GAS-CONDENSATE COMPOSITION--1 NEW CORRELATION DETERMINES RETROGRADE GAS-CONDENSATE COMPOSITION

Gustavy E. Niemtschik, Fred H. Poettmann Robert S. Thompson
Colorado School of Mines
Golden

A correlation has been developed for a retrograde condensate reservoir that relates well stream effluent composition at any depleted state to the reservoir fluid composition at its initial dew point pressure.

Thus, if the composition at a depleted state is known, one can calculate the initial composition. Or, if the initial composition is known, one can calculate the composition of the well steam effluent during pressure depletion.

This first article in a two-part series describes the derivation of the correlation. Software for the calculations, available free from OGJ and the Gas Research Institute, will be discussed in the second part.

Also, a correlation was developed to predict, if not available from other sources, the initial specific gravity of the gas condensate.

RETROGRADE CONDENSATE

In a constant-volume reservoir containing a retrograde gas condensate in a single phase at its dew point pressure, the liquid phase will condense as gas production reduces reservoir pressure. Because of the large reservoir surface exposed and the very low rate of pressure reduction, the gas phase is always in equilibrium with the reservoir liquid.

During reservoir depletion, condensation will continue until the pressure is reached at which the liquid begins to revaporize. Thus, there is a maximum liquid volume that condenses. This condensation and vaporization changes the composition of the produced gas.

Upon discovery, the fluid of a gas-condensate reservoir should be sampled and analyzed. A simulated constant volume, pressure depletion is one element of a reservoir fluid study. In commercial laboratories, the standard procedure is a series of volume expansions and constant pressure displacements of the reservoir fluid to a volume occupied by the initial gas condensate at its dew point.

At each expansion, the cell contents are equilibrated. Therefore cell volume is constant after each displacement. At each displacement, the reservoir gas produced is analyzed and measured. Also, the liquid volume in the cell is measured after each depletion.

Five to seven expansion steps are normal in commercial laboratories. An infinite number of expansion steps would, of course, be equivalent to a true differential condensation or vaporization process. But it is assumed that for a gas-condensate reservoir fluid, the produced gas composition from five to seven expansion steps will converge with the gas composition from a true differential condensation and vaporization process.

The authors do not know of any published report that verifies this assumption.

When a gas-condensate reservoir is first discovered, a reservoir fluid study is not always conducted. Thus, the compositional data from a constant volume, pressure depletion may not be available for reservoir simulations or material balance studies.

For reconstituted reservoir fluid, a knowledge of the initial composition is also important.

APPROACH

To obtain a useful correlation, two approaches were taken. These were a theoretical approach with the Peng-Robinson equation of state and a strictly empirical approach.1

Equations of state (EOS) by themselves are poor predictive tools for complex hydrocarbon mixtures. The EOS needs to be tuned against the phase behavior of a known fluid composition.

For gas condensate, the constantly changing well stream composition as the reservoir depletes compounds the problem. Although a solution was obtained with the Peng-Robinson EOS, the method proved impractical primarily because of the tuning problem.

In developing the empirical approach, the first attempt derived an analytical expression for the differential condensation/vaporization process. Although the approach did not succeed, the exercise led us to conclude that the primary variables to correlate were:

The ratio of produced gas composition for a given component over the initial gas composition of that component.
The pseudoreduced pressure (Ppr) ratio of the pressure at the depleted state over the initial reservoir pressure.

DATA

The correlation was based on the analysis of 131 constant-volume laboratory depletion studies on gas-condensate systems for a total of 907 depletion steps. Thus, there are 907 analyses for each component.

The data base is representative of a wide range of gas-condensate systems obtained worldwide. Table 1 shows the range of gas-condensate compositions and properties.2

The data were arbitrarily divided into six specific gravity ranges for the gas-condensate composition at its initial dew point. Specific gravity ranged from 0.50 to 1.70.

Based on the composition at the initial dew point, the data also were arbitrarily divided into 1.20-1.55 and 1.55-1.90 pseudoreduced reservoir temperature ranges (Tpr). In three cases to obtain greater accuracy for the C6 and C7+ components, the pseudoreduced temperature ranges were further divided in half.

Table 2 breaks down the number of depletion studies in each initial specific gravity range for the two pseudoreduced temperature ranges. Data sets containing less than four depletion studies were not used in the correlation.

Four data sets did not contain H2S and thus no correlation for the H2S component was possible. However, because in the well stream effluent during pressure depletion the H2S composition remains relatively constant, no large errors are introduced by assuming a constant H2S composition during pressure depletion.

CORRELATION

In a data set, each component's composition ratio was curve fitted using polynomial regression. This resulted in nine sets of equations. Each set of equations is for a given initial specific gravity range and pseudoreduced temperature range.

Each equation in an equation set is for a given component. The components range from H2S, CO2, N2, and C1 through C7+.

The general equation for each component in a set is shown as Equation 1 in the equation box.

Table 3 shows an example of the regression coefficients K for one of the equation sets. Each set is for a given initial specific gravity and pseudoreduced temperature range.

The specific gravity of any gas condensate may be calculated if the gas composition is known. If the initial composition of the gas-condensate is unknown, the specific gravity may be available from production records or may be calculated from production data.3

If the initial specific gravity is unavailable from other sources, it can be obtained from correlations. But if the specific gravity of the gas-condensate is known, the pseudocritical properties of the gas condensate can be calculated from Sutton's equations (Equation 2 and 3).4

After the pseudocritical properties are obtained, the pseudoreduced pressures and temperatures can be calculated.

SPECIFIC GRAVITY

Figs. 1a and b relate the gas condensate's initial and current specific gravity as a function of pseudoreduced pressure ratio of the current to initial pressure for the two pseudoreduced reservoir temperature ranges.

This correlation was developed by first comparing the current over initial specific gravity ratio as a function of the pseudoreduced pressure ratio for lines of constant initial specific gravity. Once this correlation was developed the charts were simplified to Figs. 1a and b.

To use Figs. 1a and b, one must know the pseudoreduced pressures, and thus the pseudocritical pressures. In making the first estimate of pseudoreduced pressure ratio, assume that the actual pressure ratio is the same as the pseudoreduced pressure ratio.

After the first value of specific gravity is estimated, calculate the pseudocritical properties of the gas and repeat the calculation using pseudoreduced pressure ratios. The calculated specific gravity should converge rapidly.

To select the correct chart, assume that the critical temperature of the unknown gas composition is the same as that for the known gas and calculate the pseudoreduced reservoir temperature. Select the correct chart and once the specific gravity of the unknown gas is estimated, calculate a new pseudoreduced temperature to see if it is still in the correct pseudoreduced temperature range.

If not, change charts and repeat the calculation. If the pseudoreduced temperature is 1.55 0.05, determine the initial specific gravity from both Figs. 1a and b and average the values.

ACCURACY

Four aspects were considered for determining the accuracy of the correlation:

Plots showed the difference between calculated initial composition and measured initial composition for each component.
A statistical analysis determined average percent error, average percent absolute error, and percent standard deviation of the calculated initial composition with respect to measured initial composition for each component.
To test the sensitivity of the analysis, 20 data points exhibiting the highest percent error were discarded in stages for each composition component and a statistical analysis performed on the remaining points. Frequency plots were prepared to show the distribution of the percent error of the initial composition for each component. All plots showed a normal distribution.
The sum of the calculated errors indicated the internal consistency.
Because the composition ratio correlation for each component is an independent correlation and the sum of the component compositions must equal one, the closeness to which the calculated results sum up to one before normalization indicates the consistency of the correlation.
The average percent error, the average percent absolute error, and the percent standard deviation were also calculated. A plot of the frequency distribution of the actual error was also prepared.
Comparisons indicated the difference of the calculated initial composition of a rich and lean gas condensate to the measured composition. A statistical analysis was also performed on the specific gravity correlation.

The complete analysis on the correlation's accuracy is in Reference 2. The following figures and tables illustrate the accuracy:

Fig. 2 shows the calculated initial composition-vs.-measured composition for C1, C7+, and all components. Note that the scale for the C7+ is an expanded scale.
Fig. 3 shows the frequency-vs.-percent error for C1 and C7+.
Table 4 shows statistical analysis of the error. The average percent error, the absolute percent error, and the percent standard deviation for the sum of the calculated mole fractions for a mixture indicates excellent internal consistency for the correlations.
Fig. 4 shows the frequency-vs.-sum of the mole fractions for the calculated initial composition.
Table 5 shows a comparison of the calculated-vs.-actual initial gas composition for a rich and lean gas condensate.

Overall the analysis shows excellent accuracy of the correlation.

Starting with i-C4, the standard deviation increases as the carbon number increases. The frequency distribution plots all show a normal distribution indicating good data correlation. It must be remembered that the calculated results are compared against experimentally measured values which themselves are subject to error.

The internal consistency of the correlation is excellent. The average sum of all the calculated composition before normalization is 0.9995.

ACKNOWLEDGMENT

We would like to express our sincere appreciation to W.D. McCain Jr. for the data set of constant volume laboratory depletion studies of retrograde gas-condensate reservoir fluids. We would also like to express our appreciation to Senol Yamanlar for his assistance in the regression analysis and to the Gas Research Institute for its support.

REFERENCES

Niemtschik, G.E., "Determination of the Initial Composition of a Gas Condensate System from Constant Volume Depletion Data," Thesis No. T4158, Colorado School of Mines, 1992.
Raves, D.G., Piper, L.D., McCain Jr., W.D., and Poston, S.W., "Two Phase Compressibility Factors for Retrograde Gases," SPE FE, March 1992, pp. 87-92.
Gold, D.K., McCain Jr., W.D., and Jennings, J.W., "An Improved Method for the Determination of Reservoir-Gas Specific Gravity for Retrograde Gases," JPT, July 1989, pp. 747-32.
Sutton, R.P., "Compressibility Factors for High Molecular Weight Reservoir Gases," SPE Paper No. 14265, 60th Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25, 1985.