Simulation modeling and experimental analysis of thermodynamic charge performance in a variable-mass thermodynamic system

The thermodynamic charge performance of a variable-mass thermodynamic system was investigated by the simulation modeling and experimental analysis. Three sets of experiments were conducted for various charge time and charge steam flow under three different control strategies of charge valve. Characteristic performance parameters from the average sub-cooled degree and the charging energy coefficient point of views were also defined to evaluate and predict the charge performance of system combined with the simulation model and experimental data. The results show that the average steam flow reflects the average sub-cooled degree qualitatively, while the charging energy coefficients of 74.6%, 69.9% and 100% relate to the end value of the average sub-cooled degree at 2.1, 2.9 and 0 respectively for the three sets of experiments. The mean and maximum deviations of the results predicted from those by experimental data are smaller than 6.8% and 10.8%, respectively. In conclusion, the decrease of average steam flow can effectively increase the charging energy coefficient in the same charge time condition and therefore improve the thermodynamic charge performance of system. While the increase of the charging energy coefficient by extending the charge time needs the consideration of the operating frequency for steam users.

Distribution of Equilibrium Free Energies in a Thermodynamic System with Broken Ergodicity

At low temperatures the configurational phase space of a macroscopic complex system （e.g., a spin-glass） of N - 10^23 interacting particles may split into an exponential number Ωs - exp（const × N） of ergodic sub-spaces （thermodynamic states）. It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponentied decay. But actually for some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by excited thermodynamic states. Based on this analysis, the re-weighting parameter y in the cavity approach of spin-glasses is easily understood. Depending on the free-energy distribution, the optimal y can either be equal to or be strictly less than the inverse temperature β.

On the Relationship between Statistical and Phenomenological Models of the Thermodynamic Systems

The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concepts of the statistical and phenomenological methods of describing the classical systems do not quite correlate with each other. Particularly, in these methods various caloric ideal gas equations of state are employed, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods. The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. Under such an approach, the statistical entropy is transformed into one of the forms of heat capacity. In its turn, the agreement of the methods under consideration in the question as to the dependence of the molecular distributions on the concentration of particles, apparently, will call for further refinement of the physical model of ideal gas and the techniques for its statistical description.

Thermodynamic theory of flotation for a complex multiphase solid -liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involve interactions among multiple components,the core problem facing flotation theory.Meanwhile,the combined use of multicomponent flotation reagents to improve mineral flotation has become an important issue in studies on the efficient use of refractory mineral resources.However,studying the flotation of complex solid–liquid systems is extremely difficult,and no systematic theory has been developed to date.In addition,the physical mechanism associated with combining reagents to improve the flotation effect has not been unified,which limits the development of flotation theory and the progress of flotation technology.In this study,we applied theoretical thermodynamics to a solid–liquid flotation system and used changes in the entropy and Gibbs free energy of the reagents adsorbed on the mineral surface to establish thermodynamic equilibrium equations that de-scribe interactions among various material components while also introducing adsorption equilibrium constants for the flotation reagents adsorbed on the mineral surface.The homogenization effect on the mineral surface in pulp solution was determined using the chemical potentials of the material components of the various mineral surfaces required to maintain balance.The flotation effect can be improved through synergy among multicomponent flotation reagents;its physical essence is the thermodynamic law that as the number of compon-ents of flotation reagents on the mineral surface increases,the surface adsorption entropy change increases,and the Gibbs free energy change of adsorption decreases.According to the results obtained using flotation thermodynamics theory,we established high-entropy flotation theory and a technical method in which increasing the types of flotation reagents adsorbed on the mineral surface,increasing the adsorption entropy change of the flotation reagents,decreasing the Gibbs free energy change,and improving the adsorption efficiency and stability of the flotation reagents improves refractory mineral flotation.

Thermodynamics of leaching roasted jarosite residue from zinc hydrometallurgy in NH_4Cl system

The thermal decomposition process ofjarosite residue and the solubility of various oxides presented in the decomposed residue in NH4C1-H20 system were studied. The results of heat decomposition ofjarosite residue show that the insoluble ZnFe2O4 phase in the residue can be decomposed at temperatures ranging from 500 ℃ to 650 ℃ for 1 h. The OLI Systems software was used to study the thermodynamics of the solubility of various metal oxides existing in the decomposed residue in NH4CI-H20 system. The results show that the solubility ofZnO, PbO, CdO, CuO and Ag20 is high, while the solubility of Fe203 is less than 10-4 mol/L in the pH range from 4.0 to 9.0. The calculated data are in accordance with the experimental results.

Thermodynamic assessment of Co-Cr-W ternary system

The Co-Cr-W ternary system was critically assessed using the CALPHAD technique.The solution phases including the liquid,γ-Co,ε-Co and α-Cr were described by a substitutional solution model.The σ,μ and R phases were described by three-sublattice models of（Co,W）8（Cr,W）4（Co,Cr,W）18,（Co,Cr,W）7W2（Co,Cr,W）4 and（Co,W）27（Cr,W）14（Co,Cr,W）12,respectively,in order to reproduce their homogeneity ranges.A self-consistent set of thermodynamic parameters for each phase was derived.The calculated isothermal sections at 1 000,1 200 and 1 350 ℃ are in good agreement with the experimental data.A eutectoid reaction of R μ＋γ-Co＋σ in this ternary system was predicted to occur at 1 022 ℃.

Thermodynamics analysis of LiFePO_4 pecipitation from Li-Fe(Ⅱ)-P-H_2O system at 298 K

Thermodynamics of the precipitation from Li-Fe（II）-P-H2O system at 298 K was investigated.The results demonstrate that LiFePO4 can be formed at room temperature under pH value of 0-11.3,and the impurities Li3PO4 and Fe（OH）2 will be yielded at pH value above 11.3 and 12.9,respectively.The optimum pH value for LiFePO4 precipitation is 8-10.5.Considering the low rate of phase transformation kinetics,metastable Li-Fe（II）-P-H2O system was also studied.The results indicate that equimolar ratio of co-precipitation precursor Fe3（PO4）2.8H2O and Li3PO4 cannot be obtained at the initial molar ratio 1：1：1 and 1：1：3 of Li：Fe：P.In contrast,equimolar ratio of the co-precipitation precursor can be yielded by adjusting the pH value to 7-9.2,matching the molar ratio 3：1：1 of Li：Fe：P,meaning that Li＋-excess is one of the essential conditions for LiFePO4 preparation by co-precipitation method.

Thermodynamics analysis of Ni^(2+)-C_2H_8N_2- C_2O_4^(2-)-H_2O system and preparation of Ni microfiber

According to the principles of simultaneous equilibrium and mass equilibrium, the thermodynamics model of the precipitation-coordination equilibrium of Ni2＋-C2H8N2- 2-2 4C O -H2O system was established, and calculation for the relationships between concentration of each substance in solution and parameters was carried out, including pH value, concentrations of ethylenediamine and oxalate by MATLAB program. The results show that Ni exists as Ni2＋and [Ni（C2O4）n]2-2n mainly at pH〈1 and pH=1-6, respectively. When pH〉6, the complex between Ni2＋and ethylenediamine is predominant. The precursor of Ni microfiber was prepared by an oxalate precipitation process using ethylenediamine as a coordination agent, and the role of ethylenediamine in the growth of the precursor fiber was discussed. The Ni microfiber can be obtained by a thermal decomposition-reduction process of the precursor in N2 and H2 mixed atmosphere. The diameters and aspect ratios of the obtained Ni microfibers are 0.2-1 μm and 20-30, respectively.

Thermodynamic optimization of Bi-Ni binary system

Based on the available experimental data,the Bi-Ni binary system was optimized thermodynamically by the CALPHAD method.The solution phases,including liquid,fcc_A1（Ni） and rhombohedral_A7（Bi）,were described as substitutional solution phases,of which the excess Gibbs energies were expressed with the Redlich-Kister polynomial.The intermetallic compound,BiNi,was modeled using three sublattices（Bi）（Ni,Va）（Ni,Va） considering its crystal structure（NiAs-type） and the compatibility of thermodynamic database in the multi-component systems,while Bi3Ni was treated as a stoichiometric compound.Finally,a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases in this binary system were obtained.The calculated results are in reasonable agreement with the reported experimental data.

Thermodynamics for chemical vapor synthesis of Nb nanopowder in NbCl_5-H_2-Ar system

Thermodynamics for chemical vapor synthesis （CVS） of Nb nanopowder in NbCl5-H2-Ar system was investigated by using FactSage software. The validation experiments were conducted to confirm the thermodynamics points. The results indicate that under the atmospheric pressure, the reduction approach from NbCl5（g） to Nb（s） is a stage-wise process with the formation of complex sub-chlorides, and is controllable at low hydrogen ratio （mole ratio of n（NbCl5）：n（H2）＆lt;1：180） and low temperature （＆lt;1050 ＆#176;C）. Furthermore, a reasonable amount of inert loading gas is favorable to increase the reduction ratio of NbCl5 and the powder yield. The as-synthesized Nb nanopowder with the homogeneous size of 30-50 nm and the powder yield of 85% （mass fraction） is obtained by the CVS process under n（NbCl5）：n（H2）：n（Ar）=1：120：1 and 950 ＆#176;C with the NbCl5 reduction rate of 96.1%.

Thermodynamic model of lead oxide activity in PbO-CaO-SiO_2-FeO-Fe_2O_3 slag system

According to the ion and molecule coexistence theory, a thermodynamic model of lead oxide activity in PbO-CaO-SiO2-FeO-Fe2O3 slag system was established at the temperature of 1273-1733 K. The activities of Pb O in slag were calculated, and their equal activity curves were plotted. The influences of slag basicity Q, iron oxide rate R and temperature T on activity NPb O and activity coefficient γPbO were also investigated. Results show that the calculated values of γPb O are in good agreement with the reported experimental data, showing that the model can wholly embody the slag structural characteristics. NPbO departures positively from Raoult values, and increases with increasing Pb O content in slag but changes little with T. γPbO increases with increasing Q, and goes through the maximum with increasing R for basic slag（Q0.3）. Results can be applied to the thermodynamic research and operational optimization of modern lead smelting technologies.

Parameter identification for volumetric heat capacity and thermal conductivity in a quasi-linear thermodynamic system of sea ice

This paper is intended to determine physical parameters describing volumetric heat capacity and thermal conductivity of sea ice in u quasi-linear thermodynamic system using field observations. The quasi-linear thermodynamic system of sea ice with unknown physical parameters is described, and the existence and uniqueness of its solution is proved. Then the physical parameters are taken as control variable, temperature devi- ations as objective function, and a parameter identification model is established. The existence of its optimal solution is discussed. To solve the identification model, a new algorithm containing genetic algorithm, Hooke- Jeeves algorithm and semi-implicit finite difference scheme is constructed. The physical parameters are calculated using the obser- vations measured at Nella Fjord around Zhongshan Station, Antarctic in CHINARE 2006. For comparability and consistency with other works, a new internationM standard named TEOS-10 is used. To examine the validity of the identified results, another sim- ulation for temperature profiles in different measurement period is operated. Numerical results show that better simulations of temperature distribution are possible with the identified parameters than EC1993. Therefore not only the identified parameters can be applied in sea ice modeling, but also this study can enrich and supplement observations of sea ice.

Thermodynamic re-assessment of Fe-Ti binary system

The Fe-Ti binary system was re-assessed using the CALPHAD method in order to improve the capability of being extrapolated to a ternary or higher-order system. Compared with previous assessments, the main focus was put on the thermodynamic description of the two intermetallic compounds Fe2Ti and FeTi. The C14_Laves phase Fe2Ti was described by the two-sublattice model, which is widely used at present. By checking the homogeneity range on the boundary of the ternary systems involving the binary, the phase boundary of this compound was further confirmed. The FeTi phase with a BCC_B2 crystal structure was treated as the ordered phase of the BCC_A2 phase and a unified Gibbs energy function was used to describe both the ordered and disordered phases. Reproduction of the specific heat capacities of these compounds was another aspect paid particular attention to. Comprehensive comparisons of the calculated and experimental results regarding the phase diagram and thermodynamic properties show a good agreement between them and prove the validity of the present thermodynamic description.

Thermodynamic assessment of Au-Pt system

The thermodynamic re-assessment of Au-Pt binary system was carried out by using the Calphad method and based on the recent experimental data. The Gibbs energies of face-centred cubic and liquid phases were described by a sub-regular solution model with the Redlich-Kister equation. Much effort was taken to reproduce the phase equilibrium results and thermodynamic properties of the solid phase, including the activity and mixing enthalpy. The constraint of the third law of thermodynamics was also considered in the assessment. According to the presently assessed results, the miscibility gap region in the Au-Pt system slightly shifts to the Au-rich side, and the critical !0oint of the miscibility gap is about 1200 ℃ and Au-56% Pt.

Thermodynamic assessment of Ni-Yb binary system

On the basis of the experimental data of phase equilibria and thermochemical properties available from literatures, a critical assessment for the Ni?Yb binary system was carried out using the CALPHAD (calculation of phase diagrams) method. The liquid phase is modeled as the associate model with the constituent species Ni, Yb and YbNi3, owing to the sharp change of the enthalpy of mixing of liquid phase at the composition of around 25% Yb (mole fraction). The terminal solid solutions FCC_A1 (Ni/Yb) and BCC_A2 (Yb) are described by the substitutional solution model with the Redlich?Kister polynomial. The intermetallic compounds, Yb2Ni17, YbNi5, YbNi3, YbNi2, α-YbNi and β-YbNi, are treated as strict stoichiometric compounds, since there are no noticeable homogeneity ranges reported for these compounds. A set of self-consistent thermodynamic parameters for the Ni?Yb binary system are obtained. According to the presently assessed results, the thermochemical properties and the phase boundary data can be well reproduced.

Thermodynamic modeling and phase diagram prediction of salt lake brine systems.Ⅰ. Aqueous Mg^2+–Ca^2+–Cl^- binary and ternary systems

Salt lake brine is a complex salt-water system under natural environment.Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution,the multi-temperature characteristics and predictability are still the goals of model development.In this study,a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements:(1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range;(2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients,the liquid parameters,which associated with Gibbs energy,enthalpy,and heat capacity contribution;and(3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range.Together the activity coefficient model,property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl2-CaCl2-H2 O binary and ternary systems,and it shows excellent agreement with the literature data for the ternary and binary systems.The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-idealitv system,and the ability to extrapolate the temperature.

Thermodynamic database development—modeling and phase diagram calculations in oxide systems

The databases of the FactSage thermodynamic computer system have been under development for 30 years. These databases contain critically evaluated and opthnized data for thousands of compounds and hundreds of multicomponent solutions of solid and liquid metals, oxides, salts, sulfides, etc. The databases are automatically accessed by user-friendly software that calculates complex multiphase equilibria in large multicomponent systems for a wide variety of possible input/output constraints. The databases for solutions have been developed by critical evaluation/optimization of all available phase equilibrium and thermodynamic data. The databases contain parameters of models specifically developed for different types of solutions involving sublattices, ordering, etc. Through the optimization process, model parameters are found which reproduce all thermodynamic and phase equilibrium data within experimental error limits and permit extrapolation into regions of tempea＇ature and composition where data are unavailable. The present article focuses on the databases for solid and liquid oxide phases involving 25 elements. A short review of the available databases is presented along with the models used for the molten slag and the solid solutions such as spinel, pyroxene, olivine, monoxide, corundum, etc. The critical evaluation/optimization procedure is outlined using examples from the Al203-SiO2-CaO-FeO-Fe2O3 system. Sample calculations are presented in which the oxide databases are used in conjunction with the FactSage databases for metallic and other phases. In particular, the use of the FactSage module for the calculation of multicomponent phase diagrams is illustrated.

Entransy analyses of heat–work conversion systems with inner irreversible thermodynamic cycles

In this paper, we try to use the entransy theory to analyze the heat–work conversion systems with inner irreversible thermodynamic cycles. First, the inner irreversible thermodynamic cycles are analyzed. The influences of different inner irreversible factors on entransy loss are discussed. We find that the concept of entransy loss can be used to analyze the inner irreversible thermodynamic cycles. Then, we analyze the common heat–work conversion systems with inner irreversible thermodynamic cycles. As an example, the heat–work conversion system in which the working fluid of the thermodynamic cycles is heated and cooled by streams is analyzed. Our analyses show that larger entransy loss leads to larger output work when the total heat flow from the high temperature heat source and the corresponding equivalent temperature are fixed.Some numerical cases are presented, and the results verify the theoretical analyses. On the other hand, it is also found that larger entransy loss does not always lead to larger output work when the preconditions are not satisfied.

Thermodynamic modeling and phase diagram prediction of salt lake brine systemsⅡ.Aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems

It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high concentration.The essential subsystem of sulfate type brine,aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems across a temperature range from 250 K to 643 K are investigated with the improved comprehensive thermodynamic model.Liquid parameters(Δg_(IJ),Δh_(IJ),and ΔC_(p,IJ))associated with the contributions of Gibbs energy,enthalpy,and heat capacity to the binary interaction parameters,i.e.the temperature coefficients of eNRTL parameters formulated with a Gibbs Helmholtz expression,are determined via multi-objective optimization method.The solid constantsΔ_(f)G_(k)°^((298.15))andΔ_(f)H_(k)°^((298.15))of11 solid species occurred in the quaternary system are rebuilt from multi-temperature solubilities.The modeling results show the accurate representation of(1)solution properties and binary phase diagram at temperature ranges from eutectic points to 643 K;(2)isothermal phase diagrams for Li_(2)SO_(4)-Na_(2)SO_(4)-H_(2)O,Li_(2)SO_(4)-K_(2)SO_(4)-H_(2)O and Na_(2)SO_(4)-K_(2)SO_(4)-H_(2)O ternary systems.The predicted results of complete structure and polythermal phase diagram of ternary systems and the isothermal phase diagrams of quaternary system excellently match with the experimental data.

Thermodynamic analysis and simulation for gas baffle entrance collimator of EAST-NBI system based on thermo-fluid coupled method

The world's first full Experimental Advanced Superconducting Tokamak(EAST) is designed with the auxiliary heating method of neutral beam injection(NBI)system. Beam collimators are arranged on both sides of the beam channel for absorbing the divergence beam during the beam transmission process in the EAST-NBI system.The gas baffle entrance collimator(GBEC) is a typical high-heat-flux component located at the entrance of gas baffle. An efficient and accurate analysis of its thermodynamic performance is of great significance to explore the working limit and to ensure safe operation of the system under a high-parameter steady-state condition. Based on the thermo-fluid coupled method, thermodynamic analysis and simulation of GBEC is performed to get the working states and corresponding operating limits at different beam extraction conditions. This study provides a theoretical guidance for the next step to achieve long pulse with highpower experimental operation and has an important reference to ensure the safe operation of the system.