Conversion Levels in Nonideal Flow Reactors

In the present section we indicate how tracer residence time data may be used to predict the conversion levels that will be obtained in reactors with nonideal flow patterns. As indicated earlier, there are two types of limiting processes that can lead to a distribution of residence times within a reactor network. 

A flow pattern in which the various fluid elements follow different paths without mutual mixing on a microscopic scale. An example of this case is laminar flow. 

Mixing of fluid elements having different ages. Microscopic mixing produced by eddy diffusion effects is an example of this case. 

Because these two types of processes have drastically different effects on the conversion levels achieved in chemical reactions, they provide the basis for the development of mathematical models that can be used to provide approximate limits within which one can expect actual isothermal reactors to perform. In the development of these models we define a segregated system as one in which the first effect is entirely responsible for the spread in residence times. When the distribution of residence times is established by the second effect, we refer to the system as mixed. In practice, one encounters various combinations of these two limiting effects. 

We can characterize the mixed systems most easily in terms of the longitudinal dispersion model or in terms of the cascade of stirred-tank reactors model. The maximum amount of mixing occurs for the cases where T) = oo or n=. In general, for reaction orders greater than unity, these models place a lower limit on the conversion that will be obtained in an actual reactor. The applications of these models are treated in Sections 11.2.2 and 11.2.3. 

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Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

ILLUSTRATION 11.6 USE OF THE DISPERSION MODEL TO DETERMINE THE CONVERSION LEVEL OBTAINED IN A NONIDEAL FLOW REACTOR... 

ILLUSTRATION 11.5 Use of the Segregated Flow Model to Determine the Conversion Level Attained in a Nonideal Flow Reactor... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we discuss assume that the residence-time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used with the residence-time distribution function to predict conversion levels accurately for first-order reactions that occur isothermally (see Section 11.2.1). The second... 

One engineering design area, i.e., impacted by nonideal reactor behavior and the accompanying fluid residence time distribution(s) is scaleup. Suppose that a reactor study is conducted at the pilot scale level and that the conversion (or the equivalent) associated with volume flow rate Qs are judged to be acceptable. The classical scaleup problem is to then design a larger process with flow rate qs which results in the same conversion. The scaleup factor SF is. 

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