Environ. Sci. Technol. 2010, 44, 7555–7560
Microscale Hydrodynamic Analysis of Aerobic Granules in the Mass Transfer Process LI LIU,† WEN-WEI LI,† G U O - P I N G S H E N G , * ,† Z H I - F E N G L I U , ‡ RAYMOND J. ZENG,† JUN-XIN LIU,§ H A N - Q I N G Y U , † A N D D U U - J O N G L E E * ,| Department of Chemistry, Department of Thermal Science and Energy Engineering, University of Science & Technology of China, Hefei, 230026, China, State Key Laboratory of Environmental Aquatic Chemistry, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Beijing, 100085, and China, Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei, 106, Taiwan
Received June 28, 2010. Revised manuscript received August 30, 2010. Accepted September 3, 2010.
The internal structure of aerobic granules has a significant impact on the hydrodynamic performance and mass transfer process, and severely affects the efficiency and stability of granules-based reactors for wastewater treatment. In this study, for the first time the granule complex structure was correlated with the hydrodynamic performance and substrates reactions process. First, a series of multiple fluorescence stained confocal laser scanning microscopy images of aerobic granules were obtained. Then, the form and structure of the entire granule was reconstructed. A three-dimensional computational fluid dynamics study was carried out for the hydrodynamic analysis. Two different models were developed on the basis of different fluorescence stained confocal laser scanning microscopy images to elucidate the roles of the granule structure in the hydrodynamic and mass transfer processes of aerobic granules. The fluid flow behavior, such as the velocity profiles, the pathlines and hence the hydrodynamic drag force, exerted on the granule in a Newtonian fluid, was studied by varying the Reynolds number. Furthermore, the spatial distribution of dissolved nutrients (e.g., oxygen) was acquired by solving the convection-diffusion equations on the basis of the reconstructed granule structure. This study demonstrates that the reconstructed granule model could offer a better understanding to the mass transfer process of aerobic granules thansimplyconsideringthegranulestructuretobehomogeneous.
Introduction The excellent performance of aerobic granules has much to do with their internal structure. The internal fluid mechanism has a significant role in the formation and mass transfer of * Address correspondence to either author. Fax: Guo-Ping Sheng, Fax: +86 551 3601592 (G.-P. S.); +886 2 2362 3040 (D.-J. L.). E-mail:
[email protected] (G.-P. S);
[email protected] (D.-J. L.). † Department of Chemistry, University of Science & Technology of China. ‡ Department of Thermal Science and Energy Engineering, University of Science & Technology of China. § Chinese Academy of Sciences. | National Taiwan University of Science and Technology. 10.1021/es1021608
2010 American Chemical Society
Published on Web 09/14/2010
the bioaggregates (1–4). The interior structure of aerobic granule has been investigated in several studies (5–8). Su and Yu (9) studied the fractal dimension and the permeation of granules grown on soybean-processing wastewater. They revealed that aerobic granules had a fine performance in settling ability, mass transfer efficiency, and bioactivity. So far, most of the aerobic granules are cultivated in the sequencing batch reactors (SBRs). The hydrodynamics play an important role in the granulation process, granule properties and the treatment efficiency of reactors (10, 11). The flow and concentration patterns inside granules depend on properties of solution, such as diffusivity, viscosity and density, as well as the geometrical parameters of granules like pore size, spatial distribution of pores and connectivity. There are significant effects of these geometrical parameters on the fluid velocity and concentration profiles and hence on the efficiency of the mass transfer process of aerobic granules. However, information about the internal structure associated with the mass transfer process of granules is still very limited. In many studies aerobic granule is simply assumed to have homogeneous internal structure. Onedimensional models based on this assumption have been developed to simultaneously describe the diffusion of substrate and dissolved oxygen in aerobic granules (12, 13). But apparently these models could not describe the mass transfer process veritably because of the highly heterogeneous structure characteristics of aerobic granules (14). Aerobic granules consist of cell clusters, that is, discrete aggregates of microbial cells in an extracellular polymeric substances (EPS) matrix (15). The combination of multiple fluorescence staining method and confocal laser scanning microscopy (CLSM) analysis has been proven to be a highly effective approach to identify the distributions of EPS and cells (total and dead) in aerobic granules (16, 17). Thus, this method could offer a visual insight into the complex structure of aerobic granules. In this study, the internal structure of aerobic granules was observed by multiple fluorescence stained CLSM. The granule was reconstructed based on the CLSM images using the medical science software Amira. A three-dimensional computational fluid dynamics (CFD) study was carried out to explore the granule hydrodynamic characteristics, such as porosity, permeability, stream lines, velocity field, and drag force. Two different models were developed based on the combined CLSM images and protein CLSM images respectively to explore the roles of granule inner structure in the hydrodynamic and mass transfer processes. To the best of our knowledge, this study for the first time obtained the CLSM image reconstruction of aerobic granules and applied this in the investigation into hydrodynamic performance and substrate reaction process. It is expected that this insight would offer a deep understanding of the mass transfer in aerobic granules and, thus, favor a better control of its application in the wastewater treatment systems in the future.
Experimental Section Aerobic granules with a mean diameter of 0.5 mm were cultivated as described in Adav et al. (8). Granules were first fixed with 4% paraformadehyde in phosphate-buffered saline (PBS). Then granules were stained using five different fluorescene dyes of SYTO 63, SYTOX blue, Nile red, FITC, and Con A, respectively. The staining details were available in Chen et al. (17). After staining, the granule was cut into VOL. 44, NO. 19, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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a series of slides for CLSM analysis. A CLSM (Leica TCS SP2 Confocal Spectral Microscope Imaging System, Gmbh, Germany) was employed to visualize the inside structure of the aerobic granules. The granule was imaged with a 10× objective and analyzed using Leica confocal software. The microscope scanned the samples at fixed depth and digitized the image obtained. The interior structure of granules was reconstructed using CLSM images following the processing scheme described by Chu et al. (18). Granule was sliced into 20 µm slides and more than 100 CLSM images were sampled for a typical granule, and the Otsu’s scheme was applied to determine the threshold value for each CLSM image. Then, the threshold value was applied to bilevel each image. Next, the threedimensional visualization and modeling software, Amira 3.2.0 (TGS, U.S.), was employed to reconstruct the bileveled images as a polygonal surface model. Boundaries in the binary images were classified based on connectivity and whether they lied within the object or its complement (18). The connectivity of neighboring pixels was set to four for edge detection. Once boundaries were sketched, the isosurfaces were established to demonstrate the three-dimensional shape of the object. In this study, the combined model and the protein model were reconstructed, respectively, using a series of CLSM images of combined images and protein images (stained by FITC). Models and Solution. The model initially describing the hydrodynamics flowing through granule internal structure, and then, mass transfer of solute nutrients (e.g., oxygen), including convection coupled with Fickian diffusion, and a reactive source term were solved. The computational domain was a circular tube as illustrated in Figure S1 (Supporting Information (SI)). A granule of diameter d was placed on the axis of an infinite circular tube of diameter DL. The diameter (DL) and the length (L) of the domain tube were kept 60 times of the granule diameter (d ) 2 rg) to minimize boundary
effects. The granule was assumed to be fixed and the surrounding fluid flowed with a constant bulk velocity u∞. The flow fields surrounding and inside the granule model were simulated to be subjected to an incoming unbound Newtonian fluid. The fluid with density F and dynamic viscosity µ was flowing at a uniform velocity of u∞ from infinity toward the fixed granule. According to previous study (19), the local velocity U in the aerobic granule reactor was lower than 0.045 m s-1. Thus, the Re of the single granule in the reactor would be less than 2000, and the local liquid flow in the granule surface is in the laminar range. Constructed Model. It is assumed that the flow field in the liquid phase could be described by the steady-state Navier-Stokes equation and the continuity equation. In dimensionless form, we had P0 1 2F F F ∇P′ ) ∇ u′ (u′ · ∇)u′ + Re FV2
(1)
u′ ) b u/u∞,P′ ) P/P0. The boundary where Re )u∞dF/u, b conditions were as follows: inlet: u ) u∞
(2)
outlet: ∇u ) 0, ∇p ) 0
(3a,b)
side boundary: u ) u∞
(4)
solid surface inside granule: u ) 0
(5)
Homogeneous Model. For the fluid flow exterior to the floc, the governing is the same as eq 1, while the governing equations for the fluid flow interior to the granule is the Darcy-Brinkman’s equation, which could be described as follows:
FIGURE 1. CLSM images of fluorescent stained aerobic granule: (A) protein (FITC), (B) nucleic acids (SYTO 63), and (C) dead cells (SYTO blue), and (D) r-D-glucopyranose polysaccharides (Con A), and (E) lipid (Nile red), and (F) combined image of (A)-(E) (scale bar 100 µm). 7556
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F + Eu · Re ∇P′ ) 1 ∇2u′ F u′ β2 β2
(6)
whereEu ) P0/Fu∞2 , β ) (df/2)/κ0.5, κ is the homogeneous permeability of the granule. The fluid viscosity of fluid interior to granule was assumed to be the same as that of fluid exterior to it (20). The boundary conditions were as follows: u ) uf, on the surface of granule
(7)
∇u ) ∇uf, on the surface of granule,
(8)
∂u j ′f ) 0, at the center of the granule, ∂r
(9)
Equations 7 and 8 mean that both fluid velocity and its gradient across the sphere surface were continuous. The Carman-Kozeny equation was used for calculating the hydraulic permeability κ of the homogeneous model: κ)
ε3 - ε)2
5S20(1
(10)
where ε is assumed to be equal to the granule porosity, S0 is the specific surface area of the primary particle and equals 6/dp. Mass Transfer Process for the Combined Model. The diffusion-reaction of oxygen in the granule could be described as shown: ∂CS F ) -u′ · ∇CS + DS∇2CS + rS ) 0 ∂t
(11)
The boundary condition was C S ) C0
(12)
where CS is the oxygen concentration within the granule, C0 is the oxygen concentration in the fluid, DS is the effective diffusivity and was measured to be 1.58 × 10-9 m2/s using the method reported by Chiu et al. (21). The concentration of oxygen at the granule surface was assumed to change suddenly from CdC0 to C1 at t ) 0; the time evolution of the oxygen concentration at the center of sphere could thus be approximated as follows: ln
[
]
4π2DS 1 C0 - C )t 2 C0 - C1 d2
(13)
A semilog plot of (C0 - C)/[2(C0 - C1)] versus time is a straight line that passes through the origin with a slope of (-4π2DS/ d2). A flow field adapts very rapidly to new geometries, whereas biomass growth occurs on much slower time scale (22). For the sake of simplicity, this approach ignores interactions of the biomass growth. The oxygen transfer rate can be expressed as, rS ) -qmaxX
CS K S + CS
(14)
where qmax is the maximum oxygen uptake rate, X is the biomass concentration, and Ks is the half-saturation constant. From a nonlinear regression for the oxygen consumption rate (dDO/dt) with time (13), qmax and Ks were calculated to be 7.58 × 10-6 s-1 and 1.91 g m-3, respectively. The boundary condition was CS ) CS0
(15)
FIGURE 2. Velocity vector field around the granule for (a) the combined model; and (b) protein model at Re ) 10 (scale bar 100 µm). Numerical Solution. The tetrahedral grids in SI Figure S1 was first preprocessed using geometry modeling mesh generation software, GAMBIT 2.0 (Fluent Inc., U.S.) to define the liquid-solid interface and also to generate the outside flow field grids. The governing equations and the associated boundary conditions were solved numerically by FLUENT 6.2 (Fluent Inc.), a commercial software based on a finite volume scheme. The pressure-velocity coupling algorithm was SIMPLEC (semi-implicit method for pressure-linked equations-consistent). The reaction equations that describe the mass transfer phenomena of granules were incorporated as an extension to FLUENT 6.2 code in the form of user defined function. The calculation was performed at a maximum relative error of 0.01%.
Results and Discussion CLSM Images of the Aerobic Granule. Figure 1 presents the CLSM image of proteins (FITC), nucleic acids (SYTO 63), dead cells (SYTO blue), R-D-glucopyranose polysaccharides (Con A), lipids (Nile red) in a fluorescent stained aerobic granule and their combined images. Live cells and R-polysaccharides were located at the outer rim of the granule (Figure 1B and D), whereas the protein and lipids were distributed all around the granule (Figure 1A and E). The dead cells were distributed in the core and the outer rim regimes of the granules (Figure 1C). Figure 1B shows a discontinuous thin shell layer, indicating that the living cells were primarily accumulated at the outer rim layer of the aerobic granule. Oxygen and substrates can penetrate through this shell layer easily and reach individual cells. In contrast to the other substances, the proteins were principally distributed in the granule, as shown by the CLSM images. This is because proteins have a high content of negatively charged amino acids, thus they are more involved than sugars in electrostatic bonds with multivalent cations, a key factor in stabilizing aggregate structure (23). The CSLM images show that the granules had a heterogeneous structure with bioactive layers VOL. 44, NO. 19, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Pathlines through the combined model (yellow granule) and the protein model (green granule) at different Re values (Re ) 0.5, 5, 10, and 50), lines colored by velocity magnitude (m/s) (scale bar 500 µm). distributed in the granule surface. We used the combined images (Figure 1F) and the protein images (Figure 1A) separately to analyze the spatial configuration of the granule and find out its role in the hydrodynamic performance and mass transfer process. 3D Reconstructed Model of the Aerobic Granule. The 3D reconstruction structures and tetrahedral volumetric grids for both the combined model and the protein model are shown in SI Figure S2. In Figure S2A, the combined model shows a dense surface layer because the cells and EPS materials were well-mixed and distributed in the surface layer of the granule. EPS matrix is a medium allowing cooperation and communication among cells in microbial aggregates and provides stable and close proximity of the bacteria (23). Meanwhile, it might also cause mass transfer resistance and minimized possible advection of the granule. Compared with the combined model, the protein model had a rugged surface and a porous interior (SI Figure S2A and B). The tetrahedral 7558
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volumetric grids of both models are shown in SI Figure S2C and D, which was used for subsequent calculation in FLUENT. On the basis of the constructed model in SI Figure S2, the granule porosity could be calculated by dividing the void space by the total volume. In this study, the mean porosity of granules was estimated as 0.16 and 0.53, respectively, for the combined model and the protein model. Previous studies showed that the porosity of microbial aggregates with a diameter ranging from 1.0 mm to 10.0 mm could reach up to 80-90% (1, 9, 24). For these studies, the porosity of the microbial aggregates was calculated based on the following equations:
ε)1-
6fA D-3 d πFg
(16)
Wd ) AdD
(17)
where Fg is the density of granule, Wd is the wet mass of the granule, A is the constant and D is the fractal dimension of the granule, which could be estimated from the slope and intercept of a log-log plot of the wet mass and size of granules; the ratio (f) is the wet mass to the dry mass of the granules, which is estimated to be 3.45 according to Li and Yuan (1). But considering the protein-polysaccharide composite physical hydrogel features of aerobic granules, this equation might not be able to accurately reflect the porous property of granules. Colloidal EPS were also called soluble EPS, which might be bound to cells (23). Soluble EPS produced by microorganisms could form a matrix frame for the aggregates or fill the large pores within the aggregates (25, 26). The soluble EPS were generally regarded as out of cells or clusters and were subtracted together with moisture in previous porosity calculations. Nevertheless, they could be detected by the CLSM images. In addition, small granules always have a more compact structure. Thus, for the small-size granules with a diameter of 0.2-0.6 mm, molecules greater than 137 000 Da could not penetrate the pores (27). The fringe of the combined model was more compact, compared with the protein model. For both the combined and the protein models, the porosity was much higher in the center of the granule, which means that the granule had a hollow center. The porosity changed evidently in the radius direction, which indicates a heterogeneous internal structure of granules. Hydrodynamic Characteristics of the Granule in the Fluid. Three-dimensional model could clearly show the velocity vector field distribution of granules (Figure 2A and B). Numerical simulation could help us to get the flow field information around granules, which was difficult for experiential analysis. SI Figures S3 and S4 show the velocity vectors distribution under different Re conditions for the combined model and the protein model, respectively. For both models, there were convection vectors passing though the internal of granules. SI Figure S3 shows that the internal convection in the combined model was enhanced with the increasing Re. When Re reached 500, there was apparent vortexes appeared behind granules. For the protein model (see SI Figure S4), the internal convection was much more prevalent due to its more porous structure. Figure 3 compares the pathlines through the combined model and the protein model subjected to different Re conditions (Re ) 0.5, 5, 10, 50). For the combined model, pathlines were almost symmetrical around the granule and the pathlines changed little after flowing though the granule. Wu et al. (28) revealed the pathlines would not be seriously distorted in the after-granule regime for porous interior, as the advection flow could pass through the granule. When Re was elevated, no distinct change of the pathlines for the combined model was observed. In contrast, the pathlines for the protein model at different Re values changed notably. When Re was relatively small, the pathlines were nearly paralleled to the granule surface shape when passing through the granule. But when Re was increased, the streamlines became asymmetry around the granule, and at Re ) 50 we could find streamlines flowing through the center of the granule. This reveals that if Re was sufficiently large, the convective motion of fluid becomes significant, as justified by the observations that the pathlines passed though the granule. The drag force exerting on the granule could be calculated by integrating over the entire granule surface (including the surface of channels interior of the granule), as follows:
FIGURE 4. FD versus Re plot for the solid sphere, combined model, the protein model and the homogeneous model. |FD | )
∫
surf
FF τ · dA
(18)
F where A is the directional surface area, τF is the force tensor and “surf” is the surface of granule. Figure 4 compares the FD of the combined model, the protein model and the homogeneous model with a solid sphere (i.e., no fluid could flow through the sphere) with the same equivalent diameter subjected to different Re values. For the homogeneous model, the porosity was set the same as the combined model. The drag force of the homogeneous granule was much smaller than those for the other three models. For porous permeable media, the pores formed between particles within an aggregate would permit interior flow through the aggregates, thus the drag force acting on the granule could be reduced to some degree (29). The drag forces for both the combined model and the protein model were very close to those of the solid granule. At Re ) 0.l, the drag force of the combined model was even larger than that of the solid model. This is because the reconstructed model had a truly rough granule surface and the equivalent surface area was much larger than that of the solid granule. Thus, from eq 18 we could get a relatively bigger value for the combined model. The drag force of the combined model was slightly larger than that of the protein model due to its less porous structure. But when Re was elevated to 40, the difference became much smaller. The hydrodynamic characteristics of the reconstructed granule were different from those for the homogeneous model, which further demonstrates that aerobic granules were heterogeneous and could not be treated as homogeneous porous media simply. Mass Transfer Process Analysis. The oxygen concentration distribution in aerobic granules is shown in SI Figure S5. The oxygen concentration C0 in the fluid was assumed to be 0.001 kg m-3. The granule was cut in the inlet flow direction by ten uniformly spaced cross sections from 1 to 10, from which we could get complete internal information about the granule oxygen transfer. The figure shows that the oxygen was consumed rapidly in the surface layer of the granule. This was confirmed by Chiu et al. (30), who found all oxygen was consumed in a surface layer with the thickness of 100-125 µm. In our model, the oxygen transfer process was found to depend on two mechanisms, convection and diffusion (see eq 11). For open channels, fluid could flow through it and show a higher local concentration. This phenomenon was confirmed in SI Figure S5C-F, which directly demonstrates the mass transfer mechanism base on the complex aerobic granule structure. VOL. 44, NO. 19, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Acknowledgments We thank the Natural Science Foundation of China (50625825, 50738006, and 50828802) for the support of this study.
Appendix A NOMENCLATURE A F A
constant the directional surface area oxygen concentration (kg m-3) oxygen concentration in the fluid (kg m-3) oxygen concentration at the granule surface at t ) 0 (kg m-3) oxygen concentration within the granule (kg m-3) aerobic granule diameter (m) the primary particle diameter (m) the fractal dimension of the aerobic granule sludge the diameter of the calculation domain tube (m) the effective diffusivity coefficient (m2 s-1) ratio of the wet mass to the dry mass of bacterial cells drag force (N) the half-saturation constant (g m-3) the length of the calculation domain tube (m) aerobic granule radius (m) inflow velocity (m s-1) the fluid velocity (m s-1) the fluid velocity outside the granule (m s-1) the local velocity in the reactor (m s-1) pressure (Pa) reference pressure (Pa) the maximum oxygen uptake rate (s-1) the specific surface area of the primary particle (m-1) the wet mass of granule (g) the biomass concentration (4750 g m-3)
C C0 C1 CS d dp D DL DS f FD Ks L rg u∞ b u b uf U P P0 qmax S0 Wd X
GREEK LETTERS permeability factor the porosity of the aerobic granules density of the fluid (kg m-3) density of the aerobic granules (kg m-3) the hydraulic permeability of the granule (m2) fluid viscosity (Pa s) the force tensor
β ε F Fg κ µ FF τ
Supporting Information Available Additional material including five figures. This material is available free of charge via the Internet at http://pubs.acs.org.
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