Computation Scheme for Variable-Density CSTRs

Example 4.3 represents the simplest possible example of a variable-density CSTR. The reaction is isothermal, first-order, irreversible, and the density is a linear function of reactant concentration. This simplest system is about the most complicated one for which an analytical solution is possible. Realistic variable-density problems, whether in liquid or gas systems, require numerical solutions. These numerical solutions use the method of false transients and involve sets of first-order ODEs with various auxiliary functions. The solution methodology is similar to but simpler than that used for piston flow reactors in Chapter 3. Temperature is known and constant in the reactors described in this chapter. An ODE for temperature wiU be added in Chapter 5. Its addition does not change the basic methodology. 

The method of false transients begins with the inlet stream set to its steady- 

Take one step, calculating new values for aout,bout, , and Tout at the new time, f + Af. The marching-ahead equations have the form 

Decrease At by a factor of 2 and go to Step 1. Repeat until the results converge to four or five significant figures. 

Calculate the steady-state value for the reactor volume from Vpo/Pout- If this is significantly different than the desired working volume in the reactor, go back to Step 0, but now start the simulation with the tank at the concentrations and temperature just calculated. 

Set the initial values for aoul, boul, , Tout, and Qoul. 

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