Dynamic Flexibility Analysis with Differential Quadratures

Realistic chemical processes are often operated in the presence of complex and uncertain system dynamics. Obviously, flexibility analysis comes into play in designing such systems. In order to build the mixed-integer nonlinear program (MINLP) for computing the flexibility index, the Karush-Kuhn-Tucker (KKT) conditions must be derived from the system model and this model usually consists of a set of differential- algebraic equations (DAEs). A common approach for this task is to replace these DAEs with equality constraints by using a numerical discretization technique. In the present study, the differential quadratures (DQs) are adopted to approximate the derivatives in the original system model. The time horizon is discretized at the roots of a Chebyshev polynomial for optimally mimicking the transient profiles of control and state variables. Finally, a novel concept of temporal flexibility is also proposed in this paper and a simple system is used to demonstrate its usefulness. All results obtained in case studies show that the proposed approach is convenient and effective for assessing realistic issues in operating complex dynamic chemical processes.