Multicomponent Smith-Brinkley method

Smith-Brinkley shortcut method A quick procedure used to estimate the components in a multicomponent mixture leaving the top and bottom of a disfillation column operating with continuous feed. The procedure is applicable to any stage-wise separafion process. For a distillation column with a single feed and a total condenser, the fractional recovery of any component in the bottom product is calculated from details that include the reflux ratio, internal flows of liquid and vapour above and below the feed point (i.e., the rectifying and stripping sections), and the relative volatilities of the components. In the calculation, the reboiler counts as stage one. 

Smith and Brinkley developed a method for determining the distribution of components in multicomponent separation processes. Their method is based on the solution of the finite-difference equations that can be written for multistage separation processes, and can be used for extraction and absorption processes, as well as distillation. Only the equations for distillation will be given here. The derivation of the equations is given by Smith and Brinkley (1960) and Smith (1963). For any component i (suffix i omitted in the equation for clarity)... 

---