Feasibility diagram

For example 2, Figs. 4.4(a) and (b) show the bifurcations of all singular points with respect to the Damkohler numbers of the reactive condenser and the reactive reboiler, respectively. As can be seen from the feasibility diagram in Fig. 4.4(c), at Damkohler numbers Dac > 0.830, two possible condenser products - that is, the top products of a fully reactive distillation column, are predicted. The kinetic azeotrope in the reactive reboiler is always the possible bottom product of a column. 

Fig. 4.3. Bifurcation diagrams for reactive condenser (a) and for reactive reboiler (b), and feasibility diagram (c) for ellipse-type system.

As can be seen from Fig. 4.7, the kinetic tangent pinch point at the critical Damkohler number Dar = 0.166 has an important role for the topology of the maps. This is also reflected by the feasibility diagrams given in Fig. 4.8(a-c). In Fig. 4.8(c), the stable node branch at positive Damkohler numbers are collected from the singular point analyses of the reactive condenser (Fig. 4.8(a)) and the reactive reboiler... 

Fig. 4.11. Feasibility diagrams for isopropyl acetate (IPOAc) reaction system at 1.01 x 105 Pa. 

Application of Feasibility Diagram Column Feasible Split... 

Collect the stable nodes along the singular point branches and display them in feasibility diagrams. 

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. 

The feasibility diagram provides a global view of the feasible products to exped from a continuous distillation at any rate of reaction (D). For any feed composition and for D in the range, 0 < D < 0.395, it is possible to obtain acetic add as bot-... 

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...

Rule for Feasible Products Unstable node branches in the feasibility diagram represent potential distillates while the stable node branches represent the potential bottoms from a continuous RD column. 

Fig. 9. A dry-mix grafting feasibility diagram obtained from the solubility parameter difference A between polymer and NR and Tg or Tm of the polymer where PEflA = poly(ethyl-methacrylate), PUC.= poly(vinylchloride), PCL = poly (caprolactone), PS = polystyrene, PFlflA = poly (methylmethacrylate), Pa-flS = poly (a-methylstyrene),...

As mentioned previously, ternaiy mixtures can be represented by 125 different residue curve maps or distillation region diagrams. However, feasible distillation sequences using the first approach can be developed for breaking homogeneous binaiy azeotropes by the addition of a third component only for those more restricted systems that do not have a distillation boundaiy connected to the azeotrope and for which one of the original components is a node. For example, from... 

FIG. 13-64 Feasible distillation region diagrams for breaking homogeneous binary azeotrope A-B, a) Low-boiling entranoes. 

The transformed variables describe the system composition with or without reaction and sum to unity as do Xi and yi. The condition for azeotropy becomes X, = Y,. Barbosa and Doherty have shown that phase and distillation diagrams constructed using the transformed composition coordinates have the same properties as phase and distillation region diagrams for nonreactive systems and similarly can be used to assist in design feasibility and operability studies [Chem Eng Sci, 43, 529, 1523, and 2377 (1988a,b,c)]. A residue curve map in transformed coordinates for the reactive system methanol-acetic acid-methyl acetate-water is shown in Fig. 13-76. Note that the nonreactive azeotrope between water and methyl acetate has disappeared, while the methyl acetate-methanol azeotrope remains intact. Only... 

Importance of Design Diagrams One of the first things a designer should tiy to do is lay out a carefully constructed equilibrium curve, y° = Fix), on an xy diagram, as shown in Fig. 14-2. A horizontal line corresponding to the inlet-gas composition yi is then the locus of feasible outlet-liquor compositions, and a vertical hue corresponding to the inlet-solvent-liquor composition X9 is the locus of feasible out-... 

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. 

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

Next, both composite streams are plotted on the same diagram (Fig. 3.7). On this diagram, thermodynamic feasibility of mass exchange is guaranteed when the lean composite stream is always above the waste composite stream. This is equivalent to ensuring that at any mass>exchange level (which comesponds to a horizontal line), the composition of the lean composite stream is located to the left of the waste composite stream, asserting thermodynamic feasibility. Therefore,... 

Interpreting results of the pinch diagram As can be seen from Fig. 3.12, the pinch is located at the corresponding mole fractions (y,Xi.jc ) - (0.(K)10, 0.0030, 0.0010). The excess capacity of the process MSAs is 1.4 x lO" kg mol benzene/s and cannot be used because of thermodynamic and practical-feasibility limitations. This excess can be eliminated by reducing the outlet compositions and/or flowrates of the process MSAs. Since the inlet composition of S2 corresponds to a mole fraction of 0.0015 on the y scale, the waste load immediately... 

In order to synthesize an optimal MEN for intercepting the off-gas condensate, we constnict the pinch diagram as shown in Fig. 4.9. Since the three MSA s lie completely to the left of the rich stream, they are all thermodynamically feasible. Hence, we choose the one with the least cost ( /kg NH3 removed) namely the resin. The annual operating cost for removing ammonia using the resin is ... 

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