Krichevsky-Kasarnovsky Equation Research Articles

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering (∂p∂x)T, x→0 as an infinite dilution thermodynamic function. Our research shows that (∂p∂x)T,x→0 as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: ln(∂p∂x)T, x→0=AT+B. Then, we use this equation to correlate the isothermal vapor−liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs−Duhem equation to re-derive the relationship between (∂p∂x)T,x→0 and the infinite dilution activity coefficient (γ∞) at low pressure. Based on the definition of partial molar volume, an equation for (∂p∂x)T,x→0 and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky−Kasarnovsky equation, the developed model provides more reliable results.

A constitutive model for predicting the solubility of gases in water at high temperature and pressure

In the drilling and development of gas fields, gas exhibits good solubility in drilling fluids and in the formation water under high temperatures and pressures. Therefore, the prediction of the amount of dissolved gas in water plays a vital role in the development of natural gas. In this work, the principle of equal fugacity in a gas-liquid equilibrium, a non-iterative gas solubility prediction model was established. The gas-phase fugacity coefficient was calculated by the Peng-Robinson equation of state combined with the non-random mixing rule, and the liquid phase was calculated by Henry's law. The model can predict the solubility of CO2, CH4 and C2H6 in pure water at temperatures of 273–448 K and pressures of 0–100 MPa, with an error of less than 5.5%; however, the calculation accuracy for H2S was low. It is found that the effect of moisture in the gas phase of gas-liquid equilibrium cannot be ignored. Compared with the existing mixed gas solubility experimental data, this model could accurately calculate the solubility of non-polar mixed gases, such as CO2 + CH4, and CH4 + C2H6 mixture. For the mixtures containing a polar gas, the lower the polar gas content, the smaller was the prediction error of the model for the non-polar gas in the mixture. On the contrary, the higher the content of polar gas, the larger was the deviation in the prediction of non-polar gas in the mixture, but lower was the deviation in the prediction of polar gas. Finally, the ability of Krichevsky-Kasarnovsky equation to predict the solubility of pure gas was evaluated.

Experimental investigation and thermodynamic modeling of xenon clathrate hydrate stability conditions

In this work, the equilibrium conditions of xenon hydrates have been measured within wide pressure and temperature ranges. Various experimental equipment have been used for this purpose, namely the tensimeter, the Cailletet apparatus, and the high-pressure autoclave. A number of three-phase equilibrium data points were measured for liquid water-hydrate-vapor (Lw-H-V) and the ice-hydrate-vapor (I-H-V). It was concluded that there is a good consistency between the experimental data points measured in this work and those obtained by the other groups in the literature. A modified van der Waals-Platteeuw (vdW-P) model was used to predict the xenon hydrate stability conditions. The Kihara spherical-core potential function was used to represent the intermolecular forces between the water molecules and the xenon molecules in the cavities. The fugacity of xenon in the vapor/gas phase was computed using the Peng-Robinson (PR) EoS. The solubility of xenon in the liquid phase was calculated through the Krichevsky-Kasarnovsky equation. The investigated model had the ability to predict the xenon hydrate stability conditions with good accuracy within wide ranges of pressures and temperatures, resulting in an average absolute deviation (AAD) of about 0.61 K for (Lw-H-V) and 0.42 K for (I-H-V) equilibrium temperatures.

Densities and viscosities of, and NH3 solubilities in deep eutectic solvents composed of ethylamine hydrochloride and acetamide

Deep eutectic solvents (DESs) are a novel class of green solvents with promising application in gas separation. The physical properties of, and gas solubilities in DESs are fundamental data for industrial process design. In this work, the densities and viscosities of ethylamine hydrochloride (EaCl) plus acetamide (AA) mixtures were determined in the temperature range of (313.2–353.2) K. The density data and viscosity data were fitted to a linear equation and the Vogel-Fulcher-Tammann equation respectively. Furthermore, the solubilities of NH3 in EaCl + AA mixtures were determined in the temperature range of (313.2–353.2) K and pressure range of (0–300.0) kPa. It is found that the isothermal profiles for NH3 absorption slightly deviate from ideal type, probably due to the strong hydrogen-bond interaction between NH3 and EaCl. The solubilities of NH3 in EaCl + AA mixtures are fairly good, with the value of 3.84 mol·kg−1 at 313.2 K and 96.4 kPa for EaCl + AA (1:1). The solubility data were fitted to the Krichevsky-Kasarnovsky equation to calculate the Henry’s constants of NH3 in EaCl + AA mixtures. With the Henry’s constants at different temperatures, the thermodynamic functions such as enthalpy changes, Gibbs free energy changes and entropy changes for NH3 absorption in EaCl + AA mixtures were also estimated.

Solubilities of carbon dioxide, oxygen, and nitrogen in aqueous ethylene glycol solution under low pressures

The solubilities of carbon dioxide, oxygen, and nitrogen in aqueous ethylene glycol(EG) solution with EG mass fraction 0.365 were measured at temperatures from (263–293) K and pressures from (0.009–0.101) MPa based on an isochoric saturation method. A new experimental setup was built and checked by measuring the solubility of carbon dioxide in water. The expanded uncertainty (k = 2) of the measured solubility data was estimated to be less than 4.0%. The experimental results of carbon dioxide, oxygen, and nitrogen in aqueous EG solution were successfully correlated with a modified Krichevsky–Kasarnovsky equation. The absolute average deviations of the experimental and fitted values were 5.2%, 3.2%, and 2.6%, respectively.

CO2 capture with the help of Phosphonium-based deep eutectic solvents

Deep eutectic solvents (DESs) are derived from the concomitant reaction of two or more salts i.e. between hydrogen bond acceptor (HBA) and hydrogen bond donors (HBD) components. In this work, DESs were prepared namely allyltriphenyl phosphonium bromide-diethylene glycol (ATPPB-DEG) and allyltriphenyl phosphonium bromide-triethylene glycol (ATPPB-TEG) into three molar ratios 1:4, 1:10, and 1:16 salt to HBDs. The carbon dioxide solubility in DESs at temperature of 303.15K and pressure up to 2MPa were determined and reported in terms of mole fraction, CO2 loading and Henry's law constants. Krichevsky–Kasarnovsky equation was used to correlate the solubility data and obtain Henry's law constants at 303.15K. Finally, the effects of hydrogen bonding within DESs, molar ratio, molar volume, free volume, ether group and alkyl chain length were investigated based on CO2 solubility in DESs. To the best of our knowledge, this is the first time CO2 solubility in these DESs was studied.

Gaseous absorption of 2,3,3,3-tetrafluoroprop-1-ene in three imidazolium-based ionic liquids

The properties of working pairs of refrigerant and absorbent have a great influence on the performance of absorption refrigeration cycle. In this work, the measurements of absorption properties for 2,3,3,3-tetrafluoroprop-1-ene/1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]), 2,3,3,3-tetrafluoroprop-1-ene/1-hexyl-3-methylimidazolium tetrafluoroborate ([HMIM][BF4]), and 2,3,3,3-tetrafluoroprop-1-ene/1-methyl-3-octylimidazoliumtetrafluoroborate ([OMIM][BF4]) between 283.15 and 343.15 K were performed by means of an isochoric saturation method. Experimental data were correlated using NRTL model and Krichevsky-Kasarnovsky (K-K) equation. The studied results show that absorption of gaseous 2,3,3,3-tetrafluoroprop-1-ene increases with a decrease in temperature and an increase in pressure, and absorption diminished in the following order: [OMIM][BF4] > [HMIM][BF4] > [EMIM][BF4].

Vapor–Liquid Equilibrium of R1234yf/[HMIM][Tf2N] and R1234ze(E)/[HMIM][Tf2N] Working Pairs for the Absorption Refrigeration Cycle

The solubilities of 2,3,3,3-tetrafluoropropylene (R1234yf) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([HMIM][Tf2N]) were measured at temperatures from 293 to 353 K and at pressures up to 925 kPa. A comparison of the solubilities of R1234yf, R1234ze(E), and hydrofluorocarbons in [HMIM][Tf2N] was conducted and showed that the solubilities of R1234yf and R1234ze(E) are comparable to those of hydrofluorocarbons but more sensitive to temperature. The solubilities of R1234yf and R1234ze(E) in [HMIM][Tf2N] were correlated well with a modified Krichevsky–Kasarnovsky equation and the NRTL equation.

Solubilities of propane and cyclopropane in 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate

Absorption refrigeration is an important energy saving technology that can utilize low-grade energy. A hydrocarbon and an ionic liquid are a promising working pair for the absorption refrigeration system. In this work, the solubilities of propane and cyclopropane in 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate at temperatures from 302 K to 344 K and at pressures up to 0.9 MPa were measured. The experimental results were correlated successfully with a modified Krichevsky–Kasarnovsky equation. The mean absolute relative deviations and the maximum absolute relative deviations of the modified Krichevsky–Kasarnovsky equation from the experimental results are less than 1.4 % and 3.7 %, respectively.

Solubilities of R32, R245fa, R227ea and R236fa in a phosphonium-based ionic liquid

New solubility data for difluoromethane (R32), 1,1,1,3,3-pentafluoropropane (R245fa), 1,1,2,2,3,3,3-heptafluoropropane (R227ea) and 1,1,1,3,3,3-hexafluoropropane (R236fa) in trihexyltetradecylphosphonium bis(2,4,4-trimethylpentyl)phosphinate ([P14666][TMPP]) at temperatures from 292K to 344K and at pressures from 0.01MPa to 1.07MPa is presented in this work. Low temperature and high pressure can improve the solubilities of hydrofluorocarbons in [P14666][TMPP]. Hydrofluorocarbons are more soluble in [P14666][TMPP] than their corresponding alkanes. Dispersive force, dipole–dipole interaction and hydrogen bond interaction were considered to exist between HFC and [P14666][TMPP]. A modified Krichevsky-Kasarnovsky equation was used to correlate the solubilities of R32, R227ea, R236fa and R245fa in [P14666][TMPP] with the mean absolute relative deviations and the maximum absolute relative deviations less than 2.0% and 4.3%, respectively.

Gaseous absorption of fluorinated ethanes by ionic liquids

Solubilities of 1,1-difluoroethane (R152a), pentafluoroethane (R125), fluoroethane (R161), 1,1,1-trifluoroethane (R143a) and 1,1,1,2-tetrafluoroethane (R134a) in trihexyltetradecylphosphonium bis(2,4,4-trimethylpentyl) phosphinate ([P(14) 666][TMPP]) from 302.2K to 343.6K and up to 1.14MPa are presented in this work. Effects of fluorine atoms of fluorinated ethanes, the cations and anions of ionic liquids on the solubility behaviors are investigated by comparing the solubilities of fluorinated ethanes and ethane in different ionic liquids. Moreover, the partial molar enthalpies and partial molar entropies of solutions at infinite dilution limit for R161, R143a, R125, R134a and R152a in [P(14) 666][TMPP] are obtained. The experimental results are successfully correlated with a modified Krichevsky–Kasarnovsky equation.

Ethane and Ethylene Solubility in an Imidazolium-Based Lipidic Ionic Liquid

The solubilities of ethane and ethylene in the lipidic ionic liquid 1-(Z-octadec-9-enyl)-3-methylimidazolium bistriflimide are measured at 298, 313, and 333 K from 0.1 MPa to about 2 MPa and are correlated and well reproduced with the Krichevsky-Kasarnovsky equation. Ethane is shown to have slightly higher solubility than ethylene, in agreement with results from other ionic liquids with significant nonpolar structural content, although fit Henry’s constants are the same within experimental error. Additionally, this is the first example of an imidazolium-based ionic liquid with Henry’s constants for ethane and ethylene that are below 5 MPa at room temperature. This supports the idea that these classes of solvents have “nonpolar-like” solvent properties and may be used as alternatives for reaction and separations processes that currently require volatile, nonpolar solvents, even though these species are ionic in nature. Experimental solubility data are compared to COSMO-RS predictions, which give good qualitative predictions of solubility but significantly overpredict the Henry’s constant for both species.

Vapor–Liquid Equilibrium of Three Hydrofluorocarbons with [HMIM][Tf2N

New experimental data for the vapor–liquid equilibrium of 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([HMIM][Tf2N]) with difluoromethane (R-32), 1,1-difluoroethane (R-152a), and pentafluoroethane (R-125) were presented. Measurements were performed using an isochoric saturation method at temperatures from (302.3 to 344.1) K and at pressures between (0.03 to 1.22) MPa. The relative expanded uncertainty in solubility measurement is less than 4 %. Within the investigated temperature and pressure range, the order of the solubilities for R-32, R-152a, and R-125 in [HMIM][Tf2N] is R-152a > R-32 > R-125. The experimental results were successfully correlated with the Krichevsky–Kasarnovsky equation. The AAD between the experimental data and calculated values for the solubilities of R-152a, R-32, and R-125 in [HMIM][Tf2N] are 1.4 %, 1.5 %, and 0.8 %, respectively.

Solubilities of isobutane and cyclopropane in ionic liquids

In this work, we presented the solubilities of isobutane and cyclopropane in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([HMIM][Tf2N]) and trihexyl tetradecylphosphonium bis(2,4,4-trimethylpentyl) phosphinate ([P(14)666][TMPP]) from T=(302 to 344)K up to 1.16MPa. Henry’s constants for isobutane and cyclopropane in [HMIM][Tf2N] and [P(14)666][TMPP] were calculated from experimental results. Solubilities of isobutane and cyclopropane in [HMIM][Tf2N] are apparently smaller than those in [P(14)666][TMPP]. The effects of temperature, pressure and the number of carbon atoms in the hydrocarbons on the solubility were investigated in detail. A modified Krichevsky–Kasarnovsky equation was successfully applied to correlate the experimental results. The mean absolute relative deviations and the maximum absolute relative deviations are less than (2.4 and 4.6)%, respectively.

Solubilities of R-161 and R-143a in 1-Hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Ionic liquid and hydrofluorocarbon are considered as a promising working pair of the absorption refrigeration cycle. Solubilities of R-161 and R-143a in 1-Hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([HMIM][Tf2N]) from 302.2K to 344.3K and up to 1.55MPa were presented in this work. Solubilities of these two refrigerants in [HMIM][Tf2N] decrease with increasing temperature and increase with increasing pressure. Compared with carbon dioxide and small hydrocarbons (C=1, 2, 3), R-161 and R-143a are more soluble in [HMIM][Tf2N]. The experimental results were modeled with a modified Krichevsky–Kasarnovsky equation. The AAD between the experimental data and calculated values for the solubilities of R-161 and R-143a in [HMIM][Tf2N] are 2.4% and 3.1%, respectively.

Experimental Determination of NH3 Solubility in Toluene at Pressures up to 340 kPa at 398 K

The solubility of ammonia in toluene has been measured at 398 K and at pressures up to 340 kPa using a static, synthetic and isochoric technique. The goal of the present study is to determine the equilibrium solubility of ammonia in toluene at a pressure and temperature regime that is relevant to the reaction conditions of amination of 1,3,5-trichloro-2,4,6-trinitrobenzene leading to the formation of 1,3,5-triamino-2,4,6-trinitro benzene. The ammonia solubility data in toluene were hitherto unavailable under these experimental conditions. The solubility data have also been compared with the result obtained from a direct sampling method. The results are in agreement with Krichevsky–Kasarnovsky equation. The Henry’s law constant at the reaction temperature has been determined.

CO₂ Capture and Separation Properties in the Ionic Liquid 1-n-Butyl-3-Methylimidazolium Nonafluorobutylsulfonate.

Recently, the use of ionic liquids (ILs) for carbon capture and separation processes has gained great interest by many researchers due to the high solubility of CO2 in ILs. In the present work, solubility measurements of CO2 in the novel IL 1-n-butyl-3-methylimidazolium nonafluorobutylsulfonate [C4mim][CF3CF2CF2CF2SO3] were performed with a high-pressure view-cell technique in the temperature range from 293.15 to 343.15 K and pressures up to about 4.2 MPa. For comparison, solubilities of H2, N2, and O2 in the IL were also measured at 323.15 K via the same procedure. The Krichevsky-Kasarnovsky equation was employed to correlate the measured solubility data. Henry’s law constants, enthalpies, and entropies of absorption for CO2 in the IL were also determined and presented. The CO2 solubility in this IL was compared with other ILs sharing the same cation. It was shown that the solubility of CO2 in these ILs follows the sequence: [C4mim][CF3CF2CF2CF2SO3] ≈ [C4mim][Tf2N] > [C4mim][CF3CF2CF2COO] > [C4mim][BF4], and the solubility selectivity of CO2 relative to O2, N2, and H2 in [C4mim][CF3CF2CF2CF2SO3] was 8, 16, and 22, respectively. Furthermore, this IL is regenerable and exhibits good stability. Therefore, the IL reported here would be a promising sorbent for CO2.

Determination and calculation of phase equilibrium for water + sodium sulfate + magnesium sulfate + propane system with tetrahydrofuran as additive at 0 °C

In order to develop a new process for concentrating and separating sodium sulfate (Na2SO4) and magnesium sulfate (MgSO4) of the bloedite by gas hydrate, the equilibrium of the ternary system H2O–Na2SO4–C3H8, H2O–MgSO4–C3H8 and the quaternary system H2O–Na2SO4–MgSO4–C3H8 with tetrahydrofuran (THF) additive were studied at 0°C. It showed that the mass percentage of Na2SO4 (MgSO4) in equilibrium liquid was higher than in feed. It proved that gas hydrate could be used to the concentration and separation of Na2SO4 and MgSO4. The solubility of the propane was calculated based on the Krichevsky–Kasarnovsky equation. The extended Pitzer model of electrolyte–electrolyte–nonelectrolyte–water system was derived and applied into H2O–Na2SO4–MgSO4–C3H8 system and its sub-systems. The necessary thermodynamic parameters had been derived from a least-squares optimization program. The model calculation value was in good agreement with experimental solubility for ternary and quaternary mixtures, which indicated that the Pitzer model could be successfully used to predict the phase equilibrium of the electrolyte–electrolyte–nonelectrolyte–water systems containing gas hydrate.

Determination of Henry’s law constant of light hydrocarbon gases at low temperatures

The solubility of i-butane in water at the low temperatures was measured (274K to 293K). Additionally, Henry’s law constants of light hydrocarbons (methane, ethane, propane, i-butane, and n-butane) in water at the low temperatures are reported. A modified equation based on Krichevsky–Kasarnovsky equation is proposed to consider the effect of pressure and temperature on the equation parameters. Results show that Henry’s law constant of the selected components depends on temperature. It is deduced that pressure has a considerable effect on Henry’s law constant for methane, ethane, and propane, whereas this dependency for butanes is negligible.

Solubilities Prediction and Partial Molar Volume Calculation for 2-Butanol and CO<sub>2</sub> Binary Mixture at High Pressure

A constant-volume visual cell was used to measure vapor-liquid phase equilibrium data of 2-butanol in supercritical carbon dioxide from 323.2K to 353.2K. The phase equilibrium solubilities were predicted by Peng-Robinson equation of state together with Vander Waals-2 mixing regulation. Dependence of solubility of CO2 in liquid 2-butanol on pressure was discussed by Krichevsky-kasarnovsky equation. Meanwhile, Henry’s constants and partial molar volume at infinite dilution were determined. Also partial molar volumes of vapor phase and liquid phase at equation state were evaluated from proposed model. The correlation between calculated values and the experimental data showed good agreement.