Existing Equation Of State Research Articles

Equation of state and strength of diamond in high-pressure ramp loading

Diamond is used extensively as a component in high-energy-density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first-principles theoretical models of equilibrium multiphase EOS, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to $\ensuremath{\sim}10$ TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Gr\"uneisen EOS. We also performed DFT calculations of the elastic moduli, and calibrated an algebraic elasticity model for use in simulations. We then estimated the flow stress of diamond by comparison with the stress-density relation measured experimentally in ramp-loading experiments. The resulting constitutive model allows us to place a constraint on the Taylor-Quinney factor (the fraction of plastic work converted to heat) from the observation that diamond does not melt on ramp compression.

Coupled thermo–hydro–mechanical simulation of CO2 enhanced gas recovery with an extended equation of state module for TOUGH2MP-FLAC3D

As one of the most important ways to reduce the greenhouse gas emission, carbon dioxide (CO2) enhanced gas recovery (CO2-EGR) is attractive since the gas recovery can be enhanced simultaneously with CO2 sequestration. Based on the existing equation of state (EOS) module of TOUGH2MP, extEOS7C is developed to calculate the phase partition of H2O–CO2–CH4–NaCl mixtures accurately with consideration of dissolved NaCl and brine properties at high pressure and temperature conditions. Verifications show that it can be applied up to the pressure of 100 MPa and temperature of 150 °C. The module was implemented in the linked simulator TOUGH2MP-FLAC3D for the coupled hydro–mechanical simulations. A simplified three-dimensional (3D) 1/4 model (2.2 km × 1 km × 1 km) which consists of the whole reservoir, caprock and baserock was generated based on the geological conditions of a gas field in the North German Basin. The simulation results show that, under an injection rate of 200,000 t/yr and production rate of 200,000 sm3/d, CO2 breakthrough occurred in the case with the initial reservoir pressure of 5 MPa but did not occur in the case of 42 MPa. Under low pressure conditions, the pressure driven horizontal transport is the dominant process; while under high pressure conditions, the density driven vertical flow is dominant. Under the considered conditions, the CO2-EGR caused only small pressure changes. The largest pore pressure increase (2 MPa) and uplift (7 mm) occurred at the caprock bottom induced by only CO2 injection. The caprock had still the primary stress state and its integrity was not affected. The formation water salinity and temperature variations of ±20 °C had small influences on the CO2-EGR process. In order to slow down the breakthrough, it is suggested that CO2-EGR should be carried out before the reservoir pressure drops below the critical pressure of CO2.

Temperature dependence of the velocity-density relation for liquid metals under high pressure: Implications for the Earth’s outer core

The relationship between the sound velocity, density, and temperature of liquid metals is important when one tries to interpret the seismic velocity profile and infer the chemical compositions of the Earth’s outer core. We, therefore, have experimentally measured the longitudinal acoustic (LA) velocity of liquid indium under high P-T conditions. Also, we examined a Hugoniot data of liquid iron by comparing with an existing equation of state (EoS). The LA velocities of liquid and solid indium at pressures up to 6.7 GPa and temperatures mostly at 710 K were measured using inelastic X-ray scattering (IXS) to probe samples in an externally heated diamond-anvil cell. A thermal EoS for liquid indium derived from existing literature was used to calculate the density for the IXS measurements and to provide an independent check on the sound velocities. The IXS data are consistent with the hydrodynamic LA velocity derived from the liquid EoS, implying that the positive dispersion is minimal in liquid indium. The velocity-density relation for liquid indium derived from the EoS has temperature dependence, implying that Birch’s law does not hold for the liquid phase. Similarly we calculated the temperature-velocity-density relation of liquid iron over the Earth’s core range from a recently reported EoS. The resulting velocity-density relation is also temperature dependent, indicating that liquid iron thus does not follow Birch’s law. The violation of Birch’s law implies that the Hugoniot data cannot be directly compared with seismological observations because of the different temperature ranges. Formulation of the temperature-velocity-density of liquid iron-alloys supported by experimental measurements provides better understanding of the thermodynamic state of the Earth’s core.

Combining Kohn-Sham and orbital-free density-functional theory for Hugoniot calculations to extreme pressures.

The shock Hugoniot for lithium 6 deuteride ((6)LiD) was calculated via first principles using Kohn-Sham density-functional theory molecular dynamics (KSMD) for temperatures of 0.5-25 eV. The upper limit of 25 eV represents a practical limit where KSMD is no longer computationally feasible due to the number of electronic bands which are required to be populated. To push the Hugoniot calculations to higher temperatures we make use of orbital-free density-functional theory molecular dynamics (OFMD). Thomas-Fermi-Dirac-based OFMD gives a poor description of the electronic structure at low temperatures so the initial state is not well defined. We propose a method of bootstrapping the Hugoniot from OFMD to the Hugoniot from KSMD between 10 and 20 eV, where the two methods are in agreement. The combination of KSMD and OFMD allows construction of a first-principles Hugoniot from the initial state to 1000 eV. Theoretical shock-compression results are in good agreement with available experimental data and exhibit the appropriate high-temperature limits. We show that a unified KSMD-OFMD Hugoniot can be used to assess the quality of the existing equation-of-state (EOS) models and inform better EOS models based on justifiable physics.