Effect of diffusion limitation and substrate inhibition on steady states of a biofilm reactor treating a single pollutant

Figures & data

Figure 1. Schematics of a biofilm.

Table 1. Summary of used parameters.

Parameter	Abbreviation	Unit
Flux of degredading compount	J	g m^−2 h^−1
Diffusion coefficient of degrading compount	DA	gsubstrate m^−2 h^−1
Concentration of degrading compount	cA	gsubstrate m^−3
Length coordinate	x	m
Reaction rate	r	g m^−3 h^−1
Maximum toluene degradation rate	Vmax	gsubstrate gdw substrate degrading biomass^−1 h^−1
Half-saturtion constant	Ks	gsubstrate m^−3
Inhibition constant	KI	gsubstrate m^−3
Biomass density	ρβιο	gbiomass m^−3
Biofilm thickness	L	m
Distance coordinate in the biofilm	x	m
Dimensionless distance coordinate in the biofilm	x’	–
Henry constant	H	–
Collocation points	N	–

Table 2. Model parameters for falsified kinetics (Li and De Visscher (2008) and this study).

Apparent kinetics
Parameter	Value	Unit
Biomass density ρbio	1 x 10^5	gbiomass m^−3
Maximum toluene degradation rate (Vmax)	0.28	gSubstrate gdw Substrate degrading biomass^−1 h^−1
Michaelis-Menten constant (Ks)	1.5	gSubstrate m^−3
Inhibition constant (KI)	0.893	gSubstrate m^−3
Collocation points (N)	7	–
Diffusion coefficient (DA)	5.4x10^−10	m^−2 s^−1
Biofilm thickness	100x10^−6	m

Figure 2. Concentration at the pollutant at the outside surface of the biofilm as a function of the inside surface concentration of the particle. Two stable steady states are predicted as indicated by the dashed lines (i.e., 13.7–15.4 g m⁻³). Parameters used in the calculations are shown in Table 2.

Figure 5. Diffusion profile in a biofilm as a function of biofilm depth showing two different steady states: dashed line – high active steady state; solid line – low activity steady state. Parameters used in the calculations are shown in Table 2. Outside boundary condition: 15 g m^−3.

Figure 3. Parameter space where two steady states can occur (between the lines). Top left: π₃ = 5; top right: π ₃ = 2; bottom left: π₃ = 1; bottom right: π₃ = 0.5 Definitions of π variables: see eqs. (11, 12, 13).

Figure 4. Falsified kinetics – Simulation of various biofilms thicknesses with Haldane kinetics. Parameters used in the calculations are shown in Table 2.

Li, Q., and A. De Visscher. 2008. Toluene removal biofilter modeling. J Air Waste Manage Assoc 58 (7):947–56. doi:10.3155/1047-3289.58.7.947.

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