Porosity and velocity distribution

Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance... 

A survey of literature exhibits the fact that up to now not much attention has been paid to the impact of porosity and velocity distribution on the analysis of fixed bed chemical reactors. Under non-uniform flow conditions Chaudhary et al. [8] compared measured and calculated concentration profiles for an isomerization reaction in an isothermal fixed bed chemical reactor... 

Ktifner, R. and Hofmann, H., 1990. Implementation of Radial Porosity and Velocity Distribution in a Reactor Model for Heterogeneous Catalytic Gas-Phase Reactions (Torus-Model). Chemical Engineering Science, 45(8) 2141-2146. 

Pneumatic conveying is a common method for transportation of particulate solids within or between processing plants. Particles are mobilized commonly using air and transported inside pipes or ducts. To attain a consistent flow of particles, particle mobilization and fluid pressure drop should be understood in detail. Stationary particles and excessive pressure drop could halt the flow. Figure 7.35 shows a study by Kuang et al. [84] on particle-gas behavior in a horizontal pipe with a view to investigate particle porosity and velocity distribution as well as gas pressure drop. 

Vortmeyer, D. and R. P. Winter. Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance. ACS Symp. Ser. 196 (1982) l+9 6l. 

The catalysts used in this CCR commercial service must meet several stringent physical property requirements. A spherical particle is required so that the catalyst flows in a moving bed down through the process reactors and regenerator vessel. These spheres must be able to withstand the physical abuse of being educated and transferred by gas flow at high velocity. The catalyst particles must also have the proper physical properties, such as particle size, porosity, and poresize distribution, to achieve adequate coke combustion kinetics. 

Variables It is possible to identify a large number of variables that influence the design and performance of a chemical reactor with heat transfer, from the vessel size and type catalyst distribution among the beds catalyst type, size, and porosity to the geometry of the heat-transfer surface, such as tube diameter, length, pitch, and so on. Experience has shown, however, that the reactor temperature, and often also the pressure, are the primary variables feed compositions and velocities are of secondary importance and the geometric characteristics of the catalyst and heat-exchange provisions are tertiary factors. Tertiary factors are usually set by standard plant practice. Many of the major optimization studies cited by Westerterp et al. (1984), for instance, are devoted to reactor temperature as a means of optimization. 

The lack of a method to determine the spatial distributions of permeability has severely limited our ability to understand and mathematically describe complex processes within permeable media. Even the degree of variation of intrinsic permeability that might be encountered in naturally occurring permeable media is unknown. Samples with permeability variations will exhibit spatial variations in fluid velocity. Such variations may significantly affect associated physical phenomena, such as biological activity, dispersion and colloidal transport. Spatial variations in the porosity and permeability, if not taken into account, can adversely affect the determination of any associated properties, including multiphase flow functions [16]. 

We have developed a method to spatially resolve permeability distributions. We use MRI to determine spatially resolved velocity distributions, and solve an associated system and parameter identification problem to determine the permeability distribution. Not only is such information essential for investigating complex processes within permeable media, it can provide the means for determining improved correlations for predicting permeability from other measurements, such as porosity and NMR relaxation [17-19]. 

Dimensionless, entirely empirical correlations The problem is, that the pressure drop depends on many variables the gas-and liquid velocities, uL and ug, the gas-and liquid densities, pL and pc, the particle-diameter, dp, and eventually the diameter and shape distribution, the surface tension, at, the viscosity, pi, of the liquid and eventually of the gas, Pa, the bed porosity, e, and the column diameter and height, and the type of distributor. 

For soil systems contaminated with Na+, kinematic viscosity is not significantly affected, thus the components controlling water flow velocity are the hydraulic gradient (A< >/AX) and soil permeability (k). The latter component (k) is influenced by clay dispersion, migration, and clay swelling. These processes may cause considerable alteration to such soil matrix characteristics as porosity, pore-size distribution, tortuosity, and void shape. 

The linear burning rate of a propellant is the velocity with which a chemical reaction progresses as a result of thermal conduction and radiation (at right angles to the current surface of the propellant). It depends on the chemical composition, the pressure, temperature and physical state of the propellant (porosity particle size distribution of the components compression). The gas (fume) cloud that is formed flows in a direction opposite to the direction of burning. 

The steady state head distribution shown in Figure 3a was used to calculate the velocity distribution, using a hydraulic conductivity of 200 ft/day (61 m/day) and an effective porosity of 0.30. Velocities ranged from 0.8 to 1.2 ft/day (0.24 - 0.37 m/day) but were around 1.1 ft/day (0.34 m/day) beneath most of the field. Groundwater flows in a westerly or northwesterly direction, as can be inferred from the groundwater potentials shown in Figure 3. 

The velocity field is not exactly reproduced. The model assumes constant hydraulic conductivity and effective porosity and uses an approximate head distribution to compute the velocity field. 

Figs. 7-A and 7-B shows examples of calculated results from our flow system at 75 °C, and 250 °C respectively. Physical parameters, such as porosity, water/rock ratio and fluid velocity are the same in both cases. Pure water infiltrated from the 0 cm point. Ca-montmorillonite was precipitated below 20 cm depth point, with the amount precipitated material increasing with reaction time. Laumontite precipitated later, and was distributed in lower part. Illite appeared at an early stage, and was abundant in the shallow part, as it reflects K content and has a high reaction rate at high water/ rock ratio conditions. 

Rocha and Paixao [38] proposed a pseudo two-dimensional mathematical model for a vertical pneumatic dryer. Their model was based on the two-fluid approach. Axial and radial profiles were considered for gas and solid velocity, water content, porosity, temperatures, and pressure. The balance equations were solved numerically using a finite difference method, and the distributions of the flow field characteristics were presented. This model was not validated with experimental results. 

The data required for input into the groundwater flow models to predict the hydrodynamic flow velocity include the porosity of the soil, the water table, rainfall, reversible absorption/desorption phenomena, irreversible sorption, chemical reactions, and microbial degradation kinetics 37). Mixing with seawater, air, or steam may also be considered. Based on these models, estimates of leaching and pollutant distribution can be made many years into the future although significant amounts of computer time are usually required (57). 

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