Guidelines for Selecting K-Value Method

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