Pressure Derivative Research Articles

Thermoelastic properties of materials based on the Generalized Rydberg-Vinet and the Stacey reciprocal K-primed equations of state

Most of the equations of state used in the literature are not physically acceptable because they do not satisfy the fundamental constraints derived by Stacey in the limit of infinite pressure or extreme compression. In the present study we have used the Generalized Rydberg-Vinet equation of state, and compared the results with those determined from the Stacey reciprocal K- primed equation. We have calculated the pressure-volume relationships, bulk modulus and its pressure derivatives up to third order, Grüneisen parameter and its higher order volume derivatives for MgO, hcp iron, lower mantle and the Earth outer core. The results obtained using the two equations of state have been discussed and compared with each other and also found to present good agreement with the available experimental data.

Analysis of pressure derivatives of bulk modulus for materials at high compressions

Pressure derivatives of bulk modulus play a central role in describing thermoelastic behaviour and equation of state for materials at high pressures. It is demonstrated here that the relationships between pressure derivative of bulk modulus and volume compression used by earlier workers are not consistent with the thermodynamic constraints based on the second-, and third order pressure derivatives of bulk modulus, and third order Grüneisen parameter in the limit of infinite pressure. It is pointed out that the compatibility of Keane’s equation and the Stacey reciprocal equation of state as considered by Sinha et al. does not hold at high pressures. The Keane equation does not satisfy the thermodynamic constraint according to which the third order Grüneisen parameter must be less than the pressure derivative of bulk modulus at extreme compression. Values of second-, and third order pressure derivatives of bulk modulus for the Earth lower mantle and outer core determined using the K-primed equations reported by Sinha et al. are found to deviate significantly from the results based on the seismic data at finite pressures obtained by fitting the Stacey reciprocal K-primed EOS.

A theoretical investigation on the structural stability, superconductivity, and optical and thermodynamic properties of Ir2P under pressure.

The potential applications of Ir2P are promising due to its desirable hardness, but its fundamental properties are still not fully understood. In this study, we present a systematic investigation of Ir2P's structural, electronic, superconducting, optical, and thermodynamic properties of Ir2P under pressure. Our calculations show that Ir2P has a Fm3̄m structure at ambient pressure, which matches well with experimental data obtained from high-pressure synchrotron X-ray diffraction. As pressure increases, a transition from the Fm3̄m to the I4/mmm phase occurs at 103.4 GPa. The electronic structure and electron-phonon coupling reveal that the Fm3̄m and I4/mmm phases of Ir2P are superconducting materials with superconducting transition temperatures of 2.51 and 0.89 K at 0 and 200 GPa, respectively. The optical properties of Ir2P indicate that it has optical conductivity in the infrared, visible, and ultraviolet regions. Additionally, we observed that the reflectivity R(ω) of Ir2P is higher than 76% in the 25-35 eV energy range at different pressures, which suggests that it could be used as a reflective coating. We also explored the finite-temperature thermodynamic properties of Ir2P, including the Debye temperature, the first and second pressure derivatives of the isothermal bulk modulus, and the thermal expansion coefficient up to 2000 K using the quasi-harmonic Debye model. Our findings offer valuable insights for engineers to design better devices.

(Digital Presentation) Designing New Complex Hydrides Based on Transition Metals for Hydrogen Storage Applications

The widespread implementation of the hydrogen economy demands access to materials with a high weight percentage of hydrogen. Mg-based hydrogen storage alloys have become a research hot-spot in recent years owing to their high hydrogen storage capacity, good reversibility of hydrogen absorption/desorption, low cost, and abundant resources. However, high decomposition temperature of Mg-based hydrideslimits their practical usage. Hydrogen is lightest of all elements, typically it need large volumes or high pressures to store appreciable amount of hydrogen.To overcome these challenges research activities are currently going on metal hydrides and complex hydrides based on transition metal. The main challenges come when endothermic decomposition enthalpy is considered. It becomes difficult to release the hydrogen at ambient thermodynamic conditions. On the other hand, the meta-stable hydrides are characterized by a low reaction enthalpy and a decomposition reaction that is thermodynamically favourable under the ambient conditions. The good kinetics along with evolution of hydrogen around the room temperature possessed by these materials offer much promise for underground storage and it can be used as a grid energy.The present research specifically focus on transition metal based complex hydrides such as NaMgMnH6 and NaMgFeH6 for hydrogen storage and especially predicted the crystal structure of the same using VASP simulation package. ABCX6 and AB2X6 were taken as reference composition A,B,C and X were substituted with Na, Mg, transition metals(Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu) and H, respectively.From the ICSD database search the corresponding structural variants were considered as trial structure to predict the ground state structure of these newly designed compounds. using the predicted ground state structure for these compounds, important properties like formation energy, hydrogen site energy, partial density of states(pDOS), electron density(ED), Mulliken effective charge(MEC), Bader electron charge(BEC), Born effective charge, ELF and COHP were calculated. the calculated properties of these compounds were compared with the well known reference compounds. We found that both NaMgMnH6 and NaMgFeH6 are stable with negative formation energy and als othey are semiconductors with the band gap value of 0.51eV and 1.01 eV, respectively. from the calculated electronic structure we found that both these materials are having indirect band behaviour. Analysing the electronic density of states, charge density and various charges mentioned above the chemical bonding behaviour was established as iono-covalent in nature. from the force as well as stress minimisation considering 53 structural variants as input the ground state structure, its space group, equilibrium lattice parameters and atom positions are listed. Also from the energy vs. volume curve for the ground state structure, the equilibrium volume, bulk modulus and pressure derivatives were found out. Among NaMgMnH6 and NaMgFeH6 our spin polarised calculation show that NaMgMnH6 is possesing spontaneous magnetic polarisation with substantial magnetic moment at the Mn site. Among the considered paramagnetic, ferromagnetic, as well as A-, C-,and G- antiferromagnetic configurations the G type antiferromagnetic configuration is found to be the ground state for NaMgMnH6.

Confined deflagration of propanal/air in the presence of intrinsic instability at elevated pressures

The partial oxidation process is a chemical technique with a high risk of deflagration, which involves directly mixing of fuels with oxidizers at elevated conditions. Under non-standard conditions, the deflagration behaviors of fuels are often unavailable to the general public, which hampers progress in further basic research. In this study, the deflagration behaviors of propanal-air mixtures at 75 °C and 0.1–1.0 MPa were investigated, and the effect of initial pressure (P0) and equivalence ratio (φ) on the deflagration characteristics of propanal was discussed. To explain the similarities and differences in the deflagration characteristics under various conditions, the buoyancy instability, hydrodynamic instability and thermal-diffusion instability suffered by the flames were also analyzed. Results show that the pressure generated by the burned mixture is a cubic function of time, and the state of flame propagation can be determined by the monotonicity of the second-order derivative of pressure. Moreover, the peak deflagration pressure (Pm) is more sensitive to changes in φ on the fuel-lean side, but Pm/P0 at the fuel-rich condition is markedly higher than Pm/P0 at the fuel-lean condition. At all φ, an increase in P0 effectively shortens the ignition time and reduces the minimum ignition energy. Nevertheless, there are discernible differences in the variation patterns of the deflagration time (θm) with P0 at various φ. Specifically, θm gradually prolongs with increasing P0 at fuel-lean conditions, whereas it tends to be the same at different P0 and φ = 1. Furthermore, under fuel-rich conditions, θm progressively shortens as P0 increases. The decrease in θm is attributed to the increasing flame speeds in the presence of intrinsic instability, and the self-accelerating flame yields pressure waves, which travel faster than the flame. Then a series of reflected pressure waves are formed after the pressure waves strike the vessel wall, interacting with the flame front and resulting in the pressure oscillation. Moreover, increasing P0 advances the pressure oscillation and augments the intensity of pressure oscillation.

Generalized Analytical Solutions of Vertically Fractured Wells in Commingled Reservoirs: Field Case Study

Summary Accurate identification of the individual-layer parameters for vertically fractured wells in commingled reservoirs is essential for development plan design, reservoir numerical simulation, and stimulation measure selection. Different semi-analytical and numerical models are generally applied in multilayer transient testing (MLT) analysis to determine the properties of individual layer. However, these approaches require numerous computations and are complicated to program due to the fracture and reservoir discretization. This work thus presents the generalized analytical solutions of vertically fractured wells in infinite, closed, or constant-pressure commingled reservoirs with both computational and functional simplicity. The fully analytical solutions are derived based on the early-time approximate solutions of infinite-conductivity fracture and trilinear flow models, infinite-conductivity fracture solutions, pressure superposition principle, and Duhamel principle. A systematic verification by employing a standardized well testing software and trilinear flow model is conducted to ensure the general application accuracy of the presented solutions. The results show that the developed analytical solutions are valid when the dimensionless fracture conductivity is more than 2 (FcD > 2) with an average absolute percent deviation (AAD) of ~2% for pressure and that is ~4% for pressure derivative. The developed analytical solutions also exhibit improvements in early-time pressure and derivative calculation. Finally, a field case of a four-layer fractured well is interpreted by the developed solutions and well testing software to illustrate the feasibility. The interpretation results of two methods are nearly identical, with only a minor difference. The developed analytical solutions are computationally accurate while maintaining functional simplicity and can be considered as an alternative to the current semi-analytical and numerical approaches in MLT analysis.

High-pressure single-crystal elasticity of corundum: Implication for multiple seismic structure of 660-km discontinuity

The complex multi-discontinuity structure at 660‐800 km depth is likely attributable to lateral mantle composition heterogeneities, which are closely related to the mid-ocean ridge basalts (MORB). To decipher the impact of varying composition on the seismic properties of MORB, detailed knowledge of the elasticity of candidate minerals is thus important. Here we employed Brillouin scattering coupled with diamond anvil cells to determine the single-crystal elasticity of corundum up to 14 GPa and 300 K. Using third-order finite strain equation of state, we calculate the pressure derivatives of adiabatic bulk modulus and shear modulus of corundum, which yields KS0’ = 3.8(1), G0’ = 1.8(1) with KS0 = 256(1) GPa and G0 = 163(1) GPa and ρ0 = 3.987(1) g/cm3. Combined with previous high-temperature data, the velocity and anisotropy of corundum have been calculated at 300 K or along normal geotherm. Our results are applied to model the density and velocity profiles of normal and alkali-depleted MORB. Our modeling demonstrates that varying the alkali content and temperature of MORB can significantly impact the discontinuity depth and velocity jump at 660–800 km depth. For normal MORB, reducing the temperature by 300 K from normal mantle geotherm results in a shift of the velocity jump from 670–710 to 650–710 km depth but hardly affects the magnitude of the velocity jump (5.8–6.8(3)% for VP and 10.0–10.8(5)% for VS). By contrast, in alkali-depleted MORB, the discontinuity will occur at a greater depth from 705–730 to 720–745 km depending on temperature with a VP jump of 3.8–4.6(2)% and VS jump of 6.3–7.4(4)%.

Holistic Exploration of Structural, Electronic, Magnetic, Transport, Mechanical, and Thermodynamic Characteristics, Including Curie Temperature Analysis.

Through intricate calculations, the density functional theory (DFT) implemented in the Wien2k code was employed to comprehensively investigate a wide range of material characteristics. Our study encompasses an exhaustive analysis of structural stability, electronic properties, magnetic behaviors, transport phenomena, mechanical responses, and thermodynamic profiles of two notable instances of filled Skutterudites, namely, CeNi4P12 and DyCo4Sb12, which have been thoroughly explored. These computations were performed using the WIEN 2K code, combining local orbitals and the full-potential linearized augmented plane-wave approach. The findings provided insight into the wide range of properties of these materials. In this methodology, the exchange-correlation potential relies on the local-density approximation. We conducted the calculations with and without incorporating spin-orbit interactions. The results obtained provide information about the lattice constant, bulk modulus, and pressure derivative. The stability, as indicated by the P-V graphical plot, suggests that there are no structural phase transitions from the cubic symmetry structure. Notably, our work includes an examination of Curie temperatures, which are pivotal in understanding magnetic phase transitions. The validated elastic properties further support the material's stability and corroborate its ductile nature. These alloys should be considered for spintronic and thermoelectric applications due to their estimated transport characteristics and the observed ductile nature. To enhance our understanding of the thermal stability of antimony-based compounds, we have made reliable estimations of the thermophysical characteristics. By integrating theoretical insights with practical implications, we bridge the gap between fundamental understanding and material design applications. Using DFT in the Wien2k framework, we discover connections and patterns among different properties, showing how to create materials with specific functions and better performance. This approach not only advances our fundamental comprehension of materials but also promises innovation across various technological domains.

First-principles calculations on electronic, superconducting, mechanical, and thermodynamic properties for the superhard compound Tc2C under pressure

This study presents a theoretical investigation on the electronic, superconducting, mechanical, and thermodynamic properties of the superhard compound Tc2C up to 100 GPa. The investigation is conducted via the first-principles plane-wave pseudopotential method. Furthermore, to treat the exchange-correlation potential for the total energy calculations, the revised Perdew–Burke–Ernzerhof formulation stemming from the generalized gradient approximation is employed. The results suggest that Tc2C is a potential hard compound due to the robust covalent bonding between Tc and C atoms. Moreover, the electronic structure and electron–phonon coupling reveal that Tc2C is a superconducting material with Tc of 0.59 K at 0 GPa. Additionally, using the quasi-harmonic Debye model, the variation of crucial structural parameters, such as the volume thermal expansion coefficient, heat capacity, and isothermal bulk modulus and its pressure derivatives, is predicted in terms of temperature and pressure. The results demonstrate that temperature and pressure have contrasting effects on the volume thermal expansion coefficient and heat capacity, and the effect of temperature is larger than that of pressure, especially at low temperatures. The isothermal bulk modulus decreases with increasing temperature but increases with increasing pressure. The first and second pressure derivatives of the isothermal bulk modulus for Tc2C are not the assumed constants in the equation of state study at high pressures and temperatures. To our knowledge, this study presents the first quantitative theoretical prediction of the pressure and temperature dependence of the thermodynamic parameters for Tc2C, which is essential for understanding the basic physical properties of similar transition metal carbides.

Shock Hugoniot of an equiatomic high-entropy alloy NbMoTaW up to 143 GPa

The equations of state and phase stabilities of high-entropy alloys (HEAs) under high-pressure and high-temperature conditions are of paramount importance for engineering applications. However, few reports exist on the high-pressure–temperature properties of the HfNbMoTaWV HEA system. Herein, we synthesized a NbMoTaW HEA using the vacuum arc melting method and measured its Hugoniot up to 143 GPa and ∼6200 K. A linear relationship [US = 2.61 (7) + 1.59 (5) UP] between the shock (US) and particle (UP) velocities was observed for UP > 0.7 km/s, suggesting that the NbMoTaW HEA is likely stable within the pressure–temperature range of the current study. Using the Debye–Mie–Grüneisen model and Birch–Murnaghan equation of state (EOS), we discussed the EOS of the NbMoTaW HEA. The bulk modulus (K0) and its pressure derivative (K0′) were determined to be 238 GPa and 3.3, respectively. We also found that the Hugoniot compression curve of the NbMoTaW HEA could be evaluated using the mixture rules with the Hugoniot data of the compositional elements.

Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition

Stress sensitivity and the elastic outer boundary (EOB) condition have a great effect on the analysis of the characteristics of the fluid flow in a reservoir. When researchers analyzed the characteristics of the fluid flow, they have considered the stress sensitivity and the EOB condition separately but have not considered them simultaneously. Therefore, errors are inevitable during the analysis of well testing. The main object of this work is to present a well-testing model for stress-sensitivity dual-porosity reservoir (DPR) with EOB to improve the accuracy of the analysis of well-testing data. To this end, in this paper, we established a well-testing model for the DPR, considering the stress sensitivity and the EOB simultaneously, and presented its semianalytical solution. On the basis of the consideration of the EOB condition and stress sensitivity of permeability (SSP), a seepage model for the DPR with the EOB is built using the continuity equation, motion equation, state equation, and interporosity flow equation between matrix and fracture, which considers the stress sensitivity, wellbore storage, and skin. To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. Applying the Laplace transformation, an analytical solution in the Laplace space is obtained, and curves of pressure and pressure derivative (PPD) are drawn by numerically inverting them. The model is verified by comparing it with the EOB without consideration of SSP and using case data. The sensitivity of parameters on the curves of PPD is analyzed. This work may be significant for evaluating more accurately the parameters of wells and reservoirs using well testing.

Analysis of pulse combustion processes and thermodynamic cycles in pulse combustors

This study explores the dynamic behavior of pulsating combustors during stable operation, examining pressure characteristics, flame dynamics, and thermodynamic cycles. Through analysis of pressure signal derivatives and high-speed photography, it unveils a distinctive counterclockwise thermodynamic cycle in these combustors, diverging from prior research. Crucial points in the combustion process, including zero-pressure points, valve timings, and flame ignition dynamics, were successfully identified. The research introduces a novel clockwise thermal cycle diagram based on ignition events and valve operations, providing real-time insights into combustion processes. Key findings include the identification of critical combustion process points, immediate flame ignition upon valve opening, and the introduction of an innovative thermal cycle diagram. The study's comprehensive approach, integrating pressure analysis, flame dynamics, and derivative curves, offers profound insights into the dynamics of pulsating combustors, furthering our understanding and providing avenues for optimization. Our comprehensive approach enhances the understanding of pulsating combustor dynamics and provides valuable insights for system improvement. The unconventional thermodynamic cycle underscores the novelty of our work. These findings are pivotal for enhancing combustion efficiency and reducing emissions, emphasizing the significance of further research and development in this field.

Structural and Thermodynamic Properties of Cu2ZnSnS4 Material: Theoretical Prediction

Abstract The present work aims to investigate the structural and thermodynamic properties of homogenous tetragonal Cu2ZnSnS4 (CZTS) absorber material in Kesterite phase using first-principle calculations based on density functional theory (DFT). This approach requires only knowledge of the atomic species and crystal structure to predict several physical properties of materials. The Quantum Espresso code within the Ultra Soft pseudopotentials (USPP) and the local density approximation (LDA) were used in the calculations. Equilibrium unit cell volumes, bulk modulus, as well as the pressure derivative of the bulk modulus are predicted. In addition, several thermodynamic properties, especially: the Debye’s vibrational energy, the vibrational free energy, the vibrational entropy, and the constant volume heat capacity at different temperatures T of Cu2ZnSnS4 material are calculated and discussed. Our study shows that the vibrational energy, the entropy and the constant volume heat capacity increase with increasing temperature, while the vibrational free energy decreases monotonously with the increase of temperature.

Impact of well interference on transient pressure behavior during underground gas storage: A comparative study

Underground natural gas storage (UGS) serves as an environmentally sustainable remedy for mitigating regional and temporal disparities in energy supply and demand. The phenomenon of substantial well interference and non-uniform pressure distributions in UGS, resulting from high injection and withdrawal rates, requires a comprehensive examination. This study presents an analytical model aimed at investigating the ramifications of well interference on transient pressure dynamics during UGS. Employing the Laplace transform method, an analytical framework for diverse wells within UGS is derived, with well interference effects being effectively incorporated through the application of the superposition principle. To validate the proposed analytical solutions under various scenarios, a commercial numerical simulator is employed. The analysis reveals that when an adjacent well is engaged in gas withdrawal, interference induces an initial rise in pressure derivative followed by a subsequent plateau. Conversely, during gas injection into an adjacent well, the pressure derivative curve exhibits a continuous decline, akin to situations characterized by constant pressure boundaries. Notably, the likelihood of interference with a target well is more pronounced when gas injection or production occurs in a vertical well as opposed to a horizontal one. Preliminary data from the Hutubi UGS in China, one of the largest projects of its kind, indicate cumulative gas injection and withdrawal volumes of 155.43 × 108 m3 and 130.81 × 108 m3, respectively, with a maximum storage capacity of 107 × 108 m3. Ultimately, the gas storage volume reaches 93.50% of the UGS's designated capacity. This substantial quantity of stored natural gas equates to the calorific value of 9.88 × 109 kg of crude oil or 1.29 × 1010 kg of coal. In comparison to conventional fossil fuels such as oil and coal, the utilization of natural gas in the Hutubi UGS results in a significant reduction of carbon dioxide emissions, amounting to 1.04 × 1010 kg and 1.38 × 1010 kg, respectively. This contribution advances the field by proposing an analytical model for the systematic analysis of well interference on pressure dynamics within the Hutubi UGS, thereby facilitating the transition from oil and coal to natural gas, a crucial step in the pursuit of cleaner and more sustainable energy production practises.

Physical properties of Be-based fluoroperovskite compounds XBeF3 (X = K, Rb): a first-principles study

In this study, we used the ab-initio computational tools as implemented in the CASTEP code to explore the effects of pressure on the structural, elastic, electronic, thermodynamic and optical properties of the fluoroperovskite compounds XBeF3 (X = K, Rb) based on Being. Exchange–correlation interactions were modeled using the GGA-PBEsol functional. The ground state of the title materials was characterized by calculating the optimized lattice parameter, the bulk modulus B and its pressure derivative, and the Goldsmith tolerance factor. These materials exhibit structural stability in the cubic structure even when subjected to significant pressure levels, extending up to 18 GPa. The analysis of numerical assessments of single-crystal elastic constants (Cij ), polycrystalline elastic moduli, namely shear modulus (G), Young’s modulus and Poisson’s ratio, as well as the anisotropy factor (A), highlights the mechanical stability, elastic anisotropy and ductility of considered the compounds. The thermodynamic properties of these materials were studied through the Debye quasi-harmonic model. Analysis of energy band structures and density of states spectra shows that XBeF3 (X = K, Rb) is insulating in nature, with band gaps of 7.99 and 7.26 eV, respectively. Additionally, we calculated the linear optical spectra, including dielectric function, absorption coefficient, refractive index, optical reflectivity, and energy loss function. Based on the results obtained, these materials could be used in various optoelectronic devices operating in the UV spectrum and in energy storage devices.

Pressure effect on some physical properties of calcium oxide material

The present investigation aims to study the high-pressure dependence up to 65.2GPa of the bulk modulus, Vickers hardness, mass density, Grüneisen parameter, Debye temperature, and average acoustic velocity for calcium oxide (CaO) binary compound. First, we calculated the normal conditions of Vickers hardness, which is equal to 14.8GPa, and then we employed the high-pressure Mukhanov's et al (2009) model to determine the high-pressure effect on the Vickers hardness. Using this model, commonly the hardness increases with increased pressure. Our data show that the bulk modulus, the mass density, the Debye temperature, and the average acoustic wave speed of CaO material increase gradually with increasing pressure, while both the first order pressure derivative of the bulk modulus and the Grüneisen parameter decrease with enhanced pressure up to 65.2GPa. Furthermore, we determined the normal conditions fracture toughness of CaO material; it is around 1.46MPa.m1/2, which is slightly higher than those of Si and GaP semiconducting materials.

Pressure driven polymorphic transitions in nanocrystalline Lu2O3, Tm2O3 and Eu2O3

The crystallite size of the materials considerably influences the material properties, including their compressibility and resistance to external forces and the stability of the crystalline structure; a corresponding study for which, so far, has been limited for the important class of nanocrystalline Rare Earth Sesquioxides (REOs). In the present study, we report the crystallographic structural transitions in nanocrystalline Rare Earth Oxides (REOs) under the influence of pressure, investigated via high-energy X-Ray Diffraction (XRD) measurements. The study has been carried out on three of the REOs, namely Lutetium oxide (Lu2O3), Thulium oxide (Tm2O3) and Europium oxide (Eu2O3) up to the pressures of 33, 22 and 11 GPa, respectively. The diffraction data of Lu2O3 and Tm2O3 suggests the occurrence of irreversible structural transitions from cubic to monoclinic phase, while Eu2O3 showed a transition from the cubic to hexagonal phase. The transitions were found to be accompanied by a collapse in the volume and the resulting Pressure–Volume (P–V) graphs are fitted with the 3rd order Birch-Murnaghan (BM) equation of state (EOS) to estimate the bulk moduli and their pressure derivatives. Our study establishes a qualitative relationship between the crystallite size and various material properties such as the lattice parameters, transition pressure, bulk modulus etc., and strengthens the knowledge regarding the behaviour of this technologically important class of materials.

Variation of Bulk Modulus, Its First Pressure Derivative, and Thermal Expansion Coefficient with Applied High Hydrostatic Pressure

Throughout this work, the equations of variation of the isothermal bulk modulus, its first pressure derivative, and the volumetric thermal expansion coefficient as a function of pressure were derived based on the Birch–Murnaghan equation of state (B–M EOS). The bulk modulus and its first derivative at ambient temperature for nine elements were extracted by fitting the published experimental pressure–volume data to B–M EOS, and the results were compared with other published researches, and there was a good agreement. Moreover, those extracted values were used to study the variation of the isothermal bulk modulus, its first pressure derivative, and the isothermal coefficient of thermal expansion as a function of the applied hydrostatic pressure using the equations that were derived from this work.

Effective Relative Permeabilities Based on Momentum Equations with Brinkman Terms and Viscous Coupling

Summary The relative permeability expresses the mobility reduction factor when a fluid flows through a porous medium in the presence of another fluid and appears in Darcy’s law for multiphase flow. In this work, we replace Darcy’s law with more general momentum equations accounting for fluid-rock interaction (flow resistance), fluid-fluid interaction (drag), and Brinkman terms responding to gradients in fluid interstitial velocities. By coupling the momentum equations with phase transport equations, we study two important flow processes—forced imbibition (coreflooding) and countercurrent spontaneous imbibition. In the former, a constant water injection rate is applied and capillary forces are neglected, while in the latter, capillary forces drive the process and the total flux is zero. Our aim is to understand what relative permeabilities result from these systems and flow configurations. From previous work, when using momentum equations without Brinkman terms, unique saturation-dependent relative permeabilities are obtained for the two flow modes that depend on the flow mode. Now, with Brinkman terms included, the relative permeabilities depend on local spatial derivatives of interstitial velocity and pressure. Local relative permeabilities are calculated for both phases utilizing the ratio of phase Darcy velocity and phase pressure gradient. In addition, we use the Johnson-Bossler-Naumann (JBN) method for forced imbibition (with data simulated under the assumption of negligible capillary end effects) to calculate interpreted relative permeabilities from pressure drop and average saturation. Both flow setups are parameterized with literature data, and sensitivity analysis is performed. During coreflooding, Brinkman terms give a flatter saturation profile and higher front saturation. The saturation profile shape changes with time. Local water relative permeabilities are reduced, while they are slightly raised for oil. The saturation range where relative permeabilities can be evaluated locally is raised and made narrower with increased Brinkman terms. JBN relative permeabilities deviate from the local values: The trends in curves and saturation range are the same but more pronounced as they incorporate average measurements, including the strong impact at the inlet. Brinkman effects vanish after sufficient distance traveled, resulting in the unique saturation functions as a limit. Unsteady state (USS) relative permeabilities (based on transient data from single-phase injection) differ from steady-state (SS) relative permeabilities (based on SS data from coinjection of two fluids) because the Brinkman terms are zero at SS. During spontaneous imbibition, the higher effect from the Brinkman terms caused oil relative permeabilities to decrease at low water saturations and slightly increase at high saturations, while water relative permeability was only slightly reduced. The net effect was a delay in the imbibition profile. Local relative permeabilities approached the unique saturation functions without Brinkman terms deeper in the system because phase velocities (involved in the Brinkman terms) decreased with distance. In both systems, scaling and simulations demonstrate that the relative change in relative permeabilities due to Brinkman terms increases with the Brinkman coefficient, permeability, and inverse squared distance from the inlet.

Anomalous thermal structures of subduction zones revealed by thermal properties of clinochlore at high temperature and pressure

Clinochlore is a major hydrous mineral in subduction zones, and its thermophysical properties at high temperature and pressure are critical to the thermal structures of subduction zones. Here, we used the pulse heating method to measure thermal diffusivity and thermal conductivity of clinochlore at 0.5−4.0 GPa and 298−1373 K. Our results indicate that upon heating, thermal diffusivity and thermal conductivity decrease from ∼9.6 × 10−7 m2 s−1 to 4.3 × 10−7 m2 s−1 and from ∼3.5 W m−1 K−1 to 1.9 W m−1 K−1, respectively, before dehydration, but this trend is reversed after dehydration. In general, the pressure derivatives for the thermal transport properties also decrease with temperature before dehydration. Lattice heat transfer is the dominant mechanism before dehydration, but fluid is involved after dehydration. Using our experimental data, we simulated the temperature distribution of subducting slabs containing clinochlore at volume fractions of 0%, 10%, 20%, 50%, and 100%. Our simulations showed that the heat insulation effect caused by the presence of clinochlore could result in an increase in temperature by 30−60 K for the upper part of the subducting slab.