Solution multiplicity in multicomponent distillation - A computational study

Rigorous models of staged distillation processes are formulated by setting up material balance equations, equilibrium relations, summation equations, and enthalpy balance equations (MESH equations). In these models, the extent of nonlinearity may be very severe, particularly for azeotropic and reactive distillation systems. MESH system based mathematical models can thus yield multiple solutions (multiple steady states), a fact which has been observed by many researchers. Multiple steady states (MSS) are not detected automatically by the state-of-the-art commercial simulators, despite the fact that extensive capabilities are available for complex distillation columns and the solution algorithms used are very robust and efficient. Since the implications of multiplicity could be numerous, it is of great importance to detect MSS in distillation by a systematic procedure. The approach proposed in this paper uses a recent algorithm that can track the multiple solutions of nonlinear algebraic equations (NLAE) starting from only one initial point. This optimization-based algorithm is interfaced with the MESH system to solve two case studies, an ideal distillation system with two products, and an azeotropic distillation system. For both the case studies, the proposed methodology looks very promising as it successfully tracks the MSS from a single starting point.