Calculation of Differential Gas Liberation and Shrinkage
Authors: Weinaug C.F. 
Published: December 2007

Introduction
In recent years, several methods have been proposed for correlation of physical properties and behavior of hydrocarbon systems. These correlations were found to be unsatisfactory for predicting differential gas liberation and shrinkage data now obtained experimentally. To achieve the desired accuracy, methods were developed to adjust the correlations with two experimental pieces of data. The required data are the saturation pressure at reservoir temperature and the specific volume or density at these conditions. The saturation pressure is used to adjust the vaporliquid equilibrium-ratio correlations. The density measurement is used to determine the apparent density of liquid methane. With these adjustments, differential gas liberation and shrinkage are predicted within the experimental error.

EQUILIBRIUM RATIOS
Equilibrium ratios published by the National Gas Assn. of America were used as a basis for the calculation. The convergence pressure for the sample was determined by using a hypothetical binary system, with methane as one component and the remainder of the system lumped together to form the other component. For the critical temperature of the heavy constituent, the weight average of the critical temperatures of the ethane and heavier components was used. The correlation of pseudo-critical temperature, density and molecular weight of Matthews, Roland and Katz was used in this calculation for the hexane and heavier fractions. Points for the critical properties of methane and the hypothetical heavy constituent were placed on a chart of the critical loci of hydrocarbon systems. A critical loci for the hypothetical binary system was drawn, and the critical pressure of this system was determined at the reservoir temperature. This critical pressure became the convergence pressure for which equilibrium ratios were read from the NGAA charts. The NGAA equilibrium constants for C6 through C9 were used for the C6 through C9 fractions since they were separated on the bases of normal paraffin boiling points. The correlation of Hoffman, Crump and Hocott was used to estimate the equilibrium constant for the C10+ fraction. The NGAA equilibrium-ratio charts are based primarily on paraffin systems and have to be corrected for the presence of naphthenes and aromatics. The correlations in the literature proved too unsatisfactory for determining these corrections. Experimental data, the saturation pressure, is used with the correlation of Soloman to make this adjustment. The correction factors of Soloman were cross-plotted so that the factors for ethane and heavier components were made a function of the factor for methane.
............................(1)
where a1 = correction coefficient for methane NGAAequilibrium ratio, and a2 = correction coefficient for ethane and heavier NGAAequilibrium ratios.
This equation and the equation for the, bubble point are solved simultaneously for the correction coefficients. The bubble-point equation is
...........................(2)
The equilibrium constant for the saturation pressure at reservoir temperature is used. This procedure not only corrects for the relative volatility between components, but also assures that the results will be directly related to the experimental saturation pressure.

METHANE DENSITY
After determining a set of equilibrium ratios, the apparent density of condensed methane at 60F and 14.7 psia was estimated. This was found to be necessary because the correlations of Standing were found to be unsatisfactory. The law of additive volumes was employed to make this calculation.
............................(3)
where x = mole fraction, M = molecular weight, p = density, and the subscripts refer to components.
The specific volume, at reservoir saturation pressure and temperature, was corrected to 60F and 14.7 psia. This value was substituted into Eq. 3, and the apparent liquid density for methane at 60F and 14.7 psia was computed. This apparent density was assumed to apply for all other mixtures formed during the liberation of gas.

CALCULATIONS
The saturated reservoir fluid then was flashed to the first pressure below the saturation pressure. In most cases, this pressure corresponded to the one chosen by the laboratory. The normal flash-vaporization equations were used to compute the moles and compositions of the resulting liquid.
JPT
P. 1135^