Transient PFR

The question arises as to how long it will take a reactor operating in the plug flow regime to reach a steady state for a specific set of reaction kinetics, volume, and flow rate. To solve this problem we need to solve both in time and in space. If the kinetics are simple, then we can solve the problem analytically, that is, we can derive expressions for the concentrations that are functions of time and position. However, often the kinetics are not straightforward and analytical solutions must be surrendered in favor of numerical solutions. 

The numerical solution will produce values of the concentration at specific times and positions. What happens then is that the equations are solved for a grid of times and positions. Starting with initial conditions, each new solution is based on the solution at the previous grid point. The differentials are approximated by differences and the problem reduces to one of solving the simultaneous difference equations. Many very elegant numerical recipes are used to do this, but none that need concern us here. Instead, we accept the work from decades of research and development in computing and applied math and simply use its powerful results. 

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Revisit the transient PFR example of Chapter 8, Example 8.1. Solve the problem for a range of dispersion numbers. Can you get a CSTR-Iike solution for large values of the dispersion number Can you get a PFR-like solution for small values of the dispersion number Do you have numerical accuracy problems at either of these limits ... 

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