Membrane process, mass transfer modeling

This simple mass transfer model based on simplified film theory has been proposed to describe the process of facilitated transport of penicillin-G across a SLM system [53]. In the authors laboratory, CPC transport using Aliquat-336 as the carrier was studied [56] using microporous hydrophobic polypropylene membrane (Celgard 2400) support and the permeation rate was found to be controlled by diffusion across the membrane. 

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 mass transfer modeling through an lEM also implies to know the properties of this membrane, namely, its electrochemical properties and its equilibrium state. Dialysis of model systems containing two salts (NaN03 and NaCl) is used to describe this process, although, mostly components can be encountered in real solutions to be treated. 

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. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

Comprehensive monographs are also available detailing the analysis of mass transfer though porous and dense membranes. Standard textbooks [e.g., Refs. 26, 27] provide the basis for discriminating between various possible transport mechanisms and the selection of models capable of describing the processes in quantitatively. 

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). 

Despite this last observation, for this type of simulation and modelling research, two main means of evolution remain the first consists in enlarging the library with new and newly coded models for unit operations or apparatuses (such as the unit processes mentioned above multiphase reactors, membrane processes, etc.) the second is specified by the sophistication of the models developed for the apparatus that characterizes the unit operations. With respect to this second means, we can develop a hierarchy dividing into three levels. The first level corresponds to connectionist models of equilibrium (frequently used in the past). The second level involves the models of transport phenomena with heat and mass transfer kinetics given by approximate solutions. And finally, in the third level, the real transport phenomena the flow, heat and mass transport are correctly described. In... 

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 ... 

Cheng LP, Soh YS, Dwan AH, and Gryte CC. An improved model for mass transfer during the formation of polymeric membranes by the immersion-precipitation process. J. Polym. Sci. Polym. Phys. B 1994 32 1413-1425. 

The SGMD is a temperature driven process, and it involves (a) evaporation of water at the hot feed side, (b) transport of water vapor through the pores of hydrophobic membrane, (c) collection of the permeating water vapor into an inert cold sweeping gas, and (d) condensation outside the membrane module. A decrease in driving force has been observed due to polarization effects of both temperature and concentration [80,82]. To calculate both heat and mass transfer through microporous hydrophobic membrane as well as the temperature and concentration polarization layer, the theoretical model suggested by Khayet et al. [58] can be written as... 

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. 

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