The equation-based approach to process analysis is necessary for efficient optimization of large and complex processes, and involves the problem of solving a large number of equations. To complement this approach, an improved equation-solving system using the functional matrix suggested by Mattione, Meir and Book was developed, and its capacity for the process analysis was demonstrated by case studies.
The equation-solving system developed in this work reads equations, stores them in the functional matrix, rearranges them, and, if they have degrees of freedom, selects design variables which make each partition the easiest to solve. Given the values of the design variables, the system solves the equations as it manipulates the functional matrix.
The developed equation-solving system was proved to be efficient for solving a large number of equations which involve degrees of freedom. Case studies show that the methodology established in this work is an appropriate basis for the equation-based analysis of large chemical processes.