(700e) Analytical and Triangular Representation of Flexibility Space

In process design, process parameters are usually uncertain with swift changes in the internal and external conditions. The uncertainties may lead to plant-model mismatch. A good process design should not only exhibit an optimal balance between capital and operating costs but also exhibit good operability in a practical operating environment [1]. One key process operability is the flexibility, which refers to the capability of the process to maintain feasible operation over the entire domain of uncertain parameters [2]. Evaluating the operational flexibility is an important issue that must be incorporated into design considerations. The flexibility analysis methods have been applied in many practical industries [3,4,5]. The main purpose of flexibility analysis is to determine and describe the flexibility space. Because of the inherent nonlinearity of the process design model, the flexibility space is commonly non-convex. In recent decades, the algorithms for describing non-convex flexibility spaces can be mainly divided into four types: (1) transforming the flexibility analysis model into a global or robust optimization model [6,7]; (2) iteratively constructing the boundary via the simplicial approximation method [8]; (3) generating a polygonal representation through properly sampled points [9]; (4) building the response surface of the flexibility function by using the surrogate models [10]. However, these existing methods are mainly developed by numerical calculation methods, resulting in the fact that they are used to estimate only the contour of the flexibility space, rather than providing an accurate description.

In this work, a novel method is proposed for analytically representing the flexibility space. This method can accurately describe the flexibility space and provide a triangular model to explicitly express the functional relationships between uncertain parameters. First, the original flexibility analysis model is viewed as an existential quantifier model. Then, a technique of quantifier elimination, cylindrical algebraic decomposition [11,12], is introduced to deduce the model to a set of explicitly triangular semi-algebraic systems, each of which is an analytical representation of a flexibility subspace, and any two subspaces are disjoint. Last, a logical combination of the semi-algebraic systems can be used to describe the whole flexibility space. In summary, the proposed method in flexibility analysis has four properties, that is, explicit property, nonconvex property, triangular property and operational property. In the case studies, the proposed method is successfully applied to represent non-convex flexibility spaces and disjoint flexibility spaces. The results show that the explicit expressions deduced by the proposed method can accurately and effectively describe the flexibility spaces and then guide the steady-state operations.

Keywords: process design, flexibility analysis, cylindrical algebraic decomposition.

Reference:

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