Calculation of separation columns by nonlinear block successive relaxation methods

A novel technique: nonlinear block successive relaxation (NBSR) method, is proposed to solve the steady-state balance equations describing separation columns. The NBSR methods are a generalization of point relaxation methods frequently used towards solution of elliptic partial differential equations. Aspects of partitioning of the original set of equations into blocks as well as ordering of blocks is discussed. Problems arising in construction of a universal program based on the NBSR methods are presented. A new procedure making use of grouping of equations according to the set of trays is proposed. Aspects of calculation of separation equipments by this procedure is discussed. It is shown that overlapping blocks may essentially improve the convergence properties of the algorithm. The procedure is very simple and can be easily used towards calculation of large separation problems on a small computer. The method described is illustrated on calculation of an absorption column. Application of the NBSR methods to solution of a complex plant is suggested.