Two approaches exist for solving problems involving systems of columns, the "column modular method" and the "system modular method" proposed by Hess.15 In the column modular approach, the equations for each column of a system are solved in succession, and in the system modular approach, the complete set of equations for the system are solved simultaneously. While the system modular approach may be the ultimate method for solving problems involving systems of interconnected columns, the column modular approach appears to be the most realistic approach at the present time.
Solution of Systems of Columns by Use of the Column Modular Method
In the column modular approach, the equations for each column are solved by use of the most efficient procedure for each column. After one trial has been made on each column, the terminal flow rates are placed in component-material balance and in agreement with the specified values of the terminal flow rates by use of the "capital 0 method" for systems. The entire calculational process is repeated until convergence has been achieved.
To illustrate the application of the column modular approach, consider the particular system of columns shown in Fig. 4-5, which consists of a reboiled absorber (column 1) and a distillation column (column 2). For such a system, a combination of the 6 method and the IN Newton-Raphson method is recommended. The IN Newton-Raphson method is used for solving the reboiled absorber and the 0 method is recommended for the distillation column. At the end of one complete trial for each of the two columns, the capital 0 method is applied to place the system in component-material balance and in agreement with the specified values of the terminal flow rates.
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