Filtration IntroductionFiltration is an ancient technology for cleaning waterSand and gravel filters used in India as early as 2000 BCRomans dug channels next to lakes to use natural filtrationFrench began commercializing filtration around 1750 on small scaleFiltration for municipal supply systems began in England and Scotland around 1800First modern slow sand filtration system in London in 1829 Rapid filtration began in US in 1880s First municipal plant with coagulation and filtration in Somerville, NJ, in 1885Surface Water Treatment Rule 1989-first regulation requiring widespread filtration through USComparison of filter media with suspended sedimentFilter mediaIn uniform medium of spherical particles of diameter d, a particle of diameter 0.15 d will pass through pores.Engineered filter media strain particles no smaller than 30 to 80 m depending on media type.Sand 800 mAll media 400-1500 md0.15dSize of suspended matterSoil 1-100 mCryptosporidium oocysts 5 mBacteria 0.3-3 mViruses 0.005-0.01 mFloc particles 100-2000 mVisible particles 30 mTypes of granular mediaSlow sand filters: old form of filtersTreatment by physical straining and biological degradation.Clean by scraping top layer every few weeks or monthsFine sand loaded at low rates 0.05-0.2m/hrSimple operation, no chemicalsUsed rarely for municipal-scale plants50 slow sand systems out of 50,000 water systems in US.Usually used for small systems where simple operation is advantageous.效果：浊度可降效果：浊度可降到到0 0，可不消毒。，可不消毒。Types of granular mediaRapid filtrationTypes of granular mediaRapid filtrationMedia are coarser, more uniform (often multiple)Removal is not by physical straining on surface as primary mechanismMuch higher loading rates than slow sand filters 100X typically 5-15m/hrMuch more common in U.S. Replaced slow sand filters in 20th centuryConceptually, rapid filtration is like sedimentationParticles need pre-treatment with a coagulant to destabilize electrical chargeDestabilized particles adhere to grains in filter medium and are removedHeadloss in filter increases with time as filter clogs and gets lower hydraulic conductivity.Depth filtration- removal through entire depth of bed occursTurbidity of outflow changes with timeFilter OperationRapid filtrationHeadloss tB or tHL indicates time to end the filter run.Turbidity Time Ripening Ripening 15-15-120min120minEffective filtering 1-4 daysEffective filtering 1-4 days0.1 NTU0.1 NTUBreak-throughBreak-throught tB BAt the end of filter run, filter is backwashed. Strong flow sent back through porous medium, mobilizing grains, and washing solids off of medium.Time t tHLHLRapid filters may be:Multi-mediaDual mediaSingle media Granular media are sieved and washed to make a more uniform grain size distributionMeasured by Uniformity CoefficientEffective size, ES=d10= grain size diameter at which 10% of the media by weight are smaller(usually sand)(usually sand and anthracite i.e. hard coal)(usually sand, anthracite and garnet)Rapid filtrationOther filters:Precoat filtersPressure filtersSimilar to rapid filter, but in closed vessel under high pressureDiatomaceous earth formed as cake on a filter screen or porous plateContinuous feed of diatomaceous earth renews filter surface, prevents clogging.Hydraulics of flow through granular media Head loss through clean granular filters1. Darcy flow or creeping flowReRe 1 12. Forchheimer flow1 Re 1003. Transition flow100 Re 6008004. Fully turbulentRe 600800These flow regimes not These flow regimes not encountered in filtration.encountered in filtration.Four flow regimesk- hydraulic conductivity, L/TViscousflowgovernedbyDarcyslawhL- headloss across filter, LL- depth of granular media, LHigh rate rapid filtration may be Forchheimer flowLaminarflowinfluencedbybothviscousandinertialforcesHeadloss given byInertial forces arise as fluid accelerates and decelerates in twists, turns, expansions, and contractions of media void space.Backwashing 3 Re 25Ergun (1952)Range of Reynolds number for granular filtration technology0.010.1110100Design filtration rate, m/h 0.0010.010.1110Media grain effective size, mmSlow sand filtration0.030.10.51.05.0Re=25Backwashing Typical rapid filtration High-rate rapid filtration Practical considerations for calculation of clean bed head lossRecommended parameters for equation aboveBasedonpastexperience,ithasbeenfoundthatequationbasedontheForchheimerflowregimecanbeusedtodeterminethecleanbedheadlossoverthefullrangeofvaluesofinterestinrapidfiltration.Medium kVkI , %Sand 110-1152.0-2.540-43Anthracite 210-2453.5-5.347-52Example: Clean-bed head lossCalculate the clean-bed head loss through a deep-bed dual-media filter with 1.5m of anthracite with ES=1.1 mm over 0.3 m sand with ES=0.5 mm at a filtration rate of 15 m/h and a temperature of 15 C.Head loss through two layers of media are additive. The head loss through the anthracite will be calculated using 1. No pilot or site specific information is given, so midpoint values are selected: kV=228, kI=4.4, and =0.50. Values of W =999kg/m3 and =1.14 10-3 kg/m s.2. Calculate the first term in hL:3. Calculate the second term in hL:4. Add the two terms together:Example: Clean-bed head lossCalculate the clean-bed head loss through a deep-bed dual-media filter with 1.5m of anthracite with ES=1.1 mm over 0.3 m sand with ES=0.5 mm at a filtration rate of 15 m/h and a temperature of 15 C.4. Add the two terms together:5. Repeating the calculations for sand using kV=112, kI=2.2, and =0.42 yields6. The total head loss through the filter is the sum of the head loss through the two media:Comments:Arelativelysmallcontributiontoheadlosscomesfromtheinertialterm.Nevertheless,theinertialtermbecomesmoreimportantforthelargermediaandhighervelocitiesusedinhigh-raterapidfilters.Backwash Hydraulicslog (- P)log ReRelationship of the pressure drop across packed bed and velocityABCDEABThe bed is stable, the pressure drop and Reynolds number Re are related linearly.BCThe bed is unstable, the particles adjust their position to present as little resistance to flow as possible.CDThe particles move freely but collide frequently so that the motion is similar to that of particles in hindered settling.DEBy the time point D is reached, the particles are all in motion, and beyond this point, increases in Re result in little increase in P.To expend a filter bed composed of a uniform filter medium hydraulically, the headloss must equal the buoyant mass of the granular medium in the fluid.Backwash HydraulicsForces on particlesFDFGDownward ForcesUpward (drag) ForcesExample: Force on suspended particleA filter is backwashed at 40m/h at 15 C. Determine whether a 0.1 mm particle of sand will be washed from the filter.1. Calculate the gravitational force on the particle:2. Calculate the Reynolds number3. Reynolds number less than 2, thenThe particle will be flushed away with the backwash water.4. Compare the forces:Backwash HydraulicsBed expansion and porosityThe relationship between bed expansion and porosityLE=depth of expanded bed, mLF=depth of fixed bed, m F=porosity of fixed bed, m E=porosity of expanded bed, mHead loss through a fluidized bed is calculated as the gravitational force of the entire bed.a=cross sectional area of filter bed, m2Convert the force into head lossMake use of ReExample: backwash flow rate for bed expansionFind the backwash flow rate that will expand an anthracite bed by 30 percent given the following information: LF=2m, d=1.3mm, P=1700 kg/m3, =0.52, and T=15 C. 1. Calculate LE that corresponds to a 30% expansion:2. Calculate E3. Calculate 4. Calculate Re, by using kV=228, kI=4.4 Backwash HydraulicsBed expansion and porosityAlternatively, it is frequently necessary to determine the bed expansion that occurs for a specific backwash rate. X=backwash calculation factorThe factors X and Y are defined as:Y=backwash calculation factorExample: Filter bed expansion during backwashFind the expanded bed depth of a sand filter at a backwash rate of 40 m/h given the following information: LF=0.9m, d=0.5 mm, P=2650 kg/m3, and T=15 C. 1. Calculate X by using kV=112, kI=2.25 :2. Calculate Y3. Calculate porosity4. Calculate the expanded bed depth by assuming F=0.42 5. Calculate the percent expansion of the bedParticle Removal in Rapid FiltrationFundamental aspects Straining is not important removal mechanismd0.15d Particles adhere to media grains and are removed Each grain is a collector Water must be pre-treated to destabilize negatively-charged particlesInrapidfiltration,particlesareremovedcontinuously through the filter. Particle removalwithin afilterhasbeenexperimentally observedtobedependentontheconcentrationofparticles,similartoafirst-orderequation:0Lc0cEDepth in filterParticle concentration, mg/LFiltration Models1. Fundamental model2. Phenomenological modelFiltrationmodels(microscopic)(macroscopic)Examine the actual transport and attachment mechanisms and can be useful to evaluating the relative importance of various design and operating parameters.Explain the physical progression of the filtration cycle to predict filter performance.Becauseofthecomplexityoffiltrationmechanismsandthewidevariationinsourcewaterproperties,neithertypeofmodelcanpredictfilterperformancewithoutsite-specificpilotstudies;nevertheless,theyprovideinsightandunderstandingintothefiltrationprocess.Fundamental depth filtration theoryFundamental filtration theory examines the relative importance of mechanisms that cause particles to contact media grains, which can be related to measurements of the properties of the media and suspension.(1) The models are based on an idealizedsystem in which spherical particles colloidwithsphericalfiltergrainsFundamental filtration models are not effective for predicting long-term filter performance in actual full-scale systems for the following reasons:(2)Thehydrodynamicvariabilityandeffectof streamlines introduced by the use ofangularmediaarenotaddressed(3)Themodelspredictasinglevalueofthefiltrationcoefficient,whichdoesnotchangeas a function of either time or depth,whereasinrealfiltersthefiltrationcoefficient changes both with time anddepthassolidscollectonthemedia(4)Themodelsassumenochangeingraindimensions or bed porosity as particlesaccumulate.DISADVANTAGESADVANTAGESFundamental filtration models are valuable to a student acquiring an understanding of the filtration process.They are useful for evaluating the relative importance of various filtration mechanisms.They can also be used to examine the relative impact of varying other parameters on filter performance, such as porosity, filtration rate, or temperature.The basic model for water treatment applications as presented by Yao et al. (1971)Yao, K.-M., M. T. Habibian, and C. R. OMelia. Water and Waste Water Filtration: Conceptsand Applications. Environmental Science & Technology 5, no. 11 (November 1971): 1105-1112.Transport efficiency:Efficiency of particle collection depends on:For isolated single collectorvf= filtration velocity (Q/Ap)Flow streamlineCollector grainSedimentation- particle derives from streamlineBrownian transportInterception Particle following streamline collides with collectorAttachment efficiency:Mass flow approaching collectorC= particle concentrationdc= collector particle diameterMass capture by single collector isYao Filtration ModelAs z0L= bed thicknessFor filter as a whole, need to consider number of collectors:Number of collectors= = bed porosity z= unit thickness of bedParticle mass balance over z in bed:Mass removed =mass in mass outFunction: -Chemistry (pretreatment with coagulation)L/dc-design parameter for bedn-bed porosity -single collector efficiencyYao Filtration ModelLC0Q zCzCz+ zArea, azCEYao et. al., 1971kB= Boltzmanns constantModels for :Note:interceptiongravityDiffusion (Brownian motion)dp= particle diameterT= absolute temperatureTransport efficiency in Yao Filtration ModelYao model predict that the lowest removal efficiency occurs for particles of about 1 to 2 mAttachment efficiency in Yao Filtration ModelThe attachment mechanism may involve van der Waals forces, surface chemical interactions, electrostatic forces, hydration, hydrophobic interactions, or steric interactions.The most important factor in achieving high attachment efficiency is proper destabilization of particle by coagulation.Laboratory studies have found values of attachment efficiency ranging from 0.004 to 1.0.Rajagopalan and Tien modelSeveral researchers have tried to refine the Yao model by using a different flow regime or incorporating addition transport mechanisms.The semi-empirical expression for the transport efficiencyAs= porosity function, dimensionlessThe Rajagopalan and Tien filtration model correlates to experimental data better than other fundamental filtration models and is currently considered to be the most accurate.NLO= London function, dimensionlessNR= relative-size group, dimensionlessNG= G, dimensionless = porosity function, dimensionlessHa= Hanmarker constant, JExample: application of Rajagopalan and Tien modelUse the TR model to examine the effect of media diameter (ranging from 0.4 to 2 mm in diameter) on the removal of 0.1- m particles in a filter bed of monodisperse media under the following conditions: porosity =0.48, attachment efficiency =1.0, T=20 C, P=1050 kg/m3, filtration rate v=10 m/h, bed depth L=1.0m, Hamarker constant Ha=10-20 J (10-20 kg m2/s2), and Boltzmann constant kB=1.381 10-23 J/k (1.381 10-23 kg m2/s2 K).1. Calculate :2. Calculate As:3. Calculate NG:4. Calculate NLo:Example: application of Rajagopalan and Tien modelUse the TR model to examine the effect of media diameter (ranging from 0.4 to 2 mm in diameter) on the removal of 0.1- m particles in a filter bed of monodisperse media under the following conditions: porosity =0.48, attachment efficiency =1.0, T=20 C, P=1050 kg/m3, filtration rate v=10 m/h, bed depth L=1.0m, Hamarker constant Ha=10-20 J (10-20 kg m2/s2), and Boltzmann constant kB=1.381 10-23 J/k (1.381 10-23 kg m2/s2 K).5. Calculate Pe for a media diameter of 0.4mm using6. Calculate NR for a media diameter of 0.4mm,7. Calculate ,Example: application of Rajagopalan and Tien modelUse the TR model to examine the effect of media diameter (ranging from 0.4 to 2 mm in diameter) on the removal of 0.1- m particles in a filter bed of monodisperse media under the following conditions: porosity =0.48, attachment efficiency =1.0, T=20 C, P=1050 kg/m3, filtration rate v=10 m/h, bed depth L=1.0m, Hamarker constant Ha=10-20 J (10-20 kg m2/s2), and Boltzmann constant kB=1.381 10-23 J/k (1.381 10-23 kg m2/s2 K).8. Calculate C/C09. Set up a computation table to determine particle removal for other diameter. The results are as follows:Media diameter (mm)C/C0Log removal0.40.003932.400.60.0601.220.80.1750.761.00.3010.521.20.4120.381.40.5040.301.60.5780.241.80.6370.202.00.6850.16Phenomenological depth filtration modelsThe primary function of phenomenological filtration model is to explore the progression of a filter run and the change in performance as solids collect within the filter.ADVANTAGESA solution of phenomenological model allows the particle concentration at any depth in the filter bed as well as the effluent concentration to be calculated at any point in time.Unfortunately, phenomenological model equations are complex and not easily solved. DISADVANTAGESPhenomenological model developmentThe mathematical formulation of phenomenological filtration model is based on the same overall mass balance through the filter bed. Phenomenological models do not focus on the accumulation of particle on a single collector but instead consider the increase of mass in within the differential element. Assumptions:(1) Although particles are present in the interstitial fluid and the surface of the media, the accumulation of particles in the interstitial fluid is negligible compared to the accumulation of particles on the media;(2) The number of particles entering and exiting the element by diffusion is negligible;(3) The generation or loss of particles due to reaction is ignored.Mass balance equation: = specific deposit, mass of accumulated particles per liter bed volume, mg/LAsnotedearlier,filterperformancechangesasafunctionof time as solids collect in the filter bed. Thus, thefiltrationcoefficientisnormallyexpressedasafunctionofspecificdeposit.Forinstance,filterefficiencyimprovesasafilterripens.Ripeningcanbeviewedasaconditionthat increases the filtration coefficient as solids arecollectedinthefilter.Phenomenological model developmentRelationship between and kT = breakthrough rate constant, L2/mg2 mRipening can be viewed as a conditionthatincreasesthefiltrationcoefficientassolidsarecollectedinthefilter.The value of the filtration coefficientmust be calculated as a function ofdepth because solids do not collectuniformly throughout the entire depthofthefilter.Breakthrough is a decrease of the filtrationcoefficientthatcausesanincreaseineffluentturbidity.A filtration coefficient that initially increase(ripening)andeventuallydecreasestozero(breakthrough)canbeexpressedin 0 = initial porosityDevelopment of a phenomenological model involves the simultaneous solution of the twoequationsbelow,undertheconditionswhere isafunctionof ,whichinturnvarieswithspaceandtime. issitespecificbecauseofvariationsinlocalwaterquality,characteristicsofparticulatematter,media characteristics, stratification, and operating parameters. Thus the solution of thephenomenologicalmodelsisquitecomplex.Steady-state phenomenological modelThe specific deposit can be determined byperforming a mass balance over the entirebed:Simplifying Assumptions:(1) The specific deposit is averaged over the entire filter bed;(2) Solids accumulate at a steady rate over the entire filter run ;(3) Headloss increases at a constant rate.Massaccumulation=massfluxinmassfluxout t= specific deposit at time t, mg/LDividingbythefilterbedareaandrearrangingL= filter bed depth, mThevalueofthespecificdepositatbreakthrough:Thus:Similarly, the rate of headloss buildup hasbeen observed to depend on the rate ofsolidsdepositioninafilter.hL, t= filter head loss at time t, mhL, 0= initial clean bed head loss, mkHL= headloss increase constant, L m/mgThespecificdepositatatimeoflimitingheadHTThetimeoflimitinghead,tHLExample: Determination of run length from pilot dataA pilot study was conducted involving the operation of several pilot filter columns with various media size, depths, and filtration rates. The columns were run until breakthrough occurred; data were collected for C0, CE, tB, hL,o, and hL for each experiment; and B and kHL were calculated for each experiment. A multivariate regression analysis of the data revealed that B and kHL were described by the equations: 1. Calculate B using Eq. 1The proposed design for the full-scale filter is vF=15m/h, ES=1.1mm, L=1.5m, and HT=2.0m. The expected influent and effluent particle concentrations are 2.2 and 0.035mg/L, respectively. Determine the length of the filter run and whether the filter run will be determined by breakthrough or head loss.(1)(2)2. Calculate tB 3. Calculate kHL using Eq. 2Example: Determination of run length from pilot dataA pilot study was conducted involving the operation of several pilot filter columns with various media size, depths, and filtration rates. The columns were run until breakthrough occurred; data were collected for C0, CE, tB, hL,o, and hL for each experiment; and B and kHL were calculated for each experiment. A multivariate regression analysis of the data revealed that B and kHL were described by the equations: 4. Calculate the clean bed head lossThe proposed design for the full-scale filter is vF=15m/h, ES=1.1mm, L=1.5m, and HT=2.0m. The expected influent and effluent particle concentrations are 2.2 and 0.035mg/L, respectively. Determine the length of the filter run and whether the filter run will be determined by breakthrough or head loss.(1)(2)5. Calculate tHL6. Compare tB to tHL tB =28.2h tHL =32.7h Thefilterrunwillbelimitedbybreakthroughandtherunlengthwillbe28.2h