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The perturbation theory previously shown to give good results for the equation of state of a square-well fluid at liquid densities and temperatures is applied to more realistic potentials with soft repulsion, in particular the 6:12 potential. For an arbitrary potential function a modified potential is defined involving three parameters, namely a hard-sphere diameter, an inverse-steepness parameter for the repulsive region, and a depth parameter for the attractive region. When the latter parameters are zero, the modified potential becomes the hard-sphere potential; when they are one, it becomes the original potential. The configuration integral is expanded in a double-power series in the inverse-steepness and depth parameters, the hard-sphere diameter being chosen so that the first-order term in the inverse-steepness parameter is zero. The first-order term in the depth parameter is evaluated essentially exactly and the second-order term approximately: other second-order terms and all higher-order terms are neglected. The resulting equation of state is in good agreement with molecular dynamics, Monte Carlo results, and experimental data for argon at all temperatures and densities relevant for fluids.

The equation of state for a fluid of molecules interacting according to the square-well potential is evaluated by treating the attractive potential as a perturbation on the hard-sphere potential. This leads to an expansion in inverse powers of the temperature. The first-order term is evaluated exactly (except for the approximation of using the Percus—Yevick expression for the hard-sphere radial distribution function). Two slightly different approximations for the second-order term are given and shown to lead to similar results. With first-and second-order terms included, the calculated equation of state is in excellent agreement with quasiexperimental Monte Carlo and molecular-dynamics results at all temperatures including the lowest temperatures for which such calculations have been made, far below the critical temperature and at liquid densities. The reasons for this good agreement, particularly at high densities, are discussed in terms of a novel formulation of the perturbation theory, and the implications of the results for fluids with more realistic potential functions are considered.

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Models commonly used for the analysis of hydraulic test data are generalized by regarding the dimension of the flow to be a parameter which is not necessarily integral and which must be determined empirically. Mathematical solutions for this generalized radial flow model are derived for the standard test conditions: constant rate, constant head, and slug tests. Solutions for the less common, sinusoidal test are contained within the general solutions given. Well bore storage and skin are included and the extension to dual-porosity media outlined. The model is presented as a model of fractured media, for which it is most likely to find application because of the problem of choosing the appropriate flow dimension.