Colloidal Transport: Modeling the “Irreversible” attachment of colloids to porous media

1. 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

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

3. Outline • 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

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 ηD: Brownian diffusion ηI: Interception ηG: Gravitational Settling

6. Variation of η with velocity & dp

7. Macro-scale Approach First-order deposition rate kirr = λu

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

9. Classical Theory Inferences Kirr KirrC Kirr

10. Experimental Set-up (Yoon et al. 2006) • Porous Media: Glass beads (dc= 4mm), surface roughness = 2 μm (rough beads only!) • Colloids: dp=1-25 μm (d50=7 μm), fluorescent • C0 = 50 ppm • Injection period ≈ 11.5 PV (fast/medium) & 9.5 (slow) • Flushing period ≈ 11 PV (fast/medium) & 7 (slow) • Fast (0.0522 cm/s), Medium (0.0295 cm/s)& slow (0.0124 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/C0

15. Concentration Profile (d~13 cm) Sirr

16. Collector Efficiency

17. Irreversible Adsorption

18. CXTFIT Analysis • Fast flow, rough beads • Deterministic Equilibrium Model • Predictions: • D = 0.2834 cm2/s • kirr = 0.165/s Experimental values D = 0.042 cm2/s Kirr = 1.48 x10-4/s Classic Transport Model can not explain the observed behavior

19. Variation in irreversible attachment with depth (constant kirr)

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

21. Distance dependent kirr 3.5 x10-4 Step Function like kirr kirr 8 cm Depth 1.2 x10-4

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

23. Multi-Population Modeling • Governing equations i : population

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

25. 5-Population Model

26. Predictions with constant kirr

27. Simulation Inputs

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 kirr values from slow flow test. • Very good fits were obtained when kirr were weighted according to breakthrough data.

32. Motivation for 2-population model

33. Population distribution not available. Assumptions: kirr(pop1) >kirr(pop2) Approach Least square fit to observed data (Sirr/C0) Predicted rate constants and concentrations (C0 (1) & C0 (2)) 2-Population Model

34. 2-Population model fit

35. 2-Population model predictions

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 kirr values can explain variations in kirr with transport distance.

37. Conclusions • Multi-population models capture the trend of decreasing kirr 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 kirr with transport distance are best explained by distributions in particle populations and not medium properties.

38. Suggestions for future work • Analysis of Reversible attachment (Srev) • 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.

39. Questions

40. Supplementary Slides….

41. Properties of particles