COM MUN I CAT1ON
PREDICTION OF RESIDENCE T I M E DISTRIBUTION FROM T H E UNSTEADY BEHAVIOR OF CHEMICAL REACTING S Y S T E M S The unsteady behavior of continuous-flow isothermal systems with variable inlet stream concentrations and first-order reaction is considered. The time-dependence knowledge of the reactant concentrations of the inlet and outlet streams makes prediction of the residence time distribution possible.
IT
IS known that the residence time distribution of fluids in continuous-flow systems can be measured by dynamic analysis. This is realized by introducing a nonreacting tracer into the inlet stream and measuring the outlet stream concentration. In the examples developed in a recent paper ( 6 ) on the inversion of Laplace transformations by linear programming, it is proposed to determine the residence time distribution by measuring the conversions obtained with first-order reactions when one experimentally changes the rate constant. This paper shows how the residence time distribution can be calculated from the unsteady behavior of chemical reacting systems. Let us consider a continuous flow system 'in which a firstorder reaction is steadily taking place with an inlet reactant concentration, 61, and an outlet reactant concentration, G,. We suppose that at a given instant. from which timt is calculated, the inlet concentration begins to change according to a known function, c ~ ( t ) . Generally, when one maintains isothermal conditions in both steady and unsteady operation, the outlet reactant concentration at time t is given by
where ci(t) is the inlet concentration. For the situation under consideration we can write Gi(t
-
T)
=
Gz(~
Ci(t
-
T)
-
=
G1
