DESIGN SIZING CRITERIA
FILTRATION 18-95 Objective: Determine the filter size and vacuum capacity required to dewater
and wash 15 mtph of dry solids while producing a final washed cake with a mois- ture content of 25 wt % and containing 0.10 wt % TDS based on dry cake solids.
Calculation procedure:
1. Choose cake thickness =0.75 cm, slightly thicker than the minimum in Table 18-8.
2. From Fig. 18-111, W=10 kg/m2×cycle.
3. From Fig. 18-112, form time =0.30 min.
4. From Fig. 18-115, d/W=0.04 for 25 wt % residual moisture.
5. Dry time =d=W×0.04=10.0×0.04=0.40 min.
6. Determine required wash quantity:
Calculated TDS concentration in washed cake liquor:
Liquid in final cake =10×0.25/0.75=3.33 kg/m2×cycle.
TDS in dry washed solids =10×0.001/0.999=0.010 kg/m2×cycle.
TDS in final washed cake liquor =(0.010/3.33)100=0.300 wt %.
Percent remaining, R=((C2−Cw)/(C1−Cw))100.
SinceCw=0,
Required percent remaining, R=(C2/C1)100=(0.300/4.00)100=7.5%.
From Fig. 18-116, required wash ratio N=1.35.
For design, add 10% →N=1.35×1.1=1.49.
Wash vol. =Vw=1.49×3.33/1.00=4.96 L/m2×cycle.
7. Determine wash time:
WVw=10.0×4.96=49.6 kgL/m4.
From Fig. 18-117, wash time =w=0.225 min.
8. Summary of minimum times for each operation:
Form (step 3) =0.30 min.
Wash (step 6) =0.225 min.
Final dry (step 5) =0.40 min.
9. Maximum washing arc =horizontal centerline to 15°past top dead center, or 29% of total cycle. Minimum percent of cycle between end of form and ear- liest start of wash =area between horizontal centerline and maximum apparent submergence=(50%−35%)/2=7.5%.
10. Maximum percentage of cycle for wash +final dry =75−30−7.5=37.5%.
11. Determine cycle time based on the rate-controlling operation:
a.CTform=0.30/.30=1.00 mpr.
b. CTwash=0.225/.29=0.77 mpr.
c. CTwash+dry=(0.225+0.40)/.375=1.67 mpr.
Therefore, the cake wash +final dry rate is controlling and a cycle time of 1.67 mpr must be used.
12. Since (c) is larger than (a) in the previous step, too thick a cake will be formed and it will not wash or dry adequately unless the effective submergence is artificially restricted to yield the design cake thickness. This may be accom- plished by proper bridge-block adjustment or by vacuum regulation within the form zone of the filter valve.
13. The required washing arc of (0.225/1.67)360 =48.5°is assumed to start at the horizontal center line. Careful control of the wash sprays will be required to minimize runback into the slurry in the vat.
14. Overall scale-up factor =0.9×1.0×1.0=0.9.
15. Design filtration rate =(10.0/1.67)(60×0.9).
=323.3 kg/h ×m2.
16. Total filter area required =15×1000/323.3=46.4 m2.
Nearest commercial size for a single unit could be a 10 ft dia. ×16 ft long with a total area of 502 ft2=46.7 m2.
17. Determine required vacuum capacity:
Initial dry time =1.67×0.075=0.125 min.
Calculate gas vol. through cake using data from Fig. 18-118:
Initial dry =0.125×1.22=0.153 m3/m2×rev.
Final dry =0.40×1.95=0.780 m3/m2×rev.
Total, including 10% for evacuation of drainage passages =0.933× 1.10=1.03 m3/m2×rev.
Air rate based on total cycle =1.03/1.67=0.62 m3/min×m2measured at 18 in Hg vacuum.
If pressure drop through system =1.0 in Hg and barometric pressure = 30 in Hg, design air rate =0.62×12/11=0.68 m3/min×m2measured at 19 in Hg vacuum.
Horizontal Belt Filter Since the total cycle of a horizontal belt filter occurs on a single, long horizontal surface, there is no restriction with respect to the relative portions of the cycle. Otherwise, scale-up procedures are similar.
BATCH FILTRATION
Since most batch-type filters operate under pressure rather than vac- uum, the following discussion will apply primarily to pressure filtra- tion and the various types of pressure filters.
To use Eq. (18-54) one must know the pattern of the filtration process, i.e., the variation of the flow rate and pressure with time.
Generally the pumping mechanism determines the filtration flow
characteristics and serves as a basis for the following three categories*
[Tiller and Crump, Chem. Eng. Prog.,73(10), 65 (1977)]:
1. Constant-pressure filtration. The actuating mechanism is compressed gas maintained at a constant pressure.
2. Constant-rate filtration. Positive-displacement pumps of vari- ous types are employed.
3. Variable-pressure, variable-rate filtration. The use of a cen- trifugal pump results in this pattern: the discharge rate decreases with increasing back pressure.
Flow rate and pressure behavior for the three types of filtration are shown in Fig. 18-119. Depending on the characteristics of the cen- trifugal pump, widely differing curves may be encountered, as sug- gested by the figure.
Constant-Pressure Filtration For constant-pressure filtration Eq. (18-54) can be integrated to give the following relationships between total time and filtrate measurements:
= + (18-70)
= + (18-71)
= + (18-72)
For a given constant-pressure filtration, these may be simplified to
=Kp +C=K′p +C (18-73) whereKp,K′p, and Care constants for the conditions employed. It should be noted that Kp,K′p, and Cdepend on filtering pressure not only in the obvious explicit way but also in the implicit sense that α,m, andrare generally dependent on P.
Constant-Rate Filtration For substantially incompressible cakes, Eq. (18-54) may be integrated for a constant rate of slurry feed to the fil- ter to give the following equations, in which filter-medium resistance is treated as the equivalent constant-pressure component to be deducted from the rising total pressure drop to give the variable pressure through the filter cake [Ruth, Ind. Eng. Chem.,27,717 (1935)]:
V A W
A θ
V/A
µr P V
A µαρc 2P(1−mc) θ
V/A
µr P V A µαw
2P θ V/A
µr P W
A µα
2P θ V/A
FIG. 18-119 Typical filtration cycles. [Tiller and Crump,Chem. Eng. Prog.
73(10), 72(1977), by permission.]
* A combination of category 2 followed by category 1 as parts of the same filtra- tion cycle is considered by some as a fourth category. For a method of combining the constant-rate and constant-pressure equations for such a cycle, see Brown, loc. cit.
= = (18-74) which may also be written
= = (18-75)
In these equations P1is the pressure drop through the filter medium.
P1=µr(V/Aθ)
For a given constant-rate run, the equations may be simplified to
V/A=P/Kr+C′ (18-76)
whereKrandC′are constants for the given conditions.
Variable-Pressure, Variable-Rate Filtration The pattern of this category complicates the use of the basic rate equation. The method of Tiller and Crump (loc. cit.) can be used to integrate the equation when the characteristic curve of the feed pump is available.
In the filtration of small amounts of fine particles from liquid by means of bulky filter media (such as absorbent cotton or felt) it has been found that the preceding equations based upon the resistance of a cake of solids do not hold, since no cake is formed. For these cases, in which filtration takes place on the surface or within the interstices of a medium, analogous equations have been developed [Hermans and Bredée, J. Soc. Chem. Ind.,55T,1 (1936)]. These are usefully summarized, for both constant-pressure and constant-rate conditions, by Grace [Am. Inst. Chem. Eng. J.,2,323 (1956)]. These equations often apply to the clarification of such materials as sugar solutions, vis- cose and other spinning solutions, and film-casting dopes.
If a constant-pressure testis run on a slurry, care being taken that not only the pressure but also the temperature and the solid content remain constant throughout the run and that time readings begin at the exact start of filtration, one can observe values of filtrate volume or weight and corresponding elapsed time. With the use of the known fil- tering area, values of θ/(V/A) can be calculated for various values of V/Awhich, when plotted with θ/(V/A) as the ordinate and V/Aas the abscissa (Fig. 18-120a), result in a straight line having the slope µαw/2Pand an intercept on the vertical axis of µr/P.Sinceµ,w,andP are known, αandrcan be calculated from
α =2P/µw×(slope) and r=P/µ×(vertical intercept)
The effect of the change of any variable not affecting αorrcan now be estimated. It should be remembered that αandrusually depend onPand may be affected by w.
The symbol α represents the average specific cake resistance, which is a constant for the particular cake in its immediate condition.
In the usual range of operating conditions it is related to the pressure by the expression
α = α′Ps (18-77)
whereα′is a constant determined largely by the size of the particles forming the cake; sis the cake compressibility, varying from 0 for rigid, incompressible cakes, such as fine sand and diatomite, to 1.0 for very highly compressible cakes. For most industrial slurries, slies between 0.1 and 0.8. The symbol rrepresents the resistance of unit area of filter
V A µαρc (P−P1)(1−mc) V
A µαw P−P1
θ V/A
W A µα
P−P1
1 rate per unit area θ
V/A
medium but includes other losses (besides those across the cake and the medium) in the system across which Pis the pressure drop.
It should be noted also that the intercept is difficult to determine accurately because of large potential experimental error in observing the time of the start of filtration and the time-volume correspondence during the first moments when the filtration rate is high. The value of rcalculated from the intercept may vary appreciably from test to test, and will almost always be different from the value measured with clean medium in a permeability test.
To determine the effect of a change in pressure, it is necessary to run tests at three or more pressures, preferably spanning the range of inter- est. Plotting αorragainstPon log-log paper (or log αor log ragainst the log Pon cartesian coordinates) results in an approximate straight line (Fig. 18-120b) from which one may estimate values of αorrat interpolated or reasonably extrapolated magnitudes of P.The slope of the line is the index of a power relationship between αandPorrandP.
Not uncommonly ris found to be only slightly dependent on pres- sure. When this is true and especially when the filter-medium resis- tance is, as it should be, relatively small, an average value may be used for all pressures.
It is advisable to start a constant-pressure filtration test, like a com- parable plant operation, at a low pressure, and smoothly increase the pressure to the desired operating level. In such cases, time and filtrate- quantity data should not be taken until the constant operating pressure is realized. The value of rcalculated from the extrapolated intercept then reflects the resistance of both the filter medium and that part of the cake deposited during the pressure-buildup period. When only the total mass of dry cake is measured for the total cycle time, as is usually true in vacuum leaf tests, at least three runs of different lengths should be made to permit a reliable plot of θ/VagainstW.If rectification of the resulting three points is dubious, additional runs should be made.
Pressure Tests
Leaf Tests A bomb filter is used for small-scale leaf tests to simu- late the performance of pressure-leaf (leaf-in-shell) filters. The equip- ment used is a small [50.8- by 50.8-mm (2- by 2-in)] leaf, covered with appropriate filter medium, suspended in a cell large enough to con- tain sufficient slurry to form the desired cake (Fig. 18-121). The slurry may be agitated gently, for example, by an air sparger.
Although incremental time and filtrate volume may be taken during a cake-forming cycle at a selected pressure to permit a plot like Fig.
18-120afrom a single run, it may be more satisfactory to make several successive quick runs at the same pressure but for different lengths of time, recording only the terminal values of filtrate volume, time, and cake mass. Operation of the commercial unit should be kept in mind when the test cycles are planned. Displacement washing and air blow- ing of the cake should be tried if appropriate. Wet discharge can be simulated by opening the cell and playing a jet of water on the cake;
dry discharge, by applying a gentle air blast to the filtrate-discharge tube. Tests at several pressures must be conducted to determine the compressibility of the cake solids.
Plate-and-Frame Tests These tests should be conducted if the use of a filter press in the plant is anticipated; at least a few confirm- ing tests are advisable after preliminary leaf tests, unless the slurry is very rapidly filtering. A laboratory-size filter press consisting of two plates and a single frame may be used. It will permit the observation of solids-settling, cake-packing, and washing behavior, which may be quite different for a frame than for a leaf.
Compression-Permeability Tests Instead of model leaf tests, compression-permeability experiments may be substituted with advantage for appreciably compressible solids. As in the case of con- stant-rate filtration, a single run provides data equivalent to those obtained from a series of constant-pressure runs, but it avoids the data-treatment complexity of constant-rate tests.
The equipment consists of a cylindrical cell with a permeable bot- tom and an open top, into which is fitted a close-clearance, hollow, cylindrical piston with a permeable bottom. Slurry is poured into the cell, and a cake is formed by applying gentle vacuum to the filtrate discharge line. The cell is then filled with filtrate, and the counter- weighted piston is allowed to descend to the cake level. Successive
FIG. 18-120 Typical plots of filtration data.
FILTRATION 18-97
increments of mechanical stress are applied to the solids, at each of which the permeability of the cake is determined by passing filtrate through the piston under low head.
The experimental procedure and method of treatment of compres- sion-permeability data have been explained by Grace [Chem. Eng.
Prog.,49,303, 427 (1953)], who showed that the values of αmea- sured in such a cell and in a pressure filter were the same, and by Tiller [Filtr. Sep.,12,386 (1975)].
Scaling Up Test Results The results of small-scale tests are determined as dry weight of solids or volume of filtrate per unit of area per cycle. This quantity multiplied by the number of cycles per day permits the calculation of either the filter area required for a stip- ulated daily capacity or the daily capacity of a specified plant filter.
The scaled-up filtration area should be increased by 25 percent as a factor of uncertainty. In the calculation of cycle length, proper account must be made of the downtime of a batch filter.
FILTER MEDIA
All filters require a filter medium to retain solids, whether the filter is for cake filtration or for filter-medium or depth filtration. Specifica- tion of a medium is based on retention of some minimum particle size at good removal efficiency and on acceptable life of the medium in the environment of the filter. The selection of the type of filter medium is often the most important decision in success of the operation. For cake filtration, medium selection involves an optimization of the fol- lowing factors:
1. Ability to bridge solids across its pores quickly after the feed is started (i.e., minimum propensity to bleed)
2. Low rate of entrapment of solids within its interstices (i.e., min- imum propensity to blind)
3. Minimum resistance to filtrate flow (i.e., high production rate) 4. Resistance to chemical attack
5. Sufficient strength to support the filtering pressure 6. Acceptable resistance to mechanical wear 7. Ability to discharge cake easily and cleanly
8. Ability to conform mechanically to the kind of filter with which it will be used
9. Minimum cost
For filter-medium filtration, attributes 3, 4, 5, 8, and 9 of the pre- ceding list apply and must have added to them (a) ability to retain the solids required, (b) freedom from discharge of lint or other adulterant into the filtrate, and (c) ability to plug slowly (i.e., long life).
Filter-medium selection embraces many types of construction:
fabrics of woven fibers, felts, and nonwoven fibers, porous or sin- tered solids, polymer membranes, or particulate solids in the form of a permeable bed. Media of all types are available in a wide choice of materials.
Fabrics of Woven Fibers For cake filtration these fabrics are the most common type of medium. A wide variety of materials are available;
some popular examples are listed in Table 18-10, with ratings for chem- ical and temperature resistance. In addition to the material of the fibers, a number of construction characteristics describe the filter cloth: (1) weave, (2) style number, (3) weight, (4) count, (5) ply, and (6) yarn num- ber. Of the many types of weaves available, only four are extensively used as filter media: plain (square) weave, twill, chain weave, and satin.
All these weaves may be made from any textile fiber, natural or syn- thetic. They may be woven from spun staple yarns, multifilament con- tinuous yarns, or monofilament yarns. The performance of the filter cloth depends on the weave and the type of yarn.
A recently developed medium known as a double weave incorporates different yarns in warp and fill in order to combine the specific advan- tages of each type. An example of this is Style 99FS, made by Madison Filtration, in which multifilament warp yarns provide good cake release properties and spun staple fill yarns contribute to greater retentivity.
Metal Fabrics or Screens These are available in several types of weave in nickel, copper, brass, bronze, aluminum, steel, stainless steel, Monel, and other alloys. In the plain weave, 400 mesh is the closest wire spacing available, thus limiting use to coarse crystalline slurries, pulps, and the like. The “Dutch weaves” employing relatively large, widely spaced, straight warp wires and relatively small crimped filling wires can be woven much more closely, providing a good medium for filtering fine crystals and pulps. This type of weave tends to plug read- ily when soft or amorphous particles are filtered and makes the use of filter aid desirable. Good corrosion and high temperature resistance of properly selected metals makes filtrations with metal media desir- able for long-life applications. This is attractive for handling toxic materials in closed filters to which minimum exposure by mainte- nance personnel is desirable.
Pressed Felts and Cotton Batting These materials are used to filter gelatinous particles from paints, spinning solutions, and other viscous liquids. Filtration occurs by deposition of the particles in and on the fibers throughout the mat.
Nonwoven media consist of web or sheet structures which are com- posed primarily of fibers or filaments bonded together by thermal, chemical, or mechanical (such as needlepunching) means. Needled felts are the most commonly used nonwoven fabric for liquid filtra- tion. Additional strength often is provided by including a scrim of woven fabric encapsulated within the nonwoven material. The surface of the medium can be calendered to improve particle retention and assist in filter cake release. Weights range from 270 to 2700 gm/m2 (8 to 80 oz/yd2). Because of their good retentivity, high strength, mod- erate cost, and resistance to blinding, nonwoven media have found wide acceptance in filter press use, particularly in mineral concentrate filtration applications. They are used frequently on horizontal belt fil- ters where their dimensional stability reduces or eliminates wrinkling and biasing problems often encountered with woven belts.
Filter Papers These papers come in a wide range of permeabil- ity, thickness, and strength. As a class of material, they have low strength, however, and require a perforated backup plate for support.
FIG. 18-121 Bomb filter for small-scale pressure filtration tests. [Silverblatt et al.,Chem. Eng., 81(9), 132 (1974), by permission.]
Rigid Porous Media These are available in sheets or plates and tubes. Materials used include sintered stainless steel and other metals, graphite, aluminum oxide, silica, porcelain, and some plastics—a gamut that allows a wide range of chemical and temperature resis- tance. Most applications are for clarification.
Polymer Membranes These are used in filtration applications for fine-particle separations such as microfiltration and ultrafiltration (clarification involving the removal of 1-µm and smaller particles).
The membranes are made from a variety of materials, the commonest being cellulose acetates and polyamides. Membrane filtration, dis- cussed in Sec. 22, has been well covered by Porter (in Schweitzer, op.
cit., sec. 2.1).
Media made from woven or nonwoven fabrics coated with a poly- meric film, such as Primapor, and Primapor II made by Madison Fil- tration, Gore-Tex, made by W. L. Gore and Associates, and Tetratex, made by Donaldson Company, combine the high retentivity charac- teristics of a membrane with the strength and durability of a thick fil- ter cloth. These media are used on both continuous and batch filters where excellent filtrate clarity is required.
Granular Beds of Particulate Solids Beds of solids like sand or coal are used as filter media to clarify water or chemical solutions con- taining small quantities of suspended particles. Filter-grade grains of desired particle size can be purchased. Frequently beds will be con- structed of layers of different materials and different particle sizes.
Various types of filter media and the materials of which they are constructed are surveyed extensively by Purchas (Industrial Filtration of Liquids,CRC Press, Cleveland, 1967, chap. 3), and characterizing measurements (e.g., pore size, permeability) are reviewed in detail by Rushton and Griffiths (in Orr, op. cit., chap. 3). Briefer summaries of classification of media and of practical criteria for the selection of a fil- ter medium are presented by Shoemaker (op. cit., p. 26) and Purchas [Filtr. Sep.,17,253, 372 (1980)].
FILTER AIDS
Use of filter aids is a technique frequently applied for filtrations in which problems of slow filtration rate, rapid medium blinding, or un- satisfactory filtrate clarity arise. Filter aids are granular or fibrous solids capable of forming a highly permeable filter cake in which very fine solids or slimy, deformable flocs may be trapped. Application of filter aids may allow the use of a much more permeable filter medium than the clarification would require to produce filtrate of the same quality by depth filtration.
Filter aids should have low bulk density to minimize settling and aid good distribution on a filter-medium surface that may not be horizon- tal. They should also be porous and capable of forming a porous cake to minimize flow resistance, and they must be chemically inert to the filtrate. These characteristics are all found in the two most popular TABLE 18-10 Characteristics of Filter-Fabric Materials*
Maximum
Breaking Resistance operating
tenacity, Abrasion Resistance Resistance to oxidizing Resistance Specific temperature,
Generic name and description g/denier resistance to acids to alkalies agents to solvents gravity °F†
Acetate—cellulose acetate. When not 1.2–1.5 G F P G G 1.33 210
less than 92% of the hydroxyl groups are acetylated, “triacetate”
may be used as a generic description.
Acrylic—any long-chain synthetic 2.0–4.8 G G F G E 1.18 300
polymer composed of at least 85%
by weight of acrylonitrile units.
Glass—fiber-forming substance is 3.0–7.2 P E P E E 2.54 600
glass.
Metallic—composed of metal, metal- — G
coated plastic, plastic-coated metal, or a core completely covered by metal.
Modacrylic—fiber-forming substance 2.5–3.0 G G G G G 1.30 180
is any long-chain synthetic polymer composed of less than 85% but at least 35% by weight of acrylonitrile units.
Nylon—any long-chain synthetic 3.8–9.2 E F–P G F–P G 1.14 225
polyamide having recurring amide groups as an integral part of the polymer chain.
Polyester—any long-chain synthetic 2.2–7.8 E–G G G–F G G 1.38 300
polymer composed of at least 85%
by weight of an ester of a dihydric alcohol and terephthalic acid (p—HOOC—C6H4—COOH).
Polyethylene—long-chain synthetic 1.0–7.0 G G G F G 0.92 165‡
polymer composed of at least 85%
weight of ethylene.
Polypropylene—long-chain synthetic 4.8–8.5 G E E G G 0.90 250§
polymer composed of at least 85%
by weight of propylene.
Cotton—natural fibers. 3.3–6.4 G P F G E–G 1.55 210
Fluorocarbon—long-chain synthetic 1.0–2.0 F E E E G 2.30 550¶
polymer composed of tetrafluoroethylene units.
*Adapted from Mais, Chem. Eng.,78(4), 51 (1971). Symbols have the following meaning: E =excellent, G =good, F =fair, P =poor.
†°C=(°F−32)/1.8; K =(°F+459.7)/1.8.
‡Low-density polymer. Up to 230°F for high-density.
§Heat-set fabric; otherwise lower.
¶Requires ventilation because of release of toxic gases above 400°F.