Continuous stirred tank reactor nonlinear equations

One of the simplest practical examples is the homogeneous nonisothermal and adiabatic continuous stirred tank reactor (CSTR), whose steady state is described by nonlinear transcendental equations and whose unsteady state is described by nonlinear ordinary differential equations. 

The simplest kinetic reactor model is the CSTR (continuous-stirred-tank reactor), in which the contents are assumed to be perfectly mixed. Thus, the composition and the temperature are assumed to be uniform throughout the reactor volume and equal to the composition and temperature of the reactor effluent However, the fluid elements do not all have the same residence time in the reactor. Rather, there is a residence-time distribution. It is not difficult to provide perfect mixing of the fluid contents of a vessel to approximate a CSTR model in a commercial reactor. A perfectly mixed reactor is used often for homogeneous liquid-phase reactions. The CSTR model is adequate for this case, provided that the reaction takes place under adiabatic or isothermal conditions. Although calculations only involve algebraic equations, they may be nonlinear. Accordingly, a possible complication that must be considered is the existence of multiple solutions, two or more of which may be stable, as shown in the next example. 

Insertion of Eq. (125) into mass balance equations, such as a continuous stirred tank reactor (CSTR) with constant volume, leads to a nonlinear first-order PDE [Eq. (127)]. 

Process Transfer Function Models In continuous time, the dynamic behaviour of an ideal continuous flow stirred-tank reactor can be modelled (after linearization of any nonlinear kinetic expressions about a steady-state) by a first order ordinary differential equation of the form... 

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