An Extension of Smoker's Equation That Includes the Murphree Tray Efficiency

The Smoker equation is the analytical equivalent of the graphical McCabe-Thiele construction for binary systems with approximately constant relative volatilities for which constant molar overflow is a reasonable assumption. This paper will describe an extension of Smoker's equation to include the Murphree stage efficiency. The standard McCabe-Thiele graphical construction is rather easily extended to include non-equilibrium stages. In essence, one constructs a pseudo-equilibrium curve which is then used in the same way that the real equilibrium curve is for moving between equilibrium stages. This pseudo-equilibrium curve can generally be described reasonably well using a pseudo-, or effective, relative volatility. This is the crux of the method described here. Employing this effective relative volatility in Smoker's equation instead of the thermodynamic relative volatility introduces the Murphree stage efficiency in an unconventional way. Results from this modification of Smoker's equation compare extremely well with those from a process simulator which incorporates the Murphree efficiency rigorously for all of the binary systems tested so far. Thus, this version of Smoker's equation can be utilized to study the effects of the Murphree stage efficiency on stage counts, product purities, and condenser/reboiler duties in a much more transparent way than through the use of a process simulator alone.