Filtration Theory

1. Filtration Theory

2. Field Trip To CUWTP • Monday at 2:20 pm at loading dock

3. Public Health reports • The decline happened over time and not rapidly as if it were associated with a centralized intervention • Chlorine was not responsible for the decline • Filtration was not responsible for the decline • The relatively high dose required for an infection would require gross contamination of the water supply • Therefore typhoid was generally not waterborne • There is some evidence that typhoid was greater in the summer. This suggests multiplication in the environment, most likely in food. • Improved personal hygiene was likely the dominant factor • Jakarta and Army evidence that the sources are local: (not centrally distributed like milk, water, or meat, but food preparation with contaminated hands) • Improved hygiene reduced contamination of food • Refrigeration would have reduced the summertime typhoid by reducing multiplication in food. Home refrigeration happened after the decline began, but commercial refrigeration

4. Filtration Outline • Particle Capture theory • Transport • Short range forces • Grain contact points • Dimensional Analysis • Trajectory Models • Filters • Rapid • Slow (lots of detail here…)

5. References • Tufenkji, N. and M. Elimelech (2004). "Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media." Environmental-Science-and-Technology38(2): 529-536. • Cushing, R. S. and D. F. Lawler (1998). "Depth Filtration: Fundamental Investigation through Three-Dimensional Trajectory Analysis." Environmental Science and Technology 32(23): 3793 -3801. • Tobiason, J. E. and C. R. O'Melia (1988). "Physicochemical Aspects of Particle Removal in Depth Filtration." Journal American Water Works Association 80(12): 54-64. • Yao, K.-M., M. T. Habibian, et al. (1971). "Water and Waste Water Filtration: Concepts and Applications." Environmental Science and Technology 5(11): 1105.

6. Overall Filter Performance • Iwasaki (1937) developed relationships describing the performance of deep bed filters. C is the particle concentration [number/L3] l0 is the initial filter coefficient [1/L] z is the media depth [L] The particle’s chances of being caught are the same at all depths in the filter; pC* is proportional to depth

7. Particle Removal Mechanisms in Filters collector Transport to a surface Molecular diffusion Inertia Gravity Interception Attachment Straining London van der Waals

8. Filtration Performance: Dimensional Analysis • What is the parameter we are interested in measuring? _________________ • How could we make performance dimensionless? ____________ • What are the important forces? Effluent concentration C/C0 or pC* Electrostatic London van der Waals Inertia Viscous Gravitational Thermal Need to create dimensionless force ratios!

9. Dimensionless Force Ratios • Reynolds Number • Froude Number • Weber Number • Mach Number • Pressure/Drag Coefficients • (dependent parameters that we measure experimentally)

10. What is the Reynolds number for filtration flow? • What are the possible length scales? • Void size (collector size) max of 0.7 mm in RSF • Particle size • Velocities • V0 varies between 0.1 m/hr (SSF) and 10 m/hr (RSF) • Take the largest length scale and highest velocity to find max Re • Thus viscosity is generally much more significant than inertia

11. Gravitational London Thermal Electrostatic Viscous Viscous Viscous Viscous Choose viscosity! • In Fluid Mechanics inertia is a significant “force” for most problems • In porous media filtration viscosity is more important that inertia. • We will use viscosity as the repeating parameter and get a different set of dimensionless force ratios Inertia

12. Gravity forces velocities v pore Gravity only helps when the streamline has a _________ component. horizontal Use this equation

13. Diffusion (Brownian Motion) v pore Diffusion velocity is high when the particle diameter is ________. kB=1.38 x 10-23 J/°K T = absolute temperature small dc is diameter of the collector The exponent was obtained from an analytical model

14. London van der Waals • The London Group is a measure of the attractive force • H is the Hamaker’s constant Van der Waals force Viscous force

15. What about Electrostatic? • Modelers have not succeeded in describing filter performance when electrostatic repulsion is significant • Models tend to predict no particle removal if electrostatic repulsion is significant. • So until we get a better model we will neglect this force with the understanding that filter performance is poor if electrostatic repulsion is significant

16. Geometric Parameters • What are the length scales that are related to particle capture by a filter? • ______________ • __________________________ • ______________ • Create dimensionless groups • Choose the repeating length ________ Filter depth (z) Collector diameter (media size) (dc) Particle diameter (dp) (dc) Number of collectors!

17. Write the functional relationship Force ratios Length ratios doubles If we double depth of filter what does pfz do? ___________ How do we get more detail on this functional relationship? Empirical measurements Numerical models

18. Numerical Models • Trajectory analysis (similar to the analysis of flocculation) • A series of modeling attempts with refinements • Began with a “single collector” model that modeled London and electrostatic forces with an attachment efficiency term (a) Addition assumption Interception Sedimentation Diffusion

19. Array of Spheres Model (AOS) • Includes simplified geometry describing the contact between collectors • Used trajectory analysis to determine which particles would be captured • Used the numerical model results to determine the form of the equation based on dimensional analysis

20. AOS: The Media Trap Isolated collectors Array of spheres model Collector Contacts

21. Particles that enter centered above a collector are trapped in the stagnation point. Particles that enter on a streamline that passes through a contact point between collectors get trapped between two collectors Contacts Matter! Two Particle Traps Collectorcontact straining This trajectory analysis ignores Brownian Motion

22. Array of Spheres Model Results and Critique Brownian wasn’t modeled • The transport to the media surface by either the fluid (interception, PR), gravity (Pg), or diffusion (PBr) is followed by an attachment step controlled by van der Waals (PLo) • The transport and attachment steps occur in series and thus removal should be described by the product of these groups • More work to be done! 13.6=4.04*As1/3

23. AOS model deficiencies =1! This suggests a third transport mechanisms that is constant and doesn’t require Brownian motion or sedimentation! Could be interception, but interception increases with particle size. Given this error (and the likelihood that the numerical model contained errors) the model results from the AOS model should probably not be used!

24. Tufenkji and Elimelech with Analysis by Weber-Shirk Note that my NPe is the inverse of T&E

25. Interception

26. Gravity

27. Total removal

29. For particles less than 1 mm

30. Brownian Motion • Brownian motion dominates the transport and collection of particles on the order of 1 mm and smaller • Brownian transport (diffusion) leads to nondeterministic behavior and results in trajectories defined by stochastic differential equations • The problem is traditionally decoupled using the assumption that the Brownian and deterministic transport mechanisms are additive • Sedimentation is less important for small particles because the PR group is small and the PBr group is large

31. Filter Performance as function of particle size The exact location of the minimum varies, but is generally around 1 mm. For small particles diffusion dominates and we have attachment

32. Estimate Dimensionless Brownian Transport for a Bacteria Cell Advection is 40x greater than diffusion

33. The Diffusion Surprise • As particle size decreases Brownian motion becomes more effective • Viruses should be removed efficiently by filters (if attachment is effective) bacteria viruses

34. How deep must a filter (SSF) be for diffusion to remove 99% of bacteria? • Assume a is 1 and dc is 0.2 mm • a is ____ • pfz is ____ • z is _____ • What does this mean? 1 2 3.7 cm If the attachment efficiency were 1, then we could get great particle capture in a 1 m deep filter!

35. Filtration Technologies • Slow (Filters→English→Slow sand→Biosand) • First filters used for municipal water treatment • Were unable to treat the turbid waters of the Ohio and Mississippi Rivers • Rapid (Mechanical→American→Rapid sand) • Used in Conventional Water Treatment Facilities • Used after coagulation/flocculation/sedimentation • High flow rates→clog daily→hydraulic cleaning • Ceramic

36. Rapid Sand Filter (Conventional US Treatment) Depth (cm) 30 45 45 Specific Gravity 1.6 2.65 2.65 Size (mm) 0.70 0.45 - 0.55 5 - 60 Anthracite Influent Sand Gravel Drain Wash water Effluent

37. Filter Design • Filter media • silica sand and anthracite coal • non-uniform media will stratify with _______ particles at the top • Flow rates • 2.5 - 10 m/hr • Backwash rates • set to obtain a bed porosity of 0.65 to 0.70 • typically 50 m/hr smaller

38. Backwash • Wash water is treated water! • WHY? Anthracite Only clean water should ever be on bottom of filter! Sand Influent Gravel Drain Wash water Effluent

39. Slow Sand Filtration • First filters to be used on a widespread basis • Fine sand with an effective size of 0.2 mm • Low flow rates (10 - 40 cm/hr) • Schmutzdecke (_____ ____) forms on top of the filter • causes high head loss • must be removed periodically • Used without coagulation/flocculation! filter cake

40. Typical Performance of SSF Fed Cayuga Lake Water 1 Fraction of influent E. coli remaining in the effluent 0.1 0.05 0 1 2 3 4 5 Time (days) (Daily samples) Filter performance doesn’t improve if the filter only receives distilled water

41. How do Slow Sand Filters Remove Particles? • How do slow sand filters remove particles including bacteria, Giardia cysts, and Cryptosporidium oocysts from water? • Why does filter performance improve with time? • Why don’t SSF always remove Cryptosporidium oocysts? • Is it a biological or a physical/chemical mechanism? • Would it be possible to improve the performance of slow sand filters if we understood the mechanism?

42. Slow Sand Filtration Research Apparatus Manometer/surge tube Cayuga Lake water (99% or 99.5% of the flow) Manifold/valve block Peristaltic pumps Sampling Chamber Auxiliary feeds (each 0.5% of the flow) Sampling tube Lower to collect sample To waste 1 liter sodium azide 1 liter E. coli feed Filter cell with 18 cm of glass beads

43. Quiescent Cayuga Lake water 1 Sodium azide (3 mM) Control 0.1 0.05 0 2 4 6 8 10 Time (days) Biological and Physical/Chemical Filter Ripening Continuously mixed Cayuga Lake water 1 Physical/chemical Fraction of influent E. coli remaining in the effluent Gradual growth of _______ or ________ 0.1 biofilm predator 0.05 0 1 2 3 4 5 Time (days) What would happen with a short pulse of poison?

44. 1 Control Sodium azide pulse Sodium chloride pulse 0.1 0.08 0 1 2 3 4 5 6 Time—h Biological Poison Biofilms? Abiotic? q Fraction of influent E. coli remaining in the effluent predator Conclusion? _________ is removing bacteria predator

45. Chrysophyte long flagellum used for locomotion and to provide feeding current short flagellum 1 µm stalk used to attach to substrate (not actually seen in present study)

46. Particle Removal by Size 1 control 3 mM azide 0.1 Recall quiescent vs. mixed? Fraction of influent particles remaining in the effluent Effect of the Chrysophyte 0.01 What is the physical-chemical mechanism? 0.001 0.8 1 10 Particle diameter (µm)

47. Role of Natural Particles in SSF • Could be removal by straining • But SSF are removing particles 1 mm in diameter! • To remove such small particles by straining the pores would have to be close to 1 mm and the head loss would be excessive • Removal must be by attachment to the sticky particles!

48. Particle Capture Efficiency • Sand filters are inefficient capturers of particles • Particles come into contact with filter media surfaces many times, yet it is common for filters to only remove 90% - 99% of the particles. • Failure to capture more particles is due to ineffective __________ • Remember the diffusion surprise? attachment

49. Techniques to Increase Particle Attachment Efficiency • Make the particles stickier • The technique used in conventional water treatment plants • Control coagulant dose and other coagulant aids (cationic polymers) • Make the filter media stickier • Potato starch in rapid sand filters? • Biofilms in slow sand filters? • Mystery sticky agent present in surface waters that is imported into slow sand filters?

50. Mystery Sticky Agent • Serendipity! • Head loss through a clogged filter decreases if you add acid • Maybe the sticky agent is acid soluble • Maybe the sticky agent will become sticky again if the acid is neutralized • Eureka!