Stoichiometry cannot account for finite DRE and PIC concentrations. Global kinetics can address only the former. Finite DRE can be expressed as a fractional conversion as follows:
where k is a (pseudo) first-order rate coefficient s—1 The product of rate and residence time determines the conversion (i.e., a high DRE is achieved only by a sufficiently high rate [high temperature] and sufficient residence time).
This presentation implies a plug-flow reactor and irre-versibility; the latter is usually a good assumption in combustion reactions. Some evidence exists that a modified model incorporating an ignition-delay time gives a better fit to experimental data (Lee et al. 1982).
In Equation 5.21(4), the dimensionless group —kt presents the natural log of the unreacted fraction. Conversion increases rapidly with an increase in kt. This product implies a batch reactor. For a flow reactor (plug flow), t is replaced by t, the mean residence time, defined as V/Q (reactor volume divided by the volumetric flow rate at a constant density) or L/u for tubular reactors (L = reactor/com-bustor length; u = average velocity).
Some reported data shows evidence that continuously stirred tank reactors (CSTR), or perfect mixer, behavior occurs at high conversion (Hemsath and Suhey 1974). The following equation expresses this behavior:
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