Abstract
The performance characteristics of the unsaturated granular media were described using Monod type biological kinetics and mass transfer concepts within microbial films. For this purpose computer techniques were first developed for the numerical evaluation of the normalized biofilms mathematical model. The effects of wetted surface area and the other parameters on substrate removal were then numerically evaluated. The theory enables one to transfer the experimental findings obtained from a pilot plant to another filter for design purposes. Practical application of the theory to experimental results was also demonstrated.
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Abbreviations
- A:
-
cross-sectional area, L2
- Bi :
-
dimensionless substrate concentration
- Bsi :
-
dimensionless substrate concentration at the liquid-biofilm interface
- \(\bar B_{so} \) :
-
lower limit in the definite integral\(\bar Z\) calculated using Eq. 27
- \(\bar B_o \) :
-
dimensionless effluent substrate concentration corresponding to\(\bar B_{so} \)
- b:
-
total width of parallel planes in conceptual model, L
- c:
-
bulk liquid phase substrate concentration, ML-3
- Co :
-
bulk liquid phase effluent substrate concentration, ML-3
- cs :
-
substrate concentration at the liquid-biofilm interface, ML-3
- cx :
-
substrate concentration at any location x, ML-3
- Ci :
-
bulk liquid phase inlet substrate concentration, ML-3
- C:
-
dimensionless substrate concentration defined as c/ci
- Cx :
-
dimensionless substrate concentration defined as cx/ci
- Dc :
-
diffusivity of substrate in biofilm, L2 T-1
- Dw :
-
molecular diffusivity of substrate in the liquid, L2 T-1
- E:
-
mass transfer coefficient defined as Dw/e, LT-1
- e:
-
depth of stagnant liquid layer adjacent to biofilm, L
- F:
-
mathematical expression to calculate the definite integral\(\bar Z\)
- H:
-
depth of filter, L
- h:
-
liquid film thickness, L
- K:
-
dimensionless ratio of mass transfer rate to kinetic rate
- Ks :
-
Monod-half velocity coefficient, ML-3
- k:
-
maximum utilization rate of rate limiting substrate, T-1
- k1 :
-
biological rate (equation) coefficient T-1
- k2 :
-
biological rate (equation) coefficient L-1
- k3 :
-
biological rate (equation) coefficient M-1 L3
- L:
-
wet microbial film thickness, L
- l :
-
dimensional filter length, L
- M:
-
dimensionless biofilm thickness
- N:
-
flux of substrate, ML-2 T-1
- Qa :
-
hydraulic loading rate, L3 L-2 T-1
- q:
-
rate of flow per unit width, L3 T-1L-1
- Q:
-
volumetric rate of flow, L3 T-1
- S:
-
specific surface area, L2 L-3
- wav :
-
average velocity of liquid in z direction, LT-1
- Z:
-
dimensionless distance measured in flow direction from the origin
- \(\bar Z\) :
-
value of the definite integral related to the filter length
- z:
-
axial distance measured in flow direction from the origin, L
- α :
-
dimensionless filter depth
- X:
-
dimensionless distance measured normal to flow direction
- x:
-
dimensional distance measured normal to flow direction, L
- Xc :
-
microbial density within biofilm, ML-3
- γ:
-
specific gravity, ML-2 T-2
- μ :
-
dynamic viscosity, ML-1 T-1
- λ:
-
effectiveness coefficient
- ρ :
-
mass density of liquid, ML-3
- η:
-
biological removal ratio (biological efficiency)
- ηd:
-
ksh / Dw in which ks is a proportionality constant in LT-1
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Muslu, Y. A study on performance characteristics of granular-media trickling filters. Appl Biochem Biotechnol 37, 209–224 (1992). https://doi.org/10.1007/BF02921672
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DOI: https://doi.org/10.1007/BF02921672