Difference point equation reactive systems

Example 8.1 illustrates how one may go about synthesizing a simple reactive distillation process, or at the vary least allows one to assess whether the proposed process is at all feasible. It should be noted that if either k ox p turned out to be negative, the proposed process would be infeasible since these parameters only have realistic meaning when they are positive quantities. Moreover, if the k and p were found to be positive but the node at the desired composition is found to be an unstable node, the simple process would not be feasible either. If a saddle node were found, one has to be certain of the initial composition within the reactor because there is only a single profile which will end at the desired composition. Any other initial composition would result in an entirely different ending composition because the profile will veer away from the saddle point. Lasdy, the reader should also be aware that, in the case of the three component system, there are two independent equations that may be written, implying that one may solve for two unknown process... 

Under such simplified description of the streamer development, we could model the subsequent evolution of the gas phase in a standard way, using the continuity equations for each chemical species and solving a system of mono-dimensional first-order differential equations easily and quickly tackled by numerical integration (Riccardi, 2000). From a chemical engineering point of view, indeed it means that the model can be formulated as a well-mixed reactor (Benson, 1982). The gas-phase composition in the reactor is determined by the chemical reactions among the reactive species and the transport processes. The time evolution of the concentration of the different N sp>ecies in the gas phase is determined by integrating each balance equation for the density nk of the Id spiecies ... 

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