Comparative Study of Equations of State for the Dew Curves Calculation in High Pressure Natural Gas Mixtures*
Estudio Comparativo de Ecuaciones de Estado para el Cálculo de Curvas de Rocío en Mezclas de Gas Natural a Alta Presión*
Estudo Comparativo de Equações de Estado para o Cálculo de Curvas de Orvalho em Misturas de Gás Natural de alta Pressão*
Natalia Prieto Jiménez **
Germán González Silva ***
Universidad Industrial de Santander– Colombia
 |
Fecha de Recibido: Marzo 21 del 2018
Fecha de Aceptación: Noviembre 03 de 2018
Fecha de Publicación: Enero 01 de 2019
DOI: http://dx.doi.org/10.22335/rlct.v11i2.743
*Este artículo es resultado de la investigación doctoral titulada “Estudio de la separación de fases del gas natural a alta presión usando Dinámica de Fluidos Computacional” y de la convocatoria “Capital Semilla para Investigación” de la Vicerrectoría de Investigación y Extensión de la Universidad Industrial de Santander. Proyecto 2370 del año 2017.
**Candidata a Doctor en Ingeniería Química de la Universidad Industrial de Santander, Colombia. Filiación: Grupo de Investigación en Energía y Medio ambiente de la Universidad Industrial de Santander. Correo electrónico: natispj@gmail.com. Orcid: https://orcid.org/0000-0001-9178-7758
***Doctor en Ingeniería Química de la Universidade Estadual de Campinas (Brasil) y Profesor Asistente de la Escuela de Ingeniería de Petróleos de la Universidad Industrial de Santander. Filiación: Grupo de Modelamiento de Procesos de Hidrocarburos – Universidad Industrial de Santander. Correo electrónico: germangsilva@gmail.com Orcid: https://orcid.org/0000-0002-4642-1092
___________________________________________________
Abstract
The success during the operation of natural gas processing plants depends on the correct estimation of thermodynamic properties of the system. This paper calculates the equilibrium curves of real and synthetic natural gas mixtures means of three Equations of State (EOS). These equilibrium curves were constructed and compared with experimental data found in the literature covered. The results showed that, above 4 MPa the Peng-Robinson equation presented a considerable deviation with respect to the experimental data, reaching an absolute error of 4.36%; therefore, the GERG2008 equation is recommended for systems that operate at high pressures when the components present in the mixture apply.
Keywords:
Gas Mixtures, Dew curves, Equations of State; Peng-Robinson, Soave-Redlich-Kwong, GERG2008.
Resumen
El éxito durante la operación de plantas de tratamiento de gas natural depende de la correcta estimación de las propiedades termodinámicas del sistema. Este artículo calcula las curvas de equilibrio de mezclas de gas natural reales y sintéticas por medio de tres ecuaciones de estado (EOS). Estas curvas de equilibrio fueron construidas y comparadas con datos experimentales presentes en la literatura. Los resultados mostraron que, por encima de 4 MPa la ecuación de Peng-Robinson presentó una desviación considerable con respecto a los datos experimentales, alcanzando un error absoluto de 4,36%; por lo cual se recomienda la ecuación de GERG2008 para sistemas que operen a altas presiones cuando los componentes presentes en la mezcla apliquen.
Palabras clave:
Mezclas de gas, Curvas de rocío, Ecuaciones de estado, Peng-Robinson, Soave-Redlich-Kwong, GERG2008.
Resumo
O sucesso na operação de usinas de tratamento de gás natural depende da correta estimação das propriedades termodinâmicas do sistema. Este artigo calcula as curvas de equilíbrio de misturas de gás natural reais e sintéticas por meio de três equações de estado (EOS). As curvas de equilíbrio foram construídas e comparadas com dados experimentais presentes na literatura. Os resultados mostraram que, acima de 4 Mpa a equação de Peng-Robinson apresentou um desvio considerável em relação aos dados experimentais, atingindo um erro absoluto de 4,36%; por tanto, é recomendável a equação de GERG2008 para sistemas que operam em alta pressão quando os componentes presentes no sistema apliquem.
Palavras-chave:
Misturas de gás, Curvas de orvalho, Equações de estado, Peng-Robinson, Soave-Redlich-Kwong, GERG2008.
Introduction
Natural
gas is a complex mixture of hydrocarbons, composed mainly of methane 
,
with significant amounts of ethane
,
propane 
,
butane 
and
some traces of heavy hydrocarbons and certain inorganic compounds
(Mokhatab,
Poe, & Mak, 2015). Its use
as a fossil fuel mostly depends on the treatment carried out before being sent
to the transport network. The processing carried out on natural gas is divided
into three stages: separation of the present phases; dew point adjustment and
re-compression (Khanwelkar,
2015). Conventional
processes of natural gas phases separation are carried out at operating
pressures near atmospheric, thus the third stage is essential (Figure
1). According to data from
Colombian natural gas plants, 12% of Operating Expenditures (OPEX) is
exclusively directed to compression systems. The high energy costs generated by
the re-compression led several authors to recommend that phase separation be
carried out at high pressure (Austrheim,
Gjertsen, & Hoffmann, 2008; Brigadeau, 2007; Zaghloul, 2006).
However, phase separation at high pressure is a complex
process. As the operating pressure within the equipment increases, the density
difference between the liquid phase and the gas phase considerably decreases,
as the surface tension does, which leads to the condensation of fine droplets
and therefore they are easily re-entrainment by the gas phase (Kharoua,
Khezzar, & Saadawi, 2013; Laleh, Svrcek, & Monnery, 2012).
Figure 1. Schematic diagram of the conventional gas-liquid separation process.
For the proper design and analysis of separation systems and high-pressure natural gas processing plants, it is important to know the thermodynamic properties of the mixture, which can be calculated by means of Equations of State (EOS) or empirical correlations (Guo & Ghalambor, 2014; Shoaib, Bhran, Awad, El-Sayed, & Fathy, 2018). The most relevant properties of the mixture are revealed by the thermodynamic equilibrium curves, showing, in addition to the bubble and dew points, the zone where the liquid and gas phases coexist in equilibrium and, consequently, the range of operating conditions of pressure and temperature over which multiphase separation is possible (Jia, Wu, Li, & He, 2017). The cubic equations of Soave-Redlich-Kwong – SRK (Soave, 1972) and Peng-Robinson – PR (Peng & Robinson, 1976) are two EOS widely accepted and used at academic and industrial level for the calculation of thermodynamic properties of natural gas. Additionally, Kunz and Warner (Kunz & Wagner, 2012) developed a specific equation of state for natural gas, called GERG2008 (by the acronym of Groupe Européen de Recherches Gazières - European Gas Research Group and the year it was developed) that is based on the concept of multi-fluid and it is explicit for Helmholtz free energy. The correct estimation of the thermodynamics properties of two-phase and three-phase mixtures results in an important input parameter for the development of different processes in the Oil&Gas industry using numerical simulation through Computational Fluid Dynamics (CFD) techniques (González-Silva, Matos, Martignoni, & Mori, 2012; Jiménez, Hodapp, Silva, & Mori, 2010; Silva, Jiménez, & Salazar, 2012; Silva, Prieto, & Mercado, 2018).
Cubic Equations of State
The simple mathematical structure of the cubic equations of state allows its practical use in technical and academic applications (Galatro & Marín-Cordero, 2014). These two equations are characterized by having the same general form (Poling, Prausnitz, & Connell, 2000a), which can be expressed explicit in the pressure as shown in the equation (1) or depending on the compressibility factor (equations (2) to (4)):
|
|
|
(1) |
|
|
|
(2) |
|
|
|
(3) |
|
|
|
(4) |
Where
is
pressure; 
,
temperature; 
,
molar volume of the mixture and 
,
the universal constant of gases in corresponding units. The value of the
parameters 
,
,
and
are
defined according to the critical and reduced properties of the mixture 
and
Pitzer's acentric factor 
(Pitzer
& Curl Jr, 1957), as shown in
Table 1.
· Mixing rules
The
parameters and
of
cubic equations of state require mixing rules. The parameter b represents the
effective molar volume, in the case of mixtures containing molecules of
approximately equal size; it is possible to express the mixing rule according
to equation (5)
|
|
|
(5) |
Table 1. Parameters used in cubic equations of state (Poling, Prausnitz, & Connell, 2000b).
|
Equation |
Parameters |
|
SRK |
|
|
PR |
|
Where
is
used as a variable of generic composition for both liquid and vapor roots. The
parameter represents
the molecular interactions of the mixture, therefore, its relationship with the
internal energy of the mixture 
must
be carefully considered. The generating function for internal energy indicates
the following relationship (Elliott
& Lira, 1999):
|
|
|
(6) |
In
a binary mixture there are three types of interactions for molecules 1 and 2:
the molecule interacting with itself (1-1, 2-2) or interacting with each other
(1-2). For a random fluid, the probability of finding the molecule (1) is the
fraction 
.
The probability of a 1-1 interaction is called conditional probability, this
probability is calculated as the product of the individual probabilities 
. The probability of interaction 1-2
or 2-1 is 
.
If the attraction interactions are characterized by 
,
and
;
the mixing rule for is
given by equation (7)
|
|
|
(7) |
The simplified form of equation (7) is represented by equations (8) and (9):
|
|
|
(8) |
|
|
|
(9) |
Where
represents
the binary combination parameter, which is tabulated in the literature.
Approach based on the multi-fluid concept
The
multi-fluid approach uses equations of state in their fundamental form for each
component of the mixture, in conjunction with functions developed for the
binary mixtures between the components, in order to determine the residual
behavior of the mixture (Kunz
& Wagner, 2012). The
GERG2008 EOS allows to calculate the thermodynamic properties of 21 components
of natural gas and their binary mixtures as shown in Table
2. The Multi-Fluid
Helmholtz-Free-Energy-Explicit approach, 
which
is a function of density 
,
temperature 
and
the molar composition vector 
contains
the general form of the equation (10):
|
|
|
(10) |
For modeling, the dimensionless Helmholtz free energy was used, as follows:
|
|
|
(11) |
Where
corresponds
to the Helmholtz free energy component of the mixture as ideal gas, depending
on 
:
|
|
|
(12) |
The
term 
is
the residual component of Helmholtz free energy of the mixture, depending on 
.
|
|
|
(13) |
|
|
|
(14) |
|
|
|
(15) |
|
|
|
(16) |
Where
is
the reduced density of the mixture, 
is
the inverse of the reduced temperature of the mixture and 
is
the maximum number of present components. 
is
the residual part of the Helmholtz free energy reduced from component 
and
it
is the generating function. Equation (13) takes
into account the residual behavior of the mixture, evaluated at the reduced
properties and
.
Another way to express the residual Helmholtz free energy is through equation (17); where the first term corresponds to the linear
contribution of the reduced residual Helmholtz free energy, multiplied by the
molar fractions 
. The double sum of the next term is
equivalent to the generating function.
|
|
|
(17) |
The
dimensionless form of Helmholtz free energy as the ideal gas of component in
equation (12) is defined as:
|
|
(18) |
Where
and
are
the critical parameters of the pure components. For a specific binary
generating function, the adjustable factor 
normally
it is represented as one (1) if the mixture exists and zero (0) if it does not
exist. The residual part of the Helmholtz free energy for the compound as the
ideal gas is represented by the equation
(19).
Table 2. Components of natural gas and its specific EOS of the pure component (Kunz & Wagner, 2012).
|
EOS Ref. |
Range of validity |
||
|
|
|
||
|
Main components |
|||
|
|
(Klimeck, 2000) |
90 - 623 |
300 |
|
|
(Klimeck, 2000) |
63 - 700 |
300 |
|
|
(Klimeck, 2000) |
216 - 900 |
300 |
|
|
(Klimeck, 2000) |
90 - 623 |
300 |
|
Secondary alkanes |
|||
|
|
(Span & Wagner, 2003) |
85 - 623 |
100 |
|
|
(Span & Wagner, 2003) |
134 - 693 |
70 |
|
|
(Span & Wagner, 2003) |
113 - 573 |
35 |
|
|
(Span & Wagner, 2003) |
143 - 573 |
70 |
|
|
(Lemmon & Span, 2006) |
112 - 500 |
35 |
|
|
(Span & Wagner, 2003) |
177 - 548 |
100 |
|
|
(Span & Wagner, 2003) |
182 - 523 |
100 |
|
|
(Span & Wagner, 2003) |
216 - 548 |
100 |
|
|
(Lemmon & Span, 2006) |
219 - 600 |
800 |
|
|
(Lemmon & Span, 2006) |
243 - 675 |
800 |
|
Other secondary components |
|||
|
|
(Kunz & Wagner, 2012) |
14 – 700 |
300 |
|
|
(Span & Wagner, 2003) |
54 – 303 |
100 |
|
|
(Lemmon & Span, 2006) |
68 – 400 |
100 |
|
|
(Kunz & Wagner, 2012) |
273 – 1273 |
100 |
|
|
(Lemmon & Span, 2006) |
187 – 760 |
170 |
|
|
(Kunz & Wagner, 2012) |
2,2 – 573 |
100 |
|
|
(Span & Wagner, 2003) |
83 - 520 |
100 |
* T in K and P in MPa
|
|
(19) |
The
function 
of
equation (17) depends only on
the reduced variables of the mixture and
,
it is represented in equation (20):
|
|
(20) |
The
reduced variables of the mixture and
are
calculated from equations (15) and (16) respectively by means of dependent
functions of the composition, as shown in the equations (21)
and (22).
The binary parameters 
and
of
equation (21)
and 
and
of
equation (22),
as well as the critical parameters and
are
tabulated in Kunz and Wagner (Kunz
& Wagner, 2012).
Mixing Rules
For the binary mixtures that are formed from the 21 components of the GERG2008 model, five different mixing rules are used, shown in Figure 2.
|
|
(21) |
|
|
(22) |
Figure 2. Binary combinations and mixing rules for each of the possible combinations (Kunz & Wagner, 2012).
· Calculation of the dew point
There is a variation in the prediction of the thermodynamic properties of multiphase mixtures depending on the applied equations of state, since each equation is dependent on empirical parameters and different mixing rules, it is required to determine the equation that best describes the mixture of natural gas. The general algorithm applied for the calculation of the dew point is shown in Figure 3. The equations of Soave-Redlich-Kwong, Peng-Robinson and GERG2008 were used as the procedure to determine the equation of state that allows the accurate estimation of the properties of the natural gas so as to construct the equilibrium curves of different synthetic and real mixtures of natural gas from Norway and the Middle East. These curves, performed in Aspen-Hysys v8.8 were compared with experimental equilibrium curves from laboratory tests.
Figure 3. Algorithm for the calculation of dew points.
After its validation, the selected equation of state was used to estimate the dew points and the cricondenbar and cricondentherm points of natural gas mixtures from Colombian oil fields; considered “low impact”, for having a production volume lower than 1 MMSCFD. The application of this study is focused on the determination of the appropriate conditions, limits and operating intervals on which it is possible to have a liquid gas mixture in equilibrium without reaching the supercritical fluid zone. The results will facilitate studies of phase separation systems of natural gas at high pressure by gravitational, centrifugal or supersonic techniques, in plants where the cost of re-compression is considerably high.
· Characterization of mixtures
In this study, several mixtures of natural gas with potential for phase separation in a range of operating pressure between 4 and 10 MPa were selected. In this regard, Valiollahi et al (2016) collected a set of 36 mixtures of natural gas, of which, 23 of them have the present components in the GERG2008 state equation and 5 have high separation potential at high pressure according to the analysis of the experimental equilibrium curves. Table 3 presents the molar percentage of each of the mixtures used in the thermodynamic analysis and the Table 5 shows the results of the experimental equilibrium curves of the mixtures, which were compared with the curves constructed by different EOS.
Table 3. Molar percentage of selected natural gas mixtures and its respective reference.
|
ID |
Gas 1 |
Gas 2 |
Gas 3 |
Gas 4 |
Gas 5 |
|
Ref. |
(Jarne et al., 2004) |
(Mørch et al., 2006) |
(Mørch et al., 2006) |
(Avila, et al, 2002) |
(Jarne et al., 2004) |
|
|
84.45 |
96.611 |
93.6 |
83.35 |
69.11 |
|
|
0.772 |
0 |
0 |
5.651 |
1.559 |
|
|
1.7 |
0 |
0 |
0.284 |
25.91 |
|
|
8.683 |
0 |
2.630 |
7.526 |
2.62 |
|
|
3.297 |
0 |
1.49 |
2.009 |
0.423 |
|
|
0.589 |
1.475 |
1.49 |
0.52 |
0.104 |
|
|
0.293 |
1.527 |
0.795 |
0.305 |
0.105 |
|
|
0.086 |
0.385 |
0 |
0.144 |
0.023 |
|
|
0.084 |
0 |
0 |
0.12 |
0.034 |
|
|
0.05 |
0 |
0 |
0.068 |
0.11 |
|
|
0 |
0 |
0 |
0.014 |
0 |
|
|
0 |
0 |
0 |
0.011 |
0 |
· Colombian natural gas mixtures
In addition to the real and synthetic natural gas mixtures that were extracted from the literature (Avila et al., 2002; Jarne et al., 2004; Mørch et al., 2006), two mixtures of natural gas from Colombian reservoirs were analyzed. The molar percentage of the Colombian natural gas mixtures used during the present study are shown in Table 4.
Table 4. Molar percentage of gases from Colombian fields.
|
%mol |
Gas 6 |
Gas 7 |
%mol |
Gas 6 |
Gas 7 |
|
|
97.299 |
82.867 |
|
0.013 |
0.024 |
|
|
1.507 |
0.541 |
|
0.023 |
0.033 |
|
|
0.095 |
2.008 |
|
0.009 |
0.006 |
|
|
0.69 |
8.828 |
|
0.004 |
0.004 |
|
|
0.241 |
3.86 |
|
0.002 |
0.001 |
|
|
0.062 |
1.19 |
|
0.001 |
0 |
|
|
0.054 |
0.638 |
|
|
|
Table 5. Values of the cricondentherm point (K), cricondenbar point (MPa) and experimental equilibrium curves for different mixtures of natural gas (Avila et al., 2002; Jarne et al., 2004; Mørch et al., 2006).
|
Gas 1 |
Gas 2 |
Gas 3 |
Gas 4 |
Gas 5 |
|||||
|
CricT (K) |
261.4 |
CricT (K) |
268.3 |
CricT (K) |
278.4 |
CricT (K) |
273.5 |
CricT (K) |
252.2 |
|
CricB (MPa) |
8.18 |
CricB (MPa) |
-- |
CricB (MPa) |
-- |
CricB (MPa) |
9.23 |
CricB (MPa) |
-- |
|
T(K) |
P(MPa) |
T(K) |
P(MPa) |
T(K) |
P(MPa) |
T(K) |
P(MPa) |
T(K) |
P(MPa) |
|
217.9 |
0.12 |
263.7 |
7.92 |
268.7 |
9.32 |
243.4 |
0.2 |
213.6 |
0.12 |
|
219.6 |
0.14 |
265.3 |
7.54 |
271.2 |
9.04 |
249.8 |
0.32 |
216.4 |
0.12 |
|
222.6 |
0.21 |
266.1 |
7.06 |
272.4 |
8.52 |
254.1 |
0.5 |
217.5 |
0.13 |
|
228.1 |
0.31 |
267 |
6.56 |
274.3 |
8.1 |
258.3 |
0.7 |
219.5 |
0.14 |
|
232.1 |
0.41 |
267.8 |
6.04 |
275.3 |
7.68 |
262.4 |
0.99 |
222 |
0.17 |
|
235.9 |
0.53 |
268.3 |
5.56 |
276.1 |
7.16 |
266.7 |
1.47 |
224.5 |
0.21 |
|
238.7 |
0.64 |
268.2 |
5.06 |
277.6 |
6.64 |
269.7 |
2.01 |
228.5 |
0.29 |
|
240.7 |
0.73 |
268 |
4.58 |
278.4 |
6.18 |
271.4 |
2.46 |
231.5 |
0.38 |
|
242.5 |
0.86 |
267.4 |
4.1 |
278.3 |
5.64 |
272.7 |
3.06 |
233.4 |
0.44 |
|
244.4 |
0.98 |
266.4 |
3.58 |
278.4 |
5.12 |
273.2 |
3.51 |
235.6 |
0.52 |
|
247.1 |
1.18 |
264.9 |
3.08 |
277.5 |
4.62 |
273.3 |
4 |
237.8 |
0.63 |
|
259.9 |
6.24 |
262.8 |
2.6 |
276.6 |
4.08 |
273.5 |
4.5 |
239.4 |
0.72 |
|
259.1 |
6.51 |
259.9 |
2.08 |
275.7 |
3.6 |
273.2 |
5 |
241.3 |
0.85 |
|
258.1 |
6.76 |
255.9 |
1.58 |
273.6 |
3.1 |
272.5 |
5.5 |
243.2 |
1.01 |
|
256.5 |
6.98 |
249.7 |
1.06 |
271.3 |
2.6 |
271.8 |
6.01 |
245.1 |
1.2 |
|
255.9 |
7.19 |
241.9 |
0.64 |
268.5 |
2.08 |
269.4 |
6.62 |
246.7 |
1.42 |
|
254-2 |
7.54 |
|
|
264.1 |
1.56 |
267.6 |
7.14 |
248.9 |
1.8 |
|
253.5 |
7.59 |
|
|
258.1 |
1.06 |
264.6 |
7.53 |
249.8 |
2.02 |
|
252-4 |
7.77 |
|
|
247.9 |
0.58 |
262.1 |
8.02 |
250.5 |
2.22 |
|
251-4 |
7.78 |
|
|
240.8 |
0.34 |
257.9 |
8.48 |
251.1 |
2.42 |
|
234 |
7.92 |
|
|
|
|
252.1 |
8.85 |
251.5 |
2.64 |
|
234.8 |
7.93 |
|
|
|
|
246.1 |
9.14 |
251.9 |
2.88 |
|
|
|
|
|
|
|
241.9 |
9.23 |
252.1 |
3.14 |
|
|
|
|
|
|
|
231.,4 |
9.05 |
252.2 |
3.37 |
|
|
|
|
|
|
|
228.1 |
8.87 |
252.2 |
3.83 |
|
|
|
|
|
|
|
223.3 |
8.28 |
251.3 |
4.5 |
|
|
|
|
|
|
|
215.7 |
7.42 |
250.7 |
4.79 |
|
|
|
|
|
|
|
|
|
249.5 |
5.2 |
|
|
|
|
|
|
|
|
|
248.1 |
5.61 |
|
|
|
|
|
|
|
|
|
246.4 |
6.02 |
Results and discussion
The discussion of results is divided into the analysis of the cricondentherm and cricondenbar points of the mixtures presented in the studies by Mørch et al. (2006), Jarne et al. (2004) and Avila et al. (2002), the construction and comparison of equilibrium curves and the analysis of natural gas mixtures from Colombian fields. Figure 4 shows the experimental values and the results of the calculation using the PR, SRK and GERG2008 state of equations for each of the selected natural gas mixtures. Table 6 also contains the absolute error percentage of each state equation compared to the experimental data.
Figure 4. Experimental and simulated value of the cricondentherm point for each of the analysis gases.
Table 6. . Calculation of absolute error for each one of the cricondentherm points, using the PR, SRK and GERG2008 EOS vs. Experimental data.
|
Cric (K) |
Gas1 |
%e |
Gas2 |
%e |
Gas3 |
%e |
|
Exp. |
261.4 |
-- |
268.3 |
-- |
278.4 |
-- |
|
PR |
259.4 |
0.77 |
266.2 |
0.78 |
276.1 |
0.83 |
|
SRK |
261 |
0.15 |
267.8 |
0.19 |
277.8 |
0.22 |
|
GERG2008 |
260.9 |
0.19 |
268.7 |
0.15 |
278.6 |
0.07 |
|
|
Gas4 |
%e |
Gas5 |
%e |
|
|
|
Expl |
273.5 |
-- |
252.2 |
-- |
|
|
|
PR |
271 |
0.91 |
251.4 |
0.32 |
|
|
|
SRK |
273.2 |
0.11 |
253.2 |
0.40 |
|
|
|
GERG2008 |
273 |
0.18 |
252.7 |
0.20 |
|
|
In the case of the cricondentherm point, it is observed that, for three of the five experimental mixtures, the lowest percentage of error was presented using the GERG2008 state equation. The maximum percentage reached was using the PR equation in gas 4 (0.91%). However, since all the percentages of error are so low, it is considered that it is not a sufficient measure for the selection and that other properties must be analyzed. Similarly to the cricondentherm point, Figure 5 and Table 7 present the comparison and the calculation of percentage of error of the cricondenbar points for the mixtures of natural gas that are adapted to the process of stage separation at high pressure. According to the available experimental data, it is observed that both the SRK and GERG2008 state equations have a low percentage of error when calculating the values of the maximum pressure where the liquid and gas phases coexist in equilibrium.
Figure 5. Experimental and simulated value of the cricondenbar point for each of the analysis gases.
Table 7. Calculation of absolute error for each one of the cricondenbar points, using the PR, SRK and GERG2008 EOS vs. Experimental data.
|
Cric (MPa) |
Gas1 |
%e |
Gas2 |
%e |
Gas3 |
%e |
|
Exp. |
8.18 |
-- |
-- |
-- |
-- |
-- |
|
PR |
8.134 |
0.56 |
9.269 |
-- |
9.902 |
-- |
|
SRK |
8.247 |
0.82 |
9.466 |
-- |
10.11 |
-- |
|
GERG2008 |
8.218 |
0.46 |
9.459 |
-- |
10.09 |
-- |
|
|
Gas4 |
%e |
Gas5 |
%e |
|
|
|
Expl |
9.23 |
-- |
-- |
-- |
|
|
|
PR |
8.828 |
4.36 |
7.595 |
-- |
|
|
|
SRK |
9.02 |
2.28 |
7.606 |
-- |
|
|
|
GERG2008 |
8.999 |
2.50 |
7.596 |
-- |
|
|
Once again, in light of this information, any of the three state equations would be adequate to estimate the cricondenbar and cricondentherm points; so it is not enough to make a decision, it is necessary to study the behavior of the pressure depending on the temperature for each of the mixtures of Table 3. After analyzing the cricondentherm and cricondenbar points of the five natural gas mixtures, the pressure profiles were plotted as a function to temperature (Figure 8) and later they were compared with experimental data.
The calculated equilibrium curves show that at low pressures, all the state equations analyzed have a good correlation with the experimental data, thus the equation that is used to estimate the thermodynamic properties of the mixtures is considered indifferent, that is, any of the three works with relatively low error rates. However, if the objective is to operate high-pressure multiphase separation systems, not all state equations are adequate; as it is the case of the Peng-Robinson equation, where in none of the dew curves the real behavior of the mixture was represented, especially near the cricondentherm and cricondenbar points; in this last point the Peng equation Robinson reaches the maximum error rate of 4.36% for gas 4 (Table 7).
Discarding the Peng-Robinson's equation of state for the calculation of the dew curve of high-pressure natural gas mixtures, the state equation was established that estimates the thermodynamic properties of the multi-component system. In Figure 8, it is possible to observe that in spite of not existing a significant difference between the two remaining equations of state, the dew curve calculated with the GERG2008 equation is the one that better correlates the experimental data of the literature; this trend is more evident in the results of gases 2, 3, and 4. As a special case, gas 5 starts with a favorable trend for the GERG2008 equation and as the pressure increases, the Soave-Redlich-Kwong equation is closer to the real trend in a small section of the dew curve, unfortunately there is no experimental data in the region of the cricondenbar point.
Application to Colombian natural gas mixtures
Figure 8 suggests
that the GERG2008 state equation manages to adequately reproduce the
thermodynamic behavior of different types of synthetic and real mixtures of
natural gas. For this reason, two real mixtures of natural gas from Colombian
production fields were chosen (Table 4). The first (Figure 6) corresponds to a “dry” natural gas,
mainly composed of methane and therefore has a low separation potential, due to
the lack of heavy hydrocarbons (
hereinafter), this gas is especially suitable for use in electric
power generation systems.
Figure 6. Colombian natural gas 6 phase envelope and properties calculated with the GERG2008 equation of state.
Figure 7. Colombian natural gas 7 phase envelope and properties calculated with the GERG2008 equation of state.
The
second mixture (Figure
7) is a “wet” gas, in addition to methane contains
considerable amounts of ethane, propane, butane, among others (Table
4), additionally has 2% of 
;
this gas, apart from going through a phase separation process, could be
subjected to a treatment with amines or membranes for its sweetening (removal
or reduction of 
).
Both the dew curve and the cricondentherm and cricondenbar points show that for this humid gas there is a range of pressure and temperature conditions for which it is possible to carry out phase separation and recommend an operating pressure value in the separator close to the of the container well, which for Colombian natural gas wells is between 7 and 10 MPa.
Conclusion
From equilibrium experimental curves of five real and synthetic natural gas mixtures from the literature, equilibrium curves were constructed, compared and correlated using three different equations of state: Peng-Robinson, Soave-Redlich-Kwong and GERG2008. The results showed that there is no significant difference in the calculation of the cricondentherm points, presenting a maximum absolute error of 1% with respect to the real values. The calculation of the cricondenbar points yielded a maximum absolute error of 4.36% when the Peng-Robinson equation of state was used; therefore, both the Soave-Redlich-Kwong equation and the GERG2008 equation have low error rates, compared to the experimental points. Regarding the equilibrium curves, at low pressures the equation of state used to estimate the thermodynamic properties of natural gas is indifferent, however, as the pressure increases the Peng-Robinson equation is not suitable for represent the behavior of the multiphase and multicomponent system. The results suggest that, as long as the mixture contains the 21 present components in the GERG2008 state equation, this is the equation that best estimates the thermodynamic properties of the mixtures. In case of having additional components to those of Table 2 it is possible to use the Soave-Redlich-Kwong equation to calculate the equilibrium curves, since the results show that the error percentages are low for high pressure conditions. Finally, when performing the dew curves for two gas mixtures from Colombian fields using the GERG2008 state equation, it is possible to affirm that for “wet” gases there is a potential opportunity to carry out stage separation at high pressure, thus making it possible to eliminate or reduce the expenses associated with re-compression during the natural gas processing.
Acknowledgements
The authors wish to acknowledge to the Universidad Industrial de Santander for the academic support and COLCIENCIAS for the financial support.
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