You need JavaScript to view this

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]

Journal Article:

Abstract

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.
Publication Date:
Jan 01, 1979
Product Type:
Journal Article
Reference Number:
EDB-84-130607
Resource Relation:
Journal Name: Chem. Eng. Sci.; (United Kingdom); Journal Volume: 34:3
Subject:
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
OSTI ID:
6691768
Research Organizations:
Princeton Univ.
Country of Origin:
United Kingdom
Language:
English
Other Identifying Numbers:
Journal ID: CODEN: CESCA
Submitting Site:
HEDB
Size:
Pages: 285-299
Announcement Date:

Journal Article:

Citation Formats

Chang, H C, and Calo, J M. 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]. United Kingdom: N. p., 1979. Web.
Chang, H C, & Calo, J M. 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]. United Kingdom.
Chang, H C, and Calo, J M. 1979. "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]." United Kingdom.
@misc{etde_6691768,
title = {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]}
author = {Chang, H C, and Calo, J M}
abstractNote = {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.}
journal = {Chem. Eng. Sci.; (United Kingdom)}
volume = {34:3}
journal type = {AC}
place = {United Kingdom}
year = {1979}
month = {Jan}
}