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Reservoir Fluid Properties Course (2nd Ed.)

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

3. Introduction to Physical Properties

1. Gas Behavior
2. Gas Properties:
A. Z Factor:
a. Calculation for pure components
b. Calculation for mixture components
I. Mixing rules for calculating pseudocritical properties
II. Correlations for calculating pseudocritical properties

c. Nonhydrocarbon adjustment
d. High molecular weight gases adjustment

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.
Fall 13 H. AlamiNia

Reservoir Fluid Properties Course:

5

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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equation-of-state
For an ideal gas, the volume of molecules is
insignificant compared with the total volume
occupied by the gas.
It is also assumed that these molecules have no
attractive or repulsive forces between them, and
that all collisions of molecules are perfectly elastic.
Based on the above kinetic theory of gases, a
mathematical equation called equation-of-state can
be derived to express the relationship existing
between pressure p, volume V, and temperature T
for a given quantity of moles of gas n.
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The basic properties of gases
Petroleum engineers are usually interested in the
behavior of mixtures and rarely deal with pure
component gases.
Because natural gas is a mixture of hydrocarbon
components, the overall physical and chemical
properties can be determined from the physical
properties of the individual components in the mixture
by using appropriate mixing rules.

The basic properties of gases are commonly
expressed in terms of
the apparent molecular weight, standard volume,
density, specific volume, and specific gravity.
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Behavior of Ideal Gases
The gas density at any
P and T:

Specific Volume
the volume occupied by
a unit mass of the gas

Apparent Molecular
Weight
Specific Gravity

Standard Volume

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ideal gas behavior
Three pounds of n-butane are placed in a vessel at
120°F and 60 psia.
Calculate the volume of the gas assuming an ideal
gas behavior.
calculate the density of n-butane.

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ideal gas behavior
Step 1. Determine
the molecular weight of
n-butane from the Table to give:
M = 58.123

Step 2. Solve Equation for the volume of gas:

Step 3. Solve for the density by:
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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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Corresponding States Principle for
Pure components
the critical point of a fluid is where the liquid and
vapor molar volumes become equal;
i.e., there is no distinction between the liquid and vapor
phases.
above Tc the two phases can no longer coexits.

Each compound is characterized by
its own unique (Tc), (Pc) and (Vc)

Corresponding States Principle (CSP):
All fluids behave similarly when described in terms of
their reduced temperature and pressure
Tr=T/Tc and Pr=P/Pc

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Deviation from law of ideal gases
Theory of
Correspondin
g states

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one-fluid theory (mixtures)
Generally, we apply exactly the same equations for
mixtures by treating the mixture as
a hypothetical "pure" component whose properties are
some combination of the actual pure components that
comprise it.

We call this the one-fluid theory.
To apply CSP, we use the same plot or table as pure
components but
we make the temperature and pressure dimensionless
with pseudo criticals for the hypothetical pure fluid
instead of any one set of values as scaling variables from
pure component values.
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mixing rules
Mixing rules form the pseudocritical of the hypothetical
pure component (the mixture) by
taking some composition average of
each component's critical properties.

Many mixing rules are commonly used and provide
more accuracy than kay’s mixing rule.
You see other mixing rules in your thermodynamics class.

Kay's mixing rules is the simplest possible,
It obtains the pseudocritical for
the hypothetical pure component.

It use a simple mole fraction average for both Tc and Pc:
𝑇 𝑝𝑐 (𝑇 𝑐,𝑚 ) = 𝑖 𝑦 𝑖 𝑇 𝑐,𝑖 ,
Ppc ( 𝑃𝑐,𝑚 ) = 𝑖 𝑦 𝑖 𝑃 𝑐,𝑖
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Pseudo-Reduced Properties
Calculation (for mixtures)
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:
ppc and Tpc, do not represent the actual critical properties of
the gas mixture and are used as correlating parameters in
generating gas properties.
Fall 13 H. AlamiNia


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Standing and Katz Compressibility
Factors Chart

low pressure values (0 <= Ppr <= 15)
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low pressure values (0 <= Ppr <= 15)


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Standing and Katz Compressibility
Factors Chart
Based on the concept of
pseudo-reduced properties,
Standing and Katz (1942)
presented a generalized gas
compressibility factor chart.
 The chart represents
compressibility factors of
sweet natural gas as a
function of ppr and Tpr.
 This chart is generally
reliable for natural gas with
minor amount of
nonhydrocarbons.
 It is one of the most widely
accepted correlations in the
oil and gas industry.
for higher pressure values (15 <= Ppr <= 30)
Fall 13 H. AlamiNia


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Graphical method for Pseudo-Critical
Properties approximation
a graphical method for
a convenient
approximation of the
ppc and tpc of gases
when only the specific
gravity of the gas is
available.

Brown et al. (1948)
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Mathematical method for PseudoCritical Properties approximation
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 brown et al graphical
correlation in the following mathematical forms:
Case 1: Natural Gas Systems
Case 2: Gas-Condensate Systems

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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.
Wichert-Aziz correction method
B = mole fraction of H2S in the gas mixture
ε = pseudo-critical temperature adjustment factor
• where the coefficient A is the sum of the mole fraction H2S and
CO2 in the gas mixture, or:

Carr-Kobayashi-Burrows correction method

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computational steps of incorporating
Nonhydrocarbon adjustment
Step 1.
Calculate the pseudo-critical properties
of the whole gas mixture

Step 2.
Calculate the adjustment factor ε
 for Wichert-Aziz correction method

Step 3.
Adjust the calculated ppc and Tpc (as computed in Step 1)

Step 4.
Calculate the pseudo-reduced properties, i.e., ppr and Tpr

Step 5.
Read the compressibility factor from Figure
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accuracy of
the Standing-Katz factor chart
the Standing and Katz compressibility factor chart was
prepared from data on
binary mixtures of methane with propane, ethane, and
butane, and on natural gases,
thus covering a wide range in composition of hydrocarbon
mixtures containing methane.
No mixtures having molecular weights
in excess of 40 were included in preparing this plot.

Sutton (1985) evaluated the accuracy of
the Standing-Katz compressibility factor chart
using laboratory-measured
gas compositions and z factors, and found that
the chart provides satisfactory accuracy
for engineering calculations.
Fall 13 H. AlamiNia


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Correction For
High-molecular Weight Gases
However, Kay’s mixing rules, result in unsatisfactory
z-factors for high-molecular-weight reservoir gases.
The author observed that large deviations occur to
gases with high heptanes-plus concentrations.
He pointed out that Kay’s mixing rules should not be used to
determine the pseudo-critical pressure and temperature for
reservoir gases with specific gravities greater than about 0.75.

Sutton proposed that this deviation can be minimized
by utilizing
the mixing rules developed by Stewart (1959), together with
newly introduced empirical adjustment factors (FJ, EJ, and EK)
that are related to the presence of the heptane-plus fraction
in the gas mixture.
Fall 13 H. AlamiNia


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Sutton’s proposed mixing rules
Sutton’s proposed mixing rules for calculating the
pseudo-critical properties of high-molecular-weight
reservoir gases, i.e., γg > 0.75, should significantly
improve the accuracy of the calculated z-factor.
Step 1. Calculate the parameters J and K
where
J = Stewart-Burkhardt-Voo correlating parameter, °R/psia
K = Stewart-Burkhardt-Voo correlating parameter, °R/psia
yi = mole fraction of component i in the gas mixture.

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Sutton’s proposed mixing rules (Cont.)
Step 2. Calculate the adjustment parameters FJ, EJ,
and EK

where
yC7+ = mole fraction of the heptanes-plus component
(Tc)C7+ = critical temperature of the C7+
(pc)C7+ = critical pressure of the C7+
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Sutton’s proposed mixing rules (Cont.)
Step 3. Adjust the parameters J and K by applying
the adjustment factors EJ and EK:
J′ = J − EJ and K′ = K − EK

Step 4. Calculate the adjusted pseudo-critical
temperature and pressure from the expressions:
Step 5. Having calculated the adjusted Tpc and ppc,
the regular procedure of calculating the
compressibility factor from the Standing and Katz
chart is followed.
Fall 13 H. AlamiNia


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1. Ahmed, T. (2010). Reservoir engineering
handbook (Gulf Professional Publishing).
Chapter 2

Q921 rfp lec4

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