Rate laws continued design

The reaction characteristic of the present system are best performed in a semicontinuous reactor in which the solid is stationary, as described in the previous section. This easily permits the two steps. In general, however, continuous reactors in which both the gas and solid phases move continuously are more important. We therefore briefly consider in this section the mathematical basis for the design of such a reactor. The chief reactor and operating parameters are gas and solids feed rates, product size distribution, bed size, and so on, and procedures for determining them are described. With a size distribution o(R), an elutriation stream and an arbitrary rate law for the changing particle size, a material balance on solids of size between R and R + dR yields... 

The transfer of mass as well as heat from one material phase to another is quite commonly encountered in chemical process flow sheets. The same physical laws, rate equations, and design principles can be applied to mass-transfer operations as occurring in absorption, adsorption, crystal-lization, distillation, drying, extraction, jluidization, and humidification Equipment is designed to obtain intimate contact between phases, in either a stagewise or continuous manner, and many special types of equipment have been developed for any given operation. This discussion will be limited to the conventional types of equipment. 

For the situation in which each of the series reactions is irreversible and obeys a first-order rate law, eqnations (5.3.4), (5.3.6), (5.3.9), and (5.3.10) describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For consecutive reactions in which all of the reactions do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time at which the concentration of a particular intermediate passes through a maximum. If interested in designing a continuous-flow process for producing this species, the chemical engineer must make appropriate allowance for the flow conditions that will prevail within the reactor. That disparities in reactor configurations can bring about wide variations in desired product yields for series reactions is evident from the examples considered in Illustrations 9.2 and 9.3. 

Kinetic models can be used to link the reactor design with its performance. The reaction rate may be expressed by power law functions, by more complex expressions, as Langmuit-Hinselwood-Hougen-Watson (LHHW) correlations for catalytic processes, or by considering user kinetics. There are two ideal models, continuous stirred tank reactor (CSTR) or plug flow (PFR), available in rating mode (reaction volume fixed) or design mode (conversion specified). 

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