Hydrodynamics-mass transfer

Fouling is the term used to describe the loss of throughput of a membrane device as it becomes chemically or physically changed by the process fluid (often by a minor component or a contaminant). A manifestation of fouling in cross-flow UF is that the membrane becomes unresponsive to the hydrodynamic mass transfer which is rate-controlling for most UF. Fouling is different from concentration polarization. Both reduce output, and their resistances are additive. Raising the flow rate in a cross-flow UF will increase flux, as in Eq. 

A one-parameter model, termed the bubbling-bed model, is described by Kunii and Levenspiel (1991, pp. 144-149,156-159). The one parameter is the size of bubbles. This model endeavors to account for different bubble velocities and the different flow patterns of fluid and solid that result. Compared with the two-region model, the Kunii-Levenspiel (KL) model introduces two additional regions. The model establishes expressions for the distribution of the fluidized bed and of the solid particles in the various regions. These, together with expressions for coefficients for the exchange of gas between pairs of regions, form the hydrodynamic + mass transfer basis for a reactor model. 

Precise knowledge of the bubble size is important for a better understanding of the hydrodynamics, mass transfer, and reactor design. Zun [27] concluded that small bubbles tend to have uniform radial profiles while large bubbles tend to rise in the central region. Smaller bubbles and a uniform radial profile lead to a larger interfacial area and a lower rise velocity, which increases mass transfer. 

Because of their multicomponent nature, RSPs are affected by a complex thermodynamic and difihisional coupling, which, in turn, is accompanied by simultaneous chemical reactions (57-59). To describe such phenomena adequately, specially developed mathematical models capable of taking into consideration column hydrodynamics, mass transfer resistances, and reaction kinetics are required. 

While new chemical product development has historically been the domain of chemists, the use of chemical products by consmners invariably involves some transformation of the product due to applied stresses, temperature gradients, physicochemical hydrodynamics, mass transfer, etc., making product use a process in the chemical engineering sense. [2,4] Thus the analysis of product behavior ultimately requires the same fundamentals as the analysis of process behavior, and is well suited to study by chemical engineers. 

Fleischer, C., Becker, S. and Eigenberger, G. (1995), Transient hydrodynamics, mass transfer and reaction in bubble columns, Chem. Eng. Res. Des., 73A, 649-653. 

The best possible mode of gas-liquid contact for a given process depends upon a combination of effects, including hydrodynamics, mass transfer, and chemical kinetics. In treating this combination, a dimensionless parameter P has been defined as the ratio of total volume of the liquid phase to volume of the liquid diffusion layer. Krishna and Sie reported general values of jS to be 10 0 for thin liquid films and liquid sprays, and 10 -10" for gas bubbles within a continuous liquid. The relative rates of mass transfer and chemical reaction show whether high values or low values of jS best utilize available reactor volume. 

Table 11.8 lists some of the models that have been discussed in the literature [Shalhi 1993] in chronological order. The increasing model complexity with time is illustrated by Table 11.8 with gradual recognition of the importance of hydrodynamics, mass transfer and reaction kinetics. In some of the models no account of removal is taken, and indeed in some extreme examples of chemical reaction fouling, removal of a deposit once formed is indeed negligible. 

It is very interesting, after all this discussion of hydrodynamics, mass transfer, and other properties of trickle beds, to see what people have aetually done when they get down to the task of trickle-bed reactor design. Things get fairly basie quite rapidly, and while we don t retreat all the way to the ideal triekle-bed reactor model, neither do we attempt the presumption of three or four parameters. Some have proposed simplified heterogeneous models, others consider only the degree of contact between the liquid and solid phases, and still others base the approach on the mass-transfer factors appearing in the three-phase reactor/reaction system. Finally, there are some approaches based on the directly-determined residenee time distribution funetion. We will take a brief look at each. 

Hydrodynamics, Mass Transfer, Heat Exchange, Control, and Scale-up... 

The overall description (model) of a reactor is obtained through process synthesis by combining models of reactor hydrodynamics, mass transfer and heat exchange with an appropriate cell (subcellular) or population model ( 1).Description of a population should take into consideration possible dispersed or aggregated (the distinct morphological appearances of a culture pellets, mycelium, flocks, growth on reactor wall in the form of microbial film) forms of population. Biomass support particles are gaining appreciable importance in aerobic (40) as well as in anaerobic processes. 

Ghirardini, M., Donati, G., and Rivetti, F. (1992), Gas lift reactors Hydrodynamics, mass transfer, and scale up, Chemical Engineering Science, 47(9-11) 2209-2214. 

In this chapter, fluid-fluid flow patterns and mass transfer in microstructured devices are discussed. The first part is a brief discussion of conventionai fluid-fluid reactors with their advantages and disadvantages. Further, the ciassi-flcation of fluid-fluid microstructured reactors is presented. In order to obtain generic understanding of hydrodynamics, mass transfer, and chemical reaction, dimensionless parameters and design criteria are proposed. The conventional mass transfer models such as penetration and film theory as well as empirical correlations are then discussed. Finally, literature data on mass transfer efficiency at different flow regimes and proposed empirical correlations as well as important hydrodynamic design parameters are presented. 

Indeed, as for hydrodynamics, mass transfer depends strongly on the physico-chemical properties of the gas-liquid system and many correlations have been proposed to predict the interfacial areas a and liquid mass transfer coefficient kLa, reported to the unit volume of dispersion. They have been recently reviewed by Botton et al. (97) and Hikita et al. (111). It seems that for the scale-up prevision in bubble flow regime (u <0.3 m/s), small scale experiments with the system of interest will allow scale-up on the basis of equal superficial velocity of the gas. So the data in Fig. 17, or those found in the many literature references, or of specific experiments can be used noting that a, k a, k a and a vary approximatively as For other flow regimes and for... 

Many of the mixing simulations described in the previous section deal with the modeling of mass transfer between miscible fluids [33, 70-77]. These are the simulations which require a solution of the convection-difliision equation for the concentration fields. For the most part, the transport of a dilute species with a typical diSusion coeflEcient 10 m s between two miscible fluids with equal physical properties is simulated. It has already been mentioned that due to the discretization of the convection-diffusion equation and the typically small diffusion coefficients for liquids, these simulations are prone to numerical diffiision, which may result in an over-prediction of mass transfer efficiency. Using a lattice Boltzmann method, however, Sullivan et al. [77] successfully simulated not only the diffusion of a passive tracer but also that of an active tracer, whereby two miscible fluids of different viscosities are mixed. In particular, they used a coupled hydrodynamic/mass transfer model, which enabled the effects of the tracer concentration on the local viscosity to be taken into account. 

Iliuta I. Ortiz A. Larachi F, Grandjean BP A, Wild G. Hydrodynamics mass transfer in trickle-bed reactors an overview. Chem. Eng. Sci. 1999 54 5329. 

The quality of the results obtained in this paper is limited by the uncertainty introduced by the phase hydrodynamics in the reaction zone and the phase equilibrium hypothesis. The authors foreseen additional studies in order to better describe phase hydrodynamics, mass transfer outside and inside the catalyst pellets and their influence on process performances. 

Darmana D, Henket RLB, Deen NG, Kuipers JAM (2007) Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model Chemisorption of CO2 into NaOH solution, numerical and experimental study. Chem Eng Sci 62 2556-2575... 

Martin, A., Cocero, M. J. (2004). Numerical modeling of jet hydrodynamics, mass transfer, and ciystallizatlon kinetics in the supercritical antisolvent (SAS) process, / Supercrit. Fluids, 32, 203-219. 

A number of reaction engineering models in literature have already utdized the concepts of TBC or single-bubble-class (SBC) together with the axial dispersion models to couple the hydrodynamics, mass transfer, and reaction in bubble column reactors. While some researchers claim that there is less difference in the SBC and TBC model predictions, others believe that the TBC model prediction is in better agreement with experiments. We find that the difference is actually relevant to the submodels for hydrodynamics, mass transfer, and reaction kinetic as well as gas contraction, and in particular the gas holdup model and whether the system is limited by reaction or mass transfer. Then a new reactor model is developed to replace the empirical... 

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