Rapid filtration

Water Research Pergamon Press 1970. Vol. 4, pp. 201-223. Printed in Great Britain

REVIEW PAPER RAPID FILTRATION K . J. IVES Department of Civil and Municipal Engineering, University College, London

(Received 5 December 1969) NOMENCLATURE A B C Co D d E e f f~ G g H H~, I i k L Le l m N n P p~ q R r ro

Hamaker constant Blake Number concentration of particles in suspension concentration of particles in suspension, before filtration diffusion coefficient (Stokes-Einstein) grain diameter attraction energy due to Van der Waals' forces particle diameter porosity of clean filter media porosity of filter media mean temporal velocity gradient gravitational acceleration head loss, water gauge head loss of washwater interception parameter subscript for media of given characteristics Carman-Kozeny filter constant distance in media, in flow direction expanded thickness of media during washing separation distance, particle to grain exponent for velocity inertia parameter exponent for grain size Peclet Number fraction of filter depth occupied by grains with characteristic i empiric exponent of washing equation Reynolds Number radial distance into radial filter radius of inlet face r/ro S sedimentation parameter s specific surface of media So specific surface of clean media t time from commencement of filter run t, mean residence time in filter pores v approach velocity of filtration Vo inlet face approach velocity vs settling velocity of grains vw approach velocity for washwater x empiric exponent in filter coefficient equation y empiric exponent in filter coefficient equation z empiric exponent in filter coefficient equation scour coefficient geometric coefficient filter coefficient ,~o initial filter coefficient, clean filter Ao,o initial filter coefficient, clean filter, radial filtration, at radius ro t~ dynamic viscosity v kinematic viscosity 201 w.n. 413--n

202 p p, pg cr ~u

K.J. IvEs liquid density particle density grain density specificdeposit: vol. deposit per bed vol. ultimate specificdeposit. INTRODUCTION

Trrr FUNCTIONof rapid filters in water and waste water treatment is to clarify the water by removing small particles. In some circumstances other benefits are obtained: for example primary filters in water treatment may oxidize ammonia in the water to nitrite and nitrate by the action of Nitrosomonas and Nitrobacter on the filter grains; also for example tertiary waste water treatment filters will remove some B.O.D. from the water, which is associated with the suspended solids. The principal modes of action of rapid filters are physical and physico-chemical; biological processes are unimportant or absent. It is therefore essential to distinguish them from slow filters, used mainly in water treatment, in which a great part of the filtration action is dependent upon biological processes. Apart from the rate of filtration, the slow and rapid filters are hydraulically similar, but as treatment processes they are quite distinct. To emphasize this distinction rapid filters were often called mechanical filters. However, this term is dying out. In chemical engineering such rapid filters are frequently called deep bed filters to distinguish them from cake filtration, which is commonly used in chemical industry. Cake filtration finds its counterpart in sludge dewatering by vacuum filter or filter press in water treatment, and will not be dealt with, in this paper. Screening or straining, particularly microstraining, is sometimes an alternative process to rapid filtration, but as it acts on different principles and is not in the same engineering and hydraulic form it will not be considered here. Rapid filtration finds its greatest application to clarification of dilute suspensions (less than 500 rag/l) of particles ranging in size from about 0-I/zm to about 50 t~m. Higher concentrations would be better treated by cake filtration; smaller particles should be flocculated, larger particles should be strained or sedimented. Characteristically the filter comprises fine granular media (traditionally sand--but this is being supplemented by other grain materials), in a bed many hundreds of grains deep. The bed remains saturated with suspension, which moves through the pore spaces because of an applied hydraulic pressure gradient. Detailed descriptions of practical designs will be given later. FILTRATION MECHANISMS The fluid flow in the filter pores is laminar (CLEASBYand BAUMANN, 1962), that is fluid viscous forces predominate over fluid inertia forces. The flow regime has some similarity with Poiseuille flow in a capillary; indeed the Kozeny-Carman model of flow, which describes the flow of clean fluids through porous media, is based on this similarity. This means that there will be a velocity gradient in each pore, with zero velocity at the boundary with the grain surface, and a maximum velocity near the pore centre. Due to the complexity of the pore spaces, including the enlargements and contractions of flow, it is unlikely that the velocity distribution has the paraboloid geometry of Poiseuille flow. The flow regime can be characterized by a modified

Rapid Filtration

203

Reynolds Number, in which the length term is the mean hydraulic radius of the pores, and the velocity term is the mean pore velocity• This modified Reynolds Number is called Blake Number (B) dv

-

6(1

(1)

--f)v

where d = grain diameter (range 0.3-3 mm) v = flowrate per unit face area of filter, or approach velocity (range 0.7-7 mm/ sec f = porosity of filter (range 0.38-0.55) v = kinematic viscosity of water (range 0.9-1.8 mm2/sec). A normal value for the Blake Number for rapid filtration would be 0.2. In rapid filtration the particles to be removed from suspension are smaller than the pores (Fig. 1). It follows that if particles followed the fluid streamlines, many of them

• .. • : . e

0

0

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°°

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,Grain

dia. 5 0 0 ~ m

ul

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PVC rnicrosphere1.3

::. . . . .

.:. - . . . ~

Silica particle 20/.t, •" Range of surface forces less than thickness of this line .-....

FIG. 1. Diagram of small filter pore showing typical particles to be filtered.

would never touch a grain surface and be removed from the flow. Therefore, mechanisms of transport have to be considered which move the particles across the streamlines, so that they arrive adjacent to a grain surface• When they arrive there, an attachment mechanism has to be considered• If the deposited particles are entrained again in the flow, a detachment mechanism is involved•

204

K.J. Ivrs

TRANSPORT MECHANISMS

Straining A filter is not a strainer, as can be seen from FIG. 1. If particles large enough to be strained arrive at the filtration surface they will form a mat and clog it rapidly. This is undesirable, as the depth of the filter will not be used efficiently. Such surface clogging can also take place if the concentration of particles is too high. In such conditions many particles may arrive simultaneously at a pore opening and jam in it by arching action. Such surface straining can be avoided by suitable pretreatment (e.g. microstraining or sedimentation), and can be ameliorated by increasing the flowrate. Opinions differ on the form of structure adopted by the surface mat: one view is that it is a continuous compressible cake (CLEASBYand BAUMANN, 1962), the other that it is a mat partly in and partly on the surface, with holes in it (IvEs, 1963).

Interception If particles remain in streamlines which approach the grain surface to within a particle radius, the particle will contact the surface. This interceptive effect is akin to straining, but is a valid mechanism even for very small particles, Particles transported to these boundary streamlines will owe their final contact tO interception. This mechanism was analysed by STEIN in 1940 and experimentally investigated by ISON (1969) and YAO (1968) more Iecently. The mechanism is characterized by the ratio of the particle diameter to the grain diameter: I = e/d.

Inertia Streamlines approaching a filter grain have to diverge as the flow passes round it. If particles have sufficient inertia they maintain a trajectory which causes them to collide with the grain. Solution of the equations of motion of the particle and fluid (DAVIES, 1952) indicates that the inertial action is characterized by the dimensionless group N : (p~e2v/18 iz d), where p~ is the density of the particle and/z is the dynamic viscosity of the fluid. A graph of the collection efficiency of particles on an obstacle (such as a grain) in the fluid stream, as a function of N indicates that for conditions of rapid filtration of aqueous suspensions this mechanism is unimportant. In the case of air filtration it is a highly significant mechanism and, within limits, increasing the air flow rate increases collection efficiency. In the case of water filtration the reverse is true, higher flow rates leading to lower collection efficiencies.

Sedimentation If the particles are large enough, and have a density significantly greater than that of water, they are subject to a constant velocity relative to the water, in the direction of gravity. The extent to which this will deflect particles from streamlines so that they

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205

may contact a grain surface depends on the relative orientation (divergences) of the fluid streamline velocity vector and the gravitational velocity vector. The effect of sedimentation may be characterized by the dimensionless group S----(p~--p)e2g/ 18 tw, which may be recognized as the ratio of Stokes' velocity for the particle to the fluid approach velocity (ISON and IVES, 1969). The importance of sedimentation in filtration has been demonstrated by ISON for Kaolinite (sp.gr, = 2.6) particles in the size range 2-10 t~m. For very watery flocs, such as occur in water and sewage treatment, sedimentation is not likely to be significant. The concept of sedimentation within filter pores was suggested as long ago as 1904 by HAZEN, but in a rather unsophisticated way, and in relation to slow filtration.

Diffusion Brownian motion is observed to impart a random movement to very small particles in water, due to the thermal energy of the water molecules. For particles greater than about 1 tLm in diameter the viscous drag of the fluid restricts this movement, and the mean free path of the particle is at most one or two particle diameters, and so the mechanism is not important. However, for particles less than 1 tLm the movement becomes increasingly significant v~ith decreasing sizes. This mechanism is expressed in terms of the Peclet Number P = dv/D, being the ratio of movement due to Brownian action, to advective motion of the fluid (D is the Stokes-Einstein diffusion coefficient). This has been studied extensively in air filtration; in rapid filtration IvEs and SHOLJ[ (1965) studied it indirectly and YAO (1968) by direct experimentation.

Hydrodynamic action As mentioned previously, the flow in the filter pores is laminar, with a velocity gradient, i.e. a shear field exists. In a uniform shear field a spherical particle would experience rotation, with a consequent accompanying spherical flow field. This would cause the particle to migrate across the shear field, in a manner analogous to, but not identical with, the swerving path of a spinning ball in flight. If the shear field is not uniform, as in the filter pores, the particle will be deflected by a similar effect, but not in any uniform predictable way. If in addition the particle is not spherical, it will experience further out-of-balance forces moving it across the streamlines. Finally, if the particle is also deformable, the motion will be even more irregular. The net result is that particles will exhibit an apparently random, drifting motion across the streamlines which may cause them to collide with grain surfaces. Although considerable effort has gone into theoretical studies of the motion of particles in fluid shear fields, the complexity of filter pore geometry defies theoretical analysis. Experimental studies of particle migration in capillaries have been made in relation to blood flow and paper technology. The only investigation of this phenomenon in rapid filtration has been made by IsoN (1969). He characterized the mechanism by a simple Reynolds Number (R = dr~v) for the filter bed. However he pointed out how unsatisfactory that this is, and that several alternative dimensionless numbers could equally well be used. He demonstrated experimentally that the effect was significant in the rapid filtration of Kaolinite suspension.

206

K.J. IVES

Orthokinetic floeculation Although scarcely a mechanism for transporting particles to grain surfaces, it has been suggested by CAMP (1964) that orthokinetic (velocity gradient) flocculation in the filter pores could aggregate particles, thus enhancing their probability of removal. This suggestion has not been tested experimentally, although the success of the Banks' clarifier (BANKS, 1965), in which residual sewage humus solids aggregate in the pores of a gravel bed, has been attributed to orthokinetic flocculation. If it is significant, it would be characterized either by the product Gtr (CAMPand STERN,1943) where G is the mean temporal velocity gradient and tr is the mean residence time, in the filter pores, or by the product GtrCo (IvEs, 1968a) where Co is the volume concentration of particles at the commencement of flocculation. In a rapid filter G is given by the power dissipated, shown as head loss, by fluid motion in the filter pores. G = ~pgvH~ ~" \ fizL ]

(2)

where H/L is the hydraulic gradient. The main residence time tr is given by

t, = Lf/v.

(3)

If the hydraulic gradient is taken from the Kozeny-Carman equation

L --

pgf3

(4)

the product Gt, becomes:

Gtr = 13.4 (1 - f ) L f

d"

(5)

Equation (5) indicates that the flocculation within the filter is independent of flowrate and temperature, but depends on the filter porosity, and the ratio of the bed thickness to the grain size. The ratio L i d has been described by some writers as the number of unit cells within the filter length (HEERTJESand LERK,1967; MACKRLE and MACKRLE, 1959; ISONand IVES, 1969). If the flocc~dation criterion is taken as Gt~Co, the situation is more complex as the volume concentration of suspension will vary with position in the filter, i.e. Co varies with L, and this variation is dependent on flow rate and temperature. In either case the hydraulic gradient will increase with filter run time. As the filter becomes clogged, so the flocculation conditions will change. The possibility of the filter as a flocculator has not been fully analysed theoretically, nor tested experimentally in an unequivocal manner.

Combined transport mechanisms It is unlikely that any of these mechanisms acts uniquely. Particles in the flowing suspension will be subject to all of them in varying degree; their relative importance will depend on the fluid flow conditions, the geometry of the filter pores and the nature (size, shape, density) of the particles. Experiments are difficult to perform which isolate the action of each mechanism. With some success Isoy (1969) has demonstrated the

Rapid Filtration

207

significance of interception, sedimentation and hydrodynamic mechanisms for Kaolinite in water; YAO (1968) has shown that a minimum exists in filter efficiency at about 1/~m for spherical plastic particles where they were too large for diffusion and too small for interception and sedimentation to be significant; LE GOFF and DELACI-IAMBRE (1965), have made some interesting observations on neutrally-buoyant particles where sedimentation and inertial mechanisms were absent. FIOURE 2 shows diagrammatically some of the transport mechanisms.

(a) Interception

(d) Sedimentation

(b) Diffusion

(c) Inertia

(e) Hydrodynamic

FI~. 2. Diagram showing the principle of some transport mechanisms. ATTACHMENT MECHANISMS Electrical double layer interaction Between surfaces in water the interaction of electrical double layers can lead to an attraction or repulsion, depending on whether the surfaces have electrokinetic (zeta) potentials of unlike or like sign respectively. Theories of colloid stability enable such attraction or repulsion to be calculated, providing the zeta-potentials of the grain surface and of the particles are known, together with the ionic strength of the solution. Examples of such measurements and calculations have been given by IvEs and GREGORY(1966). As sand and other filter media surfaces, and the great majority of particulate impurities in water have negative zeta-potentials, the double layer interaction will usually

208

K . J . IVES

inhibit attachment. The range of this interaction, however, is greatly dependent on the concentration of dissolved salts in the water. For sewage effluents, or lowland river waters the range will only be of the order of 10 nm. At such small distances, attractive forces of the Van der Waals type become significant and may overcome the repulsion.

Van der Waals' forces These universal attractive forces between atoms and molecules are additive, and lead to an interaction of attraction between grain surfaces and particles in water, although of limited range (usually less than 50 nm). Between a spherical particle and a grain surface (treated as a flat plate as its radius is very much greater than that of the particle) the attraction energy is /4e

E = -- - , 12l

(6)

where A is the Hamaker constant for the two materials of the particle and the grain, in water. For most materials in water A has a value of 0.2 to 5 × 10 -20 J. Equation (6) only applies for very close approach when the separation distance l is much less than the sphere diameter e. The combined action of electrical double layer and van der Waals' forces has been considered in detail by IVES and GREGORY (1966). In model experiments, filtering polyvinylchloride microsphere suspensions through ballotini (glass beads) there was .qualitative agreement with theory regarding attachment or inhibitions of attachment. Similar conclusions were drawn from the filtration of ferric hydroxide flocs through ~and beds, reported by O'MELIA and CRAPPS(1964). The equilibrium between van der Waals' and hydrodynamic forces has been the basis of mathematical models of filtration proposed by HEERTJES and LERK (1967) and by MACKRLEand MACKRLE(1959). Their concepts involved a longer range action o f van der Waals' forces than is given by physico-chemical theory.

Hydration It has been proposed by OULMAN, BURNS and BAUMANN(1964) that the attachment o f particles to filter grains could occur through hydrogen bonding of water molecules between their surfaces. This hypothesis has not been supported by theoretical or experimental evidence, and colloid particles appear to have enhanced stability, i.e. resist attachment, due to hydration layers. Mutual adsorption Another attachment mechanism can arise from the mutual adsorption of dissolved polymers, such as polyelectrolytes or hydrolysis products of alum. These polymers form links and bridges, having one end attached to the grain surface and the other to the particle. Some polymers, being electrolytes, can reduce electrical double layer repulsion; but this is not always the case as nonionic and anionic polymers are effective in promoting particle attachment. In some cases a cation can act as a

Rapid Filtration

209

link between an anionic polymer and a negative site on a surface. This has been observed with Ca 2 ÷ and H ÷. The use of polymers in filtration has been reviewed by MINTS (1964, 1969). DETACHMENT MECHANISMS The usual way of cleaning rapid filters is by reverse flow flushing with water, sometimes preceded or accompanied by scouring with air bubbles. This demonstrably detaches the particles adhering to the filter grains, and so the attachment and transport mechanisms are reversible. It is not clear whether the cleaning is due to hydraulic scour alone, or whether collision of grains during cleaning also detaches particles. However, even without reverse flow flushing, there is evidence that increase of flowrate through a filter will detach particles causing a more turbid filtrate (TuEPKER, 1968). The intensity of this effect depends not only on the magnitude of the increase of flowrate, but also on the rate of change. The effect is diminished if polyelectrolytes are applied to the suspension to be filtered. If the flowrate is maintained constant, which is the normal mode of operation of rapid filters, opinions differ on whether detachment takes place. The principal proponent of a detachment mechanism is MINTS(1951) (MINTS, PASKUTSKAYAand CHERNOVA, 1967) who has produced experimental evidence of aggregates of particles appearing in the filtrate to support his views. Similar concepts have been put forward by SHEKHTMAN(1961), but without experimental support. Detachment during filtration was considered unlikely by Ives on theoretical grounds; the experiments of Stanley, in which radioactive ferric flocs did not move after their attachment during filtration, have been quoted as evidence. Mackrle also opposed the concept of detachment because the flow of clean water through a clogged filter at constant rate produced no particles in the filtrate. The disagreement has not yet been resolved. (MINTS, 1966, MACKRLE,1960).

MATHEMATICAL MODELS Clarification Unisize media. In spite of the detailed investigations of mechanisms of filtration it is not possible to predict the degree of clarification of a particular suspension by a given filter, from knowledge of the characteristics of the suspension and the media. Nevertheless, sophisticated mathematical models of filtration have been developed, leaving certain constants of the process to be determined empirically. These mathematical models of clarification by filtration all derive from the simplest case of a homogeneous, non-flocculating suspension flowing at constant rate through an isotropic, uniform permeable bed of media. From this it is assumed that initially, when the bed is clean (i.e. contains no deposited suspension particles), every layer of the filter is equally efficient at removing particles from suspension. Also it is assumed that in every layer the suspension entering it and leaving it is uniformly dispersed. These assumptions are presented mathematically in the form ~C - - AC c~L

(7)

210

K.J. Ivrs

where C is the concentration of particles in the flow, L is the distance from the inlet face of the filter media, and A is the filter coefficient (a measure of the efficiency of clarification). Equation (7) was first proposed by IWASAKIin 1937, although in relation to slow sand filtration. It may be regarded as having a statistical basis (LITWINISZYN, 1963; HSIUNG and CLEASBY,1968) with A representing the probability of removal of a particle, by the filter. At the commencement of filtration, when the filter run time t is zero, equation (7) can be integrated to yield C = Co exp ( - '~o L),

(8)

where Co is the inlet concentration, and 2~o is the initial value of the filter coefficient at t = 0. Although this has been the basis for mathematical models of filtration since 1937, it was not until 1965 that Ison (ISON and IRES, 1969) demonstrated experimentally its validity. Ison's result also showed that, for a non-flocculating suspension, each size fraction of suspension particles followed equation (8), independently, although, of course, with different values of ~o for each fraction. Usually values of A represent a mean for the whole suspension, even though it may be heterodisperse. Only MACKRLEand MACKRLE(1959) have attempted to create a mathematical model for A (in a series form) for heterodisperse suspensions. Another basic equation, also formulated initially by Iwasaki, is the mass balance for the suspension particles. In principle it is simply a statement that particles removed from suspension are deposited in the filter pores. However, its simplicity is misleading as there are local gradients of suspension concentration and deposit concentration with respect to time and distance. Equations written for "constant time" have to take into account that suspension takes a finite time to traverse a layer of the filter, and simultaneous events (in the clock sense) are not necessarily linked. This has been reviewed in considerable depth independently by HORNER (1968) and DEB (1969) who concluded with the relationship ~C_ 1 O~q_f--crdC ~3L v ~t v Ot'

(9)

where t is the filter run time, i.e. the elapsed time since the suspension front first reached the distance L, v is the approachvelocity, and ~ is volume of deposited particles, per unit bed volume, known as the specific deposit. For dimensional consistency the concentration C should be volume by volume. Usually the t3C/St term is negligible and is omitted; this simplifies subsequent calculations. Also omitted from equation (9) is a diffusional term, as it is assumed that advective motion of the particles is very much greater than diffusional movement. However, diffusional action due to significant concentration gradients has been investigated by LITWINISZYN(1966). Most proponents of mathematical models of filtration have recognized that the filter coefficient ~ is not constant during the filtration process, due to the deposited particles altering the characteristics of the filtration action. It follows that A must be written as some function of the specific deposit ~. The most general of all the variously proposed functions is that of IvEs (1969): A ---- ,~o ( I -}- flcr/f)y ( I - - o/f) z ( I - - ~/u.) ~,

(lO)

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211

where/7 is a geometric constant relating to the packing of the filter grains, ~, is the ultimate or saturation value of the specific deposit ( < porosity f ) , y, z, x are empirical exponents. The form of equation (10) is not based on detailed examination of the filtration mechanisms, but on more general assumptions of the importance of pore geometry and interstitial velocity. The first term in brackets of equation (10) is based on an increase in specific surface in the filter due to the localized coatings of deposited particles on grains. This implies that there is an increase in filtration clarification efficiency during the initial stages of filtration; this implication is not accepted by many investigators. The second term is based on a diminution of specific surface in the filter due to accumulations of deposits in side spaces in pores. These first two terms are based on the sphere and capillary model of MACKRLE et al. (1965). The third term allows for an increase in mean interstitial velocity due to the restriction in pore cross-section by deposits. It is assumed that a limiting velocity is reached (when the specific deposit is au) such that further deposition of particles is inhibited. This term is based on MAROUDAS' (1965) model. By suitable choice of the exponents y, z, x most previous mathematical models can be expressed, viz: IWASAKI (1937):

y = 1, Z = 0 X = 0

A/ha = IrES (1960a):

(1 -t-/7
(11)

y = 1, z ---- 1, x = 1

The expansion of equation (10) equals the expansion of Ives' equation (12) which is therefore seen to be a special case of the general equation A --: Ao + aa -- b a 2 / ( f MACKRLE et al. (1965);

a).

(12)

x ---- 0

A/Ao = (1 +/Ta/f)" (1 -- a]f)L

(13)

SHEKHTMAN(1961), HEERTJESand LERK (1967): y = 0, Z ----- 1, X = 0 A/Ao -----(1 -- o/f). MAROUDAS (1965) ;

y=O,z=O,x= A/Ao = (1 -- ~/~,).

(14) I (15)

A recent specific surface model by DEB (1969) takes into account grain to grain contacts, and provides a non-monotonic relationship between A and a, similar in some respects to Mackrle's equation (13). Its form does not appear to be covered completely by the general equation (10). The form of equation (10) indicates that the pure exponential equation (8) will be modified by the specific deposit. As the value of a varies with position (L) in the filter, and with filter run time (t), the form of the concentration curves will also vary. This is shown in FIG. 3, where it can be seen that near the inlet face of the filter a zone of deposit saturation ultimately forms, through which the suspension concentration is unaltered. If filtration continues, this zone extends further and further into the filter media. This was first observed experimentally by ELIASSEN(194I).

212

K . J . IVES

~2

~ t = Dsi tanceL

O

FIG. 3. Curves of suspension concentration varying with distance in the filter media (L) and time of filter run (t).

To generate these curves mathematically it is necessary to solve the system of equations (7), (9) and (10). Explicit solutions have been attempted by most of the authors already mentioned; some, however, have found the mathematics too complex and have produced numerical solutions by automatic digital computer (IVES, 1960b). Not all authors of mathematical models have accepted the concepts of equations (7) and (10). MINa'S (1951) and SIaErAaTMA~(1965) have considered the detachment mechanism to be important, and that a constant rate of deposition (i.e. constant value of,~) is counteracted by a variable rate of detachment. Mathematically this is expressed as :

OC a =,~C---a, BL v

----

(16)

where a is a detachment or scour coefficient. Equations (9) and (16) can be combined, and a solution derived: by Mints as a series, by Shekhtman with some unresolved integral terms. These solutions give curves similar to FIG. 3, but with no phase where concentrations are improving with filter run time. A comment on the mathematical implications of equation (16) has been published, ([VES, 1969) with an attempt to reconcile it with equation (10). Some other mathematical models have been suggested, but study of them is unrewarding as their theoretical bases are obscure, and they are unsupported by any experimental evidence (KLENOV, 1960; HALL, 1957; BORELIand JOVASOVIC, 1961). Size-graded media. Except in the case of experimental filters, the media are rarely unisized, although a mixed size remaining heterogeneously mixed could be treated theoretically like a unisize media bed. Usually media are size-graded either deliberately, or because unisize media are expensive to prepare by sieving in large quantities. From the normal practice of filter washing by upflow fluidization it follows that many sizegraded filters have a size-succession from finest at the top to coarsest at the bottom. Where media of differing sizes and densities are chosen, as in the multiple layer filters

Rapid Filtration

213

to be described later, the size strata may be in any order depending on the media chosen by the designer. Both from the study of filtration mechanisms and the mathematical models dealing with specific surface, it is evident that the filter coefficient h will vary as an inverse function of grain size d. = const. × d-".

(17)

The exponent n has been variously quoted between 1 and 3, and is evidently dependent on the nature of the media (probably shape) and the characteristics of the suspension (i.e. the transport mechanism). If n is determined empirically, equation (17) can be combined with (10) and also with (7) and (9) to produce a mathematical description of the concentration curves with distance (L) and filter run time (t), providing that the variation of size d with distance L is known. Assuming a linear distribution of size with distance, which is a rather unreal simplification, DIAPER and IrES (1965) produced explicit solutions for the concentration curves. A more realistic approach is to treat the filter as comprising a series of layers each containing a discrete uniform size. This has to be treated numerically by digital computation, but has the advantage of being equally applicable to continuously size-graded as well as multiple layer filters. This computational method has been used by MO~tANKA(1969) for multilayer filtration. Radialflow. Study of the filtration transport mechanisms reveals that the flowrate has a marked effect on the efficiency of clarification by filtration. Increasing flowrates lead to diminishing probabilities of particles being retained, hence the filter coefficient Awill vary as an inverse function of filtration velocity v: •~ = const. × v-",

(18)

where the exponent m has been variously quoted between 0.7 and 4. Usually rapid filters are operated at constant rate, although some designs exist in which the flowrate declines during the filter run, as the media becomes clogged. Normally, constant rate filters, operating as a bed of fixed cross-section, cannot take any operational advantage of the variability of h with v. However, in radial flow filters, of cylindrical form where the suspension enters at the axis, filters radially outwards to be collected at the periphery, the filtration velocity varies inversely with radial distance. Hence, filtration efficiency increases in the direction of flow. This situation has been treated theoretically by SrmKHTMAN (1961) and by TRZASKA(1966) using equation (14) as a basis; Shekhtman's work was supported experimentally. MACKRLE et al. (1965) also made an experimental and theoretical study, based on equation (13), and HORNER (1968) used a wedge-shaped sector model in experimentally evaluating his theory. Homer assumed that h oc 1Iv O.e. that m ---- 1), and transformed equations (7) and (I0) into cylindrical co-ordinates, with the result: _

co.___C= ro____~Aoro (1 + fl~lf) y (1 -- a l f ) z (1 -- ,,/%)x C,

0~

(19)

Vo

where : is the ratio of the radial distance (r) to the radius of the inlet face (to) and AOrois a radial filter coefficient (equal to Ao Vo, where Vo is inlet face velocity). Together with a form of equation (9) in cylindrical co-ordinates, Homer obtained analytical and computer solutions of equation (19).

214

K.J. Ivrs

Comparisons of linear and radial filtration are difficult because of the different geometries, and the varying velocity in the latter. One basis of comparison can be the number of bed volumes filtered (as in ion-exchange technology) to a given head loss to provide a certain standard of filtrate. By comparing the mathematical models of filtration DES (1968b) has produced the following equation for equality of performance of a linear and radial filter containing the same unisized media.

L ~rO (72 _ 1).

(20)

Head loss If filter media are clarifying suspensions as they flow through, it follows that the pores of the media accumulate deposits which cause a loss of permeability, or increased flow resistance. The filter media exhibit a resistance to flow, even to clear water, which can be predicted from the Kozeny-Carman equation (21)

eH eL

--

kvvs 2 gf~ '

(21)

where H is the head loss (water gauge), s is the specific surface (surface of media per unit bed volume), andfx is the porosity, and k is usually taken as 5-0. In the case of clean filter media, s = So and f l = f, and equation (21) becomes

(eH) _ k v v s o 2 --~ o gfa

(22)

which is also the case for the commencement of a filter run when t = 0. In the case of a filter containing specific deposit a (which varies in value from layer to layer, i.e. varies with L, and which increases with filter run time t): s = So (1 + 8,~/f)" (1 -

a/f),,

A = f(1 - a/f).

It follows that

e H _ kvvso 2 (1 + flo/f) 2y (1 -- a/f) 2z-3. eL

(23)

gf 3

So the ratio of the hydraulic gradient at any time to the initial hydraulic gradient is given by: (eHleL)l(eHleL)o = (I + 8alf) 2, (1 - - a / f ) 2=-3

In the special case

y

=

z

=

(24)

1

(eH/eL)/(eH/OL)o = (1 + 8a/f)2/(1 -- a/f).

(25)

Expansion of the right-hand side gives

(OH/eL)/(OH/OL)o = 1 + (2/3 + 1 ) f + (8 + 1)2

+ (8 + 1)a

+ .... (26)

Rapid Filtration

215

To a first approximation the head loss per unit depth is proportional to the local specific deposit, particularly when a <
(27)

where Ho is the initial total head loss through the filter media. Equation (27) has been reported by various observers, summarized by MINTS (1966). Total head loss through a filter and its increase with filter run time is a normal operating observation. Usually the filter run is stopped and the bed cleaned when this total head loss reaches a predetermined limit. Sometimes the filter is cleaned on a time cycle (e.g. 24 hr) even if the head loss has not reached its limit; very occasionally the filter is cleaned when the quality of the filtrate has deteriorated. The implications of this are discussed more fully under "Optimization". The pattern of head loss, or pressure variation, through a filter given by equations (22) and (25) are shown in FIC. 4. Such patterns are also observed on experimental filter columns fitted with pressure probes throughout the depth of the media (IrEs, 1966). Such pressure lines are sometimes called Michau curves, as they were first discussed in detail by MICHAU (1951). Recently pressure probes have been fitted in operating waterworks filters at Chapel Hill, North Carolina and at Staines in the U.K. where similar patterns have been recorded (IrEs, 1968b). No details of these practical observations have yet been published, but the Staines' observations have shown that a 15 cm diameter model filter column performed in a manner identical to the full-scale filter. Optimization

In recent years it has been appreciated that knowledge of the detailed operation of filters could be applied to produce more efficient designs. One aspect of this has been the concept of optimization of the design so that both the hydraulic capacity and the clarification capacity of a filter could be used fully. An optimum is achieved when the filter design and operation cause the filter to reach its head loss limit (i.e. when the pressure line just touches atmospheric pressure in the filter media--FIG. 4) at the same time as the filtrate quality deteriorates to an unacceptable value. Formal procedures for achieving this have been published by MINTS (1966) and extended by I w s (1968b). A review of optimization of rapid filters has been produced as a thesis by GtrR (1969). These methods achieve an optimum design by altering the physical variables of media thickness, flowrate and media grain size. In addition to these physical variables it is possible to achieve optimum conditions by altering the nature of the suspension with polyelectrolytes (MINTS, 1969; MINTS et aL, 1968), or varying chemical dose (KREISSLet aL, 1968) or with polyphosphates (SMITU and MEDLAR, 1968). This is the most flexible method but is difficult to formalize in any predictive manner. One way of operating a filter so that flexibility is achieved with polyelectrolyte dosing is to have a small pilot filter with the control equipment.

216

K. LIvEs Atmospheric pressure

/

Zone belowl ~ I

\

\

\

J

f .o

. (a)

=0

__~<~t

H limit

Uniform filter

Anthracite

Sand

j

j~

HO

H

(b) Two-layer filter

FIG. 4. Pressure profiles through the depth of filter media, changing during the time of filter run.

Constant monitoring of the performance of this pilot filter gives a guide to the polyelectrolyte dose required at the main filter inlet (CONLEY, 1965). FILTER WASHING With the exception of a few unusual designs, rapid filters are washed by an upflow of water through the media which carries away the deposits from the filter pores. In most cases this flushing is preceded by some agitation of the media to scrub off

Rapid FiRration

217

the adhering deposits. In the U.K. and Europe this is usually accomplished by blowing air, as fine bubbles, up through the media: a process known as "air scour". In North America an auxiliary wash system of fixed or moving water jets, known as "surface wash", provides this scouring process. In a few filter designs a set of mechanical rakes provides agitation of the media, and in some cases--notably the Turn-over Filter, the Hydromation filter and the Simater filter--the media is removed hydraulically from the filter unit, passes through an external washing column and is returned. In some cases these various methods of agitation may accompany all or part of the upflow flushing. There is controversy concerning the principal cause of detachment of deposits from the grains during washing. One opinion is that it is due to grain collisions caused by the washwater. In this case the bed should be in its minimum expanded (just-fluidized) state. The other opinion is that it is due to the shear stress of the water flowing past the grains, in which case it is immaterial how much the bed is expanded as the maximum shear is exerted when all the grains are supported by the drag of upward flow. A thesis study on a laboratory model by ULUO (1967) supported the latter opinion. However experiments on practical filters by JOHNSONand CLEASBV(1966) tended to support the collision concept. Their work dispelled the widely-held idea that the terminal washwater turbidity was an indicator of the effectiveness of the filter wash. A number of studies in Holland (DE LAT~OUDER,1961, 1962) have been made of washing, but mainly to provide practical, rather than fundamental, information. Experiments were also conducted by BAVLIS(1954) to demonstrate the factors causing disruption of the gravel support media during washing. Because of problems of this nature, either due to, or causing, uneven distribution of washwater, a cellular design of filter has been produced (HEBERT, 1966). Each cell, about 1.5 m 2 in plan, maintains its own washwater flow in a uniform manner. A washing cell is also utilized in the Hardinge filter, but this traverses the filter, washing it strip by strip, while the rest of the filter continues to operate. Several different patented devices exist to distribute washwater evenly under the media, and to collect it uniformly from above the media; these have been subjected to some tests reported by HIRSC~ (1968). No theory of filter washing relates the amount of washwater required to the degree of clogging of the media. All that is available is a relationship between the degree of expansion of the media (Le/L, where Le is the expanded thickness of the filter bed) and the upflow washrate per unit area (v~) (FAIR, GEYrR and OICtrN, 1968). Le L

1--f 1 -

(vw/vY

(28)

where vs is the settling velocity of a single grain. The exponent q varies from 0.2 to 0.3 depending on the shape of the grains and the hydrodynamic regime. It is best determined experimentally, but the value 0-22 is attributed to rounded sand grains. Equation (28) applies to a filter bed of grains of uniform settling velocity. If, however, due to size or density distribution the grains in different layers have differing settling velocities, then a summed equation is necessary Le __ (1 - - f ) ~ P' L /-..u 1 - - (Vw/Vs~)~' i=1

w.R. 4 / 3 - - c

(29)

218

K . J . IVES

where vst represents the settling velocity of a grain present in a thickness fraction ptL. As the settling velocities of grains depend on water temperature, it follows that

the same upwash rate will produce different expansions at winter and summer water temperatures. The total head loss across the media during backwashing can be calculated as the upward pressure difference on a unit plan area will equal the downward weight of the grains in water, when the filter bed is fully fluidized. I~,, = (1 - f ) (p. -

p) L / p ,

(30)

where pg is the density of the granular media. If media of various densities (pot) and porosities (f0 are located in different fractional thickness (p~L) a summed form must replace this equation: Hw = ~

(1 -- f~) (pg, -- p) p, L/p.

(31)

i=l

Examples of measured expansions and head losses during backwashing of different media have been presented in graphical form by DIAPER and IVES(1965). Examples of calculations using the expansion equations (28) and (29) are given by FAIR, GEYER and OKUN (1968), together with some practical details of filter washing.

FILTER

DESIGNS

The structural design of a filter is a straightforward matter, taking into account the dimensions of the filter unit, the pressure differences and the need to prevent corrosion. For small units, and pressure filters the usual material is mild steel, suitably protected; for larger designs, usually open to atmosphere (and therefore called gravity filters), reinforced concrete is employed. Most filter structures are 4 or 5 m high and may be from 1 m diameter to 100 m 2 plan, or more. Differences in design usually occur: (a) in the underdrain system, (b) in the hydraulic control equipment, (c) in the types of media employed, (d) in the flow direction through the media, (e) in the method of washing. Underdrains

These serve to collect the filtered water in downflow designs, and to distribute the air, if used, and washwater during cleaning. The simplest forms are perforated lateral pipes, packed round with gravel. Other designs use a false floor through which nozzles penetrate into the base of the coarse media. Various nozzle designs have been reviewed by DE LATHOUDER(1961). False floors of porous plate, and those containing funnels with specially sized balls in them (Wheeler bottom) are discussed by FAIR, GEYERand OKUN (1968).

Rapid Filtration

219

Control equipment Usually the hydraulic control equipment maintains a constant flow through the filter in spite of the rising head loss due to clogging. The various devices usually act on the filtered water outlet pipe gradually opening a throttling valve, actuated by a float. Some filters are controlled by an outlet weir, with the water level rising over the filter media as the filter clogs; others are maintained at constant output by pumped control. These have been reviewed by HUISMAN (1969). An absence of control equipment has been suggested by HUDSON (1959), SO that the filtered water output of the unit diminishes as the media becomes clogged. Usually an orifice is placed in the filtrate pipe to provide hydraulic resistance to too great a rate of flow (which would cause poor quality filtrate) at the beginning of the filter run. Some favourable experience of operating filters without flow controllers has been reported by CLEASBY(1969).

Media Sand has been the traditional material for filtration, but in recent years some alternative materials have been considered. Most waterworks filters rely principally on sand from 0.4 to 1.0 mm size, although where they are used as prefilters to slow filtration, a coarser grade is employed (0.7 to 2.0 mm). For tertiary treatment of sewage a coarse grade is also used (1.0 to 2.5 mm), as the filtrate requirements are not so stringent as for drinking water. In some cases anthracite has replaced sand. This less dense, angular material packs to a more open porosity than sand and gives rise to lower initial head loss and lower washrates. It is, however, more expensive. Dual media filters, in which coarse anthracite overlies finer sand, are becoming increasingly used as they can sustain higher rates of flow, for comparable performance, than single media filters. Usually a layer of 1.0 to 2.5 mm anthracite is placed above 0.4 to 1.0 mm sand. Triple media filters, also referred to as multimedia filters employ a third, denser, layer below the sand. Garnet sand, 0.2 to 0.3 mm, has been used (CoNLEY, 1965), although fused alumina of the same size is an alternative, which may be cheaper. Operating experience of multimedia filters has been described by CULB~ArH (1967), particularly dealing with high turbidity waters. Experimentally, a five-layer filter has been tested (MoHANKA, 1969), with polystyrene grains above the anthracite layer, and very dense, fine magnetite below the garnet sand. Filtering suspensions of iron hydroxide floc this filter showed an advantage of 2.5 to 3 times over a conventional sand filter of equivalent grading. The principal characteristics of some filter media are as follows:

Media Sand Anthracite Garnet sand Fused alumina Magnetite

Specific gravity 2.65 1.40 3-85 4.00 4.90

Sphericity (sphere = 1.0) 0.85 0.70 0.80 -0.83

Porosity (pore vol/filter vol) 0.40 0.50 0.47 -0-42

220

K.J. IVES

Flow direction Normally the flow direction is downwards through the media. However, consideration of the theoretical advantages of filtering through successively finer layers of sand, led to the design of the contact clarifier, in which the flow is upward, and the A K X biflow filter in the Soviet Union (KAsTAL'SKIIand MINTS, 1962). At the same time the Immedium upflow and Immedium biflow filters were developed in Holland (HuISMAN, 1969). In the biflow filter about 80 per cent of the flow passes upwards to the filtrate collector pipe which is buried in the sand about 150 mm below the surface. The other 20 per cent filters downwards to the filtrate collector. This flow opposition maintains the filter bed in compression during clogging; in the upflow filters, lifting of the bed has to be prevented, either by a grid in the sand surface, or by having a very deep bed of media. A radical departure from all other designs has been made in the Simater filter (ANON., 1968), in which flow is radial from an axial inlet pipe through a cylindrical annulus of sand to a peripheral, cylindrical, filtrate collector. This unit combines continuous washing and sand recycling with the novel, but theoretically sound, concept of radial flow filtration.

Washing Filter washing by various practical methods has already been discussed. TERTIARY TREATMENT OF SEWAGE Although most studies of rapid filtration have been concerned with drinking water purification, there is a growing interest in its application to tertiary treatment of sewage. The object of such filtration is to reduce the suspended solids in the secondary tank effluent; this usually results in an accompanying reduction in biochemical oxygen demand. Usually the filters have to treat wastewater with suspended solids of about 30 mg/1, to achieve filtrates of 10 mg/1 or below, according to conditions of effluent discharge. ]NIAYLOR,EVANS and DUNSCOMBE(1967) have described the filtration experience at Luton Sewage Works. In a comparison between a down flow sand filter (0.9 m thick) and an upflow filter (1.5 m thick) the upflow produced a consistently better filtrate at both 12.5 and 8.5 m/hr filtration rates. Good results for upflow filtration were also reported by TRUESDALEand BIRKBECK(1968), with filtrates below 10 mg/1 for over 90 per cent of the time at rates up to 15 m/hr. Pilot scale experiments at a sewage works have been reported in some detail by OAKLEY and CRIPPS (1969). Parallel tests were run on sand beds 0-6 m and 0.9 m deep, one containing angular, the other, rounded media; on a three-layer anthracitesand-garnet downflow filter; on an upflow filter containing 0.6 m sand; and on an upflow filter containing 1.2 m sand. Generally the media was coarse, in the 1.0 to 2.0 mm range. By contrast a radial flow continuous filter contained finer sand, 0-5 to 1.0 ram. The angular sand downflow filter, the upflow (deep bed) and radial flow filters were all capable of maintaining a filtrate below 10 mg/1 at rates up to 12 m/hr for the vertical filters and 22 ma/hr for a 1.07 m diameter radial filter.

Rapid Filtration

221

T e r t i a r y t r e a t m e n t including H a r d i n g e c o n t i n u o u s flow filters has been described by LYNAM (1969). O p e r a t i n g m a i n l y at a b o u t 2 m/hr, with 0.28 m thickness o f 0.5 to 1-0 m m sand, these filters have p r o d u c e d filtrates o f a b o u t 5 mg/1 s u s p e n d e d solids. T h e c o n c e p t o f t e r t i a r y t r e a t m e n t o f effluent h a s n o w been extended to the r e c l a m a tion o f w a t e r f r o m wastewater. C o n s e q u e n t l y a d d i t i o n a l t r e a t m e n t units are being a d d e d to the end o f c o n v e n t i o n a l sewage t r e a t m e n t , a n d usually r a p i d filtration is a m o n g them. A s these r e c l a m a t i o n systems are p r o d u c i n g w a t e r for industrial o r r e c r e a t i o n a l use, the filtration units are often identical to those in w a t e r w o r k s practice (CULP, 1968). A l r e a d y , p o t a b l e w a t e r is being p r o d u c e d by such r e c l a m a t i o n systems (STANDER a n d VAN Vtn:REN, 1969) including filters, a n d the w a t e r has gone the full cycle. REFERENCES ANONYMOUS(1968) The Simater continuous sand filter. Wat. wat. Engng 72, 20-21. BANKSD. H. (1965) Upward flow clarifier for treating sewage effluents. Survr munic. Cry Engr 125, No. 3789, 45-46. BAYLISJ. R. (1954) Washing and maintenance of filters. J. Am. Wat. WAs Ass. 46, 176-186. BORELI M. and JovAsovIc D. (1961) Clogging of porous media. Int. Ass. Hydraulic Research. 9th Convention, Dubrovnik. pp. 516-520. CAMP T. R. and STEIN P. C. (1943) Velocity gradients and internal work in fluid motion. J. Boston Soc. Cir. Engrs. 30, 219-237. CAMPT. R. (1964) Theory of water filtration. J. San. Engng Div., Proc. Am. Soc. civ. Engrs 90, SA4, 1-30.

CLEASBYJ. L. and BAUMANNE. R. (1962) Selection of sand filtration rates. J. Am. Wat. WAs Ass. 54, 579-602. CLEASBYJ. L. (1969) Filter rate control without rate controllers. J. Am. Wat. WksAss. 61, 181-185. CONLEY W. R. (1965) Integration of the clarification process. J. Am. War. WAs Ass. 57, 1333-1345. CULBREATHM. C. (1967) Experience with a multimedia filter. J. Am. Wat. WAs Ass. 59, 1014-1022. CuLp R. L. (1968) Wastewater reclamation at South Tahoe Public Utilities District. J. Am. Wat. WAs Ass. 60, 84-94. DAVIESC. N. (1952) The separation of airborne dust and particles.Proc. Inst. mech. Engrs B1, 185-198. DEB A. K. (1969) Theory of sand filtration. J. San. Eng. Div., Proc. Am. Soc. cir. Engrs 95, SA3, 399422. DIAPER E. W. J. and IVESK. J. (1965) Filtration through size-graded media. J. San. Engng Div., Proc. Am. Soc. cir. Engrs 91, SA3, 89-114. EL/ASSESR. (1941) Clogging of rapid sand filters. J. Am. Wat. WAs Ass, 33, 926-942. FAIR G. M., GEYERJ. C. and OKUN D. A. (1968) Water and Wastewater Engineering. Vol. 2 Water Purification and Wastewater Treatment and Disposal, Chap. 2. Wiley, New York. GUR A. (1969) Optimisation and Theory of Water Filtration. Ph.D. thesis. University of London. HALL W. A. (1957) An analysis of sand filtration. J. San. Eng. Div., Proc. Am. Soc. cir. Engrs 83, SA3, 1276. 1-1276.9. HAZES A. (1904) On sedimentation. Trans. Am. Soc. cir. Engrs 53, 45-88. HEBERT R. E. (1966) Development of a new type of rapid sand filter. J. San. Engng Div., Proc. Am. Soc. cio. Engrs 92, SA1, 31-40. HEERTJES P. M. and LERK C. F. (1967) The functioning of deep bed filters. Part II, The filtration of flocculated suspensions. Trans. Inst. chem. Engrs 45, T138-T145. HiRscrt A. A. (1968) Filter backwashing tests and upflow equalization. J. San. Engng Div., Proc. Am. Soc. cir. Engrs 94, SA1,129-146. HORNERR. M. W. (1968) Water Clarification andAquifer Recharge. Ph.D. thesis. University of London. HSlUNG K. Y. and CLEASBYJ. L. (1968) Prediction of filter performance. J. San. Engng Div., Proc. Am. Soc. cir. Engrs 94, SA6, 1043-1069. HUDSON H. E. (1959) Declining rate filtration. J. Am. Wat. WAs Ass. 51, 1455-1463. HUISMANL. (1969) Trends in the Design, Construction and Operation of Filtration Plant. Special Subject No. 8, International Water Supply Congress, Vienna 1969. International Water Supply Association, London. ISON C. R. and IVES K. J. (1969) Removal mechanisms in deep bed filtration. Chem. Engng Sci. 24, 717-729.

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IvEs K. J. (1960a) Rational design of filters. Proc. Inst. cir. Engrs 16, 189-193. IvEs K. J. (1960b) Simulation of filtration on electronic digital computer. J. Am. War. Wks Ass. 52, 933-939. IVES K. J. (1963) Simplified rational analysis of filter behaviour. Proc. Inst. cir. Engrs 25, 345-364. IVES K. J. and Snotai I. (1965) Research on variables affecting filtration. J. San. Engng Div., Proc. Am. Soc. cir. Engrs 91, SA4, 1-19. IVES K. J. and St-IOLJII. (1966) Discussion. J. San. Engng Div. Proc. Am. Soe. cir. Engrs 92, SA1,328-329. IVES K. J. and SHot.Jr I. (1966) Discussion. J. San. Engng Div. Proe. Am. Soc. cir. Engrs 92, SA5, 106-109. IvEs K. J. (1966) The use of models in filter design. Effl. Wat. Trtmt. J16, 552-555, 591-596. IVES K. J. and GREGORYJ. (1966) Surface forces in filtration. Proc. Soe. War. Trtmt Exam. 15, 93-116. IvEs K. J. (1968a)Theory of operation of sludge blanket clarifiers. Proc. lnst. cir. Engrs 39, 243-260. IVES K. J. (1968b) Advances in deep bed filtration. Symposium "'Advances in Filtration". Inst. Chem. Engrs. North Western Branch, Manchester 1968. pp. TI-T14. Institution of Chemical Engineers, London. IvEs K. J. (1969) Theory of Filtration. Special Subject No. 7, International Water Supply Congress, Vienna 1969. International Water Supply Association, London. IWASAKIT. (1937) Some notes on sand filtration. J. Am. Wat. Wks Ass. 29, 1591-1602. JOI~NSON R. L. and CLEASBYJ. L. (1966) Effect of backwash on filter effluent quality. J. San. Engng Div., Proc. Am. Soc. cir. Engrs 92, SA1,215-228. KASTAL'SKn A. A. and MINTS D. M. (1962) Treatment of Water for Drinking and Industrial Water Supply. (In Russian.) State Publishing House "Vysshaya Shkola", Moscow. KLENOVV. B. (1960) Various questions on the calculation of filters. (In Russian). Izv. Akad. Nauk Uz. SSR, Ser. Tekhn. Nauk 5, 55-62. KREISSL J. F., ROBECKG. G., and SOMMERVILLEG. A. (1968) Use of pilot filters to predict optimum chemical feeds. J. Am. Wat. Wks Ass. 60, 299-314. DE LATHOUDERA. (1961) Measurements of Pressure Loss in Filter Nozzles. (In Dutch,) Communication No. 3 of the Committee for Construction of Filters of the Institution for the Testing o f Waterworks Materials. K.L W.A. 42 pp. Moormans Periodieke Pers N.V. Den Haag. DE LATHOUDERA. and SOLLMANM. (1961) Expansionofthe Sand Bed in an Experimental Filter in which Backwashing with Water is Combined with Airwash. (In Dutch.) Communication No. 4. 17 pp. Committee for Construction of Filters of the Institution for the Testing of Waterworks Materials. K.I.W.A. Moormans Periodieke Pers N.V. Den Haag. DE LATHOUDERA, and SOLLMANM. (1962) Some Orientating Experiments to Determine the Water and Air Velocities in a Filter Bed during Backwashing and the Quantities of Air in it. (In Dutch.) Communication No. 5. 21 pp. Committee for Construction of Filters of the Institution for the Testing of Waterworks Materials. K.I.W.A. Moormans Periodieke Pers N.V. Den Haag. DE LATHOUDERA. and SOLLMANM. (1962) Discussion of Some Phenomena Occurring in a Filter after putting Airwash into Operation. (In Dutch.) Communication No. 6. 20 pp. Committee for Construction of Filters of the Institution for the Testing of Waterworks Materials. K.I.W.A. Moormans Periodieke Pers N.V. Den Haag. DE LATHOUDERA. and SOLLMAN M. (1962) Separation of Filter Sand by Backwashing. (In Dutch.) Communication No. 7. 19 pp. Committee for Construction of Filters of the Institution for the Testing of Waterworks Materials. K.I.W.A. Moormans Periodieke Pers N.V. Den Haag. LE GoFF P. and DeLACrIAraBaEY. (1965) Study of a model of clogging of a filter medium. Flow of a suspension of microspheres through a mass of macrospheres. (In French.) Rev. Franc. Corps. Gras. 12, 3-1 I. LITWINISZYNJ. (1963) Colmatage considered as a certain stochastic process. Bull. Acad. Polon. Sck, Ser. Sci. Tech. 11, 81-85. LITWINISZYNJ. (1966) Colmatage accompanied by diffusion. Bull. Acad. Polon. Sci., Ser. Sci. Tech. 14, 295-301. LYNAr~ B., Ea~rELT G. and MCALOON T. (1969) Tertiary treatment at Metro Chicago by means of rapid sand filtration and microstrainers. J. Wat. Poll. Control Fed. 41, 247-279. MACKaLE V. and MACKRLES. (1959) Adhesion in filter beds. (In Czech.) Rozpravy Cesk. Acad. Ved. Rada Tech. Ved. 69, 4-85. MACI(RLE V. (1960) Study of the Phenomenon of Adherence. Clogging in Porous Medium. (In French.) Doct. D'Univ. thesis. University of Grenoble. MACKRLE V., DRACI(A O. and S w c J. (1965) Hydrodynamics o f the Disposal o f Low Level LiquM Radioactive Wastes in Soil. International Atomic Energy Agency Contract Report No. 98. Czechoslovak Academy of Science Institute of Hydrodynamics, Prague. MAROLrDASA. and EISENICLAMP. (1965) Clarification of suspensions: a study of particle deposition in granular media. Chem. Engng Sci. 20, 867-873. MIcr~AU R. (1951) Pressure diagrams in filters. (In French.)L'Eau 38, 191-194.

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223

MINTS D. M. (1951) Kinetics of filtration of low-concentration water suspensions in water purification filters. (In Russian.) Dokl. Akad. Nauk SSSR 78, 315-318. MINTS D. M. (1964) Aids to Coagulation. General Report No. 5. InternationalWater Supply Congress, Stockholm 1964. International Water Supply Association, London. MtNTS D. M. (1966) Modern Theory of filtration. Special Subject No. 10. International Water Supply Congress, Barcelona 1966. International Water Supply Association, London. MINTS D. M., PASKLrTSKAYAL. N. and Cn~RNOVA Z. V. (1967) On the mechanism of the filtration process on rapid water treatment filters. (In Russian.) Zh. Priklad. Khim. 8, 1695-1700. MINTS D. M. (1969) Preliminary Treatment of Water before Filtration. Special Subject No. 6. International Water Supply Congress, Vienna 1969. International Water Supply Association, London. MOHANKAS. S. (1969) Multilayer Filtration of Suspensions. Ph.D. thesis. University of London. NAYLOR A. E., EVANS S. C. and DUNSCOMBEK. M. (1967) Recent developments on the rapid sand filters at Luton. J. Inst. Wat. Pollut. Control66, 309-320. OAKLEY H. R. and CRIPPS T. (1969) British practice in the tertiary treatment of wastewater. J. Wat. Pollut. Control Fed. 41, 36--50. O'MELIA C. R. and CRAPPS D. K. (1964) Some chemical aspects of rapid sand filtration. J. Am. Wat. Wks Ass. 56, 1326-1344. OULMANC. S., BURNSD. E. and BAUMANNE. R. (1964) Effect on filtration of ployelectrolyte coatings of diatomite filter media. J. Am. Wat. Wks Ass. 56, 1233-1238. SHEKHTMANYu. M. (1961) Filtration of Suspensions of Low Concentration. (In Russian.) Publishing House of the U.S.S.R. Academy of Sciences, Moscow. SMrrn C. V. and MEDLAR S. J. (1968) Filtration optimization utilising polyphosphates. J. Am. Wat. Wks Ass. 60, 921-938. STANDERG. J. and VAN VUURENL. R. J. (1969) The reclamation of potable water from wastewater. J. War. Pollut. Control Fed. 41, 355-367. STEIN P. C. (1940) A Study of the Theory of Rapid Filtration of Water through Sand. Sc.D. thesis. Massachusetts Institute of Technology. TRUESDALEG. A. and BIRKBECKA. E. (1968) Tertiary treatment of activated sludge effluent. J. Inst. War. Pollut. Control 67, 483494. TRZASKA A. (1966) Some remarks on colmatage in conditions of axi-symmetric flow. Bull. Acad. Polon. Sci., Ser. Tech. Sci. 14, 433-437. TUEPKERJ. L. and BUESCHERC. A. (1968) Operation and maintenance of rapid sand and mixed-media filters in a lime softening plant. J. Am. Wat. Wks Ass. 60, 1377-1388. ULUG S. E. (1967) The Backwashing of Rapid Sand Filters. Ph.D. thesis. University of London. YAO K. M. (1968) Influence of Suspended Particle Size on the Transport Aspect of Water Filtration. Ph.D. thesis. University of North Carolina (Chapel Hill).