Thermal conductivity critical region

The general properties of supercritical fluids make them an attractive alternative to liquid solvents in column operations where transport effects come into play. If supercritical CO2 is employed as the solvent, this advantage is further supplemented by the non-flammable, non-toxic nature of the fluid, and the relative ease of solvent recovery. Supercritical solvents also offer the potential to greatly enhance thermally driven separations through dramatic changes in component solubility, adsorptive characteristics, and thermal conductivity near the critical region. 

The most extensive test which has been made of this conduction model for thermal explosion is to be found in the work of Vanp e on the explosion of CH2O + O2 mixtures. He used a calibrated thread of 10 per cent Rh-Pt alloy of 20 m diameter (jacketed by a 50-m quartz sleeve) suspended at the center of a cylindrical vessel to measure directly his reaction temperature during the induction periods preceding explosion. By Uvsing He and Ar as additives and vessels of different diameters he was able to verify the dependence of the critical explosion limits on vessel size and on thermal conductivity of the gas mixture. In addition, he was able to check the maximum predicted temperature at the center of the vessel just prior to explosion and also the value of 8c = 2 [Eq. (XIV.3.12)], the critical explosion parameter for cylindrical vessels. Finally, with a high-speed camera, he was able to show directly that the explosions in this system do start at the center, the hottest region, " and propagate to the walls. 

The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5% for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%. 

For thermal conductivity, the uncertainty for the dilute gas is 2% wifti increasing uncertainties near the triple point. For the nondilute gas, the uncertainty is 2% for temperatures greater than 170 K. The uncertainty is 3% at temperatures less than the critical point and 5% in the critical region, except for states very near the critical point. 

Uncertainty in thermal conductivity is 3%, except in the critical region and dilute gas which have an uncertainty of 5%. 

At pressures up to 30 MPa and temperatures up to 523 K, the estimated uncertainty ranges from 0.03% to 0.05% in density, 0.03% (in the vapor) to 1% in the speed of sound (0.5% in the liquid), and 0.15% (in the vapor) to 1.5% (in the liquid) in heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation (to the limits of chemical stability). The uncertainty in viscosity ranges from 0.3% in the dilute gas near room temperature to 5% at the highest pressures. The uncertainty in thermal conductivity is less than 5%. 

For a discussion of the uncertainties associated with the equation of state and thermal conductivity entries of this table, please see the source references given above. The uncertainty in viscosity is 1% in the liquid below 474 K, 2% in the liquid at higher temperatures and in the vapor, and 5% between 623 and 723 K at pressures between 16 and 50 MPa. The uncertainty in viscosity is 2% in the liquid below 623 K and in the vapor below 573 K, 5% elsewhere in the liquid and vapor, and 10% in the critical region (623 to 723 K and 21.66 to 50 MPa). 

The uncertainties in density are 0.1% in the liquid phase below the critical temperature, 0.4% in the vapor phase, 1% at supercritical temperatures up to 500 K, and 2.5% at higher temperatures. Uncertainties will be higher near the critical point, and may be lower than 0.5% between 400 and 500 K. The uncertainty in vapor pressure is 0.25%, and the uncertainty in heat capacities is estimated to be 1%. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4-6%. 

The uncertainties in density are 0.02% at temperatures below 340 K and pressures below 12 MPa (both liquid and vapor states), 0.3% at temperatures below 300 K and pressures above 12 MPa, 0.1% in the vapor phase between 340 and 450 K, and 0.5% elsewhere. In the critical region, deviations in pressure are 0.5%. Uncertainties in heat capacities are typically 1-2%, rising to 5% in the critical region and at temperatures below 200 K. Uncertainties in the speed of sound are typically 1-2%, rising to 5% at temperatures below 200 K and in the critical region. The uncertainty in viscosity varies from 0.4% in the dilute gas between room temperature and 600 K to 3.0% over the rest of the fluid surface. Uncertainty in thermal conductivity is 3%, except in the critical region and dilute gas which have an uncertainty of 5%. 

The uncertainties in the equation are 0.05% in the saturated-liquid density between 280 and 335 K and 6.2% in density in the liquid phase below 430 K and 10 MPa. The uncertainty increases to 0.3% up to 100 MPa and 0.5% up to 800 MPa. In the vapor phase and at supercritical state points, the uncertainty in density is 1%, whereas in the liquid phase between 430 K and the critical point it is 0.5% in density. Other uncertainties are 0.2% in vapor pressure between 300 and 430 K, 0.5% in vapor pressure at higher temperatures, 2% in heat capacities below 550 K, 5% at higher temperatures, and 1% in the liquid-phase speed of sound below 430 K. The estimated uncertainty in viscosity is 1.0% along the saturated-liquid line, 5% elsewhere. Uncertainty in thermal conductivity is 3%, except in the supercritical region and dilute gas which have an uncertainty of 5%. 

Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K, the uncertainty is 8%. The uncertainty in thermal conductivity is 5%. 

Many physical properties undergo dramatic changes in value as water is heated and pressurized from sub- to supercritical conditions, particularly in the region of the critical point where some properties such as heat capacity reach a singularity. This change in behavior means that more familiar correlations of properties measured at subcritical conditions are likely to be inaccurate when applied at supercritical conditions. There have been some experimental studies performed to measure, tabulate, and in some cases correlate values of key properties of supercritical water, such as the self-diffusion coefficient, viscosity,thermal conductivity," heat capacity at constant volume," dielectric constant," and selfdissociation constant." " Far more work has been devoted to calculation of property values from models fitted empirically to data or developed more rigorously through molecular simulation. For PVT data and its derivatives, several attempts... 

The uncertainties in density are 0.03% for pressures below 12 MPa and temperatures below 350 K and up to 0.07% for pressures less than 50 MPa. For the speed of sound, the uncertainty ranges from 0.03% (in the vapor phase) to 0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of 1%. The uncertainty in viscosity is 2%, except in the critical region which is 5%. The uncertainty in thermal conductivity of the dilute gas between 130 and 625 K is 2.5%. For temperatures below 130 K, the uncertainty is less than 10%. Excluding the dilute gas, the uncertainty is 2% between 110 and 725 K at pressures up to 70 MPa, except near the critical point which has an uncertainty of 5% or greater. For the vapor at lower temperatures and the dense liquid near the triple point, an uncertainty of 10% is possible. 

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