3 Overview Flocculation definition Types of flocculators Mechanical DesignFractal Flocculation Theory applied to hydraulic flocculatorsCFD analysis of hydraulic flocculatorsHydraulic Flocculator Design
4 What is Flocculation?A process that transforms a turbid suspension of tiny particles into a turbid suspension of big particles!RequiresSticky particles (splattered with adhesive nanoglobs)Successful collisions between particlesFlocs are fractals (“the same from near as from far”)The goal of flocculation is to reduce the number of colloids (that haven’t been flocculated)One goal is to understand why some colloids are always left behind (turbidity after sedimentation)Another goal is to learn how to design a flocculator
5 Mechanical Flocculation Shear provided by turbulence created by gentle stirringTurbulence also keeps large flocs from settling so they can grow even larger!Presumed advantage is that energy dissipation rate can be varied independent of flow rateDisadvantage is the reactors have potential short circuiting (some fluid moves quickly from inlet to outlet)
6 Recommended G and Gq values: Turbidity or Color Removal (Mechanical flocculators) Type“Velocity gradient” (G) (1/s)Energy Dissipation Rate (e)+Gqq*(minute)Low turbidity, color removal20-700.4 – 4.950, ,000High turbidity, solids removal70-18080, ,0007 - 45Cleasby, J. L., "Is Velocity Gradient a Valid Turbulent Flocculation Parameter?"ASCE, Journal of Environmental Engineering, Vol. 110, No. 5, Oct.,1984* Calculated based on G and Gq guidelines+ average value assuming viscosity is 1 mm2/sSincero and Sincero, 1996 Environmental Engineering: A Design ApproachG is the wrong parameter… (Cleasby, 1984)
7 Mechanical Design: mixing with paddles extraMechanical Design: mixing with paddlesRatio of relative to absolute velocity of paddlesProjected area of paddlesDrag coefficient“velocity gradient”Reactor volume
8 Mechanical Flocculators? extraMechanical Flocculators?Waste (a small amount of) electricityRequire unnecessary mechanical componentsHave a wide distribution of energy dissipation rates (highest near the paddles) that may break flocsHave a wide distribution of particle residence times (completely mixed flow reactors)
9 Ten State StandardsThe detention time for floc formation should be at least 30 minutes with consideration to using tapered (i.e., diminishing velocity gradient) flocculation. The flow‑through velocity should be not less than 0.5 nor greater than 1.5 feet per minute.Agitators shall be driven by variable speed drives with the peripheral speed of paddles ranging from 0.5 to 3.0 feet per second. External, non-submerged motors are preferred.Flocculation and sedimentation basins shall be as close together as possible. The velocity of flocculated water through pipes or conduits to settling basins shall be not less than 0.5 nor greater than 1.5 feet per second. Allowances must be made to minimize turbulence at bends and changes in direction.Baffling may be used to provide for flocculation in small plants only after consultation with the reviewing authority. The design should be such that the velocities and flows noted above will be maintained.Hydraulic flocculators allowed only by special permission!
10 Hydraulic Flocculators Horizontal baffleVertical bafflePipe flowGravel bedVery low flows and pilot plantsA bad idea (cleaning would require a lot of work)
11 Flocculator Geometry Entrance 2 Channels Port between channels Exit extraFlocculator GeometryEntrance2 ChannelsPort between channelsplanta de 50 Lps con 2 cámaras de sedimentaciónExitLower BafflesUpper Baffles
12 Why aren’t hydraulic flocculators used more often? extraWhy aren’t hydraulic flocculators used more often?Simple construction means that there aren’t any items that private companies (venders) can sell as specialized componentsConsulting firms want to be able to pass the design responsibility off to a venderThe presumed operation flexibility of mechanical flocculators (variable speed motor driving a slow mixing unit)Poor documentation of design approach for hydraulic flocculators (special permission required to use in the US!)Using electricity is cool, design innovation is suspect…Prior to AguaClara we didn’t have a design algorithm based on the fundamental physics
13 Schulz and Okun (on Hydraulic flocculators) Surface Water Treatment for Communities in Developing Countries, (1984) by Christopher R. Schulz and Daniel A. Okun. Intermediate Technology PublicationsSchulz and Okun (on Hydraulic flocculators)Recommend velocity between 0.1 and 0.3 m/sDistance between baffles at least 45 cmWater must be at least 1 m deepQ must be greater than 10,000 m3/day (115 L/s)These aren’t universal constants!The velocity might be related to creating collisions between particles or preventing breakup of flocs from too much shear. In any case, velocity is not the right parameter because it isn’t dimensionless and thus it might not scale properly across a wide range of plant flow rates.Surface Water Treatment for Communities in Developing Countries, (1984) by Christopher R. Schulz and Daniel A. Okun. Intermediate Technology PublicationsWe need to understand the real constraints so we can scale the designs correctlyWhat length scale could make a dimensionless parameter?
14 AguaClara Flocculator Design Evolution extraAguaClara Flocculator Design EvolutionWe began using conventional guidelines based on “velocity gradient” but we were aware that this system was fundamentally incorrect (it doesn’t capture the physics of turbulence)We were concerned that by using a defective model we could potentially produce defective designsIf the model doesn’t capture the physics, then it won’t scale correctly (and we are designing plants for scales that hadn’t been tested)
15 Edge of Knowledge Alert extraEdge of Knowledge AlertWhy would we ever think that the baffled flocculators invented over 100 years ago were the optimal design for flocculation?We have better coagulants, shouldn’t that influence flocculator design?We are only now beginning to understand the physics of fractal flocculationWe are improving the design of hydraulic flocculators based on our evolving understanding of the physics of flocculation
16 The Challenge of Flocculation We would like to knowHow do particles make contact to aggregate?What determines the time required for two flocs to collide?How strong are flocs?The challenge of the large changes in scaleThe Al(OH)3 nanoglobs begin at a scale of 100 nanometersFlocs end at a scale of 100 micrometers16
17 Hydraulic Flocculation Theory Turbulence is caused by the expansion that results when the water changes direction as it flows around each baffleColloids and flocs are transported to collide with each other by turbulent eddies and over short distances by viscous shear.Flocs grow in size with each successful collisionColloids have a hard time attaching to large flocs* (maybe because the surface shear is too high???)Flocculation model and collision potential for reactors with flows characterized by high Peclet numbersMonroe L. Weber-Shirk , a, and Leonard W. Liona*hypothesis from 2012!
19 Exponential growthHow many sequential collisions are required to make a 1 mm particle starting from 1 mm particles?How much larger in volume is the 1 mm diameter particle?____________1,000,000,000 !
20 Doubling Collisions 1 collision 1+1=2 2 collisions 2+2=4 Number of original particles in the floc = 2nWhat is n to obtain 1,000,000,000 = 2n?n=30This assumes volume is conserved!
21 Fractal DimensionsWhat happens to the density of a floc as it grows larger?Floc density approaches the density of water because the floc includes waterdiameter of primary particlediameter of flocFractal dimensionNumber of primary particles in the flocIf volume is conserved, what is DFractal? ____3
22 Fractal FlocculationFractal geometry explains the changes in floc density, floc volume fraction, and, ultimately, sedimentation velocity as a function of floc sizeThe fractal dimension of flocs is approximately 2.3 (based on floc measurements)Adachi Wat. Res. Vol. 31, No. 3, pp. 449~54, 1997
23 Floc Volume FractionThe fraction of the reactor volume that is occupied by flocsFor fractal dimensions less than 3 the floc volume fraction increases as floc size increasesUse conservation of volume to estimate initialWe are ignoring the initial diffusion controlled aggregation of aluminum hydroxide molecules with each other and with clay. We are assuming that this aggregation process produces particles that are relatively dense (high fractal dimension) and that this process occurs quickly relative to the subsequent shear and turbulent eddy mediated collisions (in less than a minute).dominates
24 Floc Volume Fraction Primary particle diameter (clay + coagulant) “super fluffy” flocsFractal dimension of 1 would suggest that the flocs would occupy the entire flocculator by the time they reached 0.2 mm (for this example)Fractal dimension of 3 gives volume conservation.Dense flocs
25 Buoyant Density of Flocs Will these flocs settle faster than the primary particles?Here we assume that the primary particle (clay plus coagulant) is 1 micrometer in diameter.The assumption is that we are starting with clay at 2650 kg/m^3.
26 Floc Terminal Velocity Laminar flowFloc Terminal VelocityUpflow velocity for floc blanketsCapture velocity for AguaClara plate settlersWhy flocculation is necessary!The shape factor adjusts the coefficient of drag for non spherical geometry and according to Tambo has a value of 45/24 for flocs (Tambo et al., 1979). This value is probably not yet well characterized. In any case it is expected to be order 1 because it is a correction to the drag coefficient.All fractal dimensions greater than one are expected to increase the terminal velocity as the floc diameter increases.Both floc blanket upflow velocity and plate settler capture velocity are AguaClara current design values, but are not optimized.1 mmDFractal = 2.3 and d0 = 1 mmshape factor for drag on flocsThe model takes into account the changing density of flocs
27 Analytical Model of the Flocculation Process The floc porosity increases with floc diameterThe velocity between flocs is a function of whether the separation distance is less or greater than the Kolmogorov scaleThe time required per collision is a function of the relative velocity between flocs, the average separation distance between flocs, and the floc sizeIn the next slides we will explore how to characterize collision time for flocsWe will assume that collisions occur between similar sized flocs. That assumption will need to be evaluated, but it is probably a good assumption for the initial growth of flocs.Are the two flocs in different eddies?
28 How much water is cleared (filtered) from a floc’s perspective? Volume cleared is proportional to a collision area defined by a circle with diameter = sum of the floc diametersVolume cleared is proportional to timeVolume cleared is proportional to the relative velocity between flocs
29 How much volume must be cleared before a collision occurs? What is the average volume of water “occupied” by a floc?Need to know floc diameter (dFloc)And floc volume fraction (fFloc)Floc volume Suspension volume
30 Use dimensional analysis to get a relative velocity given a length scale laminarturbulentViscous rangeInertial rangeL is separation distanceAssume linearRe=1The length scale is the average separation distance of the flocsThe origin of the G notationIf the flocculator has laminar flow, then this side doesn’t apply and the G, Gq approach applies.
31 Summary for Particle Collisions viscousinertiatc is average time per collisionFloc separation distanceYes! Because the phi.floc is a function of d!Find the time to clear the volume occupied by one floc.Then we need to find the average relative velocity of the two flocs based on their average separation distance.Is tc a function of d?Yes!
32 Successful Collision Models Number of collisions is equal to time over collision timeSuccessful Collision ModelsviscousinertiaTime for one collisionNumber of successful collisionsG is fractional surface coverage of colloids with adhesive nanoglobsdFloc is perhaps mean floc size of flocs that are capturing colloidsFor completeness we should probably include a correction for hydrodynamic effects that make it difficult for non porous particles to approach closely. This may increase the time for the first few collisions when flocs aren’t very porous
33 Relationship between laminar and turbulent Set the collisions equal to get the relationshipThe ratio of Gq to y is the number of clay particles raised to the 2/9th power!Use the target settled water turbidity as the best guess for a relationship between conventional Gq and y. For a turbidity of 1 NTU the number of clay particles is 150,000,000 per liter.Schulz and Okun suggest 20,000 as a minimum value of Gq equivalent to y = 65 m2/3. But this isn’t calculated correctly. Should take their Gq and energy dissipation rate to make the conversion.This means that we can find the relationship between Gtheta calculated the traditional way from the head loss and compare that with Gtheta calculated correctly.The
34 Minimum time to grow from colloid to large floc ViscousDFractal = 2.3d0 = 1 mme = 6 mW/kgInertial400 s120 s20 collisions to grow from 1 mm to 0.4 mm40 sTake the low NTU case because that is the most difficult to flocculate. Takes about 20 seconds per collision. About 20 collisions. Roughly 400 seconds or 7 minutes. Note that this doesn’t take into account any reactions that occur in the nm to micrometer scale. This assumes a perfectly uniform energy dissipation rate throughout the reactor.At this energy dissipation rate flocs would only grow to 0.4 mmThis is with relatively high coagulant dosages of 50 mg/L for 100 NTU, 20 mg/L for 10 NTU, and 8 mg/L for 1 NTU. We now know that with well designed plants the coagulant dose can be reduced.How much time is required to produce a 0.4 mm floc?
35 Initial Floc Growth: Phase 1 (the 50% solution) Initial growth phase of flocculation can be modeled with the equations on the previous slide (summing the collision times until the maximum floc size is reached)The end of the initial growth phase is reached when a significant fraction of the flocs reach a size that can be removed by sedimentation.Or maybe phase 1 ends when a sign
36 Observations: Collision time model The previous analysis was tracking the time required to make the first big flocsFor a highly turbid suspension it may only take a few seconds to produce visible flocsThis is why successful flocculation can be observed very early in a flocculatorThis doesn’t mean that a flocculator with a residence time of 100 s will perform wellWe need to track the colloids that are left behind!Performance is based on _______________Performance is not based on the production of big flocs!residual turbidity
37 Remember our Goal? Introduce pC* Sloppy parlance… log removal What is the target effluent turbidity for a water treatment plant?What is pC* for a water treatment plant treating 300 NTU water?
38 Tracking the residual turbidity: Phase 2 of Flocculation After the initial production of flocs at their maximum size the interaction of the colloids changeMost of the collisions are ineffective because collisions with flocs that are maximum size apparently are useless and most flocs are their maximum size
39 Flocculation Model: Integrating and tracking residual turbidity The change in colloid concentration with respect to the potential for a successful collision is proportional to the colloid concentration (the fraction of the colloids swept up is constant for a given number of collisions)Separate variablesIntegrate from initial colloid concentration to current colloid concentrationWould it make sense for design purposes to integrate from C.Colloid to C.ColloidFinal? That way the target is a final colloid concentrate as it really is in practice. The question is what would we use for the y axis with a goal of being able to plot experimental data in such a way that all of the data nicely collapses and the y axis represents progress toward an effluent turbidity goal? pCtarget=-log(Ctarget/C) so that the goal is to reach zero.Rapid growth phase produces large number of flocs at maximum size and leaves significant number of notsettleable flocs.Residual turbidity reduction phase – max size flocs are useless. Less than max size flocs continue to collide with colloids and reduce nonsettleable floc concentration.We must have a distribution of floc sizes at the end of the initial growth phase that could be predicted by statistics. We will have many big flocs, few colloids. Most colloids are colliding with flocs that are already large enough to be captured by the sed tank. Thus most collisions result in effective removal of colloids. A few collisions are between two colloids that form a floc that is still too small to be captured.Classic first order reaction with number of successful collisions replacing time
40 Laminar Flow CasesOnly colloids can collide effectively (big flocs are useless)Floc volume fraction that matters for successful collisions is the colloid (small floc) fractionColloids can attach to all flocsk has a value of approximately 0.7 (based on Karen Swetland’s data).Floc volume fraction is a function of floc size (d) (which is a function of the reaction progression and shear conditions in the reactor
41 Comparison of Flocculation Hypotheses If colloids could aggregate with all of the flocs then colloids would aggregate VERY rapidly100 NTU clay suspensionGamma of 0.1The detention time for floc formation should be at least 30 minutes (ten state standards)Ten state standards 30 minute flocculation time.The graph is laminar flow case, full scale flocculators are turbulent flow.100 NTU clay suspension, G = 0.1Show that pC* is proportional to time for “everything aggregates” model
42 Coiled Tube Flocculation Residual Turbidity Analyzer Here we plotted the residual turbidity, the turbidity of the water after settling, against the coagulant dose. We noticed that when we used a log-log plot, there was a linear trend in the data. So we explored further.Dr. Karen Swetland Dissertation research
43 Two Phase Floc Model: PACl These are the results! For a capture velocity of 0.12 mm/s the data collapses to a line with an R^2 around 0.9 for both. Keep in mind that this graph encompasses 244,000 data points…Initial floc growth
45 Solving for pC*: Lambert W or ProductLog Function (Laminar flow) Use Wolframalpha to solve for C*Get a solution from wolframalpha by entering -ln(y)/(y^(2/3))=xW is the Lambert W functionLog is base 10
46 Laminar Flow Floc Model Sedimentation velocity of ???Collisions to make first big flocs = 0.4EmpiricalFloc volume fractionFractional surface coverage of colloid by coagulantLambert W FunctionFlocculation timeSedimentation tank capture velocityVelocity gradient
47 Turbulent Flow Case Only colloids can collide and attach effectively Why are almost all of these collisions in the inertial range?Colloids can attach to all flocsCollisions are in inertial range because these are the few colloids that are left after phase 1 and thus the spacing is larger than Komogorov length scale.
48 Turbulent Flow Flocculator: “Big Flocs are useless” hypothesis After the big flocs become non reactive, then the average separation distance between the remaining flocs is larger and thus the collisions between active particles is dominated by inertia.Ten state standards 30 minute flocculation time.The predicted performance is quite similar given a wide range of influent turbiditiesThe predictions seem reasonableGamma of 0.1= 0.1 for these plotse = 2.6 mW/kg
49 Turbulent Flow Flocculator: Colloids can attach to all flocs hypothesis Here the separation distance between reactive flocs might be less than the Kolmogorov length scaleTen state standards 30 minute flocculation time.The predicted performance is quite different from what we observe. High turbidity would be very easy to treat if this hypothesis were true!Flocculators would be tiny!For this analysis I assumed that d.floc was 48 micrometers with a sedimentation velocity of 0.12 mm/s.Average energy dissipation rate average was 2.6 mW/kgConclusion is that small flocs CAN’T attach to flocs that have reached their maximum size.For these plotsG= 0.1e= 2.6 mW/kgpC* proportional to time
50 Solving for pC*: Lambert W or ProductLog (Turbulent Flow) extraSolving for pC*: Lambert W or ProductLog (Turbulent Flow)Use Wolframalpha to solve for C*Get a solution from wolframalpha by entering -ln(y)/(y^(8/9))=xW is the Lambert W functionLog is base 10
51 extraLambert W FunctionPerformance varies very little over wide range of inputs.Diminishing returns on investmentTo increase from 90% removal to 99% removal by holding all parameters constant except residence time, you would have to increase residence time by more than a factor of 10.
52 Proposed Turbulent Flocculation Sedimentation Model (missing phase 1) Lambert W FunctionFlocculation timeEnergy dissipation rateSedimentation velocity of ???Sedimentation tank capture velocity-log(fraction remaining)Characteristic colloid sizeThe term with floc time and energy dissipation rate should really be the integral of those terms over the time in the flocculator.Here eta.coag/Vcapture replaces the constants 5.6kEta.coag has a value of approximately 0.6 for the experimental conditions of Karen Swetlands dissertation.Initial floc volume fractionFractional surface coverage of colloid by coagulantGWhat does the plant operator control? ________What does the engineer control? __________𝜙0What changes with the raw water? __________
53 Turbulent Flocculation Sedimentation Model Questions Must represent a characteristic sedimentation velocity of the floc suspension. It could be the average terminal velocity of the full size flocs in the flocculator effluentIs a characteristic size of a colloid.Is a function of the characteristic size of the coagulant precipitate, geometry of the colloids, and loss of coagulant to reactor walls
54 Fractal Flocculation Conclusions It is difficult to flocculate to a low residual turbidity because the time between effective collisions increases as the number of colloids and nonsettleable flocs decreasesColloids don’t attach to full size flocsPerhaps because the surface shear on the big floc is too high for a colloid to attach (surface shear increases with diameter)If we could routinely break up full size flocs perhaps we could speed the aggregation processPerhaps related to deformability?
55 What is the model missing? The model doesn’t include any particle aggregation that occurs in the sedimentation tank. Residence time in the sed tank is long and energy dissipation rate is low. Flocculation in the sed tank (especially if there is a floc blanket) could be very important. Thus real world performance is likely better than model predictions.
56 Flocculator Collision Potential The majority of the collisions in a turbulent hydraulic flocculator are in the inertial range and the collision potential is determined by flocculator residence time, q, and energy dissipation rate, e.The collision potential is given the symbol y and has the dimension of m2/3 and this length scale will be a property of the reactor geometryThe next set of notes provides guidance for designing the geometry of a flocculator to obtain a target collision potential
57 Required Collision Potential* Agalteca, Alauca, Marcala 2 were designed to have y=100 m2/3We are currently using y=75 m2/3Atima???*The model has not been validated for turbulent hydraulic flocculator. Thus this is only a rough estimate.
58 ReviewWhy is it that doubling the residence time in a flocculator doesn’t double pC* for the flocculator?Why does increasing floc volume fraction decrease the time between collisions?Which terms in the model are determined by the flocculator design?
59 Surface coverage (G) of clay by coagulant precipitate extraSurface coverage (G) of clay by coagulant precipitateIn our modeling work we didn’t cover how to calculate what fraction of the clay surfaces are coated with coagulant. The following slides are the equation heavy derivation of that coverage. We assume coagulant precipitate has some characteristic diameter when it sticks to the clay and that the clay can be represented as a cylinder. We also assume that the coagulant sticks to everything including reactor walls. The coagulant approaches the clay surface randomly and thus accumulates in a Poisson distribution. The random bombardment means that some coagulant is wasted in double coverage of previously covered clay.
60 Floc Model Equations for G extraFloc Model Equations for GSurface area of clay divided by total surface area of clay + reactor wallsSurface area to volume ratio for clay normalized by surface area to volume ratio for a sphere
61 extraRatio of clay surface area to total surface area (including reactor walls)
62 extraPoisson distribution and coagulant loss to walls combined to get surface coverageThe surface coverage is reduced due to stacking (which is handled by the Poisson distribution) and by the loss of coagulant to the reactor walls.loss of coagulant to the reactor walls
63 Clay platelet geometry extraClay platelet geometryModel clay as cylinder with height and diameterD.Clay is the diameter of a sphere with equal volume as the clay plateletD.ClayPlatelet is the diameter of a cylinder given ratio of height to diameter and equal volume spherical diameter
65 Surface coverage of clay extraSurface coverage of clayIf you neglect wall loses
66 Solving for Coagulant Dose extraSolving for Coagulant DoseCoagulant dose is inside coagulant volume fractionSolve for dose…Given a target residual turbidity, solve for required G, then solve for coagulant dose
67 Loss of clay to reactor walls extraLoss of clay to reactor wallsFractalFlocModel.xmcd (Mathcad 15 files)Loss of coagulant to reactor walls can dominate for low turbidities and small reactors. For the LFSRSF in India treating 5 NTU water and injecting coagulant into 7.5 cm pipes the clay only gets 23% of the applied coagulant!There may be a way to design a larger contact chamber for the coagulant to reduce losses to the walls.
68 extraEffect of stacking and wall loss in a 10 cm diameter flocculator with 20 NTUStacking due to random bombardment of the clay surface with coagulant nanoglobs. Stacking becomes significant for high surface coverage. Wall losses also cause a significant reduction in clay surface coverage.