Continuum Heterogenous Biofilm Model - A Simple and Accurate Method for Effectiveness Factor Determination

ELIO E. GONZO; STEFAN WUERTZ; VERÓNICA B. RAJAL

BIOENGINEERING AND BIOTECHNOLOGY

JOHN WILEY & SONS INC

Lugar: New York; Año: 2012 vol. 109 p. 1779 - 1790

0006-3592

We present a novel analytical approach todescribe biofilm processes considering continuum variationof both biofilm density and substrate effective diffusivity. Asimple perturbation and matching technique was used toquantify biofilm activity using the steady-state diffusion–reaction equation with continuum variable substrate effectivediffusivity and biofilm density, along the coordinatenormal to the biofilm surface. The procedure allows predictionof an effectiveness factor, h, defined as the ratio betweenthe observed rate of substrate utilization (reaction rate withdiffusion resistance) and the rate of substrate utilizationwithout diffusion limitation. Main assumptions are that (i)the biofilm is a continuum, (ii) substrate is transferred bydiffusion only and is consumed only by microorganisms at arate according to Monod kinetics, (iii) biofilm density andsubstrate effective diffusivity change in the x direction, (iv)the substrate concentration above the biofilm surface isknown, and (v) the substratum is impermeable. With thisapproach one can evaluate, in a fast and efficient way, theeffect of different parameters that characterize a heterogeneousbiofilm and the kinetics of the rate of substrateconsumption on the behavior of the biological system. Basedon a comparison of h profiles the activity of a homogeneousbiofilm could be as much as 47.8% higher than that ofa heterogeneous biofilm, under the given conditions. Acomparison of h values estimated for first order kinetics andh values obtained by numerical techniques showed a maximumdeviation of 1.75% in a narrow range of modifiedThiele modulus values. When external mass transfer resistance,is also considered, a global effectiveness factor, h0, canbe calculated. The main advantage of the approach lies in theanalytical expression for the calculation of the intrinsiceffectiveness factor h and its implementation in a computerprogram. For the test cases studied convergence wasachieved quickly after four or five iterations. Therefore,the simulation and scale-up of heterogeneous biofilmreactors can be easily carried out.