The Continuum Heterogeneous Biofilm Model With Multiple Limiting Substrate Monod Kinetics

GONZO, ELIO E.; STEFAN WUERTZ; RAJAL VERONICA

Biotechnology and Bioengineering

John Wiley & Sons

Lugar: New York; Año: 2014 vol. 111 p. 2252 - 2264

1097-0290

ABSTRACT: We describe a novel procedure to estimate thenet growth rate of biofilms on multiple substrates. Theapproach is based on diffusion-reaction mass balances forchemical species in a continuum biofilm model with reactionkinetics corresponding to a Double-Monod expression. Thisanalytical model considers a heterogeneous biofilm withvariable distributions of biofilm density, activity, and effectivediffusivity as a function of depth.We present the procedure toestimate the effectiveness factor analytically and compare theoutcome with values obtained by the application of a rigorousnumerical computational method using several theoreticalexamples and a test case. A comparison of the profiles of theeffectiveness factor as a function of the Thiele modulus, f,revealed that the activity of a homogeneous biofilm could beas much as 42% higher than that of a heterogeneous biofilm,under the given conditions. The maximum relative errorbetween numerical and estimated effectiveness factor was2.03% at f near 0.7 (corresponding to a normalized Thielemodulus f ¼1). For f<0.3 or f>1.4, the relative errorwas less than 0.5%. A biofilm containing aerobic ammoniumoxidizers was chosen as a test case to illustrate the model?scapability. We assumed a continuum heterogeneous biofilmmodel where the effective diffusivities of oxygen andammonium change with biofilm position. Calculationswere performed for two scenarios; Case I had low dissolvedoxygen (DO) concentrations and Case II had high DOconcentrations, with a concentration at the biofilm?fluidinterface of 10 gO2/m3. For Case II, ammonium was thelimiting substrate for a biofilm surface concentration, CNs,13.84 g of N/m3. At these concentrations ammonium waslimiting inside the biofilm, and oxygen was fully penetrating.Conversely, for CNs>13.84 g of N/m3, oxygen became thelimiting substrate inside the biofilm and ammonium was fullypenetrating. Finally, a generalized procedure to estimate theeffectiveness factor for a systemwith multiple (n>2) limitingsubstrates is given.