The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The ...The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The experimental findings indicate a positive correlation between the solubility of Reb A(FormⅡ)and both the temperature and the methanol/ethanol content in the solvent system.To describe the solubility data,six distinct models were employed:the modified Apelblat equation,theλh model,the combined nearly ideal binary solvent/Redlich—Kister(CNIBS/R—K)model,the van't HoffJouyban-Acree(VJA)model,the Apelblat-Jouyban-Acree(AJA)model,and the non-random two-liquid(NRTL)model.The combined nearly ideal binary solvent/Redlich—Kister model exhibited the most precise fit for solubility in methanol+ethyl acetate mixtures,reflected by an average relative deviation(ARD)of 0.0011 and a root mean square deviation(RMSD)of 12×10^(-7).Conversely,for ethanol+ethyl acetate mixtures,the modified Apelblat equation provided a superior correlation(ARD=0.0014,RMSD=4×10^(-7)).Furthermore,thermodynamic parameters associated with the dissolution of Reb A(FormⅡ),including enthalpy,entropy,and the Gibbs energy change,were inferred from the data.The findings underscore that the dissolution process is predominantly endothermic across the solvent systems examined.Notably,the entropy changes appear to have a significant influence on the Gibbs free energy associated with the dissolution of Reb A(FormⅡ),suggesting that entropic factors may play a pivotal role in the studied systems.展开更多
As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic...As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.展开更多
The analysis of early stage rodingite from the ultramafic rocks of the Xialu Massif in the Xigaze Ophiolite,Tibet,in China shows that the rodingitization involved continuous changes in fluid composition during differe...The analysis of early stage rodingite from the ultramafic rocks of the Xialu Massif in the Xigaze Ophiolite,Tibet,in China shows that the rodingitization involved continuous changes in fluid composition during different stages of subduction.The early stage prehnite-bearing rodingite was produced at low pressures and temperatures along extensional fractures.Samples of rodingite were collected along a profile from the center to the margin of a rodingitized intrusive igneous rock(^10 m×30 m),and they record wide variations in bulk composition,mineralogy,and texture.The mineral assemblages,from center to margin,vary from(1)relics of primary clinopyroxene(Cpx_(r))and primary amphibole(Amp_(r))+newly formed late amphibole(Act)+primary plagioclase(Pl_(r))+clinozoisite+prehnite+albite+chlorite+titanite+ilmenite(R1 rodingite),through(2)relics of primary clinopyroxene(Cpx_(r))+newly formed late clinopyroxene(Cpx_(n))+primary and late amphiboles(Amp_(r)+Act)+clinozoisite+prehnite+albite+chlorite+titanite(R2 rodingite),to(3)newly formed late clinopyroxene(Cpx_(n))and amphibole(Act)+clinozoisite+prehnite+albite+chlorite+titanite(R3 rodingite).As a result of the metasomatic process of rodingitization,the content of CaO in the whole rock chemical composition from R1 to R3 increases,SiO_(2) decreases,and Na_(2)O+K_(2)O is almost completely removed.Massbalance diagrams show enrichments in large ion lithophile elements such as Rb,Cs,Ba,and Pb as well as Ni during rodingitization.The central part of the rodingitized intrusion(R1 rodingite)was only slightly affected by metasomatism.On the other hand,the contents of the rare earth elements(REEs),high field strength elements(HFSEs;e.g.Zr,Nb,Ta,Hf,and Y),and some highly compatible elements such as Cr and Sc decreased slightly during rodingitization.Thermodynamic modeling based on equilibrium mineral assemblages indicates that the rodingite of the Xialu Massif formed in an H_(2)O-saturated,CO_(2)-rich environment.The estimated conditions of metamorphism were-281-323℃and 0.4-3.9 kbar,representing the subgreenschist facies.In this environment,REEs and HFSEs were soluble in the fluids and partly removed.Moreover,these prehnite rodingites formed in a progressively reducing and less alkaline environment,as indicated by decreases in f(O_(2))and bulk-rock Fe^(3+)/Fe^(2+) ratios,and the records of fluidΔpH from the center to the margin of the studied rodingitized intrusion.展开更多
An electrolyte Equation of State is presented by combining the Cubic Plus Association Equation of State,Mean Spherical Approximation and the Born equation.This new model uses experimental relative static permittivity,...An electrolyte Equation of State is presented by combining the Cubic Plus Association Equation of State,Mean Spherical Approximation and the Born equation.This new model uses experimental relative static permittivity,intend to predict well the activity coefficients of individual ions(ACI)and liquid densities of aqueous solutions.This new model is applied to model water+Na Cl binary system and water+gas+Na Cl ternary systems.The cation/anion-water interaction parameters of are obtained by fitting the experimental data of ACI,mean ionic activity coefficients(MIAC)and liquid densities of water+Na Cl binary system.The cation/anion-gas interaction parameters are obtained by fitting the experimental data of gas solubilities in aqueous Na Cl solutions.The modeling results show that this new model can correlate well with the phase equilibrium and volumetric properties.Without gas,predictions for ACI,MIAC,and liquid densities present relative average deviations of 1.3%,3.6%and 1.4%compared to experimental reference values.For most gas-containing systems,predictions for gas solubilities present relative average deviations lower than 7.0%.Further,the contributions of ACI,and salting effects of Na Cl on gases are analyzed and discussed.展开更多
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 charac...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.展开更多
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 conc...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.展开更多
Most of the crude oils contain waxes which precipitate when temperature drops, resulting in deposition in pipelines and production equipment. It is necessary to set up a model which can predict the wax appearance tem-...Most of the crude oils contain waxes which precipitate when temperature drops, resulting in deposition in pipelines and production equipment. It is necessary to set up a model which can predict the wax appearance tem-perature and the amount of solid precipitated in the different conditions. A modified thermodynamic solid-liquid equilibrium model to calculate wax precipitation in crude oil systems has been developed recently. The assumption that precipitated waxes consist of several solid phases is adopted in this research, and the solid-solid transition is also considered in the modified model. The properties of the pseudo-components are determined by using empirical correlations. New correlations for properties of solid-solid and solid-liquid transitions are also established in this work on the basis of the data from the literature. The results predicted by the proposed model for three crude oil systems are compared with the experimental data and the calculated results from the literature, and good agreement is observed.展开更多
Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278....Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were con firmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.展开更多
Although vein-type silver-lead-zinc ore deposits have been extensively studied,the factors controlling their formation are still poorly understood and their genesis is a matter of ongoing debate.In this contribution,I...Although vein-type silver-lead-zinc ore deposits have been extensively studied,the factors controlling their formation are still poorly understood and their genesis is a matter of ongoing debate.In this contribution,I present new mineralogical data and the results of thermodynamic modeling that constrain the conditions of metal transport and deposition for the Aerhada epithermal Pb-Zn-Ag deposit(reserves of>1,000 t Ag@58 g/t and 1.0 Mt Pb+Zn@5.2%)in NE China.Three primary paragenetic stages have been identified,the second of which(Stage II)is the main base metal and silver mineralization.Freibergite,argentite,pyrargyrite,and canfieldite are the main Ag-bearing minerals and are spatially associated with an alteration assemblage of quartz-muscovite±chlorite±epidote.Dissolution textures and evidence of compositional heterogeneity for freibergite suggest that its decomposition may have redistributed the Ag and contributed in part to the high Ag grade ores in the deposit.Thermodynamic calculations indicate that there was extensive silver ore deposition from a strongly reducing(e.g.,∆log fO_(2)(HM)of<-8.6 to-2.4)and nearly neutral to weakly alkaline(e.g.,pH of 5.5 to 6.8)aqueous fluid at temperatures between 220℃ and 170℃.These calculations reveal that a reduction in fO_(2)and decreasing temperature,both as a result of fluid-rock interactions,were the key factors leading to silver and base metal mineral deposition.Further path modeling showed that the sole evolution of a magmatic-derived fluid is capable of forming the large Ag-Pb-Zn veins via fluid-rock interactions,which is contrary to the conclusions of some other studies that the mixture of an externally derived fluid is required to explain their formation.The genetic model for Ag-Pb-Zn ore formation developed in this study is applicable to other polymetallic vein-type deposits in comparable geological settings elsewhere.展开更多
Hydraulic fracturing is an effective technology for hydrocarbon extraction from unconventional shale and tight gas reservoirs.A potential risk of hydraulic fracturing is the upward migration of stray gas from the deep...Hydraulic fracturing is an effective technology for hydrocarbon extraction from unconventional shale and tight gas reservoirs.A potential risk of hydraulic fracturing is the upward migration of stray gas from the deep subsurface to shallow aquifers.The stray gas can dissolve in groundwater leading to chemical and biological reactions,which could negatively affect groundwater quality and contribute to atmospheric emissions.The knowledge oflight hydrocarbon solubility in the aqueous environment is essential for the numerical modelling offlow and transport in the subsurface.Herein,we compiled a database containing 2129experimental data of methane,ethane,and propane solubility in pure water and various electrolyte solutions over wide ranges of operating temperature and pressure.Two machine learning algorithms,namely regression tree(RT)and boosted regression tree(BRT)tuned with a Bayesian optimization algorithm(BO)were employed to determine the solubility of gases.The predictions were compared with the experimental data as well as four well-established thermodynamic models.Our analysis shows that the BRT-BO is sufficiently accurate,and the predicted values agree well with those obtained from the thermodynamic models.The coefficient of determination(R2)between experimental and predicted values is 0.99 and the mean squared error(MSE)is 9.97×10^(-8).The leverage statistical approach further confirmed the validity of the model developed.展开更多
In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on pe...In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.展开更多
Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article ex...Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.展开更多
Thermodynamic assessment of Ti-Co-Cu ternary system has been carried out by combining first-principle calculation and CALPHAD method. Firstly, formation enthalpies of stable and hypothesized compounds were calculated ...Thermodynamic assessment of Ti-Co-Cu ternary system has been carried out by combining first-principle calculation and CALPHAD method. Firstly, formation enthalpies of stable and hypothesized compounds were calculated by first-principles method. Then, based on reported experimental information, a thermodynamic description of the Ti-Co-Cu ternary system was performed. Solution phases were treated as substitutional solutions of which excess Gibbs energies were formulated by Redlich-Kister polynomial, and the intermediate phases were described with sublattice models. All measured isothermal sections were reasonably reproduced. In addition, liquidus projection of this ternary system was further calculated, which may be useful for relevant materials processing.展开更多
The present work deals with thermodynamic modeling of oxide systems, in the context of slags and inclusions in steelmaking. The work has emphasis on oxides encountered during the production of tire – cord steel. Cont...The present work deals with thermodynamic modeling of oxide systems, in the context of slags and inclusions in steelmaking. The work has emphasis on oxides encountered during the production of tire – cord steel. Control of inclusion chemistry and variation in eutectic temperature and eutectic composition of MnO-Al2O3-SiO2 slag system have been studied, using Thermo-CalcR software. Relatively low liquidus temperatures are obtained for ratio of MnO / SiO2 = 0.5 - 1.5 and Al2O3 content from 10 - 20 mass%. It has been observed that the addition of Alumina leads to further increase in the liquidus temperature. The stability of inclusions is analyzed in terms of free energy values of related slag systems; and an appropriate minimum of Gibbs free energy value of slag phase observed at around 50 ppm of Oxygen. The observations could not be verified using thermodynamic experiments, but have been compared with findings in the open literature.展开更多
Strategies based on thermodynamic calculations can be used to overcome the problems associated with oxides encountered in steel plant operations, which can lead to certain difficulties in the process such as clogging ...Strategies based on thermodynamic calculations can be used to overcome the problems associated with oxides encountered in steel plant operations, which can lead to certain difficulties in the process such as clogging of submerged entry nozzle during continuous casting. Approaches to producing high alloy steels by continuous casting have been taken. One of the strategies to avoid the oxidation of chromium is to add a small amount of other elements （subject to other constraints）, which do not cause subsequent problems. The problem has been studied using the Thermo-CalcR software, with related databases; and the results obtained for different process conditions or generic compositions have been presented.展开更多
Radiative fluxes are of primary importance in the energy and mass balance of the sea-ice cover. Various parameterizations of the radiative fluxes are studied in a thermodynamic sea-ice model. Model outputs of the surf...Radiative fluxes are of primary importance in the energy and mass balance of the sea-ice cover. Various parameterizations of the radiative fluxes are studied in a thermodynamic sea-ice model. Model outputs of the surface radiative and heat fluxes and mass balance are compared with observations. The contribution of short-wave radiation is limited to a long part of winter. Therefore, simple schemes are often sufficient. Errors in estimations of the short-wave radiation are due mainly to cloud effects and occasionally to multi-reflection between surface and ice crystals in the air. The long-wave radiation plays an important role in the ice surface heat and mass balance during most part of a winter. The effect of clouds on the accuracy of the simple radiative schemes is critical, which needs further attention. In general, the accuracy of an ice model depends on that of the radiative fluxes.展开更多
In order to study the major performance indicators of the twin-rotor piston engine(TRPE), Matlab/simulink was used to simulate the mathematical models of its thermodynamic processes. With consideration of the characte...In order to study the major performance indicators of the twin-rotor piston engine(TRPE), Matlab/simulink was used to simulate the mathematical models of its thermodynamic processes. With consideration of the characteristics of the working processes in the TRPE, corresponding differential equations were established and then simplified by period features of the TRPE. Finally, the major boundary conditions were figured out. The changing trends of mass, pressure and temperature of working fuel in the working chamber during a complete engine cycle were presented. The simulation results are consistent with the trends of an actual working cycle in the TRPE, which indicates that the method of simulation is feasible. As the pressure in the working chamber is calculated, all the performance parameters of the TRPE can be obtained. The major performance indicators, such as the indicated mean effective pressure, power to weight ratio and the volume power, are also acquired. Compared with three different types of conventional engines, the TRPE has a bigger utilization ratio of cylinder volume, a higher power to weight ratio and a more compact structure. This indicates that TRPE is superior to conventional engines.展开更多
The so-called low-density steels have generated a lot of interests with their high specific strength and ductility due to the addi-tion of the light element Al.ln order to accelerate the low-density steel design,a the...The so-called low-density steels have generated a lot of interests with their high specific strength and ductility due to the addi-tion of the light element Al.ln order to accelerate the low-density steel design,a thermodynamic database has been developedwithin the present author group.Two Al-containing systems,i.e.,Cr-Al-Cand Ni-Al-C,were modeled and optimirzed with CALPHAD approach based on the reliable binary descriptions.For Cr-Al-C,system,the Gibbs energy of Cr2AlC phasewas described by a temperature-dependent polynomial with the aid of the experimental data on the heat capacity,instead of estimating heat capacity from Ncumann-Kopp rule.The incongruent melting temperature of Cr2AlC is 1762 K with theinvariant reaction of liquid+Cr3C2+Al4C3→Cr2AlC.The phase equilibria between Cr2AlC and binary phases were wellreproduced by using the present model parameters.For Ni-Al-C system,the liquid,fec and bec phases have been optimizedto fit the carbon solubility in these three phases.A good agreement between the calculated and experimental data has beenobtained using the present description of Ni-Al-C system.The reliable descriptions of the two ternary systems developedin the present work can be implemented into the thermodynamic database for low-density steels.展开更多
Molten salts as heat transfer and storage materials have been used to nuclear energy and concentrated solar power（CSP） applications. In this work, the system of molten salt mixture based on thermodynamic principles ...Molten salts as heat transfer and storage materials have been used to nuclear energy and concentrated solar power（CSP） applications. In this work, the system of molten salt mixture based on thermodynamic principles was designed as thermal energy storage（TES） materials. The substitutional solution model can be employed to describe the Gibbs energies of all liquid phase. Thermodynamic model parameters for the NaCl-NaNO3-Na2SO4 subsystems were conducted by thermodynamic evaluation and optimization based on experimental phase-equilibria data. Thus, a set of self-consistent thermodynamic database was eventually obtained to reliably calculate the whole phase diagram and thermodynamic properties for the NaCl-NaNO3-Na2SO4 ternary system. The results manifest that the eutectic point of theternary system located at T=280 ℃ and XNaCl=8.4%, XNaNO3=86.3% and xNa2SO4=5.3%. Moreover, the results predicted were verified experimentally using differential scanning calorimetry（DSC） and the agreement between the measured value[T=（287±2） ℃] and predicted value（T=280 ℃） was satisfactory. Thus, the thermodynamic calculation method will be used to design and develop novel molten salt mixture as thermal energy storage materials.展开更多
In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene p...In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.展开更多
基金supported by the National Key Research and Development Program of China(2021YFC2103800)the National Natural Science Foundation of China(U21A20301)the Research Funds of Institute of Zhejiang University-Quzhou(IZQ2022RCZX004 and IZQ2021RCZX015)。
文摘The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The experimental findings indicate a positive correlation between the solubility of Reb A(FormⅡ)and both the temperature and the methanol/ethanol content in the solvent system.To describe the solubility data,six distinct models were employed:the modified Apelblat equation,theλh model,the combined nearly ideal binary solvent/Redlich—Kister(CNIBS/R—K)model,the van't HoffJouyban-Acree(VJA)model,the Apelblat-Jouyban-Acree(AJA)model,and the non-random two-liquid(NRTL)model.The combined nearly ideal binary solvent/Redlich—Kister model exhibited the most precise fit for solubility in methanol+ethyl acetate mixtures,reflected by an average relative deviation(ARD)of 0.0011 and a root mean square deviation(RMSD)of 12×10^(-7).Conversely,for ethanol+ethyl acetate mixtures,the modified Apelblat equation provided a superior correlation(ARD=0.0014,RMSD=4×10^(-7)).Furthermore,thermodynamic parameters associated with the dissolution of Reb A(FormⅡ),including enthalpy,entropy,and the Gibbs energy change,were inferred from the data.The findings underscore that the dissolution process is predominantly endothermic across the solvent systems examined.Notably,the entropy changes appear to have a significant influence on the Gibbs free energy associated with the dissolution of Reb A(FormⅡ),suggesting that entropic factors may play a pivotal role in the studied systems.
基金This work was financially supported by the National Natural Science Foundation of China (Nos. 50471095 and 50271008).
文摘As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.
基金supported by the National Natural Science Foundation of China(Grant No.41572044)the SGSTSP of the Chinese Academy of Sciences(Grant No.XDB03010201)+1 种基金SDUST Research Fund(Grant No.2015TDJH101)financial support from Chinese Scholarship Council(Grant No.201808370192)。
文摘The analysis of early stage rodingite from the ultramafic rocks of the Xialu Massif in the Xigaze Ophiolite,Tibet,in China shows that the rodingitization involved continuous changes in fluid composition during different stages of subduction.The early stage prehnite-bearing rodingite was produced at low pressures and temperatures along extensional fractures.Samples of rodingite were collected along a profile from the center to the margin of a rodingitized intrusive igneous rock(^10 m×30 m),and they record wide variations in bulk composition,mineralogy,and texture.The mineral assemblages,from center to margin,vary from(1)relics of primary clinopyroxene(Cpx_(r))and primary amphibole(Amp_(r))+newly formed late amphibole(Act)+primary plagioclase(Pl_(r))+clinozoisite+prehnite+albite+chlorite+titanite+ilmenite(R1 rodingite),through(2)relics of primary clinopyroxene(Cpx_(r))+newly formed late clinopyroxene(Cpx_(n))+primary and late amphiboles(Amp_(r)+Act)+clinozoisite+prehnite+albite+chlorite+titanite(R2 rodingite),to(3)newly formed late clinopyroxene(Cpx_(n))and amphibole(Act)+clinozoisite+prehnite+albite+chlorite+titanite(R3 rodingite).As a result of the metasomatic process of rodingitization,the content of CaO in the whole rock chemical composition from R1 to R3 increases,SiO_(2) decreases,and Na_(2)O+K_(2)O is almost completely removed.Massbalance diagrams show enrichments in large ion lithophile elements such as Rb,Cs,Ba,and Pb as well as Ni during rodingitization.The central part of the rodingitized intrusion(R1 rodingite)was only slightly affected by metasomatism.On the other hand,the contents of the rare earth elements(REEs),high field strength elements(HFSEs;e.g.Zr,Nb,Ta,Hf,and Y),and some highly compatible elements such as Cr and Sc decreased slightly during rodingitization.Thermodynamic modeling based on equilibrium mineral assemblages indicates that the rodingite of the Xialu Massif formed in an H_(2)O-saturated,CO_(2)-rich environment.The estimated conditions of metamorphism were-281-323℃and 0.4-3.9 kbar,representing the subgreenschist facies.In this environment,REEs and HFSEs were soluble in the fluids and partly removed.Moreover,these prehnite rodingites formed in a progressively reducing and less alkaline environment,as indicated by decreases in f(O_(2))and bulk-rock Fe^(3+)/Fe^(2+) ratios,and the records of fluidΔpH from the center to the margin of the studied rodingitized intrusion.
文摘An electrolyte Equation of State is presented by combining the Cubic Plus Association Equation of State,Mean Spherical Approximation and the Born equation.This new model uses experimental relative static permittivity,intend to predict well the activity coefficients of individual ions(ACI)and liquid densities of aqueous solutions.This new model is applied to model water+Na Cl binary system and water+gas+Na Cl ternary systems.The cation/anion-water interaction parameters of are obtained by fitting the experimental data of ACI,mean ionic activity coefficients(MIAC)and liquid densities of water+Na Cl binary system.The cation/anion-gas interaction parameters are obtained by fitting the experimental data of gas solubilities in aqueous Na Cl solutions.The modeling results show that this new model can correlate well with the phase equilibrium and volumetric properties.Without gas,predictions for ACI,MIAC,and liquid densities present relative average deviations of 1.3%,3.6%and 1.4%compared to experimental reference values.For most gas-containing systems,predictions for gas solubilities present relative average deviations lower than 7.0%.Further,the contributions of ACI,and salting effects of Na Cl on gases are analyzed and discussed.
基金financial support of the National Natural Science Foundation of China(U1407204,U1707602)the Yangtze Scholars and Innovative Research Team in University of Education of China+1 种基金the Innovative Research Team of Tianjin Municipal Education Commission(TD12-5004)Foundation of Tianjin Key Laboratory of Marine Resources and Chemistry(201602)。
文摘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.
基金financial support of the National Natural Science Foundation of China(U1707602,U1407204)Yangtze Scholars and Innovative Research Team in University of Education of China,the Innovative Research Team of Tianjin Municipal Education Commission(TD125004)。
文摘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.
基金Supported by the National Natural Science Foundation of China (No.10272029).
文摘Most of the crude oils contain waxes which precipitate when temperature drops, resulting in deposition in pipelines and production equipment. It is necessary to set up a model which can predict the wax appearance tem-perature and the amount of solid precipitated in the different conditions. A modified thermodynamic solid-liquid equilibrium model to calculate wax precipitation in crude oil systems has been developed recently. The assumption that precipitated waxes consist of several solid phases is adopted in this research, and the solid-solid transition is also considered in the modified model. The properties of the pseudo-components are determined by using empirical correlations. New correlations for properties of solid-solid and solid-liquid transitions are also established in this work on the basis of the data from the literature. The results predicted by the proposed model for three crude oil systems are compared with the experimental data and the calculated results from the literature, and good agreement is observed.
基金Supported by the National Natural Science Foundation of China(21376231)
文摘Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were con firmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.
基金This research was supported financially by the National Natural Science Foundation of China(42122012 and 41973038)。
文摘Although vein-type silver-lead-zinc ore deposits have been extensively studied,the factors controlling their formation are still poorly understood and their genesis is a matter of ongoing debate.In this contribution,I present new mineralogical data and the results of thermodynamic modeling that constrain the conditions of metal transport and deposition for the Aerhada epithermal Pb-Zn-Ag deposit(reserves of>1,000 t Ag@58 g/t and 1.0 Mt Pb+Zn@5.2%)in NE China.Three primary paragenetic stages have been identified,the second of which(Stage II)is the main base metal and silver mineralization.Freibergite,argentite,pyrargyrite,and canfieldite are the main Ag-bearing minerals and are spatially associated with an alteration assemblage of quartz-muscovite±chlorite±epidote.Dissolution textures and evidence of compositional heterogeneity for freibergite suggest that its decomposition may have redistributed the Ag and contributed in part to the high Ag grade ores in the deposit.Thermodynamic calculations indicate that there was extensive silver ore deposition from a strongly reducing(e.g.,∆log fO_(2)(HM)of<-8.6 to-2.4)and nearly neutral to weakly alkaline(e.g.,pH of 5.5 to 6.8)aqueous fluid at temperatures between 220℃ and 170℃.These calculations reveal that a reduction in fO_(2)and decreasing temperature,both as a result of fluid-rock interactions,were the key factors leading to silver and base metal mineral deposition.Further path modeling showed that the sole evolution of a magmatic-derived fluid is capable of forming the large Ag-Pb-Zn veins via fluid-rock interactions,which is contrary to the conclusions of some other studies that the mixture of an externally derived fluid is required to explain their formation.The genetic model for Ag-Pb-Zn ore formation developed in this study is applicable to other polymetallic vein-type deposits in comparable geological settings elsewhere.
文摘Hydraulic fracturing is an effective technology for hydrocarbon extraction from unconventional shale and tight gas reservoirs.A potential risk of hydraulic fracturing is the upward migration of stray gas from the deep subsurface to shallow aquifers.The stray gas can dissolve in groundwater leading to chemical and biological reactions,which could negatively affect groundwater quality and contribute to atmospheric emissions.The knowledge oflight hydrocarbon solubility in the aqueous environment is essential for the numerical modelling offlow and transport in the subsurface.Herein,we compiled a database containing 2129experimental data of methane,ethane,and propane solubility in pure water and various electrolyte solutions over wide ranges of operating temperature and pressure.Two machine learning algorithms,namely regression tree(RT)and boosted regression tree(BRT)tuned with a Bayesian optimization algorithm(BO)were employed to determine the solubility of gases.The predictions were compared with the experimental data as well as four well-established thermodynamic models.Our analysis shows that the BRT-BO is sufficiently accurate,and the predicted values agree well with those obtained from the thermodynamic models.The coefficient of determination(R2)between experimental and predicted values is 0.99 and the mean squared error(MSE)is 9.97×10^(-8).The leverage statistical approach further confirmed the validity of the model developed.
文摘In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.
文摘Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.
基金financially supported by the National Natural Science Foundation of China (Grant No. 50671122)
文摘Thermodynamic assessment of Ti-Co-Cu ternary system has been carried out by combining first-principle calculation and CALPHAD method. Firstly, formation enthalpies of stable and hypothesized compounds were calculated by first-principles method. Then, based on reported experimental information, a thermodynamic description of the Ti-Co-Cu ternary system was performed. Solution phases were treated as substitutional solutions of which excess Gibbs energies were formulated by Redlich-Kister polynomial, and the intermediate phases were described with sublattice models. All measured isothermal sections were reasonably reproduced. In addition, liquidus projection of this ternary system was further calculated, which may be useful for relevant materials processing.
文摘The present work deals with thermodynamic modeling of oxide systems, in the context of slags and inclusions in steelmaking. The work has emphasis on oxides encountered during the production of tire – cord steel. Control of inclusion chemistry and variation in eutectic temperature and eutectic composition of MnO-Al2O3-SiO2 slag system have been studied, using Thermo-CalcR software. Relatively low liquidus temperatures are obtained for ratio of MnO / SiO2 = 0.5 - 1.5 and Al2O3 content from 10 - 20 mass%. It has been observed that the addition of Alumina leads to further increase in the liquidus temperature. The stability of inclusions is analyzed in terms of free energy values of related slag systems; and an appropriate minimum of Gibbs free energy value of slag phase observed at around 50 ppm of Oxygen. The observations could not be verified using thermodynamic experiments, but have been compared with findings in the open literature.
文摘Strategies based on thermodynamic calculations can be used to overcome the problems associated with oxides encountered in steel plant operations, which can lead to certain difficulties in the process such as clogging of submerged entry nozzle during continuous casting. Approaches to producing high alloy steels by continuous casting have been taken. One of the strategies to avoid the oxidation of chromium is to add a small amount of other elements （subject to other constraints）, which do not cause subsequent problems. The problem has been studied using the Thermo-CalcR software, with related databases; and the results obtained for different process conditions or generic compositions have been presented.
基金This study was a part of the Sino-Finnish long-term sea-ice research cooperationsupported by the National Natural Science Foundation of China under contract Nos 40233032 and 40376006.
文摘Radiative fluxes are of primary importance in the energy and mass balance of the sea-ice cover. Various parameterizations of the radiative fluxes are studied in a thermodynamic sea-ice model. Model outputs of the surface radiative and heat fluxes and mass balance are compared with observations. The contribution of short-wave radiation is limited to a long part of winter. Therefore, simple schemes are often sufficient. Errors in estimations of the short-wave radiation are due mainly to cloud effects and occasionally to multi-reflection between surface and ice crystals in the air. The long-wave radiation plays an important role in the ice surface heat and mass balance during most part of a winter. The effect of clouds on the accuracy of the simple radiative schemes is critical, which needs further attention. In general, the accuracy of an ice model depends on that of the radiative fluxes.
基金Project(7131109)supported by the National Defense Pre-research Foundation of ChinaProject(51175500)supported by the National Natural Science Foundation of China
文摘In order to study the major performance indicators of the twin-rotor piston engine(TRPE), Matlab/simulink was used to simulate the mathematical models of its thermodynamic processes. With consideration of the characteristics of the working processes in the TRPE, corresponding differential equations were established and then simplified by period features of the TRPE. Finally, the major boundary conditions were figured out. The changing trends of mass, pressure and temperature of working fuel in the working chamber during a complete engine cycle were presented. The simulation results are consistent with the trends of an actual working cycle in the TRPE, which indicates that the method of simulation is feasible. As the pressure in the working chamber is calculated, all the performance parameters of the TRPE can be obtained. The major performance indicators, such as the indicated mean effective pressure, power to weight ratio and the volume power, are also acquired. Compared with three different types of conventional engines, the TRPE has a bigger utilization ratio of cylinder volume, a higher power to weight ratio and a more compact structure. This indicates that TRPE is superior to conventional engines.
基金Thanks are given to the support from the NationalKey R&D Program of China(Grant No.2017YFB0304402)W.S.Zheng acknowledges the support from the Shanghai Sailing Program(Grant No.19YF1415700)the National Natural Science Foundation of China(Grant No.51901124).
文摘The so-called low-density steels have generated a lot of interests with their high specific strength and ductility due to the addi-tion of the light element Al.ln order to accelerate the low-density steel design,a thermodynamic database has been developedwithin the present author group.Two Al-containing systems,i.e.,Cr-Al-Cand Ni-Al-C,were modeled and optimirzed with CALPHAD approach based on the reliable binary descriptions.For Cr-Al-C,system,the Gibbs energy of Cr2AlC phasewas described by a temperature-dependent polynomial with the aid of the experimental data on the heat capacity,instead of estimating heat capacity from Ncumann-Kopp rule.The incongruent melting temperature of Cr2AlC is 1762 K with theinvariant reaction of liquid+Cr3C2+Al4C3→Cr2AlC.The phase equilibria between Cr2AlC and binary phases were wellreproduced by using the present model parameters.For Ni-Al-C system,the liquid,fec and bec phases have been optimizedto fit the carbon solubility in these three phases.A good agreement between the calculated and experimental data has beenobtained using the present description of Ni-Al-C system.The reliable descriptions of the two ternary systems developedin the present work can be implemented into the thermodynamic database for low-density steels.
基金Supported by the National Natural Science Foundation of Ctfina（No.21703281） and the Strategic Priority Research Program of the Chinese Academy of Sciences（No.XD02002400）.
文摘Molten salts as heat transfer and storage materials have been used to nuclear energy and concentrated solar power（CSP） applications. In this work, the system of molten salt mixture based on thermodynamic principles was designed as thermal energy storage（TES） materials. The substitutional solution model can be employed to describe the Gibbs energies of all liquid phase. Thermodynamic model parameters for the NaCl-NaNO3-Na2SO4 subsystems were conducted by thermodynamic evaluation and optimization based on experimental phase-equilibria data. Thus, a set of self-consistent thermodynamic database was eventually obtained to reliably calculate the whole phase diagram and thermodynamic properties for the NaCl-NaNO3-Na2SO4 ternary system. The results manifest that the eutectic point of theternary system located at T=280 ℃ and XNaCl=8.4%, XNaNO3=86.3% and xNa2SO4=5.3%. Moreover, the results predicted were verified experimentally using differential scanning calorimetry（DSC） and the agreement between the measured value[T=（287±2） ℃] and predicted value（T=280 ℃） was satisfactory. Thus, the thermodynamic calculation method will be used to design and develop novel molten salt mixture as thermal energy storage materials.
基金supported by the National Natural Science Foundation of China(22178190)。
文摘In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.
