Stripping cascade

A Two-stage stripping cascade B Two-stage enriching cascade... 

In a stripping cascade, liquid is fed into the top. Liquid out the bottom of the cascade is partially vaporized and the vapor is recycled into the bottom of the cascade. The vapor stream at the top represents the second product stream. 

Substituting this result into (63), the operating line for a stripping cascade becomes ... 

Comment 1 Notice that the feed line for a stripping cascade is vertical, whereas the feed line for a rectifying cascade was horizontal (see page 75). This is because the feed... 

Beyond the expected changes in flowrates at the feed tray and at the top, there is a continuous drop in flowrate of both streams as we move down either the rectifying cascade or the stripping cascade. These changes in flowrates within a cascade are not consistent with the equiniolal overflow assumption. 

Figure 6.39 Purification of sour gas by a two-stage stripping cascade.27...

Edmister applied the group method to complex separators where cascades are coupled to condensers, reboilers, and/or other cascades. Some of the possible combinations, as shown in Fig. 12.24, are fractionators (distillation columns), reboiled strippers, reboiled absorbers, and refluxed inert gas strippers. In Fig. 12.24, five separation zones are delineated (1) partial condensation, (2) absorption cascade, (3) feed stage flash, (4) stripping cascade, and (5) partial reboiling. 

The combination of an absorption cascade topped by a condenser is referred to as an enricher. A partial reboiler topped by a stripping cascade is referred to as an exhauster. As shown in Fig. 12.25 stages for an enricher are numbered from the top down and the overhead product is distillate, while for an exhauster stages are numbered from the bottom up. Feed to an enricher is vapor, while feed to an exhauster is liquid. The recovery equations for an enricher are obtained from (12-64) by making the following substitutions, which are obtained from material balance and equilibrium considerations. 

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

Including (6.13) in (6.12), gives the final formulation of the stripping cascade... 

Equation (6.14) can be solved recursively for given values of the parameters,

starting with the initial condition, a , = Ap. The solution is a trajectory of liquid compositions for the stripping cascade. 

Solutions of (6.14) and (6.15), the rectifying and stripping cascade flash trajectories, can be represented in mole fraction space (three dimensional for the IPOAc system). However, we represent the solutions in transformed composition space, which is two dimensional for IPOAc system (for a derivation and properties of these transformed variables [46]). This transformed composition space is a projection of a three dimension mole fraction space onto a two dimensional transformed composition subspace for the IPOAc system. Even though the correspondence between real compositions and transformed compositions is not one-to-one in the kinetic regime, we will make use of these transforms because of ease of visualization of the trajectories, and because overall mass balance for reactive systems (kinetically or equilibrium limited) can be represented with a lever rule in transformed compositions. We use this property to assess feasible splits for continuous RD. 

Fig. 6.8 Rectifying and stripping cascade tra- formed mole fraction space. For the stripping jectories for a saturated liquid equimolar reac- cascade, X, = Xhoac + tipoAo 2 = + Xipoac...

Note that calculating the flash trajectories at (f> = 0.5 does not provide the entire feasible product regions for continuous RD, but instead generates a subset of the feasible products. Selecting an iterate on the stripping cascade trajectory as a potential bottoms and an iterate on the rectifying cascade trajectory as a potential distillate does not guarantee that these products can also be obtained simultaneously from a RD column. This is simply because these product compositions may not simultaneously satisfy the overall mass balance for a reactive column. However, when the flash trajectories are used in conjunction with the lever rule for a continuous reactive column, the feasible splits for continuous RD can be quickly predicted. 

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 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... 

Equation (6.22) is the fixed point criteria for simple distillation and also for a continuous column at total reflux and total reboil. Since there is a symmetry in the rectifying and stripping maps, we can find the fixed points for both the rectifying and stripping cascades from equation (6.22). Thus, in this limit, our model recovers the criterion for fixed points in the well-known limit of no-reaction. At D = 1 (the chemical equilibrium limit), the fixed point criteria reduce to a single equation... 

Equation (6.23) implies that fixed points lie on the reaction equihbrium surface. Equation (6.23), however, is just a necessary condition the sufficient condition for fixed points of the rectifying and stripping cascades can be written in terms of transformed variables by writing either (6.19) or (6.21) for component i and a reference component, k and adding the two, giving... 

The solutions of equation (6.24) are fixed points for simple RD at chemical equilibrium and also for a continuous RD at total reflux and total reboU. As in the non-reactive case, the fixed point criteria for the rectifying and stripping cascades are the same and is given by equations (6.23) and (6.24). Once again our model reduces to the well-known criteria for chemical equilibrium fixed points. 

Fig. 6.10 Bifurcation diagrams for the (a) rectifying and (b) stripping cascades. The filled circles denote stable node branches, open circles denote unstable node branches, and the open squares denote saddle branches...

The branches of interest are the unstable nodes in the rectifying bifurcation diagram and the stable nodes in the stripping cascade bifurcation diagram. These node branches are shown separately in a feasibility diagram, Fig. 6.11. 

Fig. 6.11 Feasibility diagram showing the feasible distillates (unstable nodes) and feasible bottom products (stable nodes) from the rectifying and stripping cascade bifurcation diagrams, respectively...

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