Nathalie Tufenkji Menachem Elimelech Department of Chemical Engineering

1. Use Slide Show (F5) in PowerPointA 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, 529-536. 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. 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 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)

6. Development of Correlation Equation Governing Equation and Boundary Conditions

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

8. Development of Correlation Equation Dimensionless Parameters Governing Filtration

9. 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 10-21 < A < 4 x 10-20 J 1.0 < p < 1.8 g/cm3 T = 298 K f = 0.36 Development of Correlation Equation General Approach – Additivity Assumption

10. Development of Correlation Equation General Approach – Additivity Assumption Correlation for D • “Turn off” mechanisms of interception and gravity • Calculate Dnumerically 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. Bank filtration U = 4 x 10-5 m/s Development of Correlation Equation General Approach – Additivity Assumption 0 0 (m) dp (m) dp (m) (m) Subsurface transport U = 9 x 10-6 m/s

19. Deep-bed granular filtration U = 2.8 x 10-3 m/s Bank filtration U = 4 x 10-5 m/s Development of Correlation Equation General Approach – Additivity Assumption 0 0 (m) dp (m) (m) dp (m) (m) dp (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 10-20 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≈ 3 - 5 x 10-21 J Asilica - quartz≈ 1 x 10-20 J

22. ~ 60% difference Comparison to RT Equation Major Limitations (2) Increased deviation for microbial particles in Brownian regime Apolio virus - quartz≈ 3 - 5 x 10-21 J Asilica - quartz≈ 1 x 10-20 J Conditions: dc = 0.40 mm U = 8 x 10-6 m/s f = 0.36 A = 3 x 10-21 J p = 1.05 g/cm3 T = 288 K 0 (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 = 0.74 slope = 0.34

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 TE YHO RT slope = 0.90 slope = 0.74 slope = 0.34

30. Accurate predictions of colloid filtration behavior are critical in several processes in natural and engineered systems Implications • 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