Mixing of Solid-Liquid Systems

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Process Engineering Guide: GBHE-PEG-MIX-703

Mixing of Solid-Liquid Systems 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 Solid-Liquid Systems CONTENTS SECTION 0 INTRODUCTION/PURPOSE 2 1 SCOPE 2 2 FIELD OF APPLICATION 2 3 DEFINITIONS 2 4 TYPICAL APPLICATIONS 2 5 AGITATED VESSELS 2 5.1 Suspension of Heavier-than-Liquid Solids 2

5.1.1 Dispersion 3 5.1.2 Agitator Speed Correlation 3

5.2 Floating Solids 10 5.3 Mass Transfer 11 6 JET MIXING FOR SOLID LIQUID AGITATION 5

6.1 Flat Bottomed Vessel 11 6.2 Changes in the Shape of the Vessel Base 12



7 NOMENCLATURE 13 8 BIBLIOGRAPHY 14 APPENDICES A WORKED EXAMPLE 15 TABLES 1 VALUES OF Po AND ZWIETERING CONSTANT "S"

FOR USE IN EQUATION 1 4 FIGURES 1 RECOMMENDED CONFIGURATION 4 2 RECOMMENDED CONFIGURATION FOR DRAW-DOWN

OF FLOATING SOLIDS IN AGITATED VESSE 10 3 ALTERNATIVE RECOMMENDED CONFIGURATION

FOR DRAW-DOWN OF FLOATING SOLIDS IN FOR AGITATED VESSEL 10

4 JET MIXING FOR SOLIDS SUSPENSION 12 5 ESTIMATION OF S FROM KNOWN DATA 16 DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE 18



0 INTRODUCTION/PURPOSE This Process Engineering Guide (PEG) is one in a series of Mixing Guides and has been prepared for GBH Enterprises. 1 SCOPE This Guide covers the mixing of solid-liquid systems; it deals with suspending particulate solids in a liquid, but does not cover slurries and other non-Newtonian solid-liquid systems. The aim of this guide is to cater for the majority of mixing duties for particulate solids in liquids. For more specialized duties, reference should be made to the GBHE Mixing and Agitation Manual and, if appropriate, to one of the experts. 2 FIELD OF APPLICATION This Guide applies to Process Engineers in GBH Enterprises worldwide. 3 DEFINITIONS No specific definitions apply to this Guide. 4 TYPICAL APPLICATIONS Typical reasons for suspending particulate solids in a liquid are: (a) Dissolving solids. (b) Contacting liquids with a solid catalyst. (c) Producing solid/liquid mixtures (e.g. paints). (d) Crystallization. (e) Wet blending of solids. Two basic methods are recommended, using either a stirred vessel or a jet-mixed vessel.



5 AGITATED VESSELS 5.1 Suspension of Heavier-than-Liquid Solids For solid suspension duties it is recommended that: (a) The vessel is fully baffled. (b) The agitator is a marine propeller or an axial flow "hydrofoil" impeller.

Pitched blade turbines with a blade angle of 45° are acceptable but require greater power.

(c) The agitator pumps downwards (or upwards if the clearance is low,

Z<T/4). (d) The liquid depth should be roughly equal to the tank diameter. For greater

liquid depths multiple agitators will be required. (e) The agitator diameter should be in the range T/3 to T/2: larger agitators

interfere with the circulation pattern. (f) The clearance between the agitator and the base of the tank should

preferably be in the range T/8 to T/4. (g) The vessel bottom should preferably be dished. Fillets will build up in

"square" bottom tanks. (h) Data from large scales is sparse. In critical cases it is common practice to

design a hypothetical small scale vessel and then scale it up on a constant power per unit volume (PoNJS

3 D5ρL /V) basis to the size required, using the power numbers (Po) from Table 1 and the method described in GBHE-PEG-MIX-701. Thus:

(1) Assume T = 0.61m. Choose D, Z and agitator type.

(2) Select most appropriate values of S and Po from Table 1.

(3) Calculate NJS from Equation (1).

(4) Calculate corresponding power per unit volume from:

P/V = PoNJS

3 D5ρL /V



(5) Calculate plant agitator diameter Dplant from required plant volume using the same H/T, D/T and Z/T.

(6) Calculate plant agitator speed Nplant from:

(Nplant) 3 = (P/V)Vplant /PoD5 plant ρL

This is a conservative method for scale-up. If the resulting P/V is greater than 0.5kW/m3 it may be over-safe.

(j) If the vessel is gassed do not use down flow impellers. Refer to GBHE-

PEG-MIX-706, and scaleup using the gassed power Pg. Note that NJS will be higher than for ungassed systems.

(k) The correlation does not work with fluid viscosities above about 200cP;

but once suspended, high viscosity duties should be easier. (l) For very small particles the correlation will be very conservative and

suspension will be dominated by viscous, not inertial forces. See Appendix A for an example.

The recommended configuration for agitated vessels is shown in Figure 1. 5.1.1 Dispersion If the solids are finely divided then the problem may be breaking down aggregates and not the suspension of the particles. If this is the case then refer to GBHE-PEG-MIX-709. Dense suspensions of fine particles such as paint should be treated as single phase for power and mixing calculations. 5.1.2 Agitator Speed Correlation The agitator speed which is just sufficient to suspend all the solid particles is known as NJS: this is the speed given by the correlations below. The solid concentration will normally decrease with height and could fall to zero near the surface. At speeds two or three times NJS the solid distribution will begin to look uniform. At speeds below NJS fillets of stationary solid will build up in areas of low flow.



Where X = 100 x weight of solid/weight of liquid: Note: X is not %Solid per Total Slurry Recommended values of S for use in the correlation are shown in Table 1. For particles greater than 0.5 mm the value of the index on d p in equation 1 increases, tending to 0.4. If the suspension is Newtonian, equation 1 can be used for values of X up to 50%. For very small particles in the micron and sub-micron range, the sedimentation will be controlled by viscous forces (Stokes' Law) rather than inertial forces (as implicitly assumed in equation 1). The calculated NJS should be adjusted in the ratio of the inertial to viscous sedimentation velocities; see the worked example in Appendix A.



FIGURE 1 RECOMMENDED CONFIGURATION



TABLE 1 VALUES OF Po AND ZWIETERING CONSTANT "S" FOR USE IN EQUATION 1



TABLE 1 Continued



TABLE 1 Continued

Notes: *1 The shaft rests in a bottom steady bearing which gives enhanced fluid flow

for solids in suspension, like a "Bourne" bottom (for more information see GBHE Mixing and Agitation Manual).

*2 There is a gas ring-sparger (Ds = 0.41T ) sited a distance T/6 below the

impeller. *3 This vessel is fitted with 2 Beaver-tail baffles; these are equivalent to 4 ×

0.1T flat wall baffles. *4 These data are for two impeller configurations, "b" refers to the bottom

one, "t" to the upper one. Twin impellers have no advantage over a single impeller for NJS, but give better concentration profiles up the vessel.

*5 The power numbers, Po, are for the twin configuration (hence no value for

the bottom impeller only). *6 D/W = 4. *7 Ref 12 gives:



5.2 Floating Solids Incorporating low density solids and solids which are not easily wetted can sometimes be a problem. The preferred designs of agitator and baffles are shown in Figures 2 and 3. Calculation of impeller speed is based on semi-technical scale trials using constant power input/unit mass of liquid as the criterion for scale-up. Other systems have been used by Shell and Exxon on large particles and coal slurries and are discussed in the GBHE Mixing and Agitation Manual. They have not been found satisfactory for general use in GBHE. FIGURE 2 RECOMMENDED CONFIGURATION FOR DRAW-DOWN OF

FLOATING SOLIDS IN AGITATED VESSEL



FIGURE 3 ALTERNATIVE RECOMMENDED CONFIGURATION FOR DRAW-DOWN OF FLOATING SOLIDS IN AGITATED VESSEL

Where an existing disc turbine in a fully baffled vessel is to be reused, the required speed can be estimated from:



5.3 Mass Transfer The recommended correlation for the mass transfer coefficient between the solid and the liquid is: Sherwood Number =

Where DL is the diffusivity in the liquid. 6 JET MIXING FOR SOLID LIQUID AGITATION A jet directed perpendicularly to the base of a cylindrical vessel is essential for this application and axial location of the jet is preferable. The general arrangement of vessel and jet is shown in Figure 4. 6.1 Flat Bottomed Vessel A flat bottomed vessel then presents the most difficult suspension duty and the velocity of liquid in the jet feed pipe, VL, is given by:

The equation is semi-empirical and not dimensionless, but has a good experimental and theoretical backing, being based on work in vessels from 0.15 to 0.6 m in diameter. X is the overall concentration of solids in the vessel as %w/w; all other parameters are in SI units.



If H/T is greater than 1, then X must be set to X.H/T since the solid is concentrated to the lower part of the tank. The equation should be used with caution outside the recommended ranges. If the particle diameter, dp , is less than 200 microns the system should be designed for a particle size of 200 microns. For particles greater than 1 mm the theoretical index on T is 1.4 and this should be used to give a conservative design. This index of 1.4 should be used to give a safe design in vessel where T is greater than 2 m.



FIGURE 4 JET MIXING FOR SOLIDS SUSPENSION

6.2 Changes in the Shape of the Vessel Base Hemispherical base Velocity 50% of that calculated above. Non Central jet Set T in equation to 2.L where L is the distance from

the impingement point to the most remote wall. Continuous flow The concentration of solid in the vessel will be higher operation than the inlet stream because the off-take will

not remove solid isokinetically. Increase X by a factor of 3.



8 BIBLIOGRAPHY Ref Source (Table 1) [1] Chem. Eng. Sci., vol.8, pp 244-253, 1958. ”Suspending solid particles in

liquid by agitators”. Th.N.Zwietering. [2] 6th European Conference on Mixing, Pavia, Italy. May 1988. ”Scale-up of

45 pitched blade agitators for gas dispersion and solid suspension”. W. Bujalski, M.Konno, A. W. Nienow.

[3] FMP 032, April 1988. ”Research review; the measurement of power,

solids suspension and distribution in a 0.61 m diameter stirred vessel. A. T. C. Mak.

[5] FMP Interim Report 1049, Feb. 1990. ”The effects of impeller pitch angle

and clearance on Power Number and NJS”. A. T. C. Mak. [6] FMP Interim Report 1041, Sept. 1989. ”Measurement of NJS, solids

distribution and power for a pitched blade turbine”. A. T. C. Mak. [7] FMP steering committee, Sept. 1989. A. T. C. Mak. [8] Chem. Eng. Res. Des. Vol. 61, March 1983. ”Particle-gas-liquid mixing in

stirred vessels, Part 1: Particle-liquid mixing”. C. M. Chapman, M. Cooke, J. C. Middleton, A.!W. Nienow.

[9] Chem. Eng. Sci., 1968, Vol. 23, pp 1453-59, ”Suspension of solid particles

in turbine agitated baffled vessels”. A. W. Nienow. [10] University of Birmingham PhD Thesis. 1991, S. Ibrahim. [11] FMP Interim Report 1063, Sept. 1991. ”A study of the effectiveness of

solid liquid mixing with twin-impeller agitators". A. T. C. Mak & S. W. Ruszkowski.



APPENDIX A WORKED EXAMPLE (SMALL PARTICLES) A latex stock tank for emulsion PVC is 7.6m diameter with H/T = 0.5 and Z/T = 1/6. It was originally agitated with a 3.79m diameter 2-bladed turbine, this has been replaced by a 1.68m diameter Lightning A310 agitator. The latex consists of 40% by weight of solids with a median diameter of 1 micron. It also contains around 1% by weight of 1 mm coagulated particles. What is the recommended speed for each agitator to suspend both the median and coagulated particles? The density of PVC is 1400 kg/m3, the viscosity of the latex is 10 mN/s (cP). A.1 SOLUTION The minimum speed for suspension can be calculated from equation 1. The density of the latex is obtained by addition of the volumes of each components as follows: Basis: 1000 kg latex

400 kg PVC at ρ = 1400 kg/m3 = 0.286 m3

600 kg water at ρ = 1000 kg/m3 = 0.600 m3

Total volume = 0.886 m3

Density of Latex = 1000/0.886 = 1.129 kg/m3

All the data required are given and S can be estimated from Table 1.



A.1.1 Original Agitator For the 2-bladed, 90° turbine, the parameters D/T=0.5 and Z/T = 1/4 are closest, giving a value of S!=!4*. From the Table it is apparent that the effect of Z/T is small† . Thus, S = 4 is used in equation 1 for the 1 mm coagulated particles:



Plotting data d, e & f in Figure 5 and extrapolating gives a value of S at D/T = 4.5 of about 10.3. Scaling this by the ratio of S for flat to dished vessels, from a & c, we get:

To cater for uncertainty, we will assume a value of 10. Substituting in equation 1, for the 1 mm particles,

A.1.3 Actual Results and their Interpretation The agitator was in fact run at 15 rpm, about 34% of the design speed compared with about 22% of design speed for the 2-bladed turbine agitator. Less sedimentation was reported. The agitators could not be run at the design speeds as this caused further coagulation of the latex. Note: If equation 1 is used to calculated NJS for the 1 micron particles it gives a value of 18 rpm for the A310 agitator. This is greatly in error as the particles do not measurably sediment over long periods even with no agitation. For such small particles sedimentation is controlled by viscous forces (Stokes' Law) and not inertial forces as is implicitly assumed in equation 1.



Viscous sedimentation velocity is given by:

Inertial sedimentation velocity is given by:



DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE This Process Engineering Guide makes reference to the following documents: ENGINEERING GUIDES GBHE-PEG-MIX-701 Mixing of Miscible Liquids (referred to in 5.1

(h)) GBHE-PEG-MIX-706 Gas-Solid-Liquid Mixing Systems (referred to in

5.1 (j)) GBHE-PEG-MIX-709 'High Shear' Mixers (referred to in 5.1.1) OTHER GBHE DOCUMENTS GBH ENTERPRISES Mixing and Agitation Manual (referred to in

Clause 1, 5.2 and Table 1).

Mixing of Solid-Liquid Systems

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