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In the last two “Tip of the Month” we briefly discussed the importance of liquid density for process simulation and equipment design. Three different methods were introduced to compute liquid density. The methods were (a) charts and monographs, (b) correlations and (c) EoS or volume translated EoS. We also presented a comparison between accuracy of different correlations and EoS methods and provided guidelines for using correlations.

In this “Tip of the Month”, we will present a comparison between accuracy of HYSYS [1] and ProMax [2] process simulation packages which normally use correlations for liquid density calculations. For HYSYS we used the “Smooth Liquid Density” option and in ProMax there are two options of COSTALD [3, 4] and Rackett [5] but we only used the COSTAD method for the reasons discussed in the last tip of the month. Both of these methods are discussed in Chapter 3 of JMC Volume 1 of Gas Conditioning and Processing Book [6]. The focus will be on the mixture of light hydrocarbons which have wider applications in gas industry. We will provide guidelines to use these process simulation programs effectively. In this study we have used the experimental data reported in GPA Research Report RR-147 [7].

We predicted the saturated liquid density of the ethane-propane mixture for the conditions reported in the GPA research report using the default option of HYSYS and ProMax. For the default option for each set of experimental conditions, we entered temperature, pressure, composition and total number of moles (100 moles was used for all cases). In Figure 1, the predicted results for 90 points are plotted as a function of the experimental values.

As can be seen in this figure, for several points the errors are very large. These large errors are due to the fact that for these points the process simulators predict partially vaporized systems and the reported densities are for a two phase mixture and not for the actual liquid mixture as reported experimentally. Therefore, we performed a flash calculation for each experimental point, separated the gas from the feed and predicted the density for the resulting liquid stream and re-plotted the results in Figure 2. This causes some changes in composition but Figure 2 indicates that considerable improvement in accuracy is obtained by degassing the feed stream.

Since the reported experimental data were at saturated liquid conditions, a second option is to predict the liquid density using the bubble point option. For this option, we entered temperature, vapor fraction of zero, composition of components, and 100 moles for total feed. By performing bubble point calculation, the liquid density and bubble point pressure were calculated. Figures 3 and 4 show the accuracy of HYSYS and ProMax in predicting the liquid densities and bubble point pressures, respectively. Again, quite an improvement is obtained by performing bubble point calculation to obtain the liquid density.

We repeated similar calculations for propane-normal butane and normal butane-normal pentane mixtures and have summarized in Table 1 the error analysis for different options using the simulation softwares.

Table 1 indicates that if the default option of HYSYS and ProMax are used, the calculated liquid density may contain a large error. On the other hand, when the mixture was flashed and the vapor was removed the calculated density was more accurate. Finally, calculating the liquid density using bubble point calculation yields more accurate density; however, the pressure may deviate slightly from the specified system pressure. The deviation of pressure does not cause a major concern because the pressure effect on liquid properties is not that much and more often it is ignored.

To learn more about liquid density and its impact on facilities calculation, design and surveillance, refer to JMC books and enroll in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. HYSYS, version 2004.2, Aspen Technology Inc., Cambridge, Massachusetts, 2005.
2. ProMax, version 1.2, Bryan Research & Engineering Inc, Bryan, Texas, 2005.
3. Hankinson, R. W.; Thomson, G. H. A new correlation for saturated densities of liquids and their mixtures. AIChE J. 1979, 25, 653.
4. Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An improved correlation for densities of compressed liquids and liquid mixtures. AIChE J., 28, 671, 1982
5. Rackett, H. G. Equation of state for saturated liquids. J. Chem. Eng. Data, 15, 514, 1970
6. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
7. Holcomb, C.D., Magee, J.W., and W.M. Haynes, “Density Measurements on Natural Gas Liquids,” Gas Processor Associations, RR-147, Tulsa, 1995.

In the previous “Tip of the Month” we briefly discussed the importance of liquid density for process simulation and equipment design and introduced different methods of their predictions. In addition to direct laboratory measurement, three different methods were introduced to compute liquid density. The methods were (a) charts and monographs, (b) correlations and (c) EoS or volume translated EoS.

In this “Tip of the Month”, we will present a comparison between accuracy of different correlations and EoS methods. The focus will be on correlations for light hydrocarbons which have wider applications in industry.

Recently, Mulero et al. [1] have evaluated nine empirical correlations for their accuracy and applicability in calculation of the liquid saturation density of pure fluids. All of them were based on the corresponding states principle, and they have included very recent correlations. One model required only the knowledge of critical parameters, but most of them needed the critical parameters and acentric factor as inputs, and one required the Lennard-Jones molecular parameters and the acentric factor as input data. As a reference, they took the numerical values for the liquid saturation density accepted by the DIPPR [2] project for 552 fluids, grouped into 30 families. Recommendations are given for the use of each model and for the choice of the adequate model for each family of fluids, including for particular fluids. For detail comparison and suggestions, the readers are referred to their paper; however, Table 1 is a summary of their comparison for pure fluids. The two most common correlations in gas industry, Rackett and COSTALD (highlighted in blue color) are also discussed in Chapter 3 of JMC Volume 1 of Gas Conditioning and Processing Book [3].

Table 1: MAPDs (Mean value of Absolute Percent Deviations) of the Calculated Liquid Saturation Densities for Several Families of Fluids with Respect to the DIPPR [2] Data when Using Correlations^a-c [1]

The numbers in italics represent the lowest MAPDs, and the numbers in bold show MAPDs that are similar (1%) to the lowest one. b YG) Yamada and Gunn; RRPS ) Reid et al.; B) Bhirud; QSMC1) Queimada et al.; QSMC2) Queimada et al.; SNM0) Mchaweh et al.; FMC) Fau´ndez et al.. c N) number of fluids, ND) number of data.

Similarly, Mchaweh et al. [12] reported the results of comparison study for light hydrocarbon mixtures containing nitrogen. A summary of their work is presented in Table 2. Their evaluation did not include COSALD; however, our experience indicates that COSTALD MAPD is below 0.5 %. It should be noted that even though Volume Translated SRK (VTSRK) improves the accuracy of the SRK EoS but still is not good enough for industrial applications.

Table 2: The MAPD for 17 multi-component low temperature systems (226 data points) using different method [12]

In another paper, Javanmardi et al. [18] evaluated several correlations and EoSs for prediction of LNG density. Among others, five LNG mixtures consisting of 22 experimental data were studied. The compositions of these LNG mixtures are presented in Table 3 and a summary of comparison between accuracies of different methods is shown in Table 4.

Analysis of Tables 1 through 4 indicates that, for pure compounds, the SNM [12] in general gives better accuracies. However, for light hydrocarbon mixtures (NGL and LNG) liquid densities prediction, it is highly recommended to use COSTALD [3, 8, 9] even though SNM correlation also give accurate and compatible results. The SRK [16] and its volume translated correction (VTSRK, [17]) accuracies are not as good as the correlations so their use for practical applications must be done with care and caution. Needless to point out that SRK predict gas densities accurately. Based on our experiences and similar observations, we have programmed, in the JMC GCAP software, SRK for gas and COSTALD for liquid densities.

In next “Tip of the Month” we will provide Part 2 of guidelines for proper use of commercial simulator to calculate liquid densities.

To learn more about liquid density and its impact on facilities calculation, design and surveillance, refer to JMC books and enroll in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. Mulero, A., Cachadina, I. and Parra, M. I., “Liquid Saturation Density from Predictive Correlations Based on the Corresponding States Principle. Part 1: Results for 30 Families of Fluids,” Ind. Eng. Chem. Res., 45, 1840-1848, 2006
2. DIPPR (Design Institute for Physical Property Data) files, Version 17.0; American Institute of Chemical Engineers: New York, 2003 (supplied by Technical Database Services, Inc., www.tds.cc).
3. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
4. Rackett, H. G. Equation of state for saturated liquids. J. Chem. Eng. Data, 15, 514, 1970 5. Yamada, T.; Gunn, R. D. Saturated liquid molar volumes: The Racket equation. J. Chem. Eng. Data, 18, 234, 1973
5. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977.
6. Bhirud, V. L. A four-parameter corresponding states theory: Saturated liquid densities of anormal fluids. AIChE J., 24, 1127, 1978.
7. Hankinson, R. W.; Thomson, G. H. A new correlation for saturated densities of liquids and their mixtures. AIChE J. 1979, 25, 653.
8. Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An improved correlation for densities of compressed liquids and liquid mixtures. AIChE J., 28, 671, 1982
9. Faundez, C. A.; Mulero, A.; Cuadros, F. Molecular Thermodynamic Models for the Vapour-Liquids Equilibrium of Non-Polar Fluids. J.. Phase Equilib., 21, 364, 2000.
10. Queimada, A. J.; Stenby, E. H.; Marrucho, I. M.; Coutinho, J. A. P. A new corresponding states model for the estimation of thermophysical properties of long chain n-alkanes. Fluid Phase Equilib., 212, 303, 2003.
11. Mchaweh, A.; Alsaygh, A.; Nasrifar, Kh.; Moshfeghian, M. A simplified method for calculating saturated liquid densities. Fluid Phase Equilib., 224, 157, 2004.
12. M.J. Hiza, W.M. Haynes, W.R. Parrish, J. Chem. Thermodyn. 9, 873–896, 1977.
13. Haynes, W. M., Measurements of Orthobaric-Liquid Densities of Multicomponent Mixtures of LNG components Between 110 and 130 K, J. Chem. Thermodynamics, 14, 603-612, 1982.
14. M.J. Hiza, W.M. Haynes, J. Chem. Thermodyn. 1, 1–10, 1980.
15. Soave, G., Chem. Eng. Sci., vol. 27, 1197-1203, 1972.
16. Peneloux, A. E., Rauzy, E., and Freze, R., Fluid Phase Equilib., Vol. 8, 7-23, 1982.
17. Javanmardi, J., Nasrifar, Kh., Moshfeghian, M., Comparing different methods for prediction of liquefied natural gas densities, Engineering Journal of the University of Qatar, Vol. 18, 39-56, 2005

Liquid density is needed for process simulation and equipment design. For example, accurate predictions of liquid density are needed for calculation of pressure drop in a piping/pipeline and vessel sizing. Accurate liquid density is also essential for custody transfer.

Liquid density ranges from a few hundred above thousand to couple of 100 kg/m³. Table 1 presents typical range of liquid densities where as typical re-injection gas has a density in the range of 125 to 150 kg/m³ and pipeline gases at 7000kPa has a density in the order of 70 kg/m³.

Liquid densities are sometime expressed in terms of relative density (specific gravity) or API gravity. The relative density,? , is defined as:

and the API (American Petroleum Index) gravity is:

Depending on the applications, three different methods can be used to compute liquid density in addition to direct laboratory measurement. These methods are (a) charts and monographs, (b) correlations and (c) EoS or volume translated EoS, of which the correlations are usually the most accurate.

For the LNG density measurement and calculation, one of the standard procedures practiced in industry is ISO 6578: 1991 [1]. This procedure specifies the calculations to be made to adjust the volume of a liquid from the conditions at measurement to the equivalent volume of liquid or vapor at a standard temperature and pressure, or to the equivalent mass or energy (calorific content). Annexes A to H of this procedure form an integral part of this standard.

Generalized Charts

There are several generalized charts for prediction of liquid density of petroleum fluids and hydrocarbons [2].

The relative density of petroleum fluids are normally expressed in terms of two of three characteristics- API gravity at 15°C, the Watson characterization factor, KW, or the mean average boiling point. The Watson characterization factor is defined in terms of mean average boiling point, Tb, and the relative density at standard condition.

The charts normally present the relative density of paraffinic hydrocarbon mixtures at their boiling point or bubble point temperature and pressure. These charts apply to mixtures as well to pure components. Alignment points for paraffinic hydrocarbon mixtures and pure components are located according to their molecular weight. The accuracy of these charts is generally within 3 % of the measured values. However, the accuracy is somewhat less for mixtures having molecular weights less than 30 where temperature is low, and where the methane content is high or reduced temperatures above 0.9 [3].

EoS Methods and Volume Translation

The EoSs are used in commercial simulation softwares for predicting phase behavior and thermodynamic properties. Generally, EoSs need a few parameters (usually two or three) that are normally obtained from critical properties. The cubic equations of state (EOS) give accurate results for prediction of vapor-liquid equilibria, especially for non-polar or slightly polar systems. Furthermore, these equations could be used to accurately predict vapor densities, enthalpy and entropy. These advantages encourage the researchers to augment EoS ability more than before, especially, liquid density, although their accuracy for liquid density prediction is not as good as correlations. The popular EoSs such as SRK [4] and PR [5] predict liquid density with an average absolute error about 8%, much more than the correlations [6]. This large magnitude of error is not acceptable by industry; therefore; they are not used for this purpose. In order to overcome this deficiency, a volume translated method has been developed by Peneloux et al. [7]. The working equations are:

In the above equation, v^SRK is calculated by SRK EoS and the correction term “c” as follows:

Correlations

In order to calculate liquid density reliably, several correlations such as COrresponding STAte Liquid Density (COSTALD) and modified Rackett equation by Spencer and Danner (RSD), have been developed.

COSTALD correlation: The COSTALD correlation, Hankinson and Thomson [8], requires two parameters, ?_SRK, the optimized value of the acentric factor based on the SRK EoS and V*, the pure component characteristic volume.

The RSD correlation: Spencer and Danner [9] improved the liquid density correlation of Rackett [10]. The improved correlation for saturated liquid density calculation requires only Z_RA, the improved compressibility factor.

In next “Tip of the Month” we will provide guidelines for use of these methods and present the results of a comparison study between these methods.

To learn more about liquid density and its impact on facilities calculation, design and surveillance, refer to JMC books and enroll in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. http://www.iso.org
2. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
3. Engineering Data Book, 10th and 11th Editions, Gas Processors and Suppliers Association Data Book, Tulsa, Oklahoma, 1998.
4. Soave, G., Chem. Eng. Sci., vol. 27, pp. 1197-1203, 1972.
5. Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., vol. 15, p. 59, 1976.
6. Nasrifar, Kh. and M. Moshfeghian, J. of Fluid Phase Equilibria, 158-160, pp. 437-445, 1998.
7. Peneloux, A. E., Rauzy, E., and Freze, R., Fluid Phase Equilib., vol. 8, pp. 7-23, 1982
8. Hankinson, R. W., Thomson, G. H., AIChE J., vol. 25, no. 4, pp. 653-663, 1979.
9. Spancer, C. F., and Danner, R. P., J. Chem. Eng. Data, vol. 17, no. 2, pp. 236-241, 1972.
10. Rackett, H. G., J. Chem. Eng. Data, vol. 15, no. 4, pp. 514-517, 1970.

In the previous “Tip of the Month”, we presented several methods for estimating Kvalues. The methods presented were the GPA correlations and charts, Raoult’s law, Wilson’s correlation, EoS approaches, activity coefficient models and JMC Charts and Tables. However, the question arises as to which equation or method should be used? The answer to this question “depends” on many factors such as pressure, temperature, composition, and components of the system.

In this “Tip of the Month” we will provide guidelines for use of these methods and present the results of a comparison study between these methods.

Table 1 presents the list of suggested methods for estimation of K-values and the applicable pressure range.

Comparison of methods:

For mixture A shown in Table 2, a series of bubble pointand dewpoint calculations were performed using Raoult’s law, Wilson correlation, GPA charts, and the SRK EoS. The summary of results is shown in tables 3 and 4, respectively.

As can be seen from Table 3 and 4, at low pressures, all of the methods produce very close answers; however, as the pressure increases they deviates considerably from each other.

In general Raoul’t law and Wilson correlation generates close answers. The GPA and SRK results are close to each other up to 1000 psia. However, at higher pressures they deviate from each other. As can be seen by this comparison, it is important to not apply these K-value equations outside of their recommended range of application.

It can also be seen that even when the equations are applied properly widely varying results can be obtained as is the case with the GPA and SRK results. In order to determine which equation is providing the most accurate results it is a good idea to compare the results with actual data. Experimental data may also be used to tune (improve the accuracy) of a correlation or an EoS.

Similarly, for the same mixture shown in Table 1, a series of flash calculations for two isotherms were performed and the calculated liquid fractions (L/F) using different methods are compared in Table 5. Again, the calculated liquid fractions by the Raoult’s law and Wilson correlations are close to each other but they deviate considerably from the GPA charts and the SRK EoS results.

Guidelines:

Due to the observation made in the previous section and other studies, care must be taken in selecting K-values correlations. Therefore, the following guidelines extracted from page 128 of Vol 1 of JMC book are suggested.

The accuracy of the results of calculations involving K-Values depends on the reliability of sampling, of the analysis of that sample, and the K-Value correlation used.

There is no single K-Value correlation that is superior for all mixtures encountered. An experienced practitioner may have two or three different models or program available. Generally, crude oil and NGL phase behavior is handled by different models.

All K-values are sensitive to composition, particularly the very volatile components like nitrogen, methane, and ethane.

For design purposes, several models may be used to determine a range of results. This range, rather than one set of “magic” numbers, is then used to size equipment. The name of the game is flexibility. It is doubtful if one ever will encounter the analyses, flow rates and exact other conditions used as the design basis.

It is most important that the K-values be internally consistent. There are several methods available for this purpose (See pages 113-116 of Vol 1 of JMC Books).

An experienced practitioner usually can predict the quantity of a specified liquid within 6% (for a specified analysis and conditions). The compositional analysis on which the calculation was based will often be in error more than this. This is important, for in many systems a series of VLE calculations is made; the output from one is the input to another. The errors thus accumulate. Many less than desirable systems results from failure to recognize this.

To learn more on applications of K-values and their impact on facilities calculation, design and surveillance, refer to JMC books [1-3] and enroll in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. Maddox, R. N. and L. L. Lilly, “Gas conditioning and processing, Volume 3: Advanced Techniques and Applications,” John M. Campbell and Company, Norman, Oklahoma, USA, 1994.
2. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
3. Campbell, J. M., “Gas conditioning and processing, Volume 2: Equipment Modules,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.

Nomenclature:

K_i – Vapor–liquid equilibrium ratio
P – Pressure, kPa [psia]
P_i^Sat– Saturation pressure of component I, kPa [psia]
T – Temperature, K [°R]
y_i – Mole fraction in the vapor phase
x_i – Mole fraction in the liquid phase
?_i^V – Fugacity coefficients of component I in the vapor phase
?_i^L – Fugacity coefficients of component I in the liquid phase
Y_i– Activity coefficient of component I in the liquid phase

Modeling and design of many types of equipment for separating gas and liquids such as flash separators at the well head, distillation columns and even a pipeline are based on the phases present being in vapor-liquid equilibrium. The thermodynamic equilibrium between vapor and liquid phases is expressed in terms equality of fugacity of component i in the vapor phase, f_i^V, and the fugacity of component i in the liquid phase, f_i^L, is written as

Equation (1) is the foundation of vapor-liquid equilibrium calculations; however, we rarely use it in this form for practical applications. For calculation purposes, Eq. (1) is transformed to a more common expression which is

Ki is called the vapor–liquid equilibrium ratio, or simply the K-value, and represents the ratio of the mole fraction in the vapor, yi, to the mole fraction in the liquid, xi. Equation (2) is also called “Henry’s law” and K is referred to as Henry’s constant. For the more volatile components the Kvalues are greater than 1.0, whereas for the less volatile components they are less than 1.0.
Depending on the system under study, any one of several approaches may be used to determine K-values. Obviously, experimental measurement is the most desirable; however, it is expensive and time consuming. Alternatively, there are several graphical or numerical tools that are used for determination of K-values. This “Tip of the Month” presents a history of many of those graphical methods and numerical techniques.

In general K-values are function of the pressure, temperature, and composition of the vapor and liquid phases. The components making up the system plus temperature, pressure, composition, and degree of polarity affect the accuracy and applicability, and hence the selection, of an approach. The widely used approaches are K-value charts, Raoult’s law, the equation of state (EoS) approach (f), activity coefficient approach (?) or combination of EoS and the EoS and ? approaches [1-5]. EoS approach requires use of a digital computer.

K-Value Charts

There are several forms of K-value charts. One of the earliest K-value charts for light hydrocarbons is presented in reference [1]. In these charts, K-values for individual components are plotted as a function of temperature on the x-axis with pressure as a parameter. In each chart the pressure range is from 70 to 7000 kPa (10 to 1000 psia) and the temperature range is from 5 to 260 ºC (40 to 500 ºF).

Early high pressure experimental work revealed that, if a hydrocarbon system of fixed overall composition were held at constant temperature and the pressure varied, the K-values of all components converged toward a common value of unity (1.0) at some high pressure. This pressure was termed the “Convergence Pressure” of the system and has been used to correlate the effect of composition on K-values, thus permitting generalized K-values to be presented in a moderate number of charts.

In more recent publications [2], the K-values are plotted as a function of pressure on the x-axis with temperature and Convergence Pressure as parameters. In order to use these charts, one should determine the Convergence Pressure first. The determination of convergence Pressure is a trial-and-error procedure and can be found elsewhere [6].

For computer use, later in 1958 these K-Value charts were curve fitted to the following equations by academic and industrial experts collaborating through the Natural Gas Association of America [7].

In Eq (3) T is temperature in ºR, P is pressure in psia and the fitted values of the bij coefficients are reported in an NGAA publication [7].
A relatively simple nomograph is normally presented in undergraduate thermodynamics and unit operations text books. In the nomograph, the K-values of light hydrocarbons, normally methane through n-decane, are plotted on one or two pages. Charts of this type do allow for an average effect of composition, but the essential basis is Raoult’s law and equilibrium constants derived from them are useful only for teaching and academic purposes.

Raoult’s Law

Raoult’s Law is based on the assumptions that the vapor phase behaves as an ideal gas and the liquid phase is an ideal solution. Under these conditions the fugacities are expressed as

The saturation pressure of a component is represented by P_i^Sat and the pressure of the system is represented by P. Substituting from Eqs (4) and (5) in Eq (1) gives

The vapor pressure may be read from a Cox chart or calculated from a suitable equation in terms of temperature. A typical Cox chart may be found in reference [8]. The Antoine [5] equation is recommended for calculating vapor pressure:

Values of A, B, and C for several compounds are reported in the literature [5]. Complex vapor pressure equations such as presented by Wagner [5], even though more accurate, should be avoided because they can not be used to extrapolate to temperatures beyond the critical temperature of each component. Raoult’s law is applicable to low pressure systems (up to about 50 psia or 0.35 MPa) or to systems whose components are very similar such as benzene and toluene. This method is simple but it suffers when the temperature of the system is above the critical temperature of one or more of the components in the mixture. At temperatures above the critical point of a component, one must extrapolate the vapor pressure which frequently results in erroneous K-values. In addition, this method ignores the fact that the K-values are composition dependent.

Correlation Method

As mentioned earlier, determination of K-values from charts is inconvenient for computer calculations. Therefore, scientists and engineers have developed numerous curve fitted expressions for calculation of K-values. However, these correlations have limited application because they are specific to a certain system or applicable over a limited range of conditions. Some of these are polynomial or exponential equations in which K-values are expressed in terms of pressure and temperature. One of these correlations presented by Wilson [9], is:

where Tci, critical temperature, in ºR or K, Pc_i, critical pressure, in psi, kPa or bar, ?_i is the acentric factor, P is the system pressure, in psi, kPa or bar, T is the system temperature, in ºR or K. (P and Pc, T and Tc must be in the same units.) This correlation is applicable to low and moderate pressure, up to about 3.5 MPa (500 psia), and the K-values are assumed to be independent of composition.

EoS Approach

The fugacity of each component is determined by an EoS. In other words, both phases are described by only one EoS. It is a powerful tool and relatively accurate if used appropriately. This approach is widely used in industry for light hydrocarbon and non polar systems. Under these conditions the fugacities are expressed by

The fugacity coefficients for each component in the vapor and liquid phases are represented by ?_i^V and ?_i^L
, respectively. Substitution of fugacities from Eqs (9) and (10) in Eq (1) gives

The EoS method has been programmed in the GCAP for Volumes 1 & 2 of Gas Conditioning and Processing Software to generate K-values using the SRK EoS [10].

EoS-Activity Coefficient Approach

The approach is based on an EoS which describes the vapor phase non-ideality through the fugacity coefficient and an activity coefficient model which accounts for the non-ideality of the liquid phase. This approach is widely used in industry for polar systems exhibiting highly non-ideal behavior. Under these conditions the fugacities are expressed by

The fugacity coefficients for each component in the vapor phase are represented by f_i^V . The saturation fugacity coefficient for a component in the system, f_i^Sat is calculated for pure component i at the temperature of the system but at the saturation pressure of that component. Normally, an EoS is used to calculate both f_i^V and f_i^Sat . Substitution of fugacities from Eqs (12) and (13) in Eq (1) gives

Activity coefficients are calculated by an activity coefficient model such as that of Wilson [11] or the NRTL (Non-Random Two Liquid) model [12]. In order to calculate K-values by equation 14, the mole fractions in both phases in addition to the pressure and temperature must be known. Normally not all of these variables are known. As is the case for the EoS approach, calculations are trial and error. This approach is applicable to polar systems such as water – ethanol mixtures from low to high pressures.

Normally, for low pressures, we can assume that the vapor phase behaves like an ideal gas; therefore both ?_i^V and ?_i^Sat are set equal to 1.0. Under such circumstances, Eq (14) is reduced to

Eq (15) is applicable for low pressure non-ideal and polar systems. Assuming the liquid phase is an ideal solution, ? i becomes unity and Eq (15) is reduced further to a simple Raoult’s law.

The JMC K-Values

Two sets of K-values are summarized in Appendices 5A and 5B at the end of Chapter 5 of Gas Conditioning and Processing, Vol. 1. Appendix 5A is a series of computer-generated charts using SRK EoS. The values shown are useful particularly for calculations of vapor liquid equilibrium wherein liquid being condensed from gas systems. Appendix 5B is based on the data obtained from field tests and correlations on oil-gas separators. The data set was based on over 300 values. This correlation has bee used for often for oil separation calculations.

To learn more on applications of K-values and their impact on facilities calculation, design and surveillance, refer to JMC books [12-13] and enroll in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. Natural Gasoline Supply Men’s Association, 20th Annual Convention, April 23-25, 1941.
2. Engineering Data Book, 10th and 11th Editions, Gas Processors and Suppliers Association Data Book, Tulsa, Oklahoma, (1998).
3. Prausnitz, J. M.; R. N. Lichtenthaler, E. G. de Azevedo, “Molecular Thermodynamics of Fluid Phase Equilibria,”, 3rd Ed., Prentice Hall PTR, New Jersey, NY, 1999.
4. Maddox, R. N. and L. L. Lilly, “Gas conditioning and processing, Volume 3: Advanced Techniques and Applications,” John M. Campbell and Company, Norman, Oklahoma, USA, 1994.
5. Reid, R. C.; J. M. Prausnitz, and B. E. Poling, “The properties of Gases and liquids,” 4th Ed., McGraw Hill, New York, 1987.
6. Engineering Data Book, 7th Edition, Natural Gas Processors Suppliers Association, Tulsa, Oklahoma, 1957.
7. Equilibrium Ratio Data for Computers, Natural Gasoline Association of America, Tulsa, Oklahoma, (1958).
8. Natural Gasoline and the Volatile Hydrocarbons, Natural Gasoline Association of America, Tulsa, Oklahoma, (1948).
9. Wilson, G., “A modified Redlich-Kwong equation of state applicable to general physical data calculations,” Paper No15C, 65th AIChE National meeting, May, (1968).
10. G. Soave, Chem. Eng. Sci. 27, 1197-1203, 1972.
11. Wilson, G. M., J. Am. Chem. Soc. Vol 86, pp.127-120, 1964
12. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.
13. Campbell, J. M., “Gas conditioning and processing, Volume 2: Equipment Modules,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.

In the last “Tip of the Month”, we evaluated the accuracy of two commercial process simulators against the experimental data. In this “Tip of the Month”, we will evaluate the accuracy of three shortcut methods for prediction of depression of hydrate formation temperature in the presence of two common inhibitors, methanol (MeOH) or mono ethylene glycol (MEG). We have used the same set of experimental data from the previous “Tip of the Month” as the basis for our evaluation. These shortcut methods may be used to calculate the required concentration of inhibitor and the injection rate for dew point correction process, NGL (Natural Gas Liquid) recovery, or pipeline transportation of natural gas. The detail of the calculation procedure is presented in chapter 6 of Volume 1 of Gas Conditioning and Processing [1]. The three methods evaluated are the Hammerschmidt (HA) [2], Nielsen- Bucklin (NB) [3], and Moshfeghian-Maddox (MM) [4]. These methods were used to predict hydrate formation temperature in the presence of inhibitors. Pure compounds as well as multi component natural gas mixtures covering a wide pressure range of up to 14500 psia (100 MPa) have been studied. Even though the shortcut methods presented in reference [1] could have been used, the required hydrate formation temperatures in the absence of inhibitor (pure water) were predicted by Parish and Prausnitz (PP) [5] for all three methods. This assured the same basis and accurate results. The strength and limitation of these methods are identified and recommendations for industrial applications have been made.

Table 1 presents the composition, inhibitor weight % range, pressure range, number of points, the reference of the experimental data for the gas mixtures studied in this work. The ability of the three methods to predict the hydrate formation temperature for gas E is shown in Figure 1. The accuracy of these methods, for CH4, C2H6, C3H8, CO2, H2S and their mixtures as shown in Table 1, are presented in Figures 1 and 2 for MeOH and Figures 3 and 4 for MEG.

Figure 1 indicates that the PP method predicts the hydrate formation temperature for gas E in the presence of pure water (0 wt% MeOH) accurately. This method was used to add its perdition temperature to the depression temperature predicted by the three shortcut methods for the sake of easy comparison with the experimental data. Figure 1 also indicates that all three methods give good results for 20 wt% MeOH; however, for 40 wt% MeOH, the HA results deviate from the experimental data considerably.

The analysis of Figures 2 indicates that all three methods give accurate results for temperature as low as 20 °F (-6.7 °C) equivalent to maximum of 25 wt% MeOH, but at lower temperature (or higher MeOH concentration) the HA method deviates from the experimental data considerably. For lower temperatures, the MM gives better results than the NB method.

Figure 3 and 4 indicate that all three methods give accurate results for gas mixture F up to concentration of 50 wt% MEG (as low as 0 °F or -18 °C) for which experimental data were available but their prediction for some of the pure compounds below this temperature is questionable.

To learn more about inhibitor injection we suggest participating in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Campbell, J. M., “Gas Conditioning and Processing, Vol. 1, the Equipment Modules, 8th Ed., J. M. Campbell and Company, Norman, Oklahoma, 2001
2. Hammerschmidt, E.G., ‘Formation of gas hydrates in natural gas transmission lines,” Ind & Eng. Chem, Vol. 26, p. 851, 1934
3. Nielsen, R. B. and R.W. Bucklin, “Why not use methanol for hydrate control,” Hydrocarbon Processing, Vol 62, No. 4, P 71, April 1983
4. Moshfeghian, M. and R. N. Maddox, “Method predicts hydrates for high- pressure gas streams,” Oil and Gas J., August 1993.
5. Parrish, W. R. and J. M. Prausnitz. “Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures”, Ind. Eng. Chem. Proc. Dev.,11, 1, 26-35, (1972).
6. Ng, Heng-Joo, and D.B. Robinson, Research Report RR-66, Gas Processors association, Tulsa, Oklahoma, 1983
7. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-106, Gas Processors Association, Tulsa, Oklahoma, 1987
8. Blanc, C., and Tournier-Lasserve, J., World Oil, November, 1990.
9. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-92, Gas Processors Association, Tulsa, Oklahoma, 1985

Many materials may be added to water to depress both hydrate and freezing temperatures. For many practical reasons an alcohol or one of the glycols is injected as an inhibitor, usually methanol, diethylene glycol (DEG) or mono ethylene glycol (MEG). All may be recovered and recirculated, but economic of methanol recovery may not be favorable in many cases. Total injection rate is that needed to provide the necessary inhibitor concentration in the liquid water plus that inhibitor which enters the vapor and hydrocarbon liquid phases. Any inhibitor in the vapor phase or liquid hydrocarbon phase has little effect on hydrate formation conditions. Determination of the amount and concentration of inhibitors and their distribution in different phases are very important for practical purposes and industrial applications. Therefore, in order to determine the required amount and concentration of these inhibitors, several thermodynamic models for hand and rigorous calculations have been developed and incorporated into the computer software.

In this Tip of the Month, we will evaluate the accuracy of two commercial process simulators “A” and “B” against the experimental data. These softwares were used to predict hydrate formation condition in the presence of inhibitor. Pure gas component as well as multi component natural gas mixtures covering a wide pressure range of up to 100 MPa have been studied. These softwares may be used to simulate an integrated NGL (natural gas liquid) plant with inhibitor injection and regeneration process. The optimum concentration and circulation rate are determined using different softwares. The strength and limitation of these softwares are identified and recommendations for industrial applications have been made.

Table 1 presents the composition, inhibitor weight % range, pressure range, number of points, the reference of the experimental data for the gas mixtures studied in this work. The ability of the two softwares to predict the hydrate formation temperature for gas E is shown in Figure 1. The accuracy of these softwares for CH₄, C₂H₆, C₃H₈, CO₂, H₂S and their mixtures as shown in Table 1 are presented in Figures 2 and 3; for methanol and MEG, respectively

The analysis of Figures 2 and 3 indicates that for methanol inhibition, the lower limits of hydrate formation temperatures are -75°F (-60°C) for Sim A (maximum of 70 wt% methanol) and -25°F (-32°C) for Sim B (Maximum of 50 wt% methanol). It should be pointed out that Sim B could not converge for cases of 85 wt% methanol. For MEG, both softwares give accurate results down to 25°F (-4°C) corresponding to 25 wt% MEG; however, for lower temperatures the accuracy drops while the Sim A gives better results. To learn more about inhibitor injection we suggest participating in our G4 (Gas Conditioning and Processing) and G5 (Gas Conditioning and Processing – Special) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Ng, Heng-Joo, and D.B. Robinson, Research Report RR-66, Gas Processors association, Tulsa, Oklahoma, 1983
2. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-106, Gas Processors association, Tulsa, Oklahoma, 1987
3. Blanc, C., and Tournier-Lasserve, J., World Oil, November, 1990.
4. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-92, Gas Processors association, Tulsa, Oklahoma, 1985

In this Tip of the Month, we will study two alternatives for removal of H₂S and CO₂ from natural gas. The process objective is to produce a sweet gas with less than 4 PPM H₂S and the near total removal of CO₂ due to the presence of a downstream nitrogen rejection unit (NRU). Each alternative consist of two stages of acid gas removal. The schematic diagrams for both alternatives are shown in Figure 1. The detail of gas sweetening may be found in the Gas Conditioning and Processing, Vol. 4, “Gas and Liquid Sweetening”.

In option A, sour natural gas is treated in the MDEA unit to selectively remove H₂S and part of the CO₂. The partially treated gas is then sent to the DEA unit for removal of the remaining CO₂. The acid gas from the MDEA unit is sent to the sulfur recovery unit (SRU). The acid gas from the DEA unit, mainly CO_2, and tail gas from the SRU are sent to the incinerator.

In the second alternative (Option B), all of the H₂S and CO₂ are removed in the DEA unit and sent to the MDEA unit where H₂S is selectively removed at low pressure. The H₂S enriched acid gas from the MDEA unit is sent to the SRU. The CO₂ from the MDEA contactor is routed directly to the incinerator unit.

We performed rigorous computer simulation for both alternatives with typical process specifications. The simulation results showed that arrangement of the MDEA and DEA units and the order of their utilization make a difference in the concentration of H₂S in the acid gases fed to the sulfur recovery unit. Our study indicated that option B produces richer H₂S in the acid gases stream, producing a more suitable feed for sulfur recovery unit. A drastic reduction of pumping was obtained for option B. Smaller diameter and fewer number of trays for the contactor of the MDEA unit in Option B are needed. An additional benefit of option B is that less pick up of heavy hydrocarbons from the feed gas was obtained. This will benefit both the operation of the amine units and the SRU. The preliminary evaluation indicates that the overall energy consumption is lower for option B which has more favorable performance. However, for decision making process, a detail economic analysis for both options is highly recommended.

Similar cases in gas sweetening are discussed in our GAS TREATING AND SULFUR RECOVERY (G-6) and REFINERY GAS TREATING, SOUR WATER, SULFUR AND TAIL GAS (RF-61) courses

By: Dr. Mahmood Moshfeghian and Mark E. Bothamley

References:

Maddox, R.N., and D.J. Morgan, “Gas Conditioning and Processing, Vol. 4, Gas and Liquid Sweetening,” 4^th Ed., John M. Campbell & Company, Norman Oklahoma, (1998)