Plug flow, reactor model uniqueness

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

Chemical reaction and mass transfer are two unique phenomena that help define chemical engineering. Chapter 8 described problems involving chemical reaction and mass transfer in a porous catalyst, and how to model chemical reactors when the flow was well defined, as in a plug-flow reactor. Those models, however, did not account for the complicated flow situations sometimes seen in practice, where flow equations must be solved along with the transport equation. Microfluidics is the chemical analog to microelectro-mechanical systems (MEMS), which are small devices with tiny gears, valves, and pumps. The generally accepted definition of microfluidics is flow in channels of size 1 mm or less, and it is essential to include both distributed flow and mass transfer in such devices. 

An RTD, however, does not represent the mixing behavior in a vessel uniquely, because several arrangements of the internals of a vessel may give the same tracer response, for example, any series arrangements of reactor elements such as plug flow or complete mixing. This is a consequence of the fact that tracer behavior is represented by linear differential equations. The lack of uniqueness limits direct application of tracer studies to first-order reactions with constant specific rates. For other reactions, the tracer curve may determine the upper and lower limits of reactor performance. When this range is not too broad, the result can be useful. Tracer data also may be taken at several representative positions in the vessel in order to develop a realistic model of the reactor. 

The H-Oil reactor (Fig. 21) is rather unique and is called an ebullated bed catalytic reactor. A recycle pump, located either internally or externally, circulates the reactor fluids down through a central downcomer and then upward through a distributor plate and into the ebullated catalyst bed. The reactor is usually well insulated and operated adiabatically. Frequently, the reactor-mixing pattern is defined as backmixed, but this is not strictly true. A better description of the flow pattern is dispersed plug flow with recycle. Thus, the reactor equations for the axial dispersion model are modified appropriately to account for recycle conditions. 

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