4-3-1 System definition and basic assumptions
Figure 4-3-1. Conceptual basis of biological activated carbon coordinate system.
The physical concept of the biofilm on activated carbon is shown in Figure 4-3-1.
The first major component is the activated carbon. The external surface of activated carbon acts as a supporting medium for the attached growth of bacteria. The activated carbon is highly porous, and its interior surface has high adsorption capacities for organic matters, in this research for the target compounds.
The second major component is the biofilm. A biofilm is a layer-like aggregation of microorganisms attached to a solid surface (Rittmann and McCarty, 1978). The
rs Rs
rf Lf
Bulk liquid Liquid-film
interface Biofilm Activated
carbon
Biofilm are idealized as being composed of a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface.
The third component is the operating system of the BAC. In this research a column system with interparticle axial-dispersion and advection is combined with the medium stated above to construct the whole one-dimensional partial differential equation system.
In order to write the mathematical expressions describing the adsorption and biodegradation mechanisms in an axial-dispersion column, some assumptions were made as:
1. The granules used in BAC are sphere.
2. Biodegradation reaction can be neglected in the pores of the granules, because the size of pores can not permit bacteria to penetrate.
3. The biofilm is homogeneous.
4. The bulk density of biofilm keeps constant.
5. Bacteria growing on granular surface can hardly utilize the substrate absorbed on the meso or micro pores of the granular.
6. Biofilm will be peeled due to the shear force of water, and the peeling rate is proportional to the thickness of biofilm.
7. Mass transfer phenomenon is dominated by Fick’s law.
8. Growth of biofilm can affect the flow in the column because the porosity of the column can be changed by the thickness of biofilm.
Overall, the conceptual diagram of the developed model is shown in Figure 4-3-2.
Figure 4-3-2. The conceptual diagram of the developed model.
Determining Mechanisms (Intraparticle)
*diffusion
*biodegradation
*adsorption
Determining Mechanisms (Interparticle)
*dispersion
*advection
Basic Assumptions
Governing equation (Intraparticle)
* adsorption [3-1]
* biodegradation [3-7], [3-10]
Governing equation (Interparticle)
* [3-12], [3-14] or [3-15]
Major Criteria:
Mass Conser vation
Boundary and Initial Conditions
* B.C. [3-2]-[3-4], [3-8], [3-17]-[3-20]
* I.C. [3-21]-[3-24]
Mathematical Systemization
Solving
4-3-2 Model development
4-3-2-1 Adsorption description
A homogenous solid diffusion model for activated carbon adsorption is used in this research. The dispersion of substrate in the pores is:
r R
Where q is substrate concentration on solid phase, t is time, Ds is substrate diffusivity on solid phase, rs is radius distance from the center of granular, and R is the radius of granular.
The assumption of a homogeneous biofilm implies that the substrate concentration does not vary laterally on the carbon surface and that diffusion is in the radial direction in the biofilm only. Under the assumption of symmetry, the boundary conditions are:
1. There is no concentration gradient in the granular center
0
2. The increase of substrate on solid phase is identical to the flux between biofilm and granular interface.
3. The equilibrium relation of substrate between biofilm and granular can be described interface, respectively; and Kq and n are Freundlich isotherm coefficient.
II. Diffusion and reaction within biofilm
The non-steady-state form of mass transfer and biodegradation reaction within biofilm, based on Fick’slaw and Monod equation, can be described as (Rittmann and McCarty, 1981): concentration, Xf is biofilm density, and Lf is biofilm thickness.
Equation [3-7] describes the condition of n0n-steady-state diffusion and reaction within the biofilm. Therefore, the substrate concentration varies only along rf. The boundary condition at the interface between biofilm and granule is described as Equation [3-4] to [3-6]; the other one between biofilm and bulk liquid is based on that substrate flux from bulk liquid is identical to the substrate gradient within their
interface. bulk liquid, and Ss is substrate concentration in the interface.
III. Growth of biofilm
Substrate diffusing into biofilm will be utilized by bacteria for metabolism. In addition, interception bacteria from bulk liquid also can increase the amount of biofilm. On the other hand, the thickness of biofilm will be decreased by the shear of water, and the self decay of bacteria. As a result, biofilm thickness can be Xsusp is biomass concentration for the suspended growth, â is the filtration efficiency, a is the specific surface area of granular, è is the empty bed contact time, and btot is the overall loss rate of bacteria due to both decay and fluid shear.
The deposition of bacteria on the filter media was derived from the filtration equation of Yao et al. (1971)
( ) ( )
where Ne is the effluent particle concentration, Ni is the influent particle concentration, å is the media porosity, ç is the collection efficiency, dc is the collector grain size.
The collision efficiency á is typically determined from experimental particle removal data.
IV. Bacterial density in the bulk liquid
The factors affecting bacterial density in the bulk liquid include: mass transfer of dispersion and advection, growth and decay of bacteria, peeled bacteria from biofilm due to shear force, and the interception loss by the granular. As a result, the mass balance equation can be written as:
θε
Where Dbact is the dispersion coefficient of bacteria in bulk liquid, x is axial distance of column, í is the fluid velocity, ó is the biofilm shear loss coefficient, b is the microbial decay coefficient, and å is the porosity of the column.
However, the dispersion term, and the affects of growth and decay are insignificant in a macro scope (Hozalski and Bouwer, 2001), so that equation [3-12] can be simplified as:
V. Governing equation in the column system
The mechanisms occurring on the BAC granular can be assorted to three categories, so the governing equations describing the concentration of substrate in bulk liquid are as below:
Case 1: adsorption only, without bio-reaction.
( )
Case 2: both adsorption and biodegradation.
( ) ( ) ( )
Case 3: without adsorption capacity such as anthracite sand.
The governing equation is same to equation [12]. It is noted that there is no substrate flux between the interface of biofilm and the granular, so the boundary condition should be revised as:
VI. Boundary and initial conditions for column system
The substrate concentration is identical to the influent at the column entrance:
0 0
0 = ≥
=S x , t
Sb [3-17]
0
There is no concentration gradient for substrate at the outlet of the column:
Lc
The overall initial conditions are:
0
Chapter V CONCLUSIONS
The mechanisms occurring on BAC combine both adsorption and biodegradation.
The effects of extending the contact time on biodegradation are a lower minimum effluent concentration and increased removal efficiencies; however, these effects are insignificant. On the other hand, lowering the HL can make the equilibrium more complete for adsorption, thereby improving the performance of BAC.
The result of mass balance, observed from the GAC column, indicates that the measured residual adsorption capacity can be used for estimation of organic removal by adsorption for GAC and for the BAC column. The absorbed organic carbon on BAC is less than that in sole adsorption case. Even at high loading rate the BAC column still maintained a certain amount of adsorption capacity, while the residual capacity of GAC was quite low. In general, the ratio of adsorption to biodegradation on the BAC column increases as HL decreases, and the result implies that adsorption will be dominant in a low organic mass loading condition.
In practice, BAC can prevent adsorption from sudden terminating and further reduce Smin by adsorption. However, increasing the HL of the BAC column will simultaneously increase Smin for biodegradation and make adsorption not at equilibrium. Avoiding too high HL, under which adsorption does not reach equilibrium (in this research it was 12 m/hr) is a possible way to optimize the design and operation of BAC.
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