Densities Of Fluid Phases Research Articles

Equation of State of the H2O–CO2–CaCl2 Fluid System and Properties of Fluid Phases at Р-Т Parameters of the Middle and Lower Crust

A numerical thermodynamic model is proposed for one of the most important geological fluid system, ternary H2O–CO2–CaCl2 system, at P-T conditions of the middle and lower crust and crust–mantle boundary. The model is based on the previously proposed equation for concentration dependence of the excess Gibbs free energy and on the first obtained P-T dependencies of the coefficients of the equation of state (EOS) expressed via molar volumes of the components. The EOS allows to predict the properties of the fluid participating in the majority of deep petrogenetic processes: its phase state (homogeneous or multi-phase), densities of fluid phases, concentrations of components in the co-existing phases, and the chemical activities of the components. The model precisely reproduces all available experimental data on the phase state of the ternary H2O–CO2–CaCl2 fluid system in the ranges of temperatures 773.15–1073.15 K and pressures 0.1–0.9 GPa and also allows the correct application of the EOS beyond the experimentally studied range of temperatures and pressures up to P = 2 GPa and T = 1673.15 K. The possibility of the correct extrapolation of our EOS is ensured by using the parametrization of P-T dependencies via the molar volume of water. The latter remains in the experimental domain of values or falls slightly beyond its boundaries, when increasing temperatures and pressures.

Modelization of the $$\hbox {H}_{2}$$ H 2 adsorption on graphene and molecular dynamics simulation

In the search for efficient molecular dynamics simulation models both simplicity and acceptable accuracy matter. In the present study, a model of the graphene- $$\hbox {H}_2$$ physisorption system is used to explore its performance and limitations under canonical NVT and microcanonical NVE simulation conditions. The model implies several simplifications that can be summarized in (a) a single ideal planar frozen graphene-like layer of C atoms, (b) rigid rotor $$\hbox {H}_2$$ molecules and (c) interaction potentials written as C–H2 and $$\hbox {H}_2$$ – $$\hbox {H}_2$$ site–site Improved Lennard-Jones potentials parameterized to reproduce DFT calculations. This model can be used in a variety of molecular dynamics simulation conditions, both in NVT and NVE ensembles. Such simulations lead to the formation of a single layer of adsorbed $$\hbox {H}_2$$ molecules in dynamically stable equilibrium with a fluid-phase region. In addition, the incipient formation of secondary layers for high-density conditions is also observed. Some properties as average pressure, temperatures and fluid-phase densities are discussed as well as possible improvements of the model.

Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs

Summary Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs). We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations. The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.

Investigation of the hydrogen adsorbed density inside the pores of MOF-5 from path integral grand canonical Monte Carlo at supercritical and subcritical temperature

We examine the high density limit of the adsorption isotherms of hydrogen on MOF-5. The isotherms are calculated using quantum GCMC simulations over the pressure range: 0–150atm (1atm = 1.01325 × 105Pa) in the subcritical and supercritical state at 30, 50, 77, 113, 196 and 296K. The fluid phase density in the pores for each temperature is calculated and shown to reach values higher than normal liquid density. The fluid phase density obtained at 30K is observed to correspond to a highly compressed liquid. The radial distribution function of the adsorbed phase at 30 and 50K are calculated. The adsorption isotherms are compared with available experimental data at 30, 50, 77 and 298K.

Inverting reservoir parameters in a two-phase fractured medium with a niche genetic algorithm

In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversion problem of the wave equation in a two-phase medium. We propose a niche genetic multi-parameter (including porosity, solid phase density and fluid phase density) joint inversion algorithm based on a two-phase fractured medium in the BISQ model. We take the two-phase fractured medium of the BISQ model in a two-dimensional half space as an example, and carry out the numerical reservoir parameters inversion. Results show that this method is very convenient for solving the parameters inversion problem for the wave equation in a two-phase medium, and has the advantage of strong noise rejection. Relative to conventional genetic algorithms, the niche genetic algorithm based on a sharing function can not only significantly speed up the convergence, but also improve the inversion precision.

EOS calculations for hydrothermal diamond anvil cell operation

The hydrothermal diamond anvil cell (HDAC) is an excellent tool for high-temperature, high-pressure (hydrothermal) experiments. For an accurate determination of pressure induced by a certain temperature in an isochoric sample chamber volume, an equation of state (EOS) of water can be used instead of direct measurement. This paper reviews the theoretic background and provides all needed equations for the application of EOS of water to HDAC experiments summarizing state-of-the-art knowledge and incorporating up-to-date thermodynamic data. The p-T conditions determined using the IAPWS-95 formulation for the thermodynamic properties of ordinary water are in agreement with values obtained from direct methods or other established EOS formulations. In particular, (1) the calculation of density through the (a) melting point or (b) homogenization method along with determining (2) pressure as a function of density and temperature or (3) density as a function of pressure and temperature is explained. As a new aspect in the context of HDAC operations, the critical influence of nucleation and a strategy to overcome this problem are discussed. Furthermore, we have derived new polynomial equations, which allow the direct calculation of the fluid phase's density from the melting temperature. These are implemented in a spreadsheet program, which is freely available for interested users.

Sensitivity analysis of Gassmann's fluid substitution equations: Some implications in feasibility studies of time-lapse seismic reservoir monitoring

Here, we discuss the sensitivity of the seismic response to uncertainties in the physical parameters of the reservoir rock. For this purpose, a probabilistic sensitivity analysis of Gassmann's fluid substitution equations using a Monte Carlo approach was carried out. We represented uncertainties related to each parameter as probability density functions to evaluate the contribution of each parameter uncertainty to the variance of the seismic response ( V p), calculated by means of the Monte Carlo approach. We show that uncertainties related to grain density ( ρ gr), dry shear modulus ( G d) and dry bulk modulus ( K d) contribute more significantly on the variance of V p, if all parameters are uncorrelated. This outcome changes, when physical dependencies are represented as correlations in the Monte Carlo sampling of some of the parameters. In this sense, correlations distribute more evenly the contributions to uncertainty in V p. On the other hand, we also evaluated scenarios of fluid substitution, in which fluid 1 is replaced by fluid 2, with the corresponding variations in seismic response. In this case, V p2 is the P-wave velocity of rock saturated with a fluid 2. If V p2 were forecasted from an initial set of parameters of the rock saturated with fluid 1 ( V p1, V s1, etc.) the uncertainties related to V p1, V s1 and K gr would contribute more significantly to the variance of V p2. From these three initial parameters, the most important contributions come form V p1 and V s1. Concomitantly, we evaluated the contribution of possible variations in fluid phase density and bulk modulus and of a pore pressure perturbation (4MPa) for several scenarios of connate and injection fluids on the variance of V p. We did this for several values of initial differential pressure. Results indicate that the contribution of the elastic piezosensitivity and possible changes in the fluid phase properties depend not only on the initial differential pressure, but also on the type of fluids involved in substitution process. We conclude that sensitivity information, limited in this case to Gassman's equations, can be used as a tool to improve feasibility studies in time-lapse seismic reservoir monitoring and as a priori qualitative knowledge. The latter can guide the inversion process or help to diminish the uncertainties due to poorly constrained inversion schemes.

Phase Separation in Polymer Blends and Diblock Copolymers Induced by Compressible Solvents

The influence of compressed carbon dioxide sorption on the phase behavior of polymer blends and diblock copolymers exhibiting lower critical solution temperatures (LCSTs) and lower disorder-to-order transitions (LDOTs), respectively, was studied using in situ high-pressure small-angle neutron scattering. Homogeneous blends of poly(deuterated styrene) and poly(vinyl methyl ether) phase separate at temperatures more than 115 °C below the ambient pressure LCST upon sorption of less than 3.3 wt % CO2. The LDOTs in symmetric poly(deuterated styrene)-block-poly(n-butyl methacrylate) copolymers having total molecular weights of 78 000 and 32 000 g/mol are depressed by as much as 250 °C upon exposure to supercritical CO2 at modest fluid-phase densities.

A subpopulation analysis of f-MLP stimulated granulocytes migrating in filters

Leukocyte migration in vitro has been studied extensively during many years without providing satisfactory theoretical models for the different migratory behaviors (chemotaxis and chemokinesis) of leukocyte populations. The present study utilized the fluid gradient chamber, which is a new method to study leukocyte migration in filters. Human neutrophils were applied between two stacked filters and migrated in all directions under the influence of constant concentrations or chemotactic gradients of f-MLP, maintained in fluid phase density gradients. The distributions of the granulocytes over filter depth were fitted to theoretical functions composed by 1–3 Gaussian distributions, representing subpopulations. The results showed that the neutrophils migrated as two discrete subpopulations during chemokinetic stimulation (a constant concentration of f-MLP). One of the subpopulations showed less active and passive (slow sedimentation under the influence of gravity) translocation. The most mobile subpopulation was divided into two new subpopulations when exposed to chemotactic stimulation (concentration gradient of f-MLP), one of which responded chemotactically and one of which migrated in random directions. The properties of the different subpopulations where characterized in terms of diffusion coefficient (random migration), convection velocity (chemotactic migration) and sedimentation coefficient (passive translocation).

NMR measurements on 3He adsorbed on Grafoil at submonolayer coverages and millikelvin temperatures.

Precise nuclear magnetic susceptibility results on $^{3}\mathrm{He}$ adsorbed on Grafoil are presented for submonolayer coverages in the temperature reange 5--600 mK. At low areal densities, the film is in a two-dimensional homogeneous liquid state. Some $^{3}\mathrm{He}$ atoms, however, are localized by the substrate heterogeneity; our quantitative measurements show that their amount increases from 2% to 4% of a monolayer thereby leading to significant corrections of the fluid-phase density. The Fermi tempreature of the liquid has been determined as a function of coverage; it decreases continuously for densities larger than 0.01 atoms/A${\mathrm{\r{}}}^{2}$. At high fluid densities, the susceptibility is enchanced by one order of magnitude with respect to the ideal-gas value. At \ensuremath{\rho}=0.0449 atoms/A${\mathrm{\r{}}}^{2}$, a two-phase coexistence region begins on a Grafoil sample; \ensuremath{\rho}=0.0434 atoms/A${\mathrm{\r{}}}^{2}$ is estimated for a perfect graphite surface. The coexistence is characterized by a linear increase (linear decrease) of the solid (liquid) fraction and a constant Fermi temperature of the liquid phase. Finally, at \ensuremath{\rho}=0.0646 atoms/A${\mathrm{\r{}}}^{2}$, the liquid phase disappears completely. Our results are compared to previous heat capacity and NMR measurements at submonolayer coverages.

Near-critical and supercritical fluid densities of CO2-SF6 mixtures

Abstract Super, M.S., Beckman, E.J. and Enick, R.M., 1992. Near-critical and supercritical fluid densities of CO2-SF6 mixtures. Fluid Phase Equilibria, 86: 275-292 A recently proposed technique for the separation of the major recyclable thermoplastics incorporates the variable density of CO2-SF6 mixtures at mild temperatures and elevated pressures. Therefore, near-critical liquid and supercritical fluid densities of these mixtures were determined at temperatures between 294 K and 338 K and pressures up to 47 MPa. Mixtures containing SF6 mole fractions from 0.230–0.849 were used. The temperature-pressure conditions required to attain a specified density were determined in a high-pressure, variable-volume cell by isothermally compressing a fluid of known composition until a glass density float remained suspended in the fluid. The densities of the eight floats used in this study ranged from 900.0 to 1449.4 kg m−3. The results were correlated with the modified Lawal-Lake-Silberberg (MLLS) EOS, designed specifically for accurate near-critical liquid and supercritical fluid phase densities, the mean field lattice gas (MFLG) EOS and the Benedict-Webb-Rubin-Starling (BWRS) EOS. Both the MLLS and the MFLG equations had three adjustable parameters for mixture density correlations, while the BWRS had only one. Better results for mixture densities were obtained with the MLLS EOS, which yielded an average absolute pressure deviation (AAPD) of 4.49% at a specified temperature, density and composition. The AAPDs for the MFLG and the BWRS EOS were 7.07% and 7.64%, respectively.

A focus on the behaviour of certain thermodynamic properties of saturated cryogenic liquids

The products of saturation temperature T and liquid density rho f, fluid phase density difference rho f- rho g, heat of vaporization hfg, difference between the critical and the saturation pressure pc-p and velocity of sound in the liquid phase uf show maxima at certain temperatures. Furthermore, the product of saturation pressure and the difference between the critical and the saturation temperature (p(Tc-T)), and the vapour enthalpy hg also show maxima. It is shown that all these extrema occur within a limited range of a characteristic temperature T*. This paper lists, for Ne, Ar, Kr, Xe, N2, O2, CH4, C2H6 and C2H4, the temperatures at which the maxima occur and the magnitudes of the maxima in reduced quantities. If equations of state can take into account these criteria, their accuracy and ability to predict the slope properties can be enhanced.

Analytical two-phase flow void prediction method

An analytical formula has been derived, without empirical constants, that predicts the lower limit void fraction as a function of quality and pressure. The derivation utilizes a functional relationship for the slip and the boundary conditions at the limits as ~* 0 and x ~* !• The formula has been compared with two state-of-theart correlations, in the parameter range of operation of a Boiling Water Reactor (BWR) at steady state, and with some air-water data. It fits the first case data rather well, and correlates the air-water data with even greater accuracy. The potential applicability of this formula to countercurren t flow cases has not yet been explored. This paper concentrates on the derivation of the formula and comments on the data correlations. Nomenclature A = flow area, m2 (without subscript: total flow area) C0 = parameter defined in text F = intermediate function defined in text / = intermediate function defined in text g = intermediate function defined in text m = mass flow rate, kg/s (without subscript: total flow rate) S = slip, velocity ratio VgIVi V = average velocity of each phase Vgj = parameter defined in text a = void fraction, area ratio AgIA p = fluid phase density, kg/m3 X = flow quality, mass flow ratio mg/m Subscripts g = gas phase t = liquid phase

Saturated liquid densities of cryogenic liquids and refrigerants

The saturated liquid density, ϱ lr, data along the liquid vapour coexistence curve published in the literature for several cryogenic liquids, hydrocarbons and halocarbon refrigerants are fitted to a generalized equation of the following form ϱ lr = 1 + A(1 − T r + B(1 − T r) β The values of β, the index in phase density differences power law, have been obtained by means of two approaches namely statistical treatment of saturated fluid phase density difference data and the existence of a maximum in T( ϱ 1 − ϱ v) along the saturation curve. Values of the constants A and B are determined utilizing the fact that T ϱ1 has a maximum at a characteristic temperature T. Values of A, B and β are tabulated for Ne, Ar, Kr, Xe, N 2, O 2, methane, ethane, propane, iso-butane, n-butane, propylene, ethylene, CO 2, water, ammonia, refrigerants-11, 12, 12B1, 13, 13B1, 14, 21, 22, 23, 32, 40, 113, 114, 115, 142b, 152a, 216, 245 and azeotropes R-500, 502, 503, 504. The average error of prediction is less than 2%.

Solubilities of naphthalene and indole in supercritical fluids

Solubilities of naphthalene and indole in carbon dioxide, ethylene, and ethane were measured at 308.15 K over a pressure range of 5 to 20 MPa. The solubility data were obtained, using a newly developed static method that utilizes supercritical fluid chromatography. The data obtained are well correlated by applying the Soave-Redlich-Kwong equation of state to the fugacity coefficient of the fluid phase. In addition, the relation between the solubility and the fluid phase density is briefly discussed for each binary system by use of the virial equation of state.

Derivation of basic equations of mass transport in porous media, Part 2. Generalized Darcy's and Fick's laws

This is the second part of a series of two papers on the development of a general thermodynamic basis for the study of transport phenomena in porous media. The porous medium is modelled as a superposition of one solid continuum coexiting and interacting with an N-component fluid-phase continuum. Macroscopic balance laws derived in Part 1 provide the equations of mass and momentum for the mean motion of the fluid phase and diffusive motions of individual components. The Coleman and Noll's method of exploitation of the entropy inequality is applied to restrict a rather general set of constitutive equations. Gradients of the fluid-phase density and concentrations of N-1 components are included among independent variables to account for buoyancy and cross-coupling effects properly. Extensions of certain classical relations for fluid-phase pressure, solid stress tensor, and components' chemical potentials are obtained as results of the constitutive theory. Further simplifications and linearizations of constitutive equations and balance laws yield a general extension of Darcy's and Fick's laws, applicable to cases where the fluid has more than one main component. It is found out that both relations have to be modified to account for the effect of high concentrations. It is shown that classical forms of those laws are valid only if fluid components exists at low concentrations. All assumptions are carefully and explicitly stated during the course of development. As an illustration of the theory, proper forms of Darcy's and Fick's laws for the flow and transport of concentrated brine in porous media are given. The development here also provides a fundamental basis to equations used in the description of chemico-osmosis effects.

Capillary phenomena. Part 19.—Systems subjected to various gravitational field strengths

A scheme is described which allows quantities relating to axially symmetric capillary systems to be computed for various values of the gravitational field strength, or of the fluid-phase density difference, or of the fluid/fluid interfacial tension. Examples are given using pendent and sessile drops. The treatment deals with zero-gravity conditions (or Δρ= 0) under which these drops become spherical, but fluid bridges, for instance, possess a variety of shapes. Analytical formulae exist for many gravity-free axially symmetric cases, but they are not always convenient to use and may not be available for sufficient quantities. The approach used here involving an explicit capillary parameter ζ is quite general.