Hydrodynamic model transport

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

In modeling an RO unit, two aspects should be considered membrane transport equations and hydrodynamic modeling of the RO module. The membrane transport equations represent the phenomena (water permeation, solute flux, etc.) taking place at the membrane surface. On the other hand, the hydrodynamic model deals with the macroscopic transport of the various species along with the momentum and energy associated with them. In recent years, a number of mathematical... 

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... 

Models of chemical reactions of trace pollutants in groundwater must be based on experimental analysis of the kinetics of possible pollutant interactions with earth materials, much the same as smog chamber studies considered atmospheric photochemistry. Fundamental research could determine the surface chemistry of soil components and processes such as adsorption and desorption, pore diffusion, and biodegradation of contaminants. Hydrodynamic pollutant transport models should be upgraded to take into account chemical reactions at surfaces. 

Annular flow. Modeling the interfacial shear is central to the problem of modeling hydrodynamics and transport during annular flow. The mechanisms are not clear, and the extent of basic modeling that has appeared is still very limited (Dukler and Taitel, 1991b). Only empirical treatments are currently available (see Sec. 3.5.3.3). 

The high temperatures and pressures created during transient cavitation are difficult both to calculate and to determine experimentally. The simplest models of collapse, which neglect heat transport and the effects of condensable vapor, predict maximum temperatures and pressures as high as 10,000 K and 10,000 atmospheres. More realistic estimates from increasingly sophisticated hydrodynamic models yield estimates of 5000 K and 1000 atmospheres with effective residence times of <100 nseconds, but the models are very sensitive to initial assumptions of the boundary conditions (30-32). 

Keywords Aqueous multiphase catalysis Regioselective hydrogenation Hydrodynamics Mass transport Kinetic modelling... 

To understand and ultimately to forecast the performance of a reactor, it is essential to study the coupling of "true" (intrinsic) kinetics with mass and energy transport, and to determine the flow regimes of the three phases (hydrodynamics). Modelling... 

In surface waters advective currents often dominate the transport of toxicants, and they can be estimated from hydrodynamic models or current measurements. In many cases advective flow can be approximated by the volume of water exchanged per unit... 

J.S. Xiang, P. Maijanovic, Hydrodynamic model of gas-solid flow in circulating fluidised bed, Proceedings of the 7th International Conference on Bulk Materials Storage, Handling and Transportation, Newcastle, Australia, October 2001, pp. 825-832. 

The molar fluxes appear in engineering design models. One of the main objectives of this text is to consider ways in which these fluxes may be calculated from a knowledge of the hydrodynamics and transport properties of the system. The boundary conditions (Eq. 1.3.13), or the simplified versions (Eqs. 1.3.14 and 1.3.15), are well known to chemical engineers (see, e.g., the book by Bird et al., 1960), but it is instructive to follow the general derivations of these relations [see Standart (1964) and Slattery (1981)]. 

Once the equations have been solved to obtain the composition and temperature profiles, the diffusion fluxes can be calculated and the interfacial transfer rates determined. It is customary to determine, on the basis of the chosen hydrodynamic model, mass transfer coefficients that reflect the overall transfer facility (molecular and turbulent transport) of the phase under consideration. 

A brief comment should be made concerning the use of the Nernst-Planck equations for ion transport across the liquid film (e.g., Copeland and Marchello [1969], Kataoka et al. [1987]). This is a nonlinear, three-ion problem because of the presence of at least one coion at comparable concentration. The Nernst film model relies on the assumption of a linear concentration gradient in the liquid film. The film has no physical reality, and the calculation of nonlinear concentration profiles in it overburdens the model and offers little improvement over the much simpler linear driving force approximation. For higher accuracy, more refined and complex hydrodynamic models would have to be used (Van Brocklin and David, 1975). 

A.G. Winger, R. Ferguson and R. Kunin, The electroosmotic transport of water across permselective membranes, J. Phys. Chem., 1956, 60, 556 B.R. Breslau and I.F. Miller, A hydrodynamic model for electroosmosis, Ind. Eng. Chem., Fundam., 1971, 10, 554-565 T. Okada, G. Xie, O. Gorseth, S. Kjelstrup, N. Nakamura and T. Arimura, Ion and water transport characteristics of Nafion membranes as electrolytes, Electro-chim. Acta, 1998, 43, 3741-3747. 

The most important of recent theoretical studies on semi-flexible polymers is probably the formulation of Yamakawa and Fuji [2,3] for the steady transport coefficients of the wormlike cylinder. This hydrodynamic model, depicted in Figure 5-2, is a smooth cylinder whose centroid obeys the statistics of wormlike chains. In the figure, r denotes the normal radius vector drawn from a contour... 

INFLUENCE OF HYDRODYNAMIC MODEL PARAMETERS ON THE ESTIMATION OF INTRAPARTICLE AND INTERPHASE TRANSPORT RATES IN A TRICKLE BED... 

Dynamic analysis of a trickle bed reactor is carried out with a soluble tracer. The impulse response of the tracer is given at the inlet of the column to the gas phase and the tracer concentration distributions are obtained at the effluent both from the gas phase and the liquid phase simultaneously. The overall rate process consists the rates of mass transfer between the phases, the rate of diffusion through the catalyst pores and the rate of adsorption on the solid surface. The theoretical expressions of the zero reduced and first absolute moments which are obtained for plug flow model are compared with the expressions obtained for two different liquid phase hydrodynamic models such as cross flow model and axially dispersed plug flow model. The effect of liquid phase hydrodynamic model parameters on the estimation of intraparticle and interphase transport rates by moment analysis technique are discussed. 

Dynamic analysis of TBR by sitimules response technique has been succesfully applied to determine the extent of liquid axial mixing. There are number of learning and predictive models proposed in literature 2. Among them the ones having less number of parameters such as cross-flow model and axially dispersed plug flow ADPF model are the most adequate ones. A more realistic model profound for a TBR can be the one which includes the simultaneous effect of interphase and intraparticle transport rates, and the adequate hydrodynamic model, to minimize the relative importance of liquid mixing on these rates. 

Chesters et al. [46 have addressed the transport of low concentrations of surfactant in a theoretical framework. A hydrodynamic model of steady wetting was extended to include the effect of a nonionic surfactant. This model indicated that under certain conditions surfactant may concentrate at the contact line between a surface and a meniscus to significantly reduce the contact angle. 

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