VDelR condition

CONCEPT Critical a policies in three - V dimensions—the vDelR condition... 

For systems in R, we can use the vDelR condition as a shortcut method to determining critical a policies in a critical DSR. 

The vDelR condition, specific to three-dimensional problems described in Chapter 6, may also be employed. 

For DSRs, the vDelR condition for critical a policies must still apply, although the conditions must be amended to include the temperature parameter as well. 

Since the system is three-dimensional in nature, the VdelR condition may be used to compute the critical a policy for the system. Since the system is no longer expressed in terms of concentrations, however, the specific critical a policy given by Equation 7.3 cannot be used. Rather, the Jacobian matrix expressed in terms of mass fractions dr(z) must be computed and then used to compute (p(z), as in Chapter 7. The computations are somewhat lengthy, and hence this approach will not be adopted here. Instead, the parallel complement automated AR construction method discussed in Chapter 8 shall be employed, providing a quick means to compute the AR for use in comparisons. 

We also described how concrete equations for critical DSR and CSTRs may be computed. These expressions are complicated to compute analytically, which are derived from geometric controllability arguments developed by Feinberg (2000a, 2000b). These conditions are intricate, and thus it is often not possible to compute analytic solutions to the equations that describe critical reactors. For three-dimensional systems, a shortcut method involving the vDelR condition may be used to find critical a policies. Irrespective of the method used, the conditions for critical reactors are well defined, irrespective of the legitimacy of the kinetics studied, and thus these conditions must be enforced if we wish to attain points on the true AR boundary. 

---