The continuum heterogeneous biofilm model with multiple limiting substrate Monod kinetics

Authors

  • Elio Emilio Gonzo,

    Corresponding author
    1. INIQUI (CONICET)—Facultad de Ingeniería, Universidad Nacional de Salta, Salta, Argentina
    • Correspondence to: E.E. Gonzo

      telephone: +54-387 425 1006; fas: +54-387 425 1006

      e-mail: gonzo@unsa.edu.ar

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  • Stefan Wuertz,

    1. School of Biological Sciences, Singapore Centre on Environmental Life Sciences Engineering (SCELSE), Nanyang Technological University, Singapore, Singapore
    2. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore
    3. Department of Civil and Environmental Engineering, University of California, Davis, Davis, California
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  • Veronica B. Rajal

    1. INIQUI (CONICET)—Facultad de Ingeniería, Universidad Nacional de Salta, Salta, Argentina
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ABSTRACT

We describe a novel procedure to estimate the net growth rate of biofilms on multiple substrates. The approach is based on diffusion-reaction mass balances for chemical species in a continuum biofilm model with reaction kinetics corresponding to a Double-Monod expression. This analytical model considers a heterogeneous biofilm with variable distributions of biofilm density, activity, and effective diffusivity as a function of depth. We present the procedure to estimate the effectiveness factor analytically and compare the outcome with values obtained by the application of a rigorous numerical computational method using several theoretical examples and a test case. A comparison of the profiles of the effectiveness factor as a function of the Thiele modulus, φ, revealed that the activity of a homogeneous biofilm could be as much as 42% higher than that of a heterogeneous biofilm, under the given conditions. The maximum relative error between numerical and estimated effectiveness factor was 2.03% at φ near 0.7 (corresponding to a normalized Thiele modulus φ* = 1). For φ < 0.3 or φ > 1.4, the relative error was less than 0.5%. A biofilm containing aerobic ammonium oxidizers was chosen as a test case to illustrate the model's capability. We assumed a continuum heterogeneous biofilm model where the effective diffusivities of oxygen and ammonium change with biofilm position. Calculations were performed for two scenarios; Case I had low dissolved oxygen (DO) concentrations and Case II had high DO concentrations, with a concentration at the biofilm–fluid interface of 10 g O2/m3. For Case II, ammonium was the limiting substrate for a biofilm surface concentration, CNs, ≤13.84 g of N/m3. At these concentrations ammonium was limiting inside the biofilm, and oxygen was fully penetrating. Conversely, for CNs > 13.84 g of N/m3, oxygen became the limiting substrate inside the biofilm and ammonium was fully penetrating. Finally, a generalized procedure to estimate the effectiveness factor for a system with multiple (n > 2) limiting substrates is given. Biotechnol. Bioeng. 2014;111: 2252–2264. © 2014 Wiley Periodicals, Inc.

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