Numerical evaluation of the stability of stationary points of index-2 differential-algebraic equations: Applications to reactive flash and reactive distillation systems

Abstract The dynamic behavior of many chemical processes can be represented by an index-2 system of differential-algebraic equations. This index can be reduced by differentiation, but unfortunately the index reduced systems are not guaranteed to possess the same stability characteristics as that of the original system. When the set of differential-algebraic equations can be written in Hessenberg form, the matrix pencil of the linearized system can be used to directly evaluate the stability of a steady state without the need for index reduction. Direct evaluations of stability of reactive flash and reactive distillation are presented. It is also shown that a commonly used index reduction will always result in null eigenvalues at steady state. Stabilization methods were successfully applied to this reduced system. An alternative index reduction method for a reactive flash is generalized and shown to be highly sensitive to minor changes in the jacobian.

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