Distillation Smith-Brinkley Method

The Smith-Brinkley Method uses two sets of separation factors for the top and bottom parts of the column, in contrast to a single relative volatility for the Underwood Method. The Underwood Method requires knowing the distillate and bottoms compositions to determine the required reflux. The Smith-Brinkley Method starts with the column parameters and calculates the product compositions. This is a great advantage in building a model for hand or small computer calculations. Starting with a base case, the Smith-Brinkley Method can be used to calculate the effect of parameter changes on the product compositions. 

Smith fully explains the Smith-Brinkley Method and presents a general equation from which a specialized equation for distillation, absorption, or extraction can be obtained. The method for distillation columns is discussed here. 

Why not put new lyrics to an old tune This is an excellent idea, and many have done this very thing. Rice " started with the Smith-Brinkley method" used to calculate distillation, absorption, extraction, etc., overhead and bottoms compositions, and developed distillation equations for determining the liquid composition on any tray. This together with bubble point calculations yield a column temperature profile useful for column analysis. 

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)... 

The Smith and Brinkley (58) method is more convenient for the anal-ysis of existing columns than for the design of new ones. This method applies to absorption and extraction as well as distillation. For distillation, this method gives... 

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