Turbulent rapid mixing in direct filtration by Scott Lee Trusler A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Montana State University © Copyright by Scott Lee Trusler (1983) Abstract: The fundamental physical processes which occur in the initial mixing step of coagulation are not fully understood at this time. This work focuses on initial mixing within a direct filtration treatment scheme, in order to gain some insight into the nature of the mixing process. A direct filtration pilot plant incorporating a variable speed, baffled tank mixer was operated with various mixing intensities during the investigation. Filtrate quality and filter head-loss data from the pilot plant were used to establish the effectiveness of a given mixing condition. Also, mixing within a hydraulic jump was similarly investigated in order to compare hydraulic mixing to mechanical (stirred baffled tank or backmix reactor) mixing. An idealized mixing model, which was based on the interaction of the coagulant carrying turbulent microscales with colloid particles, was proposed. The results of the pilot plant studies indicate that a colloid-microscale size correlation similar to the correlation proposed by the mixing model may exist. Also, a method_was proposed for calculating the mean velocity gradient (G-value) of a hydraulic jump occurring on a sloping channel. The usefulness of this calculation method was confirmed in this study. Finally, the pilot plant data collected during this investigation indicated that the hydraulic jump was comparable to the baffled tank for initial rapid mixing (based on similar velocity gradients). However, the inflexibility of the hydraulic jump, in regard to variable degrees of mixing, was also evident. TURBULENT RAPID MIXING IN DIRECT FILTRATION by Scott Lee Trusler A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science - in Civil Engineering MONTANA STATE UNIVERSITY Bo ze ma n, Montana May 1983 MAIN LIB. N 3*7% T fPtI (0 6op. Si APPROVAL of a thesis submitted by Scott Lee Trusler This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding c o n t e n t , English usage, f or ma t, citat io ns , bibliographic s t y l e , and consistency, and is ready for submission to the college of Graduate Studies. ________________ ^ __________ __ Chairperson, Graduate Committee Date Approved for the Major Department 1 A£ Head, Date^ ___________ Major Department Approved for the College of Graduate Studies ~Z Date Wt'Z Graduate Dean iii STATEMENT OF PERMISSION TO USE In presenting the requirements this for Un i v e r s i t y , I agree able' to borrowers quotations from a thesis master's that under this permission, provided in partial degree the Library the thesis that rules are at shall of the allowable accurate fulfillment Montana make of State it avail­ Library. without Brief special acknowledgment of the source is made. Permission for extensive quotation from or reproduction of this thesis may be granted by my major professor, or in his absence, by the director of Libraries when, in the opinion of either, the proposed use of the material is for scholarly purposes. Any copying or use of the material in this thesis for financial permission. S ignature gain shall not be allowed without my written iv ACKNOWLEDGEMENTS I wish to express my appreciation to Dr. A. Amirtharajah for his guidance, assistance and encouragement.,' throughout this investigation. Also, I wish to thank Mary Mullen, for her assistance during the collection of data, Mrs. Bonnie Recktenwald, who typed this thesis and my family, for their encouragement. F i n a l l y , I am grateful for the support provided by the Engineering Experiment and the National Station Science Project, grant No. at Montana State University Foundation/State of Montana MONTS ISP-8011449. I V TABLE OF CONTENTS Page LIST OF FIGURES . ................... LIST OF T A B L E S ......... .. NOMENCLATURE ABSTRACT vii . ............ .. . ... ix ............................. X ...................... . . . . ' ........... xii. 1. I N T R O D U C T I O N ...................... ................ I 2. OBJECTIVES . . . . . 3 3. PREVIOUS RELATED STUDIES ......................... 4 .............................. Turbulent Initial Mixing ....................... Mixing in baffled tanks 4 ................ Mixing in hydraulic jumps ......... 5 . . . . 8 Mixing in Water Treatment ................ 10 Initial mixing studies ............. 10 Turbulent flocculation Filtration Analysis . . . . . .......... 13 ......... 14 ............................ 16 . . . . . . . . 4. IDEALIZED MIXING MODEL 5. EXPERIMENTAL W O R K ......................... . . . . . Plan .................. 22 Direct Filtration Pilot Plant Baffled tank reactor 22 ................ 22 . . . . . . . . . . . ^ " ................ 27 - Details of flume Dual media f i l t e r .................. .. .\ . 29 31 V . vi TABLE OF CONTENTS— Continued Page Filter Performance Data ....................... 34 Dye Trace S t u d i e s ...................... 6. RESULTS AND DISCUSSION ............................ Calculated Mixing Parameters Velocity gradients 38 . . ..................... 38 .................. 40 ........... 44 Filter response to baffled tank mixing . . Filtrability numbers for baffled tank mixing .................. Hydraulic Mixer Comparisons 44 52 Electrophoretic Mobility D a t a ........... .. 7. 38 .................. Hydraulic residence times Filtration Results 37 . ................... C O N C L U S I O N S ........... 56 5.7 63 ■ R E F E R E N C E S .................................. APPENDIX - Sample Calculations ......... 65 . . . . 68 vi i LIST OF FIGURES Page 1. Power Dissipation Zones in a Stirred Tank * ......... (Cutter [5] ) ................ .. 7 Design and Operation Diagram for Alum T r e a t m e n t ....................................... 12 Idealized Colloid-Microscale Interaction Visualization ............... 17 Schematic Diagram-of Direct Filtration Pilot Plant ..................................... 23 5. Size Distributions for Turbidity Particles 26 6. Details of Baffled Tank Reactor and DiscTurbine I m p e l l e r .............................. 28 7. Details of Hydraulic Jump F l u m e ......... .. 30 8. Details of Dual Media F i l t e r .................... 32 9. Residence Time Distributions for the Baffled Tank R e a c t o r ......................... 41 Residence Time Distributions for Two Hydraulic J u m p s ............. ................... 43 Typical Filter Data for Baffled Tank Mixing with Alum Treatment ■ ’ (n = 700 R P M ) ................... . ............ .. 45 Typical Filter Data for Hydraulic Jump Mixing with Ferric Chloride Treatment (Slope = 2.0 in/ft) ................ .. 46 2. 3. 4. 10. 11. 12. 13. 14. . . . ... . . . . Rate of Headless and Average Effluent Turbidity for Baffled Tank Mixing with Alum Treatment .............. 48 Rate of Headloss and Effluent Turbidity. for Baffled Tank Mixing with Ferric Chloride Treatment ............ . . . . . . . 49 viii LIST OF FIGURES— Continued Page 15. .16. 17. 18. 19. 20. 21. 22. Rates of Headless and Average Effluent Turbidity for Baffled Tank Mixing with Ferric Chloride Treatment. .............. 51 Filtrability Numbers for Baffled Tank Mixing with Alum T r e a t m e n t .................. . 53 Filtrability Numbers for Baffled Tank Mixing with Ferric Chloride Treatment ;. . . . 54 Filtrability Numbers for Baffled Tank Mixing with Ferric Chloride Treatment . . . . 55 Rates of Headless for Hydraulic Jump and Open Channel Mixing with Ferric Chloride Treatment ......................... * 59 Average Effluent Turbidities for Hydraulic Jump and Open Channel Mixing with Ferric Chloride Treatment .................... 61 Filtrabiiity Numbers for Hydraulic Jumji and Open Channel Mixing with Ferric Chloride Treatment .............. ........... 62 Hydraulic Jump Length, L, for Jumps in Sloping C h a n n e l s ..............^............... 70 ix LIST OF TABLES < 1. Page Water Analysis of Feed Water for Direct Filtration Pilot Plant ....................... ........... 2. Size Characteristics of Filter Media 3. List of Pilot Plant Runs Including Coagulant Dosages and pH Conditions 4. 5. 33 ......... Calculated Velocity Gradients for Baffled Tank Mixer ................................ .. 24 .36 . 39 Calculated Velocity Gradients for Hydraulic Mixers . * .................................... 40 6,. Mean Hydraulic Residence Times for Baffled ..................................... Tank Mixer 42 7. Electrophoretic Mobility Data for Treatment of M30 and SB325 Colloids . . . . . . . . 58 X NOMENCLATURE C Average effluent turbidity - TU Co Filter influent turbidity - TU Eiji Channel flow energy - ft F Filtrability number Fl Upstream Froude number for hydraulic jump G Average velocity gradient - s~l Hip . Total filter headless at time T - in No Number; of particle collisions N Number of colloid-microscale ■P interactions Average power dissipated - ft*Ib/s Po Power number 0 Flow rate - cfs Re Impeller Reynolds number T Filter run length - hr V Power dissipation volume - ft^ Vr Filtration rate - in/hr aI Colloid diameter d Impeller diameter - ft; Water depth in flume-ft g Acceleration of gravity - ft/s^ n Impeller speed - rev./s n I , n2 Colloid number counts ri r r2 Colloid radii - xi NOMENCLATURE— Continued t Theoretical mixing time - V/0 - s u, v, w Respective velocity components X, y, z Respective coordinate directions Y2 Water depth downstream of jump - ft z Channel elevation - ft n Microscale E Power dissipation per unit mass. - ft^/s^ Y Specific weight of water - Ib/ft^ y Fluid viscosity - l b •s/ft^ V Fluid kinematic viscosity - ft^/s P Fluid density - slugs/ft3 B Flume slope angle S xi i ABSTRACT The fundamental physical processes which occur in the initial mixing step of coagulation are not fully understood at this time. This, work focuses on initial mixing within a direct filtration treatment scheme, in order to gain some insight into the nature of the mixing p r o c e s s . A direct filtration pilot plant incorporating a variable speed, baf­ fled tank mixer was operated with various mixing intensities during the investigation. Filtrate quality and filter headloss data from the pilot plant were used to establish the effectiveness of a given mixing condition. . Also, mixing within a hydraulic jump was similarly investigated in order to compare hydraulic mixing to mechanical (stirred baffled tank or backmix reactor) mixing. An idealized mixing model, which was based on the in­ teraction of the coagulant carrying turbulent microscales with colloid particles, was proposed. The results of the pilot plant studies . indicate that a colloid-microscale size correlation similar to the correlation proposed by the mixing model may e x i s t . Also, a method_was proposed for calculating the mean velocity gradient (G-value) of a hydraulic jump occurring on a sloping channel. The usefulness of this calculation method was confirmed in this study. Finally, the pilot plant data, collected during this investigation indicated that the hydraulic jump was compar­ able to the baffled tank for initial rapid mixing (based on similar velocity gradients). However, the inflexibility of the hydraulic jump, in regard to variable degrees of mix­ ing, was also evident. I CHAPTER I INTRODUCTION In this day and a g e , the treatment of water to provide a potable supply for consumers has developed faceted science incorporating and fluid dynamics. certain processes Within and ideas from chemistry, physics the overall treatment p i c tu re , treatment methods have received con­ siderable attention over the past d e c a d e . which is filtration into a multi­ not preceded by Direct filtration, sedimentation, is one treatment scheme where attention has been focused. Another aspect which has received considerable attention is that of chemical reactions within agitated vessels. the role of the mixing intensity In particular, itself within the overall chemical process is of considerable interest. In addition a b o v e , turbulent at te nt io n. ing in studied. jump is The water A to the hydraulic usefulness treatment rational important hydraulic jump leads to high agitated mixing mixing of has, design for reliability. has mixing also mentioned received some the hydraulic jump for mix­ however, not been recently procedure for the several is vessel reasons. operationally Also, hydraulic First of simplistic hydraulic mixers all, which usually require less total power input than mechanical mixers which 2 further enhance their operational attractiveness. son for the lower power requirements The rea­ are two fo l d . First, the power dissipation volumes for hydraulic mixers are usu­ ally much smaller than the Secondly, hydraulic mixers volumes lack for mechanical the frictional cies common to motor driven mixers. hydraulic mixing has its, share primary disadvantage with mixers. inefficien­ There is no doubt that of drawbacks the hydraulic as well. jump being the The in­ ability to change, the mixing intensity to accomodate varia­ tions in the influent %ater quality. The present study focused on initial mixing direct filtration treatment scheme. red baffled tank) and were investigated. on the need mixing step will, no for of doubt, The a hydraulic importance better lead Both mechanical (hydraulic to more jump) (stir­ mixing of this study was based understanding coagulation. within a This of better efficient use the initial understanding of employed in water treatment mixing operations. the energy 3 CHAPTER 2 OBJECTIVES The overall objective of this study was to investigate the initial mixing step of coagulation and to gain some in­ sight into the fundamental nature of the mixing process. The following were the specific objectives: 1. To study the initial mixing stirred baffled the role of tank mixing step reactor intensity charge neutralization using in in of coagulation order to in a determine destabilization a direct by filtration pilot plant. 2. To attempt to relate the results of the mixing study to the microscale of turbulence. 3. To propose a methodology for design of hydraulic jump mixers. 4. To compare (backmix) hydraulic jump reactor mixing. mixing with baffled tank 4 CHAPTER 3 PREVIOUS RELATED STUDIES The theoretical studies which are related to this work can be divided into three categories. First ,, there is the material which deals with turbulence and mixing in general. Second, are the studies which have focused on mixing in the water treatment field. studies are of Both flocculation and initial mixing importance here. Finally, some aspects re­ garding filtration analysis will be presented. TURBULENT INITIAL MIXING As defined by Hinze [1] , turbulence is a flow condition characterized by irregular motion in which various parameters vary in time and space. the random variations, obtainable. The Hinze also points out that within statistically distinct averages are concepts underlying turbulence, such as fluctuating velocities and turbulent intensities, are fully z-' . developed in the literature [I, 2] and will not be discussed here. Of more concern to the present study, are the funda­ mentals of energy dissipation, within a turbulent flow. In any given turbulent flow it can be shown that regions of high velocity approximation, correlation these regions exist. where In all a the somewhat fluid rough exhibits 5 a similar velocity can he interpreted as eddies or vo rt i c e s . Kolmogorof £ [3,4] from an eddy or tegral length was the length scale first scale and to rationalize viewpoint a microscale. turbulence by defining The an integral in­ scale is related to large eddies which carry energy and the micro­ scale is the eddy size at which energy dissipation by viscous friction b e g i n s . Kolmogoroff noted that these small eddies (microscale) would have to be in a state of equilibrium and their size would be a function of the energy the fluid viscosity. By dimensional analysis input and Kolmogoroff quantified the microscale as (I) n = where H is the microscale, V the fluid and Since mixing is the kinematic viscosity of e is the power dissipated per unit mass. is usually power dissipation, it interpreted as being a function of is the turbulent microscale which is of particular importance here. Mixing in Baffled Tanks Several ideas in regard to mixing in baffled tanks are important to this investigation. of Cutter [5] which dissipation within distinct regions a of First'there are the results illustrate the baffled tank. power nonuniformity dissipation Cutter to of power found exist three within a 6 baffled tank. He impeller stream trates the labeled zone three and zones tion within each zone, the regions the bulk and the as the tip zone. Figure zone, I the illus­ approximate power dissipa­ in relation to the mean dissipation. More recently, O k a m o t o , Nishikawa and Hashimoto [6] have con­ firmed the existence of the impeller stream and bulk zones of a baffled tank as described by Cutter. Long before Cutter's work. Camp and Stein [7] formulated the velocity g r ad i en t, or G —v a l u e , as a design parameter for determining the Stein utilized power requirements laminar fluid shear of a mixer. concepts Camp and to derive the velocity gradient as G = 0.5 (2 ) where G is the average velocity gradient, P is the power dis­ sipated within volume V and U is the fluid viscosity. Camp and Stein also generalized the velocity gradient expression for turbulent flows by defining the root mean square (RMS) velocity gradient as G 3v. 2 + 3x' (3) where u, v and w are the velocities in the x, y and z direc­ tions respectively. Equation (2) thus represents an average value within a turbulent field. ZONE OF MAXIMUM TURBULENCE IMPELLER ZONE TOTAL VOLUME = V= V, ♦ V3 AVERAGE POWER DISSIPATION = P FIGURE I. Pm3 ^ ° - 25P V3 ^ ° - 9V Power Dissipation Zones in a Stirred Tank (Cutter [5]). 8 Another parameter which is important in tank mixing is the dimensionless power number, P 0 . explain the power number concept Leentvaar and Ywema [8] in detail and show the quantified expression as — — I —3 “5 P = Pp n d o (4) where P is again the average power dissipated, p is the den­ sity of the fluid, impeller diameter. tion, the power n is the impeller speed and d is the For a given reactor^impeller configura­ number remains constant beyond a certain Reynolds number Re (^ssIO4 for cylindrical baffled tanks) where (5) R e- and all symbols are as previously defined. power number of a given reactor T h u s , once the is known, power inputs and corresponding G-values can be computed for various impellers and rotation speeds. Mixing in Hydraulic Jumps At p r e s e n t , mixing in hydraulic jumps is somewhat less well defined than mixing in baffled tanks. all the tionale. tools necessary to formulate Chow [9] presents a possible design ra­ The hydraulic jump can be defined as the mechanism by which an open channel flow transforms from supercritical 9 to subcritical of the jump the power flow.. Looking from, a G-value dissipated at the mixing capabilities s t a n dp oi nt , necessitates within a specific volume be that related to the jump chara ct eri st ics . Power dissipation in a hydraulic jump is actually well understood and the mechanism is undoubtedly Theory pertaining to energy losses in a jump detail by steep Chow for both mild and turbulence. is derived channels. in Actual energy losses are easily computed from water depth measure­ ments in the vicinity of the j u m p , since 2 E = z T where E? is the total + dCosG + — (6) 2g flow energy, z is the channel eleva­ tion, d is the water d e p t h , .6 is the slope angle, v is the flow velocity and g is the acceleration due to g r a v i t y . Thus, by computing E t upstream and downstream of the jump, the loss of energy in the jump can be estimated. Then utilizing the expression for power ''-P = YQ(AEt ) where (7) y is the specific weight of water, and 0 is the flow rate and Et is power dissipated The volume most likely the in in related energy the which to lost in. the jump, P the the power is ju m p , the determined dissipation characteristic r average as well. occurs jump is length. 10 Chow illustrates that the the available flow energy nel slope) jump ■ length L is a function'of (upstream Froude number and chan­ and presents empirical data which can be used to estimate the length of a jump which occurs in a sloping chan­ nel. The actual power dissipation occur in the fluid volume can then be in the jump contained assumed to length L . Since the power and dissipation volume are k n o w n , a G-value for the jump can be com put ed . MIXING IN WATER TREATMENT Mixing studies numerous, however, within only a the few water treatment studies are field relevant are here. These relevant investigations may be split into- those which have dealt with initial rapid mixing directly and those which have dealt with flocculation. Initial Mixing Studies Wilson [10] attempted to define optimum rapid mixing by studying the flocculation different mixing methods. efficiencies The resulting actual from optimization two was based on a floe strength model where optimum mixing was de­ fined as the within the condition which produced flocculator. reactor and.a tubular that uniform, Wilson reactor the employed in his strongest a studies baffled and floes tank concluded instantaneous, plug-flow mixing was the opti­ mum condition based on floe strength. J 11 Sometime la te r , Stenquist a series pared a mixer of continuous flash (pipe iency was Their backmixing for used alum as the results of alum of the coagulation [11] a. multiple results was completed to when ■Even though to plugeffic­ Stenquist th os e• of been more of grid conclusive flocculation studies may have than no inferior contradict chemistry orifice produced inherently ga u g e . seem both to treatment-, Kaufman's conclusions Kaufman flow experiments in which they com­ (backmix) flow). evidence that flow mixing mixer and mixing and Wilson, a function itself. The actual effects of alum dosage in relation to mixing are dis­ cussed below. Amirtharajah and Mills [12] developed the design diagram for alum treatment as shown in Figure 2. The diagram is based on thermodynamic principles and delineates the region of solid phase aluminum hydroxide as a function of pH. Also shown on the diagram are regions where specific coagulation mechanisms predominate. the diagram to various degrees rapid Amirtharajah and Mills then applied mixing by performing jar (G-values) of rapid m i x i n g . tests with They concluded that intense, short duration mixing was. essential if adsorp­ tion-destabilization was ation. the primary mechanism of coagul­ They also found that when sweep coagulation was the predominant mechanism, mixing important to n o t e , that Wilson effects were m i n i m a l . and Stenquist It is both operated Co Kju afi>n 300 IOO IO (boundori with col 3 I Adsorption 0.3 pH FIGURE 2 OF MIXED SOLUTION Design and Operation Diagram for Alum Treatment ALJUM os Aj(SO4)s.l4.3H20-mg/l 30 Zone 13 their mixers in the sweep zone during their investigations. Amirtharajah [13] also relationship between suggested the that a fundamental turbulent microscale and size the par­ ticles which were to be destablized may e x i s t . Only one tiveness as Ellms [14] an investigation of initial mixer conducted full the hydraulic has been scale effec­ reported. . Levy and alum treatment utilizing a hydraulic jump for rapid m i x i n g . that the jump's studies They concluded hydraulic jump was a very effective means for mixing co ag ul an t s. For the energy expended. Levy and Ellms concluded that the jump produced mixing of great rapid­ ity and thoroughness. Turbulent Flocculation Of primary importance to this investigation are particle collision theories which were first, introduced by von Smoluchowski [15] . He derived the collision theories for laminar shear but the original formulations have now been generalized for turbulent flow conditions. Saffman and Turner [16] uti­ lized Smoluc how ski 's ideas to predict.the collision of fain droplets in a turbulent cl o u d . They quantified the number of coll isi ons , N0 , as ' .3 Sire 0.5 . Np = nln2 (rl + r 2 (l5^' (8) 14 where and ng are respective drop number counts, rj and r 2 are respective drop radii, and all other symbols are as pre­ viously defined. Spielman [17] has also pointed out that Saffman and Turner's Equation (8) is applicable to turbulent flocculation. Most recently, Smolu cho wsk i's ideas theory which into, incorporates Adler a [18] general has incorporated particle hydrodynamic effects collision as well electric field, double layer and Van der W a a l s ' forces. as He subdivides coagulation into homocoagulation and heterocoagu­ lation, where homo^ particles and hetero- sized particles. almost always refers the above better, at to least his von turbulent coagulation that equal-sized within the develdment. seem to of unequal­ homocoagulation Smol uc ho ws ki 's flow, of coagulation concluded of studies, extension to refers Adler physical constraints to chemical and Considering, all ideas, be is far and their reaching and may thus be applicable to the rapid mixing process. FILTRATION ANALYSIS Since this study is not an investigation of filtration fundamentals per se, the only literature of interest is that which deals with response of a analysis filter to of the filtration data. depostion media is a function of both headless Several researchers have attempted to The overall of mass within the and effluent quality. define the response of a filter to mass loading by combining headless and efflu­ 15 ent quality data 21, 22, 23]. into a single filtrability index [19, 20, Recently, Janssens, Adam and Buekens [24] did a statistical analysis on various filtrability indexes uti­ lizing direct filtration pilot plant data as a base. were interested best tool that the for in determining filter response Filtrability the most useful. which Number, index analysis. proposed by would They be the They concluded Iyes [21] , was The expression for the Filtrability Number F , is given by F V (9) V r where T is the filter run length defined by effluent quality degradation, H t is the total headloss at time T , C is the average filter effluent turbidity through time T , C0 is the filter influent turbidity Consistent units inspection of minimized, V is the F a dimensionless the arrangement in the' expression F is make and of the filtration parameter. rate. Close individual parameters for F , leads to the. conclusion that when an optimum filtration condition exists. 16 CHAPTER 4 IDEALIZED MIXING MODEL The first step model involved in developing an a visualizatiori process idealized whereby mixing the micro­ scopic aspects underlying mixing could be postulated., Since mixing is most often associated with power dissipation, teractions between colloid particles in­ in suspension and the turbulent microscale can be rationalized as being of primary importance. . The visualization was confined to a homogeneous turbulent field consisting represented by of the microscale eddies whose formulation size (I). c o u l d .be Also, the development was restricted to the adsorption-destabilization process where a uniform particle treated with a,chemical co ag ul an t. scale eddies for the in the transport field of the were suspension was Furthermore, assumed coagulant to be to be the micro­ responsible hydrolysis species, which are most likely in incipient form. Turning to the visualization. simplistic particle-microscale Case I represents Figure 3 illustrates two interaction possibilities. a condition where the microscale larger than the colloids and thus, ded within the eddy. Particles is much the particles are imbed­ in the eddy will experience a laminar like shear field and are also exposed to the coagu- COLLOID DIA. a MICROSCALE \ IDEALIZED MICROSCALE-COLLOID INTERACTION © COLLOID COAGULANT CASE 2 t) I r 2 ^ I - O POWER DISSIPATION FIGURE 3. Idealized Colloid-Microscale Interaction Visualization 18 Iant. Under the conditions of Case I, the efficiency of the rapid mix (based on destabilization) would seem to be con­ trolled by the coating, mechanisms which cause the coagulant to be adsorbed onto the colloid. The exact nature of the coating mechanisms is presently not fully understood. As more power is made available to the system, sition is made to smaller and smaller eddies. a tran­ Finally, the condition exists where the microscale and colloids are equal in size and this The Case condition is shown as Case 2 in Figure 3. 2 condition is such that the particles and eddies can be considered as separate entities and in order for the colloids to sorts must be exposed occur. to Thus, the the coagulant, efficiency of a collision mixing in of the Case 2 situation may be controlled by a collision or inter­ action phenomenon. In looking more closely at the transition zone between Case I and Case 2, Amirtharajah lowing colloid-microscale of the idea was the colloid that [25] has proposed the fol­ interaction theory. The basis for colloid destabilization to occur, particles must be coated with the positively charged aluminum hydroxide solid phase species which are incipiently formed in transported by the the fluid. fluid eddies with the colloid particles. These species have so that they will to be interact 19 Starting with Saffman and Turner's Equation is applicable for the condition where scale is larger than the particles (8), which the turbulent micro­ and with some minor re­ arrangement. N = Icn1Ii2 Ca1 + n)3 (^) (10) I where N is the number of colloid-microscale i n te ra ct io ns , k is a constant, ai is the colloid diameter, n is the micro­ scale, v is the fluid kinematic viscosity, dissipation per and microscale mixer, stant. unit mass and number counts ni e is the power t\2 are and respectively. the colloid Within a given the number count of colloids can be considered con­ Furthermore, in this first approximation the number count of microscale eddies even though microscale there is little doubt is reduced, crease within the that as the constant, size of the the number count of eddies will in­ mixing 'volume. tions, Equation (10) is assumed model, With the above assump­ is reduced to the form N = k 1 (a 1 + n)3 (^)°*5 (ID 20 Rearranging the microscale exp re ss io n, Equation (I), in the form (12) e = and substituting into Equation N = R1Vta1 (11) yields (13) n)3'(i)2 The fluid viscosity is assumed to be independent of q and is, therefore, incorporated into the constant yielding 3,1.2 N = R2 (a1 + n) (^) (14) as the proposed mixing theory expression. In order theory, to Equation identify the extreme points of the mixing (14) was expanded and differentiated with respect to n giving dN dn 4 -> 2 (15) 21 Setting Equation (15) equal to zero leads to ai T aI 2 2 (-^) 3 + 3 " I = 0 and a real root of (a]/n) = 0.5. (16) Taking the second deriva­ tive of Equation 14, 3-4 6k2 (ajn and substituting Equation 14. = 2-3 + a^n 0 . 5 n gives (17) ) a positive value for (17) for all n indicating a minimum for Equation Thus, when the microscale minimum number of is twice the colloid colloid—microscale interactions size a should occur. Although the above derivation orous, as a first approximation, is not complete or rig­ it provides some interest­ ing insights into the initial mixing process. 22 CHAPTER 5 EXPERIMENTAL WORK PLAN The experimental portion of this study consisted pri­ marily of measuring the response of a dual media various methods of rapid mixing the coagulant. filter to Both mechan­ ical and hydraulic mixing were utilized during the investi­ gation. A baffled tank reactor served as the mechanical mixer and hydraulic mixing was provided by a flume apparatus. Mixing within the flume was produced by either turbulent open-channel flow or a hydraulic j u m p . The sensitivity of a dual media filter to small changes in the known characteristics [26] . of its influent suspension is well T h u s , the filter makes an ideal gauge for measur­ ing the effectiveness of the rapid mix. DIRECT FILTRATION PILOT PLANT A direct filtration pilot plant was constructed in order to study the initial mixing step of coagulation. illustrates the pilot plant flow scheme. 2.0 gpm (8 g pm/ft 2 filtration all pilot plant runs. to insure constant rate) Figure 4 A constant flow of was maintained through Both hot and cold, tap water were used temperature conditions. A Powers Foto- h c A. B. C. D. E. F. G. H. THERMAL BLENDING VALVE 20 MICRON FILTER RAW WATER PREPARATION BUFFER FEED TURBIDITY FEED COAGULANT FEED RAPID MIXER DUAL MEDIA FILTER 0 0 PUMP FLOW METER BACKWASH WASTE FIGURE 4 Schematic Diagram of Direct Filtration Pilot Plant 24 guard Model hot and 440-1500 cold thermostatic blending streams feed water. The for all plant to provide temperature runs. of valve mixed the the constant the feed temperature water A chemical analysis of the was performed during the investigation and the was 80°F feed water results are listed in Table I. Table I. Water Analysis of Feed Water for Direct Filtration Pilot Plant. PARAMETER QUANTITY Total Hardness Total Alkalinity Total Dissolved Solids Turbidity PH 105 mg/1 as CaCOg 80 mg/1 as CaCOg 150 mg/1 0j5 to 1.0 TU 7,4 - 7.7 -2 8.0 m g /1 SO 4 —3 PO4 < 0.2 mg /1 None of the analysis except for the results are particularly significant sulfate concentration of 8.0 mg/1. Sulfate concentrations of 8.0 mg /1 and up have been shown to have a considerable impact on the effectiveness of alum when it is , used as a coagulant. It is believed that the sulfate anion neutralizes the charge on the aluminum hydroxide solid phase . which greatly reduces its destabilization potential [27] . The remainder of the raw water preparation was carried out in a 20 gallon continuously stirred tank. The raw.water tank was fed continuously with the constant temperature.feed water as well as a turbidity slurry and pH buffer solution. 25 Hydrochloric acid (Baker R e a g e n t , 37% H C l ), at a concentra­ tion of 30 milliliters for the buffer water tank acid solution. provided a per liter Feeding near the constant of water, buffer raw was used into the raw water pH through all plant r u n s . A suspension of Min-U-Sil bidity slurry. Two (Si 0 2 ) was used for the tur­ different particle size distributions were used in the experimental work and Figure 5 illustrates the distributions. . It is tions by weight bers are shown obtained by as well important as distributions in Figure, 5. standard Omnimet Image Analyzer to note by particle num­ The weight distributions were hydrometer (IA) that distribu­ tests. (ASTM D422) . An by Buehler (Bausch & L o m b ) was employed to provide the number count distributions. The IA consists of a microscope which is coupled to a visual monitor. The lA's electronics scan for shading differentiation (par­ ticles against background) and then count the particles which are greater than a specified size. Samples for"the IA were diluted samples of the turbidity slurry. The IA samples were analyzed in suspension form be^ cause drying the samples caused particles to agglomerate which led to erroneous results. The Min-U-Sil material itself is a product of the Pen­ nsylvania Glass Sand Corporation (PGS). the coarsest grind manufactured by Min-U-Sil 30 (M 3 0 ), P G S , served as one of 26 A SB 325 A • o M 30 A o % BY WEIGHT % BY NUMBER PERCENTAGE FINER Ae PARTICLE FICUPE 5. Size Distributions SIZE (;jm ) for Turbidity Pa rt i c l e s . 27 the particle distributions. was obtained from Berkeley 325 which is t h e , feed the M30 grinding mills.. below, was The other distribution, employed SB325, stock for A sedimentation process, outlined to produce the SB325 from the Berkeley 325 material. Suspensions of 50 grams per liter of Berkeley 325 were prepared in 5 gallon buckets and allowed to sit for one h o u r . The particles which settled in this time period were lected and dried resulting in the SB325 distribution. sedimentation process was developed col­ This based on the ASTM D422 hydrometer test and was designed to remove a major fraction of the particles smaller than 5 micrometers. F r o m .the raw water t a n k , the rapid mix unit where either alum chloride (FeCl3 water proceeded to the (AlgfSO^j^'lGHgO) or ferric was introduced to destabilize the sus­ pension, by charge neutralization. After rapid m i x i n g , the destabilized suspension passed directly into the dual media filter. The details of each of the- rapid mix u n i t s , as well as the details of the filter, are described below. Baffled Tank Reactor Based on the designs scale up considerations, structed as the details for mixing of in the the research [5, 6 , 8 ] and the baffled tank reactor was shown in Figure of other 6.. Also discturbine baffled tank. con­ shown in Figure 6 are impeller Both which the tank was and used the 28 IMPELLER PLANE BUSHING D= 8 .0 H= 12.0 R= 4.0 (a) POZ O FIGURE 6 . Details of Baffled Tank Reactor and Disc-Turbine Impeller. / 29 impeller were constructed of p l e x i g l a s . A constant water depth of 8.0 inches was maintained in the reactor during all pilot plant runs. The influent to the reactor was fed 6.0 inches above the reactor bottom and the effluent off was This reactor drawn configuration inches 2.0 forces all above the the flow bottom. to pass through the impeller plane center line which was 4.0 inches above the bottom. system on the The coagulant impeller plane inches from the blade tips. was center fed into line at the reactor a point 0.25 A Bodine NHS-54 variable speed motor was used to drive the impeller. Details of Flume As a comparison for the baffled t a n k , a hydraulic mix­ ing device which incorporated a narrow flume and a hydraulic jump was constructed. figuration and slopes could sliding block 2.5 all be on Figure 7 illustrates the important attained the dimensions. by adjusting aluminum base. flume Various the channel position Slopes of con­ 1.5, of a 2.0, and 3.5 inches per foot were utilized in the experiments. These slopes produced highly conditions within the c ha nn el , which the turbulent, channel. essentially By inserting acted hydraulic jump could be produced. supercritical as a a flow barrier sluice in gate, a FIGUPF 7. Details of Hydraulic Jump Flume. 31 The flume-jump apparatus was placed in exactly the same location as the.baffled tank within the overall plant s c h e m e . . Raw water entered the channel via a stilling with stones to disperse the flow. basin filled Once the water passed in- v* to the channel section of the coagulant. it was destabilized by the addition When a hydraulic jump was being used, the coagulant feed point was approximately of the jump toe. During plant alone provided the mixing, used inches upstream runs where the channel flow the coagulant feed point was mid­ way along the channel length. flume was 1.5 It should be noted, that the to treat the M30 suspension o n l y . Finally, the destabilized suspension passed directly into the filter rise tube as shown in Figure 7. - . . Dual Media Filter Since the response of the filter was to be used as the principal method of determining mixing filter itself was carefully designed. of the filter is shown rapid mixer enters the tube. in the in Figure 8 . An overall schematic The effluent from the filter via a 2.0 inch diameter rise As the filter media clogs during a. run, the water level rise tube increases, thus filtration with influent control. of 16 ef fe ct iv en es s, the inches of anthracite coal sand. L providing constant rate The filter media consisted over 8.0 inches of silica 32 INFLUENT RISE TUBE BACKWASH FILTER BOX LEVELS COAL - • SAND I I II I MANOMETER BOARD DRIP SAMPLES ORIFICE PLATE UNDERDRAIN FIGURE 8 - BACKWASH EFFLUENT Details of Dual Media Filter 33 Table 2 . Size Characteristics of Filter Media. SIZE CHARACTERISTIC (Effective Size) SAND COAL 0.46 0.8 6 D 10 (mm) d6 0 (mm) 0.62 1.25 d90 (mm) ■ 0.70 1.52 1.35 1.46 Uniformity Coefficient Table 2 lists the size characteristics of the sand and coal media. The literature media sizes were carefully chosen, based on [28] guidelines, to insure a good zone of inter­ mixing and compatible expansion characteristics. A 6x6x48 box. This feet of inch plexiglas configuration filter (6 x 6 surface which flow 2.0 based on a plant column of inch) served provided yielded gpm, as a the filter 0.25 square filtration of 8 gpm/ft^. rate, The box was divided into five levels with a continuous-drip turbid­ ity sampler and manometer port placed le v e l s . Level (I inch above were spaced one the was 25 media) at 5 inch inches and the intervals. at each above the successive Also, of the five orifice plate lower levels a sixth level was established below the orifice plate to collect effluent tur­ bidity and total headless d a t a . The drip sampler consisted of an aluminum tube extending into the center of the filter box. The manometer ports were, similarly constructed but . 34 only projected 0.5 inches into the media. with twenty five 0.25 orifice plate. A plexiglas plate inch diameter holes was used for the The function of the orifice plate was to sup- V I port the media (in addition to a nylon mesh) and to provide even filtration. Also, the orifice plate provided even dis­ persion of the backwash water during cleaning. Cleaning of the filter was systematically performed by using both air scour and water b a c k w a s h . Air was blown intp the submerged filter media through each of the drip samplers. The necessity for air scour was established after water wash­ ing alone proved to be ineffective in breaking up the chunks of material which were sheared off the m e d i a . x After the air flow was st o p p e d , the filter was washed with water for an ex­ tended period of time.. The washing flow rate employed was sufficient to provide a fifty percent expansion of the bed. FILTER PERFORMANCE DATA To insure the stability of the pilot plant and to determine the filter res po n s e , various physical and chemical parameters were each run. recorded at half hour throughout Measurements of pH were made on the raw water and filter effluent (level 6) in order chemistry within the flow system. from Beckman ments. intervals Also, Instruments the raw was water used to maintain constant An Altex digital pH meter for all the pH measure­ turbidity was monitored to insure constant mass loading of the rapid mixer and filter. 35 Filter response to the various rapid mix conditions was established by each of the recording drip d a t a , headless the turbidity samplers. data was In of addition obtained by the to water the monitoring from turbidity the total available head at each level in the filter. The electrophoretic mobility of the particles after destabilization parameter. (level I) was also monitored as a secondary A G.K. Turner Zeta Meter was employed to measure the mobility of the particles. The mobility measurement pro­ cedure consisted t h e . average of recording mobility of ten particles found in each of the samples collected at half hour i nt erv als . The reflect the ten range particles of were mobilities and randomly selected particle sizes to that were seen in the sample. A list of all the pilot plant r u n s , including coagulant dosages and pH conditions total number ■ of plant runs can be found in where . coagulant Table 3. The was used was thirty-eight. An additional run without coagulant was also made in to order efficiency. establish the filter's baseline removal All the pilot plant runs were between three and five hours in length . 36 Table 3. List of Pilot Plant Runs Including Coagulant Dosages and pH Conditions. COAGULANT DOSAGE/ COLLOID MIXER VELOCITY GRADIENT-G (s- 1 ) 75 Alum8 mg/1 @ pH 6.9 Baffled Tank M30 Ferric Chloride 8 mg/1 @ pH 6.2 Baffled Tank M30 Ferric Chloride 8 mg/1 @ pH 6.3 Baffled Tank SB325 Ferric Chloride @ pH 6.2 Hydraulic 8 mg/1 Jump M30 Ferric Chloride 8 m g / 1 @ .pH 6.2 Open Channel M30 2 2 210 I 38 5 810 1640 3000 3800 75 ' 210 810 1640 2290 3000 3800 NUMBER OF RUNS 2 2 I 2 2 I I I 2 I , 210 810 1640 3000 3800 2 2 2 2 I I 705 690 680 870 I I I I 1080 1360 1700 2300 I I I I Alum Dosage = 8 mg/1 as A l 2 (SO4) 3 -14.3H20 Ferric Chloride Dosage = 8 mg/1 as Fe C l 3 *6H20 , 37 DYE TRACE STUDIES In order to determine the macroscopic mixing character­ istic of both the baffled tank and the hydraulic jump, stan­ dard dye trace studies were pe r f o r m e d . By utilizing fIuor- ometric techniques and common analysis procedures explained by Weber [29], a fairly good representation of the residence time distribution (RTD) for the given mixer was obtained. Weber also explains a numerical integration procedure which yields the centroid of the R T D . By definition, the centroid of the rector RTD is the mean hydraulic residence time (MHRT) for the reactor. Furthermore, Weber illustrates a theoret­ ical RTD calculation for a complete mix reactor. Rhodamine W T , a nonreactive in the tracer studies. was introduced During into the mixers lant feed conduits. The dye, was used the tracer studies, as a pulse, Samples were effluent after the dye was Turner Fl uorometer. fluorescent collected via the the dye coagu­ from the mixer injected and analyzed on a G.K. fluorometer detected R h o d a m i n e 'WT at concentrations as low as 0.0001 mg/1. The data from the f luorometer was later plotted and statistically analyzed as a described by Weber [29], to establish the mean hydraulic residence time for the given mixer. 38 CHAPTER 6 RESULTS AND DISCUSSION The results of this investigation fall into three major categories. F i r s t > there is the calculated mixing parameters for the various mixers. filtration results are Secondly, the pilot plant data and considered. Finally, the hydraulic and mechanical mixer comparisons are made. CALCULATED MIXING PARAMETERS The parameters which were chosen to describe the mixing in the baffled tank and hydraulic jump were mean hydraulic residence time (MHRT) and the average mixer, velocity gradient (G) . For comparison purposes, Gt values have also been cal­ culated. regard to the value of t used was V/Q for the the MHRT for the MHRTs and hydraulic given G-values Studies section and jump, jump. were the t was The methods outlined in assumed for reactor. equal In to the calculating the the. Previous following paragraphs focus Related on the results of the above mentioned calculations. Velocity Gradients Power dissipation within the baffled tank can be calcu­ lated by using the power number Equation tor power number is kn o w n . Leentvaar (4) once the reac­ [8 ] reported that the I 39 power number impeller, was for a cylindrical 5.0. It is baffled important t a n k , with to note a disc that power losses computed using the power number expression represent average losses within the entire tank volume. Thus, by using the power number losses in the expression for G, Equation (2) , an average found. velocity gradient for the baffled tank can be Table 4 lists the results of the power loss, G-value and Gt-value calculations for the baffled tank. Table 4. Calculated Velocity Gradients 50 0 .0.2 , 75 100 0.18 0.62 2.74 210 150 250 400 500 600 700 Baffled VELOCITY GRADIENT-G (s- 1 ) ' POWER DISSIPATION (ft'lbs/s) IMPELLER RPM for Gt 3,900 10,900 385 810 1640 •2290 3000 3800 11. 2 1 21.90 37.84 60.09 Tank. 20, 0 0 0 42,100 85,300 119,100 156,000 197,600 G-values and Gt values for the hydraulic jump and open channel, A sample for the for various channel calculation jump can be of found the slopes , are shown power in the loss and Appendix. in Table 5. the It G-value should be noted here that the open channel G-value for the 3.5 inches per foot slope, is related to may the be in error. extreme The reason curvature in the flume at this large s l o p e . of the for the error water surface Since the flume was only 40 Table 5. Calculated Velocity Gradients for Hydraulic M i x e r s . CHANNEL SLOPE (in/ft) FROUDE NUMBER 1.5 3.41 4.49 6 .29 9.68 3.41 . 4.‘4 9 6.29 9.68 ■ F1 2.0 HYDRAULIC JUMP 2.5 3.5 1.5 2.0 OPEN CHANNEL 1.0 .2.5 3.5 - POWER DISSIPATION f t •Ibs/s G, (s- 1 ) Gt 3595 2970 0.121 705 690 680 870 3480 0.046 0.061 0.075 0.103 1080 1360 1700 2300 530 550 550 560 0.022 0.035 0.054 2920 inches wide, all the calculations had to be based on the center line depth. have thus The curvature of the water surface may yielded a low center line depth the calculated *G-value to be too high. reading None of causing the other channel slopes employed produced flows with extreme surface curvat ur e. ' In looking at the actual values for power dissipation for the j u m p , channel and baffled t a n k , it can be seen that the power requirements for the hydraulic mixers are signifi­ cantly lower than the power requirements for the baffled tank. Hydraulic Residence Times . . The data collected from the dye trace studies was used to determine the residence time distributions for the baffled tank and the hydraulic jumps. for three different impeller Figure 9 represents the RTDs speeds in the baffled, tank. O & 4 A A N= 50 RPM O N = 100 RPM O N = 7 0 0 RPM A \ / > X \ ——— THEORETICAL D PO Bx O 50 ' 100 150 TIME (SEC) FIGURE 9. Residence Time Distributions for the Baffled Tank Reactor 42 The RTDs do not impeller speed and curve derived However, the seem to all be the from a mass mean distribution) for particularly follows the on of residence the times impeller the theoretical balance across the reactor hydraulic each data dependent [27] . (centroid speeds, listed of in Table 6 , are significantly different. Note that changes I in the dye concentration within the baffled tank during the first ten seconds were not included in the numerical integra­ tion. procedure Table 6 . used to obtain the MHRTs listed Mean Hydraulic Residence Times IMPELLER RPM \ for Baffled T a n k . MEAN HYDRAULIC RESIDENCE TIME (Seconds) . 65.6 56.6 50.3 50 100 700 in Table 6 . \ Reactor Volume/Flow Rate = 52.0 seconds Two typical RTDs Figure 10. above, two for the hydraulic important RTDs differences are more respective MHRTs (plug-flow). for the hydraulic nitude less ju m p s ) . in In comparison to the baffled tank RTDs discussed hydraulic jump or, MHRT jumps are shown than Thus, the the tank are closely evident. First, centered about the their Also, the average mixing time jumps MHRTs macroscopic is about an (4-5 second mixing in order MHRT the of mag­ for all hydraulic jumps and the baffled tank used in the experiments are vastly di f f e r e n t . DYE CONCENTRATION ( m g /lx IO ) 43 SLOPE- O IO I.5 7 F T 20 TIME (SEC) FIGURE 10. Residence Time Distributions for Two Hydraulic Jumps. 44 FILTRATION RESULTS As outlined filter data rea di ng s. by vthe consisted The level loss data in the Experimental Work turbidity (1-6) on the levels through of various data will be and headless referenced directly other ha n d , is coded by referring the headless in the uppermost loss occurred. layer of the total headless would be Hl -6 Figures 11 and turbidity from which the sample was t a k e n . which Two typical sect io n, the raw examples 12. of coal He a d - . to the For example, would the be Hl-2 and (see Figure 8 ). raw filter data are The top graph in each shown in figure, shows the turbidity removal as a function of time and the lower graph illustrates the corresponding headlosses. Note that the headless lines are very linear, which is characteristic of a stable well designed filter system with good depth removal. A single plant added. This run was also made in which no treatment run was establish a base for the other plant the no run coagulant move any of the showed that nondestabilized no coagulant was performed the runs . filter material. in The order to results of would not re­ This also led to a zero headless bu i l d u p . Filter Response to Baffled Tank Mixing As a first attempt to define the effectiveness of vari­ ous mixing conditions for. the baffled t a n k , the rate of headloss buildup and average effluent turbidity for each run was 45 ▲ 2 TURBIDITY (TU) ■ INF HEADLOSS (IN) TIME (HRS) • A ■ HI - 2 HI - 4 HI - 6 TOTAL TIM E (HRS) FIGURE 11. Typical Filter Data for Baffled Tank Mixing with Alum Treatment (n = 700 PPM). 46 A 2 o 4 • 6 TURBIDITY (TU) ■ INF A l TIME (HRS) H I-2 A H I -4 ■ H I- 6 TOTAL HEADLOSS (IN) • TIME (HRS) FIGURE 12. Typical Filter Data for Hydraulic Jump Mixing with Ferric Chloride Treatment (slope = 2.0) in/ft) . 47 calculated and co m p a r e d . ' The rate of headless is simply the slope of the linear headless lines which were illustrated in Figures 11 and 12. various plant, runs headloss d a t a . in as the Rates of headloss by performing were calculated linear regressions for on the Average effluent turbidity is defined here­ average of all the effluent turbidity readings up to and including a specified, breakthrough turbidity (C). The breakthrough turbidity was used to determine the run le n g t h , T , and was set at 1.5 TU for M30 suspensions and 1.0 TU for SB3 25 suspensions. In other w o r d s , when the effluent turbidity of a given plant run reached the appropriate break­ through turbidity v a l u e , the run was terminated. The rates of headloss development and average effluent turbidity for alum treatment of the M30 suspension are shown in Figure 13. The rates of headloss do not vary significantly above a G of approximately 800 s- 1 , however, a minimum rate seems to have been reached at a G of 3000 s- -*-. ly, the average turbidity for alum treatment did significantly with velocity of the in data was most water. shown likely gradient. Figure related to 13 the seemed The to ferric chloride sulfates and the not vary insensitivity unreasonable, in In order to avoid the sulfate problem, was changed Corresponding­ the and influent the coagulant experiments were repeated. Figure 14 illustrates the rates of headloss for ferric chloride treatment of the M30 suspension. All trends in • A HI-2 HI-4 ■ HI- 6 o TREATMENT — EFFLU ENT AVERAGE TURBIDITY M 3 0 PARTICLES TURBIDITY (TU) RATE OF HEADLOSS (IN/HR) — ALUM IOOO 2000 MEAN VELOCITY GRADIENT - 3000 4000 G (s') FIGURE 13. Rates of Headloss and Average Effluent Turbidities for Baffled Tank Mixing with Alum Treatment. — FeCU TREATMENT — AVERAGE ▲ HI- 4 EFFLUENT TURBIDITY M 3 0 PARTICLES TURBIDITIY UJ 4.0 (TU) b 2.0 1000 2000 3000 4000 MEAN VELOCITY GRADIENT - G (s') FIGURE 14. Rates of Headloss and Average Effluent Turbidities for Baffled Tank Mixing with Ferric Chloride Treatment. 50 Figure 14 are similar to the trends for alum treat me nt ; how­ ever, note the 1 0 0 % change in the rate of headless and near 300% change in the average turbidity over the G-value range shown. As a result of the increased sensitivity of the ferric chloride system, no further alum treatment experiments were performed. The SB325 suspension was also treated with ferric chloride and the resulting headless rates and corresponding turbidities are shown in Figure 15. headless changes Once again, the rate of significantly over the velocity grandient range employed, with high G-values producing lower rates of headless. The average ' effluent turbidities are somewhat less sensitive to changes in mixing for the SB325 suspension in comparison to lower sensitivity basis turbidities was for the actually M30 suspension. expected, since on The a mass (mg/ 1 ), a finer distribution of colloids will produce higher turbidities (light scattering) than a coarser distri­ bution. It was evident from. Figures 13 through 15, that no clear cut optimum condition could be identified because the headloss and turbidity data opposed each other. necessary to combine single filtrability optimum mixing headless index in con di t io ns . turbulent microscale and and the turbidity order Also, T h u s , it became to pinpoint correlations colloid data into a possible between distributions the could — FeCI3 TREATMENT — ■ HI-6 AVERAGE ▲ EFFLUENT TURBIDITY TURBIDITY (TU) RATE OF HEADLOSS (IN /H R ) SB 32 5 PARTICLES iO 2000 3000 4000 MEAN VELOCITY GRADIENT - G (s-') FIGURE 15. Rates of Headless and Average Effluent Turbidities for Raffled Tank Mixing with Ferric Chloride Treatment. probably not be identified unless a single parameter was used to describe the filter response. Filtrability Numbers for Baffled Tank Mixing Filtrability numbers for various plant runs were calcu­ lated using Equation (9) and plotted against average reactor velocity gradients. shown in Figures .The filtrability 16 through numbers 18. - Also obtained are plotted in Figures 16 through 18 are the turbulent microscales for the impeller stream zone (see Appendix). Figure 16 is for alum treatment of the suspension the M30. evident. Figures once again that and 17 and the 18, ferric expected insensitivity on the other hand, chloride system is illustrate provides much more information in regard to the filter's response to vari­ ous degrees of are indicative and 18 seem mixing. Since of poorer to for filtrability numbers filtration conditions, Figures 17 that filtration indicate conditions exist larger both the relative M30 minimum and the SB325 distribu­ tions. Looking back and SB325, shown at the grain size distributions in Figure 5, it can be seen that the mean particle size for M30 and SB325 distributions (number count) is approximately 3.0 pm and 6.0 p m respectively. to the mixing interactions for M3Q interaction (filtration turbulent microscales are model developed conditions) twice the According herein, minimum should exist when the colloid size. Thus, — ALUM TREATMENT — STREAM MICROSCALE ( >jm) M 3 0 PARTICLES O 0 .7 5 z 0 .5 0 H 0 .2 5 D 2000 MEAN VELOCITY GRADIENT - 3000 4000 G (s*') FIGUPF 16. Filtrahility Numbers for Baffled Tank Mixing with Alum Treatment — F e C I, TREATM ENT — STREAM MICROSCALE M 3 0 PARTICLES 3 0 .5 0 (/jm ) < 0 .2 5 2000 MEAN VELOCITY GRADIENT - 3000 4000 G (s') FIGURF 17. FiltrahiIity Nunhers for Raffled Tank Mixing with Ferric Chloride Tre at m en t. ----- FeCI 3 TREATMENT PARTICLES ILTRABILITY NUMBER xIO STREAM MICROSCALE (/jm) SB 3 2 5 D MEAN VELOCITY GRADIENT - FIGURE 18. 3000 2000 G Filtrability Numbers for Baffled Tank Mixing with Ferric Chloride Tre at m en t. 4000 56 for the M30 and SB325 distributions, minimum filtration con­ ditions should exist when the microscales zare approximately 6 and 12 pm respectively. of course, The preceding statement assumes, that the colloid distribution can be represented by its mean size. The to velocity gradients and 6 12 p m microscales correspond of 3000 s- -*- and 810 s--*-. Inspection of Figures 17 and 18 show that minimum filtration conditions for the experimental very close to 6 that the in the systems at stream microscales pm for M30 and 12 pm for SB325. coagulant was impeller stream, tion in the occur stream introduced into the a microscale-colloid region would Recalling baffled tank size correla­ seem the most reasonable. A secondary minimum filtration condition is also shown in Figure 18 likely related (G=3000). to the This minimum of particles fraction SB325 distribution which particles have greatest the secondary are of small size impact 3.0 on pm; is most in these the small the measurement of turbidity. ELECTROPHORETIC MOBILITY DATA . Recall that the electrophoretic mobility of the desta­ bilized (level I) suspension throughout each plant actuality, the thus, between during a given run. average 60 and run. was Each mobility 90 particle Table also measured regularly recorded mobility was, for ten particles, mobilities 7 lists the in and were measured average mobilities 57 obtained from the treat the M30 and SB325 Table 7 the highest that close to, the discussed in data seems drawn from various the of In f a c t , statistical any at, or correlation points which supported by which make up the average analysis of very the mobility conclusion is to can be seen from Although measurements samples employed occur size section. scattered, mobility It mobilities previous somewhat conditions suspensions. mic ros cale-colI o id the large number mixing is the va lues. the mobility data yielded O 9 5 % confidence intervals could the mobility intervals be data bulent microscale considered and gest the existence which a size so sm a l l , insignificant. filtrability of and were numbers correlation the mean that Thus, seem between the both to sug­ the tur­ size of the colloid distri­ bution. HYDRAULIC MIXER COMPARISONS Comparing hydraulic mixing to baffled tank mixing was handled by utilizing the velocity gradient c o n c e p t . Within the context comparing mixers from a related quest io ns . First,' of this G-value standpoint investigation, answered two the comparisons gave some insight into whether the proposed method for calculating re as ona bl e. G-values for hydraulic jumps was Secondly, comparisons based on G established the jumps mixing effectiveness l of the baffled t a n k . in relation to the effectiveness ' . It should be noted here that a similar 58 Table 7. Electrophoretic Mobility Data for Treatment of M30 and SB325 Colloids ' ELECTROPHORETIC* MOBILITY MEAN + 95% C.I. (lim* cm/volt •s ) VELOCITY GRADIENT (s- 1 ) CONDITIONS 0.90 + 1 .01 + 1.00 + 0.94 + 0.98 + 1.15 + 1.16 + 75 Alum Treatment of M30 Particles 210 385 810 1640 3000 3800 ' 810 1640 2290 3000. 3800 *Non destabilized 1.60 1.52 1.70 1.55 1.44 810 1640 3000 3800 G-value for the particle mobility jump and tank does value. In fact, for the hydraulic = not 2.2 imply for a given G (600— 900 S- M jump are an 0.03 0.04 1.19 + 0.03 1.27 + 0.02 1.31 + 0.03 1.11 + 0.03 ’ 210 Ferric Chloride Treatment of SB325 Particles 0 .02 0.02 0 .01 1.22 + 0.02 1 .21 + 0.02 1.09 + 0.01 75 210 Ferric Chloride Treatment of M30 Particles 0.02 0.04 order + + + + + 0.03 0.04 0 .02 0.04 0.03 ym*cm/volt*s a similar Gt the Gt values of magnitude smaller than than the Gt values for the baffled t a n k . The rates and channel) of headloss of both hydraulic are shown in Figure 19. mixers (jump The data in Figure 19 indicates that the rates of headloss produced in the filter -H Y D R A U L IC JUMP FeCL TREATMENT - H I- 4 H I- 6 JUMP o CHANNEL 2000 A D 3000 H I-2 HI - 4 H I- 6 4000 MEAN VELOCITY GRADIENT - G (•-') FIGURE 19. Rates of Headloss for Hydraulic Jump and Open Channel Mixing with Ferric Chloride Treatment. 60 for both the jump and the channel are higher than the rates which resulted ,from baffled tank mixing. At first g l a n c e , Figure 19 might suggest that the G-values for the jump, were tod large since the hydraulic and mechanical data would align if the jump G-values were less. dient calculation However, the velocity gra­ for open channel mixing is well defined, yet the channel data as w e l l , does not align with the baffled tank data. From a turbidity stan dp oi nt , Figure 20 indicates the hydraulic mixers produced a effluent than the baffled loss depicted in Figure 19 was understandable. tank. slightly Thus, the higher that quality increased head- Combining the headless and turbidity data to form,cor­ responding filtrability numbers leads to the comparison il­ lustrated in Figure 21. port the G-value The filtrability data tends to sup­ calculation method arid jump data are in good agreement. since the baffled tank Furthermore, Figure 21. indicates that the hydraulic jump and open channel are equal­ ly as effective as the baffled tank in regard to rapid mixing of chemical coagulants. Once again, the actual power dissipations it should be noted that \ in the hydraulic mixers were .. significantly less than the power dissipations for the baffled tank. FeCL TREATMENT • JUMP o CHANNEL --R EA C TO R AVERAGE TURBIDITY (JTU) HYDRAULIC JUMP O 3000 2000 MEAN VELOCITY GRADIENT - 4000 G (#*') FIGURE 20. Average Effluent Turbidities for Hydraulic Jump and Open Channel Mixing with Ferric Chloride Treatment. — HYDRAULIC JUMP rO 0.75 FeCl3 TREATMENT — • JUMP CHANNEL — — REACTOR / 0 CE UJ X Z Z Z CD \ / 3 \ / 0 .5 0 \ / \ Z > \ \ / 2 \ \ Z t Z \ / CD < CE b 0 .2 5 ' V - IOOO 2000 MEAN VELOCITY GRADIENT - _ 3000 G 4000 (s') FIGURE 21. Filtrability Numbers for Hydraulic Jump and Open Channel Mixing with Ferric Chloride Treatment. 63 CHAPTER I CONCLUSIONS Based on the results of this s t u d y , the following con­ clusions can be. d r a w n : 1. A size and the correlation colloid rapid mixing between distribution process of of this correlation was tration data the as well turbulent seemed to exist coagulation. supported as particle microscale The for the existence by pilot plant electrophoretic fil­ mo­ bility data. 2. The microscale-colloid interaction model proposed here­ in may provide some mentioned above. insight The into the size mixing model may correlation not actually define the physical nature of the rapid mixing p r o c e s s , however, the model seems to predict the minimum inter­ action condition 3. In regard for the mixer to optimum mixing used in this study I con di ti on s, the data col­ lected indicates that the size of the colloid suspension being treated must be considered before optimum condi­ tions can be defined. The filtr.ability data indicated that average velocity gradients from 700 to 1500 s- l or, possibly gradients above 4000 s ~ " , were best for the 64 particle suspension used in this study. 4. Use of the hydraulic here resulted in jump G-values functionally correct. here was for jumps design procedure which were developed reasonable and Although the procedure developed occurring in sloping channels, a similar methodology could be developed for jumps occur­ ring downstream of a critical flow flume. 5. In the average s- 1 , the velocity mixing was found to gradient effectiveness be equal Fu rt he rmo re , because to of range of that of 600 to 900 the of the the difference hydraulic jump baffled tank. in the size of the power dissipation volumes of the jump and the t a n k , significantly less above G-values 6 . The power of a hydraulic also very app are nt. to gradient, all range. to limit It is the operations. required to produce in the hydraulic jump . inflexibility this study was In spite produce the jumps this use jumps fell the ' jump as a mixer was of the attempts made in of variable within a inflexibility of the narrow that hydraulic velocity will jump G-value continue in mixing 65 REFERENCES 1. H i n z e , J .0. Tu rb ule nc e. Hill, 1975. 2. Bradshaw,?. An Introduction to Turbulence and its Me as ur em e nt . New Y o r k :Pergamon Press, 1971. 3. K o l m og or o ff , A.N. "The Local Structure of Turbulence in Incompressable Viscous Fluid for Very Large Re y n o l d s •N u m b e r s ." C.R, Acad. Science U . R .S .S .31 . (1941) :518. 2nd ed. New YorkzMcGraw ) 4. Ko lm o go r of f, A.N. "On Degeneration of Isotropic Tur­ bulence in an Incompressible Viscous Liquid." C.R. Acad. Science U . R . S . S . 31 (1941):5 38 . 5. Cutter, Louis, A. "Flow and Turbulence in a Stirred Tank." American Institute of Chemical Engineers Journal 12 (January, 1966) :35-4 5 , 6. O k o m o t o , Y., Nishikawa, M . and Hashim.oto, K . "Energy Dissipation Rate Distribution and its Effects on Liquid-Liquid Dispersion and Solid-Liquid Mass Transfer." International Chemical Engineering 21 (January 1981):88-94. 7. Camp, 8. Le en tva ar , J. and Y w e m a , T.S.J. "Some Dimensionless Parameters of Impeller Power in Coagulation-Floc­ culation. " Water Research 14 (1.980 ): 135-140 . 9. Chow, T.R. and Stein, P.C. "Velocity Gradients and Internal Work in Fluid Motion." Journal of the Boston Society of Civil Engineers 30 (1943):219237 . V.T. Open Channel H y d r au li cs . Hill, 1953. New YorkzMcGraw 10. Wilson, G .E . "Initial Mixing and Turbulent tion" Ph.D. dissertation. University fornia, 1972 Floccula­ of Cali­ 11. S t e n qu i st , R.J. and Kaufman, W.J. Initial Mixing in Coagulation Pro c e s s e s . U.S. Environmental Pro­ tection A g e n c y , EP A-R2-72-053, (1972). 66 12. Ami rt ha r aj ah f A. and Mills, K . M . "Rapid-Mix Design for Mechanisms of Alum Coagulation." Journal of the American Water Works Association 74 (April 1982): 210-216. 13. Am i r t h a r a j a h , A. "Initial Mixing." American Water Works A s s o c i a t i o n , Seminar Proceedings, Coagulation and Filtration: Back to the B a s i c s . St. L o u i s , MO, 1981. 14. L e v y , A.G . and F i l m s , J.W. "The Hydraulic Jump as a Mixing D e v i c e ." Journal of the American Water Works Association 17 (January 1927):1-23. 15. Smo luc h ow sk i , 16. Saffman, P.G. and Turner, J.S. Drops in Turbulent C l o u d s ." chanics 16 (1956):16-30. 17. Spi el ma n , L .A . "Hydrodynamic Aspects of Flocculation" The Scientific Basis of Flocculation (K.J. Ives, editor) Netherla nd s:Sijthoff and No o r d h o f f , 1978. 18. Adler, P.M. "Hetrocoagulation in Shear Flow." Journal of Colloid and Interface Science, 83 (September 19 8 1 ) :106-115. 19. Garnet, M.B. and Ra de ma ch er , J.M. . "Measuring Filter Performance." Water Works Engineering 112 (1959): 117-149. 20. C l e a s b y rJ . L . "Approches to a Filtrability Index fqr Granular Filters." Journal of the American Water Works Association 61 (August 1969):372-381. 21. Ives, 22. B i s k e r , C.D. and Young, J.C. "Two-Stage Filtration of Secondary Effluent." Journal of the Water Pollu­ tion Control Federation 69 (February 1977).:319351. 23. L e k k a s , T.D. "A Modified Filtrability Index for Gran­ ular Bed Water Filters." Filtration and Separa­ tion 18 (May/June 1981): 214-216. M. Physical Chemistry 92 (1917):129. "On the Collision of Journal of Fluid Me­ K.J. "A New Concept on Filtrability." ' Prog'. Water Technology 10-' (1978) :123-137. « 67 24. • J a n s s e n s , J.G., A d a m , C . and B u e k e n s , A. "Statistical Analysis of Variables Affecting Direct-Filtration" European Federation of Chemical Engineers, Pro­ ceedings of the International Symposium on Water Filtr at ion . Antwerp, Be l g i u m :1982. 25. Amirth ara j a h , 26. Ba u m a n n , E .R . Chapter 2 "Granular-Media Deep-Bed Filtration" Water Treatment Plant Design (R .L . Sa n k s , editor) Ann ArbortAnn Arbor Science Pub­ lishers, 1978 . L e tt er ma n , R . D . and V a n d e r b r o o k , S.G. "Effect of Solution Chemistry on Coagulation with Hydro­ lyzed A l ( I I I ) !Significance of Sulfate Ion and pH." Water Research 17 (1983): 195-204. ' 27. A., Personal communication. May 1982. 28. Amirtharaj a h , A. Chapter 28 "Design of GranularMedia Filter Units." Water Treatment Plant De­ sign (R.L. S a n k s , editor) Ann ArbortAnn Arbor Science Publishers, 1978. 29. Weber, W.J. Physicochemical Process for Water Quality C o n t r o l . New YorktWiley and S o n s , 1972. ) ( 68 APPENDIX SAMPLE CALCULATIONS i 69 Hydraulic jump velocity g r a d i e n t . Measurements of depth and elevation within the flume led to the following data for the 1.5 inches per foot slope. , Ef = 0.078 ft' F1 = 3.42 -y S = 0.128 ft" = sin 6 = 0.124 The power dissipated in the jump can then be found using Equation (7) where Y = 62.2 Ibs/ft-3 (80°F) 0 = 2.0 gpm = 4.46xl0_3cfs P = Y Q(Et ) Using F1 , y and S in Figure 22 yields a jump 2 length: L= Thus, 0.461 ft the dissipation volume, V, is approximated by a triangular wedge of 1.0 inch width or V = 1/2 Ly 2 (0.0 8 3) ft 3 Finally, substitution into equation y = 1.799x10-3 (2) where lb* s/ft 3 G = 705 s-1 The above G-value being an approximation of the velocity gradient for. the hydraulic jump generated on the 1.5 inches per foot slope. 70 S = 0.25 IO FROUDE **- - F 1 FIGURE 22. Hydraulic Jump L e n g t h , L, for Jumps Ch a n n e l s . in Sloping 71 2. Impeller stream microscale Taking the case for a velocity gradient of 3000 s ~ l , Table 3 lists an average power dissipation of 37.84 ft'lb/s. Referring to Figure I, the approximate power dissipation in the impeller stream would be P m2 = 5.4 (37.84) = 204.3 ft'lb/s Converting P m 2 to the power dissipation per unit mass is accomplished by realizing that where P= 1.934 .slugs/ft"* and V 2 = 0.095V = 0.022 ft^ thus e = 4792.9 ft 2 / S 3 Substituting into Equation V = 9.3x10-6 n = 2x10-5 (I) ft2/s where (80°F) ft = 6.2 ym 3 1762 00163740 N378 T776 cop. 2 / /(/5# /776 MfTERUBRARY