Residence Time Distribution Function of a Stirred-Tank Cascade (E-Curve)
A first-order isothermal reaction ( product ) is carried out in a stirred-tank reactor cascade. The -curve is determined from a pulse input by setting the reaction rate constant equal to zero. The -curve is usually determined experimentally. It is a measure of exit-normalized concentration versus time for a tracer impulse input. We plot the steady-state concentration versus tank number using the -curve and a first-order reaction rate constant equal to 0.05. Of course, one can solve the governing equations (a system of ODEs) when the reaction is taking place and get the steady state concentrations of species A. Here the -curve is used instead.
The -curve is obtained by using .
The steady-state concentration is obtained using the -curve and this relationship: