Flash cascade

As an alternative method, Qi et al. [14] proposed to use a reactive condenser (see Fig. 4.1) to predict possible top products of a countercurrent reactive distillation column. The feasibility analyses of the reactive condenser and the reactive reboiler are analogous to the flash-cascade approach. The latter authors used transformed... 

For this system, Venimadhavan et al. [7] have studied the bifurcation of the singular points in a reactive reboiler, while Chadda et al. [13] demonstrated the flash-cascade approach. In the present investigation, the same thermodynamic properties and kinetic expression were used (see Tab. 4 in Ref. [7]). 

The above flash cascade technique provides a rigorous, assumption-free, completely stable, iterative calculation of unknown stream flow rates, temperatures, and compositions, as well as reboiler and condenser duties. The rate of convergence is relatively slow, however, particularly at high reflux ratios, because the initial vapor and liquid flow rates for all streams except F and B are initially zero, and only (F — B — D) moles are added to the column at each... 

The determination of the singular points appearing in these maps yields important information about the attainable bottom product compositions in real counter-current columns. However, as shown by Chadda et al. [3], both the distillate and the bottom product compositions can be better obtained as singular points of a reactive enriching flash cascade or a stripping flash cascade, respectively. As will be shown, singular point analysis can also provide valuable information about the role of interfacial mass-transfer resistances in RD processes. 

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. 

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... 

Fig. 6.7 A CO current flash cascades arrangement. The top half is the rectifying cascade and the bottom half is the stripping cascade...

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. 

Hypothesis The trajectories of the flash cascades lie in the feasible product regions for continuous RD. 

Parametric column simulations for the I POAc system were performed with different Damkohler numbers, reflux ratios, reboil ratios as well as total number of stages, (N-I-) and feed tray location, (/). The distillate and bottoms compositions obtained were recorded in transformed composition space. Fig. 6.9 compares the products obtained from column simulations with 30 stages and using different values of r and s at D = 0.25 and D = 0.75. The column feed specification is the same as that to the co-current flash cascade. The flash trajectories provide a good estimate of the product compositions from a continuous column. We also compared the product compositions from column simulations with the flash trajectories in mole fraction space. We found that product compositions from column simulations surrounded the flash trajectories, in agreement with the hypothesis that the flash trajectories lie in the feasible product regions for continuous RD. 

Next, we derive the fixed-point criteria for the flash cascades and use bifurcation theory to propose rules to estimate feasible products. 

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... 

One difficulty with the cascade shown in Figure 3-1 is that the intermediate product streams, L, L2, V4, and V5, are of intermediate concentration and need further separation. Of course, each of these streams could be fed to another flash cascade, but then the intermediate products from those cascades would have to be sent to additional cascades, and so forth. A much cleverer solution is to use the intermediate product streams as additional feeds within the same cascade. 

Adapted from [18, 37, 38], Note that more or fewer flash cascade stages may be optimal. 

Once successful, the flash cascade can be added. Add three adiabatic flash blocks (specify zero for heat duty) in series with pressures of 13.8 bar, 6.9 bar, and 1.4 bar, respectively, and add the corresponding vapor and liquid product streams for each. After running and verifying that the results make sense (the vapor product of the first flash should have some H2 in it, and the last vapor product should be mostly CO2), add compressors for the first and third vapor products (via the Pressure ChangelCom-pressor button). The compressor for the first product should compress the stream to 16.2 bar (the absorber pressure), and the other compressor should compress to 6.5... 

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