Showing papers on "Compressibility published in 1988"
TL;DR: In this article, the authors describe a new approximate Riemann solver for compressible gas flow, where a numerical approximation for the pressure and the velocity at t t is given.
Abstract: In this paper we describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at t...
1,008 citations
TL;DR: The Tait equation as discussed by the authors is a modification of the original equation of Tait, published 100 years ago, to fit his results on the compressibility of fresh water and seawater at different pressures.
Abstract: The “Tait equation,” which is now widely used to fit liquid density data over wide pressure ranges, is a modification of the original equation of Tait, published 100 years ago, to fit his results on the compressibility of fresh water and seawater at different pressures. The range of applicability of these different equations is discussed and it is concluded that their simplicity and accuracy in reproducing high pressure density data for dense gases, liquids, solids, and liquid mixtures will ensure their continued use.
419 citations
TL;DR: In this paper, a nonorthogonal coordinate system for viscous flows at all Mach numbers has been described, where pressure has been selected as a primary dependent variable in preference to density.
Abstract: A calculation procedure for viscous flows at all Mach numbers has been described. The scheme has been developed for a nonorthogonal coordinate system. In order to handle both incompressible and compressible flows, pressure has been selected as a primary dependent variable in preference to density. The pressure field is evaluated using the compressible form of the SIMPLER algorithm. The accuracy of the proposed scheme has been assessed by comparing the results with experimental data or other numerical results available in the literature.
392 citations
TL;DR: In this article, an alternate thermodynamic formalism is developed to correlate the solubility of a nonvolatile solute in a supercritical fluid (SCF) as a function of the density of the fluid phase.
Abstract: An alternate thermodynamic formalism is developed to correlate the solubility of a non-volatile solute in a supercritical fluid (SCF) as a function of the density of the fluid phase. We show that this solubility varies approximately in a linear fashion with the solvent density when examined in either log-log or log-linear coordinates, depending on the system in consideration. The slope of this plot is related to the solvent isothermal compressibility and the partial molar volume of the solute present at infinite dilution in the SCF phase. From literature solubility data, we obtain estimates for the partial molar volumes for some infinitely dilute mixtures of solutes in SCF which are in agreement with independently measured experimental values.
339 citations
TL;DR: In this paper, Lagrangian-Eulerian vortex methods are applied to simulate the motion of an interface between inviscid fluids of different densities, and the simulation results show that the interface as a vortex sheet eliminates numerical diffusion, and by coupling the tracked interface with z stationary grid (using the well-known vortex-inceil method) the high cost associated with traditional vortex m&hods is reduced.
280 citations
TL;DR: In this paper, the ionization constants of water, NH3, HCl, NaCl, and NH3 have been fitted in terms of a model with dependence on density and temperature.
Abstract: Electrochemical and electrical conductance cells have been widely used at ORNL over the years to quantitatively determine equilibrium constants and their salt effects to 300°C (EMF) and 800°C (conductance) at the saturation pressure of water (EMF) and to 4000 bars (conductance). The most precise results to 300°C for a large number of weak acids and bases show very similar thermodynamic behavior, which will be discussed. Results for the ionization constants of water, NH3(aq), HCl(aq), and NaCl(aq), which extend well into the supercritical region, have been fitted in terms of a model with dependence on density and temperature. The entropy change is found to be the driving force for ion-association reactions and this tendency increases (as it must) with increasing temperature at a given pressure. Also, the variation of all thermodynamic properties is greatly reduced at high fixed densities. Considerable variation occurs at low densities. From this analysis, the dependence of the reaction thermodynamics on the P-V-T properties of the solvent is shown, and the implication of large changes in hydration for solutes in the vicinity of the critical temperature will be discussed. Finally, the change in the molar compressibility coefficient for all reactions in water is shown to be the same and dependent only on the compressibility of the solvent.
227 citations
190 citations
TL;DR: The numerical scheme used by the present time-accurate FEM numerical method for incompressible Navier-Stokes equations, using primitive variables as the unknowns, is a Crank-Nicholson implicit treatment of all equation terms with central differencing for space derivatives as discussed by the authors.
178 citations
TL;DR: In this paper, a theoretical analysis is presented for determining the elastic non-linear vibrations of a prestressed thin-walled cylindrical shell filled with an ideal fluid, taking the fluid as non-viscous and incompressible, and the coupling between the deformable shell and this medium is taken into account.
119 citations
TL;DR: In this article, two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel were dealt with and the flow was assumed to be steady, one-dimensional and fully developed.
Abstract: This study dealt with two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel. Both phases were incompressible and the flow was assumed to be steady, one-dimensional and fully developed. The present study was expected to be useful in the understanding of the effect of the presence of slag layers on the heat transfer characteristics of a coal-fired MHD generator.
108 citations
TL;DR: In this paper, the velocity of sound in ethanol has been measured in the temperature range between 273.15 and 333.15 K and at pressures up to 280 MPa using the phase comparison pulse-echo method with two reflectors, which has been described previously.
Abstract: The velocity of sound in ethanol has been measured in the temperature range between 273.15 and 333.15 K and at pressures up to 280 MPa using the phase comparison pulse-echo method with two reflectors, which has been described previously. The density, isothermal compressibility, isobaric thermal expansion and the specific heat at constant pressure of ethanol have been evaluated from the measured sound velocity, using an improved method of computation.
TL;DR: In this article, the wave field generated by a point source in an axisymmetric fluid-filled borehole embedded in a saturated porous formation is studied in both the spectral domain and time domain.
Abstract: The wave field generated by a point source in an axisymmetric fluid‐filled borehole embedded in a saturated porous formation is studied in both the spectral domain and time domain. The formation is modeled following Biot theory modified in accordance with homogenization theory. When the borehole wall is permeable, guided waves can be significantly affected by the permeability of the formation. Whatever the formation, fast or slow, Stoneley‐wave phase velocity and energy decrease and attenuation (in the sense of Q-1) increases with increasing permeability. These effects are more important in the very low‐frequency range, where Darcy’s law governs the fluid motion and the wave energy at the interface is maximum, than at higher frequencies. The effects increase and persist over a larger frequency range with decreasing viscosity and increasing compressibility of the saturant fluid, with increasing pore‐fluid volume, and with decreasing borehole radius. In contrast, the effects decrease with decreasing stiffne...
TL;DR: In this article, the authors use low frequency asymptotics to unify two approaches that both describe tube wave properties: the first approach is due to White, in which the low-frequency tube wave velocity and attenuation are expressed explicitly as functions of frequency.
Abstract: Low‐frequency tube waves in permeable boreholes are of interest because their propagation depends upon in‐situ rock permeability. In this paper, we use low‐ frequency asymptotics to unify two approaches that both describe tube waves. The first approach is due to White, in which the low‐frequency tube‐wave velocity and attenuation are expressed explicitly as functions of frequency. The expressions include contributions from three factors: the borehole fluid compressibility, the wall rigidity, and the wall impedance due to the permeability of the solid. The second approach is the full solution of tube‐wave properties based on Biot theory and the appropriate boundary conditions between the fluid and the porous solid. By taking the low‐frequency approximations to the full solution, we derive an explicit expression for the tube‐wave properties, similar to White’s expression. White’s formulation is hereby corrected to include the elasticity of the solid frame around the borehole. For a 20 cm diameter borehole, ...
Book•
01 Jan 1988
TL;DR: In this paper, the authors present a model for gas reservoir engineering based on the K-value method and a flow-after-flow test. But they do not consider the effect of gas injection on the phase behavior.
Abstract: 1. Introduction. Natural gas. Gas reservoir engineering. Objective and organization. Units and symbols. 2. Reservoir properties. Introduction. Rock types. Porosity. Viscous flow resistance. Inertial flow resistance. Rock compressibility. Capillary pressure. Relative permeability. 3. Gas properties. Introduction. Composition. Phase behaviour. Real-gas law. Z-factor. Compressibility. Condensate/gas ratio. Formation-volume factor. Viscosity. 4. Phase behaviour. Introduction. K-value method. Equation-of-state method. Laboratory experiments. Multistage separation. 5. Recoverable reserves. Introduction. Bulk volume. Pore volume. Hydrocarbon pore volume. Gas and condensate initially-in-place. Recoverable reserves. Uncertainty. 6. Material balance. Introduction. Wet-gas reservoirs. Gas-condensate reservoirs. Non-volumetric depletion. Aquifer influx. 7. Single-phase gas flow. Introduction. Steady-state Darcy flow. Steady-state radial flow. Non-Darcy flow. Transient flow. Linear flow - constant terminal rate. Linear flow - constant terminal pressure. Radial flow - Constant terminal rate. Non-radial flow. 8. Gaswell testing. Introduction. Backpressure equations. Flow-after-flow tests. Isochronal and modified isochronal tests. Transient well-pressure equations. Drawdown tests. Buildup tests. Multiple-rate transient tests. Example of multiple-rate transient test analysis. 9. Wellbore flow mechanics. Introduction. Single-phase flow equations. Pressure distribution in shut-in wells. Rate-dependent pressure losses. Pressure distribution in producing wells. Multi-phase flow. Minimum unloading rate. 10. Water coning. Introduction. Dupuit critical production rate. Schols critical production rate. Cone breakthrough. Water/gas ratio. 11. Natural depletion. Introduction. Development chronology. Reservoir performance. Well-inflow performance. Tubing-flow performance. Well deliverability. Depletion simulator. 12. Gas injection. Introduction. Injection-well performance. Microscopic mixing. Viscous fingering. Gravity overlay. Stratification. Well Pattern. Pattern-flood model. Appendices. Units and conversion factors. Physical and mathematical constants. Physical properties natural-gas components. Author index. Subject index.
TL;DR: In this article, a simplified system of equations which can simulate the development and mature stages of tropical cyclones is presented, where the assumption of incompressible fluid layers is relaxed, and the governing equations for a compressible fluid in isentropic coordinates are discretized vertically by considering three fluid layers with constant potential temperature.
Abstract: A simplified system of equations which can simulate the development and mature stages of tropical cyclones is presented. The model is similar to that presented by Ooyama, except that the assumption of incompressible fluid layers is relaxed. Instead, the governing equations for a compressible fluid in isentropic coordinates are discretized vertically by considering three fluid layers with constant potential temperature. This makes the inclusion of thermodynamic processes more straightforward. The governing equations in the adiabatic case are mathematically equivalent to the equations used by Ooyama, except with an extra term in the pressure gradient force. The model equations are solved using a spectral method where the basis functions are the normal modes of the linearized equations. Numerical simulations show that the model sensitivity to vertical stability, sea surface temperature and midlevel moisture are similar to results from more general models. The sensitivity to these factors can be expl...
TL;DR: In this paper, a 2D Lennard-Jones fluid above the liquid-gas transition is considered and the distribution function of the density of the order parameter is computed for different block sizes.
Abstract: We consider a 2D Lennard-Jones fluid above the liquid-gas transition. By extending methods developed for lattice models, we divide the simulation cell in subsystems or blocks and compute the distribution function of the order parameter, the density, for different block sizes. In this way we can study the behaviour of the distribution and its moments as a function of the temperature, the density and the block size. In particular, from the second moment we can get the compressibility in the thermodynamic plane, just above the critical point, by extrapolating the results for the finite blocks. We propose the possibility of locating, with high accuracy, the critical point of the liquid-gas transition with this method.
TL;DR: In this paper, ultrasonic velocity measurements in ethanol aqueous solutions from +30 to −40°C over the entire composition range and in the frequency range 10-70 MHz are presented.
Abstract: Ultrasonic velocity measurements in ethanol aqueous solutions from +30 to −40 °C over the entire composition range and in the frequency range 10–70 MHz are presented. The results, in combination with previous determinations up to +80 °C, allow us to follow the peculiar behavior of the adiabatic compressibility of this system in a very large temperature range extending from a region where the anomalies of pure water tend to disappear, down to the supercooled region where these anomalies are noticeably enhanced. A ‘‘normal’’ and an ‘‘anomalous’’ contribution to the isothermal compressibility of water, as derived from these data, is compared with previous evaluations and discussed in the framework of the existing theoretical models. The compressibility of the diluted solutions is interpreted in terms of stabilization of water into ordered, less dense, and more rigid structures around the solute. We show that a simple two‐state model based on this concept and on the hypothesis of a structural breakdown at the...
TL;DR: In this paper, the authors used laser-induced iodine flourescence and mean and fluctuating streamwise velocities using laser Doppler anemometry to predict turbulent mixing in fully developed pipe flows injected into still air.
Abstract: Turbulent mixing in adapted and weakly underexpanded (underexpansion ratios less than 1.4) round jets, involving fully developed pipe flows injected into still air, was studied experimentally. Measurements included mean and fluctuating concentrations and mean static pressures using laser-induced iodine flourescence and mean and fluctuating streamwise velocities using laser Doppler anemometry. Predictions were used to help interpret the measurements and to initiate evaluation of methods for analyzing these processes. The predictions were based on k-e turbulence models, including a proposed extension to treat compressibility effects at high convection Mach numbers. In conjunction with other measurements, the results show that the near-field region of underexpanded jets is influenced by compressibility, which tends to reduce turbulent mixing rates at high convective Mach numbers, and high turbulence levels at the jet exit, which tends to increase turbulent mixing rates. Predictions based on effective-ada pted-jet exit conditions yielded reasonably good estimates of mixing levels near the exit of underexpanded jets for both fully developed and slug flow jet exit conditions; however, such methods provide no information concerning the near-field region containing the shock waves. Predictions based on solution of parabolized Navier-Stokes governing equations, using the SCIPVIS algorithm, were encouraging for slug flow exit conditions, but this approach must be extended to treat fully developed flow at the jet exit.
TL;DR: In this article, the authors present a computational model for estimation of both sound velocities and isothermal compressibilities within much of the compositional ternary Na2SiO3NaAlSiO4SiO2.
TL;DR: In this paper, the problem posed by sample compressibility and pore-filling as interacting processes in a mercury penetration experiment is discussed, and the fractal dimension is observed to be inversely correlated with pore volume and the volume of trapped mercury.
TL;DR: In this article, the adiabatic compressibility of aqueous sodium chloride solutions has been determined as a function of both concentration and temperature, and a simple model has been employed to interpret the data in terms of size and compression of hydration shells.
Abstract: The adiabatic compressibility of aqueous sodium chloride solutions has been determined as a function of both concentration and temperature. A simple model has been employed to interpret the data in terms of size and compressibility of hydration shells. On the basis of the analysis performed it has been possible to estimate the values of the volume contraction caused by ion–water interactions, the intrinsic volume of ions, the hydration numbers, the compressibility and density of water hydration shells, and their variation with temperature and salt concentration.
TL;DR: The speed of sound in liquid methanol has been measured at temperatures from 273 to 333 K and at pressures up to 280 MPa, using a phase comparison pulse-echo technique operating at 2 MHz as mentioned in this paper.
Abstract: The speed of sound in liquid methanol has been measured at temperatures from 273 to 333 K and at pressures up to 280 MPa, using a phase comparison pulse-echo technique operating at 2 MHz. The density, the isobaric thermal expansivity, the isothermal compressibility, the entropy, the enthalpy, and the specific heat have been evaluated from the measured sound speed following a modified computational method. The derived density data were fitted to a 16-constant equation of state within the accuracy of the measurement. In the region of overlap, the experimental data agree well with those determined by direct measurement.
TL;DR: In this article, heat capacity measurements and cell volume data are presented for a very magnesian glaucophane from a Tauern Window eclogite, which are combined with estimated entropy, thermal expansion, and compressibility data to generate an enthalpy of formation.
Abstract: New heat capacity measurements and cell volume data are presented for a very magnesian glaucophane from a Tauern Window eclogite. These data are combined with estimated entropy, thermal expansion, and compressibility data to generate an enthalpy of formation for glaucophane from experimentally determined phase equilibria. The data are supported by preliminary experiments of the author and provide consistent calculations on the pressure of formation of the Tauern eclogites and on the position of the blueschist-greenschist transformation reaction as studied experimentally by Maruyama et al. (1986). The resulting thermodynamic data for glaucophane may be combined with the dataset of Holland and Powell (1985) to calculate phase relations for blueschists and eclogites. The stability of magnesian glaucophane lies in the pressure range between 8 and 32 kbars at 400° C and between 13 and 33 kbars at 600° C, and the unusual eclogite assemblage of glaucophane+kyanite from the Tauern Window is restricted to pressures above 20 kbars at high water activity.
TL;DR: Time domain reciprocity theorems of the time convolution and the time correlation type for acoustic wave fields in linear, time invariant, and locally reacting fluids are discussed in this paper.
Abstract: Time‐domain reciprocity theorems of the time‐convolution and the time‐correlation type for acoustic wave fields in linear, time‐invariant, and locally reacting fluids are discussed. Inhomogeneity, inertial anisotropy, and arbitrary relaxation effects in inertia and compressibility properties, both of the active and the passive type, are included. The theorems also apply to the ‘‘equivalent fluid model’’ of a solid in which only compressional waves are considered and shear is neglected. The analysis is entirely carried out in space‐time, without intermediate recourse to the frequency or the wave vector domains. The application to inverse source and inverse constituency (or inverse profiling/scattering, or imaging) problems is briefly indicated.
TL;DR: In this paper, a microscopic statistical mechanical theory for the virial equation of state of polymer liquids is developed by combining reference interaction site model (RISM) integral equation methods for flexible chain molecules with a superposition approximation for threebody orientational correlation functions.
Abstract: A microscopic statistical mechanical theory for the virial equation of state of polymer liquids is developed by combining reference interaction site model (RISM) integral equation methods for flexible chain molecules with a superposition approximation for three‐body orientational correlation functions. A compact expression for the pressure is obtained for athermal (hard core) fluids by neglecting explicit chain end effects. An analytical analysis of three‐body contributions to the equation of state is carried out for flexible polymers and the scaling dependence on chain length and monomer density is derived. The merits and disadvantages of the compressibility route to the equation of state are briefly discussed, along with the inclusion of attractive intermolecular forces via thermodynamic perturbation theory.
TL;DR: It is shown that regularities of apparent molar adiabatic compressibilities can be described as a consequence of partial 'normalization' of some of the properties of water around the bases, namely, weaker structural contribution to compressibility, less negative temperature slope of compressibility and less negativeStructural contribution to the coefficient of thermal expansion of water.
TL;DR: In this article, the authors investigated the acoustical absorption and scattering cross sections of spherical bubble clouds subject to harmonic farfield pressure excitation, and the equations of motion for the average flow and for the bubble radius were linearized and a closed-form solution was obtained.
Abstract: The present work investigates the acoustical absorption and scattering cross sections of spherical bubble clouds subject to harmonic farfield pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility, and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed-form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross sections of a single large bubble with the same volume of vapor and gas. In general, the acoustical properties of any give volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow.
TL;DR: The two-dimensionsal compressibility of electrochemically deposited lead on silver using grazing incidence x-ray scattering is reported, in good agreement with that of a two-dimensional, free-electron gas.
Abstract: We report the two-dimensional compressibility of electrochemically deposited lead on silver (111). Measurements were made in situ (in contact with solution) using grazing incidence x-ray scattering. Between monolayer formation and bulk deposition, the near-neighbor distance of the lead monolayer decreases linearly with applied potential. Since the lead monolayer is in equilibrium with the lead in solution, the isothermal compressibility of the monolayer can be calculated and is 0.98 ${\mathrm{\AA{}}}^{2}$/eV. This is in good agreement with that of a two-dimensional, free-electron gas.
11 Jan 1988
TL;DR: In this article, a spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids, and the fit of the computations to the analytical theory is seen to be close.
Abstract: A spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids. The computations are used to test and extend the analytical theory of density variations in slightly compressible magnetofluids given by Montgomery, et al. (1987) and used to infer inertial-range density-fluctuation spectra for the nearby interstellar medium and solar wind. A local equation of state is assumed, relating density to pressure. Constant, scalar resistivities and viscosities are used. In the limit of low Mach numbers and high mechanical-to-magnetic pressure ratios, the fit of the computations to the analytical theory is seen to be close.