Showing papers on "Compressibility published in 1989"

A new equation of state for athermal chains

Abstract: A new equation of state for fluids containing athermal chain molecules is developed and compared to simulation results and existing theories in three, two, and one dimensions The new expression, which builds upon the generalized Flory theory, contains no adjustable parameters and relates the compressibility factor of an n‐mer fluid to the compressibility factors of monomer and dimer fluids at the same volume fraction Comparisons with Monte Carlo results for three‐ and two‐dimensional freely jointed chains show very good agreement, and the overall accuracy of the new expression appears comparable to Wertheim’s thermodynamic perturbation theory of polymerization In one dimension the new expression reduces to the exact result Application of the equation to chain models with internal constraints and overlapping hard sites is discussed and illustrated through comparisons with Monte Carlo results for rigid trimers An extension of our approach to arbitrary reference fluids shows that the generalized Flory and new equations are the first two members of a family of increasingly accurate equations of state for chains

The influence of formation material properties on the response of water levels in wells to Earth tides and atmospheric loading

Abstract: The water level in an open well can change in response to deformation of the surrounding material, either because of applied strains (tidal or tectonic) or surface loading by atmospheric pressure changes. Under conditions of no vertical fluid flow and negligible well bore storage (static-confined conditions), the sensitivities to these effects depend on the elastic properties and porosity which characterize the surrounding medium. For a poroelastic medium, high sensitivity to applied areal strains occurs for low porosity, while high sensitivity to atmospheric loading occurs for high porosity; both increase with decreasing compressibility of the solid matrix. These material properties also influence vertical fluid flow induced by areally extensive deformation and can be used to define two types of hydraulic diffusivity which govern pressure diffusion, one for applied strain and one for surface loading. The hydraulic diffusivity which governs pressure diffusion in response to surface loading is slightly smaller than that which governs fluid flow in response to applied strain. Given the static-confined response of a water well to atmospheric loading and Earth tides, the in situ drained matrix compressibility and porosity (and hence the one-dimensional specific storage) can be estimated. Analysis of the static-confined response of five wells to atmospheric loading and Earth tides gives generally reasonable estimates for material properties.

Mathematical structure of the black-oil model for petroleum reservoir simulation

Abstract: This model incorporates compressibility and general mass transfer between phases. It consists of the conditions of thermodynamic equilibrium, an equation of state for the volume balance between the fluidand the rock void, Darcy’s Law for the volumetric flow rates, and component conservation equations. These relations are manipulated to form a pressure equation and a modified system of component conservation equations. It is shown that the pressure equation is parabolic and that, in the absence of diffusive forces such as capillary pressure and mixing, the component conservation equations are hyperbolic, subject to technical conditions on the relative permeabilities. This sequential formulation of the flow equations forms types of wave structures that occur for the system.

Linear instabilities in two‐dimensional compressible mixing layers

Abstract: Linear instability waves in supersonic shear layers are analyzed. Both viscous and inviscid disturbances are considered. The basic state is obtained by solving the compressible laminar boundary‐layer equations or is specified by the hyperbolic tangent profile. The effects of the velocity ratio and temperature ratio are determined. The numerical results show that the maximum growth rate depends nonlinearly on the velocity ratio. The results also substantiate the convective Mach number as a compressibility parameter for mixing layers.

Direct numerical simulation of compressible free shear flows

Abstract: Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. A simple explanation of the stabilizing effect of compressibility is offered. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified.

An equation for acoustic propagation in inhomogeneous media with relaxation losses

Abstract: An equation for acoustic propagation in an inhomogeneous medium with relaxation loss is systematically derived from the classical dynamic equations together with an equation of state for relaxation. The derivation assumes small acoustic perturbations but accommodates arbitrary spatial inhomogeneities in material compressibility, density, and parameters of relaxation. The linearized wave equation obtained for n relaxation mechanisms has order n + 2, is causal, and yields the expected dependence of attenuation on frequency. Exact analytic expressions valid at all frequencies are given for the spatially varying attenuation coefficient, as well as phase velocity. A Green's function is calculated for the equation. The results may be used to model scattering for image reconstruction and the determination of statistical properties, such as average differential scattering cross section.

Linearized dynamics of spherical bubble clouds

Abstract: The present work investigates the dynamics of the one-dimensional, steady flow of a spherical bubble cloud subject to harmonic far-field 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 the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-resonant, trans-resonant and super-resonant) with different properties depending on the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms. Finally the results for the case of Gaussian-shaped far-field pressure change are presented and the most important limitations of the theory are briefly discussed. The simple linearized dynamical analysis developed so far clearly deminstrates the importance of the complex phenomena connected to the interaction of the dynamics of the bubbles with the flow and provides an introduction to the more realistic study of the same flows with nonlinear bubble dynamics.

Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

Abstract: The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.

On theCp toCv conversion of solid linear macromolecules II

Abstract: A modification is proposed for the Nernst-Lindemann equation that is used to convert calculated heat capacities at constant pressure (C p ) to heat capacities at constant volume (C v ) for solid, linear macromolecules. the constant A0 per mole of repeating unit in this equation is derived by taking into account the variable number of vibrators excited at different temperatures. With the new equation it is possible to calculateC p for solid polymers over a wider temperature range. The constant is calculated for solid polymers from experimental thermal expansivity, isothermal compressibility and heat capacity data obtained from the literature. An average value of (3.9±2.4)×10−3(K mol)/J was obtained for A0 (new) from data on 22 solid polymers. This average value may be used as a universal constant in case no experimental data on compressibility and expansivity are available for computation ofA 0. The remaining variation of A0 (new) with temperature is discussed and example calculations are shown for polyethylene. Effects of premelting and possibly large-amplitude motion are discovered for polyethylene in the temperature range 290 to 410 K.

Effect of temperature on the compressibility of native globular proteins

Abstract: La compressibilite adiabatique de deux proteines globulaires (lysozyme et BSA) est determinee en mesurant la celerite du son en solutions aqueuses a differentes temperatures (10, 15, 25, 40°C). La compressibilite isothermale des deux proteines est estimee a partir de la valeur de la compressibilite adiabatique en utilisant le coefficient de dilatation thermique et les donnees de la capacite calorifique

On the stabilization of a two-dimensional vortex strip by adverse shear

Abstract: An isolated strip of anomalous vorticity in a two-dimensional, inviscid, incompressible, unbounded fluid is linearly unstable or is i t ? It is pointed out that an imposed uniform shear, opposing the shear due to the isolated strip alone, can prevent all linear instabilities if the imposed shear is of sufficient strength, and that this is highly relevant to current thinking about ‘two-dimensional turbulence ’ and related problems. The linear stability result has been known and goes back to Rayleigh, but its implications for the behaviour of the thin strips of vorticity that are a ubiquitous feature of nonlinear two-dimensional flows, as revealed for instance in high-resolution experiments, appear not to have been widely recognized. In particular, these thin strips, or filaments, almost always behave quasi-passively when being wrapped around intense coherent vortices, and do not roll up into strings of miniature vortices as would an isolated strip. Nonlinear calculations presented herein furthermore show that substantially less adverse shear than suggested by linear theory is required to preserve a strip of vorticity. Taken together, and in conjunction with results showing the further stabilizing effect of a large-scale strain field, these results explain the observed quasi-passive behaviour.

Primitive model of water

Abstract: Using the extended thermodynamic perturbation theory of Wertheim, closed simple analytic expressions for the internal energy and pressure of the primitive model of water are derived and examined in detail. The equation of state, which has a form of a perturbed hard sphere equation, exhibits the same anomaly in temperature dependence of the isothermal compressibility as real water. The low value of the critical compressibility factor is in close agreement with the experimental value for real water.

The analysis and modeling of dilatational terms in compressible turbulence

Abstract: It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Optical properties of gallium selenide under high pressure

Abstract: Compressibility, optical-absorption, Raman-scattering, and refractive-index measurements for GaSe are reported at 300 K and pressures up to 8 GPa. A model which separates intra- and interlayer contributions along the c axis is used, with adequate deformation potentials, to quantitatively reproduce the compressibility along the c axis, the refractive-index variation, and the shift of both direct and indirect gaps under pressure. The shape of the absorption edges are calculated by the Elliott-Toyozawa formalism at all pressures, between 1.6 and 2.4 eV, with only one constant, and two pressure-dependent parameters: the exciton Rydberg and the matrix element for the direct transition. The decrease of the former, together with the measured shift of the TO and LO modes are interpreted by a large increase of the longitudinal effective charge under pressure which can be assigned to either intralayer-to-interlayer charge transfer, or to an increase of the total ionicity, or both.

A general theory of thermoporoelastoplasticity for saturated porous materials

Abstract: A general theory of thermoporoelastoplasticity for saturated porous materials is presented. The theory is derived from the thermodynamics of open systems and irreversible processes. The thermal effects, due to the saturating fluid, are taken into account through a latent heat associated with the increase of fluid mass content. The theory does not assume incompressibility nor infinitesimal displacements for the saturating fluid. To take into account the plastic compressibility of the skeleton, the notion of plastic porosity is introduced. This plastic porosity is different from the overall plastic dilatation. The usual isothermal phenomenological theories appear to be particular cases of the proposed general theory.

Compressible convection in the Earth's mantle: A comparison of different approaches

Abstract: Numerical models of mantle convection using the Boussinesq, extended Bousinessq and anelastic-liquid approximation are compared. For steady state solutions there is good quantitative agreement between the results if they are scaled in a proper way. Time-dependent extended Boussinesq and anelastic-liquid flows show only qualitative agreement, the main difference being a distortion of timescale. Compressibility induces an asymmetry in the structure of upper and lower boundary layers that cannot be observed in Boussinesq fluids.

Absolute/convective instabilities and the convective Mach number in a compressible mixing layer

Abstract: In this paper two aspects of the stability of a compressible mixing layer are considered: absolute/convective instability and the convective Mach number It is shown that, for Mach numbers less than unity, the compressible mixing layer is convectively unstable unless there is an appreciable amount of backflow A rigorous derivation of a convective Mach number based on linear stability theory for the flow of a multispecies gas in a mixing layer is also presented In particular, the definition is based on the free‐stream Mach number in the laboratory frame and is independent of the speed of the large‐scale structures and the speed of the most unstable wave The result is compared with the heuristic definitions of others and to selected experimental results

Penetrative convective flows induced by internal heating and mantle compressibility

Abstract: Penetrative convective flows induced in a spherical shell by combined effects of internal heating and mantle compressibility are investigated using mathematical and numerical formulations for compressible spherical shell convection. Isothermal stress-free boundary conditions applied at the top and the bottom of the shell are solved using a time-dependent finite difference code in a temperature, vorticity, stream function formulation for Rayleigh numbers ranging from the critical Rc up to 2000 Rc. Results indicate that compressibility, together with internal heating, could be a mechanism capable of generating spontaneously layered convection and local melting in the mantle and that non-Boussinesq effects must be considered in interpretations of geophysical phenomena.

One-dimensional adiabatic flow of equilibrium gas-particle mixtures in long vertical ducts with friction

Abstract: The equations of the steady, adiabatic, one-dimensional flow of an equilibrium mixture of a perfect gas and incompressible particles, in constant-area ducts with friction, are derived taking into account the effects of gravity and of the finite volume of the particles. As is the case for a pure gas, the mixture is shown to be subject to the phenomenon of choking, and the possibility of an adiabatic heating of the mixture in a subsonic expansion is also theoretically predicted for certain flow inlet conditions. The model may be used to approximately describe the conditions existing in portions of volcanic conduits during the Plinian phases of explosive eruptions. Some results of the numerical integration of the equations for a typical application of this type are briefly discussed, thus showing the potential of the model for carrying out rapid analyses of the influence of the main geometrical and flow parameters describing the problem. A non-volcanological application is also analysed to illustrate the possibility of the adiabatic heating of the mixture.

Viscous Fluid Mechanics

Abstract: First we give the governing equations for an incompressible viscous newtonian fluid completed with boundary conditions.

A mathematical model for pressure evaluation in an infinite-conductivity horizontal well

Abstract: A mathematical model was developed to study the transient pressure behavior in a well with an infinite-conductivity horizontal drainhole in an infinite slab reservoir. The physical model includes a fluid of small and constant compressibility flowing through an infinitely large anisotropic reservoir with upper and lower impermeable boundaries. The analytical solution is obtained by applying the concepts of instantaneous sources and Green's functions. The authors discuss the uniform-flux model, a special case of the infinite-conductivity model, and present a simple way to use it to calculate the pressure at the wellbore face. They suggest that the pressure for the infinite-conductivity case can be evaluated with the uniform flux model at a fixed point along the wellbore with an error of less than 1% for combinations of the various parameters that may be encountered in real situations. They show to what extent the accuracy of the model will be affected by neglecting gravitational effects.

Direct numerical simulation of compressible free shear flows

Abstract: Direct numerical simulations of compressible free shear layers in open domains are conducted. Compact finite-difference schemes of spectral-like accuracy are used for the simulations. Both temporally-growing and spatially-growing mixing layers are studied. The effect of intrinsic compressibility on the evolution of vortices is studied. The use of convective Mach number is validated. Details of vortex roll up and pairing are studied. Acoustic radiation from vortex roll up, pairing and shape oscillations is studied and quantified.

Pressure-jump volume-relaxation studies of polystyrene in the glass transition region

Abstract: An apparatus has been constructed that permits the measurement of time-dependent changes in pressure near the point of vitrification. The same instrument is used for measuring steady-state PVT properties, which are necessary for a proper analysis of the dynamic measurements. The former experiments are referred to as pressure-jump volume-relaxation (PJVR) measurements and serve as a direct probe of the structural relaxation process that occurs in all glasses. Experiments have been performed on polystyrene from 110 to 150°C and up to 2 kbar using pressure steps of 500 bars. The qualitative observations are analogous to those obtained at atmospheric pressure by rapid changes in temperature, namely (1) nonlinearity, (2) asymmetry, and (3) memory effects associated with complicated temperature or pressure histories. Each of these effects is accounted for semiquantitatively by a phenomenological order-parameter model that has been extended to include the effect of pressure. Deviations between theory and experiment increase as temperature and pressure increase, this being manifest mostly in a predicted recovery curve (expansion isobar) that recovers the equilibrium volume more quickly than the experimental data; the contraction isobars are in most cases predicted within experimental error. The adjustable parameters of the model are found to vary somewhat with pressure and temperature, apparently due to variations in δ and Δκ. The activation volume suggests that 10–20 monomer segments are involved in the recovery process, assuming that the activation volume itself represents only a fraction of the dynamic unit (as observed in molecular glasses).

Properties of riblets at supersonic speed

Abstract: The properties of a riblet surface at a Mach number of 1.25 are described. Direct measurement has been made of the surface shear stress on a riblet surface attached to a skin-friction balance mounted beneath the turbulent boundary layer growing along a wall of the RAE 2 ft×1 1/2 ft variable density transonic wind tunnel. Comparison of the data with that for a smooth wall indicates a reduction of about 7% in skin friction at optimum flow conditions. Misalignment of the riblet surface with the flow direction reduces this benefit and beyond 30° misalignment a drag penalty occurs. Analysis of the velocity profiles indicates that compressibility effects may be accounted for with the use of an appropriate transformation.