Proof of the PFR Equations

The reactions are:

1 A->B -r_1A = k₁c_A; r_1A = -k₁c_A

2 B->A r_2B = k₂c_B

3 B->C -r_3B = k₃c_B

4 2A->D -r_4A = k₄c_A²

The mole balances around a differential volume in the PFR give:

F_A = v₀c_A; F_B = v₀c_B

where t = V/v₀
And similarly for the mole balance on component B.
Thus the equations describing the PFR are:

dc_A/dt = -k₁c_A + k₂c_B - k₄c_A²

dc_B/dt = k₁c_A - k₂c_B - k₃c_B

Trying a PFR > Proof of PFR Equations