Membrane process, mass transfer modeling separation

The clogging effect can be considered as a reduction in the value of the surface filtration constant for practical purposes. Indeed, when clogging takes place, the surface filtration constant can be given by its initial value ko multiplied by a decreasing time function. This assumption is frequently used when the function is obtained from experiments [3.19, 3.20]. In our example, if we do not consider the friction (and heat transfer) we can note that only a concrete mass transfer problem can be associated with the membrane separation process. The first step before starting to build the general mathematical model, concerns the division of the system into different elementary sections. Indeed, we have a model for the filtration device (i.e. the membrane and its envelope), for the pump (P) and for the reservoir of concentrated suspension (RZ) (Fig. 3.7). 

The second set of simulations is oriented towards the analysis of the simultaneous heat and mass transfer when two fluids are separated by a porous wall (membrane). The interest here is to couple the species transport through a wall associated with the heat transfer and to consider that the wall heat conduction is higher than the heat transported by the species motion. The process takes place through a cylindrical membrane and we assume the velocity to be quite slow in the inner compartment of the membrane. The process is described schematically in Fig. 3.65. The transformation of the above general model in order to correspond to this new description gives the following set of dimensionless equations ... 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

The previous chapter outlined the phenomena and theory associated with gas-separation membranes. The fundamentals of mass transfer and the process design equations that model membranes were also addressed. In this chapter, our attention turns to the industrial application of gas-separation membranes, specifically separations with polymeric membranes. 

He et al used a binary mixture-based film model to perform a theoretical analysis on the concentration polarization in a generic membrane. They defined a concentration polarization coefficient for both the two species involved in the separation as the ratio of the actual flux to the ideal one (without polarization), quantifying the polarization effect by means of the ratio of the actual fluxes of the components. Although this is a simplified approach that cannot be generalized to multi-component systems, nevertheless, under some operating conditions, the authors predicted a significant influence of the external mass transfer on the process. 

The membrane model is able to describe the mass transfer through membranes and takes into account the specific effects of different membrane materials. Simulation studies with the non-equilibrium model for distillation and the semi-empirical membrane model illustrate the influence of the mass flow of the side stream and the heating energy on the required membrane area. Both parameters have a major effect on the membrane area. Rigorous models for both unit operations are necessary to perform detailed process studies of the integrated process, because all physical effects have to be taken into account especially for membrane separation. 

Since Norman N. Li (1) introduced the emulsion liquid membrane in 1968, many publications have appeared both on experimental work and on theoretical modeling of such separations. Most of the theoretical work was concentrated on mass transfer in the ELM process in a mixing vessel where the water-in-oil emulsion is mixed with an external aqueous phase and globules of emulsion are formed and suspended in the external phase. The solute, after a series of mass transfer steps, is transferred from the external aqueous phase to the internal aqueous receiving phase through the oil membrane phase. Many mathematical... 

Atchariyawut, S., Jiraratananon, R., Wang, R., 2008. Mass transfer study and modeling of gas-liquid membrane contacting process by multistage cascade model for CO2 absorption. Separation and Purification Technology 63 (1), 15—22. 

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