Distillation towers curves

Equipment Constraints These are the physical constraints for individual pieces of eqiiipment within a unit. Examples of these are flooding and weeping limits in distillation towers, specific pump curves, neat exchanger areas and configurations, and reactor volume limits. Equipment constraints may be imposed when the operation of two pieces of equipment within the unit work together to maintain safety, efficiency, or quahty. An example of this is the temperature constraint imposed on reactors beyond which heat removal is less than heat generation, leading to the potential of a runaway. While this temperature could be interpreted as a process constraint, it is due to the equipment limitations that the temperature is set. 

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

Hence, Eq. (7.23) approximates the operating lines at total reflux and, because i and h are dimensionless variables and Eq. (7.19) is identical in form, the residue curves approximate the operating lines of a distillation tower operating at total reflux. 

An example of pressure-swing distillation, described by Van Winkle (1967), is provided for the mixture, A-B, having a minimum-boiling azeotrope, with the T-x-y curves at two pressures shown in Figure 7.36a. To take advantage of the decrease in the composition of A as the pressure decreases from Pj to P[, a sequence of two distillation towers is shown in... 

Figure 10.42 Positioning distillation towers between hot and cold composite curves (a) exchange between hot and cold streams (b) exchange with cold streams.

When integrating a differential equation numerically, one would expect the suggested step size to be relatively small in a region in which the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with a slope of nearly zero. Unfortunately, this is not always the case. The DDEs that make up the mathematical models of most chemical engineering systems usually represent a collection of fast and slow dynamics. For instance, in a typical distillation tower, the liquid mechanics (e.g., flow, hold-up) is considered as fast dynamics (time constant seconds), compared with the tray composition slow dynamics (time constant minutes). Systems with such a collection of fast and slow ODEs are denoted stiff systems. 

Light-component analysis and the TBP and API gravity for the feed are given in Table 13-29. Representation of this feed by pseudocomponents is given in Table 13-30 based on 16.7°C (30°F) cuts from 82 to 366°C (180 to 690°F), followed by A1.1°C (TS T) and then 55.6°C (100°F) cuts. Actual tray numbers are shown in Fig. 13-114. Corresponding theoretical-stage numbers, which were determined by trial and error to obtain a reasonable match of computed- and measured-product TBP distillation curves, are shown in parentheses. Overall tray efficiency appears to be approximately 70 percent for the tower and 25 to 50 percent for the sidecut strippers. 

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