Stability and Instability in Isothermal CFSTRs with Complex Chemistry: Some Recent Results Guy Shinar Javelin Medical Ltd., 4 Pekeris St., Rehovot 76702, Israel Daniel Knight The William G. Lowrie Department of Chemical & Biomolecular Engineering, Ohio State University, Columbus, OH 43210 Haixia Ji Dept. of Mathematics, Ohio State University, Columbus, OH 43210 Martin Feinberg The William G. Lowrie Department of Chemical & Biomolecular Engineering, Ohio State University, Columbus, OH 43210 Dept. of Mathematics, Ohio State University, Columbus, OH 43210 DOI 10.1002/aic.14110 Published online in Wiley Online Library (wileyonlinelibrary.com) Although the classical 1955 paper by Bilous and Amundson was largely devoted to the study of nonisothermal systems, they also found it worthwhile to establish the stable behavior of a model isothermal multireaction continuous flow stirred tank reactor for all values of residence time, rate constants, and feed concentrations. Over a half century later, there remains a predisposition to the idea that isothermal reactors are prone to dull, stable behavior even when the underlying chemistry is complex. That idea is revisited in light of some recent findings in chemical reaction network theory. V C 2013 American Institute of Chemical Engineers AIChE J, 00: 000–000, 2013 Keywords: bistability, chemical reaction network theory, mathematical modeling, multistability, reactor analysis Introduction In a seminal 1955 article, 1 Bilous and Amundson devoted much of their attention to the stability characteristics of noni- sothermal continuous flow stirred tank reactors (CFSTRs). In their examples, the chemistry was mostly simple, often first order, with instabilities resulting largely from an interplay of heating effects and the occurrence of chemical reactions. Usually unnoticed, however, is that Bilous and Amundson also examined the behavior of an isothermal CFSTR driven by the somewhat more complicated three-reaction Network 1, taken with mass action kinetics. They found that regardless of the rate constants, feed composition, and residence time the steady state is asymptotically stable. Left implicit in their nar- rative was that the steady state is invariably unique. “Thus,” they wrote, “the isothermal system is always stable.” A þ B  ! C þ F C ! E (1) That Bilous and Amundson saw fit to study the stability characteristics of an isothermal CFSTR was rare for its time. Even today, it is often taken for granted that isothermal CFSTRs—including ones with highly complex chemistry— admit just one steady state and, moreover, that all composi- tion trajectories approach that steady state in the limit with increasing time. It is common, for example, to refer, without justification, to the steady state, as if there could not be more than one. A little thought will indicate why this predisposition to- ward dull behavior is surprising. If the kinetics is, for exam- ple, mass action, then a positive steady state* is a solution of a (perhaps large) system of nonlinear polynomial equa- tions in the species concentrations—a system in which many parameters (e.g., the residence time, rate constants, and feed concentrations) appear. Uniqueness of a positive steady state regardless of parameter values is mathematically surprising in itself. That this uniqueness should persist over very large families of distinct reaction networks is more surprising still. Although it would have been extremely difficult at the time, had Bilous and Amundson undertaken the study of an isothermal CFSTR driven not by Network 1 but, rather, by the augmented Network 2, also taken with mass action * By a positive steady state we mean one in which all species concentrations are strictly positive. Work initiated while GS was in the Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel. Correspondence concerning this article should be addressed to M. Feinberg at feinberg.14@osu.edu. V C 2013 American Institute of Chemical Engineers AIChE Journal 1 2013 Vol. 00 No. 00