Transport reactors modeling

GL 26] [R 3] [P 28] A simple reactor model was developed assuming isothermal behavior, confining mass transport to only from the gas to the liquid phase, and a sufficiently fast reaction (producing negligible reactant concentrations in the liquid phase) [10]. For this purpose, the Hatta number has to be within given limits. 

This equation may be used as an appropriate form of the law of energy conservation in various pseudo homogeneous models of fixed bed reactors. Radial transport by effective thermal conduction is an essential element of two-dimensional reactor models but, for one-dimensional models, the last term must be replaced by one involving heat losses to the walls. 

The application of CFD to packed bed reactor modeling has usually involved the replacement of the actual packing structure with an effective continuum (Kvamsdal et al., 1999 Pedernera et al., 2003). Transport processes are then represented by lumped parameters for dispersion and heat transfer (Jakobsen... 

The types of systems we deal with are primarily gas-solid (Section 9.1) and gas-liquid (Section 9.2). In these cases, we assume first- or second-order kinetics for the intrinsic reaction rate. This enables analytical expressions to be developed in some situations for the overall rate with transport processes taken into account. Such reaction models are incorporated in reactor models in Chapters 22 and 24. 

In general, liquid-phase reactions (Sc > 1) and fast chemistry are beyond the range of DNS. The treatment of inhomogeneous flows (e.g., a chemical reactor) adds further restrictions. Thus, although DNS is a valuable tool for studying fundamentals,4 it is not a useful tool for chemical-reactor modeling. Nonetheless, much can be learned about scalar transport in turbulent flows from DNS. For example, valuable information about the effect of molecular diffusion on the joint scalar PDF can be easily extracted from a DNS simulation and used to validate the micromixing closures needed in other scalar transport models. 

When we use a tracer study to develop reactor parameters for an environmental system, we are inherently assuming that the details of the transport processes are not essential to us. All that we have is an input and an output, and any sets of reactors that will simulate the output for a given input are acceptable. What you can learn about the system from a reactor model depends on your understanding of the transport processes and how they are simulated by reactor models. 

The catalyst and particulate filter models were developed individually with different university partners. They are described in the following sections. A key issue for all models is robustness and scalability as the applications range from passenger cars to heavy-duty commercial vehicles. The models are physical and chemically based, consisting of a transport model for heat and mass transfer phenomena in the monolith in gas and solid phases, cf. Fig. 6. The monolith reactor modeling is discussed in more detail in Section III. 

The mathematical models of the reacting polydispersed particles usually have stiff ordinary differential equations. Stiffness arises from the effect of particle sizes on the thermal transients of the particles and from the strong temperature dependence of the reactions like combustion and devolatilization. The computation time for the numerical solution using commercially available stiff ODE solvers may take excessive time for some systems. A model that uses K discrete size cuts and N gas-solid reactions will have K(N + 1) differential equations. As an alternative to the numerical solution of these equations an iterative finite difference method was developed and tested on the pyrolysis model of polydispersed coal particles in a transport reactor. The resulting 160 differential equations were solved in less than 30 seconds on a CDC Cyber 73. This is compared to more than 10 hours on the same machine using a commercially available stiff solver which is based on Gear s method. 

These results show that the proposed technique provides a fast and reliable method for the solution of stiff ODE models of reacting polydispersed particles. Recently, Turton (9) applied this method successfully to the modeling of wood char combustion in a transport reactor. 

For example, when we consider the design of specialty chemical, polymer, biological, electronic materials, etc. processes, the separation units are usually described by transport-limited models, rather than the thermodynamically limited models encountered in petrochemical processes (flash drums, plate distillations, plate absorbers, extractions, etc.). Thus, from a design perspective, we need to estimate vapor-liquid-solid equilibria, as well as transport coefficients. Similarly, we need to estimate reaction kinetic models for all kinds of reactors, for example, chemical, polymer, biological, and electronic materials reactors, as well as crystallization kinetics, based on the molecular structures of the components present. Furthermore, it will be necessary to estimate constitutive equations for the complex materials we will encounter in new processes. 

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. 

Chemical vapor deposition and heterogeneous catalysis share many kinetic and transport features, but CVD reactor design lags the corresponding catalytic reactor analysis both in level of sophistication and in scope. In the following we review the state of CVD reactor modelling and demonstrate how catalytic reactor design concepts may be applied to CVD processes. This is illustrated with an example where fixed bed reactor concepts are used to describe a commercial "multiple-wafers-in-tube" low pressure CVD reactor. 

With each of the six reactor models just described, the transport of energy from regions with high conversion to those with low conversion causes destabilization. Each model has its own unique way of characterizing the transport process. For these results to be of practical use, a common measure of energy transport is required. 

Trickle bed reactors Slurry reactors Three-phase fluidized beds No Little Little Modeling on basis of unit cell approach + development of correspondence rules for macroscopic system behavior Modeling of the effect of the solids phase on interfacial transport phenomena Modeling of the effect of the solids phase on interfacial transport phenomena -I- development of refined models for particle-particle and particle-wall interaction... 

As mentioned earlier, most membrane reactor models are based on isothermal macroscopic balances in the axial direction and do not solve the transport equations for the membrane/support matrix. They all account for the effects of membrane permeation through the use of some common relevant parameters (as a permeation term) in the transport equations for both the feed and permeate sides. Those parameters are to be determined experimentally. The above approach, of course, is feasible only when the membrane (or membrane/support) is not catalytic. 

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