Residence Time Distribution: Screencasts
Introduces the idea that not all molecules spend the same time in a chemical reactor and explains how the residence time distribution can be measured with a tracer.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Solves mass balances for a tracer injected into the first CSTR in a series to determine the residence time distribution (RTD) for CSTRs in series. Note that for this screencast, V is the volume of each CSTR, so the total volume is nV and τ is the space time for each CSTR.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Shows plots of the residence time distribution for CSTRs in series. Note that for this screencast, V is the volume of each CSTR, so the total volume is nV.
We suggest that after watching this screencast, you list the important points as a way to increase retention.
Important Equations:
Residence time distribution \(p(t)\) or exit age distribution \(E(t)\)
\[p(t) = E(t) = \frac{c(t)}{\int_{0}^{\infty}c(t)dt}\]
\(p(t)\) = probability a molecule will reside in reactor for time \(t\)
\(p(t)dt\) = fraction of material that has a residence time between \(t\) and \(t + dt\)
\(c(t)\) = tracer concentration at reactor exit as a function of time for a pulse injection of tracer at reactor inlet
\(t\) = time
\[\overline{t} = \frac{\int_{0}^{\infty}t\,c(t)dt}{\int_{0}^{\infty}c(t)dt}\]
where \(\overline{t}\) = average residence time
For a single ideal CSTR, the residence time distribution is
\[p(t) = E(t) = \frac{e^{-t/\tau}}{\tau}\]
where \(\tau = \frac{V}{\nu}\) = space time
\(V\) = volume of the CSTR
\(\nu\) = volumetric flowrate leaving CSTR
For n CSTRs in series, where \(\tau\) is the space time for each CSTR, the residence time distribution is:
\[p(t) = E_n(t) = \frac{t^{n-1}\,e^{-t/\tau}}{(n-1)! \,\tau ^n}\]
The residence time distribution is often written using \(\tau\) as the space time for the system of n CSTRs; i.e.,
\[\tau_{total} = \frac{V_{total}}{\nu}\]
\[E_n(t) = \frac{t^{n-1}}{(n-1)!} \left( \frac{N}{\tau_{total}} \right)^n \,e^{-tN/\tau_{total}}\]