G. Saville

Modelling of two-phase blowdown from pipelines—II. A simplified numerical method for multi-component mixtures

Abstract A simplified numerical method is proposed to solve general two-phase flow equations for multi-component mixtures. The method is applied to solve the marginal stability model proposed in the first part of this paper. Case studies are performed and validated against experimental data for the blowdown of pipelines containing one- or two-component mixtures. The results show that the marginal stability model performs better than the simple homogeneous model for blowdown from short pipes. For blowdown from long pipes, the results of both models are quite similar. Concentration stratification is found to be insignificant in the overall blowdown predictions.

Modelling of two-phase blowdown from pipelines—I. A hyperbolic model based on variational principles

Abstract In this paper, Geursts variational priciple for bubbly flow is extended to generalised multicomponent two-phase dispersions. The present variational principle allows both phases to be compressible in deriving the momentum equations. A mixture energy equation is obtained using Noethers invariant theorem and is shown to be comparable with the averaging formulation. The hyperbolicity of the equations is achieved by forcing the flow to be marginally stable. Under the marginally stable condition, all the information related to the structure of the flow is found to be embedded in an inertial coupling constant and an expression for this constant is obtained based on critical flow data. The marginally stability model gives correct sonic characteristics up to void fractions of 0.8. The clearly defined sonic characteristics make possible the rigorous determination of the critical flow condition for rapid depressurisation of pipelines.

Rapid depressurization of pressure vessels

Abstract Experiments were conducted on the rapid depressurization of large pressure vessels. Measurements taken included the pressure, temperatures at a large number of positions both within the fluid phase(s) and on the wall of the vessel, and composition, all as a function of time during the blowdown process. The systems studied included subcritical and supercritical, condensing and non-condensing. From these experiments, an understanding of the physical processes involved during blowdown was evolved. This was incorporated into a mathematical model of blowdown, and implemented in a computer program. The model correctly predicts all the major phenomena observed in the experiments, as a function of time.

Methane-based equations of state for a corresponding states reference substance

Abstract Two equations of state have been developed, one valid over the reduced temperature range 0.2–26 and the other over 0.35–26. Both are intended for use as reference equations of state in the calculation of thermodynamic properties via the principle of corresponding states. The equations are essentially equations of state for methane in that they reproduce the experimentally measured properties of the fluid phase over the whole region for which they exist (reduced temperatures of 0.47 to 3.3) but the extension to higher temperatures was made by utilizing experimental measurements made on nitrogen and hydrogen. An empirical scheme was used for temperatures below 0.47.

Phase equilibrium measurements in gas-condensates

Abstract A new, automated apparatus for the study of two- and three-phase equilibrium in multicomponent fluid systems is described. At present the apparatus is intended to cover the range of pressures to 40 MPa and temperatures up to 150°C, but further extensions of the temperature and pressure range are foreseen. The equipment is capable of determining the density and composition of up to three co-existing phases in a fluid system and is intended to operate under computer control so as to ensure that the path around the phase envelope of a particular system is guided by a computer model to obtain the most useful information in the minimum time. The apparatus has been designed for the study of hydrocarbon mixtures representative of gas-condensate systems. However, preliminary results are presented for a less hazardous system which has been studied previously in order to verify the operation of the instrument.

Apparatus for phase equilibrium measurements at high temperatures and pressures

An apparatus for high pressure studies of phase equilibrium in multicomponent fluid systems is completely described. The apparatus has been designed to yield a complete thermodynamic description of fluid mixtures containing any number of components which have up to three coexisting phases in the pressure range up to 100 MPa and for temperatures up to 423 K. It therefore makes possible the determination of liquid and vapour phase densities and composition at prescribed pressures and temperatures for two phases as well as the determination of the same quantities for a second liquid phase should one exist. At present, owing to the temperature and pressure limitations imposed by some of the commercial parts, the apparatus works within the temperature range up to 393 K and the pressure range up to 40 MPa. The instrument has the capability for complete automation if it is desired. The results of preliminary measurements in the normal hydrocarbon systems CH4–C6H14 and CH4–C6H14–C14H30 are presented.

Vapor–liquid equilibrium in the ternary system methane-n-hexane-n-tetradecane

Abstract The paper presents the results of new measurements of the phase behavior of the ternary system methane-n-hexane-n-tetradecane. The measurements have extended over the range of compositions at 348.15 K and 383.15 K for pressures from 2 MPa up to the vicinity of the critical pressure of around 25 MPa. As well as the phase envelope itself, measurements of the density of both phases have been carried out simultaneously. The experimental data provide the opportunity to examine the effectiveness of three different thermodynamic models for the prediction of the properties of ternary mixtures from prescribed information on the constituent binary systems. The models employed for the tests include the cubic equation of Peng–Robinson, the one-fluid corresponding-states model and the more flexible, multiple-reference fluid corresponding-states model. It will be shown that only the multiple-reference fluid model provides a satisfactory description of the fluid density. The same model also represents the phase compositions moderately well, but not quite as well as the Peng–Robinson equation.

Second virial coefficients of carbon monoxide

Abstract A Burnett-type apparatus was built for measuring second virial coefficients of gases at low temperatures and pressures, using the Burnett expansion method. Second virial coefficients of carbon monoxide have been measured at temperatures from 100 to 230 K. The results obtained are in good agreement with those reported by several authors. They are used to assess the conformality of gaseous carbon monoxide and nitrogen.

Excess enthalpies for (water + nitrogen) (g) and (water + carbon dioxide) (g) at 520 to 620 K and up to 4.5 MPa

Abstract A flow-mixing calorimeter has been constructed and used to measure the excess molar enthalpy H m E of [ x H 2 O + (1 − x )N 2 ](g) and [ x H 2 O + (1 − x )CO 2 ](g) at temperatures in the range 520 to 620 K and pressures up to 4.5 MPa. The values of H m E , essentially symmetric functions of x at a given pressure and temperature, were fitted to two equations, one for each mixture, for convenience in interpolating with respect to composition, pressure, and temperature.

Two-fluid corresponding states model : a new mixing rule approximation

Abstract A semi-empirical approximation of the generalised Percus-Yevick (PY) equation for a mixture of hard spheres by Lebowitz (1964) is used to improve the reprentation of the thermodynamic properties of dense fluid mixtures. The radial distribution function obtained by Lebowitz has been used to derive mixing rules in which a difference of the size of the constituent molecules has a direct effect. The performance of the new approximation is illustrated by comparing the results obtained from it with those from two earlier models for fluid mixtures with different molecular sizes within the framework of the principle of corresponding states. In order to separate the examination of the effect of changes in the mixing rules from the effects of uncertainties in the pair potential for real fluids, the tests conducted here make use of the results of computer simulation for prescribed and simple intermolecular potential models.