Formulation of Reactor Problems

A differential equation for a function that depends on only one variable is called an ordinary differential equation. The independent variable is frequently time, t, but for reactors it can also be length down a plug flow reactor. An example of an ordinary differential equation is 

The general solution to the differential equation includes many possibilities the engineer needs to provide initial conditions to specify which solution is desired. If aU conditions are available at one point [as in Eq. (8.1)], then the problem is an initial value problem and can be integrated from that point on. If some of the conditions are available at one point and others at another point, then the ordinary differential equation becomes a two-point boundary value problem (see Chapter 9). Initial value problems as ordinary differential equations arise in the control of lumped parameter models, transient models of stirred tank reactors, and generally in models where there is no diffusion of the unknowns. 

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