“…This crossover behavior is also presented at atmospheric pressure. 9 Densities of MDEA and of each mixture were correlated using a volume explicit equation of six parameters, 36 which is a modification of the equations reported by Toscani and Szwarc. 37 where d i parameters are reported in Table 6 and were obtained using a Marquardt-Levenberg least-squares optimization procedure using the following objective function, S Temperature, pressure, and density ranges, the number of data points used to obtain the optimized parameters for MDEA and for each mixture, along with statistical values are reported in Table 6.…”
Section: Resultsmentioning
confidence: 99%
“…Densities of MDEA and of each mixture were correlated using a volume explicit equation of six parameters, which is a modification of the equations reported by Toscani and Szwarc where d i parameters are reported in Table and were obtained using a Marquardt−Levenberg least-squares optimization procedure using the following objective function, S 2 Relative deviations of experimental densities from this work (ρ(exptl)) and values calculated (ρ(calcd)) with the six-parameter equation using the parameters reported in Table for MDEA, at the following temperatures: ○, 313.09 K; ▿, 323.01 K; □, 332.95 K; ◇, 342.78 K; ▵, 352.68 K; ☆, 362.52 K. 3 Relative deviations of experimental densities at atmospheric pressure reported by Al-Ghawas et al (ρ(lit)) and values calculated (ρ(calcd)) with the six-parameter equation using the parameters reported in Table for MDEA (1) + water (2), at the following mole fraction compositions: ○, 0.0369; ▿, 0.0607; □, 0.0893 K; ◇, 0.1302. 4 Isotherms for the isothermal compressibilities of the MDEA (1) + water (2) binary mixture at x 1 = 0.1302, at the following temperatures: ○, 313.13 K; ▿, 323.09 K; □, 333.03 K; ◇, 342.91 K; ▵, 352.84 K; ☆, 362.72 K.…”
Section: Resultsmentioning
confidence: 99%
“…Derived Thermodynamic Properties. The isothermal compressibility ( K T ) and the isobaric thermal expansivity ( a p ) can be obtained from density data using the following expressions In this work, the six-parameter equation was substituted in eqs 6 and 7; therefore, K T and a p are calculated using the following two expressions 36 The uncertainties of these two thermodynamic derived properties were obtained on the basis of the parameters obtained for the six-parameter equation and were obtained according to the procedure presented in a previous work . The uncertainties were estimated to be ± 0.005 GPa -1 and ± 5·10 -7 K -1 for K T and α p , respectively.…”
PρT properties in the compressed liquid phase were measured for the system N-methyldiethanolamine (MDEA)
(1) + water (2) at temperatures between (313 and 363) K and pressures up to 20 MPa. Densities of MDEA and
four gravimetrically prepared mixtures of MDEA (1) + water (2), at x
1 = 0.0369, 0.0607, 0.0893, and 0.1302,
were determined using a vibrating tube densimeter. The classical calibration method of the vibrating tube densimeter
was used, using nitrogen and water as reference fluids. The uncertainty was estimated to be ± 0.2 kg·m-3 for the
measured densities. The densities of each mixture and of MDEA were correlated using a volume explicit equation
of six parameters. Isothermal compressibilities and isobaric thermal expansivities were calculated using the six-parameter equation with the correlated parameters obtained for MDEA and for the four mixtures. The uncertainties
on these properties were estimated to be ± 0.005 GPa-1 and ± 5·10-7 K-1, respectively. Excess molar volumes
for the mixtures were determined using the measured densities of the mixture and MDEA volumes calculated
from the six-parameter equation and water volumes calculated from a multiparameter reference equation of state
(EoS). The uncertainty in excess molar volumes was estimated to be ± 0.006 cm3·mol-1.
“…This crossover behavior is also presented at atmospheric pressure. 9 Densities of MDEA and of each mixture were correlated using a volume explicit equation of six parameters, 36 which is a modification of the equations reported by Toscani and Szwarc. 37 where d i parameters are reported in Table 6 and were obtained using a Marquardt-Levenberg least-squares optimization procedure using the following objective function, S Temperature, pressure, and density ranges, the number of data points used to obtain the optimized parameters for MDEA and for each mixture, along with statistical values are reported in Table 6.…”
Section: Resultsmentioning
confidence: 99%
“…Densities of MDEA and of each mixture were correlated using a volume explicit equation of six parameters, which is a modification of the equations reported by Toscani and Szwarc where d i parameters are reported in Table and were obtained using a Marquardt−Levenberg least-squares optimization procedure using the following objective function, S 2 Relative deviations of experimental densities from this work (ρ(exptl)) and values calculated (ρ(calcd)) with the six-parameter equation using the parameters reported in Table for MDEA, at the following temperatures: ○, 313.09 K; ▿, 323.01 K; □, 332.95 K; ◇, 342.78 K; ▵, 352.68 K; ☆, 362.52 K. 3 Relative deviations of experimental densities at atmospheric pressure reported by Al-Ghawas et al (ρ(lit)) and values calculated (ρ(calcd)) with the six-parameter equation using the parameters reported in Table for MDEA (1) + water (2), at the following mole fraction compositions: ○, 0.0369; ▿, 0.0607; □, 0.0893 K; ◇, 0.1302. 4 Isotherms for the isothermal compressibilities of the MDEA (1) + water (2) binary mixture at x 1 = 0.1302, at the following temperatures: ○, 313.13 K; ▿, 323.09 K; □, 333.03 K; ◇, 342.91 K; ▵, 352.84 K; ☆, 362.72 K.…”
Section: Resultsmentioning
confidence: 99%
“…Derived Thermodynamic Properties. The isothermal compressibility ( K T ) and the isobaric thermal expansivity ( a p ) can be obtained from density data using the following expressions In this work, the six-parameter equation was substituted in eqs 6 and 7; therefore, K T and a p are calculated using the following two expressions 36 The uncertainties of these two thermodynamic derived properties were obtained on the basis of the parameters obtained for the six-parameter equation and were obtained according to the procedure presented in a previous work . The uncertainties were estimated to be ± 0.005 GPa -1 and ± 5·10 -7 K -1 for K T and α p , respectively.…”
PρT properties in the compressed liquid phase were measured for the system N-methyldiethanolamine (MDEA)
(1) + water (2) at temperatures between (313 and 363) K and pressures up to 20 MPa. Densities of MDEA and
four gravimetrically prepared mixtures of MDEA (1) + water (2), at x
1 = 0.0369, 0.0607, 0.0893, and 0.1302,
were determined using a vibrating tube densimeter. The classical calibration method of the vibrating tube densimeter
was used, using nitrogen and water as reference fluids. The uncertainty was estimated to be ± 0.2 kg·m-3 for the
measured densities. The densities of each mixture and of MDEA were correlated using a volume explicit equation
of six parameters. Isothermal compressibilities and isobaric thermal expansivities were calculated using the six-parameter equation with the correlated parameters obtained for MDEA and for the four mixtures. The uncertainties
on these properties were estimated to be ± 0.005 GPa-1 and ± 5·10-7 K-1, respectively. Excess molar volumes
for the mixtures were determined using the measured densities of the mixture and MDEA volumes calculated
from the six-parameter equation and water volumes calculated from a multiparameter reference equation of state
(EoS). The uncertainty in excess molar volumes was estimated to be ± 0.006 cm3·mol-1.
“…22 In this case, the sensitivity coefficients are the parameters of the sixparameter equation, and the standard uncertainty refers to the number of significant decimals of the parameters of the equation as previously described. 23 The uncertainty for the isothermal compressibilities was estimated to be ( 3 • 10 -6 MPa -1 , and the uncertainty for the isobaric thermal expansivities was estimated to be ( 4 • 10 -7 K -1 . 2) mixture at 313.13 K: O, AMP; 3, x 1 ) 0.0480; 0, x 1 ) 0.0736; ], x 1 ) 0.1188; 4, x 1 ) 0.1668.…”
Section: Resultsmentioning
confidence: 99%
“…The uncertainties of the calculated isothermal compressibilities and the calculated isobaric thermal expansivities were calculated with the law of propagation of errors . In this case, the sensitivity coefficients are the parameters of the six-parameter equation, and the standard uncertainty refers to the number of significant decimals of the parameters of the equation as previously described . The uncertainty for the isothermal compressibilities was estimated to be ± 3·10 −6 MPa −1 , and the uncertainty for the isobaric thermal expansivities was estimated to be ± 4·10 −7 K −1 .…”
PFT properties in the compressed liquid phase were determined for 2-amino-2-methyl-1-propanol (AMP) and AMP + water (at x 1 ) 0.0480, 0.0736, 0.1188, and 0.1668) at temperatures from (313 to 363) K and pressures up to 24 MPa. A vibrating tube densimeter (VTD) was used to measure the densities. The classical calibration method of using two reference fluids (water and nitrogen) was used for the calibration of the VTD. The uncertainty of the measured densities was estimated to be ( 0.2 kg • m -3 . The liquid densities of aqueous AMP solutions reported in this work were correlated using a six-parameter equation. Isothermal compressibilities and isobaric thermal expansivity are calculated using the six-parameter equation within uncertainties estimated to be ( 3 • 10 -6 MPa -1 and ( 4 • 10 -7 K -1 , respectively. Also, the excess molar volumes were calculated for the mixtures using densities of AMP calculated with the obtained correlation and densities of water calculated with a reference equation of state. The uncertainty of the excess molar volumes was estimated to be ( 6 • 10 -6 m 3 • kmol -1 .
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