Colloidal Transport: Modeling the “Irreversible” attachment of colloids to porous media Summer School in Geophysical Porous Media, Purdue University July 28, 2006 Son-Young Yi, Natalie Kleinfelter, Feng Yue, Gaurav Saini, Guoping Tang, Jean E Elkhoury, Murat Hamderi, Rishi Parashar Advisors: Patricia Culligan, Timothy Ginn, Daniel Tartakovsky

Jean E. Elkhoury Grad. Student Geophysics, UCLA Son-Young Yi PhD Mathematics, Purdue Guoping Tang PhD Civil Engg., Northeastern Gaurav Saini Grad. Student Env. Engg., OSU Murat Hamderi Grad. Student Civil Engg., Drexel Rishi Parashar Grad. Student Civil Engg., Purdue Feng Yue Grad. Student Civil Engg., UIUC Natalie Kleinfelter PhD Mathematics, Purdue

3 Motivation Classical Filtration Theory Experimental Setup Limitation of Classical Theory Single Population Model Multi Population Model 5-population model 2-population model Conclusions Future Work Outline

4 Motivation Decrease in attachment rate with transport distance indicates deficiencies in classical clean-bed filtration theory. Modeling unique experimental dataset to explore alternative approaches to describe irreversible attachment of colloids. Distance dependent attachment rate constant “Multi-population” based modeling approach.

5 Classical Clean-Bed Filtration Theory η D : Brownian diffusion η I : Interception η G : Gravitational Settling

6 Variation of η with velocity & d p

7 Macro-scale Approach First-order deposition rate k irr = λu

8 Classical Transport Equations Rate of Change of Fore Fluid Concentration Rate of Change of Adsorbed Concentration Hydrodynamic dispersion term Advection term k irr =attachment rate constant

9 Classical Theory Inferences K irr K irr C

10 Experimental Set-up (Yoon et al. 2006) Porous Media: Glass beads (d c = 4mm), surface roughness = 2 μm (rough beads only!) Colloids: d p =1-25 μm (d 50 =7 μm), fluorescent C 0 = 50 ppm Injection period ≈ 11.5 PV (fast/medium) & 9.5 (slow) Flushing period ≈ 11 PV (fast/medium) & 7 (slow) Fast ( cm/s), Medium ( cm/s)& slow ( cm/s) flow Laser induced fluorescence and digital image processing

11 Schematics (Yoon et al., 2006)

12 Rough Beads (Contact + Surface Filtration)

13 Smooth Beads (Contact Filtration)

14 Breakthrough Curve C/C 0

15 Concentration Profile (d~13 cm) S irr

16 Collector Efficiency

17 Irreversible Adsorption

18 CXTFIT Analysis Fast flow, rough beads Deterministic Equilibrium Model Predictions: D = cm 2 /s k irr = 0.165/s Experimental values D = cm 2 /s K irr = 1.48 x10 -4 /s Classic Transport Model can not explain the observed behavior

19 Variation in irreversible attachment with depth (constant k irr )

20 Approaches Explored Distance dependent attachment rate constant Multi-Population approach 5-population 2-population

21 Distance dependent k irr Step Function like k irr k irr 8 cm Depth 3.5 x x10 -4

22 Summary Constant or step function distribution of rate constant (k irr ) does not explain the observed behavior. Particle sorption can be predicted given the distribution of k irr with depth (which is unlikely!)

23 Multi-Population Modeling Governing equations i : population

24 Analytical Solution Runkel (1996) where, (t<τ) (t>τ)

25 5-Population Model

26 Predictions with constant k irr

27 Simulation Inputs Average particle size (μm)k irr (10 -4 ) Mass fraction (input)weighted Mass fraction

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31 Summary of 5-Population model results 5-population model provides good fit to the observed data. Mass fraction weighting alone does not explain the observations. Mass fraction weighted with specific surface provides good fit, using k irr values from slow flow test. Very good fits were obtained when k irr were weighted according to breakthrough data.

32 Motivation for 2-population model

33 2-Population Model Population distribution not available. Assumptions: k irr(pop1) > k irr(pop2) Approach Least square fit to observed data (S irr /C 0 ) Predicted rate constants and concentrations (C 0 (1) & C 0 (2) )

34 2-Population model fit

35 2-Population model predictions SlowMediumFast K irr 1 (Experimental K irr values) 5.34E-03 (2.36E-04) 4.44E-03 (2.25E-04) 1.75E-03 (1.48E-04) K irr E E E-05 C 0 (1) / C 0(1+2) 3.75E-02 (3.75%) 3.34E-02 (3.34%) 7.60E-02 (7.60%)

36 Summary Results 2-population model approach is a potent tool when particle distribution is unknown. Optimized k-values found using 2-population model are of the same order as the observed values. A small fraction (~5%) of population having high k irr values can explain variations in k irr with transport distance.

37 Conclusions Multi-population models capture the trend of decreasing k irr with transport distance. Multi-population models can be used to obtain reasonable predictions if particle population distribution is known. If particle population distribution is unknown, a 2- population model with optimization can be used to obtain parameters for predictions. In homogenized, clean bed-filters, decreases in k irr with transport distance are best explained by distributions in particle populations and not medium properties.

38 Suggestions for future work Analysis of Reversible attachment (S rev ) k = f (particle size, media roughness,fluid velocity)? Quantitative measurements of C & S (use of fluorescent bacteria…) Explore 1-site model with long-tail distribution functions for residence time.

Questions

Supplementary Slides….

41 Properties of particles

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