Exact criteria for uniqueness and multiplicity of an nth order chemical reaction via catastrophe theory approach. [Determines boundaries between unique and multiple steady state conditions]
Chang, H C; Calo, J M
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 74 ATOMIC AND MOLECULAR PHYSICS; TANK TYPE REACTORS; CHEMICAL REACTIONS; ACTIVATION ENERGY; ANALYTICAL SOLUTION; CATALYSIS; FUNCTIONS; HEAT TRANSFER; NONLINEAR PROBLEMS; PELLETS; STEADY-STATE CONDITIONS; ENERGY; ENERGY TRANSFER; REACTORS; 400000* - Chemistry; 640300 - Atomic, Molecular & Chemical Physics
A simple, generalized technique for the exact determination of the boundaries between regions of unique and of multiple solutions to certain nonlinear equations was developed by applying catastrophe theory to the mapping of implicit and explicit functions. Its application to an nth order reaction in continuous stirred tank reactor (CSTR) yields exact, explicit expressions for the boundaries between regions of single and multiple steady states, expressed in terms of the dimensionless heat transfer coefficient and activation energy. An exact implicit expression for the boundaries between regions of uniqueness and multiplicity was also derived for an nth order reaction in a catalyst particle with an intraparticle concentration gradient and uniform temperature and is fully demonstrated for the first-order reaction. In addition, explicit criteria were developed by assuming the limits on d ln g/d ln q, where g is the effectiveness factor and q the Thiele modulus, proposed by van den Bosch and Luss.
Princeton Univ.
United Kingdom
1979-01-01
English
Journal Article
Journal Name: Chem. Eng. Sci.; (United Kingdom); Journal Volume: 34:3
Medium: X; Size: Pages: 285-299
Journal ID: CODEN: CESCA
EDB-84-130607
2010-05-17
6691768