An insight into the role of the association equations of states in gas hydrate modeling:a review

Encouraged by the wide spectrum of novel applications of gas hydrates,e.g.,energy recovery,gas separation,gas storage,gas transportation,water desalination,and hydrogen hydrate as a green energy resource,as well as CO2 capturing,many scientists have focused their attention on investigating this important phenomenon.Of course,from an engineering viewpoint,the mathematical modeling of gas hydrates is of paramount importance,as anticipation of gas hydrate stability conditions is effective in the design and control of industrial processes.Overall,the thermodynamic modeling of gas hydrate can be tackled as an equilibration of three phases,i.e.,liquid,gas,and solid hydrate.The inseparable component in all hydrate systems,water,is highly polar and non-ideal,necessitating the use of more advanced equation of states(EoSs) that take into account more intermolecular forces for thermodynamic modeling of these systems.Motivated by the ever-increasing number of publications on this topic,this study aims to review the application of associating EoSs for the thermodynamic modeling of gas hydrates.Three most important hydrate-based models available in the literature including the van der Waals-Platteeuw(vdW-P) model,Chen-Guo model,and Klauda-Sandler model coupled with and SAFT EoSs were investigated and compared with cubic EoSs.It was concluded that the CPA and SAFT EoSs gave very accurate results for hydrate systems as they take into account the association interactions,which are very crucial in gas hydrate systems in which water,methanol,glycols,and other types of associating compounds are available.Moreover,it was concluded that the CPA EoS is easier to use than the SAFT-type EoSs and our suggestion for the gas hydrate systems is the CPA EoS.

New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

Extension of LCVM-type mixing rule to three-parameter equations of state for vapor-liquid equilibria of mixtures

In this paper, the LCVM mixing rule is extended to the multi-parameter equations of state by combining infi- nite-pressure and zero-pressure mixing rule models. The new LCVM-type mixing rule, coupled with Patel-Teja equation of state (EOS) is applied for vapor-liquid equilibria of different polar and non-polar systems in which the NRTL activity coefficient model is used to calculate the excess Gibbs free energy. The tested results agree well with existing experimental data within a wide range of temperatures and pressures. In comparison with the Van der Waals mixing rule, the new mixing rule gives much better corre- lations for the vapor-liquid equilibria of non-polar and polar systems.

Simulated Equations of State of MgSiO3 Perovskite

The equation of state of MgSiO3 perovskite under high pressure and high temperature is simulated using the molecular dynamics method. It was found that the molecular dynamics simulation is very successful in accurately reproducing the measured molar volumes of MgSiO3 perovskite over a wide range of temperatures and pressures. The simulated equation of state of MgSiO3 perovskite matched experimental data at up to 140GPa at 300K, as well as the fitting data of others and results from the first-principles simulation based on the local density approximation. The simulated equations of state of MgSiO3 perovskite at higher temperatures and higher pressures also correspond to the other calculations. In addition, the volume compression data of MgSiO3 perovskite is simulated up to 120 GPa at 300, 900, 2000 and 3000 K, respectively.

Evaluation of attraction terms in equations of state on the prediction of solubility of some biomolecules in supercritical carbon dioxide

In the present work, effect of the attraction terms of four recently modified Peng-Robinson （MPR） equations of state on the prediction of solubility of caffeine, cholesterol, uracil and erythromycin was studied. The attraction terms of two of these equations are linear relative to the acentric factor and for the other two are exponential. It is found that the later show less deviation. Also interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation （%AARD） in each calculation is displayed.

Generalization of vdW Type of Equations of State

The importance of equations of state (EOS) has brought about the proliferation of hundreds of EOS. Nearly all prevailing cubic EOS could be regarded as the results of reforming the original vdW EOS. However, the accuracy of the vdW EOS is so low. In view of this, a new general equation is proposed that could be used to value or compare vdW type of EOS, and consequently develop a better vdW type of EOS.

A New Approach to Investigation of vdW Type of Equations of State

A new approach to the investigation of vdW type of equations of state (EOS) is developed by embedding a vapor pressure equation and a saturated liquid volume equation into vdW type EOS, which results in a new function AS(T). The AS(T) possesses the properties of an attractive parameter A(T), and if an EOS is accurate in the whole PVT space, then its numerical value equals A(T). As a useful tool for investigating EOS, the As(T) has been used to make comparisons among RKS, PRSVII, PT and ALS EOS, and to indicate where the shortcomings of the EOS are coming from. Based on the AS(T), a possible way to develop a real predictive equation of state is also suggested.

How far away are accurate equations of state determinations? Some issues on pressure scales and non-hydrostaticity in diamond anvil cells

The equations of state(EOSs)of materials are the cornerstone of condensed matter physics,material science,and geophysics.However,acquiring an accurate EOS in diamond anvil cell(DAC)experiments continues to prove problematic because the current lack of an accurate pressure scale with clarified sources of uncertainty makes it difficult to determine a precise pressure value at high pressure,and nonhydrostaticity affects both the volume and pressure determination.This study will discuss the advantages and drawbacks of various pressure scales,and propose an absolute pressure scale and correction methods for the effects of non-hydrostaticity.At the end of this paper,we analyze the accuracy of the determined EOS in the DAC experiments we can achieve to date.

Influence of Different Equations of State on Simulation Results of Supercritical CO_(2) Centrifugal Compressor

Supercritical CO_(2)(SCO_(2))Brayton cycle has received more and more attention in the field of power generation due to its high cycle efficiency and compact structure.SCO_(2) compressor is the core component of the cycle,and the improvement of its performance is the key to improving the efficiency of the entire cycle.However,the operation of the SCO_(2) compressor near the critical point has brought many design and operation problems.Based on the Reynolds Averaged Navier-Stokes(RANS)model,the performance and flow field of SCO_(2) centrifugal compressors based on different CO_(2) working fluid models are numerically investigated in this paper.The stability and convergence of the compressor steady-state simulation are also discussed.The results show that the fluid based on the Span-Wanger(SW)equation can obtain a more ideal compressor performance curve and capture a more accurate flow field structure,while the CO_(2) ideal gas is not suitable for the calculation of SCO_(2) centrifugal compressors.But its flow field can be used as the initial flow field for numerical calculation of centrifugal compressor based on CO_(2) real gas.

Implications of neutron skin measurements on Skyrme equations of state

The recent measurements of neutron skins via parity violation in electron scattering have extracted an abnormally thick neutron skin for 208 Pb,which has significant consequences in nuclear equation of state(EoS)and neutron star observations.In this study,we perform optimizations of extended Skyrme forces in a consistent manner by including neutron skin thicknesses from PREX-Ⅱand CREX experiments and investigate nuclear EoSs and neutron stars in the GW170817 event By varying the fitting weights of neutron skins,several new Skyrme parameterizations are obtained.Our results show the competition in the fitting procedure to simultaneously describe neutron skins,other properties of finite nuclei,and neutron star observations.The prospects of resolving neutron skin issues are also discussed.

Experimental study on the size effect on the equation of state of concretes under shock loading

Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.

Semiempirical equations of state of H_(2)O/CO_(2) binary mixtures in graphite nanoslits

The existence of confining walls limits the prediction accuracy of nanoconfined fluids using macroscopic equations of state(EOSs);moreover,appropriate EOSs for multicomponent mixture fluids in nanoconfined spaces are missing.Here,we derive the EOS of multicomponent mixture fluids confined in nanospaces at high temperatures and pressures,mainly considering the nanoconfinement effect and the competitive adsorption effect between different components.Then,the EOSs are validated through comparison with the molecular dynamics-simulated Pv T data of CO_(2)/H_(2)O mixtures in graphite nanoslits.To consider the above effects,we derive two EOSs via two modeling methods:EOS I is obtained through modification of the actual component occupation volume in the Peng-Robinson equation of state(PR EOS)by fitting the binary component interaction coefficient and the number of adsorbed molecules according to a selectivity coefficient,while EOS II is obtained by considering the decreased pressure of the fluids in PR EOS by adding an attractive term between components and walls.With the simulation results as a benchmark,the two EOSs exhibited good prediction accuracies under low CO_(2) concentrations,and generally,EOS II was more accurate than EOS I.This study fills the gap in the EOSs of nanoconfined mixture fluids,and the obtained equations can help to further describe the thermodynamic properties of confined mixture fluids.

Equations of state for aqueous solutions under mantle conditions

With unique physical and chemical properties, aqueous solutions in the mantle may play important roles for a number of geochemical and geodynamical processes. However, since experimental data available are very limited, people still know little about the aqueous solutions and their interactions with surrounding rocks and melts. From the perspective of thermodynamics, equation of state(EOS) is the key to push forward the modeling of aqueous solutions. Nevertheless, up to now accurate EOSs suitable for the mantle conditions are still in shortage. With discussions over several recognized EOSs, we summarize several ways to enhance the predictability of EOS: utilizing high quality data from molecular simulations, choosing functions with sound physical background, and improving the regression procedures for the empirical parameters. In the meantime, we find that the ion-bearing systems are still the focus of challenges in this area. New developments of experiments and computer simulations effectively deal with these challenges and in-depth understandings of aqueous solutions in the mantle are expected in the near future.

Hydration effects on crystal structures and equations of state for silicate minerals in the subducting slabs and mantle transition zone

There are potentially huge amounts of water stored in Earth's mantle, and the water solubilities in the silicate minerals range from tens to thousands of part per minion(ppm, part per million). Exploring water in the mantle has attracted much attention from the societies of mineralogy and geophysics in recent years. In the subducting slab, serpentine breaks down at high temperature, generating a series of dense hydrous magnesium silicate(DHMS) phases, such as phase A, chondrodite, clinohumite, etc. These phases may serve as carriers of water as hydroxyl into the upper mantle and the mantle transition zone(MTZ). On the other hand, wadsleyite and ringwoodite, polymorphs of olivine, are most the abundant minerals in the MTZ, and able to absorb significant amount of water(up to about 3 wt.% H_2O). Hence, the MTZ becomes a very important layer for water storage in the mantle, and hydration plays important roles in physics and chemistry of the MTZ. In this paper, we will discuss two aspects of hydrous silicate minerals:(1) crystal structures and(2) equations of state(Eo Ss).

Hydration Effect on Equations of State for Minerals in the Peridotite System:Implication for Geotherms in the Mantle

Water in the deep Earth’s interior has important and profound impacts on the geodynamical properties at high-temperature(T)and high-pressure(P)conditions.A series of dense hydrous Mg-silicate(DHMS)phases are generated from dehydration of serpentines in subduction slabs below the lithosphere,including phase A,chondrodite,clinohumite,phase E,superhydrous phase B and phase D.On the other hand,olivine and its high-P polymorphs of wadsleyite and ringwoodite are dominant nominally anhydrous minerals(NAMs)in the upper mantle and transition zone,which could contain significant amount of water in the forms of hydroxyl group(OH-)defects.The water solubilities in wadsleyite and ringwoodite are up to about 3 weight percent(wt.%),making the transition zone a most important layer for water storage in the mantle.Hydration can significantly affect the pressure-volumetemperature equations of state(P-V-T EOSs)for the DHMS and NAM phases,including the thermal expansivities and isothermal bulk moduli.In this work,we collected the reported datasets for the DHMS and NAM phases,and reconstruct internally consistent EOSs.Next,we further evaluated the thermodynamic Grüneisen parameters,which are fundamental for constraining the temperature distribution in an isentropic process,such as mantle convection.The adiabatic temperature profiles are computed for these minerals in the geological settings of normal mantle and subduction zone,and our calculation indicates that temperature is the dominant factor in determining the gradient of a geotherm,rather than the mineralogical composition.

LOCV calculation of the equations of state and properties of rapidly rotating neutron stars

In this paper, we have investigated the structural properties of rotating neutron stars using the numerical RNS code and equations of state which have been calculated within the lowest order constrained variational（LOCV）approach. In order to calculate the equation of state of nuclear matter, we have used UV（14） ＋TNI and AV（18） potentials.We have computed the maximum mass of the neutron star and the corresponding equatorial radius at different angular velocities. We have also computed the structural properties of Keplerian rotating neutron stars for the maximum mass configuration, MK, RK, fK and jmax.

CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES

A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.

GC-MCSPT-A MODIFIED HARD-SPHERE THREE-PARAMETER EQUATION OF STATE WITH GROUP MODEL FOR VLE PREDICTION

The mixing rule for a new group-contribution equation of state was proposed by combining the excess Gibbs energy model with the modified Hard-Sphere Three-Parameter Equation of State designated as the MCSPT equation. Low-and high-pressure vapor-liquid equilibria of 28 binary and 9 ternary systems containing strongly polar substances were predicted by using the interaction parameters of the original and modified UNIFAC model. Predicted results have shown that the proposed GO-MCSPT equation has an extensive applicability with satisfactory accuracy.

Thermodynamic study of fluid in terms of equation of state containing physical parameters

We introduce a simple condition for one mole fluid by considering the thermodynamics of molecules pointing towards the effective potential for the cluster. Efforts are made to estimate new physical parameter f in liquid state using the equation of state containing only two physical parameters such as the hard sphere diameter and binding energy. The temperature dependence of the structural properties and the thermodynamic behavior of the clusters are studied. Computations based on f predict the variation of numbers of particles at the contact point of the molecular cavity（radial distribution function）.From the thermodynamic profile of the fluid, the model results are discussed in terms of the cavity due to the closed surface along with suitable energy. The present calculation is based upon the sample thermodynamic data for n-hexanol, such as the ultrasonic wave, density, volume expansion coefficient, and ratio of specific heat in the liquid state, and it is consistent with the thermodynamic relations containing physical parameters such as size and energy. Since the data is restricted to n-hexanol, we avoid giving the physical meaning of f, which is the key parameter studied in the present work.

Basic quantities of the equation of state in isospin asymmetric nuclear matter

Based on the Hugenholtz-Van Hove theorem six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the single-nucleon potentials U_(0)(ρ,k)and U_(sym,i)(ρ,k).The six basic quantities include the quadratic symmetry energy E_(sym,2)(ρ),the quartic symmetry energy E_(sym,4)(ρ),their corresponding density slopes L_(2)(ρ)and L_(4)(ρ),and the incompressibility coefficients K_(2)(ρ)and K_(4)(ρ).By using four types of well-known effective nucleon-nucleon interaction models,namely the BGBD,MDI,Skyrme,and Gogny forces,the density-and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density q_(0)are explicitly given.The contributions to these quantities from t(k)U_(0)(ρ,k),and U_(sym,i)(ρ,k)are also analyzed at the norma nuclear density q_(0).It is clearly shown that the first-order asymmetric term U_(sym,1)(ρ,k)(also known as the symmetry potential in the Lane potential)plays a vital role in determining the density dependence of the quadratic symmetry energy E_(sym,2)(ρ).It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials(U_(sym,i)(ρ,k)with i>1)cannot be neglected in the calculations of the other five basic quantities Moreover,by analyzing the properties of asymmetric nuclear matter at the exact saturation densityρ_(sat)(δ),the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation K_(sat,2)=K_(2)(ρ_(0))-4.14L_(2)(ρ_(0))