Abstract
Vapor pressure is a fundamental thermodynamic property, the measurement of which is particularly important. Coal-fired pollution control research needs basic data on the vapor pressure of heavy metals, but it is very low and is difficult to measure. A common method for measuring very low vapor pressure is thermogravimetric analysis, wherein vapor pressure is estimated using the evaporation rate. The key factors affecting the measurement accuracy are the conditions under which the linear relationship between the vapor pressure and the evaporation rate is established and the similarity of the calibration constants k of different substances.
Taking the TA Q500 thermogravimetric analyzer as an example, this paper establishes a mathematical model for isothermal evaporation in a thermogravimetric analyzer. The thermogravimetric analyzer's flow field and evaporation process are analyzed via computational fluid dynamics (CFD) method. Numerical simulations are conducted for six organic substances and 160 model substances under various temperature and carrier gas flow conditions. The independence of the grids used in the numerical simulations is verified through examination of the x-direction velocities, y-direction velocities, and mass fraction distributions for different numbers of grids. The reliability of the calculated results is verified using the experimental results obtained for the vapor pressure of benzoic acid.
A comparison of the mass distribution diagrams of organic substances revealed that the evaporative mass transfer in the thermogravimetric analyzer was due to the combined effect of molecular diffusion and convective transport. The evaporation process, which was typically analyzed using the Langmuir equation, was based on molecular diffusion, which meant that the Langmuir equation was not be applicable to describe the evaporation process inside the thermogravimetric analyzer. The experimental conditions (carrier gas flow rate and temperature) and substance properties (molar mass, vapor pressure, and diffusion coefficient) would affect the evaporation and mass transfer of the substance and further affected the calibration constant k. A numerical simulation of the isothermal evaporation process of 160 model substances revealed that the difference in the physical properties of these substances could result in significant differences in k. k increased with decreasing molar mass and diffusion coefficient and increasing vapor pressure. The dimensionless analysis of the governing equations showed that the evaporation process was determined by the dimensionless quantities Re(Reynolds number), Pe(Peclet number), and wi(the dimensionless form of the sample vapor mass fraction on the crucible surface). Through the dimensionless analysis of the governing equations, the nonlinear relationship between evaporation rate and vapor pressure was obtained via fitting. When the molar mass and vapor pressure of the substance were small, the relationship between the vapor pressure and the evaporation rate was more linear. The deviations obtained from the different calibration-constant calculation methods were compared. The results confirmed that the calibration constant k was related to the vapor pressure. The results also proved that the key influencing parameters obtained through the dimensionless analysis of the governing equation were reliable. The influence of physical properties on pressure measurement deviation was analyzed, and the results revealed that the closer the molar mass and diffusion coefficient values between the substance to be measured and the calibration substance, the smaller the difference in k between the two substances.
Based on the analysis of the results, it is found that: The relationship between evaporation rate and vapor pressure is approximately linear only when the molar mass and vapor pressure of the substance are small. When choosing a calibration substance, in order to reduce the measurement deviation of vapor pressure, the substance with the diffusion coefficient and molar mass of the substance to be measured should be selected as close as possible.
