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An empirical technique - the O'Connell correlation - is widely used to estimate the efficiency of cross-flow trays. This article proposes a modification and clarifies the relationship between the empirical and theoretical approaches.
(ProQuest: ... denotes formulae omitted.)
Distillation - the most important unit operation for separating liquid mixtures - is carried out in columns equipped with either packing or trays. In a conventional tray column, vapor rises vertically up through the column while the liquid flows downward and across the trays in alternate directions on successive trays (Figure 1). Column simulation and design software calculates the number of theoretical stages and the section efficiency is used as an efficiency factor to translate theoretical stages to actual trays. The efficiency of a particular section of a column (y\seclio„) is the number of theoretical stages (nlh) found in a section of a column divided by the number of actual trays (nlravs):
... (1)
O'Connell published a graph showing section efficiencies for bubble cap trays, which can be represented by (1):
... (2)
where p; is the liquid viscosity in mPa-s and a is the relative volatility.
The relative volatility and the liquid viscosity serve as the only input variables in calculating conventional distillation tray efficiencies with the empirical correlation developed by O'Connell (1). This simple method has survived all attempts at being replaced by more rigorous models, despite lacking a sound theoretical explanation for its success. This article presents a simple, but fundamentally sound, theoretical approach that achieves results equivalent to O'Connell's correlation using the same number of variables - revealing the hitherto unrecognized relationship between O'Connell's empirical correlation and other theoretical models. In addition, the article introduces a modification to O'Connell's correlation that produces a close-to-perfect match between the updated correlation and the derived theoretical model.
The traditional Murphree efficiency approach to tray design
The section efficiency is calculated based on fundamental mass-transfer considerations, including the approach to equilibrium both locally on the tray (point efficiency) and on the tray as a whole (tray efficiency). The conventional method of designing trays (2) employs Murphree's definition of efficiency to quantify the approach to equilibrium.
The overall number of transfer units for the gas phase (Nog) is (3):
... (3)
where NG and NL represent the...