Flash cascade model

We formulate the reactive flash modd for an equimolar chemistry. Next, we hypothesize a condition under which the trajectories of the flash cascade model lie in the feasible product regions for continuous RD. This hypothesis is tested for an example mixture at different rates of reaction. The fixed point criteria for the flash cascade are derived and a bifurcation analysis shows the sharp split products from a continuous RD. 

A schematic of the co-current flash cascade arrangement is shown in Fig. 6.7. There are two sections. In the rectifying cascade, vapor from each flash reactor 

The overall mass balance for the/ unit in the stripping cascade in Fig. 6.1 is 

This is the ratio of the characteristic liquid residence time to a characteristic reaction time, kf is the forward rate constant at a reference temperature, No reaction occurs in the limit Doj — 0 and reaction equilibrium is achieved as Duj — oo. At intermediate Daj, the stage operates in the kinetically controlled regime. Incorporating j j and Doj in (6.8), we find 

0j and DUj are two independent parameters for each flash unit. We study the cases in which 

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In this chapter, we describe an algorithm for predicting feasible splits for continuous single-feed RD that is not limited by the number of reactions or components. The method described here uses minimal information to determine the feasibility of reactive columns phase equilibrium between the components in the mixture, a reaction rate model, and feed state specification. This is based on a bifurcation analysis of the fixed points for a co-current flash cascade model. Unstable nodes ( light species ) and stable nodes ( heavy species ) in the flash cascade model are candidate distillate and bottom products, respectively, from a RD column. Therefore, we focus our attention on those splits that are equivalent to the direct and indirect sharp splits in non-RD. One of the products in these sharp splits will be a pure component, an azeotrope, or a kinetic pinch point the other product will be in material balance with the first. 

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... 

The flash cascade provides a two parameter (f> and D) model ((6.14) and (6.15)). The iterates depend primarily on the value of D. The pinch points towards which these iterates evolve depend only on a single parameter, (Da/ ). Therefore, the solution structure is not dependent on the value of rp, and we may choose any value of (j> (we pick rj> = 0.5). This simply rescales the value of Da at which bifurcations occur. 

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