#### Isothermal Plug Flow Reactors (PFRs): Screencasts

A brief overview of plug flow reactors, their properties, equations, and uses.

We suggest you list the important points in this screencast as a way to increase retention.

Derives the mole balance for a plug flow reactor (PFR) and describes how to account for changes in volumetric flow rates with distance down the PFR.

We suggest you list the important points in this screencast as a way to increase retention.

##### Important Equations:

The mass balance for the irreversible reaction A → 2B whose rate is \(n^{th}\) order in \(C_A.\)

\[\frac{dF_A}{dV} = -kC_A^n\]

\[\frac{dF_B}{dV} = 2kC_A^n\]

where \(F_A\) and \(F_B\) are molar flow rates (mol/s) of A and B, respectiviely, \(V\) is the cummulative volume of the reactor (L), \(k\) is the rate constant, and \(C_A\) is the molar concentration of A (mol/L). An example of initial conditions for these differential equations are at \(V\) = 0 (reactor inlet), then \(F_A = F_{A_{0}}\) and \(F_B = F_{B_{0}}\). These equations are integrated until \(V = V_T\) (the total reactor volume).

These equations use the relations \(F_A = vC_A\) where \(v\) is the volumetric flow rate (L/s). For a liquid phase system, \(v\) can be assumed to be constant (constant density). For a gas-phase system in which the gases can be considered ideal.

\[v = \frac{F_TRT}{P}\]

where \(F_T = F_A +F_B\) = total molar flow rate (L/s), \(R\) is the ideal gas constant, \(T\) is the absolute temperature (K), and \(P\) is the pressure (bar). Thus, the volumetric flow rate can increase or decrease (as a function of distance down the reactor) for a gas-phase reaction.

For a tubular reactor with constant cross section section, the mass balances can also be written in terms of the distance down the reactor (\(z\)):

\[\frac{dF_A}{dz} = -kA_xC_A^n\]

\[\frac{dF_B}{dz} = 2kA_xC_A^n\]

where \(A_x\) is the cross-sectional area of a tubular reactor, and the mass balances are integrated from \(z\) = 0 to \(z\) = L (length of reactor).

Space velocity (\(SV\)) is often used as a variable for a plug flow reactor:

\[SV = \frac{v_0}{V_T}\]

where \(v_0\) is the feed volumetric flow rate to the reactor.

Fraction conversion for component a:

\[X_A = \frac{F_{A_{0}} – F_A}{F_{A_{0}}}\]

Percent conversion = \(100X_A\)