Modelling biofilm-induced formation damage and biocide treatment in subsurface geosystems

Abstract

Biofilm growth in subsurface porous media, and its treatment with biocides (antimicrobial agents), involves a complex interaction of biogeochemical processes which provide non-trivial mathematical modelling challenges. Although there are literature reports of mathematical models to evaluate biofilm tolerance to biocides, none of these models have investigated biocide treatment of biofilms growing in interconnected porous media with flow. In this paper, we present a numerical investigation using a pore network model of biofilm growth, formation damage and biocide treatment. The model includes three phases (aqueous, adsorbed biofilm, and solid matrix), a single growth-limiting nutrient and a single biocide dissolved in the water. Biofilm is assumed to contain a single species of microbe, in which each cell can be a viable persister, a viable non-persister, or non-viable (dead). Persisters describe small subpopulation of cells which are tolerant to biocide treatment. Biofilm tolerance to biocide treatment is regulated by persister cells and includes 'innate' and 'biocide-induced' factors. Simulations demonstrate that biofilm tolerance to biocides can increase with biofilm maturity, and that biocide treatment alone does not reverse biofilm-induced formation damage. Also, a successful application of biological permeability conformance treatment involving geologic layers with flow communication is more complicated than simply engineering the attachment of biofilm-forming cells at desired sites.

Fig. 1

Schematic showing definitions relevant to our pore network model including flow through pore spaces and biofilm adsorption on pore walls. An enlarged picture of a Pseudomonas fluorescens biofilm is presented and highlights key components of biofilm in our model, which are cells and EPS matrix. White arrow indicates bacterial cell and black arrow indicates EPS produced by bacteria.

Fig. 2

Schematic description of the different phases and species considered at the pore level in our model. Biocide and nutrient are dissolved in the aqueous phase and can be injected simultaneously. EPS stands for extracellular polymeric substance produced by bacterial cells.

Fig. 3

A simplified model algorithm depicting the general sequence of model calculations during each timestep. Biofilm is treated as an adsorbed phase on pore walls and detached biofilms are produced via the network outlet.

Fig. 4

Schematic of a layered network used to idealize artificially induced or geologically intrinsic layering in subsurface porous systems. The white arrows indicate that a communication (liquid flow, biofilm growth) exists between the two layers. They do not necessarily suggest the direction of liquid or biofilm movement. Pore-size distribution of the top layer is representative of a consolidated sandstone reservoir rock.

Fig. 5

Simulated time evolution of spatial nutrient concentration and biofilm morphology for Cases N1, N2 and N3 with and without biofilm detachment in a 2.5 cm × 2.5 cm model. Nutrient concentration is dimensionless with respect to injected nutrient concentration. Principal flow direction is from left (inlet) to right (outlet). For each case, the first column shows nutrient concentration in the network whereas the second column shows biofilm morphology – aqueous phase pores are shown as black while biofilm-saturated pores are shown as green/white [seeded biofilm sites = 60; no biocide].

Fig. 6

Time evolution of network biofilm saturation for cases N1, N2 and N3. The solid curve indicates simulation without biofilm detachment (Case N1), whereas the dashed line represents simulation with biofilm detachment (Cases N2 and N3) – [seeded biofilm sites = 60; no biocide]. A. Network biofilm saturation versus time. B. Dimensionless permeability versus time.

Fig. 7

Temporal evolution of (A) network biofilm saturation in Cases N2, N4 and N5; (B) fraction of persisters in the network and (C) ratio of persisters to non-persisters in the network. Inset shows the ratio of persisters to non-persisters over the biocide-treatment period. [K_v/p = K_p/v = 5.0 × 10⁻⁹ s⁻¹; K_r = 1.0 × 10⁻³ s⁻¹; seeded biofilm sites = 60; β = 1.0 × 10⁻⁵ s⁻¹].

Fig. 8

Time evolution of spatial nutrient concentration (upper images) and biofilm morphology (lower images) for Cases L1 and L2 layered network in 2.5 × 2.5 cm model. In each network, pore sizes of the bottom layer have been multiplied by 70. Nutrient concentration is dimensionless with respect to injected nutrient concentration. The principal flow direction is from left (inlet) to right (outlet). Aqueous phase pores are shown in black whereas biofilm-saturated pores are shown in white [seeded biofilm sites = 60, in top layer only; β = 1.0 × 10⁻⁵ s⁻¹]. A. Case L1. B. Case L2.

Fig. 9

Time evolution of dimensionless PI [PI(t)/PI(0)] in top (low permeability) and bottom (high permeability) layers. Pore sizes of the bottom layer have been multiplied by 70 [seeded biofilm sites = 60; β = 1.0 × 10⁻⁵ s⁻¹].