Continuous tubular reactor PFR

The ideal tubular reactor presents the velocity constant in the cross section of the tube with a plug flow through the reactor. There is no velocity gradient in both radial and axial directions. However, the concentration varies throughout the reactor and thus the molar balance should be differential. The molar flow varies throughout the reactor. Initially, we will assume isothermal PFR reactor. 

Assuming steady-state regime, we obtain generically  

Considering A as the limiting reactant in the reaction A + B R, we have Fa and Fb or Fr with respect to the product. Using the conversion X  

Therefore, with respect to the limiting reactant A, we obtain the equation  

The equation above is valid for any gas or liquid system. The reaction rate will depend on the reaction kinetic model. The reaction may be irreversible, reversible, simple, multiple, elementary or not, enzymatic or polymeric. If the reaction occurs with varying the number of moles or variable volume, one should take into account the factor b defined previously. 

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