Phase Mole Fraction Research Articles

Correlating vapour-liquid equilibria of binary HI + H2O mixtures using Pitzer’s model of electrolyte solutions

Abstract The need to produce Hydrogen in an environmentally friendly manner has increased as the transportation industry has started to employ cleaner sources of energy. One of the cleaner ways to produce H2, is to use the Bunsen S-I cycle. This includes the separation of the H2 from an ionic mixture of Hydrogen Iodide and water using distillation. In this work, the Pitzer’s model for electrolyte solutions has been employed to represent the vapour-liquid equilibrium (VLE) of the binary system of HI and H2O. The activity coefficient (γ) is calculated from the equation which indicated the non-ideal nature of the system and aided the calculation of the vapour phase mole fraction. The experimental VLE data was obtained from a recirculating still at 101.3 kPa pressure for the binary system. This experimental data and data from literature was used to estimate the parameters of the Pitzer’s model to represent the activity coefficient of HI in this mixture. These optimized parameters could explain all the variations in the data with more that 90% accuracy for most of the data, with an average standard deviation of about 0.04. Furthermore, the temperature dependent form of the Pitzer’s equation was used to predict the VLE data at higher pressures of 3 and 5.7 bars and higher temperature conditions.

Vapor liquid equilibria for binary mixtures of difluoromethane (R32) + fluoroethane (R161) and fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E))

Abstract Developing new refrigerants with low global warming potential (GWP) is the major challenge for the refrigeration industry with the Paris Agreement going into effect on 4 November 2016. In this work, we reported the isothermal vapor liquid equilibrium (VLE) data for the low GWP binary refrigerants of difluoromethane (R32) + fluoroethane (R161) and fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)). The measurements were carried out with a quasi-static analytical apparatus along five isotherms from (283.15 to 323.15) K. The experimental data were correlated by Peng-Robinson-Stryjek-Vera equation of state combined with the Wong and Sandler mixing rule and the non-random two-liquid activity coefficient (PRSV + WS + NRTL) model. The correlated results and the experimental data show good consistency. The average absolute deviation of pressure (AAD(p)) and average absolute deviation of vapor phase mole fraction (AAD(y)) are 0.12% and 0.0011 for R32 + R161, 0.20% and 0.0014 for R161 + R1234ze(E), respectively.

Salts effect on isobaric vapor−liquid equilibrium for separation of the azeotropic mixture allyl alcohol + water

Allyl alcohol and water can form an azeotrope with the minimum boiling point. To separate the azeotrope of allyl alcohol and water by salt distillation, three salts calcium chloride, calcium nitrate and magnesium nitrate were selected to break the azeotrope. The vapor-liquid equilibrium (VLE) data for the systems allyl alcohol + water, allyl alcohol + water + calcium nitrate, allyl alcohol + water + calcium chloride and allyl alcohol + water + magnesium nitrate were measured at pressure of 101.3 kPa. The results indicated that the relative volatility of allyl alcohol to water increased by adding the salts at the molar fraction of allyl alcohol higher than 0.2. With increasing the concentrations of the salts, the azeotropic point of the system allyl alcohol + water moved. When the concentrations of calcium chloride and magnesium nitrate were 0.10, 0.15, respectively, the azeotropic point was broken. The effect of salts on the azeotropic point of the system allyl alcohol + water follows the order: calcium chloride > magnesium nitrate > calcium nitrate. Moreover, the experimental VLE data were correlated by the NRTL model. All the root-mean-square deviations for the temperature (T) and the mole fraction of the vapor phase (y1) between the measured and calculated data were less than 0.26 K and 0.005, respectively. Meanwhile, the binary interaction parameters of the NRTL model were regressed.

Isothermal vapor liquid equilibrium measurements for difluoromethane (R32) + fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) ternary mixtures

Difluoromethane (R32) + fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) ternary system could be a promising alternative refrigerant mixture. The vapor liquid equilibrium (VLE) data for this system are important for the evaluation of its performance. In this work, the VLE of R32 + R161 + R1234ze(E) were measured for the first time by a quasi-static analytical apparatus over the temperature range of 283.15 to 323.15 K. The ternary system of R32 + R161 + R1234ze(E) is a zeotropic system within the studied temperature range. The Peng–Robinson–Stryjek–Vera (PRSV) equation of state combined with the Wong–Sandler (WS) mixing rule and the non-random two-liquid (NRTL) activity coefficient model was used to predict the ternary VLE data by using the parameters of binary mixtures (R32 + R161, R32 + R1234ze(E) and R161 + R1234ze(E)). The calculated values show excellent agreement with the experimental results. The average absolute deviation (AAD) of pressure is 0.16%. The average absolute deviations of vapor phase mole fractions for R32 and R161 are 0.0021 and 0.0028, respectively.

Measurements of isothermal (vapour + liquid) equilibrium for the 1,1,2,2-1,1,2,2-tetrafluoroethane (R134) + cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) system at temperatures from (303.150 to 343.150) K

The isothermal (vapour+liquid) equilibrium data for the 1,1,2,2-1,1,2,2-tetrafluoroethane (R134)+cis-1,3,3,3-tetrafluoropropene (R1234ze(Z)) system were determined by the static-analytical method at five temperatures from (303.150 to 343.150)K. The standard uncertainties of the temperature, pressure and composition were less than 5mK, 0.0005MPa, and 0.005, respectively. The experimental results were correlated by the Peng–Robison (PR) equation of state (EoS) with the Huron–Vidal (HV) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The correlated results show good agreement with the experimental data. The average absolute relative deviations of pressure are between 0.20% and 0.35%, while the average absolute deviations of vapour phase mole fraction lay between 0.006 and 0.007. Azeotropic behaviour can be observed at four temperatures from (303.150 to 333.150)K, while zeotropic behaviour can be found at 343.150K.

The investigation on the vapour liquid phase equilibrium of (ammonia + 1,1,1,2-tetrafluoroethane) system over the temperatures ranging from (243.150 to 283.150) K

To blend ammonia with some hydrofluorocarbons may give these mixed refrigerants lower flammability and global warming potential. In this paper, the isothermal vapour liquid equilibrium (VLE) of (ammonia+1,1,1,2-tetrafluoroethane) system at temperatures ranging from (243.150 to 283.150) K are presented. Two models were employed to regress the experimental VLE results, namely the Peng–Robinson (PR) equation of state with the simple van der waals (VDW) mixing rule; the Peng–Robinson equation of state combined non-random two-liquid (NRTL) activity coefficient model with the modified Huron-Vidal one-order (MHV1) mixing rule. The maximum average absolute relative deviation of pressure (AARDp) and average absolute deviation of the vapour phase mole fraction (AADy) for PR-VDW are 0.56% and 0.010, respectively, while the maximum AARDp and AADy for PR-MHV1-NRTL are 0.27% and 0.014, respectively. Positive azeotropic behaviour was exhibited at each temperature investigated.

Vapor liquid equilibrium measurements for difluoromethane (R32) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and fluoroethane (R161) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf)

Vapor liquid equilibrium data for difluoromethane (R32) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and fluoroethane (R161) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) were measured over the temperature range of (283.15–323.15) K and at pressures from (0.4–3.2) MPa and from (0.4–1.8) MPa, respectively. A quasi-static analytical apparatus, improved from a recirculation analytical apparatus, was used to carry out the measurements. The Peng-Robinson-Stryjek-Vera equation of state combined with the Wong-Sandler mixing rule and the non-random two-liquid activity coefficient (PRSV + WS + NRTL) model were used to correlate the experimental data. The average absolute deviation of pressure (AAD(p)) and average absolute deviation of vapor phase mole fraction (AAD(y)) are 0.57% and 0.0018 for R32 + R1234yf, 0.14% and 0.0008 for R161 + R1234yf, respectively.

Relaxation Analysis of LixNiO2 and Lix(NCA)O2 in the Deeply Lithium Extracted Region (x ≤ 0.12)

Structural relaxation has been investigated on LixNiO2 and Lix(Ni0.933Co0.031Al0.036)O2 after the electrochemical lithium extraction to x ≤ 0.12. These relaxation analyses have been carried out using X-ray diffraction coupled with the Rietveld analysis assuming two phases (H2 and H3) co-existence with symmetry. For all the compositions of LixNiO2, mole fraction of H3 phase decreases with the relaxation time accompanied by the reduction of c-axis, while H2 phase retains c-length almost constant. Therefore, H3 phase excessively formed at the lithium extraction process partly transforms into the H2 phase during the relaxation. Although the similar relaxation phenomena reducing the mole fraction of H3 phase have been observed for Lix(Ni0.933Co0.031Al0.036)O2, difference in c-length between the H2 and H3 phases is much smaller, which would facilitate the phase change to improve the battery performance utilizing such a higher potential region.

Theoretical Investigation on the Properties of R744/R290 Mixtures

At present, an interesting research is to find promising environmentally-friendly refrigerants in auto-cascade refrigeration cycle. This paper proposed a refrigerant mixture of R744 and R290 due to its zero ozone depletion potential and negligible global warming potential. The properties of R744, R290 and the mixtures refrigerant were analyzed. And performances comparisons between R744, R290, R22 and R134a were investigated based on the simulation data. Then, the vapor-liquid phase equilibrium properties of mixture were calculated. And the conversion relations of total mole fraction, vapor phase mole fraction, liquid phase mole fraction, quality, equilibrium temperature and pressure were systematically analyzed. The results show that R744 and R290 are potential refrigerant. But each pure refrigerant has obvious disadvantage, it is a good choice that R744 and R290 are mixed together into non-azeotropic mixture, which is suitable for auto-cascade refrigeration cycle due to a large temperature glide during the phase changing.

Isothermal vapour-liquid equilibrium data for the binary systems 2-propanone + (2-butanol or propanoic acid)

Isothermal vapour-liquid equilibrium (VLE) data were measured for 2-propanone + 2-butanol at (333.15 and 353.15) K and 2-propanone + propanoic acid at (333.15, 353.15, and 373.15) K. For the sub-atmospheric pressure measurements, a dynamic recirculating VLE glass still operated isothermally was used, whilst a novel recirculating stainless steel of similar architecture, capable of operating at pressures up to 750 kPa was used for measurements above atmospheric pressures. The experimental VLE data for the 2-propanone + 2-butanol system at (333.15 and 353.15) K were correlated to the Wilson and NRTL models using the gamma-phi approach with the Hayden and O'Connell correlation employed for calculating the second virial coefficients. For the 2-propanone + propanoic acid system, the considerably more complex iterative procedure of Prausnitz et al. [J.M. Prausnitz, T.F. Anderson, E.A. Grens, C.A. Eckert, R. Hsieh, J.P. O'Connell, Computer Calculations for Multicomponent Vapour-Liquid and Liquid-Liquid Equilibrium, Prentice- Hall, New Jersey, 1980] was utilized to account for acid dimerization in the vapour phase. In the computational procedure for finding liquid phase activity coefficients, true species vapour phase mole fractions (ηi) are solved for, with the equilibrium association constant, Ki emerging from the computations. The thermodynamic consistency of the data was verified through the point and direct test methods of Van Ness.

Measurements and correlations of isothermal (vapour + liquid) equilibrium for the {isobutane (R600a) + cis-1,3,3,3-tetrafluoropropene (R1234ze(Z))} system at temperatures from (303.150 to 353.150) K

In this paper, the (vapour+liquid) phase equilibrium for the (isobutane+cis-1,3,3,3-tetrafluoropropene) system was measured by the static-analytical method at six temperatures from (303.150 to 353.150)K. The combined standard uncertainties of the temperature, pressure and composition were less than ±5mK, ±0.0005MPa and ±0.005, respectively. The experimental results were correlated by means of the Peng–Robison (PR) equation of state (EoS) with Van der Waals (VDW) mixing rule and Huron–Vidal (HV) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. Good consistency is found by both models. The average absolute relative deviations of pressure are between 0.44% and 0.58% for the PR-VDW model, while the average absolute relative deviations of pressure are between 0.12% and 0.44% for the PR-HV-NRTL model. The average absolute deviations of vapour phase mole fraction lay between 0.007 and 0.008 for the PR-VDW model, while the average absolute deviations of vapour phase mole fraction lay between 0.004 and 0.008 for the PR-HV-NRTL model. The results show that the PR-HV-NRTL model has better performance than that of the PR-VDW model for the binary system. Obviously an azeotropic behaviour can be observed for the system.

On a choice of independent variables in Newton iterations for multiphase flash calculations

Multiphase split calculations consist in the minimization of the Gibbs free energy. If the second-order Newton method is used, either component mole numbers or the logarithms of equilibrium constants (lnK) are selected as independent variables. Several recent papers advocated the use of the phase mole fractions together with lnK as independent variables in Newton iterations (lnK-θ). Unlike in the lnK approach, there is no explicit resolution of the Rachford-Rice (RR) equations, which are solved implicitly during the Newton update. The resulting linear system is non-symmetric and is solved by Gaussian elimination. In this study, this latter choice of variables is analyzed in detail, and an efficient formulation is proposed in which algebraic transformations are used to recast the lnK-θ method in a way that enables using the symmetry efficiently, both for constructing the Jacobian matrix and for solving the linear system of equations using a Cholesky factorization. Taking advantage of the block structure of the Jacobian matrix, it is revealed that the matrix of the linear system is formally identical to the Jacobian of lnK (evaluated at a lower implicitness level) and phase mole fraction can be updated separately using the partial solution of this system. Numerical experiments carried out on several multiphase mixtures exhibiting complex phase envelopes show the robustness and the efficiency of the proposed approach as compared to the original lnK-θ methodology, with the observed computational time savings up to 25%.

Rietveld Relaxation Analysis on LixNi0.5Mn1.5O4 (x = 0.1, 0.2) 5V Cathode Material

Introduction We have investigated the structural variation of γ-Fe2O3 after the termination of lithium insertion, and revealed the relaxation process from the discharging state to thermodynamically stable state [1-3]. We named this technique as “Relaxation analysis” and conducted this technique to various types of cathode or anode materials, such as LiMn2O4[4], LiFePO4[5], LiCoO2[6], or graphite [7] to clarify the insertion/extraction process as well as relaxation mechanism. In the present study, relaxation analysis has been made on the LixNi0.5Mn1.5O4 (x = 0.1, 0.2) after Li-extraction. LiNi0.5Mn1.5O4 with spinel-type structure is a promising cathode material because it operates at a higher voltage of ~4.7V [8] in comparison with the spinel cathode LiMn2O4. In the lithium extraction process, it has been reported that LixNi0.5Mn1.5O4 exhibits two existing phases (Li-rich and Li-lean phases) below x = 0.5 [9]. We investigated the structural relaxation of LixNi0.5Mn1.5O4 (x = 0.1, 0.2) by means of X-ray diffraction and the Rietveld analysis focusing on the change in molar ratio and structure parameter of two phases. Experiment Working electrode was prepared by LiNi0.5Mn1.5O4 powder (TOSHIMA Manufacturing Co.,Ltd) with Acetylene Black (AB) as a supplemental conductor and PVdF powder as an adhesive agent with ratio of 80 : 10 : 10 (weight ratio). Lithium foil was employed as the counter electrode and 1 mol·dm-3 LiPF6 in EC/EMC (3:7 v/v%, Kishida chemical Corp.,Ltd) was used as the electrolyte. Lithium was electrochemically extracted from LiNi0.5Mn1.5O4 using two electrode cell (Hohsen Corp.) at a constant current of 0.3C rate to obtain the sample of LixNi0.5Mn1.5O4 (x = 0.1,0.2). After the termination of Li extraction, we immediately removed the working electrode from the cell in a glove box to avoid the local cell reaction between the electrode material and the current collector. XRD data were collected from 10° to 120° in 2θ by using CuKα radiation (UltimaIV, Rigaku corp., Japan) at various relaxation time up to 70 hours. XRD data were analyzed by the Rietveld method using RIEVEC program [10]. Lattice constants and scale factors were obtained. Results and discussion Fig.1(a) and (b) show the X-ray diffraction patterns of x = 0.1 and x = 0.2 for LixNi0.5Mn1.5O4 measured after the termination of lithium extraction for 3h to 68h. Diffraction pattern gradually evolves with increasing relaxation time, i.e. the intensity of 400 peak of Li-rich phase develops while that of Li-lean phase does not change largely during relaxation. Each XRD profile can be well fitted with the Rietveld calculation. Fig.2 shows mole fraction changes of Li-rich phase. The mole fraction of Li-rich phase increases while that of Li-lean phase decreases with the relaxation time after lithium extraction. Fig.3 shows the variation of distance between oxygen and lithium for both phases. The O-Li distance of Li-lean phase is larger than that of Li-rich phase for both compositions. With the relaxation time up to 300-600 hours, Li-lean phase shrinks the O-Li distance, while Li-rich phase stretches it. It is found that, during the lithium extraction process, Li-lean phase is formed with excess amount of lithium ions, and it separates the Li-lean and Li-rich phases during the relaxation process. At the lithium extraction process, Li-lean phase with larger number of vacancy is favorable for lithium diffusion, while the ratio of Li-rich/Li-lean get into the equilibrium at the relaxation process. The decrease of the amount of lithium ion in Li-lean phase appears as the changes in the distance of oxygen and lithium. This phenomenon appears more clearly than when lithium extracted at a current of 0.1C rate.

Ti–V–Cr–Ni alloys as high capacity negative electrode active materials for use in nickel–metal hydride batteries

TiV2.1−xCrxNi0.3 (x = 0.1–0.6 and 1.0), TiyV1.7Cr0.4Ni0.3 (y = 0.9–1.1) and TiV1.7Cr0.4Niz (z = 0.3–0.5) alloys were prepared by arc-melting, and their negative electrode properties such as the maximum discharge capacity (Cdis), charge–discharge cycle performance and high-rate dischargeability (HRD) were evaluated. All the alloys consisted of two phases. The V and Cr constituents were mainly distributed in the primary phase, whereas the Ti and Ni constituents were mainly distributed in the secondary phase. The Cmax was dependent on the lattice volume of the primary phase, mole fraction of the primary phase and the plateau potential in charging. The average decrement of discharge capacity (ΔCdis) from Cmax to the discharge capacity at 30th cycle was used as an indicator of charge–discharge cycle performance. The ΔCdis was decreased or cycle performance was improved with the Cr content in the primary phase. The discharge potential at DOD = 50% (ΔE50) was linearly changed with specific discharge current (idis), and the ΔE50/Δidis and charge transfer resistance (Rct) as indicators of HRD were decreased with an increase in the Ni content in the secondary phase.

Relaxation Analysis of LiNi<sub>0.5</sub>Mn<sub>1.5</sub>O<sub>4</sub> 5 V Cathode Material by Means of the Rietveld Refinement

After electrochemically extracting lithium ions from LiNi0.5Mn1.5O4, we have investigated the structural variation during the relaxation process by means of X-ray diffraction coupled with the Rietveld analysis, assuming Li-rich and Li-lean spinel phases with symmetry coexistence. For both x = 0.1 and 0.2 of LixNi0.5Mn1.5O4, mole fraction of Li-lean phase decreases with the relaxation time, although any apparent change in lattice parameter does not occur for both phases. This indicates that Li-lean phase with larger oxygen tetrahedron size, presumably favorable for lithium diffusion, is formed with excess amount during the lithium extraction, and then it transforms into Li-rich and Li-lean phases with smaller lithium concentration during the relaxation process. Slight increase in the size of oxygen tetrahedron and decrease in that of octahedron during relaxation for Li-lean phase of x = 0.1 are also consistent with above phase change.

Isothermal (vapour + liquid) equilibrium measurements and correlation for the {n-butane (R600) + 1,1,1,3,3-pentafluoropropane (R245fa)} system at temperatures from (303.150 to 373.150) K

The isothermal VLE for the {n-butane (R600)+1,1,1,3,3-pentafluoropropane (R245fa)} system was measured at five temperatures from (303.150 to 373.150)K based on the static-analytical method. The experimental values were correlated by the Peng–Robison equation of state with the Huron–Vidal mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The results show that the experimental values are in good agreement with the calculated value. The maximum average absolute relative deviation of pressure and vapour phase mole fraction are 0.35%, 0.0047, respectively. Obviously azeotropic behaviour can be observed for the binary system.

(Vapour + liquid) equilibrium data for the {1,1-difluoroethane (R152a) + 1,1,1,3,3-pentafluoropropane (R245fa)} system at temperatures from (323.150 to 353.150) K

In this paper, (vapour+liquid) equilibrium (VLE) for the {1,1-difluoroethane (R152a)+1,1,1,3,3-pentafluoropropane (R245fa)} system was determined by a static-analytical method at T=(323.150 to 353.150)K. Values of the VLE were correlated by the Peng–Robison equation of state (PR EoS) using two different models, the van der Waals (vdWs) mixing rule and the Huron–Vidal (HV) mixing rule involving the non-random two-liquid (NRTL) activity coefficient model. The correlated results show good agreement with the experimental values. For the two models, the maximum average absolute deviations of the vapour phase mole fraction are 0.0034 and 0.0035, respectively.

Isothermal Vapor–Liquid Equilibrium (VLE) and Vapor–Liquid–Liquid Equilibrium (VLLE) Data for Two Binary Systems Containing Perfluorohexane with Carbon Monoxide or Hydrogen Sulfide at (293, 313, and 333) K

Isothermal vapor–liquid equilibrium (VLE) and vapor–liquid–liquid equilibrium (VLLE) data are presented for binary systems containing perfluorohexane (C6F14) with carbon monoxide (CO) or hydrogen sulfide (H2S). Measurements were undertaken at three temperatures, viz. (293, 313, and 333) K, with pressures ranging from (0.322 to 24.497) MPa. An apparatus based on the “static-analytic” technique was used for the measurements. The equilibrium cell is equipped with a pneumatic capillary sampler, and equilibrium phase analysis is undertaken using a gas chromatograph. The uncertainties in the experimental measurements are 0.02 K, 0.0012 MPa, and 0.006 for temperature, pressure, and equilibrium phase mole fraction, respectively. The experimental data was modeled using the direct method using three different sets of thermodynamic models. The VLE data measured for the CO + C6F14 system were correlated using the Peng–Robinson equation of state with the Mathias–Copeman alpha function and the Wong–Sandler mixing rule ...

Relaxation Structure Analysis of LixNiO2 (x=0.09) after Li-Extraction

Introduction We have investigated the structural variation of γ-Fe2O3 after the termination of lithium insertion, and revealed the transition of electrode material from kinetic state to equilibrium state clear [1,2]. We named this technique as “Relaxation analysis” and conducted this technique to various types of cathode or anode materials, such as LiMn2O4[3], LiFePO4[4], LiCoO2[5], or graphite [6] to clarify the insertion/extraction process as well as relaxation mechanism . LiNiO2 is one of the major cathode materials with low cost and low toxic nature in comparison with the widely used LiCoO2. LiNiO2 shows the rock-salt type structure with the space group, . When lithium is electrochemically extracted from the sample, two phases with similar structures (Li-rich and Li-lean phases) coexist below x = 0.32 of LixNiO2 [7,8]. In the present study, relaxation analysis has been performed on LixNiO2 (x = 0.09) after Li-extraction. We have investigated the structural relaxation of LixNiO2 (x = 0.09) by means of X-ray diffraction and the Rietveld analysis focusing on both the change of molar ratio and structure parameter in each phase. Experiment Working electrode was prepared by mixing LiNiO2 powder (Sumitomo Metal Mining Co., Ltd.) with Acetylene Black (AB) as a supplemental conductor and PVdF powder as an adhesive agent with the weight ratio of 80:10:10. Lithium foil was employed as the counter electrode and 1 mol∙dm-3 LiPF6 in EC/DMC (2:1 v/v%, Kishida chemical Co., Ltd) was used as the electrolyte. Lithium was electrochemically extracted from LiNiO2 using two electrode cell (Hohsen Co.) at a constant current of 0.01C rate to obtain the sample of Li0.09NiO2. After the termination of Li extraction, we immediately removed the working electrode from the cell in a glove box to avoid the local cell reaction between the electrode material and the current collector. XRD data were collected from 15 ° to 75° in 2θ for CuKα radiaton (RINT-TTR, Rigaku Co., Japan) at various relaxation time and were served for Rietveld structure analysis using RIEVEC program [9]. Results and discussion Fig.1 shows X-ray diffraction patterns of two phases of Li0.09NiO2 at various relaxation time after the termination of lithium extraction. Diffraction pattern gradually evolves with increasing relaxation time, i.e. the intensity of 003rich peak decreases and 003lean shifts toward the higher angle as observed in the inset. Each XRD profile can be well fitted with the Rietveld calculation. Fig.2 shows mole fraction changes of Li-lean phase. The mole fraction of Li-lean phase decreases while that of Li-rich phase increases with the relaxation time after lithium extraction. Fig.3 shows the variation of lattice constant (c-axis) for both phases. The Li-rich phase retains the c-length almost constant during the relaxation time, while Li-lean phase shrinks the c-axis. It is found that, during the lithium extraction process, Li-lean phase is formed with excess amount of lithium ions, and it separates the Li-lean phase without excess lithium ion and Li-rich phase during the relaxation process. At the lithium extraction process, Li-lean phase with larger number of vacancy is favorable for lithium diffusion, while the ratio of Li-rich/Li-lean get into the equilibrium with relaxation time.

Multiphase equilibrium calculations using a reduction method

Phase equilibrium problems (phase stability testing and multiphase flash) have to be solved repeatedly, sometimes a very large number of times, in process simulators and in compositional reservoir simulation. The computational effort can be significant, particularly when a detailed description (with a large number of components nc) of the mixture is required. The reduction method represent an attractive technique in the attempt to reduce the computational time, by significantly reducing the dimensionality of the problem, from nc×(np−1) in the conventional methods to a maximum of (2c+3)×(np−1), where np is the number of equilibrium phases and c the number of components with non-zero binary interaction parameters (BIP). The number of independent variables does not depend on nc, but only on c, and the computation time increases linearly with nc. Traditionally, the reduction approaches use the reduction parameters and the phase mole fractions as independent variables. In this work, a recent improvement of two-phase reduced flash calculations (Nichita and Graciaa, Fluid Phase Equilib. 302, 2011, 226–233) is extended to multiphase equilibrium calculation with any number of phases. Two approaches are proposed: (i) a direct extension of the reduction method for two-phase flashes and (ii) a constrained minimization Gibbs free energy with respect to a specific set of variables and constraints (taking advantage of symmetry). The proposed algorithms are tested for several multiphase systems (with up to four phases and exhibiting complex phase envelopes) containing hydrocarbon components, carbon dioxide and hydrogen sulfide. Numerical experiments show that the reduction methods for multiphase flash calculations are robust and they become faster than the conventional methods when (i) the number of components increases, (ii) the number of equilibrium phases increases and (iii) the number of BIP families decreases. For mixtures with many components and few BIP families, the reduction method may be at least one order of magnitude faster than conventional methods.