This document provides an overview of methods for calculating gas properties including: 1. Empirical correlations for calculating z-factors such as Hall-Yarborough and Dranchuk-Abu-Kassem. 2. Calculation of gas compressibility, gas formation volume factor, and gas expansion factor using real gas equations of state. 3. Empirical correlations for calculating gas viscosity including Carr-Kobayashi-Burrows and Lee-Gonzalez-Eakin.

1. Reservoir Fluid Properties Course (3rd Ed.)

2. 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

3. 1. empirical correlations for calculating z-factors
2. Gas Properties:
A. isothermal gas compressibility (Cg)
B. gas formation volume factor (Bg) and
gas expansion factor (Eg)
C. Gas Viscosity correlations

5. 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
• It is not recommended for application if Tpr is less than one.
Dranchuk-Abu-Kassem (DAK)
• is applicable over the ranges: 0.2 < ppr < 15 and 1.0 < Tpr < 3.0
Dranchuk-Purvis-Robinson
• is valid within the ranges: 1.05 < Tpr < 3.0 and 0.2 < ppr < 3.0
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 5

6. The Hall-Yarborough (1973) Method
They presented an equation-of-state that accurately
represents the Standing and Katz z-factor chart.
The proposed expression is based on the Starling-Carnahan
equation-of-state.
where
t = reciprocal of the pseudo-reduced temperature, i.e., Tpc/T
Y = the reduced density and obtained as the solution of:
• X1 = −0.06125 ppr t exp [−1.2 (1 − t)2]
• X2 = (14.76 t − 9.76 t2 + 4.58 t3)
• X3 = (90.7 t − 242.2 t2 + 42.4 t3)
• X4 = (2.18 + 2.82 t)
It is a nonlinear equation and can be solved for the reduced density
Y by using the Newton-Raphson iteration technique.
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7. The computational procedure of
solving F(Y) at any specified Ppr & Tpr
Step 1. an initial guess of the unknown parameter, Yk,
 where k is an iteration counter.
Step 2. Substitute this initial value in F(Y) and
evaluate the nonlinear function.
Step 3. A new improved estimate of Y, i.e., Yk+1, from:
Step 4. Steps 2–3 are repeated n times, until the error, i.e., abs(Yk
− Yk+1), becomes smaller than a preset tolerance, e.g., 10^−12.
Step 5. The correct value of Y is then
used for the compressibility factor.
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8. The Dranchuk-Abu-Kassem Method
prerequisite
Dranchuk and Abu-Kassem (1975)
derived an analytical expression
for calculating the reduced gas density ρr
that used to estimate the gas compressibility factor.
ρr is defined as the ratio of the gas density at a
specified pressure and temperature to that of the
gas at its critical pressure or temperature, or:
The critical gas compressibility factor zc is
approximately 0.27, which leads to:
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 8

9. Calculation of the reduced gas density
The authors proposed the eleven-constant
equation-of-state for calculating the reduced gas
density:
The coefficients have the following values:
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 9

10. The Dranchuk-Abu-Kassem Method
(DAK)
The eleven-constant equation-of-state for
calculating the reduced gas density ρr can be solved
by applying the Newton-Raphson iteration
technique.
The correct value of ρr is then used to evaluate the
compressibility factor, i.e.:
The proposed correlation was reported
to duplicate compressibility factors
from the Standing and Katz chart
with an average absolute error of 0.585 percent.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 10

11. The Dranchuk-Purvis-Robinson
Method
Dranchuk, Purvis, and Robinson (1974) developed a
correlation based on the Benedict-Webb-Rubin
type of equation-of-state.
Fitting the equation to 1,500 data points from the
Standing and Katz z-factor chart optimized the eight
coefficients of the proposed equations. The equation has
the following form:
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 11

12. The Dranchuk-Purvis-Robinson
Method (Cont.)
where ρr is defined by
(the same as The Dranchuk-Abu-Kassem Method)
the coefficients A1 through A8 have the following
values:
The solution procedure is similar to that of
Dranchuk and Abu-Kassem.
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14. 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.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 14

15. Compressibility of Natural Gases
(Cont.)
From the real gas equation-of-state:
Differentiating with respect to p at constant T gives:
Substituting, produces the generalized relationship of:
For an ideal gas, z = 1 and (∂z/∂p) T = 0, so:
It is useful in determining the expected order of magnitude of
the isothermal gas compressibility.
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16. Cg In Terms of
the Pseudoreduced Properties
The Equation can be conveniently expressed in terms of
the ppr and Tpr 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 z-
factor chart.
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17. Trube (1957) graphs (the isothermal
compressibility of natural gases)
Trube’s pseudo-reduced compressibility Trube’s pseudo-reduced compressibility
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 17

18. analytical technique for calculating the
isothermal gas compressibility
Matter, Brar, and Aziz (1975) presented
an analytical technique for calculating the
isothermal gas compressibility.
The authors expressed cpr as a function of ∂p/∂ρr rather
than ∂p/∂ppr.
Where:
where the coefficients T1 through T4 and A1 through A8 are
defined previously by the Dranchuk-Purvis-Robinson Method.
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21. 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.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 21

22. Bg Calculation
Applying the real gas
equation-of-state, and
substituting for the
volume V, gives:
Assuming that the
standard conditions:
psc =14.7 psia and
Tsc = 520, zsc = 1.0
Bg = gas formation
volume factor, ft3/scf,
z=gas compressibility
factor, T=temperature, °R
It can be expressed in
terms of the gas density
ρg:
Where: 𝜌 𝑔[lb/ft3]
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 22

23. Bg & Eg Calculation
In other field units, the
gas formation volume
factor can be expressed
in bbl/scf to give:
The reciprocal of the gas
formation volume factor
is called
the gas expansion factor
is designated by the
symbol Eg, or:
or in terms of the gas
density ρg:
In other units:
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 23

25. 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.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 25

26. 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.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 26

27. Methods Of Calculating The Viscosity
Of Natural Gases
Two popular methods that are commonly used in
the petroleum industry are the:
Carr-Kobayashi-Burrows Correlation Method
Carr, Kobayashi, and Burrows (1954) developed graphical
correlations for estimating the viscosity of natural gas
• as a function of temperature, pressure, and gas gravity.
Lee-Gonzalez-Eakin Method
standard deviation of 2.7% and a maximum deviation of 8.99%.
less accurate for gases with higher specific gravities
the method cannot be used for sour gases
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 27

28. Carr-Kobayashi-Burrows Correlation
Method
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.
Corrections to these pseudocritical properties for the presence
of the nonhydrocarbon gases (CO2, N2, and H2S) should be
made if their concentrations are greater than 5 mole percent.
Step 2. Obtain the viscosity of the natural gas at one
atmosphere and the temperature of interest (μ1) from
next slide.
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29. Carr’s Atmospheric Gas Viscosity
Correlation
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30. The Carr’s Method (Cont.)
μ1, must be corrected for the presence of nonhydrocarbon
components by using the inserts of previous slide.
• nonhydrocarbon fractions increases the viscosity of the gas phase
• The effect of nonhydrocarbon components on the viscosity of the
natural gas can be expressed mathematically by:
o 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.
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 30

31. Carr’s Viscosity Ratio Correlation
The term μg
represents the
viscosity of
the gas at the
required
conditions.
Carr’s viscosity ratio correlation
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 31

32. The Lee-Gonzalez-Eakin Method
Lee, Gonzalez, and Eakin
(1966) presented a semi-
empirical relationship for
calculating the viscosity
of natural gases.
𝜇 𝑔in terms of
reservoir temperature,
gas density, and the
molecular weight of the
gas.
Where
ρg = gas density at
reservoir pressure and
temperature, lb/ft3
T =
reservoir temperature, °R
Ma = apparent molecular
weight of the gas mixture
Spring14 H. AlamiNia Reservoir Fluid Properties Course (3rd Ed.) 32

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

34. 1. Crude Oil Properties:
A. Density (ρo), Gravity (γo, API)
B. Gas Solubility (Solution gas) (Rs)
C. Bubble-point pressure (Pb)