Multi-phase reactor model

Syamlal M, Gidaspow D (1985) Hydrodynamics of fluidization Prediction of wall to bed heat transfer coefficients. AIChE J 31 127-135 Tayebi D, Svendsen HP, Jakobsen HA, Grislingas A (2001) Measurements Techniques and Data Interpretations for Validating CFD Multi Phase Reactor Models. Chem Eng Comm 186 57-159... 

A major limitation of the present work is that it deals only with well-defined (and mostly unidirectional) flow fields and simple homogeneous and catalytic reactor models. In addition, it ignores the coupling between the flow field and the species and energy balances which may be due to physical property variations or dependence of transport coefficients on state variables. Thus, a major and useful extension of the present work is to consider two- or three-dimensional flow fields (through simplified Navier-Stokes or Reynolds averaged equations), include physical property variations and derive lowdimensional models for various types of multi-phase reactors such as gas-liquid, fluid-solid (with diffusion and reaction in the solid phase) and gas-liquid-solid reactors. 

Examination of several two-equation models reveals that there is only very small differences between the various models of this t3q>e [106]. This may be expected since all proposals for formulating the 2nd equation are closely related, though they differ in the forms of diffusion and near wall terms employed [95]. However, as mentioned above, the k-e model of Jones and Launder [78] has been predominant in the literature, and this model also determine the basis for most multi-phase turbulence models adopted in the more fundamental (CFD) reactor modeling approaches. 

In view of the multi-phase reactor flow structure characteristics summarized in sect 3.1, it is obvious that dispersed flow systems are dominating. For these flows roughly three different computational strategies can be distinguished based on the scales resolved by the model formulation ... 

Models considering detailed flow patterns in multi-phase reactors are similar to those presented in Section 13.7 for fluidized bed reactors. The models are based on the Navier-Stokes equations for each of the moving phases. The different phases are assumed to be fully penetrating each other. Interphase mass, momentum, and energy transfer is accounted for. The methods accounting for the fluctuations in the flow field discussed in Chapter 12 for single phase flow can be extended to multi-phase flow. Application to the simulation of a bubble column reactor is illustrated in Example 14.3.6.A. 

In most cases the only appropriate approach to model multi-phase flows in micro reactors is to compute explicitly the time evolution of the gas/liquid or liquid/ liquid interface. For the motion of, e.g., a gas bubble in a surrounding liquid, this means that the position of the interface has to be determined as a function of time, including such effects as oscillations of the bubble. The corresponding transport phenomena are known as free surface flow and various numerical techniques for the computation of such flows have been developed in the past decades. Free surface flow simulations are computationally challenging and require special solution techniques which go beyond the standard CFD approaches discussed in Section 2.3. For this reason, the most common of these techniques will be briefly introduced in... 

At the other extreme, it may be argued that the traditional low-dimensional models of reactors (such as the CSTR, PFR, etc.) should be abandoned in favor of the detailed models of these systems and numerical solution of the full convection-diffusion reaction (CDR) equations using computational fluid dynamics (CFD). While this approach is certainly feasible (at least for singlephase systems) due to the recent availability of computational power and tools, it may be computationally prohibitive, especially for multi-phase systems with complex chemistry. It is also not practical when design, control and optimization of the reactor or the process is of main interest. The two main drawbacks/criticisms of this approach are (i) It leads to discrete models of very high dimension that are difficult to incorporate into design and control schemes. 

The overall reactor model comprises, as the heart of it, the single catalyst pellet model which is formulated in an overall framework that includes the changes in the bulk fluid phase. The equations for the catalyst pellet coupled with the equations for the bulk fluid phase represent what we may call in certain cases, the overall reactor model or in a more restricted sense, the catalyst bed module. This catalyst bed module may represent the overall reactor model in certain cases such as the single adiabatic catalytic packed bed reactor. In other cases, this module may represent only the essential part of the overall reactor model such as in non-adiabatic and multi-bed reactors. 

Mitsubishi Heavy Industries computer code CHAMPAGNE is a multi-phase, multi-component thermodynamics model originally created for the assessment of severe accidents in fast breeder nuclear power reactors. It was recently modified to also treat the formation and spreading of hydrogen gas clouds. CHAMPAGNE has been successfully applied both as a 2D and 3D version to the NASA LH2 spill tests from 1980 (Fig. 8-9) [30]. 

The calculation principle on which the assessment of design for such reactors is based is a substitution of the multi-phase reaction system by a quasi-single-phase model. In two-phase systems both reactants have to get into contact at a certain place. Consequently a reaction and a transport phase are distinguished. If the mass transfer rate from the transport to the reaction phase is veiy fast compared to the actual reaction rate, the process in total is dominated by the reaction kinetics. In order to discriminate this situation from one taking the mass transfer into account, it is referred to as micro-kinetically dominated In this ease all formal kinetic laws presented for homogeneous systems may be applied directly. 

Multi-phase membrane reactors fundamental concepts, modelling and operations... 

Modelling of multi-phase catalytic membrane reactors... 

Several authors have reported modelling of multi-phase membrane reactors and, in particular, of three-phase catalytic membrane reactors. Harold and Watson (1993) have considered the situation of a porous catalytic slab partially wetted by a liquid from one side and by a gas phase on the other side, and they have pointed out the complexity of the problem in presence of an exothermic reaction, capillary condensation and vaporization. 

Recently, Endre (2011) attempted a comprehensive approach to the modelling of catalytic membranes for multi-phase membrane reactors, showing the mutual effects of mass transfer and some typical kinetics laws. 

The same group further developed the model to include mass transfer effects, where mass is transferred from the gas phase to a reacting wall [84]. Given a solution for the bubble shape, it is a simple matter to include mass transfer, as this involves only the addition of a scalar equation with the flow-field kept frozen . The entire approach represents a clever use of CFD both to determine the bubble hydrodynamics and then to explore the influence of the flow on mass transfer, enabling them to generate useful data for the design of multi-phase monolith reactors. 

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