Dynamic responses to perturbations in the non-isothermal CSTR: Times to ignition and times for temperature decay—I. Adiabatic operation
✍ Scribed by P. Gray; W. Kordylewski
- Book ID
- 103003626
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 658 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0009-2509
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✦ Synopsis
When a simple exothermic reaction is carried out in an open system, discontinuous jumps between stationary states (ignitions and extinctions) may occur in response to continuous variation ofcontrol parameters such as inflow-temperature or average residence-time. This paper examines the dynamics of such jumps for reaction in a CSTR operating adiabatically. Two problems are analysed: (a) the dependence of time-to-ignition on the degree of supercriticality and (b) the decay of small perturbations to the steady state for marginally sub-critical conditions ("critical slowing down"). It is shown that both the time-to-ignition (and time-to-extinction) and the decay to a stationary state obey universal formulae characteristic of the category of instability, increasing rapidly as criticality is approached: time-to-ignition cc (degree of supercriticality)-"*. We illustrate our resultschiefly by reference to a single, first-order, deceleratory reaction. We at first exploit the exponential approximation to the Arrhenius temperature law but the treatment is quite general and can cope with any temperature-dependence of reaction-rate. 2. CRITICAL CONDITIONS FOR IGNITION IN ADIABATIC CSTR We consider a continuous flow at a volumetric rate v through a well-stirred reactor of volume V. The vessel and its outflow contain the reactant at concentration c and temperature T. Inflow values are co and To. The mass-balance equation assumes the form Vg = vc,,-vc-Vkc"',