)

1. Reservoir Fluid Behaviors
2. Petroleum Reservoirs
A. Oil
B. Gas

3. Gas Behavior
4. Gas Properties:
A.
B.
C.
D.

Z Factor
Isothermal gas compressibility (Cg)
Gas formation volume factor (Bg)
Gas Viscosity

Multiphase Behavior
Naturally occurring hydrocarbon systems found in
petroleum reservoirs are mixtures of organic
compounds that exhibit multiphase behavior over
wide ranges of pressures and temperatures.
These hydrocarbon accumulations may occur in the
gaseous state, the liquid state, the solid state, or in
various combinations of gas, liquid, and solid.

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Reservoir Engineering 1 Course: Petroleum Reservoirs Gas Properties

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Petroleum Engineers Task
These differences in phase behavior, coupled with
the physical properties of reservoir rock that
determine the relative ease with which gas and
liquid are transmitted or retained, result in many
diverse types of hydrocarbon reservoirs with
complex behaviors.
Frequently, petroleum engineers have the task to
study the behavior and characteristics of a
petroleum reservoir and to determine the course of
future development and production that would
maximize the profit.
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Classification of Reservoirs and
Reservoir Fluids
Petroleum reservoirs are broadly classified as oil or gas
reservoirs. These broad classifications are further
subdivided depending on:
The composition of the reservoir hydrocarbon mixture
Initial reservoir pressure and temperature
Pressure and temperature of the surface production

The conditions under which these phases exist are a
matter of considerable practical importance.
The experimental or the mathematical determinations
of these conditions are conveniently expressed in
different types of diagrams commonly called phase
diagrams. One such diagram is called the pressuretemperature diagram.
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Typical P-T Diagram
for a Multicomponent System

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Pressure-Temperature Diagram
Although a different hydrocarbon system would have a
different phase diagram, the general configuration is
similar. These multicomponent pressure-temperature
diagrams are essentially used to:
Classify reservoirs
Classify the naturally occurring hydrocarbon systems
Describe the phase behavior of the reservoir fluid

To fully understand the significance of the pressuretemperature diagrams, it is necessary to identify and
define the following key points on these diagrams:
Cricondentherm (Tct), Cricondenbar (pcb), Critical point,
Phase envelope (two-phase region), Quality lines, Bubblepoint curve, Dew-point curve
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Oil Reservoirs
Depending upon initial reservoir pressure pi, oil
reservoirs can be subclassified into the following
categories:
Undersaturated oil reservoir. If the initial reservoir
pressure pi, is greater than the bubble-point pressure Pb
of the reservoir fluid
Saturated oil reservoir. When pi is equal to the bubblepoint pressure of the reservoir fluid
Gas-cap reservoir or two-phase reservoir. If pi is below
the bubble point pressure of the reservoir fluid
The appropriate quality line gives the ratio of the gas-cap
volume to reservoir oil volume.
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Crude Oils
Crude oils cover a wide range in physical properties and
chemical compositions, and it is often important to be
able to group them into broad categories of related oils.
In general, crude oils are commonly classified into the
following types:
Ordinary black oil
Low-shrinkage crude oil
High-shrinkage (volatile) crude oil
Near-critical crude oil

The above classifications are essentially based upon the
properties exhibited by the crude oil, including physical
properties, composition, gas-oil ratio, appearance, and
pressure-temperature phase diagrams.
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Ordinary Black Oil

A typical p-T diagram for an ordinary black
Liquid-shrinkage curve for black oil
oil Reservoir Engineering 1 Course: Petroleum Reservoirs Gas Properties
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Low-Shrinkage Oil

A typical phase diagram for a low-shrinkage
Oil-shrinkage curve for low-shrinkage oil
oil Reservoir Engineering 1 Course: Petroleum Reservoirs Gas Properties
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Volatile Crude Oil

A typical p-T diagram for a volatile crude oil
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A typical liquid-shrinkage curve for a volatile
Reservoir Engineering 1 Course: Petroleum Reservoirscrude oil
Gas Properties
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Near-Critical Crude Oil

A schematic phase diagram for the nearA typical liquid-shrinkage curve for the nearcritical Properties
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Reservoir Engineering 1 Course: Petroleum Reservoirs Gas crude oil
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Liquid Shrinkage for Crude Oil Systems

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Gas Reservoirs
In general, if the reservoir temperature is above the
critical temperature of the hydrocarbon system, the
reservoir is classified as a natural gas reservoir. On
the basis of their phase diagrams and the prevailing
reservoir conditions, natural gases can be classified
into four categories:
Retrograde gas-condensate
Near-critical gas-condensate
Wet gas
Dry gas

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Retrograde Gas-Condensate

A typical phase diagram of a retrograde
A typical liquid dropout curve (liquid
system Reservoir Engineering 1 Course: Petroleum Reservoirs Gas Propertiesa condensate19
shrinkage volume curve for
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system)

Near-Critical Gas-Condensate

A typical phase diagram for a near-critical
Liquid-shrinkage curve for a near-critical gasgas
condensate system
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Wet Gas

Phase diagram for a wet gas

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Dry Gas

Phase diagram for a dry gas

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Compositions of
Various Reservoir Fluid Types

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Reservoir Fluid Properties
To understand and predict the volumetric behavior
of oil and gas reservoirs as a function of pressure,
knowledge of the physical properties of reservoir
fluids must be gained.
These fluid properties are usually determined by
laboratory experiments performed on samples of
actual reservoir fluids.
In the absence of experimentally measured
properties, it is necessary for the petroleum
engineer to determine the properties from
empirically derived correlations.
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Natural Gas Constituents
A gas is defined as a homogeneous fluid of low
viscosity and density that has no definite volume
but expands to completely fill the vessel in which it
is placed.
Generally, the natural gas is a mixture of
hydrocarbon and nonhydrocarbon gases.
The hydrocarbon gases that are normally found in a
natural gas are methanes, ethanes, propanes, butanes,
pentanes, and small amounts of hexanes and heavier.
The nonhydrocarbon gases (i.e., impurities) include
carbon dioxide, hydrogen sulfide, and nitrogen.
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Properties of Natural Gases
Knowledge of PVT relationships and other physical and
chemical properties of gases is essential for solving
problems in natural gas reservoir engineering. These
properties include:
 Apparent molecular weight, Ma
 Specific gravity, γg
 Compressibility factor, z
 Density, ρg
 Specific volume, v
 Isothermal gas compressibility coefficient, cg
 Gas formation volume factor, Bg
 Gas expansion factor, Eg
 Viscosity, μg

The above gas properties may be obtained from direct
laboratory measurements or by prediction from generalized
mathematical expressions.
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Behavior of Ideal Gases
The gas density at any
P and T:

Specific Volume

Apparent Molecular
Weight

Specific Gravity

Standard Volume

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Ideal Gases vs. Real Gases
In dealing with gases at a very low pressure, the
ideal gas relationship is a convenient and generally
satisfactory tool.
At higher pressures, the use of the ideal gas
equation-of-state may lead to errors as great as
500%, as compared to errors of 2–3% at
atmospheric pressure.

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Behavior of Real Gases
Basically, the magnitude of deviations of real gases
from the conditions of the ideal gas law increases
with increasing pressure and temperature and
varies widely with the composition of the gas.
The reason for this is that the perfect gas law was
derived under the assumption that the volume of
molecules is insignificant and that no molecular
attraction or repulsion exists between them.
Numerous equations-of-state have been developed in the
attempt to correlate the pressure-volume-temperature
variables for real gases with experimental data.

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Gas Compressibility Factor Definition
In order to express a more exact relationship
between the variables p, V, and T, a correction
factor called the gas compressibility factor, gas
deviation factor, or simply the z-factor, must be
introduced to account for the departure of gases
from ideality. The equation has the form of pV =
znRT
Where the gas compressibility factor z is a
dimensionless quantity and is defined as the ratio
of the actual volume of n-moles of gas at T and p to
the ideal volume of the same number of moles at
the same T and p:
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Pseudo-Reduced Properties
Calculation
Studies of the gas compressibility factors for natural
gases of various compositions have shown that
compressibility factors can be generalized with
sufficient accuracies for most engineering purposes
when they are expressed in terms of the following two
dimensionless properties:
Pseudo-reduced pressure and Pseudo-reduced temperature

These dimensionless terms are defined by the following
expressions:


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Standing and Katz Compressibility
Factors Chart

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Pseudo-Critical Properties Calculation
In cases where the composition of a natural gas is
not available, the pseudo-critical properties, i.e.,
Ppc and Tpc, can be predicted solely from the
specific gravity of the gas.
Standing (1977) expressed this graphical
correlation in the following mathematical forms:
Case 1: Natural Gas Systems
Case 2: Gas-Condensate Systems

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Pseudo-Critical Properties of Natural Gases

Brown et al. (1948) presented a
graphical method for a convenient
approximation of the pseudo-critical
pressure and pseudo-critical
temperature of gases when only the
specific gravity of the gas is
available.

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Nonhydrocarbon Components of
Natural Gases
Natural gases frequently contain materials other
than hydrocarbon components, such as nitrogen,
carbon dioxide, and hydrogen sulfide.
Hydrocarbon gases are classified as sweet or sour
depending on the hydrogen sulfide content.
Both sweet and sour gases may contain nitrogen, carbon
dioxide, or both.
A hydrocarbon gas is termed a sour gas if it contains one
grain of H2S per 100 cubic feet.

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Effect of Nonhydrocarbon
Components on the Z-Factor
The common occurrence of small percentages of
nitrogen and carbon dioxide is, in part, considered
in the correlations previously cited.
Concentrations of up to 5 percent of these
nonhydrocarbon components will not seriously affect
accuracy. Errors in compressibility factor calculations as
large as 10 percent may occur in higher concentrations
of nonhydrocarbon components in gas mixtures.

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Nonhydrocarbon Adjustment Methods
There are two methods that were developed to
adjust the pseudo-critical properties of the gases to
account for the presence of the nonhydrocarbon
components. These two methods are the:
Wichert-Aziz correction method

Carr-Kobayashi-Burrows correction method

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Direct Calculation of
Compressibility Factors
After four decades of existence, the Standing-Katz
z-factor chart is still widely used as a practical
source of natural gas compressibility factors.
As a result, there has been an apparent need for a
simple mathematical description of that chart.
Several empirical correlations for calculating z-factors
have been developed over the years including:
Hall-Yarborough
Dranchuk-Abu-Kassem
Dranchuk-Purvis-Robinson

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Compressibility of Natural Gases
Knowledge of the variability of fluid compressibility
with pressure and temperature is essential in
performing many reservoir engineering calculations.
For a liquid phase, the compressibility is small and
usually assumed to be constant.
For a gas phase, the compressibility is neither small nor
constant.
By definition, the isothermal gas compressibility is the change
in volume per unit volume for a unit change in pressure or, in
equation form:

Where cg = isothermal gas compressibility, 1/psi.
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Compressibility of Natural Gases
(Cont.)
From the real gas equation-of-state:
Differentiating the above equation with respect to pressure at
constant temperature T gives:

Substituting into Equation produces the following generalized
relationship:

For an ideal gas, z = 1 and (∂z/∂p) T = 0, therefore:
It should be pointed out that the equation is useful in determining
the expected order of magnitude of the isothermal gas
compressibility.
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Cg In Terms of
the Pseudoreduced Properties
The Equation can be conveniently expressed in terms of
the pseudoreduced pressure and temperature by
simply replacing p with (Ppc Ppr), or:

The term cpr is called the isothermal pseudo-reduced
compressibility and is defined by the relationship: cpr =
cg Ppc,
Values of (∂z/∂ppr) Tpr can be calculated from the
slope of the Tpr isotherm on the Standing and Katz zfactor chart.
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Gas Formation Volume Factor
The gas formation volume factor is used to relate
the volume of gas, as measured at reservoir
conditions, to the volume of the gas as measured at
standard conditions, i.e., 60°F and 14.7 psia.
This gas property is then defined as the actual
volume occupied by a certain amount of gas at a
specified pressure and temperature, divided by the
volume occupied by the same amount of gas at
standard conditions. In an equation form, the
relationship is expressed as
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Bg & Eg Calculation
Applying the real gas equation-of-state, and
substituting for the volume V, gives:
Assuming that the standard conditions:
Bg = gas formation volume factor, ft3/scf, z = gas
compressibility factor, T = temperature, °R
The reciprocal of the gas formation volume factor is
called the gas expansion factor and is designated by the
symbol Eg, or:
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Viscosity
The viscosity of a fluid is a measure of the internal
fluid friction (resistance) to flow.
If the friction between layers of the fluid is small,
i.e., low viscosity, an applied shearing force will
result in a large velocity gradient.
As the viscosity increases, each fluid layer exerts a larger
frictional drag on the adjacent layers and velocity
gradient decreases.
The viscosity of a fluid is generally defined as the ratio of
the shear force per unit area to the local velocity
gradient. Viscosities are expressed in terms of
centipoise.
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Gas Viscosity
The gas viscosity is not commonly measured in the
laboratory because it can be estimated precisely from
empirical correlations.
Like all intensive properties, viscosity of a natural gas is
completely described by the following function:
μg = (p, T, yi)
Where μg = the viscosity of the gas phase.

The above relationship simply states that the viscosity
is a function of pressure, temperature, and
composition. Many of the widely used gas viscosity
correlations may be viewed as modifications of that
expression.
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Methods of Calculating
the Viscosity of Natural Gases
Carr, Kobayashi, and Burrows (1954) developed
graphical correlations for estimating the viscosity of
natural gas as a function of temperature, pressure,
and gas gravity. The computational procedure of
applying the proposed correlations is summarized
in the following steps:
Step 1. Calculate the Ppc, Tpc and apparent molecular
weight from the specific gravity or the composition of
the natural gas.
Step 2. Obtain the viscosity of the natural gas at one
atmosphere and the temperature of interest from next
slide.
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Carr’s Atmospheric Gas Viscosity
Correlation

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The Carr’s Method (Cont.)
 This viscosity, as denoted by μ1, must be corrected for the
presence of nonhydrocarbon components by using the inserts
of previous slide.
The nonhydrocarbon fractions tend to increase the viscosity
of the gas phase. The effect of nonhydrocarbon components
on the viscosity of the natural gas can be expressed
mathematically by the following relationships:
 μ1 = (μ1) uncorrected + (Δμ) N2 + (Δμ) CO2 + (Δμ) H2S

Step 3. Calculate the Ppr and Tpr.
Step 4. From the Ppr and Tpr, obtain the viscosity ratio
(μg/μ1) from next slide.
Step 5. The gas viscosity, μg, at the pressure and temperature
of interest is calculated by multiplying the viscosity at one
atmosphere and system temperature, μ1, by the viscosity
ratio.
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Carr’s Viscosity Ratio Correlation

The term μg represents the viscosity
of the gas at the required
conditions.

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1. Ahmed, T. (2006). Reservoir engineering
handbook (Gulf Professional Publishing). Ch1,2

1. Crude Oil Properties:
A.
B.
C.
D.
E.
F.

Density
Solution gas
Bubble-point pressure
Oil formation volume factor (Bo)
Total formation volume factor (Bt)
…

Q921 re1 lec2 v1

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