Optimal decomposition of process networks



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Chemical process systems which have recycle of material and energy require the simultaneous solution of non-linear algebraic equations when these systems are modeled mathematically. Iterative methods are required in solving the non-linear systems, the simplest being the successive substitution method. These iterative procedures can consist of either repeated linearization or various convergence acceleration techniques (such as steepest-descent or Newton-type strategies or mixtures of the two). Included in these iterative procedures is the decomposition of the process network by choosing certain tear or cutvariables (or streams) that reduce the original cyclic directed graph of the process to an acyclic graph for which sequential calculations become possible. The convergence acceleration procedure then is applied to these cut-variables. The efficiency of the computational effort in process simulation is considerably influenced by the choice of the decomposition scheme since, generally, the set of cut-variables is not unique for a process network. In this research, a technique is developed for finding the alternate cut-stream sets which may be used to decompose the system. After the alternate cut-stream sets are found, an analysis of the sensitivities is made to select the proper cut-streams to enhance convergence acceleration to the solution; the alternate cut-stream set which minimizes the eigenvalues of the sensitivity (Jacobian) matrix is chosen. A convergence acceleration routine is developed which employs a quasi-Newton method that is applied to more than one cut-stream.