(11d) Singularities in Reactive Separation Process Problems

In this article we present some results for isothermal isobaric reactive separation process problems. We also demonstrate that even in isothermal isobaric reactive separation processes which is probably the least nonlinear of all reactive separation processes we get nonlinear phenomenon such as Hopf bifurcations. While it has been shown that Hopf bifurcations are impossible in isothermal CSTR problems involving the MTBE and TAME reactions, and also in non-reactive flash problems, we demonstrate in this paper that isothermal reactive flash processes involving both MTBE and TAME mixtures exhibit Hopf bifurcations. This shows that instabilities and oscillations can occur even in isothermal reactive separation systems and are not necessarily due to multiple stages. Additionally, we show that the Rachford-Rice procedure can be extended to reactive systems.

During the last decade there has been a tremendous interest in the field of reactive distillation. A review of the various models used in reactive distillation can be found in Taylor and Krishna(2000). Of special interest is the existence of multiple steady-states in these problems, since the combination of separation and reaction can in principle introduce the nonlinearity that can cause multiplicity. 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). The most commonly investigated situations include the MTBE synthesis in the Jacobs-Krishna (1993) column configuration and the TAME Synthesis in the column of Mohl et. al (1999). The multiple steady-states for these two columns were investigated by Chen, Huss, Doherty and Malone, (2002) who conclude that multiplicities are lost for high values of Da for TAME, while the opposite is found for MTBE. This conclusion, however is specific to the column configuration descrbed in Jacobs-Krishna (1993) and Mohl et al (1999). Rodriguez et al (2002, 2004) discuss causes for the existence of multiple steady-states in binary and ternary systems. The most important reactive separation process problems where multiplicity exists such as MTBE and TAME processes involve more than three components. In order to understand what causes multiplicity in these problems one must look at the simplest reactive separation process problem involving the MTBE and TAME mixture and hence we are motivated to look at the isothermal reactive flash problem. Mohl et al (1999) prove that isothermal CSTR problems involving the MTBE and TAME reactions do not exhibit Hopf bifurcations while, on the other hand, for non-reactive isothermal flash processes involving homogeneous mixtures Hopf bifurcations are impossible (Lucia 1986). However we demonstrate that isothermal reactive flash processes involving both TAME and MTBE exhibit Hopf bifurcations and that is one of the important contributions of this paper. This paper is organized in the following manner. First, a brief description of the isothermal reactive flash process is given along with the equations involved.. We then demonstrate the existence of Hopf bifurcations in the isothermal reactive flash processes involving both the MTBE and TAME mixtures. Dynamic simulations are performed demonstrating the existence of limit cycles that are a characteristic feature of problems with Hopf bifurcations and the behavior of these Hopf bifurcation points with temperature and pressure variations are presented.