Article pubs.acs.org/est
Effect of Permeable Biofilm on Micro- And Macro-Scale Flow and Transport in Bioclogged Pores Wen Deng,*,† M. Bayani Cardenas,† Matthew F. Kirk,‡,§ Susan J. Altman,‡ and Philip C. Bennett† †
Department of Geological Sciences, The University of Texas at Austin, Austin, Texas, United States Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico, United States § Department of Geology, Kansas State University, Manhattan, Kansas, United States ‡
S Supporting Information *
ABSTRACT: Simulations of coupled flow around and inside biofilms in pores were conducted to study the effect of porous biofilm on micro- and macro-scale flow and transport. The simulations solved the Navier−Stokes equations coupled with the Brinkman equation representing flow in the pore space and biofilm, respectively, and the advectiondiffusion equation. Biofilm structure and distribution were obtained from confocal microscope images. The bulk permeability (k) of bioclogged porous media depends on biofilm permeability (kbr) following a sigmoidal curve on a log−log scale. The upper and lower limits of the curve are the k of biofilm-free media and of bioclogged media with impermeable biofilms, respectively. On the basis of this, a model is developed that predicts k based solely on kbr and biofilm volume ratio. The simulations show that kbr has a significant impact on the shear stress distribution, and thus potentially affects biofilm erosion and detachment. The sensitivity of flow fields to kbr directly translated to effects on the transport fields by affecting the relative distribution of where advection and diffusion dominated. Both kbr and biofilm volume ratio affect the shape of breakthrough curves. simulate the growth of biofilms.15,16 However, other studies considered this assumption as not entirely justified.17−19 Experimental work showed that biofilm morphology was often extremely heterogeneous and contained voids and channels;19,20 both stagnant and flowing water are found in the biofilm,21 but typically flowing water occupies the voids and channels. Therefore, biofilms could be permeable, and the permeability of biofilm depends on both the permeability of the EPS matrix and the volume fraction of water within the voids and channels of the biofilm.22 Usually, the permeability of biofilm is greater than the permeability of the EPS matrix. More recent bioclogging models were focused on understanding the effect of biofilm permeability. Assuming permeable biofilms, Pintelon et al. 23 implemented Lattice-Boltzmann simulations to investigate the effect of biofilm permeability on biofilm growth rate and the velocity shear distribution. In the above study, only one continuous domain was considered with biofilm treated as a fluid region with larger viscosity instead of treating biofilm as a separate permeable and porous media. Kapellos et al.22 and Radu et al.24 took biofilm permeability into account in their modeling by solving the Brinkman equations (BE) for the flow within biofilm and treated biofilm as a separate domain. However, the sensitivity of the flow and transport processes to biofilm permeability was not systemati-
1. INTRODUCTION Biofilms are present in many engineered and natural environments, and play an important role in myriad processes and applications. Because of their high specific surface area, porous media commonly host biofilms. Numerous studies have shown that the growth of biofilms in porous media leads to bioclogging (a reduction of permeability) due to modification of local and bulk hydrodynamics.1−5 Bioclogging also plays a critical role in chemical and ecological processes,6−9 both directly through metabolism of the bacteria that make and reside in the biofilm and through modifying chemical mass transfer processes. Therefore, when present, biofilm can exert first-order control on flow and reactive transport processes. Micro-organisms attach to the surface of grains in porous media by excreting extracellular polymeric substance (EPS). The EPS matrix, which is a fibrous gel-type matrix, consists of polysaccharides, proteins, and DNA materials; cells are embedded in this EPS matrix. The permeability of the EPS matrix was estimated,10 usually in the order of 10−18−10−15 m2.11,12 Therefore, with such low permeability of the EPS matrix, most studies of the influence of biofilm growth on hydrodynamic processes assumed that biofilms were impermeable and that solutes were transported into and through biofilms by molecular diffusion,13−16 i.e., advection does not occur within the biofilm. On the basis of this assumption, computational fluid dynamics (CFD) or Lattice-Boltzmann simulations have been utilized to solve the Navier−Stokes equations (NSE) and advection-diffusion-reaction equations to study the flow and nutrient transport in biofouled media and to © 2013 American Chemical Society
Received: Revised: Accepted: Published: 11092
June 12, 2013 August 20, 2013 August 23, 2013 August 23, 2013 dx.doi.org/10.1021/es402596v | Environ. Sci. Technol. 2013, 47, 11092−11098
Environmental Science & Technology
Article
Figure 1. Geometry of the pore space between packed beads and the biofilm structure after 1, 2, and 4 days of the biofilm growth. The domain size is 450 × 450 μm2. The red areas represent liquid/free pore space; the green areas represent biofilms; the black/gray areas represent the solid beads; the white lines are streamlines.
threshold. The RGB above the threshold is considered as pore space or biofilm. On the basis of this threshold, we also removed noise and converted the RGB images to binary images. Circles were fitted to represent solid grains and remaining noise was removed manually. Figure 1 shows the segmented geometry of the pore space between packed beads before inoculation with bacteria and different biofilm structures approximately 1, 2, and 4 days after inoculation. The 3D porosity of the experimental column reactor was ∼47% which was calculated by stacking the porosity of 2D confocal images; the individual 2D images had 2D porosities which varied from 24% to 77%. The porosity of our 2D segmented porous media (i.e., 11 μm deep from the surface) for Day 0, when biofilm was still absent, was 58%, which is slightly larger than the 3D porosity. The ratio of biofilm volume to the preinoculation pore-space volume (i.e., biofilm volume ratio) is 0.20, 0.24, and 0.40 for Day 1, Day 2, and Day 4 images, respectively. The segmented images were then imported to the finiteelement modeling software COMSOL Multiphysics. COMSOL Multiphysics was used to solve for the flow field. Single-phase incompressible steady-state fluid flow in the free pore space is governed by the NSE:
cally studied. Here, we similarly conducted CFD simulations based on the coupled NSE and BE. Different biofilm structures in the CFD simulations were taken from confocal microscope images obtained previously,25 and the CFD simulations did not account for biofilm growth. We systematically investigated the sensitivity of the bulk permeability and the shear stress distribution of bioclogged porous media to biofilm permeability. A broad range of biofilm structure (representing sequential growth stages), permeability, and porosity was considered. Further, we analyzed local and bulk transport processes.
2. METHODOLOGY The biofilm structures in our two-dimensional CFD simulations were obtained from confocal microscope images. The complete details are in Kirk et al.25 but key information is repeated here. A column reactor was filled with 105−150 μm diameter glass beads. Rhodamine dye was used in the experiments for pore space imaging, and green fluorescent protein was expressed by cells in the biofilm thereby distinguishing it from the liquid in the free pore space. The biofilm consists of Pseudomonas f luorescens (P. f luorescens), EPS, and water within the voids and channels of the biofilm. The confocal microscope images had 1024 × 1024 pixels with a resolution of 0.44 μm/pixel. The original experiments were run for multiple days to track the growth of biofilms and the progression of bioclogging. We took original 2D confocal images from a portion of the column reactor (i.e., 11 μm deep from the surface) which clearly showed biofilm growth progression. These images from four days were then segmented using the software ImageJ into solid grains (the glass beads), open pore space, and biofilm. The open pore space and biofilm were mapped from separate original images (Supplement Figure 1 in Supporting Information, SI) in two different channels. For images used for open pore space mapping, the color varied from RGB (0,0,0) to RGB (255,0,0). The black areas are solid grains; the red is pore space or biofilm. For the biofilm images, the color varied from RGB (0,0,0) to RGB (0, 255,0). The black areas are solid grains or pore space; the green zones are biofilms. For both images, we set the RGB (85,0,0) and RGB(0,85,0) as the
ρ(u ·∇)u = ∇·[−pI + μ(∇u + (∇u)T )]
(1)
∇·u = 0
(2)
where ρ is the fluid density, u=[u,v] is the free flow velocity vector for 2D simulation, μ is the fluid dynamic viscosity, and p is the pressure. The flow in pore space is coupled with the flow within biofilm (i.e., green in Figure 1) described by the BE: u ⎞ ρ⎛ u ⎜⎜(ubr ·∇) br ⎟ = −∇·pI + ∇· (∇ubr + (∇ubr)T ) εp ⎝ εp ⎠ εp μ − ubr k br (3)
∇·ubr = 0
(4)
where εp is the porosity of biofilm, kbr is the permeability of biofilm, and ubr = [ubr,vbr] is the Darcy flux vector. 11093
dx.doi.org/10.1021/es402596v | Environ. Sci. Technol. 2013, 47, 11092−11098
Environmental Science & Technology
Article
Triangular mesh elements were used in the both pore space and biofilm, but quadrilateral mesh elements were used near the walls of solid beads to ensure a high mesh quality. The whole computational domain was discretized into ∼660 000 mesh elements.
In the CFD simulations, the pressure and velocity were coupled at the interface between the free pore space and biofilm: the p in the pore space is equal to the p in the biofilm at the interface; u is equal to ubr at the interface. Thus, momentum and mass are conserved across the interface. Noslip boundary conditions were applied at the solid surfaces (glass bead walls). A constant pressure drop Δp of 10 Pa was imposed between the inlet and outlet boundaries for the convenience of bulk permeability calculations; imposing a constant inlet flux boundary may result in a nonuniform pressure distribution at the inlet. The Δp imposed in CFD simulations is comparable to the minimum experimental pressure drop.25 The upper and lower boundaries were prescribed as symmetry boundaries. The initial pressure and velocity are assumed to be zero everywhere. Fluid properties of water were used in the simulations: ρ = 1000 kg/m3 and μ = 0.001 Pa·s. We conducted a sensitivity study of the bulk permeability k of the bioclogged porous media to kbr and εp. The k can be calculated by applying Darcy’s law: k=
μLQ ρg ΔpW
3. RESULTS AND DISCUSSIONS 3.1. Microscale Flow Fields and Shear Stress Distribution. The streamlines were sensitive to kbr (Figure 2),
(5)
where Q is the discharge through bioclogged porous media, g is the gravitational acceleration, L is the length between inlet and outlet boundaries, and W is the cross sectional area. In our simulations, L is 450 μm, and W is assumed a unit length of 450 μm since the simulation is 2D. In order to systematically study the sensitivity of k to kbr, we implemented a wide range of kbr from 10−15 to 5 × 10−9 m2, while we took εp from 0.6 to 0.9 in the simulations.20 In addition to the flow simulations, we conducted conservative solute transport simulations. The transport process is described by the advection-diffusion equation: ∂C = D∇2 C + ∇·(ucC) ∂t
(6)
where C is solute concentration, t is time, and D is the molecular diffusion set at 1 × 10−9 m2/s. The velocity vector uc in eq 6 is equal to u in the pore space and ubr in the biofilm, respectively. A Dirichlet condition is set at the inlet: ⎧C = 0, t
