TY - JOUR
TI - 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]
AB - 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.
AU - Chang, H C
AU - Calo, J M
KW - 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
KW - 74 ATOMIC AND MOLECULAR PHYSICS
KW - TANK TYPE REACTORS
KW - CHEMICAL REACTIONS
KW - ACTIVATION ENERGY
KW - ANALYTICAL SOLUTION
KW - CATALYSIS
KW - FUNCTIONS
KW - HEAT TRANSFER
KW - NONLINEAR PROBLEMS
KW - PELLETS
KW - STEADY-STATE CONDITIONS
KW - ENERGY
KW - ENERGY TRANSFER
KW - REACTORS
KW - 400000* - Chemistry
KW - 640300 - Atomic, Molecular & Chemical Physics
DO -
UR -
PB -
CY - United Kingdom
PY - 1979
DA - 1979-01-01
LA - English
J2 - Chem. Eng. Sci.; (United Kingdom)
C1 - Princeton Univ.
C2 -
ER -