Macromixing residence time distribution

In a continuous reaction process, the true residence time of the reaction partners in the reactor plays a major role. It is governed by the residence time distribution characteristic of the reactor, which gives information on backmixing (macromixing) of the throughput. The principal objectives of studies into the macrokinetics of a process are to estimate the coefficients of a mathematical model of the process and to validate the model for adequacy. For this purpose, a pilot plant should provide the following ... 

The term macromixing refers to the overall mixing performance in a reactor. It is usually described by the residence time distribution (RTD). Originally introduced by Danckwerts (1958), this concept is based on a macroscopic lumped population balance. A fluid element is followed from the time at which it enters the reactor (Lagrangian viewpoint - observer moves with the fluid). The probability that the fluid element will leave the reactor after a residence time t is expressed as the RTD function. This function characterises the scale of mixedness in a reactor. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

In the statistical theory of fluid mixing presented in Chapter 3, well macromixed corresponds to the condition that the scalar means () are independent of position, and well micromixed corresponds to the condition that the scalar variances are null. An equivalent definition can be developed from the residence time distribution discussed below. 

A further important conclusion is that for a given C-curve or residence time distribution obtained from tracer studies, a unique value of the conversion in a chemical reaction is not necessarily obtainable unless the reaction is first order. Tracer measurements can certainly tell us about departures from good macromixing. However, tracer measurements cannot give any further information about the extent of micromixing because the tracer stimulus-response is a first-order (linear) process as is a first-order reaction. 

The experimental SCISR is the same as that used for the measurements of macromixing and residence time distribution, as shown in Fig. 10.2, while its major dimensions are shown in Fig. 10.6 and the equipment system scheme is illustrated in Fig. 10.7. 

When the fluid elements pass through the reactor, the exchange of mass between the fluid elements occurs both on a microscale as well as on a macroscale. The mixing process on a macroscale is characterized by the residence-time distribution of the fluid elements. Usually, only the macromixing is considered to have a... 

RESIDENCE-TIME DISTRIBUTION AND MODELS FOR MACROMIXING IN THE REACTORS... 

Chapters 2, 3, and 4 review the tools for modeling the performance of three-phase reactors. Chapter 2 evaluates the use of film and penetration theory for the calculation of absorption rate in three-phase reactors. Chapter 3 describes various techniques for characterizing residence time distribution and the models which take into account the macromixing in a variety of three-phase reactors. The concepts described in these two chapters are vital to the simulation of an entire reactor. Chapter 4 illustrates the development of the mathematical models for some important pilot scale and commercial reactors. In Chapter 5 some advantages and disadvantages of three-phase laboratory reactors are outlined. 

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