Bifurcation Analysis of the Flash Cascade Model

The fixed points of the flash cascade model are the solutions of equations (6.14) and (6.15) for j — . In other words, successive liquid and vapor mole fractions reach constant values. The fixed points, x, for the stripping cascade (6.14) are solutions of 

Similarly, the fixed points, y, for the rectifying cascade (6.15) are solutions of 

The fixed points obtained by solving (6.15) for a large number of iterates are stable nodes in the rectifying cascade. The same fixed points will form a subset of solu- 

Equation (6.21) has the same fixed points as (6.20) except that their stability is reversed. Thus, a fixed point which is a stable node in equation (6.20) becomes an unstable node for equation (6.21). 

The solutions for equations (6.19) and (6.21) behave as follows. At D = 0 (the non-reactive limit), the fixed point criteria for both the rectifying and stripping cascades reduce to the same equation 

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