Dispersion flow-rate influence

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

More disagreement exists with respect to axial dispersion—for example, regarding the applicability of the diffusion model, and regarding the influence of gas and liquid flow rates. More work on these aspects and on the influence of fluid distribution and method of packing is required. Some of the available results are compared in Fig. 3. 

The slopes of the peaks in the dynamic adsorption experiment is influenced by dispersion. The 1% acidified brine and the surfactant (dissolved in that brine) are miscible. Use of a core sample that is much longer than its diameter is intended to minimize the relative length of the transition zone produced by dispersion because excessive dispersion would make it more difficult to measure peak parameters accurately. Also, the underlying assumption of a simple theory is that adsorption occurs instantly on contact with the rock. The fraction that is classified as "permanent" in the above calculation depends on the flow rate of the experiment. It is the fraction that is not desorbed in the time available. The rest of the adsorption occurs reversibly and equilibrium is effectively maintained with the surfactant in the solution which is in contact with the pore walls. The inlet flow rate is the same as the outlet rate, since the brine and the surfactant are incompressible. Therefore, it can be clearly seen that the dynamic adsorption depends on the concentration, the flow rate, and the rock. The two parameters... 

The liquid flow rate directly influences the dispersion coefficient. Investigate its influence on peak width. 

The influence of dispersed-phase viscosity was found to be negligible by Hayworth and Treybal (H5), but found to be significant (K2) when a greater range of dispered-phase viscosity was investigated. From the graph of Hayworth and Treybal, the influence of interfacial tension appears, as in the case of bubbles, to be more at low flow rates than at high flow rates. 

However, the model of Rao et al. (R3) does not consider the influence of dispersed-phase viscosity. Further, the maximum size of the drop is limited to static drop size, which is true only for low flow rates. 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

The carrier properties have been studied in numerous in vitro studies to understand the influence on powder performance, especially drug detachment. The particle size distribution of the carrier is of paramount importance for the delivery and dispersion of drug particles by a device at given flow-rate conditions (Steckel and Mueller 1997 French et al. 1996 Kassem et al. 1989). An increased proportion of fine particles results in more efficient dispersion (Podczeck 1999), which has led to the proposal to deliberately add microfine lactose as a ternary agent (Lukas et al. 1998). 

For absorption controlled by diffusion through a gas film, it is necessary to provide a large enough interface area the interface area depends on the liquid to gas flow rate ratio, VL/VG, essentially for a defined dispersity of the absorbent. On the other hand, increasing VJV,c must lead to increased power consumption so it is important to optimize the flow rate ratio.. The experimental results on the influence of VL/VG on the sulfur-removal efficiency are shown in Fig. 7.13. To keep the conditions of atomization essentially the same, all the experiments in this set were carried out at a fixed volumetric liquid flow rate, VL while the gas flow rate, VG, for each run varies according to the required liquid to gas flow rate ratio and, simultaneously, the corresponding concentration of Ca(OH)2 was used to keep the ratio of Ca/S the same as 1.4. 

Figure 8. Influence of liquid flow rate on axial Figure 9. Influence of liquid flow rate on dispersion at atmospheric pressure. liquid hold-up at atmospheric pressure.

Factors effecting the peak separation include column volume, particle porosity, pore size distribution and solute conformation. Column dispersion is influenced by column length, particle size and the mobile phase temperature, viscosity and flow rate. 

The first HTU term contains the physical and fluid-dynamic parameter and the second NTU term expresses the number of theoretical stages as function of the solute concentration difference. The extractor-specific HTU value is, on the one hand, described by the quotient of flow rate and cross-sectional area of the column, and, on the other hand, it is characterised by the interfacial area per unit volume and the mass transfer coefficient. The former is mainly influenced by drop size and phase hold-up, the latter by the relative movement of the dispersed phase. These characteristic HTU values can be experimentally measured for a certain extractor type and are used for comparison with other extractors or for the projection of larger units. 

Compared with Bo , which is independent of the interstitial velocity (Eq. 7.32), Steffi is inversely proportional to interstitial velocity (Eq. 7.20). This means that the influence of mass transfer resistance will grow and surpass the influence of axial dispersion at high interstitial velocity, which is almost always the case for preparative chromatographic processes. In some extreme cases, where the mass transfer coefficients are small and the chromatographic column is operated at high flow rates, the HETP equation for the calculation of Nt can even be simplified further to ... 

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