02 BOPs / Woods D.R 2008 rules-of-thumb-in-Engineering-practice (epdf.tips)

7.1 Liquids 281

–Turnover rate: pumping capacity/liquid volume. Sufficient turnover rate is an important consideration in mixing design, especially in those applications requiring axial flow.

–Mixing time: tM is the time it takes for a mixer to create a homogeneous liquid. For turbines and marine propellers, the product of the rpm q tM z constant and is in the range 20–100. The mixing time should be I 60 s and NtMDi3 = 2 to 3. For an STR the mixing times should be less than 0.1 q residence time.

–Power required P = kporDi5N3 where kpo is a constant dependent upon the

impeller, but the value of kpo is relatively independent of the impeller Re for Re i 103 provided the effect of the Froude number is negligible.

–rpm. The impeller running speed is selected based on the impeller type, impeller diameter as well as the pumping capacity and turnover rate. Usually the rpm is I 400 rpm if the viscosity is i 200 mPa s or the volume is i 7 m3. Use I 1150 rpm if the viscosity is i 50 mPa s or the volume is i 2 m3. Use at least two impellers on the shaft if the viscosity is i 100 mPa s or the depth of liquid is i 4 impeller diameters, i.e. H i 4Di.

–Baffles. Baffles help the impellers to form the mixing flow pattern. Baffles should be installed vertically along the wall side of the cylindrical tank. Normally, the baffle width is 0.1D and reduces as the fluid viscosities increase, for example, there may be no baffles needed for fluids with viscosities i 5000 mPa s. The number of the baffles is normally the same as the number of the impeller blades. The effective baffle width for a heat exchanger coil is 0.5 q the projected area of the coil.

–Impeller configuration. There are many types of impeller configuration, the typical types of impellers include:

x three-bladed marine propeller (with square pitch) which supplies

axial pumping (usually for viscosities I 2500 mPa s). The propeller agitator may be portable (for I 4 kW), side entry (for

I 40 kW and tanks H i 5 m) or top entry. However, the diameter of the marine propeller is limited due to its weight and manufacturing cost.

xhydrofoil impellers which are a recent development to maximize axial flow capacity and are widely used in low viscosity media (I 1000 mPa s); typical applications include general blending and solids suspension.

xaxial 45h four-bladed turbine which supplies a combination of pumping and shear.

xcurved bladed turbine or backward bladed turbine which supplies shear and some pumping (for viscous media, as in polymer reactors, or liquids with fibers).

xradial four-bladed turbine which supplies radial pumping and

shear (usually for viscosities I 50 000 mPa s).

xflat-blade-disc turbine (Rushton Turbine) which supplies shear and gas holding for gas involved mixing applications.

2827 Mixing

x saw-disc turbine which supplies very high shear, mostly to be used to disperse very fine particles, typical applications are in the

paint and ink industries.

xanchor which runs at a very low rpm to promote (jacket type) heat transfer in high viscosity fluids.

xdouble spiral with 2 helical flights which supply a downwards pushing movement in one flight and an upwards pulling movement in another flight to force the high viscosity fluids in blending.

– Number of impellers on a single shaft: Use at least two impellers on the shaft if the viscosity is i 100 mPa s or the depth of liquid is i 4 impeller diameters, i.e. H i 4Di. Indeed, as the volume of the vessel increases, and the height of the liquid increases, impellers should be placed about every 4Di vertical distance. The power required doubles if there are two impellers, triples if there are three and quadruples if there are four. For example, for a 100 m3 fermenter requiring about 2– 5.5 kW/m3, the depth of the vessel is such that four impellers are needed on the single shaft; the total power requirement is about 250 kW. The impeller configuration is such that a single impeller would require about 63 kW.

Now that the fundamental principles have been reviewed, consider the application of mixing miscible liquids. Related topics: Stirred Tank Reactors, Sections 6.27–6.29. For the blending of miscible liquids the main characteristic is to create flow or pumping. However, there is a tradeoff between pumping and power.

x Area of Application

A wide range of applications: blending miscible liquids; heat transfer (Section 3.3) and chemical reactions (Sections 6.27–6.29).

Fluids viscosity, fluids ratio and volume to be mixed are the most significant factors.

Propellers: viscosity I 3000 mPa s; volume I 750 m3. Turbines-paddles: viscosity I 50 000 mPa s; volume I 75 m3. Liquid jets: viscosity I 1000 mPa s; volume i 750 m3.

Air agitation: viscosity I 1000 mPa s; volume i 750 m3.

Anchors: viscosity I 100 000 mPa s; Re I 10 000; volume I 30 m3. Kneaders: viscosity 4000 to 1.5 q 106 mPa s; volume 3 to 75 m3. Roll mills: viscosity 103 to 200 000 mPa s; volume 60 to 450 m3.

For viscosity i 106 consider extruders, Banbury mixers and kneaders.

Static mixers: viscosity ratio I 100 000:1; continuous and constant flowrates; residence times I 30 min and flowrate ratio of I 100:1. Other related sections: size reduction, Sections 8.1 and 8.3; reactors, Section 6.10; heat transfer Section 3.5.

x Guidelines

For blending and heat transfer, identify the viscosity when turbulent mixing occurs. This usually occurs at an impeller Re of 200.

7.1 Liquids 283

For heat transfer, usually for coils or jackets: select Di = 0.3D for low viscosity fluids and increase diameter with an increase in viscosity. Power is 0.4 to 2 kW/m3. Turbines, propellers and paddles: For blending miscible liquids, usually the tank height, H, = tank diameter D. If H i 1.5D, then use dual impellers; if H I I D, then place impeller 1.25Di or 1/3H off the bottom and 2–3Di below the liquid surface. For low viscosity fluids select diameter of impeller, Di = 0.25 to 0.22D; for higher viscosity, select 0.4–0.5D. Power = 0.2–1.5 kW/m3 for mixing liquids with impeller discharge rate i 20 q liquid flowrate into tank. For fluids of low viscosity and similar densities, use 12 to 15 turnovers to give uniform mix; for fluids with different viscosities, increase the turnovers to 30 to 40 to achieve uniformity. Heat transfer, 0.4–2 kW/m3; mass transfer 2–4 kW/m3. There is a tradeoff between power and blend time: if 0.2 kW/m3 blends the fluids in 4 h; then 0.4 kW/m3 could achieve the same degree of blend in 2 h.

Turbines, propellers and paddles: Power = 1–4 kW/m3 for mass transfer.

Air agitation: diffused air: 0.3 to 0.5 Ndm3/s m3. 1.5 to 6 dm3/s m of linear distance along the basin. Diffusers 15 to 30 dm3 air/s m2 diffuser area with a pressure loss across the diffuser of 1.3 kPa. For 45 min detention time, 0.6 to 1 dm3/L. See related topic: flocculation, Section 9.3. Air agitation is also used in Pachuca leachers.

Anchor: Power = 4–9 kW/m3.

Static mixers: for viscosity ratio I 100:1 and Re i 10 000, use turbulent vortex element; for viscosity ratio i 100:1 and Re I 10 000 use helical elements. For pipe diameter I 0.3 m, element is 1.5 q pipe diameter; for pipe diameter i 0.3 m; element = pipe diameter. For ReI 10 use 18 elements with the number of elements reducing to 2 as Reynolds no. increases to i 5000.

Annular sparger in pipe: annular sparger blends liquid of equal viscosity and density in 50 pipe diameters; central injection blends liquid of equal viscosity and density in 80 pipe diameters; in mixing tee, after 10 pipe diameters. For viscosity differences I 10:1 inject the viscous liquid into the thin liquid.

x Good Practice

Prefer static mixers to intensify (H). For systems where the viscosity increases with time (e.g. polymer reactors) prefer turbines to propellers because turbines are power self-limiting. Check shaft wobble to ensure that impeller will not hit vessel walls if turned on in an empty tank. Consider a foot bearing.

x Trouble Shooting

Propeller/impeller mixers:

“Shaft wobble/vibration”: impeller speed too close to the first critical speed/shaft runout at the impeller and impeller eccentricity too large/insufficient support. “Excessive gear-reducer maintenance”: excessive load/high shock loads/excessive shaft bending/excessive temperature of gearbox lubricant/incorrect lube oil selection and oil changing.

“Excessive stuffing box packing wear”: insufficient lubrication/excessive shaft wobble/shaft is out of round/improper packing installation and maintenance.

284 7 Mixing

“Failure of the mechanical seal”: dirty seal lubricant/not enough seal lubricant pressure/excessive shaft wobble.

“Nonuniformity of blend”: insufficient turnover/not enough time/improper impeller selection/pumping capacity I design/volume i design/relative difference in viscosity increases or differs from design.

“Power trips”: viscosity too high/impeller diameter too large/rotational speed too high.

“Entrained air”: usually entrained air is only a problem when the viscosity is high (i 2000 to 3000 mPa s) because otherwise the bubbles will rise out of the liquid/ [unwanted vortex]*.

“Insufficient heat transfer”: improper impeller selection/fouled tubes/no baffling/ tube bundles poorly located so as not to supply good baffling.

[Unwanted vortex]*: baffles not high enough (not above liquid level)/no baffles/ poor design/radial turbine selected instead of axial flow impeller/not sufficient baffles/rpm too high/impeller diameter too small.

7.2

Liquid–liquid (Immiscible)

The main characteristics are that the agitators should provide shear (and some pumping) to create the dispersion. Related topics: solvent extraction, Section 4.10, size reduction Section 8.3 and reactors, Sections 6.13–6.20, 6.27–6.29, 6.5.

x Area of Application

Three general areas: (i) emulsions–dispersions (as in cosmetics and formulations) drop size I 10 mm (for related topic see Section 8.3); (ii) solvent extraction with drop sizes 1 to 3 mm (for related topic see Section 4.10) and (iii) liquid–liquid reactions, usually with intermediate drop sizes.

For emulsion–dispersions: with a mechanical agitator it is difficult to get an emulsion I 2 mm; need to use colloid mill or homogenizer (as described in Section 8.3). For emulsions it is possible for 10–30 mm with a mechanical agitator. In general, the phase ratio should differ by less than 1:5. Ratios of 1:10 and 1:50 with the small one as continuous phase are extremely difficult to work with.

Fluid viscosity, interfacial tension and volume to be mixed are the most significant factors.

Propellers: viscosity I 3000 mPa s; volume I 750 m3. Turbines-paddles viscosity I 300 000 mPa s; volume I 75 m3. Static mixers viscosity I 50 mPa s.

For surface area generated see Sections 1.6.2 and 8.3.

x Guidelines

For emulsion-dispersions: Impeller should be located just below the interface (or just above) provided it is in the continuous phase (locate about 1/5 to 1/10 of the impeller diameter from the interface). Use impeller that provides shear

7.3 Liquid–Solid 285

with some axial flow. For propellers and turbines: power: 1 to 4 kW/m3 for emulsification and mass transfer.

For solvent extraction: want uniform and diameter that is a balance between surface area for mass transfer and settling velocity. Suitable drop size for dispersed phase is about 1 to 3 mm. The impeller should be selected for both pumping capacity and shear. If the impeller is primarily shear, then the drops close to the impeller will be very small and the drops far from the impeller will be very large. Also, sufficient pumping capacity is the key to maintaining phase ratio stability in a continuous operation. Propellers and turbines: power: 0.2 to 1.5 kW/m3 for mixing immiscible liquids with values decreasing as the interfacial tension decreases and for heat transfer.

For reactors: propellers and turbines for STR reactors: in the kinetic regime: use tip speed 2.5–3.3 m/s and 0.1 kW/m3; for reactions in the fast regime, tip speed 5–6 m/s and 2 kW/m3

Static mixers: see Section 8.3.

x Trouble Shooting

Drop size too large”: shear insufficient/rpm too low/faulty selection of impeller/ power too low/baffles missing/surface wettability wrong for the dispersed phase/order of feeding phases into mixer wrong (discontinuous phase sent first)/phase ratio incorrect/impeller not in the continuous phase at startup/surface tension higher than expected.

“Mass transfer I design”: mixing not uniform/impeller in the dispersed phase instead of the continuous phase/phase ratio not stable/residence time too short/ [holdup too small]*/flowrate i design/wrong impeller/[drop too large]*.

[Drop too large]*: rpm too small/surface tension larger than expected.

[Holdup too small]*: phase flowrate uneven/mixing in the wrong phase/impeller not enough pumping capacity/wrong impeller (designed for shear and not for flow).

[Impeller not in the continuous phase]*: phase ratio differs from design/faulty design/wrong direction of mass transfer.

7.3

Liquid–Solid

For liquid–solid systems, mixing can be used for six general applications: solids suspension, solids dispersion, solids dissolving, solids flocculating, solids forming (as in crystallization) and solids reacting. The latter two are discussed elsewhere in crystallizers, Section 4.6 and reactors, Sections 6.27–6.29. Liquids and solids are also mixed in liquid fluidized beds; details are given in the specific applications of liquid fluidized beds: reactors, Section 6.30; liquid adsorption, Section 4.12, ion exchange, Section 4.13 and backwash fixed bed operations such as deep bed filters, Section 5.14, liquid adsorbers, Section 4.12 and ion exchangers, Section 4.13.

286 7 Mixing

Sections 7.3.1 to 7.3.4 consider solids suspension, solids dispersion, solids dissolving, and solids flocculating respectively. General issues related to mixing using a fluidized bed are given in Section 7.3.5.

7.3.1

Solids Suspension

x Areas of Application

Solids suspension: three separate suspension conditions are employed in practice:

(i) to create a uniform suspension (as might be needed in mineral leaching); (ii) to have all solids off the bottom but the concentration of suspended solids is not uniform; all solids in motion in liquid; (iii) particles on the bottom but the particles are kept moving along the bottom.

(i) Uniform concentration: usually in the mineral processing industry, leaching; solids concentration by weight 30 to 60 %, solids and particle size I 70 mm; see immersion leach, Section 5.15. Also for slurry drawoff by overflow or i 80 % of the height, solids concentration for slurry can be up to 65 to 70 % by weight.

(ii)All particles completely off bottom: usually for dissolving solids; uniformity in 1/3 of the fluid batch height; suitable for slurry drawoff at low exit nozzles.

(iii)Particles move along bottom; minimal suspension required.

x Guidelines

The key design is the relationship between the vertical flow velocity and the settling velocity of the particles. In general, baffle 4 @ 90h; off-the-wall distance = 0.015 q tank diameter or about 50 to 100 mm. to allow fluid circulation between the baffle and the wall. For low viscosity I 500 mPa s the baffle width = 0.10–0.11 tank diameter; for more viscous fluids, baffle width = 0.08–0.09 tank diameter. The baffle should be from the bottom up to or slightly above, the liquid surface. 1. Uniform concentration: design with the vertical flow velocity 10 q the particle settling velocity. Vertical flow velocity of a circulating axial flow pattern can be evaluated by the impeller’s pumping capacity plus its induced flow (adjacent to impeller) divided by its cross sectional area for flow in one direction; use the same amount of total flow divided by the rest of the cross sectional area inside the tank for flow in the other direction, then, take the smaller velocity to compare with the largest particle settling velocity.

For minerals processing, usually the application is on a relatively large scale with tank diameters being 5 to 10 m; height 10 to 15 m and volume several hundreds m3. The impeller diameter is not chosen based on a % of the tank diameter; but rather is selected on its pumping capacity. Use multiple impellers per shaft with the lowest one being 0.5 impeller diameter off the bottom, next one up 1 to 2 impeller diameters and the top one at least 0.5 impeller diameter below the liquid surface. The multiple impellers are to maintain the flow pattern. Usually the fluid flow is downward in the center. For very large tanks, the rpm is of the order of 16 to 20 rpm.

7.3 Liquid–Solid 287

The properties of solids that need to be known include the solids concentration, the particle size distribution, settling velocity (free settling or hindered settling), and the slurry rheology.

2.All particles off the bottom: design with vertical flow velocity 2 to 3 q the settling velocity.

In mixing process design for solid suspension, normally, once the proper type of impeller is selected, the major job is to tradeoff the impeller diameter with rpm to get desire vertical flow velocity.

3.Particles move along the bottom: design for vertical flow velocity = settling

velocity. Add rake to move the solids to a central exit. Power =1 kW at a cross sectional area, 35 m2 with n = 0.44, for range 2–400 m2. Power = 1 (area/35)0.44.

x Good Practice

Startup may be tricky; liquid should be fed first, once the lower impeller is immersed, turn the motor couplings by hand to check that the impeller can turn completely around once unimpeded. If there is no obstacle, turn on the motor to start the mixing and start to feed solids with liquid. Try not to have a bottom bearing, but could use a bottom limit ring.

Restart: if accidentally there is a power outage and then we want to restart, some of the issues are: if the particles settled, are they densely packed or loose packed? How long does it take to settle? For most slurries, the restart procedure outlined above can be used if the restart can be done within 1Z2 h. However, if longer and if the particles pack densely, then water or liquid injection near the lower impeller is needed to loosen the solids. From the solids concentration one can estimate how many impellers are immersed in the bed of particles. Perhaps use a two-speed motor or variable speed driver so that we can start at a lower rpm if the particles are loosely packed or only lower impellers are sitting in the bed of particles.

x Trouble Shooting

“Particles not suspended”: power too small/wrong impeller/solids differ from design/ concentration i design/not enough startup power/vertical flow velocity I settling velocity/temperature too cold/impeller eroded or missing, rpm wrong direction/impeller pitch wrong with successive impellers having contradictory pitches.

“Vortex happens at baffle”: no gap between the baffle and wall or incorrect gap/diameter of impeller too large.

“Solids floating on the surface”: particles not wetted/particles density close to density of liquid/small particle diameter/no vortex present/impeller supplies radial flow instead of axial flow.

“Power overload”: solids concentration i expected/solids denser than expected/ rpm i design/improper mechanical lubrication and maintenance.

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7.3.2

Solids Dispersion

x Areas of Application

Creation of dispersions, slurries, pastes and compounds. For concentrations of solids in liquid I 50 % see Section 7.3.1 on solids suspension to achieve a uniform concentration. For more concentrated solids and more viscous liquids, see Solids, Section 7.4 where pastes, melts, plastics and extrusion compounding are discussed.

x Guidelines

For blending powders into liquids, the wettability of the powder is important. Consider using a propeller with a vortex if some powders are floating on the surface. Size based on principles outlined in Section 7.3.1. For example, provide an additional pitched-bladed turbine a distance of 0.5Di below the liquid surface and reduce the baffle height from the top portion of the fluid to create a vortex (provided the vortex does not reach the eye of an impeller and then disperse air into the fluid). If clumps formed, use a pitched-bladed turbine which provides a combination of pumping and shear to break clumps quickly and to supply good blending so as to keep dispersion uniformity.

x Trouble Shooting

“Solids floating on the surface”: particles not wetted/particles density close to density of liquid/small particle diameter/no vortex present/not proper baffles/impeller supplies radial flow instead of axial flow.

7.3.3

Solids Dissolving

x Area of Application

For readily soluble solids, use the principles of solids suspension, in Section 7.3.1, where flow and shear are supplied by the impeller to provide the mass transfer. However, select for flow because the resistance to mass transfer is usually low.

A unique challenge is polymer powder to be dissolved in a solvent.

x Guidelines

For dissolving polymer in solvent, the major problem is the small clumps of polymer formed in the viscous fluid. These clumps are difficult to break up. We need sufficient shear combined with axial flow in order to break the polymer quickly and immediately spread the polymer into the liquid for subsequent dissolution. Leave a small gap between the baffle and the tank wall in order to avoid the dead corner of undissolved polymer. If multiple impellers are used, then to save on power consumption, the bottom impeller might supply axial flow plus shear (as an open turbine) with the impeller above supplying axial flow. The Power number for the open turbine might be, for example, 1.2, whereas for axial flow the Power number value might be about 0.3.

7.4 Dry Solids 289

x Trouble Shooting

“After a batch, lots of polymer encrusted on the bottom and on the shaft”: insufficient shear/poor operating sequence/incorrect impeller arrangement with axial above axial-shear/impeller too large.

“Analysis of the liquid shows undissolved polymer”: polymer added to the tank before the solvent/insufficient solvent added before starting.

7.3.4

Solids Flocculating

x Area of Application:

Paddle reel/stator-rotor: gentle mechanical mixing for coagulation, viscosity I 20 mPa s, volumes large. Size increase for particles, with details in Section 9.3.

x Guidelines

Gentle mechanical mixing, such as paddle reel or stator-rotor for flocculation, 0.035 to 0.04 tapering to 0.001 to 0.009 kW/m3.

7.3.5

Liquid Fluidized Bed

In general particle diameter 0.5–5 mm with density and diameter of the particle dependent on the application. The superficial liquid velocity to fluidize the bed depends on both the diameter and the density difference between the liquid and the particle. Usually the operation is particulate fluidization.

Particle diameter 0.2–1 mm reactors; superficial liquid velocity 2–200 mm/s. Fluidized adsorption: bed expands 20–30 %; superficial liquid velocity for usual carbon adsorbent = 8–14 mm/s.

Fluidized ion exchange: bed expands 50–200 %; superficial liquid velocity for usual ion exchange resin = 40 mm/s.

Backwash operations: fixed bed adsorption: superficial liquid velocity = 8– 14 mm/s; fixed bed ion exchange: superficial backwash velocity = 3 mm/s.

7.4

Dry Solids

Use the Johanson indices to characterize dry particles: (details in Section 1.6.4; see also related topics: bins, Section 2.6, storage bins, Section 10.3).

Free flowing particles: AI I 0.06 m; RI I 0.3 m.

Moderately free flowing: AI I 0.18 m and mixtures of particles whose angle of repose or RAS differ by i 4h.

Moderately cohesive: 0.15 m I AI I 0.3 m; RI I 1 m; FRI i 0.225 kg/s and mixtures of particles whose angle of repose or RAS differ by I 3h.

290 7 Mixing

x Areas of Application

For free flowing particles that do not segregate, use mixers where the outside shell moves (cone, double cone, zig-zag).

For pastes, plastics, foodstuffs, ceramic pastes and powders that tend to segregate, use mixers with the outside shell fixed (ribbon, edge mill, double arm, Banbury, extruder).

For extrusion compounding, if the components have different densities (e.g. polymer versus fillers) or different shapes (pellets versus regrind flakes) then prefer to use the extruder for mixing. That is, operate the extruder with starved feeding conditions with the components metered separately into the extruder, see Section 9.11. On the other hand, for the blending of polymer feedstock for extrusion, if the components have very similar properties, then use tumble, rotating drum or ribbon blenders or rotor-stator blenders of the feed upstream of the extruder and use flood feeding of the mixture to the extruder.

More specifically:

Air pulse: OK for free flowing and wide range in particle size; i.e. one size i 3 times the other. Use when have fines with FRI I 2.2 kg/s and other components that have about the same size or are in same FRI range. OK for moderately free flowing dry solids.

Double cone: (tumble, V-mix; moving shell) limited to moderately cohesive solids that do not have sifting or repose-angle demixing.

Screw mixer: (rotating screw aligned along the inside of a cone hopper. Lifts solids from the bottom to the top. Progresses around the periphery of the cone.) Most effective when solids move along the conical hopper walls. Use for: moderately cohesive fines; different types of particles that have RAS differences I 3h; and usually require moderate amounts of liquid addition. Not for moderately free flowing.

Ribbon: For moderately cohesive components with 1 I RI I 3 m; FRI i 0.75 kg/s; CI I 60h.

Plough or paddle: (horizontal rotating shaft with fixed arms attached (plough or paddles): single shaft, double shaft.) Have sufficient liquid addition to produce AI i 0.18 m and RI i 1 m. Do not use single point feeding of the particles. Not for moderately free flowing.

Gravity flow: The solids must be free flowing. Large volumes to mix i 5.6 m3. Kneader double arm (Vertical shaft impeller mixer): Use to mix solids with liquids; blend solids that are nondegrading, fine, free flowing particles with melting temperature i temperature induced through mixing. AI i 0.18 m, FRI i 0.75 kg/s, AAI I 10h. Cannot be used for heat sensitive solids. Not for moderately free flowing. Rpm needs to be high enough to create a vortex. Power input/ volume is large.

x Guidelines

Working capacity is 50 to 60 % of total internal volume. Mixing residence times are 3 to 10 min. Mixing time increases with (particle diameter)0.5. Rpm 20 to 100 rpm.