| The accurate knowledge
of the thermodynamic properties of natural gases and
other mixtures consisting of natural-gas components
is of indispensable importance for the basic engineering
and performance of technical processes. The processing,
transportation through pipelines or by shipping, storage
and liquefaction of natural gas are examples for technical
applications where the thermodynamic properties of a
variety of mixtures of natural gas components are required.
For these processes, the design of fractionation units,
compressors, heat exchangers, and storage facilities
requires property calculations over wide ranges of mixture
compositions and operating conditions in the homogeneous
gas, liquid and supercritical regions, and for vapour-liquid
equilibrium (VLE) states. These data can be calculated
in a very convenient way from equations of state.
There exists, however, not any equation of state for
natural gases that is appropriate for all of the exemplified
applications and that satisfies the demands on the accuracy
in the description of thermodynamic properties over
the entire fluid region. This statement not only includes
the AGA8-DC92 equation of state, which is only valid
for a limited range in the homogeneous gas region. It
also includes the different cubic equations of state
and particularly the correlation equations applied for
a limited range in the liquid region.
Therefore, we developed a wide-range equation of state
for natural gases and other mixtures that meets the
requirements of standard and advanced natural gas applications.
This research project was supported by the European
natural-gas companies E.ON Ruhrgas (Germany), Enagás
(Spain), Gasunie (The Netherlands), Gaz de France (France),
Snam Rete Gas (Italy) and Statoil (Norway), which are
members of GERG (Groupe Européen de Recherches
Gazières).
This equation of state covers mixtures consisting of
up to 18 components that are listed in the table; originally,
n-nonane, n-decane and hydrogen sulphide did not belong
to these components. In contrast to the AGA8-DC92 equation,
there are basically no limitations in the concentration
range. In 2004, the new equation of state was evaluated
by the GERG group and then adopted under the name GERG-2004
equation of state (or GERG-2004 for short) as an international
reference equation of state for natural gases and similar
mixtures (GERG standard).
Until 2008, we further developed GERG-2004 by incorporating
the three components n-nonane, n-decane and hydrogen
sulphide. Thus, the equation can now be applied to mixtures
consisting of an arbitrary combination of the 21 components
listed in the table. This expanded equation of state
is called GERG-2008. The GERG-2008 equation of state
is under consideration to be adopted as an ISO Standard
(ISO 20765-2 and ISO 20765-3) for natural gases. The
ISO group ISO TC 193/SC 1/WG 13 is working on this matter.
All of the statements made in the following are valid
for GERG-2004 as well as for GERG-2008. The only difference
is that GERG-2008 covers mixtures that can also contain
the three additional components n-nonane, n-decane and
hydrogen sulphide. For simplification, just the term
“GERG-2008” is used for the equation of
state at most places in the following. However, GERG-2004
yields exactly the same results like GERG-2008 except
for mixtures that contain the additional components.
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Components
that were taken into account in the development
of the equations of state GERG-2004 (without the
components n-nonane, n-decane and hydrogen sulphide)
and GERG-20008, which covers all of the listed
components. Yellow fields: natural gas main components;
red fields: further hydrocarbons; blue fields:
further components. |
Structure
of the equations of state GERG-2004 and GERG-2008
The two equations of state,
GERG-2004 and GERG-2008, have the same form. The only
difference is that the summations, which are shown in
the two following figures, are performed up to N
= 18 for GERG-2004 and up to N = 21 for GERG-2008.
The equations are based on a multi-fluid approximation,
which is explicit in the reduced Helmholtz energy α
= a/(RT) [α = Alpha in
the figures] dependent on the density ρ,
the temperature T and the composition x
(mole fractions) of the mixture. The structure
of the equations of state is shown in the following
figure.
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The basic
structure of the equations of state GERG-2004
(N = 18) and GERG-2008 (N
= 21) for natural gases and other mixtures.
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Three elements are necessary to set up a multi-fluid approximation:
The reducing functions
as well as the departure function were developed to
describe the behaviour of the mixture and contain substance
and mixture specific parameters. From the reducing functions,
the reducing values ρr and Tr
for the density and the temperature of the mixture are
calculated. They only depend on the mixture composition
and turn into the critical properties ρc
and Tc, respectively, for
the pure components. The departure function depends
on the reduced density δ, the inversely
reduced temperature τ ( τ
= Tau in the figures) , and the composition x
of the mixture. It contains the sum of
binary specific and generalized departure functions,
which can be developed for single binary mixtures
(binary specific) or for a group of binary
mixtures (generalized). The following equation illustrates
this summation:
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| The
departure function for the mixture in a multi-fluid
approximation as a double summation over all
binary specific and generalized departure functions
developed for the binary subsystems; GERG-2004:
N = 18; GERG-2008: N = 21. |
The
mathematical structure of the part of the binary specific
and generalized departure functions that depends on
δ and τ is similar to the
structure of pure substance equations of state and is
determined by our method for optimizing the structure
of equations of state. Furthermore, the departure functions
contain a factor that only depends on the composition
of the mixture. For further details, see the references
given at the end of this description.
In order to obtain a reference equation of state that
yields accurate results for various types of natural
gases and other multi-component mixtures over wide ranges
of composition, the reducing and departure functions
were developed using only data for binary mixtures.
The 18 pure components covered by GERG-2004 form 153
different binary mixtures, and the 21 pure components
covered by GERG-2008 result in 210 possible binary mixture
combinations. Departure functions Δαrij(δ,τ,
x)
were developed only for such binary mixtures for which
accurate experimental data existed. For binary mixtures
with limited or poor data, no departure functions were
developed, and only the parameters of the reducing functions
ρr(x)
und Tr(x)
were fitted; in case of very poor data, simplified reducing
functions without any fitting were used.
The multi-fluid approximation used enables a simple
inclusion of additional components in future developments.
This means that, for example, fitted parameters of the
existing equation of state do not have to be refitted
when incorporating new components. This also holds for
the departure function with its optimized structure,
which remains unchanged when expanding the model.
Range
of validity and accuracy of GERG-2004 and GERG-2008
The statements given below are valid for GERG-2008
as well as for GERG-2004. For simplicity, GERG-2004
is also referred to as GERG-2008 in the following text.
The entire range of validity of GERG-2008 covers the
following temperatures and pressures:
• Normal range: 90 K ≤ T ≤ 450
K
p ≤ 35 MPa
• Extended range: 60 K ≤ T ≤ 700
K p
≤ 70 MPa.
Moreover, the equation can be reasonably extrapolated
beyond the extended range, and each component can basically
cover the entire composition range, i.e. (0-100)%.
GERG-2008 represents most of the experimental data,
including the most accurate measurements available,
to within their uncertainties. The uncertainty values
given in the following correspond to the uncertainties
of the most accurate experimental data.
In the gas region, the uncertainties in density and
speed of sound are 0.1%, in enthalpy differences (0.2-0.5)%
and in heat capacities (1-2)%. In the liquid region,
the uncertainty in density is (0.1-0.5)%, in enthalpy
differences (0.5-1)% and in heat capacities (1-2)%.
In the two-phase region, vapour pressures are calculated
with a total uncertainty of (1-3)%, which corresponds
to the uncertainties of the experimental VLE data. For
mixtures with limited or poor data, the uncertainty
values stated above can be somewhat higher.
These accuracy statements are based on the fact that
GERG-2008 represents the corresponding experimental
data to within their experimental uncertainties (with
very few exceptions).
Further details and an
assignment of the uncertainties to the ranges of validity
given above can be found here.
Quality of GERG-2004 and
GERG-2008 for “normal” natural gases and
special mixtures
The statements given below are valid for GERG-2008 as
well as for GERG-2004. For simplicity, GERG-2004 is
also referred to as GERG-2008 in the following text.
There is no difference between GERG-2008 and GERG-2004
except for mixtures that contain one of the “new”
components.
Comparisons with experimental data for natural gases
show that the reference equation of state GERG-2008
describes the thermodynamic properties in the “classical”
natural-gas region more accurately than the current
standard, the AGA8-DC92 equation, which is a pure gas
equation. For example, GERG-2008 achieves important
improvements in representing caloric properties (such
as the speed of sound of natural gases) and significantly
extends the range of composition, in which natural gases
can be described in high accuracy. The pρT
data of most natural gases in the “classical”
natural-gas region are described by GERG-2008 to within
the required uncertainty of 0.1% in density (in the
temperature range from 270 K to 450 K at pressures up
to 35 MPa). Significant improvements were achieved for
temperatures ranging from 250 K to 275 K.
In contrast to the AGA8-DC92 equation, GERG-2008 is
also able to describe the liquid phase and vapour-liquid
equilibrium states with the highest possible accuracy.
The experimental data for densities, enthalpy differences
and heat capacities are represented to within the experimental
uncertainties over the entire fluid region. Moreover,
the vapour pressure can be calculated with comparatively
high accuracy, which is, however, clearly lower than
for the properties in the homogeneous liquid. Thus,
GERG-2008 also meets all requirements in accuracy for
the liquid phase and the phase equilibrium. In comparison
with cubic equations, significant improvements were
achieved for the saturated liquid densities of liquefied
natural gases (LNG) and LNG-like mixtures; the uncertainties
were reduced from more than 10% to (0.1-0.5)%.
Aside from the accurate description of the thermodynamic
properties of common natural gases, the so far achieved
results have shown that GERG-2008 also allows the at
present most accurate description of natural gases consisting
of high fractions of nitrogen, carbon dioxide, ethane
or higher alkanes. Moreover, for the first time, GERG-2008
also enables the accurate description of “Rich
Natural Gas” (RNG), “Compressed Natural
Gas” (CNG), “Liquefied Petroleum Gas”
(LPG) and “Liquefied Natural Gas (LNG). Furthermore,
GERG-2008 is able to very accurately describe natural
gases containing a high fraction of hydrogen and binary
mixtures of natural-gas components with hydrogen as
well as natural gases with a low calorific value, light
oil and other mixtures related to natural gas. In addition,
the properties of mixtures consisting of non-typical
natural-gas components can be accurately calculated,
including dry air, humid air, and binary and multi-component
mixtures of the flue gases water, carbon dioxide, carbon
monoxide, nitrogen, oxygen and argon. For such calculations,
the values of temperature and pressure can exceed the
limits defined for the extended range of validity of
GERG-2008. However, due to the lack of sufficiently
accurate experimental data, the uncertainty in calculating
the thermodynamic properties of such mixtures is higher
than for natural gases and related mixtures.
Range of validity and accuracy of GERG-2004
and GERG-2008
Due to the wide range of validity, GERG-2004 and GERG-2008
can be used for standard and extended applications with
natural gases and similar mixtures. This includes the
following processes: the transport of natural gas through
pipelines and its storage in underground storage facilities,
providing compressed natural gas (CNG), the removal
of undesired components from natural gas, the liquefaction
of natural gas, advanced processes with liquefied natural
gas and sour gas (natural gases containing water and
hydrogen sulphide), the production of liquefied petroleum-gas
(LPG), working with light oil, coming applications of
natural gas/hydrogen mixtures and also very efficient
refrigeration processes with mixtures of natural-gas
components (e.g. mixtures of propane and butane). Moreover,
the application of GERG-2004 and GERG-2008 for processes
with dry and humid air as well as mixtures of flue-gas
components (e.g. mixtures of CO2 and H2O)
is possible. The equations of state GERG-2004 and GERG-2008
can also be used for the calculation of dew points of
all the mixtures mentioned.
References
The reference equation of state GERG-2004 is described
in detail in the GERG-Monograph TM15, where the complete
numerical information and the comprehensive comparisons
with experimental data are given. This reference reads:
Kunz, O., Klimeck,
R., Wagner, W., Jaeschke, M. The GERG-2004 wide-range
equation of state for natural gases and other mixtures.
GERG TM15 2007. Fortschr.-Ber. VDI, Reihe 6, Nr. 557,
VDI Verlag, Düsseldorf, 2007; also available as GERG
Technical Monograph 15 (2007).
An electronic version (PDF
file) of the GERG Technical Monograph 15 (GERG TM15) can
be downloaded from the internet page of GERG http://www.gerg.info/publications
The expanded equation of state GERG-2008 will be described
in the article:
Kunz, O., Wagner,
W. The GERG-2008 wide-range equation of state for
natural gases and other mixtures: An expansion of GERG-2004.
To be submitted to J. Chem. Eng. Data (2011).
Software
for the reference equation of state GERG-2008 for natural
gases and other mixtures
For the reference equation of state GERG-2008 described
above, a comprehensive and user-friendly software package
is available. The software enables to calculate several
thermodynamic properties in the homogeneous gas, liquid,
and supercritical regions and allows to carry out VLE
calculations at arbitrary mixture conditions where the
prior knowledge of the number of phases (one or two)
is not required. The VLE calculation options include
different flash options as well as phase envelope, dew
point, and bubble point calculations.
For details about software see this page.
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