Modelling of Membrane Bioreactors

The modeling of membrane bioreactors is in the initial stage. There are not available more or less sophisticated mathematical tools to describe the complex biochemical processes. It is not known how the mass-transport parameters, diffusion coefficients, convective velocity, biological kinetic parameters might vary in function of the operating conditions, of the biolayer (enzyme/micro-organism membrane layer)... 

Mathematical Modeling of Membrane Bioreactor 314 Modeling of Enzyme Membrane Layer/Biofilm Reactor 314... 

Steady state models of membrane bioreactors utilizing a multi-enzyme system, which in addition to the main reaction promotes the simultaneous regeneration of the co-factor (for further discussion see Chapter 4) have been developed by different groups in Japan [5.109, 5.110]. Several of these studies have also considered the effect of backmixing [5.111, 5.112]. A model of an enzymatic hollow fiber membrane bioreactor with a single enzyme, which utilizes two different substrates (reaction 5.42) has been developed recently by Salzman et al [5.113]. 

Computational fluid dynamics (CFD) analysis of membrane reactors modelling of membrane bioreactors for municipal wastewater treatment... 

Some of the efforts, so far, to model such membrane bioreactors seem to not have considered the complications that may result from the presence of the biomass. Tharakan and Chau [5.101], for example, developed a model and carried out numerical simulations to describe a radial flow, hollow fiber membrane bioreactor, in which the biocatalyst consisted of a mammalian cell culture placed in the annular volume between the reactor cell and the hollow fibers. Their model utilizes the appropriate non-linear kinetics to describe the substrate consumption however, the flow patterns assumed for the model were based on those obtained with an empty reactor, and would probably be inappropriate, when the annular volume is substantially filled with microorganisms. A model to describe a hollow-fiber perfusion system utilizing mouse adrenal tumor cells as biocatalysts was developed by Cima et al [5.102]. In contrast, to the model of Tharakan and Chau [5.101], this model took into account the effect of the biomass, and the flow pattern distribution in the annular volume. These effects are of key importance for conditions encountered in long-term cell cultures, when the cell mass is very dense and small voids can completely distort the flow patterns. However, the model calculations of Cima et al. [5.102] did not take into account the dynamic evolution of the cell culture due to growth, and its influence on the permeate flow rate. Their model is appropriate for constant biocatalyst concentration. 

Naessens, W., Maere, T., Nopens, L, Critical review of membrane bioreactor models—Rart 1 Biokinetic and filtration models. Bioresource Technology 2012, 122, 95-106. 

The aim of this chapter is to give a detailed overview of the characterization of biocatalysts and the development of membrane bioreactors, in particular, the main aspects of biocatalyst kinetics and their immobilization/ entrapment, either within the porous membrane structure, or on its surface. Thansport models that can help to predict the behaviour of membrane bioreactors, as well as the most relevant theoretical models and operating parameters, are presented below. This data is then analysed in order to ascertain how to improve effectiveness and productivity of the membrane bioreactors. Some relevant fields of application are also discussed in order to show the potential of such systems. 

Steinmeyer, D. E., and Shuler, M. L. Mathematical modeling and simulations of membrane bioreactor extractive fermentations. Biotechnol. Progr. 6(5), 362-369, 1990. 

Wang, Y (2010b). Evaluation of Membrane Bioreactor Mixing Performance via Computational Fluid Dynamics Modelling, UNESCO Centre for Membrane Science Technology, School of Chemical Engineering,The University of New South Wales, PhD thesis, Sydney, Australia. 

Figure 14.3 also shows the concentration-polarization layer that also forms during the filtration. Due to it, there is a backdiffusion of the retained compound that has higher concentration on the membrane surface. These phenomena can also decrease the efficiency ofthe filtration. This effect should also be taken into account during the mathematical modeling of the transport processes of the membrane bioreactor, as will be discussed later. 

We developed a PEEK-WC hollow-fiber (HF) membrane bioreactor for the maintenance of human peripheral lymphocytes as a model system for the in-vitro investigation of disease pathogenesis, chemical effects and individual drug sensitivity. Peripheral lymphocytes isolated from the donor s human buffy coat were cultured in the shell compartment of the PEEK-WC-H F bioreactor. Lymphocytes in the PEEK-WC-HF membrane bioreactor produced IL-2 and IL-10 throughout the culture period of 14 days (Figure 19.5). 

The obtained results demonstrated that a PEEK-WC-H F membrane bioreactor is able to support the proliferation and functions of human peripheral lymphocytes isolated from the buffy coat of healthy individuals. Therefore, the lymphocyte HF membrane bioreactor can be used as a valuable tool to maintain viable and functional lymphocytes and as an in-vitro model for pharmacological and adoptive immunotherapy. 

There are a number of membrane reactor systems, which have been studied experimentally, that fall outside the scope of this model, however, including reactors utilizing macroporous non-permselective membranes, multi-layer asymmetric membranes, etc. Models that have been developed to describe such reactors will be discussed throughout this chapter. In the membrane bioreactor literature, in particular, but also for some of the proposed large-scale catalytic membrane reactor systems (e.g., synthesis gas production) the experimental systems utilized are often very complex, in terms of their configuration, geometry, and, of course, reaction and transport characteristics. Completely effective models to describe these reactors have yet to be published, and the development of such models still remains an important technical challenge. 

Membrane bioreactors have been modelled using approaches that have proven successful in the more conventional catalytic membrane reactor applications. The simplest membrane bioreactor system, as noted in Chapter 4, consists of two separate units, a bioreactor (typically a well-stirred batch reactor) coupled with an external hollow fiber or tubular or flat membrane module. These reactors have been modelled by coupling the classical equations of stirred tank reactors with the mathematical expressions describing membrane permeation. What makes this type of modelling unique is the complexity of the mecha-... 

A comprehensive model of a membrane bioreactor has been developed by Moueddeb et al [5.103] for a simple irreversible reaction A B. The goal of the model was to describe their experimental reactor system, which was described earlier in Chapter 4. The model equations were established by taking into account the effect of the biomass on the permeate flow rate in the annular volume. The mass balance equations for the substrate (A) and the product (B) in cylindrical coordinates, utilized by Moueddeb et al [5.103] are given as ... 

The modelling of enzymatic membrane reactors follows, in general, the same approach as described previously. In enzymatic membrane reactors the catalyst is a macromolecule (enzyme). It can be found either in a free form in the reactor or supported on the membrane surface, or inside the membrane porous structure by grafting it or in the form of a gel obtained by ultrafiltration. As in the case of the whole-cell membrane bioreactors discussed above, the proper calculation of the mass transfer characteristics is of great importance for the modelling of this type of reactor. One of the earliest models of enzymatic membrane bioreactors is by Salmon and Robertson [5.108]. These authors modelled an enzymatic membrane bioreactor, which was made of four coaxial compartments the enzyme is confined within one of the compartments, and one of the substrates is fed in a gaseous form. 

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