Complex Numerical Calculations Research Articles

An extended law of corresponding states for the equilibrium and transport properties of the noble gases

This paper proposes a new law of corresponding states which provides us with a thermodynamically consistent and accurate correlation of the properties B, μ, k, b, D, μ 12, k 12, D 12, B 12 for the monatomic gases and their binary mixtures. The law of corresponding states, based on the hypothesis that all monatomic gases obey the same two-parameter pair potential, leads to the empirical determination of a number of universal functionals which replace the corresponding integrals of the Chapman-Enskog theory. The use of these functionals together with a list of empirically determined scaling factors for pure gases and binary mixtures allows us to compute the above quantities over an unusually large range of temperatures and a modest range of pressures, thus making it possible to employ measurements of a limited class of properties in a limited range of states to compute all others over wider ranges of states, as well as utilizing data on one gas, to generate them for another. Judged from the practical point of view of a user, the correlation is accurate and complete as far as monatomic gases and their binary mixtures are concerned, except for the evaluation of the pressure effect on the transport properties of mixtures. Taking into account the fact that the specific heat, c v , (or, equivalently, c v ) is a constant, and that it together with the equation Pv = RT + BP [or, equivalently, Pv = RT (1 + B/v)] fully determines all equilibrium properties of a monatomic gas in a reasonable range of pressures and a wide range of temperatures, the paper provides the basis for a thermodynamically consistent formulation of equilibrium as well as transport properties of the monatomic gases and their binary mixtures. The law of corresponding states provides us also with a sharp criterion which permits us to disqualify guessed analytic forms of the pair potential. It turns out that no member of the ( n-6) family of potentials is adequate, but that the (11-6-8) potential proposed by Klein and Hanley is acceptable as a correlator of data (for 1 ≤ T ∗ ≤ 20), even though it leads to considerably more complex numerical calculations. Even this potential fails for helium at high reduced temperatures.

Analysis of Reservoir Performance kg/ko Curves and a Laboratory kg/ko Curve Measured on a Core Sample

Published in Petroleum Transactions, AIME, Volume 204, 1955, pages 128–131. Abstract Two methods are used to obtain the relationship between ratio of gas to oil permeability and gas saturation. One method is to calculate a curve from field measurements of reservoir behavior: the other is to measure the relationship on a core sample in the laboratory. The curves resulting from these two methods are often compared and seldom found to agree. The most important reason for the nonagreement is often overlooked. This reason is that the performance kg/ko curve is calculated with the assumption of uniform pressure and saturation throughout the reservoir. To show the difference between performance type kg/ko curves and laboratory type kg/ko curves, two performance type kg/ko curves for two different production rates were calculated from the production performance of a hypothetical reservoir for which a laboratory type curve was assumed. Production performance of the hypothetical reservoir was calculated by use of International Business Machine's 701 Computer. The performance type kg/ko curves differed from the laboratory curve for the hypothetical reservoir. The performance type curve for the lowest production rate most nearly coincided with the laboratory curve. Introduction Predictions of oil reservoir performance are often made with the aid of complex numerical calculations. An important quantity required in these calculations is the ratio of gas permeability to oil permeability (kg/ko) at a particular gas saturation. Two methods are used to obtain a relationship between this ratio and gas saturation. The curves resulting from these two methods are called performance kg/ko curves and laboratory kg/ko curves. The performance curve is obtained from field measurements of reservoir behavior. Particular kg/ko values are calculated from the producing gas-oil ratio, the cumulative reservoir withdrawals, the original oil in place. the average reservoir pressure and the PVT properties of the reservoir fluids. The particular kg/ko values are then plotted against the average reservoir gas saturations for the entire history period. In order to use this derived kg/ko relationship for performance predictions, a curve through these points is extrapolated to higher gas saturations.