Simulations transient mass transfer

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Using Equation (13), the external mass transfer coefficient at 723 K was calculated to be 60 cm/s. Since the reactor operating conditions at th s temperature (723 K, slightly above atmospheric pressure, 247 cm /s) were very similar to those of our transient chemisorption experiments, the external mass transfer coefficient calculated above was used for the simulations. 

Abstract The objective of this chapter is to present some recent developments on nonaque-ous phase liquid (NAPL) pool dissolution in water saturated subsurface formations. Closed form analytical solutions for transient contaminant transport resulting from the dissolution of a single component NAPL pool in three-dimensional, homogeneous porous media are presented for various shapes of source geometries. The effect of aquifer anisotropy and heterogeneity as well as the presence of dissolved humic substances on mass transfer from a NAPL pool is discussed. Furthermore, correlations,based on numerical simulations as well as available experimental data, describing the rate of interface mass transfer from single component NAPL pools in saturated subsurface formations are presented. 

A glib generalization is that the design equations for noncatalytic fluid-solid reactors can be obtained by combining the intrinsic kinetics with the appropriate transport equations. The experienced reader knows that this is not always possible even for the solid-catalyzed reactions considered in Chapter 10 and is much more difficult when the solid participates in the reaction. The solid surface is undergoing change. See Table 11.6. Measurements usually require transient experiments. As a practical matter, the measurements will normally include mass transfer effects and are often made in pilot-scale equipment intended to simulate a full-scale reactor. Consider a gas-solid reaction of the general form... 

In general, it can be concluded that substantial progresses have been made in the experimental and theoretical analysis of trickle-bed reactors under unsteady-state conditions. But until now these results are not sufficient for a priori design and scale-up of a periodically operated trickle-bed reactor. The mathematical reactor models, which are now available are not detailed enough to simulate all of the main transient behavior observed. For solving this problem specific correlations for specific model parameters (e.g. Hquid holdup, mass transfer gas-solid and liquid-solid, intrinsic chemical kinetic, etc.) determined under dynamic conditions are required. The available correlations for important hydrodynamic, mass-and heat-transfer parameters for periodically operated trickle-bed reactors leave a lot to be desired. Indeed, work for unsteady-state conditions on a larger scale may also be necessary. 

The above set of partial differential equatimis are highly coupled to each other. As an example, the solution of the Poisson equation (Eq. 1) is affected by the ionic mass transfer (c,) and the electric potential ( ). The Nemst-Planck equation (Eq. 5) is a fimction of the ionic mass transfer (c,), the velocity ( m ), and the electric potential ((f)). The Stokes equation (Eq. 8) is also a function of all these variable (C,-, u, and ). Therefore, these equations must be solved simultaneously with the corresponding boundary conditions to model the electrokinetics in the nanochannels. Here, it should be mentioned again that the transient response of the electrokinetics in the nanochannels is negligible, and in the simulations, the steady-state forms of the governing equations are usually solved. 

The model species, total mass, momentum, and energy continuity equations are similar to those presented in Section 13.7 on fluidized bed reactors. Constant values of the gas and liquid phase densities, viscosities, and diffusivities were assumed, as well as constant values of the interphase mass transfer coefficient and the reaction rate coefficient. The interphase momentum transfer was modelled in terms of the Eotvos number as in Clift et al. [1978]. The Reynolds-Averaged Navier-Stokes approach was taken and a standard Computational Fluid Dynamics solver was used. In the continuous liquid phase, turbulence, that is, fluctuations in the flow field at the micro-scale, was accounted for using a standard single phase k-e model (see Chapter 12). Its applicability has been considered in detail by Sokolichin and Eigenberger [1999]. No turbulence model was used for the dispersed gas phase. Meso-scale fluctuations around the statistically stationary state occur and were explicitly calculated. This requires a transient simulation and sufficiently fine spatial and temporal grids. 

To understand the heat and moisture flow characteristics of textile fabrics, many mathematical models have been propounded. Matty computational tools like Computational Fluid Dynamics (CFD), artificial neural networks, fuzzy logic and many more are also being used to understand the complex relationships between the clothing parameters and the perception of comfort. This chapter deals with the studies on heat and mass transfer properties of textile assemblies. The phenomena covered here are diy steady state heat transfer, transient heat transfer, moisture vapor and liquid moisture transfer and coupled heat and moisture transfer properties of fibers, fiber bundles, fibrous materials and other textile stmctures. The processes involved in each and the woik done on modeling and simulation of the transfer processes till date, from the point of view of clothing comfort have been discussed. 

Improvements to the model have been made by Lawson et al. [44-46]. The improvements use estimates of thermal conductivity, specific heat and thermo-optical properties (transmittance, reflectance and absorptance) obtained from the thermal data collected from the testing of a variety of fabrics typically used in fire fighters protective clothing. A detailed mathematic model is developed to study transient heat and moisture transfer through multilayered fabric assemblies with or without air gaps. First principles are used to derive the governing equations for transient heat and moisture transfer. The equations also account for the effect of moisture on thermodynamic and transport properties. Numerical simulations are used to study heat and mass transfer. A software tool (Protective Clothing Performanee... 

Simulator) is developed which allows users to study transient heat and mass transfer through multi-layered assemblies with or without air gaps. Fabric l er characteristics, air gap thickness, moisture levels, compression and boimdary conditions are considered. 

Returning again to our overall model, we now have a complete representation of the polarization curve. If we know several key paramaters relating to the kinetic, ohmic, and mass transfer processes, we can predict the overall polarization curve of the fuel cell. Much more complex models exist in the literature to cover multidimensional, multiphase, and transient aspects as well as approach the problem from various length scales from molecular to full-size stack simulation. However, the approach taken here does include the most important physicochemical phenomena that affect fuel cell performance ... 

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