Membrane processes hydrodynamic characteristics

Mathematical modeling and determination of the characteristic parameters to predict the performance of membrane solvent extraction processes has been studied widely in the literature. The analysis of mass transfer in hollow fiber modules has been carried out using two different approaches. The first approach to the modeling of solvent extraction in hollow fiber modules consists of considering the velocity and concentration profiles developed along the hollow fibers by means of the mass conservation equation and the associated boundary conditions for the solute in the inner fluid. The second approach consists of considering that the mass flux of a solute can be related to a mass transfer coefficient that gathers both mass transport properties and hydrodynamic conditions of the systan (fluid flow and hydrodynamic characteristics of the manbrane module). 

Both, flux and rejection tend to vary with time. The underlying mechanisms are described below by a summary of models for each process. Some models apply to several processes and others only to a particular process under certain conditions. The application of models requires caution as membrane-solute interactions will depend on many factors. These include solute size, charge and morphology membrane pore size, charge, surface roughness and chemical characteristics solution chemistr) and, hydrodynamics, which influence permeation drag, shear forces, and cake compaction. 

Many strategies are available for the enhancement of the performance of manhrane processes. The practical applications of these techniques depeud on the membrane module cou-figuratiou, the operation scale, and the process characteristics. Table 10.5 sununarizes the potential application of the hydrodynamic manbrane performance enhancanent techniques discussed in this chapter. All of these techniques aim to limit the effect of couceutratiou polarization at the membrane surface. The majority of the techniques is hydrodynamic and therefore involves additional energy input or some extra design feature. In order to obtain the enhancement in performance, there is an investment that requires a payback. Thus, in each case, there will be a trade-off between operating and capital cost that provides an optimum condition that minimizes the total production cost. The most prevalent... 

The extent of absorption and rate of transport are important properties of a membrane. Physicochemical characteristics such as electrical conductivity and ion selectivity are closely related to the amount of water sorption. On the other hand, mass transport in solutions next to membranes depends on the buildup of the hydrodynamic boundary layers, especially at high current densities. Therefore, the maximum current density is determined by the diffusion of chemical species through the boundary layers outside the membrane and not so much by processes that occur inside the membrane. The limiting current density, therefore, is not strongly affected by the water content of the membrane or by the processes of water transport through it. 

Preparatory work for the steps in the scaling up of the membrane reactors has been presented in the previous sections. Now, to maintain the similarity of the membrane reactors between the laboratory and pilot plant, dimensional analysis with a number of dimensionless numbers is introduced in the scaling-up process. Traditionally, the scaling-up of hydrodynamic systems is performed with the aid of dimensionless parameters, which must be kept equal at all scales to be hydrodynamically similar. Dimensional analysis allows one to reduce the number of variables that have to be taken into accoimt for mass transfer determination. For mass transfer under forced convection, there are at least three dimensionless groups the Sherwood number, Sh, which contains the mass transfer coefficient the Reynolds number. Re, which contains the flow velocity and defines the flow condition (laminar/turbulent) and the Schmidt number, Sc, which characterizes the diffusive and viscous properties of the respective fluid and describes the relative extension of the fluid-dynamic and concentration boundary layer. The dependence of Sh on Re, Sc, the characteristic length, Dq/L, and D /L can be described in the form of the power series as shown in Eqn (14.38), in which Dc/a is the gap between cathode and anode Dw/C is gap between reactor wall and cathode, and L is the length of the electrode (Pak. Chung, Ju, 2001) ... 

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