Reachable regions

E.xample problems are included to highlight the need to estimate the entire set of products that can be reached for a given feed when using a particular type of separation unit. We show that readily computed distillation curves and pinch point cur es allow us to identify the entire reachable region for simple and e.xtractive distillation for ternary mixtures. This analysis proves that finite reflux often permits increased separation we can compute exactly how far we can cross so-called distillation boundaries. For extractive distillation, we illustrate how to find minimum. solvent rates, minimum reflux ratios, and, interestingly, ma.xinnim reflux ratios. 

For nearly ideally behaving mixtures, the above completes the analysis needed to identify the reachable region at total reflux. For nonideally behaving mixtures, the shape of the distillation curves can lead to very interesting reachable-product regions. An S-shaped curve, for example, can lead to two disjoint reachable regions, a situation we shall examine later. The rule to remember for total reflux is that the column can produce any distillate product D and bottoms product B where... 

If the feed is Fi, a point lying between D and P, then the pinch curve through D lies entirely to one side of the point F and curves back to cross at P. The corresponding distillation curve lies even farther away to the same side (the pinch point curve turns more sharply than the distillation curve). The reachable region for D excludes all points between D and P. Thus the points between F and P are unreachable by the top part of the column. As D could move to be coincident with F, points beyond F are not excluded. 

We see that the S-shaped region makes the process of discovering reachable regions more difficult (but not impossible). 

If the shaded regions do not overlap, no conventional column can produce these two products at the same time. We need to argue that the converse is true namely, if the regions overlap, a column exists that can produce these two products. We would have no trouble making that statement for this particular column as B is reachable from D directly using tray-by-tray computations. We would feed the bottom tray in this column (very likely not the best way to run a column to get these two products). 

The required information about the distillation boundary is obtained from the pinch distillation boundary (PDB) feasibility test [8]. The information is stored in the reachability matrix, as introduced by Rooks et al. [9], which represents the topology of the residue curve map of the mixture. A feasible set of linear independent products has to be selected, where products can be pure components, azeotropes or a chosen product composition. This set is feasible if all products are part of the same distillation region. The singular points of a distillation region usually provide a good set of possible product compositions. The azeotropes are treated as pseudo-components. 

Improvement in the transport of active substances to particularly inaccessible sites (in the case of bacterial or parasitic infections in intra- or extracellular regions. ncM reachable by simple diffusion). 

Depending on the process parameters a specific consolidation degree is reached. In the best case it will be on the same level as received, for example by autoclave consolidation. But, the consolidation region is very limited during the process and due to the limited time available for build-up of a pronounced interdiffusion of the polymer chains the degree of consolidation is in most cases below the maximum reachable value. - ... 

A reflux ratio R, is minimal (at a constant F/V) if x is reachable from Xch at R=Rmia but with zero recovery. The specified Xd is reachable if there is a still path leading to a momentary Xs that can be connected to Xq with a column profile. The actual situation of the feasibility boundary depends on R. All the points of the calculated still path lie in Region-II for any / [Pg.206]

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