This paper examines the accuracy of algebraic and data-based approximations of substrate flux into a biofilm, computed from the solution of a boundary value problem using Monod kinetics. A pseudo analytical approach is tested, along with data-based approximations including nearest neighbour interpolation (NN), multi linear regression (MLR), and multi-layer perceptrons (ML). MLR, ML and NN perform with low errors on the flux boundary value problem. These approximations are used in a Continuously Stirred Tank Reactor (CSTR) model, which involves a system of ordinary differential equations which require repeated flux evaluations. The errors on steady states of dependent variables are reported. Lowest errors were achieved by the pseudo analytical approximation and an algebraic approximation. It is suggested that data based approximations be trained on steady states of dependent variables instead of flux to improve results.