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This presentation discusses a new correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media, highlighting its development, comparison to current approaches, and implications. It addresses limitations of existing models and presents dimensionless parameters governing filtration. The correlation equation's general approach, unique features, and comparison with experimental data are also explored.
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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
Outline • Background and Motivation • Development of Correlation Equation • Comparison to Current Approaches and Experimental Data • Implications
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.
Background and Motivation Transport Mechanisms in Filtration A Collector B C A. Sedimentation B. Interception C. Brownian Diffusion
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)
Development of Correlation Equation Governing Equation and Boundary Conditions
I Dimensionless Parameters Governing Filtration Development of Correlation Equation Determination of Single-Collector Contact Efficiency
Development of Correlation Equation Dimensionless Parameters Governing Filtration
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
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
Development of Correlation Equation General Approach – Additivity Assumption Correlation for I • “Turn off” mechanism of gravity • Calculate over range of NR, NPe, and NvdW
Development of Correlation Equation General Approach – Additivity Assumption Correlation for G Calculate over range of NR, NPe, NvdW, and Ngr
Development of Correlation Equation General Approach – Additivity Assumption
Development of Correlation Equation General Approach – Additivity Assumption D
Development of Correlation Equation General Approach – Additivity Assumption I
Development of Correlation Equation General Approach – Additivity Assumption G
Development of Correlation Equation General Approach – Additivity Assumption 0 dp (m) Subsurface transport U = 9 x 10-6 m/s
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
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
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)
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
~ 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)
Unique Features of Correlation Equation • Include HI and vdW forces on transport by diffusion
Unique Features of Correlation Equation • Include HI and vdW forces on transport by diffusion • Transport by gravity is not a strong function of porosity
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
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
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
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
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
Acknowledgements • Natural Sciences and Engineering Research Council of Canada (NSERC) • National Science Foundation (NSF) • US EPA