Vibrating tube densimeters are well-established tools for measuring fluid densities precisely at elevated temperatures and pressures. However, the conventional method of calibrating them utilises a model in which the apparatus parameters are represented as polynomials of temperature and pressure that contain a variable number of terms. Here a robust, physically-based model is presented and demonstrated for six different instruments at temperatures from (273 to 473) K, pressures from (0 to 140) MPa and densities from (0 to 1050) kg m -3 . The model's physical basis ensures that only seven apparatus parameters are required to relate the measured resonant period to fluid mass density with an average r.m.s. deviation of ±0.23 kg m -3 across all six densimeters. Estimates for each of the apparatus parameters were made based on the geometry and material properties of the vibrating tubes, and these estimates were consistent with the parameter values determined by calibration with reference fluids. Three of the apparatus parameters describe the temperature dependence of the resonant period: for the six vibrating tubes tested, the relative standard deviations of these parameters were all within the range of values estimated from the thermoelastic properties of the Hastelloy tubes. Two distinct parameters are required to describe the pressure dependence of the vibrating tube's volume and effective spring constant, both of which are estimable from equations describing the elastic deformation of thick-walled tubes. The extensive calibrations conducted demonstrate that, for these densimeters, the variations with pressure of the tube's spring constant and its volume have a ratio that is neither 0 nor 1, as has been assumed previously. The model's physical basis allows vibrating tube densimeters to be calibrated accurately using fewer reference fluid measurements than required by the conventional method. Furthermore, use of the physically-based model reduces the uncertainty of measurements made at densities, temperatures or pressures beyond the range of the calibration.1

Unfortunately, Eqs. (26) and (27) of the original article 1 were erroneous; the correct expressions are as follows:None of the other results or conclusions of the work are affected by this revision.1

No abstract

Understanding the thermophysical properties for mixtures of CO2 and hydrocarbons at reservoir conditions is very important for the correct design and optimization of CO2-enhanced oil recovery and carbon storage in depleted oil or gas fields. In this paper, we present a comprehensive thermodynamic study of the prototype system (CO2 + n-heptane) comprising highly-accurate measurements of the saturated-phase densities, compressed-fluid densities, and bubble and dew points at temperatures from 283 K to 473 K and pressures up to 68 MPa over the full range of composition. We use these results to examine the predictive capability of two leading thermodynamic models: the Predictive Peng-Robinson (PPR-78) equation of state and a version of the Statistical Associating Fluid Theory for potentials of the Mie form, known as SAFT-γ Mie. Both of these models use group contribution approaches to estimate interaction parameters and can be applied to complex multi-component systems. The comparison shows that both approaches are reliable for the phase behavior. Neither model is entirely satisfactory for density, with each exhibiting absolute average relative deviations (AARD) from the experimental data of about 4 % for the saturated-phase densities and 2 % for the compressed-fluid densities; however, SAFT-γ Mie is found to be much more accurate than PPR-78 for the compressibility, with an overall AARD of 6 % compared with 18 % for PPR-78.

The aggregation of clay particles in aqueous solution is a ubiquitous everyday process of broad environmental and technological importance. However, it is poorly understood at the all-important atomistic level since it depends on a complex and dynamic interplay of solvent-mediated electrostatic, hydrogen bonding, and dispersion interactions. With this in mind, we have performed an extensive set of classical molecular dynamics simulations (included enhanced sampling simulations) on the interactions between model kaolinite nanoparticles in pure and salty water. Our simulations reveal highly anisotropic behavior, in which the interaction between the nanoparticles varies from attractive to repulsive depending on the relative orientation of the nanoparticles. Detailed analysis reveals that at large separation (>1.5 nm), this interaction is dominated by electrostatic effects, whereas at smaller separations, the nature of the water hydration structure becomes critical. This study highlights an incredible richness in how clay nanoparticles interact, which should be accounted for in, for example, coarse-grained models of clay nanoparticle aggregation.