Flexibility index and design of chemical systems by cylindrical algebraic decomposition

Abstract

The traditional methods for the solution of flexibility index and design problems are mainly developed by numerical calculation methods. In this work, a new solution approach is proposed for chemical systems described by polynomials to deduce explicit expressions of flexibility index on the value of the continuous design variables without solving any optimization problems. First, the flexibility index and design problems are reformulated as an existential quantifier model. Then, the cylindrical algebraic decomposition (CAD) method is introduced to project the solution space onto the dimension of design variables, flexibility index and uncertain parameters. Last, the analytical expressions between design variables and flexibility index can be deduced by the inscribed hyperrectangle checking rule. The case studies show that the proposed method is applicable to relatively small- or medium- scaled problems and the explicit relationship between the flexibility index and design variables can be deduced, regardless of linear or nonlinear systems.