Approximate Shortcut Methods for Multicomponent Distillation
Develop approximate shortcut methods for binary and multicomponent distillation by deriving the Fenske equation and using the Underwood equation and Gilliland correlation.
Chapters 5 and 6 introduced multicomponent distillation. Matrix methods are efficient, but they still require a fair amount of time even on a fast computer. In addition, they are simulation methods and require a known number of stages and a specified feed plate location. Fairly rapid approximate methods are required for preliminary economic estimates, for recycle calculations where the distillation is only a small portion of the entire system, for calculations for control systems, and as a first estimate for more detailed simulation calculations.
In this chapter, we first develop the Fenske equation, which allows calculation of multicomponent separation at total reflux. Then we switch to the Underwood equations, which allow us to calculate the minimum reflux ratio. To predict the approximate number of equilibrium stages, we then use the empirical Gilliland correlation that relates the actual number of stages to the number of stages at total reflux, the minimum reflux ratio, and the actual reflux ratio. The feed location can also be approximated from an empirical correlation.
In this chapter, we develop approximate shortcut methods for binary and multicomponent distillation. After completing this chapter, you should be able to satisfy the following objectives:
Derive the Fenske equation, and use it to determine the number of stages required at total reflux and the splits of non-key (NK) components
Use the Underwood equations to determine the minimum reflux ratio for multicomponent distillation
Use the Gilliland correlation to estimate the actual number of stages in a column and the optimum feed stage location