## LSU Historical Dissertations and Theses

1988

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Adrian E. Johnson, Jr

#### Abstract

The ability to predict methane solubility in underground reservoirs is essential to eventual exploitation of geothermal-geopressured reservoirs as an alternate energy source. In this study, second-order Leonard-Barker-Henderson perturbation theory was applied to brine solutions containing H$\sb2$O, CH$\sb4$, C$\sb2$H$\sb6$, CO$\sb2$, and NaCl to develop a fundamentally-based thermodynamic approach to handle more effectively the broad temperature and pressure ranges encountered in underground reservoirs, and to include the effect of the presence of various salts and other gases on methane solubility. The apparent ideal solution fugacity, f$\sbsp{i}{o\sp\prime}$, for each solute gas is proposed and developed through perturbation theory as a direct measure of the net forces acting upon the solute gas from all the species in the system. Since f$\sbsp{i}{o\sp\prime}$ depends on the brine composition, there is no need to use a Henry's law constant evaluated at infinite dilution along with an activity coefficient that varies with the solute gas mole fraction. Instead, the product, (x$\sb{i}$f$\sbsp{i}{o\sp\prime})$, gives the fugacity of each solute gas in the equations representing phase equilibrium. Both the partial molar volume of solute gas and the isothermal compressibility of its partial molar volume were self-generated from the perturbation theory approach to predict the gas solubility at high pressure, and they both agreed well with reported values. Essentially all published experimental data on methane solubility were utilized to test the relationships developed in this work. The ranges of conditions covered by this study are: temperatures from 298 to 589 K, pressures from 10 to 2000 atm, and salinities from 0 to 5 m. The parameters used in this study were all based upon reported literature values. Because of the extreme sensitivity of calculated methane solubilities to the values of $\sigma$ parameter in the Lennard-Jones potential, it was found necessary to determine the best values for these parameters for each component to insure a minimum least-squares global fit of the solubility data. In addition, it was found that allowing the $\sigma$ parameter for water to vary with temperature significantly improved the overall global fit to the data.

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