(200c) Singularities in Non-Equilibrium Reactive Flash Processes

Multiple steady-states in reactive distillations was demonstrated by several workers (Jacobs and Krishna; 1993, Nijhuis, Kerkhof and Mak, 1993, Bravo, Pylahathi and Jarvelin, 1993, Hauan, Hertzberg and Lien; 1995, 1997; Hauan, Schrans and Lien, 1997; Sneesby, Tade and Smith; 1998a, 1998b; Eldarsi and Douglas, 1998; Mohl Kienle and Gilles, 1998, 1999; Rapmund, Sundmacher and Hoffmann, 1998; Higler, Taylor and Krishna, 1999; Guttinger and Morari (1999a, 1999b); Chen, Huss, Doherty and Malone, 2002). In a recent article Ruiz et al (2006) analyzed the isothermal isobaric reactive flash problem and showed that the MTBE reactive flash process, under isothermal, isobaric conditions exhibited Hopf bifurcations. In this paper we modify the approach used by Ruiz et al (2006), where a continuation procedure implemented in CL_MATCONT was used to solve all the equations for the reactive flash taken together. In this article, we express the reactive flash problem as a set of differential algebraic equation system (DAE) and demonstrate Hopf bifurcations for the MTBE and TAME system even when such an approach is used. We then investigate the nature of the singularities in the non-equilibrium reactive flash problems described in Sridhar et al (2000) and show that the effect of imposing mass transfer rate equations on the equilibrium reactive flash problem causes the occurrence of limit points for the TAME mixture and branch points for the MTBE mixture in single stage non-equilibrium reactive flash problems.