The use of inequalities in the design and optimisation of complex chemical and metallurgical plants

Abstract

An interconnected chemical or metallurgical plant is viewed as a combination of separators, reactors and mixers. The operation of these units may be described in terms of non-linear split factors, conversions and yields. The mass balance coefficient matrix may be transformed into an M-Matrix. Ostrowski's inequality may then be used to provide linear inequalities based on the row sums of the transformed coefficient matrix. The production rates of components are “quasi” monotonic with regard to these row sums. The mass balance equations, together with the inequalities may be transformed into linear constraints for use in either Parametric Linear or Non-Linear Programming. If split factors, conversions and yields are independant, then Parametric L. P. may be used directly. If dependant, however, the row sums are useful parameters which may be used to improve objective functions depending monotonically on production rate in Non-Linear systems. The method has been applied to a flotation plant where production is maximised using L. P.