Evolution possible final steady state

The transient behavior of a continuous countercurrent multicomponent system was considered in detail by Rhee, Aris and Amimdson [22,23] from the perspective of the equilibrium theory, i.e., assuming that axial dispersion and the mass transfer resistances are negligible and that equilibrium is established everywhere, at every time along the colinnn. The final steady-state predicted by the equilibrium theory is simply a uniform concentration throughout the colimm, with a transition at one end or the other. Therefore, the equilibriinn theory analysis is of lesser practical value for a coimtercurrent system, which normally operates rmder steady-state conditions, than for a fixed-bed (i.e., an SMB) system, which normally operates under transient conditions. The equilibrium theory analysis, however, reveals that, under different experimental conditions, several different steady-states are possible in a coimtercurrent system. It shows how the evolution of the concentration profiles may be predicted in order to determine which state is obtained in a particular case. 

Consider a thermal explosion that is to say, a process in which the rate of removal of the heat released by an exothermic reaction is insufficient to maintain a relatively low level of temperature in the system. Let us idealize as much as possible and treat the process as adiabatic (all the reaction heat is disposed in the heating of the mixture). It is true that this condition is never strictly realized in real world situations. However, it should still provide a reasonable description of the ignition period in an open system, whereby an abrupt transient is observed during the evolution toward the final steady state. 

As reactant concentration increases, heat evolution at fixed temperature also increases. Critical conditions finally arise such that explosion is inevitable. At the critical concentration (curve 2) T. and coalesce the steady state is unstable to local temperature fluctuations and ignition occurs. The external temperature is too high to permit sufficient heat loss to the surroundings. At yet higher initial concentration (curve 3) no steady state is possible when the external temperature is TqI explosion always occurs. 

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