USE OF EQUATIONS OF STATE AND EQUATION OF STATE SOFTWARE PACKAGES

Adam G. Hawley
Darin L. George

Southwest Research Institute

6220 Culebra Road
San Antonio, TX 78238

Introduction Peng-Robinson (PR)

Determination of fluid properties and phase The Peng-Robison (PR) EOS (Peng and Robinson,
conditions of hydrocarbon mixtures is critical 1976) is referred to as a cubic equation of state,
for accurate hydrocarbon measurement, because the basic equations can be rewritten as cubic
representative sampling, and overall pipeline polynomials in specific volume. The Peng Robison
operation. Fluid properties such as EOS is derived from the basic ideal gas law along
with other corrections, to account for the behavior of
compressibility and density are critical for flow a real gas. The Peng Robison EOS is very
measurement and determination of the versatile and can be used to determine properties
hydrocarbon due point is important to verify such as density, compressibility, and sound speed.
that heavier hydrocarbons will not condense out The Peng Robison EOS can also be used to
of a gas mixture in changing process conditions. determine phase boundaries and the phase conditions
of hydrocarbon mixtures.
In the oil and gas industry, equations of state
(EOS) are typically used to determine the Soave-Redlich-Kwong (SRK)
properties and the phase conditions of
The Soave-Redlich-Kwaon (SRK) EOS (Soave,
hydrocarbon mixtures. Equations of state are
1972) is a cubic equation of state, similar to the Peng
mathematical correlations that relate properties Robison EOS. The main difference between the
of hydrocarbons to pressure, temperature, and SRK and Peng Robison EOS is the different sets of
fluid composition. Various software packages experimental data that were used to generate the
are available that use different equations of state parameters for the two separate equations of state.
to calculate a range of natural gas properties and The SRK equation of state parameters were
phase conditions. This paper discusses the generated from data collected prior to 1950, while
different equations of state that are available, the the parameters for the Peng-Robison equation of
properties that can be obtained from each EOS, state were generated from data compiled through the
and practical uses of EOS software for natural early 1970s. Similar to the Peng Robison, the SRK
gas pipeline applications. also can be used to determine fluid properties, phase
boundaries, and phase conditions.
Equations of State
GERG-2008
Various EOS are available to calculate
One of the most recently published equations of state
properties and phase conditions of hydrocarbon was developed at Ruhr-Universitt Bochum (the
mixtures. Typically, the EOS are integrated into University of Bochum) in Germany. This EOS is
a software package that allows the user to select known as GERG-2008. GERG-2008 uses
the equations of state to use for the calculations. Helmholtz energy as a key variable to derive the
Four of the most common EOS correlations are hydrocarbon fluid properties. GERG-2008 can be
briefly discussed herein. used to determine various fluid properties specific to
natural gas. GERG-2008 can also be used to
calculate phase boundaries.
AGA-8, AGA-10, and API Chapter 14.2 to using an equation of state software package.
Screen shots will be presented from the Multiflash
American Gas Association Report No. 8 (AGA-8) software package, however, other equation of state
was originally developed by Gas Research Institute. software packages will follow the same general steps
AGA-8 was developed specifically to determine to determine fluid properties and phase conditions.
compressibility of natural gas for high accuracy flow
measurement applications. American Gas Step 1: Define the Fluid Composition
Association Report No. 10 (AGA-10) was later
developed to build on AGA-8 by adding the ability The first step to performing a calculation using
to calculate density and sound speed. Both AGA-8 equation of state software is to define the fluid
and AGA-10 were specifically designed to composition. Typical software packages have a
determine properties of natural gases only. As a library of hydrocarbons (typically through C9+) and
result, AGA-10 cannot calculate phase boundaries. inert fluids to choose from to define the fluid
The American Petroleum Institute (API) also composition. In a field application, the fluid
adopted the AGA equation of state, and has composition is typically measured by a gas
published the standard as API Chapter 14.2. chromatograph. Figure 1 shows a screen shot of the
interface used to select the components of the fluid
Using a Typical EOS Software Package to be analyzed. In Figure 1, components were
selected that are typically found in transmission-
As discussed in the introduction, various software quality natural gas.
packages are available that allow computations to be
executed using different equations of state. Many After the general makeup of the fluid composition is
software packages allow the user to select the type selected, the molar ratio (percentage) of each
of equation of state correlation that they would like component must be defined. This information is
to use for the calculations. Multiflash is one of typically obtained from a gas chromatograph.
many such programs that allow access to the Peng- Table 1 shows an example of how this information is
Robison and SRK equations of state. Other equation input into an EOS software package. For most EOS
of state software packages includes Aspen HYSIS, software packages, the total molar ratio must add up
REFPROP, and VLEFlash, to name a few1. The 100% (on a percent basis) or 1 (on a fraction basis).
subsections that follow will outline the general steps

Figure 1. Selecting Components in the Equation of State Software

Components are selected that make up the fluid composition of interest.

1) References to trade names or specific commercial products does not represent or constitute an endorsement,
recommendation, or favoring by SwRI of the specific commercial product.
 Table 1. Assign the Molar Ratio of Each performed by AGA-10. In a single-phase property
Component calculation, it is assumed that the fluid is single-
After the components have been selected, the molar phase.
ratio of each component must be entered into the
equation of state software. In addition to flash calculations and single-phase
property calculations, some EOS software can also
Component lbmol determine the phase diagram of a fluid. This can be
METHANE 75.000 very helpful in the field to determine if a phase
ETHANE 12.500 change will occur due to a change in temperature
CARBON DIOXIDE 0.400 and/or pressure of the process fluid. Phase diagrams
will be discussed in more detail later in this paper
NITROGEN 2.800
under Practical Uses of EOS Software.
PROPANE 6.000
ISOBUTANE 1.000 Step 3: Define Flash Conditions
N-BUTANE 1.600
With the fluid composition and type of calculation
ISOPENTANE 0.180
defined, the fluid conditions for the calculation must
N-PENTANE 0.240 be defined. Based on the chosen calculation type,
N-HEXANE 0.146 different fluid conditions will need to be entered in
N-HEPTANE 0.068 the software. For the constant pressure and
N-OCTANE 0.048 temperature flash condition, the pressure and
N-NONANE 0.018 temperature of the fluid will need to be defined.
Likewise, for the constant pressure and enthalpy
Step 2: Select Type of Calculation case, the pressure and enthalpy will need to be
defined, and so on. The units for the defined
After the fluid composition has been defined, the conditions are specified in the EOS software
next step is to select the type of calculation that will package.
be executed. Three different types of calculations
are discussed in this paper: 1) flash calculations, 2) For generating a phase diagram, the fluid conditions
single-phase property calculations, and 3) phase are not required. Instead, the EOS software iterates
diagrams. through a range of pressures and temperatures to
define the curve of the phase diagram. A starting
Flash calculations can be used to determine the pressure and temperature can be defined for the
phases of the fluid and the fluid properties of all iteration to help expedite the calculation, but it is not
phases present. Flash calculations are useful if it is required
unknown whether or not the fluid will be single or
multiphase at the given state. Typical flash Step 4: Perform the Calculations and Review the
calculations are defined by the two properties that Results
define the state. For a flash calculation, two of the
following six variables must be fixed: With all the parameters defined, a flash calculation
or a phase diagram can be created. Figure 2 shows
x Temperature the results of a flash calculation at a fixed pressure
x Pressure and temperature of 40 F and 100 psi. In Figure 2, it
x Density can be seen that a range of fluid properties have been
x Enthalpy calculated at the defined conditions.
x Entropy
x Internal Energy In addition to the fluid properties, the flash
calculation has indicated that two phases are present
Flash calculations at constant pressure and at the defined conditions. The EOS software
temperature are the most common, because these supplies fluid properties for the liquid and the gas
properties are the most readily available in a field phase as well as the amounts of each phase at the
application. defined conditions. For the example at 40 F and
100 psi, the fluid is more than 99.9% gas with trace
A single-phase property calculation can be done on amounts of liquid (~0.0643%).
single-phase fluids only, such as the gas calculations
 Figure 2. Results from a Fixed Pressure and Temperature Flash Calculation
At the defined conditions, the flash results show that the fluid has two phases. Properties for both the liquid and
gas phases are given by the flash calculation.

Practical Uses of EOS Correlations Sound Speed Verification

Two example cases are discussed in this paper to Ultrasonic meters measure fluid velocity to
illustrate situations where equation of state determine the flow rate of a process fluid through a
correlations can be used in field applications: 1) to pipeline. In addition to fluid velocity, ultrasonic
verify sound speed measurements for an ultrasonic meters also measure the sound speed of the process
meter and 2) to check if the conditions through a fluid. As a result, comparing the sound speed
sample line could cause liquid to condense out of the measured from an ultrasonic meter to the calculated
gas phase. sound speed, using an equation of state correlation,
is a good method to verify that an ultrasonic meter is lines typically contain a regulator that drops the
functioning properly. pressure of the gas from the pipeline pressure to a
lower level that a gas analyzer can accept. If liquids
AGA-10 is a good option for sound speed condense out of the gas phase in a gas sample,
determination, since it is the standard in the natural equipment downstream from the sample location
gas industry. Following the steps that were could be damaged. In addition, if liquids condense
previously outlined, the composition must first be out of the gas phase, the composition of the
defined. A gas chromatograph is the most common remaining gas sample will be compositionally
option to obtain the compositional makeup of the distorted from the actual gas that was sampled. This
gas in the field. Keep in mind that the accuracy of could cause a discrepancy in the gas properties
the properties, determined by an equation of state determined from the gas samples.
correlation, are only as good as the input information
that is used to determine the gas properties. As a A phase diagram can be generated using equation of
result, it is important to check and verify the state software that references PR, SRK, or GERG-
compositional information of the process fluid 2004 equation of state. AGA-10 was designed for
before it is used to calculate properties that will be single-phase gas only and cannot be used to generate
used for analysis. phase diagrams.

After the composition of the fluid is defined, the To generate a phase diagram, the composition of the
type of analysis and the conditions must also be natural gas is required. Using the composition that
defined. For the AGA-10 equation of state, the fixed was previously displayed in Table 1 and using the
pressure and temperature condition is used to SRK equation of state, the calculated phase diagram
calculate properties of the fluid (including sound in Figure 3 was generated. The liquid, two-phase,
speed). Once the temperature, pressure, and gas and gas regions have been labeled in Figure 3.
composition are entered into the AGA-10 equation
of state, the calculation can be initiated and the Figure 3 shows an example of a condition in which
properties of the gas, at the given conditions, will be liquids could be generated in a sample line. Assume
determined. The sound speed determined from that point 1 on Figure 3 is the process pressure and
AGA-10 can then be compared to the sound speed temperature of a natural gas pipeline (1000 psi and
measured by an ultrasonic meter. If there is a 100 F). Also assume that a gas analyzer was
discrepancy in the sound speed, it could be due to connected to the pipeline that required a 200 psi inlet
the flow meter. Keep in mind, however, that if the pressure. If a regulator was installed that dropped
pressure, temperature, or compositional data that the pressure from 1000 psi to 200 psi without
were used to determine the fluid properties are heating, then the gas would follow the line from
biased, the bias will also be present in the calculated point 1 to point 3. At point 3, the pressure is 200
fluid properties. psi, however, the gas has cooled to approximately
44F due to Joule Thomson cooling. As a result, the
Liquid Condensate in Sample Line gas in the sample lines would be two-phase as some
of the heavier hydrocarbons would have started to
As discussed earlier, equation of state correlations condense out of the gas phase. Ideally, the path
can be used to determine phase boundaries and from point 1 to point 2 would maintain the fluid in
generate phase diagrams. This information can be the gas phase. To obtain the path from point 1 to
especially useful in field applications with natural point 2, a heater can be installed on the sample line
gas sampling. A phase diagram can be used to to offset the Joule-Thomson cooling effect and
determine if liquids could condense out of the gas maintain the temperature of the gas above the dew
due to a change in the pressure and/or temperature point line in Figure 3.
during the sampling process. Natural gas sample
 Figure 3. Phase Diagram Results Using SRK Equation of State
The liquid, two-phase, and gas regions are labeled in the figure. The green path from paths 1-2 represent an
ideal isothermal pressure drop with heating, while the path from 1-3 represents a realistic drop in pressure
taking into account the drop in temperature from Joule-Thomson cooling.

Comparison of Gas Properties from Different result, it is important to use the correct EOS
EOS Correlations correlation for fluid calculations, especially if they
are to be used to high-accuracy flow measurement.
This paper has discussed four different EOS AGA-10 should be used for all natural gas property
correlations that can be used to determine properties determination for flow measurement, unless
of natural gas. Since all of the EOS correlations use otherwise noted in tariff agreements.
data that was derived from different experiments, it
is expected that slightly different fluid properties Table 2. Density Results from AGA-10, SRK, and
will be obtained from each EOS correlation for PR Equation of State Correlations
identical input conditions. This begs the question of The SRK equation of state and PR equation of state
which EOS correlation should be used? For natural yielded density results -1% and 2.2% different from
gas measurement, AGA-10 is the standard for AGA-10, respectively.
computing properties. All flow calculations for
natural gas refer to the AGA-10 equation of state. Equation Density
3 Percent Difference
Table 2 shows an example of the difference between of State (lbm/ft )
the AGA-10, SRK, and Peng-Robison EOS for a AGA-10 3.3729 --
density calculation for natural gas at 800 psi, 100F
SRK 3.3386 -1.0%
using the composition previously outlined in
Table 1. In Table 2, it can be seen that differences PR 3.4456 2.2%
ranging from -1% to 2.2% were observed for the
SRK and PR EOS in comparison to AGA-10. As a
 Savidge, J., Compressibility of Natural Gas,
ISHM Presentation, May 2012.
Conclusions

Equation of state correlations can be valuable tools Soave, G., Equilibrium Constants from a
in the natural gas industry to determine properties of Modified Redlich-Kwong Equation of State,
gas and phase boundaries. Many different software Chemical Engineering Science, Vol. 27, pp.
packages are available that allow a straight-forward 1197-1203, 1972.
approach to applying and comparing the different
equation of state correlations. Knowing the Adam Hawley
advantages and limitations of the available equations
of state is very useful in deciding which correlation
is best suited to determine phase boundaries or fluid
properties.

As discussed throughout this paper, equations of

state are only as good as the data that is input into
the correlations. As a result, if high accuracy
determination of fluid properties and phase
boundaries is critical, verify the inputs into the
equation of state correlations (pressure, temperature,
composition, etc.) before the calculations are carried
out.

References

American Gas Association, AGA Report No. 8,

Compressibility Factors of Natural Gas
and Other Related Hydrocarbon Gases, Second
Edition, Second Printing, American Gas
Darin George
Association, Arlington, Virginia, 1994.

American Gas Association, AGA Report No.

10, Speed of Sound in Natural Gas by Multipath
Ultrasonic Meters, Second Edition, American
Gas Association, Arlington, Virginia, April
2007.

Kunz, O., Klimeck, R., Wagner, W., and

Jaeschke, M., The GERG-2004 Wide-Range
Equation of State for Natural Gases and Other
Mixtures., GERG TM 15, 2007.

Mayeaux, M., Use of Equation of State (EOS)

Software, ASGMT Presentation, September
2011.

Peng, D.Y., and Robinson, D. B., A New Two-

Constant Equation of State, Industrial and
Engineering Chemistry Research Fundamentals,
Vol. 15, pp. 59-64.,1976.