mixing of miscible liquids

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Process Engineering Guide: GBHE-PEG-MIX-701

Mixing of Miscible Liquids Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the suitability of the information for its own particular purpose. GBHE gives no warranty as to the fitness of this information for any particular purpose and any implied warranty or condition (statutory or otherwise) is excluded except to the extent that exclusion is prevented by law. GBHE accepts no liability resulting from reliance on this information. Freedom under Patent, Copyright and Designs cannot be assumed.



Process Engineering Guide: Mixing of Miscible Liquids CONTENTS SECTION 0 INTRODUCTION/PURPOSE 4 1 SCOPE 4 2 FIELD OF APPLICATION 4 3 DEFINITIONS 4 4 SELECTION OF EQUIPMENT 4 4.1 Mechanically Agitated Vessels 4 4.2 Jet Mixed Vessels 4 4.3 Tubular ('Flow') Mixers 5 5 AGITATED VESSELS 5 5.1 Mixing Time for Liquids in Stirred Tanks 6 5.2 Power Requirements 9 5.3 Vortex Formation and Surface Entrainment in

Unbaffled and Baffled Vessels 34 5.4 Heat-Transfer in Stirred Vessels 39 5.5 Flow and Circulation 44 6 JET MIXED TANKS 45

6.1 Introduction 45 6.2 Recommended Configuration 45 6.3 Design Procedure 46 6.4 Design for Continuous Mixing 51



7 TUBULAR JET FLOW MIXERS FOR MISCIBLE LIQUIDS 51 7.1 Recommended Configurations 55 7.2 Mixer Design 55 7.3 Additional Considerations 60 8 MOTIONLESS MIXERS 63 8.1 Recommended Types 63 8.2 Correlations 63 TABLES 1 TYPICAL CONSTANTS FOR EQUATION (1) 7 2 POWER CURVES FIGURES AND CORRECTION

FACTORS 10 3 VORTEX PARAMETERS, TURBINE, PROPELLER

AND SAWTOOTH 35 4 CHARGING A HOT VESSEL WITH A COLD PRODUCT 43 5 INJECTING A HOT FLUID INTO THE JACKET OF

A COLD VESSEL 44 6 TYPICAL DISCHARGE COEFFICIENTS 45 7 CONSTRAINTS FOR LAMINAR FLOW MOTIONLESS

MIXERS 64 8 CONSTANTS FOR TURBULENT FLOW MOTIONLESS

MIXERS 65 9 LENGTH FACTORS FOR HIGH VISCOSITY RATIOS 65



FIGURES 1 POWER NUMBERS FOR 45° ANGLED-BLADE TURBINES 12 2 CORRECTION FACTORS FOR DIAMETER RATIOS 13 3 BLADE ANGLE AND THICKNESS CORRECTION FACTORS 13 4 POWER NUMBERS FOR SINGLE 60° ANGLED-BLADE

TURBINES 14 5 POWER NUMBERS FOR TWIN 60° ANGLED-BLADE

TURBINES 15 6 POWER NUMBERS FOR TRIPLE 60° ANGLED-BLADE

TURBINES 16 7 BAFFLE WIDTH AND NUMBER CORRECTION FACTORS

FOR DIFFERENT DIAMETER RATIOS 19 8 CORRECTION FACTORS FOR SUBMERGENCE 19 9 CORRECTION FACTORS FOR SEPARATION 19 10 POWER NUMBERS FOR DISC-TURBINES 20 11 CORRECTION FACTORS FOR BAFFLES 22 12 CORRECTION FACTORS FOR BASE CLEARANCE 22 13 CORRECTION FACTORS FOR SUBMERGENCE 23 14 POWER NUMBERS FOR RETREAT-CURVE IMPELLERS 24 15 CORRECTION FACTORS FOR PARTIAL BAFFLES 26 16 POWER NUMBERS CORRECTION FACTORS FOR RETREAT-

CURVE AND IMPELLERS H/T RATIOS OF 2.0 26 17 POWER NUMBERS FOR FLAT-BLADED TURBINES 27 18 BOTTOM CLEARANCE CORRECTION FACTOR 29



19 POWER NUMBERS FOR ANCHOR AND GATE AGITATORS 30 20 POWER NUMBERS FOR PROPELLERS 32 21 IMPELLER SPACING CORRECTION FACTORS 33 22 STANDARD NOTATION FOR VORTEX CALCULATIONS 37 23 VORTEX DATA FOR 2 - BLADED PADDLES

(W/D = 0.33, T/D = 2) 37 24 VORTEX CORRECTION FACTORS FOR PADDLES 38 25 JET DIRECTION 47 26 SINGLE JET MIXERS 52 27 MULTIJET MIXERS 53 28 SERIES ARRANGEMENT OF MIXERS 54 29 BATCH MIXERS 54 30 DESIGN PROCEDURE 56 31 EMPIRICAL FACTORS 60 32 RECIRCULATION ZONES 62 33 FRICTION FACTOR DATA FOR KENICS AND SULZER MIXERS 66 DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE 67



0 INTRODUCTION This Guide is one in a series of Mixing Guides and has been produced for GBH Enterprises. 1 SCOPE This Guide caters for the majority of mixing duties for miscible liquids, but does not cover the more specialized cases for which reference should be made to mixing experts. The Guide is divided into 4 main sections dealing with the mixing devices most commonly employed for miscible liquid systems, namely Stirred Vessels, Jet-mixed Vessels, Jet Flow Mixers and Static (or Motionless) Mixers. 2 FIELD OF APPLICATION This Guide applies to Process Engineers in GBH Enterprises worldwide. 3 DEFINITIONS No specific definitions apply to this Guide. 4 SELECTION OF EQUIPMENT All considerations refer to macro-mixing, i.e. blending and uniformity throughout the vessel. Mixing on smaller, local scales (micro-mixing) is not covered at present, and will follow different trends and rules. The operating costs, as measured by the energy required per unit throughput, for the mixers are likely to be similar.



4.1 Mechanically Agitated Vessels Mechanically agitated vessels are very versatile. They can be operated in either a batch or continuous mode. They are suitable for use where long mixing times (10 - 10000 secs or longer) can be tolerated and where long residence times are desirable. The mixing time is generally independent of throughput, in contrast to 'flow' mixers. With the appropriate choice of agitator they can handle the entire range of liquid viscosities. Power input per unit volume is usually low. The capital cost of the tank and agitator system is high. Heat transfer area per unit volume is not large, especially for large vessels. It can be extended either by the use of internal coils, or by an external recycle pumped through a heat exchanger. Exotherms can also be handled by boiling and condensation and, since the vessel is backmixed, some of the heat of reaction can be absorbed by feeding in ”cold” inlet streams. 4.2 Jet Mixed Vessels Jet mixed tanks are usually used only to blend low viscosity liquids (so that Re j 1000) with a jet to bulk density difference of less than about 30%. They can be operated in either a batch or continuous mode. Mixing times are of the same order of magnitude as stirred tanks. For the same mixing duty, a jet mixed tank has a lower energy efficiency than a mechanically agitated tank. For a given duty the capital cost of a jet mixed tank will be lower than that of a mechanically agitated vessel. Jet mixing can be particularly attractive in terms of capital cost for very large, irregularly shaped vessels such as lagoons and reservoirs. 4.3 Tubular ('Flow') Mixers Tubular mixers e.g. jet mixers, motionless mixers, orifice plates, venturis, etc are essentially continuous flow devices although they can be used in batch loop recycle systems. Their principal uses are:



(a) the continuous blending of miscible liquids over the whole range of liquid viscosity;

(b) the rapid (0.01 - 5 seconds) contacting of low viscosity reactants for a

`”fast” reaction especially when the product spectrum is affected by the mixing rate;

(c) the processing of hazardous liquids where the amount being processed at

any instant must necessarily be small. High heat transfer rates are possible with these devices because of the intense turbulence and the high surface area to volume ratio. The capital costs of this type of mixer are very low compared with jet mixed and mechanically agitated tanks. However, the continuous, plug flow short residence time characteristics of these devices may mean that instrumentation costs are higher. When used in 'single pass' configurations the mixing performance depends upon the throughput. The requirement of mixing intensity determines the diameter and residence time fixes the length for a given process flowrate. This means that the tube gets narrower and longer with scale-down. 5 AGITATED VESSELS The main parameters in the design of agitated (or stirred) vessels for mixing miscible liquids are: (a) Mixing time; (b) Power requirements; (c) Vortex formation; (d) Heat transfer; (e) Flow and circulation.



5.1 Mixing Time for Liquids in Stirred Tanks In many processes it is important to mix reactants quickly and thoroughly. This can be assessed for any system by the overall 'mixing time', which is the time taken to reduce the root mean square concentration variations by a factor, frequently 20. This is the 95% mixing time, tm95%. Prediction of mixing time from the literature is not easy and values should not be relied on to better than ± 50%. In practice the designer usually only wants to know if a vessel is "adequately mixed" so this degree of precision is normally sufficient. If more precise values are required, specific experiments carefully related to the particular problem are recommended. If scale model measurements can be done easily, they are more reliable than prediction from the correlations given below. Mixing time depends strongly on circulation flows through the vessel, especially for low viscosity systems, so results in the turbulent region (Re > 104) scale up well with the relation "mixing time × agitator speed = constant". The constant is called 'the dimensionless mixing time'. 5.1.1 Low Viscosity Newtonian Liquids For low viscosity Newtonian liquids mixing is usually best performed with a turbine or propeller type agitator. The best configuration is with:

(See Figure 1 for definition of symbols. Pitch is the liquid progression distance per revolution; a is the angle of the blade to the horizontal. Down-pumping turbines have a!< 90°.)



Baffles increase the vertical circulation and thus are an effective means of shortening mixing time (but at the cost of increase power) and also reduce the complicating factors of vortex formation on prediction. Data on mixing times in unbaffled vessels is sparse but for a crude estimate the mixing time for the same vessel with baffles, at the same power, can be used. Fluid density differences can significantly increase mixing time. Mixing times (95%) for these systems can be predicted from correlations involving the power number (Po). These can be calculated by the methods given in 5.2. For low viscosity liquids;

The density and viscosity is that of the mixed liquid. First calculate Po1/3 × Re. If the value is greater than or equal to 6400 then use the appropriate constant as listed in Table 1. For values less than 6400 use equation (3) developed for high viscosity Newtonian liquids.



TABLE 1 TYPICAL CONSTANTS FOR EQUATION (1)

5.1.2 High Viscosity Liquids For high viscosity liquids the best agitators are either stacked pitched blade turbines, helical screws, straight anchors or bent anchors (see GBHE-PEG-MIX-700). As fluid motion decays more rapidly with distance from the agitator than with low viscosity fluids, relatively larger agitators are needed which sweep a greater volume of liquid. To estimate mixing times (and power) with Newtonian liquids use:

For turbine-type agitators with Newtonian liquids the formula developed by FMP can be used.



If the liquid is known or suspected to be non-Newtonian a rheogram of shear stress versus shear rate should be obtained (see GBHE-PEG-FLO-302). If the data is not available it should be measured. If the shear stress is low at low shear rates, then the mixing time should be calculated as if the liquid were Newtonian. (If in doubt calculate Ns as described below and check it is an order of magnitude smaller than the working speed.) For determination of the appropriate "apparent" viscosity use the Metzner and Otto relation:

Values of k s for typical configurations are:

If there is a significant shear stress at zero shear rate (a "yield stress") and a turbine-type agitator is being used then a cavern of well mixed material may form round the agitator while the material near the walls and surface of the vessel remains unmixed. In this case rather than try to estimate mixing times it is better to use a correlation from the work of Solomon (1981) and Elson (1985) to estimate the minimum agitator speed for the cavern size to equal the vessel size (equation 5). Under this condition the vessel can be considered well mixed.



It is assumed that the agitator is half way up the vessel. If this is not so, for a safe design, replace H by twice the distance from the agitator to the surface or twice the distance from the agitator to the bottom, whichever is the greater. Etchells (1987) suggests that this approach should apply to materials where the "yield stress" is at least (5 × the viscosity at infinite shear × the shear rate). This is the case for many slurries. 5.2 Power Requirements

5.2.1 Levels of Power Input

Power inputs from agitators to low-viscosity Newtonian liquids are usually in the range 100 to 2000 W/m3; though for some applications, inputs of 4000 to 10000 W/m3 are used. Power inputs above this level are rare in stirred tanks and are difficult to achieve using conventional agitators. They tend to be restricted to tanks of 2 m3 capacity or smaller, where very short mixing times are required, as in polythene reactors which run at 100 to 200 W/m3.



5.2.2 Factors Affecting Power Dissipation

Power dissipation is a function of agitator geometry, speed of rotation, fluid properties, vessel fittings, vessel geometry and fluid aspect ratio. Fluid properties are characterized by Reynolds and/or Froude Numbers: up to Re of the order of 10 to 30 the flow is mainly viscous and power dissipation is proportional to viscosity and independent of density. As Re increases above about 1000, the flow is essentially turbulent and the power is much more dependent on density than viscosity. Geometries, fittings and speed are usually interdependent in complex ways and their effects vary between systems.

5.2.3 Power Correlation

It has been shown that the power supplied by an agitator can be expressed by:

P/(ρ N3 D5) = fn ((N D2 u/µ).(N2 D/g). R1....RI)

where R1....Ri represent the various geometric ratios describing the agitator and vessel. For a given agitator-vessel system this gives:

P/(ρ N3 D5) = Po = K (N D2 ρ/µ)m. (N2 D/g)n

where Po is the Power Number of the agitator-vessel system and is comparable to the drag coefficient in a flowing fluid system. At Re < 10, m tends to -1 and at high Re it tends to zero, especially in baffled vessels. In fully baffled vessels and systems with no free liquid surface, n becomes zero. K depends upon the geometry.

The correlation of Po with Re is universally recognized as a reliable means of predicting power requirements at widely differing scales of operation for geometrically similar vessels. The correlation must be established experimentally for each geometric system, which has a unique Po-Re relationship. Graphs of Po vs Re data for a number of basic impeller designs are presented here: deviations from the "standard" designs have to be allowed for by using a series of correction factors.



5.2.4 Calculation of Power

(a) Calculate the agitator Reynolds Number (ND2ρ/µ).

(b) Select appropriate power curve for the type and geometry of agitator (see Table 2), and read the value of Po for Re obtained under (a).

(c) Tabulate the variations between the actual agitator and the

"standard" design, as illustrated in the same Figure as the power curve.

(d) Use appropriate Figure for the agitator (as listed in Table 2).

(e) Determine the relevant correction factors for each variation from the

"standard".

(f) Multiply the value of Po by these correction factors.

(g) Calculate the power (P = Po ρ N3 D 5).

Note: that commercially available programs are available to calculate the power.



TABLE 2 POWER CURVES FIGURES AND CORRECTION FACTORS

Power numbers for 'hydrofoils' can be found in the GBHE Mixing and Agitation Manual.

5.2.5 Correction Factors for Power Numbers of 45° Angled-Blade Turbines

For impellers and vessel configurations different from the standard system shown in Figure 1, multiply the standard power number by each correction factor described below:

(a) Vessel diameter (T )

No correction factor recommended.

(b) Baffle-width (W b )

T/10 flat baffles, Cb = 1.10 no wall gap T/12 flat baffles, Cb = 1.0 no wall gap.



(c) Non-standard internals: assume an otherwise unbaffled vessel except for the helical coil:

Single finger baffle, C i = 0.71 Twin finger baffles, C i = 0.81 Beavertail baffle, C i = 0.74 Triangular wall baffle, C i = 0.97 ... projected W b = T/9 Single dip-pipe, C i = 0.56 ... diameter = T/23 Ringlet coil (a), C i = 0.73 ... tube od = T/55

pitch!= T/34 coil pitch = T/8



(j) Blade angle and thickness (a and X)

The correction factor Ca is plotted in Figure 3, note that Po is a very strong function of angle and errors of 2.5 will alter Po by 10%. All the data refers to downward pumping impellers; for upward pumping impellers use an additional correction factor of 0.9. Data from 3 bladed turbines will probably be within 10% of that for 4 blades.

FIGURE 1 POWER NUMBERS FOR 45° ANGLED-BLADE TURBINES



FIGURE 2 CORRECTION FACTORS FOR DIAMETER RATIOS

FIGURE 3 BLADE ANGLE AND THICKNESS CORRECTION FACTORS



FIGURE 4 POWER NUMBERS FOR SINGLE 60° ANGLED-BLADE TURBINES



FIGURE 5 POWER NUMBERS FOR TWIN 60° ANGLED-BLADE TURBINES



FIGURE 6 POWER NUMBERS FOR TRIPLE 60° ANGLED-BLADE TURBINES



5.2.6 Correction Factors for Power Numbers of 60° Angled-Blade Turbines For impellers and vessel configurations different from the standard system shown in Figure 4, multiply the standard power number by each correction factor described below. Note that these correction factors, where relevant, also apply to dual and triple 60° angled-blade impellers. (a) Vessel diameter (T )

C t = (T/0.304) -0.08 range 0.2 T 3.0 m (b) Baffle width (W b )

Use Figure 7. (c) Non-standard internals: assume an otherwise unbaffled vessel, except for

the helical coil:

4 × T/12 flat wall baffles + T/40 wall-gap Ci = 1.00 4 × T/10 flat wall baffles + no wall-gap Ci = 1.10 4 × T/10 profiled (triangular) wall baffles Ci = 0.97 4 × T/12 + wall gap.....half vessel height Ci = 0 92 1 × finger baffle Ci = 0.70 2 × finger baffles Ci = 0.80 1 × beavertail baffle Ci = 0.84 2 × beavertail baffles Ci = 1.10 1 × ringlet coil Ci = 0.73 1 × dip-pipe or tubular thermopocket Ci = 0.40 2 × dip-pipes or tubular thermopockets Ci = 0.50 Helical coil (coil pitch > tube diameter) Ci = 1.00 Helical coil....treat supports as baffles.

(d) Diameter ratio (D/T )

See Figure 2, also for 45° impellers. (e) Bottom clearance (Z/D)

Cc = (Z/0.537D) -0.20 range 0.33 Z/D 1.10



(f) Submergence (S/T )

See Figure 8. (g) Number of blades (n) n = 2 3 4 5 6 7 8 C n = 0.60 0.87 1.00 1.17 1.28 1.31 1.41

(h) Blade width (Wp)

C w = (Wp/0.336D)1.17 range 0.2 Wp/D 0.34 (j) Blade angle (a to the horizontal)

Ca = ( [sin a ] /0.866)2.10 range 55° a 75° (k) Blade thickness (X )

C x = 1.0 range 0.04 X/W 0.10 (l) Blade roundness

Cr = 0.95 corner radius, r/W = 0.2 blade thickness, X/W = 0.05 to 0.08

Cr = 0.56 corner radius, r/W = 0.5

blade thickness, X/W = 0.30 (m) Pumping direction

Pumping down Cp = 1.00; Pumping up Cp = 0.91



(n) Vessel base shape

Dished base C v = 1.00; Flat base C v = 0.98 (p) Multiple impellers

For multiple impellers of the same geometry, use Figures!5 and 6. For multiple impellers of mixed geometries, use Figure 21 or the sum of the individual power numbers, which would give high (safe) values.

(q) Impeller separation

Use Figure 9. FIGURE 7 BAFFLE WIDTH AND NUMBER CORRECTION FACTORS FOR

DIFFERENT DIAMETER RATIOS



FIGURE 8 CORRECTION FACTORS FOR SUBMERGENCE

FIGURE 9 CORRECTION FACTORS FOR SEPARATION



FIGURE 10 POWER NUMBERS FOR DISC-TURBINES



5.2.7 Correction Factors for Flat-Bladed "RUSHTON" Disc-Turbines

For impellers and vessel configurations different from the standard shown in Figure 10, multiply the standard power number by each correction factor described below:


Ct = T0.065. (b) Baffle width (W b)

Use Figure 11. (c) Non-standard internal fittings

No information.




Cd = 1.0 (at Z/T = 0.30) range 0.14 D/T 0.70 (e) Bottom clearance (Z/T )

Use Figure 12. (f) Submergence (S)

Use Figure 13. (g) Number of blades (n)



(n) Multiple impellers

Use Figure 21 or the sum of individual impellers, where multiple impeller power number data is not available: this gives high (safe) values.

FIGURE 11 CORRECTION FACTORS FOR BAFFLES

FIGURE 12 CORRECTION FACTORS FOR BASE CLEARANCE



FIGURE 13 CORRECTION FACTORS FOR SUBMERGENCE

FIGURE 14 POWER NUMBERS FOR RETREAT-CURVE IMPELLERS



5.2.8 Correction Factors for Power Numbers of Retreat-Curve Impellers

For impellers and vessel configurations different from the standard system shown in Figure 14, multiply the standard power number by each correction factor described below.


No information available.

(b) Baffle-width (W b)

T/10 flat baffles, C b = 1.0 no wall gap T/12 flat baffles, C b = 1.0 T/40 wall gap



(c) Non-standard internals: 4x flat wall-baffles taken as the reference power number

Also see Figure 15.


C d = (0.8T/D)0.58 range, 0.5 D/T 0.80

(e) Bottom clearance (Z/D)

No information available normally, 0.061 Z/D 0.1


No information available.

(g) Batch height (H/T )

See Figure 16.

(h) Blade width (W/D)

C w = (W/0.125D)0.6 range, 0.1 W/D 0.194

(i) Blade angle and thickness (a and X )

No information available normally, a is 10° or 15°.



FIGURE 15 CORRECTION FACTORS FOR PARTIAL BAFFLES

FIGURE 16 POWER NUMBERS CORRECTION FACTORS FOR RETREAT-

CURVE AND IMPELLERS H/T RATIOS OF 2.0



FIGURE 17 POWER NUMBERS FOR FLAT-BLADED TURBINES



5.2.9 Correction Factors for Power Numbers of Flat-Bladed Turbines

For impeller and vessel configurations different from the standard system shown in Figure 17, multiply the standard power number by each correction factor described below:



(b) Baffle width (W b)

Use Figure 7.

(c) Non-standard internals: assume an otherwise unbaffled vessel

apart from the helical-coil, which is located on a 4x flat wall-baffle cage:


Use Figure 7.

(e) Bottom clearance (Z/T )

Use Figure 18.


Use Figure 13.



(g) Number of blades (n)

See the relationships for Blade width (h) below.

(h) Blade width (W )

(j) Blade thickness (X )

Po varies by less than 5% in the range, 0.01 X/D 0.0332

(k) Vessel shape (V )

Flat bottom C v = 1.11 Dished bottom Cv = 1.00



FIGURE 18 BOTTOM CLEARANCE CORRECTION FACTOR

FIGURE 19 POWER NUMBERS FOR ANCHOR AND GATE AGITATORS



5.2.10 Correction Factors for Power Numbers of Anchor and Gate

Agitators

For impellers and vessel configurations different from the standard system shown in Figure 19, multiply the standard power number by each correction factor described below:



(b) Blade height (L/D)

C l = 0.86L/D + 0.11.



(c) Agitator shape

Cf = 0.89L/D + 0.11n n = number of cross-bars Cf ' = C f (1 + (D i /D)5) for gates > 2 vertical bars


See (e) below.

(e) Side & bottom clearance (e/T )

(f) Number of blades (n)

No correction factors recommended.

(g) Blade width (W/D)

C w = 1.0 W/D = 0.083 to 0.125



FIGURE 20 POWER NUMBERS FOR PROPELLERS



5.2.11 Correction Factors for Power Numbers of Propellers



(b) Baffle width (W b)

FIGURE 21 IMPELLER SPACING CORRECTION FACTORS

1 Disc turbines 2 Angled-blade turbines & propellers

(pumping in the same direction)



5.2.12 Power Numbers for Multiple Impellers Notation Po(c) = combination power number Po(1) = bottom impeller power number Po(2) = 2nd impeller power number Po(n) = nth. Impeller power number (a) Twin impellers - Po(1) + Po(2) × (Po(n)/Po). (b) Triple impellers - Po(1) + [Po(2) + Po(3)] × [Po(n)/Po]. MIXED IMPELLERS, use Po(n)/Po = 1.0 until data becomes available. 5.3 Vortex Formation and Surface Entrainment in Unbaffled and Baffled

Vessels Unbaffled vessels were formerly preferred for liquid blending and solid suspension duties. The impeller is usually mounted centrally and except in the case of a sawtooth disc, the designer must check that the vortex does not reach it. The rise of the vortex is obviously critical in open vessels and could be critical in closed vessels where instrument probes or vent lines need to be kept clear of liquid. The general configuration of vessel, impeller and vortex is shown in Figure!22. Off-centre mounting of the agitator can give a flow regime closer to that of a baffled vessel but causes large fluctuating forces on the agitator shaft. Little design information is available and this option is not recommended. A major vortex is not normally generated in fully baffled vessels. In both baffled and unbaffled systems, it may be necessary to avoid gas entrainment into the liquid or to specify conditions under which a light solid may be rapidly incorporated into a liquid surface. (a) Agitator types

Data are given for disc-turbines, flat bladed paddles, sawtooth, propeller and anchor agitators. Extensive information is available in the GBHE Mixing and Agitation Manual on paddle mixers, covering a wide range of geometries. Table 3 gives vortex parameters for modern mixers and Figure 22 shows h1 and h2: the displacement of the vortex below and above the original liquid level.



(b) Parameters covered

Vortex depths are related to impeller Reynolds Number (ND2ρ/µ) and Froude Number!(N2D/g). Experimental checks at GBHE have shown that separate equations are not needed for Froude Numbers less than 0.1.

5.3.1 Recommendations

Vortex configuration in unbaffled vessels

(a) Turbine, propeller and sawtooth relevant k values are in Table 3.

(1) For all T/D ratios and Re below 2000:

(2) At Reynolds Numbers greater than 5000:



TABLE 3 VORTEX PARAMETERS, TURBINE, PROPELLER AND

SAWTOOTH



where:

Vortex Parameter is shown in Figure 23, and generally f = f1 gives correction factors for h1 and f = f 2 for h2 from the respective graphs in Figure 24. This work performed for GBHE, is the most comprehensive range of correction factors available for paddles.

5.3.2 Avoidance of Gas Entrainment in Standard Baffled Vessels It may be necessary to avoid gas entrainment from the surface in a standard baffled vessel, in which case a maximum impeller speed, above which entrainment could occur, is given below for agitator/vessel diameter ratios in the range 0.33 to 0.47.



FIGURE 22 STANDARD NOTATION FOR VORTEX CALCULATIONS



FIGURE 23 VORTEX DATA FOR 2 - BLADED PADDLES (W/D = 0.33, T/D = 2)

FIGURE 24 VORTEX CORRECTION FACTORS FOR PADDLES



5.4 Heat-Transfer in Stirred Vessels

It is seldom that heat-transfer is the only operation to be promoted by agitation and the choice is often a compromise between conflicting requirements. In those cases where heat-transfer considerations are a prime factor in the design, the aim should be to select an impeller design which gives high bulk flowrates of the fluid with good general mixing and high fluid velocities close to the heat-transfer surfaces.



For low viscosity fluids (up to 1 N.s/m2) flat paddles, angled blade turbines, disc turbines or propellers with D/T ratios of 1/3 to 1/2 can meet these requirements and give broadly similar rates of heat-transfer. The choice between them can be based on other mixing criteria for the process, e.g. suspension of solids, gas dispersion. Note however that relatively small changes of viscosity can influence heat-transfer performance quite markedly. As viscosity increases further to about 3 N.s/m2 the impeller diameter should be increased to give D/T = 2/3 or more, whilst at the same time reducing the blade width to conserve power. At higher viscosities (> 3 N.s/m2) anchor stirrers and dual or triple wide-diameter impellers are used whilst at very high viscosities (> 25 N.s/m2) screw and helix impellers are preferred.

Jackets and limpet coils are used extensively on carbon steel, stainless steel and glassed steel vessels. Limpet coils show advantages over jackets in cost, pressure rating and heat-transfer performance. However there can be fatigue problems on limpet coils subjected to thermal cycling. Typical pressure ratings of jackets and limpet coils are 6 bar and 14 bar respectively. Jackets and limpet coils are preferred to internal coils when processing viscous liquids. Jacket heat-transfer performance can be influenced markedly by the use of aids such as jetted feed, tangential inlets, baffles, and multiple outlets. Internal coils are used primarily to supplement heat-transfer area in jacketed vessels and in cases where heat-transfer through the wall is very poor or impracticable, e.g. rubber lined tanks, GRP tanks. Coils are suitable for higher pressure service fluids and in cases where a large corrosion allowance must be provided. Large helical coils are used in two-piece vessels when a long service life is expected. Hairpin and ringlet coils are used in one-piece vessels and often act as baffles in the agitation system. They have the advantage of being easily removed if the process duty changes or in the event of failure. Broadly speaking, jackets, helical coils and ringlet coils of reasonable proportions in a given vessel, are capable of meeting similar heat transfer duties.



5.4.1 Correlations and Design Guides

Heat-transfer in stirred vessels is brought about primarily through conduction and forced convection. The process is assumed to be governed by the combined resistance of:

(a) the wall separating the service and process fluids;

(b) the dirt films on each side of the wall and

(c) laminar films of process and service fluids adjacent to the

wall.

Correlations for local coefficients of heat-transfer are of the form:

ᵞ = bulk liquid viscosity/viscosity at the wall. (1) Use any Standards which apply, e.g. vessels, jackets, limpet coils,

helical coils, ringlet coils, impellers, service pumps, etc. (2) Check that the batch depth lies between about 0.8 and 1.0 vessel

diameters. If below this range consider using a smaller vessel; if above the range consider putting additional impellers on the shaft.

(3) With low viscosity fluids (< 1 N.s/m2) use an impeller which meets

other process duties. A simple, cheap design should be chosen giving high circulation rates and moderate power inputs, e.g. 0.5 to 0.7 kW/m3 in baffled vessels, 0.2 to 0.5 kW/m 3 in unbaffled vessels.



(4) In viscous fluids, impeller blades should reach close to the fluid surface, even if this means adding additional impellers or cross-members. Blade widths and wall clearances should be about 1/10 of the vessel diameter.

(5) In non-jacketed vessels, helical coil diameters are close to the tank

diameter: the coil often being supported by the tank wall about 50 to 150 mm away from it. In jacketed vessels where the coil is supplementing the jacket, the coil diameter should be about 90% of the vessel diameter.

(6) When multiple concentric helical coils are used, care must be taken

to stagger and increase the pitch to ensure they do not shield each other.

(7) Tube diameters for coils vary between 25 and 100 mm; by far the

most common sizes being 37 to 50 mm.



5.4.2 Correlations

(a) Service-Side Heat Transfer Coefficients

(1) Conventional Jackets with low flows [ velocity < 0.03 m/s, no phase change ] (enhanced natural convection)

(2) Conventional jackets with high flows

(sensible heating/cooling)



All physical properties, except µw, are evaluated at bulk temperature. Two cases arise: (i) Radial fluid inlet [Re i > 9000] (ie no swirl)

(ii) Tangential fluid inlet: [Re i > 20000]

(3) Conventional jackets with condensing heating medium

(ii) Turbulent condensate film, see HTFS Design Report



(4) Limpet coils (sensible heating/cooling)

(5) Limpet coils (condensing service fluid)

See HTFS Design Report

(6) Spiral jackets (sensible heating/cooling)

Use the same correlation as the limpet coils.

(7) Immersed coils (sensible heating/cooling)

where:

d i = pipe inside diameter D c = coil diameter



(8) Immersed coils (condensing service fluid)

As for limpet coils.

(b) Process-Side Heat Transfer Coefficients

(1) Vessel Wall Surface

5.4.3 Thermal Shock in Glass-Lined Steel (GLS) Vessels When using a GLS vessel for heating or cooling duties, it is important to prevent thermal shock from damaging the glass lining. Table 4 shows the maximum allowable temperature difference when charging into a heated vessel.



TABLE 4 CHARGING A HOT VESSEL WITH A COLD PRODUCT

* use this ΔT for vessel temperatures up to 121°C. Table 5 shows the maximum allowable temperature difference when charging into a cooled vessel. TABLE 5 INJECTING A HOT FLUID INTO THE JACKET OF A COLD

VESSEL

* use this ΔT for vessel temperatures up to 121°C.



5.5 Flow and Circulation Details of flow patterns, velocities and local concentrations may be obtained from the CFD computer program. The following other measurements are sometimes used in mixing vessels: (a) Agitator discharge volumetric flowrate, Q p

Where Flρ is a discharge coefficient for the agitator (because of entrainment the actual circulation flow will usually be much greater than, Qp). Values of Flp are given in Table 6.

(b) Circulation time, tc

tc is the average time interval for successive passages of a fluid element through the agitator. For a 6 bladed disc turbine (D/T = 0.3 to 0.5; Z/T = 0.3 to 0.5; H/D = 0.2; L/D = 0.25):

As this is not dimensionless, V must be in m 3. For turbulent, baffled stirred vessels the following rule of thumb is frequently used:



TABLE 6 TYPICAL DISCHARGE COEFFICIENTS

6 JET MIXED TANKS 6.1 Introduction Jet mixing in tanks can be used for the batch or continuous mixing of miscible low viscosity (µj < 0.1 Ns/m2) liquid systems. In tank jet mixing, a fast moving stream of liquid, the 'jet' liquid, is injected into a very slow moving, almost stationary liquid, the 'bulk' or 'tank' or 'secondary' liquid. The velocity gradient between the jet and bulk liquids creates a mixing layer at the jet bulk boundary. This mixing layer entrains bulk liquid into the jet flow. Turbulence within the jet flow then mixes the jet and bulk liquids. Side entry jets (i.e. jets through the tank wall) or axial jets (i.e. jets directed along the axis of the tank) are commonly used. Such jets are usually positioned either near the tank floor pointing towards the liquid surface or near the liquid surface pointing towards the tank floor. Swirl decreases the efficiency of mixing.



6.2 Recommended Configuration The design objective should be to produce liquid motion throughout the whole tank. The tank should be cylindrical with a vertical axis, for other shapes consult the GBHE Mixing and Agitation Manual. The liquid height, HL, to tank diameter, T, ratio should preferably be in the range:

although other HL /T ratios are permissible. Depending on the tank geometry and the mixing duty, a single jet through the tank wall (a side entry jet) or a single jet on the axis of the tank (an axial jet) or multiple jets may be used. The jet can be positioned either near the tank floor pointing towards the liquid surface or near the liquid surface pointing towards the tank floor. The jet nozzle should always be submerged during the mixing operation. The side entry jet should protrude no more than 5 nozzle diameters either from the tank wall or from the tank base or liquid surface. The axial jet nozzle should be as close to the tank floor or liquid surface as possible. The side entry jet should be installed along a radius to the tank wall and the axial jet on the tank axis perpendicular to the tank floor or liquid surface. For the same mixing duty, the mixing rates achieved by axial and side entry jets are essentially the same.



6.3 Design Procedure The procedure for design for a given mixing time t99 for a given volume, V, of liquid is as follows:

(a) Choose a tank diameter such that:

This, of course, may not be possible if either T and/or HL are fixed by site or mechanical considerations, or if the tank already exists. The recommended tank/jet configuration, which depends on HL/T, is:

The design for side entry or axial jets is detailed below. For multiple jets the tank should be considered as divided into separate volumes of H/T 1, each with their own jet, see the GBHE Mixing and Agitation Manual for more detail.

(b) Jet direction

A jet can be positioned pointing either upwards or downwards, see Figure 25. If the jet is pointed upwards then it may break the surface and give rise to spray. Aeration may occur. The spray may induce a build up of static charge. These problems will not occur when the jet is pointed downwards towards the base of the tank and is adequately submerged. The centre line exit velocity should be 1 to 2 m/s. When the mixing duty is merely to maintain homogeneity in a tank, the density of the jet liquid is essentially the same as the density of the bulk liquid, and stratification is not a problem. In this case the choice of jet direction is arbitrary.



FIGURE 25 JET DIRECTION



FIGURE 25 JET DIRECTION (Continued)



(c) Position of recycle suction

For an upward pointing side entry jet in a flat base tank the recycle suction should be positioned either as near as possible to the tank floor on the opposite side of the tank to the jet, or as near as possible to the liquid surface on the same side of the tank as the jet. For a dished base tank the recycle suction must be placed at, or very near, the lowest point of the base.

For a downward pointing side entry jet in a flat base tank the recycle suction should be positioned either as near as possible to the liquid surface, on the opposite side of the jet, or as near to the tank floor on the same side as the jet. Again, for this type of jet in a dished base tank, the recycle suction must be placed at, or very near, the lowest point of the base.

For an upward pointing axial jet in a flat base tank the recycle suction should be positioned either as near as possible to the tank floor, or as near as possible to the liquid surface in a tank with a dished base. Jet protrusion should be as small as possible in a dished base tank.

For a downward pointing axial jet in a flat base tank the recycle suction should be placed either as near as possible to the liquid surface or as near as possible to the tank floor. For this type of jet in a dished base tank, the recycle suction should be placed near the liquid surface.

(d) Mixing time

(1) Upward pointing jets

The mixing time, t99, for upward pointing jets is given by:



where for both side entry and axial jets:

This correlation is based on experimental work on small tanks, (T up to about 1 m) for low viscosity liquid mixing,

The correlation is for flat based tanks. It applies to side entry jets with nozzles which are no more than 5 nozzle diameters either from the nearest tank wall or from the tank base and axial jets with nozzles which are close to the tank base. (2) Downward pointing jets

For downward pointing jets in tanks where



(3) Hemispherical based tanks The mixing time in hemispherical based tanks is less than that in flat bottomed tanks:

(e) Jet diameter

The jet diameter, Dj, should be chosen such that:

Here, X is the jet path length, for both upward and downward side entry jets placed as recommended above:

Initially choose the smallest Dj.

The choice of jet velocity, vj, depends on the mixing duty being undertaken. If one liquid is being mixed with a second liquid of different density there is a danger of stratification (see GBHE Mixing and Agitation Manual) if the jet velocity is too low.



(f) Number of jets

As stated in (a), multiple jets should only be used for HL /T > 3.0. There is no advantage in mixing from multiple jets for the same overall flowrate in other cases.

6.4 Design for Continuous Mixing If the tank is run at a constant level, HL, and the fresh feed fed through a nozzle near the recycle line nozzle, then the tank will be well mixed if:

VT is the volume of liquid in the tank and Qf is the fresh liquid feed rate. t99 is the batch mixing time calculated by the method given in 6.3. 7 TUBULAR JET FLOW MIXERS FOR MISCIBLE LIQUIDS

Jet flow mixers are recommended for mixing low viscosity liquid phase systems i.e. systems where turbulent pipe flow can be achieved (Re > 5000). Mixing times from a few milliseconds on the small scale to several seconds on the large scale are possible with this type of device.

In jet flow mixers a stream of liquid, the primary liquid is injected into another liquid, the secondary liquid. The velocity gradient between the jet and secondary liquids creates a turbulent mixing layer at the jet boundary. The mixing layer grows in the direction of the jet flow entraining and mixing the jet with the secondary liquid. Pressure drop at and along the pipe after the mixing point provides the energy required for mixing the two streams.



There are three basic types of jet flow mixer geometries, the coaxial jet mixer, the side entry jet mixer and the impinging jet mixer, see Figure 26. In the coaxial jet mixer the jet liquid is introduced through a small diameter pipe running coaxially inside a large diameter pipe. In the side entry jet mixer the jet liquid is introduced at an angle (usually 90 degrees) into the secondary liquid stream. In the impinging jet mixer the two feed streams are fed through directly opposing branches of a tee-piece. Multiple jet flow mixers, see Figure 27, are also sometimes used.

A series arrangement of mixers, Figure 28, can be used to mix more than two streams. This arrangement can also be used either when the flowrate ratio of the feed streams is very high or when the mix temperature rise due to mixing would be unacceptably high if the mixing were to be carried out in one stage. Interstage cooling can then be used. A series arrangement of mixers, Figure 28, can be used to mix more than two streams. This arrangement can also be used either when the flowrate ratio of the feed streams is very high or when the mix temperature rise due to mixing would be unacceptably high if the mixing were to be carried out in one stage. Interstage cooling can then be used.



FIGURE 26 SINGLE JET MIXERS



FIGURE 27 MULTIJET MIXERS



FIGURE 28 SERIES ARRANGEMENT OF MIXERS



Batch mixing operations can be carried out if storage volume and recycle are exploited, see Figure 29. This can be particularly attractive if precise control of the mixing is required as, for example, in batch pH adjustment duties. Note that the recycle stream can be used to maintain homogeneity of the storage vessel by jet mixing. Jet flow mixers operate in the plug flow regime; very little backmixing occurs in the pipe after the mixing point. Thus, accurate control of the feed streams is essential. Moreover, jet mixers should not be fed by positive displacement pumps unless the pumps are fitted with efficient pulsation dampeners. The residence time distribution in jet flow mixers is covered in 7.3.1. Blockage by solids is a potential problem when mixing suspensions of solids or reagents which react rapidly to form a solid, especially on the small scale, see 7.3.2. The heat transfer rates achieved in the mix after the mixing point are greater than those achieved in turbulent flow in a straight pipe because of the greater intensity of turbulence. However, this effect has not yet been adequately quantified, see 7.3.3. 7.1 Recommended Configurations Coaxial jet and side entry jet flow mixers are recommended for mixing two feed streams. Impinging jet flow mixers should not be used because of the difficulty of balancing the momentum fluxes of the streams in the two opposing feed branches of the mixer. Because of design uncertainty, the use of multiple jet flow mixers is not recommended.



7.2 Mixer Design In the design procedure, the streams into and out of the mixer are assumed to be fully turbulent. The usual constraints on the design of jet flow mixers are: - the degree of mixing required; - the mixing time required; - the available pressure drop; - the turndown required. The design procedure is iterative; for a given degree of mixing, the mixing time achieved has to be balanced against the available pressure drop, see Figure 30.



FIGURE 30 DESIGN PROCEDURE



If turndown is a constraint, the mixing time and pressure drop should be calculated for the range of flowrates being considered - the lowest flowrate to be processed will yield the longest mixing time and the highest flowrate the highest pressure drop. In this design procedure, the degree of mixing required for a particular duty is specified by the variation coefficient, M, (see the GBHE Mixing and Agitation Manual). M is defined as the ratio of standard deviation of concentration to the mean concentration measured over a cross-section mixer. A reasonable mixture quality, sufficient usually for temperature or concentration homogenization, and for many chemical applications, can be obtained with M = 0.05. However, for applications which involve color homogenization, a value of M!= 0.01 or less may be necessary. The choice of jet and secondary streams is arbitrary. For minimum pressure drop the stream with the smaller flowrate should be jetted into the stream with the higher flowrate. If the liquid density ratio (heavy to light) is greater than 2, jet the light liquid into the heavy liquid. If the liquid viscosity ratio (viscous to less viscous) is greater than 5, jet the less viscous liquid into the more viscous liquid. If neither of these two options are possible then do not use a jet mixer; use a motionless mixer. The solution of some design problems may require that both jet flow and motionless mixers are evaluated. In the design calculations, it is assumed that the flowrates, Q, the densities, u, and the viscosities, o, of the streams into and out of the mixer are known. The following subscripts are used to designate the streams:

j = jet or primary liquid flow t = secondary liquid flow m = combined stream.

The design procedure is as follows: (a) Choose the jet flow mixer geometry and the jet and secondary liquid

streams. (b) Choose the inlet pipe diameters Dj and Dt.

For coaxial jet flow mixers, the choice of Dj and Dt is arbitrary.

For side entry jet flow mixers, Dj and Dt shall be chosen such that:



(c) Calculate the flow velocities v j, v t and v m from:

where A jo is calculated using the diameter of the outside wall of the jet, D jo.

(e) Calculate the Reynolds Numbers to check that the inlet and outlet flows are turbulent:



For coaxial jet flow mixers

If these criteria are not satisfied then the flow velocities are too low. Return to step (b) and decrease the appropriate pipe diameter. (f) For coaxial jet flow mixers, the mixing length is given by:

L is the length of pipe required downstream of the mixing point to achieve the desired degree of mixing, M (M = 1 for 99% mixed, M = 10 for 90% mixed, etc.).



If t is more than the specified design mixing time then either return to step (b) and decrease Dm (which will increase V m and thus decrease t ) or specify a lower mixing quality (a higher value of M).

If t is less than specified, then v m is higher than necessary and the pressure drop to be calculated in the next step will be more than necessary.

(g) Calculate the pressure drop in the mixer.

Pressure losses arise from losses in the feed lines to the mixer (Pi), losses at the mixing point (Pg) and losses in the mix pipe (Po). Pi and Po can be calculated using appropriate procedures for calculating pressure losses in turbulent pipe flow.

For coaxial jet flow mixers, the pressure losses at the mixing point are given by:

The km, k t and k j are empirical factors which depend on the jet to main pipe cross sectional area ratio, A j / Am (see Figure 31).

(h) If the total pressure drop for either the jet or the secondary stream exceed

the available pressure drop then return to step (b), increase the appropriate pipe diameter and repeat the whole design calculation. This iterative procedure will eventually be limited either by the feed stream velocity ration (step (d)) or by the Reynolds Numbers (step (e)).

If the pressure drop and mixing time requirements can not be satisfied simultaneously then return to step (a), change the jet and secondary streams and repeat the calculation.



If the design constraints still cannot be satisfied then the chosen jet flow mixer geometry is not suitable for a given mixing duty. Another type of jet flow mixer or the use of a motionless mixer should be considered. FIGURE 31 EMPIRICAL FACTORS



7.3 Additional Considerations 7.3.1 Residence Time Distribution

There is no published data on residence time distributions in jet flow mixers. However, intuitively, since the mix flow is turbulent the residence time distribution should approach that of plug flow.

Deviations from plug flow will be caused by recirculation regions which occur near the jet orifice, see Figure 32.

These zones can be reduced in size if sharp edged orifices are avoided - this will decrease the tendency for flow separation.

Recirculation zones can also occur near where the jet flow hits the pipe wall, see Figure 32. These zones occur when the flow of secondary liquid is less than the entrainment capacity of the jet flow.

7.3.2 Solids

Solids blockage is a potential problem when processing solid suspensions or reagents which react rapidly to form a solid. Solids buildup can occur in the recirculation zones, see 7.3.1.

Solids buildup and subsequent blockage is difficult to predict. However, problems which occur on the small scale often disappear on the large scale. Solids also add another constraint to the design problem - pipe velocities must be high enough to maintain the suspension.

7.3.3 Heat Transfer

The inside heat transfer coefficient, h, along the initial part of the mix pipe is greater than that in ordinary turbulent pipe flow because the intense mixing action of the jet increases the temperature gradient at the pipe wall. For a side entry jet flow mixer the heat transfer coefficient can be doubled (depending on vj /v t ) over the first 5 mix pipe diameters. The coefficient then decreases rapidly over the next 10 diameters and reaches the value for ordinary pipe flow after 20 diameters.



FIGURE 32 RECIRCULATION ZONES



8 MOTIONLESS MIXERS Motionless mixers (also known as Static Mixers) are devices which fit into pipes and homogenize the flow. Their action depends on the rearrangement of the liquid produced by flow past stationary mixing elements. The energy for mixing comes from the pressure drop. Motionless mixers usually have a shorter mixing length than jet mixers. Motionless mixers have a narrow residence time distribution, so accurate control of the feed is essential if a consistent mixture quality is to be achieved. They are used in polymer melt processing to homogenize the temperature. There are about 20 different designs commercially available. These can be divided into two broad categories, those which split the flow into two or three streams, which usually have a helical motion imposed on them (for example the Chemineer-Kenics) and those in which the flow is channeled into several streams (for example the Sulzer mixers). The first few elements of a mixer can be redundant if the element does not "cut" the added stream. When adding a small flow to a large one the former should be introduced in the centre of the main flow if the flow is laminar. If the flow is turbulent side entry may be used provided the inlet velocity is at least twice that of the main flow. When blending liquids of widely differing viscosities the length of the mixer may need to be increased. When the low viscosity component has the lower flow the length should be increased by the factors given in Table 9. There is no data available for blending a low flow of a high viscosity component into a low viscosity component. Some motionless mixers can be obtained with the mixing elements removable, tack welded or with continuous welds. This choice between these types depends on the risk of fouling and the need for cleaning. Motionless mixers increase the wall heat transfer coefficient, especially if continuous welded. More details can be found in the GBHE Mixing and Agitation Manual.



8.1 Recommended Types

SMX and SMXL (Laminar Flow) - Sulzer Bros (UK) Ltd SMV (Turbulent Flow) - Sulzer Bros (UK) Ltd Static-mixer - Chemineer-Kenics Ltd Statiflo - Statiflo (UK) Ltd Etoflo HV (Laminar Flow) - Wymbs Engineering

8.2 Correlations L is the length of mixer required X is the ratio of the flows of the streams being mixed M is the percentage deviation from uniformity

(e.g. for M = 1 the concentrations will lie between 0.99 and 1.01 of the mean value)

D is the internal diameter of the pipe v is the superficial velocity (= 4 × vol. flow/sD2) Ep is the pressure drop across the elements Re is based on the internal pipe diameter. All logs are to base!10 E is the fraction of pipe cross sectional area available for flow. Transition from laminar to turbulent flow is smoother than in empty pipes and starts at a Reynolds Number of 100 to 200 and is complete at a Reynolds Number of 500 to 1500. The constants C1, C2, C3, C4, C5, C6 and K for different mixing elements are given in Tables 7 and 8.



TABLE 7 CONSTRAINTS FOR LAMINAR FLOW MOTIONLESS MIXERS



TABLE 8 CONSTANTS FOR TURBULENT FLOW MOTIONLESS MIXERS

TABLE 9 LENGTH FACTORS FOR HIGH VISCOSITY RATIOS

FIGURE 33 FRICTION FACTOR DATA FOR KENICS AND SULZER MIXERS



DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE This Process Engineering Guide makes reference to the following documents: GBHE ENGINEERING GUIDES GBHE-PEG-MIX-700 How to Use the Mixing Guides (referred to in 5.1.2) GBHE-PEG-FLO-302 Interpretation and Correlation of Viscometric Data

(referred to in 5.1.2) OTHER GBHE DOCUMENTS GBHE Mixing and Agitation Manual (referred to in

Clause 1, 5.2.4, 5.3 (a), 6.2, 6.3 (a) and (e) and Clause 7)

OTHER DOCUMENTS HTFS Design Report Heat Transfer to Newtonian and Non-Newtonian

Fluids in Agitated Vessels Part 1: Design Guide Part 2: Main Text Part 3: Table of Correlations (referred to in 5.4.2).