2.2.2 Constant molar overflow and other assumptions
Constant molar overflow. This assumption is a substitute for the energy balances. It states that the mixture has a constant heat of vaporization and that sensible heat and heat of mixing effects are negligible. Equations (2.7) and (2.8) give a mathematical expression of this assumption. Detailed thermodynamic implications of this assumption are described elsewhere (e.g., Refs. 6-8).
Generally, constant molar overflow holds well for systems where the components are similar in nature and molecular weights, and where heat-of-solution effects are not significant. When heat-of-solu-tion effects Eire small, the ratio of the molar latent heats of the pure components provides insight into the suitability of the assumption (Table 2.1). The assumption holds well for the benzene-toluene, isobu-tane-normal butane, propane-normal butane, and normal heptane-ethylbenzene systems, where the latent heat ratios are close to unity. The assumption is less satisfactory for the acetone-water and methane-ethylene systems, where this ratio is higher. The assumption is poor for the ammonia-water system where the latent heat ratio is close to 2.
When in doubt, it is best to adjust the x-y diagram for heat effects. This can be achieved by one of the following techniques.
■ When a computer simulation is available, the component balance lines (Sec. 2.2.3) can be constructed from compositions printed out by the simulation. The simulation energy balances adjust the component balance lines for heat effects. These heat effects convert each component balance line thus constructed into a curve (Sec. 2.4.1).
■ Using an H-x diagram to adjust Eqs. (2.9) and (2.10) for latent heat effects. This approach also converts each component balance line into a curve, but the curve is constructed using an H-x diagram instead of a computer simulation. Further details are described by Fisher (10).
■ Using an H-x diagram to derive pseudo molecular weights and pseudo latent heats of vaporization for the components. These pseudo properties are then applied to construct an x-y diagram. This method is described in detail by Robinson and Gilliland (6).
Other assumptions. Two additional assumptions are inherent in the x-v diagram method:
1. The separation is at constant pressure. This assumption is usually good unless the column operates under vacuum. For vacuum systems, the equilibrium curve needs adjustment for pressure variations.
2. The feed stream mixes with the feed-stage fluids prior to any separation. This assumption is good for a single-phase feed, but less satisfactory for a partially vaporized feed (11). A partially vaporized feed splits prior to mixing; the feed liquid then mixes with liquid of the tray below, while vapor mixes with vapor of the tray above. Ledanois and Olivera-Fuentes (11) derived a simple correction to the x-y diagram construction to alleviate the inaccuracy. Their correction is valid where tray efficiency is high (i.e., above 60 to 70 percent); at lower tray efficiencies, the inaccuracy is more difficult to quantify.
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