Hard-spin mean-field theory for the lattice gas: a refined pedagogical approach to phase transitions in three dimensions

Ideal gases adhere to the principles of the kinetic theory of gases. To illustrate their non-ideal characteristics, we derive the equation of state for the lattice gas model defined on a cubic lattice through the application of mean field theory. This distinctive equation incorporates a logarithmic term in volume that closely resembles the Saha-Basu equation of state. We investigate the critical points and critical exponents associated with the continuous phase transition relevant to this equation. Furthermore, we compare the universal aspect of the law of corresponding states with other non-ideal equations of state. In addition, the equations related to the critical constants, including Boyle’s temperature, the Joule–Thomson coefficient, inversion temperature, and heat capacity relationships, have been derived from the equation of state. We are confident that this research will be beneficial for both undergraduate and postgraduate students specializing in statistical mechanics.

Computer simulation and equation of state study of the Boyle and inversion temperature of simple fluids

This work deals with a theoretically and technologically important thermodynamic study on the correlation of the Boyle temperature , the inversion temperature and the acentric factor of cesium, rubidium and potassium. This correlation is established through a generalized van der Waals equation of state. The obtained correlation fits the experimental data for the Boyle temperature , the inversion temperature and the acentric factor of cesium, rubidium and potassium. It has also been established that cesium, rubidium and potassium obey the single-parameter law of corresponding states. It is shown that the ratio of the inversion temperature and the Boyle temperature or the acentric factor can be used as the thermodynamic similarity parameter for cesium, rubidium and potassium.

Hard spin mean field theory for an Ising model with pair and three site interactions

The Saha–Basu equation of state, which has attracted little attention from the scientific community, is here revisited. This equation has been derived using an approach that is different from the original approach. Expressions for some physical parameters, such as critical constants, Boyle’s temperature, critical coefficients etc, have been derived and the equation has been expressed in terms of reduced parameters. Amagat’s curves have been explained using the virial form of the equation. Some thermodynamic quantities, such as the Joule–Thomson coefficient, inversion temperature and heat capacity relations, have been arrived at from this equation of state. The comparison has been made with other related equations of state.

In this paper, we study the thermodynamic of the charged AdS black holes in Rastall gravity. Firstly, the thermodynamic quantities of the charged AdS black holes in Rastall gravity are reviewed and the state equation of this black hole is obtained. Then, we investigate the [Formula: see text] critical and the Joule–Thomson expansion of the charged AdS black holes in Rastall gravity in which the critical temperature and the critical exponents are obtained. In addition, we get the inversion temperature and plot the isenthalpic and inversion curves in the [Formula: see text] plane, and also determine the cooling-heating regions of this black hole through the Joule–Thomson expansion. Finally, we investigate the ratio between the minimum inversion and critical temperatures, and find that the Rastall constant [Formula: see text] does not affect of this ratio.

The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.

Inversion temperatures and pressures for cryogenic gases and their mixtures

Depleted gas fields offer advantages for CO2 storage, including proven containment, extensive existing data, and readily available infrastructure. However, there is a major challenge because the Joule-Thomson (JT) effect can cause significant formation cooling, resulting in e.g. hydrate formation and undesired thermal stresses. For all cases of planned CO2 injection, it is important to carry out geomechanical fault stability analyses (e.g. as part of a Seismic Hazard Assessment, SHA) to estimate the potential impact of depletion, re-pressurization and cooling on reactivation of nearby faults. Here we present a fault stability study for CO2 injection into a depleted low-temperature gas field in the Black Sea. CO2 injection is modeled by 1D radial fine-grid reservoir simulations using the Span-Wagner equation-of-state (EoS), including phase transition, and with thermal diffusion from the reservoir and cap- and baserock. Resulting temperature and pressure distributions are used within a Green's function approach to compute stress changes at nearby faults. CO2 injection in the gas phase can involve turbulence effects around the injector potentially having a significant impact on the JT effect. In order to circumvent uncertainties related to the high number of different models for the turbulence factor in literature, we estimated turbulence effects during CO2 injection from the results of Flow-After-Flow gas production tests during the depletion phase. The above approach was applied to conduct sensitivities of fault stability, hydrate formation risk, and CO2 storage capacity as a function of relevant parameters such as injection rate, injection temperature, reservoir temperature, etc. The results show that for depleted reservoirs, reservoir temperature is an important parameter determining total CO2 storage capacity. Furthermore, the (adiabatic) JT effect can be significantly reduced by thermal diffusion within the reservoir and to cap- and baserock. It should be noted that, contrary to the analogous case of cold water injection, for CO2 injection thermal diffusion within the reservoir can often not be neglected. This is contrary to (water-injection-based) general consensus. When reservoir pressure increases with increasing cumulative CO2 injected, the JT effect is reduced. However, low-temperature "echo's" can remain deep in the reservoir, potentially contributing to nearby fault reactivation. CO2 storage into a depleted gas reservoir often will require initial injection in the gas phase. We demonstrate several scenarios with pre-heating and/or initial injection ramp-up to prevent excessive cooling of the reservoir.

We define thermodynamic pressure P by work density W as the conjugate quantity of thermodynamic volume V from field equation. We derive the equations of state P=P(V, T) for the Friedmann–Robertson–Walker (FRW) universe in Einstein gravity and a modified gravity respectively. We find that the equation of state from Einstein gravity shows no P-V phase transition, while the equation of state from the modified gravity does, where the critical exponents are the same as those in mean field theory.

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordstr\"om anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as $p_q=\omega\rho_q$ in which $-1<\omega<-\frac{1}{3}.$ Our calculations are restricted to ansatz: $\omega=-1$ (the cosmological constant regime) and $\omega=-\frac{2}{3}$ (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature $T_i$ of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure $P_i.$ Position of the inverse point $\{T_i,P_i\}$ is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point verse different numerical values of the mass $M$ and the charge $Q$ of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for $M>Q$ in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point $\{T_i,P_i\}$ position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge $Q$. In other words the quintessence dark energy dose not affects on position of the inverse point when the AdS RN black hole takes on small charges.

The Joule-Thomson (JT) effect will occur when the gas flows through the components of filters, valves, orifices and end faces in the system of the dry gas seal, which may cause the temperature of the seal gas to decrease, and even the emergence of liquid condensation. Generally, the Joule-Thomson effect is reflected by the Joule-Thomson coefficient. As to the hydrogen, nitrogen, carbon dioxide and air, which are often met in the dry gas seal, the corresponding Joule-Thomson (JT) coefficients were calculated by four classical equations of state (EOS) of VDW, RK, SRK and PR, which are compared with the experimental data in the literature. The results show that the JT coefficients calculated by RK equation are most close to the experimental data in the literature, whose relative error is lowest and less than 4%. When the JT effect of real gas in the dry gas seal is analyzed, the RK equation of state is recommend.

Consistent phase-change modeling for CO2-based heat mining operation

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A practical and field-tested guideline for CO2 mixture modeling, mainly focused on injection wells but applicable to pipelines/flowlines is presented that describes the phase behavior, transport and thermal properties of CO2 mixtures for the optimal and economical Carbon Capture and Storage (CCS) design applications. Actual operating field data sets of flowing bottomhole pressure/temperature and wellhead pressure/temperature for 600 hours of stable operations are collected and used for calibration from seven CO2 injectors in the Gorgon project, Australia. Four Equations of State (Peng-Robinson 78A, CPA Infochem, GERG 2008 and EoS-CG) which are reported as conventionally used for CO2 modeling are tested and validated using commercial transient software. The study investigates the contributions from friction, hydrostatic, and acceleration terms in the estimation of pressure drop; overall heat transfer coefficient (conduction, convection, and radiation) and the Joule-Thomson coefficient in temperature estimation along the injection system. The results show that GERG-2008 and EoS-CG with a reasonable roughness factor (0.0018") give a good pressure match with the field measured pressures, while PR and CPA-Infochem show some discrepancies, even with a very small roughness factor (0.00039"). Analysis indicates that for CO2 mixture injection of 0.2 ~ 0.6 MTA (million tons per annum) in 4.5" tubing, the hydrostatic pressure drop is the main contributor to total pressure drop, while the frictional pressure drop contributes only 2 ~ 4%. All the above EOS's show good temperature matches (approximately 1 ~ 2 °C difference average) with field data when estimating overall heat transfer coefficient (U) from material heat properties and Joule-Thompson (JT) effect from the fluid PVT file – CPA Infochem calculates the most accurate temperature followed by PR, GERG, and EoS-CG in that order. The JT effect contributes approximately 70% of the total temperature change while the remaining 30% temperature change is due to heat transfer by conduction, convection and radiation. The JT effect is also validated with actual data across the choke proving all four EoS's accurately calculate the JT effect. This paper includes a practical engineering guideline for modeling phase behavior, transport, and thermal properties of CO2 mixtures for field applications, which would be beneficial for production engineers, reservoir engineers, and facility engineers in the optimal and economical design and operation of CCS facilities.