Isothermal Compressibility Values Research Articles

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + methane up to 463K

High-pressure phase equilibrium and volumetric properties of highly asymmetric mixtures related to reservoir fluids are critical to the development of high-pressure and high-temperature (HPHT) reservoirs. However, there is a lack of the relevant data and accurate modeling tools. In this work, we prepared asymmetric pseudo-binary mixtures of methane (CH4) + stock tank oil (STO) and systematically measured their phase equilibrium and densities at temperatures from (298.15 to 463.15) K and pressures up to 140 MPa. The methane mole fraction in these mixtures range from 0.20 to 0.61 for the density measurement, and from 0.20 to 0.81 for the phase equilibrium measurement. From the experimental densities, the isothermal compressibility values, as well as the pseudo-excess volumes, were determined. Moreover, phase envelopes, relative volumes, and liquid volume fractions below the saturation point were also measured. These data are valuable for evaluating and improving thermodynamic models for HPHT reservoir fluids. The experimental results were modeled by the Soave-Redlich-Kwong (SRK) equation of state (EoS), the Peng-Robinson (PR) equation of state, their volume translated versions SRK-VT and PR-VT, and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). For density, SRK and PR gave large deviations of ~18% and ~8%, respectively, as compared with ~3% for PC-SAFT. Inclusion of volume translation reduced their deviations to the same level as that for PC-SAFT. For isothermal compressibility, all the models gave deviations of 20-30%, with PC-SAFT, SRK-VT and PR-VT being slightly better. The excess volumes calculated by SRK, PR and PC-SAFT were similar and close to the experimental values. The deviations in the calculated excess volumes resulted in only ~1% deviations in the calculated densities if the experimentally determined STO densities were used. It was illustrated that the small deviations could be utilized in the excess volume method to accurately estimate the high-pressure live oil densities from the high-pressure STO densities. This excess volume method gave ~1% density deviation on average for all the models, with PC-SAFT giving the smallest maximum deviation. The deviations in calculated saturation pressures were ~5% for all the models with the overall deviation for PC-SAFT being slightly smaller.

Relation between excess volume, excess free energy and isothermal compressibility in liquid alloys

Excess volume data of 32 liquid alloys were reviewed and plotted versus their excess free energies. It is hereby found that all combinations of the signs of EV and EG are possible. The excess volume data split into two different curves which are monotonous in EG. For one of these curves the signs of EV and EG are equal and they are opposite for the other.We improved our previously developed model and found that there is an unspecified sign which can be chosen either + or -, depending on the system. This explains why there are two curves corresponding to the experimental finding. The model relates excess volume, excess free energy and isothermal compressibility with each other whereby the concept of internal pressure is used.The model can also predict the excess volume as function of the excess free energy, when the correct sign, either + or -, is known and a reasonable assumption is made for the effective isothermal compressibility. In the present work, the latter has been estimated as an average from the isothermal compressibility values over the involved pure elements. Good qualitative and quantitative agreement with the experimental data is obtained for the systems investigated. The model is valid at least for -3RT < EG < +1RT.

Process integrating two-stage hydrocracking and a hydrotreatment process

Excess volume data of 32 liquid alloys were reviewed and plotted versus their excess free energies. It is hereby found that all combinations of the signs of EV and EG are possible. The excess volume data split into two different curves which are monotonous in EG. For one of these curves the signs of EV and EG are equal and they are opposite for the other.We improved our previously developed model and found that there is an unspecified sign which can be chosen either + or -, depending on the system. This explains why there are two curves corresponding to the experimental finding. The model relates excess volume, excess free energy and isothermal compressibility with each other whereby the concept of internal pressure is used.The model can also predict the excess volume as function of the excess free energy, when the correct sign, either + or -, is known and a reasonable assumption is made for the effective isothermal compressibility. In the present work, the latter has been estimated as an average from the isothermal compressibility values over the involved pure elements. Good qualitative and quantitative agreement with the experimental data is obtained for the systems investigated. The model is valid at least for -3RT < EG < +1RT.

Turbidity data obtained from image analysis in near critical hydrogen.

Video images are being used with increased frequency in science, supplanting current methods such as light scattering by statistical evaluation of the images. In this study we use light turbidity data due to density-induced refractive index fluctuations to obtain critical amplitudes from image analysis. In order to bring hydrogen (H_{2}) very close to its critical point, we place the sample cell under weightlessness using a magnetic levitation device. Images of an H_{2}-filled cell are taken near its critical temperature of 33K by illuminating the cell with three different filters. We fit the turbidity data to a theoretical expression that allows us to estimate the critical amplitudes of isothermal compressibility and fluctuation correlation length. The values of isothermal compressibility and correlation length obtained from turbidity fitting are compared against literature values. Our data analysis shows a large sensitivity of the fitting parameters to the refractive index value and to even minute density deviations from criticality.

Experimental determination of the isothermal compressibility of drilling fluids in high pressures and temperature

The present work aims at the experimental determination of the isothermal compressibility of drilling fluids under high pressure and high temperature. For that, a high-resolution PVT (Pressure-Temperature-Volume) cell was used to measure data through the Constant Composition Expansion method. The isothermal compressibility values of the studied fluid were similar to the data found in the literature.

Experimental and predictive PC-SAFT modeling results for density and isothermal compressibility for two crude oil samples at elevated temperatures and pressures

Rapid growth in world oil demand is driving the oil and gas industry to search for petroleum in deep wells where elevated temperatures and pressures prevail. Accurate knowledge of thermodynamic properties such as density and isothermal compressibility at in-situ conditions is necessary to estimate the recoverable oil from these deep reservoirs. Yet, crude oil density data in the open literature for pressures exceeding 155 MPa are scarce or nonexistent.In this study, we present density data for two Gulf of Mexico crude oils at pressures from 3 to 276 MPa and temperatures up to 523 K. Measurements on the liquid fraction of the crude oil were made along three isotherms at temperatures T = (323, 423, and 523) K and at pressures from near-ambient platform to ultra-deep reservoir conditions. The liquid fraction of the crude oils or “dead” oils contained numerous components including alkanes, branched-alkanes, cyclo-alkanes, aromatics, resins, and asphaltenes. For simplicity, the composition of each dead oil was represented as three pseudocomponents - saturates, aromatics and resins, and asphaltenes. Methane gas at two concentrations (5 and 10 wt%) was added to the dead oils to obtain synthetic live crude oils. Experimental density data for the two live oil samples are also reported at four isotherms and similar pressure conditions. The uncertainty in the reported densty data is less than ±1%. A Tait relationship was used to correlate the measured density data; from this relationship, a reference value for isothermal compressibility was obtained. The present density and isothermal compressibility data have been compared with predictions from the Perturbed Chain version of the Statistical Associating Fluid Theory (PC-SAFT) without the use of any fitting parameters. A special set of new PC-SAFT parameters accurate for one-phase calculations at high-pressure, high-temperature conditions was used; these parameters were predicted with a knowledge of the measured aromaticity of the oil under investigation. Oil density values were predicted to within 1–4% of experimental values on average, and isothermal compressibility values were within 1–10% on average.

Estimation of the isothermal compressibility from event-by-event multiplicity fluctuation studies

The first estimation of the isothermal compressibility (kT) of matter is presented for a wide range of collision energies from √sNN = 7.7 GeV to 2.76 TeV. kT is estimated with the help of event-byevent charged particle multiplicity fluctuations from experiment. Dynamical fluctuations are extracted by removing the statistical fluctuations obtained from the participant model. kT is also estimated from event generators AMPT, UrQMD, EPOS and a hadron resonance gas model. The values of isothermal compressibility are estimated for the Large Hadron Collider (LHC) energies with the help of the event generators.

Density and Compressibility of Multicomponent n-Alkane Mixtures up to 463 K and 140 MPa

Density measurements of two ternary alkane mixtures (methane/n-butane/n-decane and methane/n-butane/n-dodecane) and two multicomponent mixtures composed of methane/n-butane/n-octane/n-dodecane/n-hexadecane/n-eicosane were performed in the temperature range from (278.15 to 463.15) K and pressures up to 140 MPa. The isothermal compressibility values of these mixtures were obtained by differentiation from a Tait-type fitting of experimental densities as a function of temperature and pressure. Excess volume of the studied mixtures was also determined. Four different equations of state, that is, Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), and Soave-Benedict-Webb-Rubin (Soave-BWR) were used for predicting the experimental density values as well as the excess volumes.

Density and phase equilibrium of the binary system methane + n-decane under high temperatures and pressures

Densities of the binary system methane + n-decane have been determined through a vibrating tube densitometer from (278.15–463.15) K at pressures up to 140 MPa, and for methane mole fractions up to 0.8496. Negative excess volumes were found under the experimental conditions studied. Moreover isothermal compressibility values were obtained by differentiation from the Tammann-Tait correlation of the determined density values. Isobaric thermal expansion coefficients were also calculated based on differentiation from the isobaric fit of density data. We also measured the phase equilibrium of this binary system by using a variable volume cell with full visibility from (293.15–472.47) K for three mixtures with methane mole fractions of 0.4031, 0.6021 and 0.8496. Liquid fraction upon expansion below the saturation pressure has also been determined. Finally different equations of state were used to calculate the experimental density and excess volume data as well as the phase envelope data. No direct regression of the experimental data was involved in most of the calculation in order to provide a fair comparison of the performance of different models.

Densities of the Binary Systems n-Hexane + n-Decane and n-Hexane + n-Hexadecane Up to 60 MPa and 463 K

The densities of the binary systems n-hexane + n-decane and n-hexane + n-hexadecane have been measured up to 60 MPa using a vibrating tube densimeter. The measurements covered the whole composition range; for the first system they were performed from (278.15 to 463.15) K, while for the latter they were performed from (298.15 to 463.15) K because n-hexadecane is a solid at 278.15 K. The densities were correlated for every composition as a function of temperature and pressure using a modified Tammann–Tait equation with standard deviations lower than 8·10–4 g·cm–3. Isothermal compressibility values were calculated from the experimental density data. Moreover, the excess volumes were found to be negative for all of the studied mixtures, with absolute values less than or equal to 3.25 cm3·mol–1 for the n-hexane + n-decane system and 7.65 cm3·mol–1 for the n-hexane + n-hexadecane system. Various equations of state were used to model the measured density data.

Erratum to: “Interactions in L-Phenylalanine/L-Leucine/L-Glutamic Acid/L-Proline + 2 M Aqueous NaCl/2 M NaNO3 Systems at Different Temperatures”

Density (ρ) and speed of sound (u) in 2 M aqueous NaCl and 2 M NaNO3 solutions of amino acids: L-phenylalanine, L-leucine, L-glutamic acid, and L-proline have been measured for several molal concentrations of amino acids at different temperatures. The ρ and u data have been used to calculate the values of isothermal compressibility and internal pressure at different temperatures. The trends of variations of κT and Pi with an increase in molal concentration of amino acid and temperature have been discussed in terms of solute-solvent and solute-solute interactions in the systems.

Equation of state for ionic liquids

A simple form of equation of state for ionic liquids is proposed as an asymptotic low-temperature variant of the fluctuational equation of state developed by author. This function predicts reliably the properties of the pure substances and mixtures with the quite different molecular structures in the wide temperature- and pressure-ranges including the critical region. It is essentially important at evaluation, for example, of the near-critical carbon-dioxide’s solubility in the set of ionic liquids. Re-establishing of the gas-liquid phase diagram from the triple point up to the point of thermal decomposition on the base of measurable data at atmospheric pressure has been chosen as the method for the thermodynamically-consistent calculation of coefficients. Especially complex problem is the consistent description of very small values of isothermal compressibility and vapor pressure. The developed method is verified for water, ethylene, argon and several ionic liquids. It is applicable, in principle, to such complex molecular structures as polymers, non-organic salts, liquid metals for which the equation of state is necessary to solve a variety of the practical usage questions.

Speeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory’s statistical theory and hard sphere models

Speeds of sound and densities of three ternary liquid systems namely, toluene + n-heptane + n-hexane (I), cyclohexane + n-heptane + n-hexane (II) and n-hexane + n-heptane + n-decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory’s statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory’s statistical theory has been established quite reasonably over hard sphere models.

Studies of Thermodynamic Properties of Binary and Ternary Methanolic Solutions Containing KBr and 18-Crown-6 at 298.15 K

Experimental measurements of the speed of sound, density and osmotic vapour pressure are reported for binary 18-Crown-6 (18C6) + CH3OH, KBr + CH3OH and ternary KBr + 18C6 + CH3OH solutions at 298.15 K. The density and compressibility data were processed to obtain the apparent molar volume (o V ) and apparent molar isentropic compressibility (\(\phi _{K_S } \)) of the solutes in methanol. Expansivity data were obtained for the 18C6 + CH3OH system from density data at different temperatures and were used for calculation of the isothermal compressibility values at 298.15 K. The isothermal compressibility and expansivity data are further used to obtain the apparent molar isothermal compressibility (\(\phi _{K_T } \)) and apparent molar expansivity (o E ) of 18C6 in methanolic solutions and as well as the energy-volume coefficient parameter (∂ U/∂ V) T in methanol solutions. The volume and compressibility changes due to complexation of KBr with 18C6 are obtained at infinite dilution for o V and o K . The results are compared with the similar data obtained by us previously for aqueous and CCl4 solutions. The osmotic coefficient data were used to calculate activities and activity coefficients of each component at 298.15 K as a function of the concentration of binary and ternary methanolic solutions containing KBr and 18C6. The activity and activity coefficient data are used to evaluate the pair and triplet interaction parameters by making appropriate use of the McMillan-Meyer theory of solutions. The calculation of the thermodynamic equilibrium constant (K) is made using the pair interaction parameter, g NE (non-electrolyte – electrolyte pair interaction), for the complexation equilibria. The nature of interactions present in the CH3OH solutions is discussed.

P−ρ−TData of Liquids: Summarization and Evaluation. 8. Miscellaneous Compounds

The published experimental data for 53 compounds (eight amines, eight nitriles, four N-heterocyclic compounds, six nitro compounds, four amides, four other compounds containing C, H, O, and N atoms, six halogenated alcohols, five fluoroethers, and eight miscellaneous compounds) are summarized and reviewed, and the parameters of the Tait equation are given for 49 substances. This equation allows the calculation of smoothed values of either the volume ratio, V(P)/V(Pref), and related properties (relative density, ρ(P)/ρ(Pref), compression, {1 − ρ(Pref)/ρ(P)}) or, using density data at atmospheric pressure (Pref = 0.1 MPa) or at saturation (Pref = Psat), the liquid densities of the substances over a temperature and pressure range. Experimental values of isothermal compressibility at atmospheric pressure compiled from the literature are also summarized and compared with values calculated from the Tait equation.

Volume Expansivities and Isothermal Compressibilities of Imidazolium and Pyridinium-Based Ionic Liquids

From ambient- and high-pressure density measurements, we report the volume expansivities and isothermal compressibilities of four room-temperature ionic liquids and 1-methylimidazole at temperatures between 298.2 and 343.2 K and pressures to 206.9 MPa. The compounds studied are 1-butyl-3-methylimidazolium hexafluorophosphate ([C4mim][PF6]), 1-octyl-3-methylimidazolium hexafluorophosphate ([C8mim][PF6]), 1-octyl-3-methylimidazolium tetrafluoroborate ([C8mim][BF4]), and N-butylpyridinium tetrafluoroborate ([NBuPy][BF4]). The density is affected by the natures of the anion, cation, and substituents on the cation, with lower densities observed for longer alkyl chains. Density decreases fairly linearly with increasing temperature but at a rate less than that for molecular organic compounds. In addition, the high-pressure measurements reveal that ionic liquids are significantly less compressible than organic solvents, with isothermal compressibility values similar to that of water. The high-pressure density dat...

P−ρ−T Data of Liquids: Summarization and Evaluation. 7. Selected Halogenated Hydrocarbons

The published experimental data for 41 halogen derivatives of hydrocarbons (2 fluoro derivatives, 22 chloro derivatives, 11 bromo derivatives, and 6 iodo derivatives) are summarized and reviewed, and the parameters of the Tait equation are given for 39 substances. This equation allows the calculation of smoothed values of either the volume ratio, V(P)/V(Pref), and related properties (relative density, ρ(P)/ρ(Pref), compression, {1 − ρ(Pref)/ρ(P)}), or, using density data at atmospheric pressure (Pref = 0.1 MPa) or at saturation (Pref = Psat), the liquid density of the substances over a temperature and pressure range. Experimental values of isothermal compressibility at atmospheric pressure compiled from the literature are also summarized and compared with values calculated from the Tait equation.

Molecular dynamics simulation studies of liquid acetonitrile: New six‐site model

Molecular dynamics (MD) simulations are carried out for liquid acetonitrile using a new six-site model for the solvent molecules. The recent force field of Cornell et al. ( J Am Chem Soc, 1995, 117, 5179) was used under the RESP approach to obtain the atomic charges. A new flexible all-atom solvent model was achieved whose density, heat of vaporization, and isothermal compressibility values are in good agreement with available experimental data, especially for a generic force field. Radial distribution functions are calculated and discussed to study the liquid structure in detail. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 901–908, 2000

Molecular dynamics simulation studies of liquid acetonitrile: New six-site model

Molecular dynamics (MD) simulations are carried out for liquid acetonitrile using a new six-site model for the solvent molecules. The recent force field of Cornell et al. ( J Am Chem Soc, 1995, 117, 5179) was used under the RESP approach to obtain the atomic charges. A new flexible all-atom solvent model was achieved whose density, heat of vaporization, and isothermal compressibility values are in good agreement with available experimental data, especially for a generic force field. Radial distribution functions are calculated and discussed to study the liquid structure in detail. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 901–908, 2000

Thermodynamic Interactions in Binary Mixtures of Styrene with n-Alkanes at 298.15 K

Abstract Thermodynamic interactions in binary mixtures of styrene with n-alkanes have been studied in terms of excess quantities using the experimental results of density, viscosity, and speed of sound at 298.15 K. Flory as well as Prigogine–Flory–Patterson equations were used to calculate the excess molar volume in addition to enthalpy, entropy, and free-energy mixing functions. The viscosity results were analysed using Bloomfield and Dewan theory to predict viscosity deviations, while the speed-of-sound results were analysed by Benson and Kiyohara theory to predict the deviations in isentropic compressibility. The Prigogine–Saraga theory was used to calculate the deviations in internal pressure of liquids and liquid mixtures. Furthermore, isothermal compressibility values were predicted from the Flory equation of state and compared with the experimentally obtained values. Overall, the computed and experimental results are discussed in terms of thermodynamic interactions between the mixing components.