Transient pressure profiles model

Figure 13. Experimental and model transient pressure profiles. Model results are shown with solid lines. Experimental data points (symbols) are connected by dashed lines.

Milton et al. (1997) proposed the manometric temperature measurement (MTM) the transient pressure response is mathematically modeled under the assumption that four mechanisms contribute to the pressure rise, namely the direct sublimation of ice through the dried product layer at a constant temperature, the increase in the ice temperature due to continuous heating of the frozen matrix during the measurement, the increase in the temperature at the sublimation interface when a stationary temperature profile is obtained in the frozen layer and, finally, the leaks in the chamber. The four contributions are considered purely additive the values of the thickness and of the thermal gradient are needed but they are not known exactly. The values of the vapor pressure over ice, of the product resistance and the heat transfer coefficient at the vial bottom are determined with regression analysis. 

A model for transient simulation of radial and axial composition and temperature profiles In pressurized dry ash and slagging moving bed gasifiers Is described. The model Is based on mass and energy balances, thermodynamics, and kinetic and transport rate processes. Particle and gas temperatures are taken to be equal. Computation Is done using orthogonal collocation In the radial variable and exponential collocation In time, with numerical Integration In the axial direction. 

Figure 9. Transient fluorescence decay profile of 4.76 X 10 7 mol/g DP A on Cab-O-Sil, with Gaussian model simulated decay profiles at 18 °C and various pressures of oxygen ( ex = 337 nm and Xob = 430 nm).

The TAP reactor is very well suited for kinetic studies. At low pressure, all transport of gas-phase species is by (Knudsen) diffusion, thus ruling out any external mass transfer limitations. The diffusion as a random movement also eliminates all radial concentration gradients. Very low amounts of reactants are pulsed into the reactor, which are on the order of a few nanomoles. Thus, the amount of heat generated is very small even in the case of strongly exo- or endothermic reactions. Therefore, the reactor is operated isothermally and no heat transfer limitations occur. Concentration profiles inside the pores for transient experiments might arise even in the absence of chemical reaction. If significant diffusion of reactants and products inside the catalyst pores occurs, it will be revealed by the transient response and then needs to be addressed correctly by a modeling approach. This is often the case for microporous materials [26,27,72]. 

FIGURE 5.3 Modeling of transient water flux data for Nation 117. (a) The relaxation of the experimental outlet vapor pressure (open circle) for Nafion 117 in LE mode at 50°C, flow chamber volume V = 0.125 L, flow rate V = 0.1 L min membrane area A = 2 cm, and saturation vapor pressure = 12336.7 Pa. Plotted for comparison are model simulations for a slow transport coefficient (dash dot), fast transport coefficient (dash), and a concentration-dependent transport coefficient (gray), (b) Water concentration profiles calculated in the model at different time. (Reprinted from Electrochem. Commun. 13, Rinaldo, S. G. et al. Vaporization exchange model for dynamic water sorption in Nafion Transient solution, 5-7, Figures 1 and 2, Copyright (2011) Elsevier. With permission.)... 

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