Approximate analytical solution of the concentration of phenol and oxygen and rate of phenol degradation in fluidized bed bioreactor

A theoretical model for fluidized bioreactor (FBR) is presented. The model is based on system of reaction-diffusion equation containing a non-linear term related to specific growth rate of biomass. Homotopy analysis method (HAM) is successfully employed in the development of non-linear steady state phenol degradation. In this paper simple and approximate polynomial expression of concentration of phenol and oxygen and rate of phenol degradation are derived for all possible values of parameters ϕO (dimensionless modulus for oxygen), ϕS (dimensionless modulus for phenol), Ki* (dimensionless inhibition constant for phenol) and KO*, KS* (dimensionless monod constant for oxygen and phenol). The limiting case results are compared with our common results and are found to be in good agreement.

► The solutions for rate of phenol degradation which yet to be reported.
► Established the efficiency of the HAM for handling non-linear structures.
► Our results are in good agreement with the limiting cases.
► A validation of the procedure shows good results in fluidized bed bioreactor.