Mesoscale Reactors

Domain Cross-Channel Dimension, m Diffusion Time in Laminar Flow Characteristic Reynolds Number 

Chapter 8 ignored axial diffusion, and this approach would predict reactor performance like a PFR so that conversions would be generally better than in a laminar flow reactor without diffusion. However, in microscale devices, axial diffusion becomes important and must be retained in the convective diffusions equations. The method of lines ceases to be a good solution technique, and the method of false transients is preferred. Application of the false-transient technique to PDFs, both convective diffusion equations and hydrodynamic equations, is an important topic of this chapter. 

A solvent is used to dissolve the uncrosslinked areas. What remains are the walls of the reactor. Typical minimum dimensions for the flow channels are 10-100 pm. This scale reactor is used to study the chemistry of individual cells. The cell is introduced to the system, isolated, and lysed, and the effluent mixture is analyzed. 

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Chemical engineers of the future will be integrating a wider range of scales than at r other branch of engineering. For example, some may work to relate the macroscale of the environment to the mesoscale of combustion systems and the microscale of molecular reactions and transport (see Chapter 7). Others may work to relate the macroscale performance of a composite aircraft to the mesoscale chemical reactor in which the wing was formed, the design of the reactor perhaps having been influenced by studies of the microscale dynamics of complex liquids (see Chapter 5). 

In all of the above cases, a strong non-linear coupling exists between reaction and transport at micro- and mesoscales, and the reactor performance at the macroscale. As a result, the physics at small scales influences the reactor and hence the process performance significantly. As stated in the introduction, such small-scale effects could be quantified by numerically solving the full CDR equation from the macro down to the microscale. However, the solution of the CDR equation from the reactor (macro) scale down to the local diffusional (micro) scale using CFD is prohibitive in terms of numerical effort, and impractical for the purpose of reactor control and optimization. Our focus here is how to obtain accurate low-dimensional models of these multi-scale systems in terms of average (and measurable) variables. 

To the limited extent that mesoscale and smaller reactors are used for production, the obvious approach is to scale in parallel. More conventional scaleups, that is, increasing reactor dimensions, could be needed when the small reactor is used to find the perfect molecule by means of combinatorial chemistry. With possible exceptions where the ultimate in mixing and heat transfer is required, scaleups to conventional macroscale reactors should be possible. 

A complete phenomenological mathematical model for olefin polymerization in industrial reactors should, in principle, consider phenomena taking place from microscale to macroscale, but this is seldom the case. Most models assume that the conditions in the polymerization reactor are uniform and neglect any mesoscale phenomena, which may be a good approximation for solution polymerization reactors, but may not apply to polymerizations using heterogeneous catalysts. 

Mesoscale chemical plant Microchemical factory Microplants Microstmctured reactor plant (MRP) Tabletop microreaction system Tabletop plant... 

Olefin polymerization reactors will now be modeled using a bottom-up approach, from microscale to macroscale. In this section polymerization kinetic models will be introduced to describe polymerization rates and polymer microstructures, ignoring any phenomena that may take place in the mesoscale and macroscale. These models depend on the concentration of reagents and temperatures at the active site. As explained in the previous... 

Length scale Macroscale (reactor scale) Mesoscale (particle scale)... 

It will be assumed that the polymerization conditions at the active site are known in this present section we will worry about them in a later section. In Section 2.4, mesoscale models will be developed that will tell us how the concentration of reagents, as well as temperature, varies as a function of radial position in the polymer particle. If radial gradients in the polymer particles are significant, the models developed in this section are still valid for the mesoscale, but only locally, at a given radial position in the particle. Finally, at the end of Section 2.5, a simple way to connect micro-, meso- and macroscale in one unified approach for modeling olefin polymerization reactors will be proposed. 

Phan, A. N., Harvey, A. P., Rawchffe, M. (2011). Continuous screening of base-catalysed biodiesel production using new designs of mesoscale oscillatory baffled reactors. Fuel Processing Technology, 92, 1560—1567. 

In this work a mesoscale/macroscale level approach of the Borstar plant is attempted focusing on the study of average polymer properties, dynamic behaviour and control of process units. To describe the kinetic of ethylene-1-butene copolymerization in the plant a unified kinetic scheme for the three reactor units based on a two-site Ziegler catalyst is employed (Table 1). The symbol denotes the concentration of live copolymer chains of total length n ending in an i monomer unit, formed at the k catalyst active site. Pp and denote the concentrations of the activated vacant catalyst sites of... 

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