1. Use Slide Show (F5) in PowerPoint A New Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media
Tufenkji, N. and Elimelech M. “Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media”, Environmental Science and Technology, 2004, Vol. 38,
Nathalie Tufenkji
Menachem Elimelech
Department of Chemical Engineering
Environmental Engineering Program
Yale University

2. Outline Background and Motivation Development of Correlation Equation
Comparison to Current Approaches and Experimental Data
Implications

3. Background and Motivation
Transport and fate of colloidal particles in saturated porous media
In-situ bioremediation
Riverbank filtration
Deep-bed granular filtration
Tufenkji, Ryan and Elimelech, ES&T, 2002.

4. Background and Motivation
Transport Mechanisms in Filtration A
Collector B C
A. Sedimentation
B. Interception
C. Brownian Diffusion

5. Background and Motivation
Limitations of Current Approaches
Yao, Habibian and O’Melia, 1971, ES&T (5) 1105.
First model suggesting 3 mechanisms are additive
Do not consider:
(i) hydrodynamic interactions (HI)
(ii) van der Waals attractive forces (vdW)
Rajagopalan and Tien, 1976, AIChE J (22) 523.
Improved YHO model, however, has several limitations
Omitted HI and vdW forces for mechanism of Brownian diffusion

6. Development of Correlation Equation
Governing Equation and Boundary Conditions

7. Development of Correlation Equation
Determination of Single-Collector Contact Efficiency I
Dimensionless Parameters Governing Filtration

8. Development of Correlation Equation
Dimensionless Parameters Governing Filtration

9. Development of Correlation Equation
General Approach – Additivity Assumption
Parameter Values
0.01 < dp < 10 m
0.05 < dc < 0.50 mm
7 x 10-6 < U < 2 x 10-3 m/s
3 x < A < 4 x J
1.0 < p < 1.8 g/cm3
T = 298 K
f = 0.36

10. Development of Correlation Equation
General Approach – Additivity Assumption
Correlation for D
“Turn off” mechanisms of interception and gravity
Calculate D numerically over range of NR, NPe, and NvdW

11. Development of Correlation Equation
General Approach – Additivity Assumption
Correlation for I
“Turn off” mechanism of gravity
Calculate over range of NR, NPe, and NvdW

12. Development of Correlation Equation
General Approach – Additivity Assumption
Correlation for G
Calculate over range of NR, NPe, NvdW, and Ngr

13. Development of Correlation Equation
General Approach – Additivity Assumption

14. Development of Correlation Equation
General Approach – Additivity Assumption D

15. Development of Correlation Equation
General Approach – Additivity Assumption I

16. Development of Correlation Equation
General Approach – Additivity Assumption G

17. Development of Correlation Equation
General Approach – Additivity Assumption 0
dp (m)
Subsurface transport
U = 9 x 10-6 m/s

18. Development of Correlation Equation
General Approach – Additivity Assumption
Bank filtration
U = 4 x 10-5 m/s 0 0
dp (m)
(m)
dp (m)
(m)
Subsurface transport
U = 9 x 10-6 m/s

19. Deep-bed granular filtration
Development of Correlation Equation
General Approach – Additivity Assumption
Bank filtration
U = 4 x 10-5 m/s
Deep-bed granular filtration
U = 2.8 x 10-3 m/s 0 0
dp (m)
(m)
dp (m)
(m)
dp (m)
(m)
Subsurface transport
U = 9 x 10-6 m/s

20. Comparison to RT Equation
Major Limitation
(1) Overestimates  over wide range of dp in Brownian regime
Conditions:
dc = 0.40 mm
U = 8 x 10-6 m/s
f = 0.36
A = 1 x J
p = 1.05 g/cm3
T = 288 K 0
~ 50% difference
dp (m)

21. Comparison to RT Equation
Major Limitations
(2) Increased deviation for microbial particles in Brownian regime
Apolio virus - quartz ≈ x J
Asilica - quartz ≈ 1 x J

22. Comparison to RT Equation
Major Limitations
(2) Increased deviation for microbial particles in Brownian regime
Apolio virus - quartz ≈ x J
Asilica - quartz ≈ 1 x J
Conditions:
dc = 0.40 mm
U = 8 x 10-6 m/s
f = 0.36
A = 3 x J
p = 1.05 g/cm3
T = 288 K 0
~ 60% difference
(m)

23. Unique Features of Correlation Equation

24. Unique Features of Correlation Equation
Include HI and vdW forces on transport by diffusion

25. Unique Features of Correlation Equation
Include HI and vdW forces on transport by diffusion
Transport by gravity is not a strong function of porosity

26. Unique Features of Correlation Equation
Include HI and vdW forces on transport by diffusion
Transport by gravity is not a strong function of porosity
Include influence of vdW forces in gravity term

27. Comparison with Experimental Data
Data taken from well-controlled column experiments, under favorable conditions, using uniform spherical latex particles and glass beads
YHO Model
EXP
YHO
slope = 0.34

28. Comparison with Experimental Data
Data taken from well-controlled column experiments, under favorable conditions, using uniform spherical latex particles and glass beads
YHO Model
RT Model
EXP
YHO
RT
slope = 0.34
slope = 0.74

29. Comparison with Experimental Data
Data taken from well-controlled column experiments, under favorable conditions, using uniform spherical latex particles and glass beads
YHO Model
RT Model
TE Model
EXP
YHO
RT
TE
slope = 0.90
slope = 0.34
slope = 0.74

30. Implications
Accurate predictions of colloid filtration behavior are critical in several processes in natural and engineered systems
Predictions of  with TE equation show remarkable agreement with exact theoretical values
Experimental data are in much closer agreement with predictions based on TE equation in comparison to current approaches

31. Acknowledgements
Natural Sciences and Engineering Research Council of Canada (NSERC)
National Science Foundation (NSF)
US EPA