Feasible bottoms

Figure 4.27 shows residue curve maps for the reactive reboiler at three different Damkohler numbers. In the nonreactive case (Da = 0 Fig. 4.27(a)), the map topology is structured by one unstable node (pure B), one saddle point (pure C), and one stable node (pure A). Since pure A is the only stable node of nonreactive distillation, this is the feasible bottom product to be expected in a continuous distillation process. 

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...

Distillation boundaries always exist if there is more than one origin or terminus of residue curves in the system, which means more than one feasible bottom or top product. Typical residue curves for the system benzene-cyclohexane-acetone are shown in Figure 11.11. The most important lines are the distillation boundaries, which cannot be crossed by distillation. While the residue curves are connections between the high-boiling compound (stable node) and the low-boiling compound (unstable node), the distillation boundaries are connecting lines between the saddle point and the stable or the unstable node, respectively. 

In the first class, azeotropic distillation, the extraneous mass-separating agent is relatively volatile and is known as an entrainer. This entrainer forms either a low-boiling binary azeotrope with one of the keys or, more often, a ternary azeotrope containing both keys. The latter kind of operation is feasible only if condensation of the overhead vapor results in two liquid phases, one of which contains the bulk of one of the key components and the other contains the bulk of the entrainer. A t3q)ical scheme is shown in Fig. 3.10. The mixture (A -I- B) is fed to the column, and relatively pure A is taken from the column bottoms. A ternary azeotrope distilled overhead is condensed and separated into two liquid layers in the decanter. One layer contains a mixture of A -I- entrainer which is returned as reflux. The other layer contains relatively pure B. If the B layer contains a significant amount of entrainer, then this layer may need to be fed to an additional column to separate and recycle the entrainer and produce pure B. 

Distillation boundaries for continuous distillation are approximated by simple distillation boundaries. This is a very good approximation for mixtures with nearly linear simple distillation boundaries. Although curved simple distillation boundaries can be crossed to some degree (16,25—30,32,33), the resulting distillation sequences are not normally economical. Mixtures such as nitric acid—water—sulfuric acid, that have extremely curved boundaries, are exceptions. Therefore, a good working assumption is that simple distillation boundaries should not be crossed by continuous distillation. In other words, for a separation to be feasible by distillation it is sufficient that the distillate and bottoms compositions He in the same distillation region. 

Classical Adiabatic Design Method The classical adiabatic method assumes that the heat of solution serves only to heat up the liquid stream and that there is no vaporization of solvent. This assumption makes it feasible to relate increases in the hquid-phase temperature to the solute concentration x by a simple eutnalpy balance. The equihbrium curve can then be adjusted to account For the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will become more concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-8 in Example 6. 

Complex structures such as tank farms, tank bottoms and marine installations have complicated attenuation patterns and it is not feasible to use complex equations to determine the effect. This must be determined by a current drain test or by practical experience. For pipelines the attenuation depends on the linear resistance of the pipe, coating resistance, and to some extent the resistivity of the soil. Connections to foreign structures and the method of termination of the line also affect the attenuation (see Section 10.1). 

For the stripping and rectifying sections to become a feasible column, the two operation leaves must overlap. Figure 12.20 shows the system chloroform, benzene and acetone. The operation leaf for a distillate composition D intersects with the operation leaf for a bottoms composition... 

Bi in Figure 12.20. This means that there is some combination of settings for the reflux ratio and reboil ratio that will allow the section profiles to intersect and become a feasible column design. By contrast, bottoms composition B2 shows an operation leaf that does not intersect with the operation leaf of distillate D. This means that the two products D and B2 cannot be produced in the same column, and the design is infeasible. No settings of reboil ratio or reflux ratio can make the combination of B2 and D a feasible design. 

As long as this middle section operation leaf intersects with those for the top section (above the entrainer feed) and the bottom section (below the feed point for the feed mixture), the column design will be feasible. Note that there will always be a maximum reflux ratio, above which the separation will not be feasible because the profiles in the top and bottom sections will tend to follow residue curves, which cannot intersect. Also, the separation becomes poorer at high reflux ratios as a result of the entrainer being diluted by the reflux of lower boiling components. 

Additives often form a problem in recycling processes. Material recycling is often not possible or only with a considerable loss of quality. Plastics recycling is notoriously difficult due to the mixed composition of the plastics waste stream. The recycled material can only be used in certain applications that do not demand a pure material. Recycling of the additives themselves is theoretically possible only for metals, but in practice this type of recycling is not feasible. The metals occur only in low concentrations. Recovery from fly ash and bottom ash is possible, but expensive in view of growing scarcity problems it may become a viable options for at least some metals. 

Upper bounds on the objective function can be found from any feasible solution to (3-110), with y set to integer values. These can be found at the bottom or leaf nodes of a branch and bound tree (and sometimes at intermediate nodes as well). The top, or root, node in... 

In spite of these limitations, estimates for ocean storage capacity in excess of 100,000 billion GtC have been cited (Herzog et al., 1997). Such numbers would only be feasible if alkalinity (i.e., NaOH) is added to the ocean to neutralize the corresponding amounts of carbonic acid formed. Over thousands of years, the dissolution of calcareous oozes at the bottom of the ocean could provide such alkalinity (Archer et al., 1997 Broecker and Takahashi, 1978). 

Climate change will impact on water quality and quantity and hydromorphology and may thus remobilise historic pollutants from river bottom sediments and/or floodplain soils. However, the extent of this impact is still largely unclear and there is also a lack of feasible measures to mitigate the (potential) impacts. 

One major objective of this feasibility was to assess the potential of acoustic chemometrics to monitor the general process state of the granulation reactor in order to give reliable early warning if a critical situation occurs in the bed. Critical situations in the fluidized bed are often a result of lump formation and/or layering on the perforated bottom plate of the reactor (see Figure 9.5). 

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