10 - Mixing & Agitation - Lecture notes 2-5 PDF

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10 MIXING AND AGITATION

M

ixing – the movement of fluids and solids to enhance a process result – is accomplished by means of an agitation source. For example, the sun is the agitation source for mixing in the earth’s atmosphere. Similarly, an air compressor and/or a mechanical mixer is the agitation source in any municipal wastewater treatment plant to enhance the process results of (1) solids suspension and (2) oxygen absorption from sparged or entrained air. In its most general sense, the process of mixing is concerned with all combinations of phases, of which the most frequently occurring are:

reactions. Scale-up is addressed here, and, as we cover scale-up, the reader will discover that an understanding of mixing fundamentals is essential to the proper handling of scale-up. This introduction would be incomplete without a short discussion of the place of this chapter in the toolbox of the practicing engineer. Today’s engineer is faced with the daunting task of separating the truly practical and immediately useful design methods from the voluminous available literature. For example, the recent Handbook of Industrial Mixing (Paul et al., 2004) is comprised of 1377 pages devoted only to the topic of Mixing and Agitation. Some of the coverage in that tome can be used with a minimum of effort; however, much of the coverage includes a literature survey with little emphasis on sifting the “truly useful” from the “mundane and ordinary.” It is our intent here to sift through the entire literature in the field of Mixing and Agitation and present only that material which is most useful to the busy practicing engineer and to present worked examples that apply the design methods. In addition to the Handbook of Industrial Mixing there are at least 20 Mixing and Agitation books listed in the References. In today’s electronic world there are also many web sites of equipment vendors that provide very valuable vendor design information. Among those sites are www. chemineer.com, www.clevelandmixer.com, www.lightninmixers.com, www.proquipinc.com, www.philadelphiamixers. com, and www.sulzerchemtech.com. All of these mentioned sites contain product information, but the Chemineer site (to a great extent) and the Lightnin site (to a lesser extent) contain useful design-oriented technical literature. The annual Chemical Engineering Buyer’s Guide is a good source for vendor identification. Many references are cited in the text; however, several useful references – not cited in the text – are included in the references section; they are: Brodkey (1957); Holland and Chapman (1966); McDonough (1992); Tatterson (1994); Uhl and Gray (1986); Ulbrecht and Patterson (1985); Zlokarnik (1988); Armenante and Nagamine (1996); Myers, Corpstein, Bakker and Fasano (1994); Lee and Tsui (1999); Baldyga and Bourne (1997); Knight, Penney and Fasano (1995); Taylor, Penney and Vo (1998); Walker (1996); Penney and Tatterson (1983).

1. Gases with gases 2. Gases into liquids: gas dispersion 3. Gases with granular solids: fluidization, pneumatic conveying, drying 4. Liquids into gases: spraying and atomization 5. Liquids into liquids: dissolution, emulsification, dispersion 6. Liquids with granular solids: solids suspension, mass transfer, and dissolution 7. Pastes with each other and with solids 8. Solids with solids: mixing of powders Interaction of three phases – gases, liquids, and solids – may also occur, as in the hydrogenation of a vegetable oil in the presence of a suspended solid nickel catalyst in a hydrogen-sparged, mechanically agitated reactor. Three of the processes involving liquids – numbers 2, 5, and 6 in the preceding list – employ the same equipment; namely, tanks in which the liquid is circulated and subjected to a desired level of shear. Mixing involving liquids has been most extensively studied and is most important in practice; thus, fluid mixing will be given most coverage here. Many mixing process results can be designed a priori, by using the mixing literature without resorting to experimental studies. These include agitator power requirements, heat transfer, liquid-liquid blending, solids suspension, mass transfer to suspended particles, and many solid-solid applications. However, many other applications invariably involve experimental work followed by scale-up. These include liquid-liquid, gas-liquid, and fast competitive chemical

10.1. A BASIC STIRRED TANK DESIGN Figure 10.1 gives a “typical” geometry for an agitated vessel. “Typical” geometrical ratios are: D/T = 1/3; B/T = 1/12 (B/T = 1/10 in Europe); C/D = 1 and Z/T = 1. This so-called typical geometry is not economically optimal for all process results (e.g., optimal C/D for solids suspension is closer to C/D = 1/3 than to C/D = 1); as appropriate, the economical optimum geometry will be indicated later. Four “full” baffles are standard; they extend the full batch height, except baffles for dished bottoms may terminate near the bottom head tangent line. Baffles are normally offset from the vessel wall about B/6. The typical batch is “square” – that is, the batch height equals the vessel diameter (Z/T = 1). The vessel bottom and top heads can

277 Copyright © 2012 Elsevier Inc. All rights reserved. DOI: 10.1016/B978-0-12-396959-0.00010-0

be either flat or dished. For axial flow impellers (discussed later) a draft tube, which is a centered cylinder with a diameter slightly larger than the impeller diameter and about two-thirds Z tall, is placed inside the vessel. Sterbacek and Tausk (1965, p. 283) illustrate about a dozen applications of draft tubes, and Oldshue (1983, pp. 469–492) devotes a chapter to their design. OFF-CENTER ANGLED SHAFT ELIMINATES VORTEXING AND SWIRL For axial flow impellers, the effect of full baffling can be achieved in an unbaffled vessel with an off-center and angled impeller shaft location. J. B. Fasano of Chemineer uses the following

278 MIXING AND AGITATION

Top View not Intended to Correspond Exactly to Side View

Platecoil Baffle

Rotated Harp Tube Bank Baffle

Rotated Platecoil Baffle

45⬚

45⬚

Harp Tube Bank Baffle

T

1.5 x d1, Typical Helical Coils Attached to Wall Baffles

2 x d1

Wall Baffles, Four Total T/12

d1 = T/30, Typical

Typical Tube Row Spacing = d1

d1 = T/30, Typical

Z = T, Typical

T/3, Typical

T/3

Figure 10.1. Agitated vessel standard geometry showing impeller, baffles, and heat transfer surfaces. guideline: (1) vendors normally supply a 10° angled riser (2) at the vessel top, looking along the vessel centerline, move up (a) 0.19T and then (b) 0.17LS to the right (3) position the agitator with the angled shaft pointing left. Vendors can help to provide optimum positioning.

An offset impeller location, illustrated in Figure 10.3(b) will not totally eliminate vortexing, but it will eliminate most swirl, give good top-to-bottom turnover, and keep the vortex from reaching the impeller.

10.2. VESSEL FLOW PATTERNS

INTERNAL HEAT TRANSFER SURFACES Heat transfer surfaces – helical coils, harp coils, or platecoils – are often installed inside the vessel and jackets (both side wall and bottom head) so that the vessel wall and bottom head can be used as heat transfer surfaces. Figure 10.1 gives a suggested geometry for helical coils and harp coils.

(g)

IMPELLER SPEEDS With 1750 rpm electric motors, standard impeller speeds (Paul et al., 2004, p. 352) are 4, 5, 6, 7.5, 9, 11, 13.5, 16.5, 20, 25, 30, 37, 45, 56, 68, 84, 100, 125, 155, 190, 230, 280, 350, and 1750. In addition, 1200 rpm electric motors are readily available.

(h)

IMPELLER TYPES Twelve common impeller types are illustrated in Figure 10.2. Impellers (a) through (i) and (k) in Figure 10.2 are available worldwide. Impellers (j) (the Intermig) and (l) (the Coaxial [Paravisc Outside and Viscoprop inside]) are available only from Ekato. Key factors to aid in selection of the best impeller to enhance desired process result(s) are as follows: (a) The three-bladed Marine Propeller (MP) was the first axialflow impeller used in agitated vessels. It is often supplied with fixed and variable speed portable agitators up to 5 hp with impeller diameters (D) up to 6″. Above D = 6″, marine propellers are too heavy and too expensive to compete with hydrofoil impellers. They are usually applied at high speeds (up to 1750 rpm) in vessels up to 500 gal, with a viscosity limit of about 5000 cp. Lower NRe limit: ~ 200. (b) The impeller shown is the Chemineer HE-3 hydrofoil, high efficiency impeller, but all vendors have competitive impellers (e.g., Lightnin offers the A310 hydrofoil impeller). Hydrofoils are used extensively for high flow, low shear applications such as heat transfer, blending, and solids suspension at all speeds in all vessels. The economical optimum D/T(0⋅4 > [D/T] optimum > 0⋅6) is greater for hydrofoils than for higher shear impellers. Lower N Re limit: ~ 200. (c) The 6-blade disk (the 6BD and, historically, the Rushton turbine) impeller is ancient; nevertheless, it still has no peer for some applications. It invests the highest proportion of its power as shear of all the turbine impellers, except those (e.g., the Cowles impeller) specifically designed to create stable emulsions. It is still the preferred impeller for gas-liquid dispersion for small vessels at low gas rates, it is still used extensively for liquid-liquid dispersions, and it is the only logical choice for use with fast competitive chemical reactions, as will be explained in a later section of this chapter. Lower NRe limit: ~ 5. (d) The 4-blade 45° pitched blade (4BP) impeller is the preferred choice where axial flow is desired and where there is a need for a proper balance between flow and shear. It is the preferred impeller for liquid-liquid dispersions and for gas dispersion from the vessel headspace (located about D/3 to D/2 below the free liquid surface), in conjunction with a lower 6BD or a concave blade disk inpeller. Lower NRe limit: ~ 20. (e) The 4-blade flat blade (4BF) impeller is universally used to provide agitation as a vessel is emptied. It is installed, normally fitted with stabilizers, as low in the vessel as is practical. An upper 1 HE-3 or a 4BP is often installed at about C/T = to provide 2 effective agitation at high batch levels. Lower NRe limit: ~ 5. (f) The 6-blade disk-style concave blade impellers (CBI) [the Chemineer CD-6, which uses half pipes as blades, is shown] are used extensively and economically for gas dispersion in large vessels

(i)

(j)

(k)

(l)

279

(in fermenters up to 100,000 gal) at high gas flow rates. The CBIs will handle up to 200% more gas without flooding than will the 6BD, and the gassed power draw at flooding drops only about 30%, whereas with a 6BD, the drop in power draw exceeds 50%. The sawtooth (or Cowles type) impeller is the ultimate at investing its power as shear rather than flow. It is used extensively for producing stable liquid-liquid (emulsions) and dense gas-liquid (foams) dispersions. It is often used in conjunction with a larger diameter axial-flow impeller higher on the shaft. Lower N Re limit: ~ 10. The helical ribbon impeller and the Paravisc (l) are the impellers of choice when turbines and anchors cannot provide the necessary fluid movement to prevent stratification in the vessel. The turbine lower viscosity limit, for a Newtonian fluid, is determined primarily by the agitation Reynolds number (Re = ND 2ρ/μ). For 6BD and 4BF turbines, Fasano et al. (1994, p. 111, Table 1) say Re > 1, and Hemrajani and Tatterson (in Paul (2004), 345) say R e~10, although Novak and Rieger (1975, p. 68, Figure 5) indicate a 6BD is just as effective for blending as a helical ribbon above Re~ 1. Using Re = 5 as the 6BD lower limit with T = 80″, D = 32″, N = 56 rpm, SG = 1, the upper viscosity limit for a 6BD is about μ = ND2 ρ/Re = 2 ð56/60Þð0:0254 × 32Þ ð1,000Þ/5 = 120 Pa⋅s = 120,000 cp: Thus, with this system, the helical ribbon is the impeller of choice for μ>~100,000 cP. Lower N Re limit:= 0. Anchor impellers are used for an intermediate range of 0.5 > Re >10 because they are much less expensive than helical ribbons and they sweep the entire vessel volume; whereas a turbine leaves stagnant areas near the vessel walls for Re < 10. Lower N Re limit: ~ 2. The Ekato intermig impeller has reverse pitch on the inner and outer blades and they are almost always used with multiple impellers. They are used at high D/T and promote a more uniform axial flow pattern than other turbine impellers. They are advertised to be very effective for solids suspension, blending, and heat transfer in the “medium viscosity” range. Lower N Re limit not given by Ekato (9), perhaps ~ 5. The hollow-shaft self-gassing impeller can, if properly designed, eliminate the need for a compressor by taking the headspace gas and pumping it through the hollow shaft and dispersing it into the batch as it leaves the hollow blades. As indicated in the Ekato Handbook, “Handbook of Mixing Technology” (2000, p. 164), the “self-gassing” hollow-shaft impeller is often used in hydrogenation vessels where the sparged hydrogen rate drops to very low levels near the end of batch hydrogenation reactions. According to Ekato (2000, p. 85), “The paravisc is particularly suitable for highly viscous and rheologically difficult media. …” With products that are structurally viscous or have a pronounced flow limit or with suspensions having a low liquid content, the paravisc is used as the outer impeller of a coaxial agitator system.” The Ekato viscoprop is a good choice for the counter-rotating inner impeller. There is not a lower N Re limit. The coaxial, corotating agitator is an excellent choice for yield stress fluids and shear thinning fluids.

10.2. VESSEL FLOW PATTERNS The illustrations in Figure 10.3 show flow patterns in agitated vessels. In unbaffled vessels with center mounting (Figure 10.3(a)) much swirl and vortexing is produced, resulting in poor topto-bottom movement, reduced turbulence, and subsequent poor

280 MIXING AND AGITATION

(a)

(b)

(c)

(d)

(e)

(f)

Double Ribbon

(g)

(j)

Bottam Scraper

(k)

(h)

(i)

(l)

Figure 10.2. Representative impellers for fluid mixing in mechanically agitated vessels (descriptions are in the text).

mixing. For these reasons, this system is never used in practice. Swirl and vortexing can be minimized by an offset location of the impeller (Figure 10.3(b)) or can be eliminated, to give the effect of full baffling, by an offset, angled positioning, as explained on the 1st page of this chapter. With full baffling, axial flow impellers give the full looping flow pattern, as illustrated in

Figure 10.3(c), and with radial flow impellers the figure 8 flow pattern illustrated in Figure 10.3(d) is achieved. This flow pattern somewhat partitions the vessel into two zones, one above and another below the impeller. Mixing between zones is relatively rapid; however, for certain chemical reactions this zoning can be undesirable.

10.5. TANK BLENDING

281

LIQUID LEVEL

a

b

c

d

Figure 10.3. Agitator flow patterns. (a) Axial or radial impellers without baffles produce vortexes. (b) Offcenter location reduces the vortex. (c) Axial impeller with baffles. (d) Radial impeller with baffles.

10.3. AGITATOR POWER REQUIREMENTS FOR A GIVEN SYSTEM GEOMETRY For all impellers with Newtonian fluids, dimensional analysis indicates NP = f ðNRe , NFr , GeometryÞ

(10.1)

The effect of off-bottom clearance (C) is pronounced for all impellers, as indicated in Figure 10.7. For a 6BD (Rushton) impeller, the power draw (P) decreases as the impeller is moved closer to the vessel bottom from the typical impeller location of C/D = 1; for a 4BF turbine, P initially decreases as the impeller is moved down from C/D = 1, reaches a minimum at about C/D = 0.7 and then rises again as C/D drops below 0.7; and for a 4BP, the power draw continually increases as the impeller moves down from C/D = 1.

Thus, for geometrically similar systems 10.4. IMPELLER PUMPING NP = f ðNRe , NFr Þ

(10.2)

And, for geometrically similar fully baffled (or with anti-swirl impeller positioning) NP = f ðNRe Þ

(10.3)

Figure 10.4 presents the power correlations for the Chemineer Standard 4BP and HE-3 impellers as a function of D/T at a C/T of 1/3. Figure 10.5(a), (b), and (c) present power correlations for myriad impellers, with the figure title and figure caption explaining the details for each impeller. Figure 10.6 presents additional power correlations for six additional impellers in fully baffled vessels. The application of the presented power correlations are illustrated in Examples 10.1 and 10.2. EFFECT OF KEY GEOMETRICAL VARIABLE ON POWER DRAW The effect of impeller spacing (S) is complex for S/D < 1, as indicated by Tatterson (1991, p. 39, Figure 2.6). However, S/D < 1 is not recommended in practice, and for S/D > 1, the power requirements of the individual impellers are additive to determine the total power requirement(s) of all impellers on a single shaft.

Agitation impellers act as caseless pumps. Measured pumping capacities for various impellers have been used to develop correlations of the flow number (N Q = Q/ND 3), as a function of N Re and system geometry. Figure 10.8 presents such a correlation for a 4BP and Figure 10.9 presents a pumping correlation for the HE-3. Examples 10.3 and 10.4 determine the pumping capabilities of a 4BP and an HE-3. 10.5. TANK BLENDING For NRe >~ 200 the high efficiency impellers (e.g., propeller, Chemineer HE-3, Lightnin A310, and others) are most economical. For 5 ~ < NRe 10,000, k m is only a function of geometry, independent of NRe. km is related to N, D, and T as follows (Fassano et al., 1994):      b 1/2 Km = aN D T D Z

NRe = 616,000ð1/123,000Þ = 5 From Figure 10.6, NP = 16, thus

2

NRe = ND2 ρ/μ = ð56/60Þð0:0254 × 32Þ 1,000/ð1/1,000Þ = 616,000

3

EXAMPLE 10.2 Impeller Power at High Viscosity Let’s take Example 10.1 and increase the viscosity to 123,000 cP, and recalculate P.

ð10:7Þ

The correlation parameters a and b are given in Table 10.1. The a’s and b’s of Table 10.1 are for surface addition; however, blend times for similar fluids are relatively insensitive to addition location. Equation (10.7) is restricted to: 1. Newtonian fluids of nearly the same viscosity and density as the bulk fluid 2. Additions of 5%, or less, of the liquid volume of the vessel

This is still a low power level of 6.2/1.74 = 3.55 HP/1,000 gal. With this agitator, a reasonable upper limit for agitator speed would be 100 rpm, for which the impeller power would be 22 HP with a specific power input of 13 HP/1,000 gal and NRe = 9. This change would move up into the Reynolds number near the lower limit recommended by Hemrajani and Tatterson (in Paul (2004), 345). This example illustrates the great impact of fluid viscosity on (1) the power requirement of a 6BD and (2) the choice of an impeller style between a turbine and a helical ribbon impeller.

3. Additions made to a vessel already undergoing agitation (blend times of stratified fluids can be considerably longer) One can account for the increased blend time at a lower Reynolds number (NRe < 10,000) and for the effects of fluids having different densities and viscosities using the following equation (Fasano et al., 1994): Tu = tu, turb f Re fμf Δp

(10.8)

where tU,turb is determined from Eq. (10.6); the NRe correction is given by Figure 10.10; the viscosity correction is given by Figu...