Smith-Brinkley method

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) 

V and L are the total molar vapour and liquid flow rates, and the superscript denotes the stripping section. 

Equation 11.54 is for a column with a total condenser. If a partial condenser is used the number of stages in the rectifying section should be increased by one. 

The procedure for using the Smith-Brinkley method is as follows  

Estimate the flow-rates L, V and L, V from the specified component separations and reflux ratio. 

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The procedure proposed for the optimization work is the Smith-Brinkley Method. It is especially good for the uses described in this section. The more accurately known the operating parameters, such as tray temperatures and internal traffic, the more advantageous the Smith-Brinkley Method becomes. 

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. 

The Smith-Brinkley Method can therefore be used to generate a hand base case beginning with either a heat and material balanced plant case, a rigorous computer solution of a plant case, or computer solution of a design case. Once the hand base case is established, alternate cases can be done by hand (or small computer having limited core) using the Smith-Brinkley Method. 

This section is a companion to the section titled Fractionators-Optimization Techniques. In that section the Smith-Brinkley method is recommended for optimization calculations and its use is detailed. This section gives similar equations for simple and reboiled absorbers. 

If it is desired to estimate the overhead and bottoms molar flows of a single component, this can be done without performing the full calculation. This is another advantage of the Smith-Brinkley method. 

Time permitting, the more lengthy Smith-Brinkley Method (Reference 19) could also be used as an analysis troubleshootins tool. 

Examples of the application of the Smith-Brinkley method are given by Smith (1963). 

Analysis or existing columns the Smith-Brinkley method... 

Application. Previous methods (Secs. 3.2.1 to 3.2.6) produce a design. They take product compositions and deliver the number of stages, reflux, and optimum feed stage. The Smith-Brinkley method rates a column using the reverse sequence of steps. It takes the number of stages, reflux ratio, and actual feed location, and yields the product compositions. 

The above features make the Smith-Brinkley method valuable for on-line optimization (e.g., using microprocessor or computer control). It can be beneficial for assessing the effects of perturbations on column performance and driving the control point toward an optimum. It is also valuable for off-line optimization and for revamp studies. Rice (58a) extended the Smith-Brinkley method to yield individual stage temperatures and compositions and successfully applied it for control. 

Rice extension of Smith-Brinkley method. 120 Robbins ... 

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. 

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