Composite curves constraint

The appropriate placement of distillation columns when heat integrated is not across the heat recovery pinch. The grand composite curve can be used as a quantitative tool to assess integration opportunities. The scope for integrating conventional distillation columns into an overall process is often limited. Practical constraints often prevent integration of columns with the rest of the process. If the... 

Maximum water reuse can be identified from limiting water profiles. These identify the most contaminated water that is acceptable in an operation. A composite curve of the limiting water profiles can be used to target the minimum water flowrate. While this approach is adequate for simple problems, it has some severe limitations. A more mathematical approach using the optimization of a superstructure allows all of the complexities of multiple contaminants, constraints, enforced matches, capital and operating costs to be included. A review of this area has been given by Mann and Liu21. 

By calculating the class 1 FI target, the process engineer can identify the critical uncertainty point and critical constraint (appearance of new pinches, nonnegative heating or cooling, and so on). This uncertainty point and constraint limit the resilience of a completely countercurrent (e.g., infinitely cyclic) HEN structure able to mimic the composite curves thus they seem the most likely uncertainty point and constraint to limit the resilience of a practical but well-designed (almost completely countercurrent) HEN structure. 

Exploitation of Boundary Curvature A second approach to boundaiy crossing exploits boundaiy curvature in order to produce compositions in different distillation regions. When distillation boundaries exhibit extreme curvature, it may be possible to design a column such that the distillate and bottoms are on the same residue curve in one distillation region, while the feed (which is not required to lie on the column-composition profile) is in another distillation region. In order for such a column to meet material-balance constraints (i.e., bottom, distillate, feed on a straight hne), the feed must be located in a region where the boundary is concave. 

Fig. 14. Data (points) for G (co) and G (co) for a range of compositions of a blend of two polyisoprene stars of molecular weights 28 and 144 kg mol The fractions of the bigger star are in order 0.0,0.2,0.5,0.8 and 1.0. Curves are theoretical predictions of the tube model with co-operative constraint release treated by dynamic dilution [56]. The choice of 2.0 rather than 7/3 for the dilution exponent p is compensated for by taking M = 5500 kg mol" ...

To a first approximation, the composition of the distillate and bottoms of a single-feed continuous distillation column lies on the same residue curve. Therefore, for systems having separatrices and multiple regions, distillation composition profiles are also constrained to lie in specific regions. The precise boundaries of these distillation regions are a function of reflux ratio, but they are closely approximated by the RCM separatrices. If a separatrix exists in a system, a corresponding distillation boundary also exists. Also, mass balance constraints require that the distillate composition, the bottoms composition, and the net feed composition plotted on an RCM for any feasible distillation be collinear and spaced in relation to distillate and bottoms flows according to the well-known lever rule. 

The contrasting temperature-induced shifts of the pyroxene 1 and 2 pm bands could lead to erroneous estimates of the composition and, to a lesser extent, structure-type of a pyroxene-bearing mineral assemblage deduced from the remote-sensed reflectance spectrum of a hot or cold planetary surface if room-temperature determinative curves, such as that shown in fig. 10.5, are used uncritically. For example, remote-sensed spectra of planets with hot surfaces, such as Mercury and the Moon, would lead to overestimates of Fe2+ contents of the orthopyroxenes and underestimated Fe2+ contents of the clinopyroxenes (Singer and Roush, 1985). Planets with cold surfaces, such as Mars and the asteroids, could produce opposite results. On the other hand, the room-temperature data underlying the pyroxene determinative curve shown in fig. 10.5 may impose constraints on the compositions of pyroxenes deduced from telescopic spectra of a planet with very high surface temperatures, such as Mercury. 

The only observational constraint on the internal structure of satellites is density. The bulk composition (rock to ice ratio) of icy satellites is obtained by comparing tlieir density vs. radius relationship witli model curves calculated by Lupo and Lewis [6] as shown in Fig. 9.2. From this comparison, we can estimate tlie rock to ice (to pore) ratio of the satellites. 

This constraint follows from the definition of a distillation curve. Each point along a distillation curve represents both the vapor and the liquid compositions just above (or below) any tray, including those at the ends of the column where products would normally be withdrawn. This constraint, together with the material balance constraint, completely defines the reachable products for a column at total reflux. 

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