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The main purpose of operational flexibility analysis is to determine and describe the flexibility region. The existing methods are mainly developed by numerical calculation methods to estimate the contour of the flexibility region. In this article, a novel method is proposed for solving operational flexibility models described by polynomials. The proposed method can accurately describe the flexibility region and explicitly express the functional relationships between uncertain parameters and control variables. First, the original flexibility analysis model is represented as an existential quantifier formula. Then, a technique of quantifier elimination is introduced to deduce the formula to a series of explicitly triangular quantifier‐free formulas. Last, a logical combination of the quantifier‐free formulas can be used to depict the complete flexibility region. The case studies show that the deduced explicit expressions can accurately and effectively describe the flexibility region and guide the steady‐state control operations, regardless of convex or nonconvex systems. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3894–3911, 2018

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Flexibility index is an effective indicator for characterizing the operational flexibility of a process design model. In this work, the concept of δ‐space projection is proposed and defined from the view of solution space, and the flexibility index can be quantified without solving any optimization problems. First, the flexibility index problem is reformulated as an existential quantifier model. Then, the projection operator in the cylindrical algebraic decomposition (CAD) method is introduced to project the solution space onto the one‐dimensional feasible space of the flexibility index. Subsequently, all the candidate values of the flexibility index, which may refer to the locations of the critical points, that is, vertexes and tangency points, are extracted. Last, two δ‐checking rules based on the traditional and improved CAD methods are proposed for finding the flexibility index. The case studies show that the proposed method can exactly find the flexibility index, regardless of convex or nonconvex systems.