#### Energy Balance in Steady-State PFR: Screencasts

Introduction to setting up the general energy balance for a plug flow reactor (PFR).

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

Explains the terms in the energy balance for steady-state plug flow reactors.

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

Optional screencast: Reactor Runaway/Parametric Sensitivity (PFR)

##### Important Equations:

Energy balance for steady-state PFR-tubular reactor where A is reactant

\[(\sum F_iC_{Pi})\frac{dT}{A_xdz} = \Delta H_Rr_A – \frac{4U}{D} (T-T_C)\]

This can also be written in terms of cumulative volume instead of distance down the reactor

\[(\sum F_iC_{Pi})\frac{dT}{dV} = \Delta H_Rr_A – \frac{4U}{D} (T-T_C)\]

Initial conditions: at \(z = 0\) (inlet to reactor), \(F_i = F_{i0}, T = T_0, C_i = C_{i0}\)

The corresponding mass balances to be solved simultaneously with the energy balance are :

\[\frac{dF_i}{A_zdz} = r_i \hspace{1cm} or \hspace{1cm} \frac{dF_i}{dV} = r_i\]

where \(F_i\) = molar flow rate component of i

\(C_{Pi}\) = molar heat capacity of component i

\(T\) = temperature

\(A_x\) = cross-sectional area of tubular reactor

\(z\) = distance down reactor

\(V\) = cumulative volume of reactor

\(\Delta H_R \) = heat of reactor per mole of A reacting

\(U\) = heat transfer coefficient

\(D\) = reactor tube diameter

\(T_C\) = temperature of coolant on outside of tube