Consider a second-order reaction 2A –> B with a reaction rate, -r_A = kC_A², that takes place in a plug flow reactor with recycle. The recycle ratio a = V_r/ V_out where V_r is the volume of fluid returned to the reactor inlet and V_out is the volume leaving the system. There are two limiting cases:
a –> 0 gives a plug flow reactor without recycle case (where V has the lowest value).
a –> infinity  gives a mixed flow reactor behavior (where V has the higher value).