Descriptor Impulsive Modeling of an Isothermal CSTR with Reactant Injection: Consistency-Preserving and Consistency-Violating Resets

This work presents a chemical-process example of descriptor impulsive system (DIS) modeling based on an isothermal continuous stirred-tank reactor (CSTR) with a first-order irreversible reaction and instantaneous reactant injection. The model retains the total concentration as an algebraic state, allowing the chemical composition constraint to be represented and verified explicitly. Consistency-preserving and consistency-violating dosing resets are formulated and compared, illustrating how an impulsive event may either preserve the admissible descriptor manifold or produce a physically inconsistent post-injection state. The example includes time-domain simulation, algebraic-residual analysis, a geometric representation of the constraint manifold, and a comparison of singular, reduced regular, impulsive, and descriptor impulsive formulations. The accompanying reproducibility package contains the manuscript, Python simulation code, generated figures, and supporting files. This chemical CSTR example complements the preceding electrical RLC and constrained mechanical mass-spring examples and provides a further physical application of the descriptor impulsive modeling framework.