The paper presents the method of modelling and numerical simulation of bioreactors with biofilm and axial dispersion of the liquid. Such bioreactors belong to systems with distributed state variables. The mathematical model was compared with a model assuming perfect mixing and a model assuming piston-flow of the liquid. According to calculations performed, the piston flow of the liquid can be assumed for Peclet numbers above 40. In turn, Peclet numbers below 0.5 justify perfect-mixing approximation. It was shown that there may exist an optimal value of Peclet number for which a maximum degree of conversion of the limiting substrate at the bioreactor outlet is obtained. The existence of the optimal Peclet number depends on the operating conditions of the bioreactor. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.