Figure 2. Empirical Correlation of Saturation Carrying Capacity in Horizontal Lines (10). (Click to enlarge.)

While the saltation velocity for the largest particle in the suspension is usually used, particle size distribution may be more important. For instance, a slurry with a large percentage of very fine particles may behave as a single larger particle and overshadow the effect of a few large particles. The fine particles may cluster and cause the larger particles to settle at an even higher rate, which would require a higher slurry velocity. One method to overcome this design problem is to calculate the loading of each particle size, determine the average particle size of the settling mixture, and then use it to determine the effective saltation velocity.

By using the loading that can be carried by each particle size to establish the particle size distribution of the suspension, the average particle size of the suspension give a more realistic picture of viscometric and drag forces. In this analysis, the designer must account for the piping layout to minimize settling of the solids since this will change the local solids concentration (usually increase it). Best practice dictates longer pipe runs with the minimum of elbows to prevent settling from acceleration losses at the elbows.

Determining the largest particle in the slurry can be tricky, but practical experience suggests that the particle size representing the upper 10% of the total mass in large particles works best. The exception is for particles not well distributed, or with a range of sizes covering over two orders-of-magnitude. In these cases we have to rely completely on past experience. The finer particles will agglomerate in the wake of the larger particles and hydraulically act as even larger particles (i.e., the small particles carry the larger particles).

The two distinct lines in Figure 2 are for uniform and mixed particle size solids. The wider the distribution, the quicker the correlation deviates from a straight line (when W/Vρf > 0.1). If the particle size varies by only 3 to 4 fold, the following equation, which is valid for uniform particle size, can be used until W/Vρf > 10:
V²/g D_p ρ_p² = 0.0556 (W/V ρ_f)^0.33       (2)
where:
 V = Superficial fluid velocity at the saltation point, ft/s;
 D_p = Particle diameter, ft;
 ρ_p = Particle density, lb/ft³;
 ρ_f = Fluid density, lb/ft³;
 W = Solids mass flow rate at the saltation point, lb/s/ft²; and
 g = 32.2 ft/s².

Defining suspension requirements

Some questions to ask regarding particle suspension are:

1. Where is this slurry going? If a filter or centrifuge will be next, it will be important to maintain the slurry integrity. If a dryer follows one of those, this may be less of a concern; the solids could be re-mixed in the dryer. However, operational problems can result in the filter or centrifuge due to settling of the solids. Not maintaining enough motion of the solids can cause problems with the feed to centrifuges or downstream reactors. One very common complaint when feeding batch centrifuges or filters is the variability of the slurry feed particle size. When the feed tank is full, the centrifuge or filter receives mostly large sized particles and the filtration rate is very good. As the tank empties the particle size becomes smaller, the filtration rate is slower, and cake quality becomes poorer. Eventually, the centrifuge or filter may plug. The root cause of the problem is often over-sizing of the feed tank (either too large or too tall for the agitator height). One easy fix when this problem is encountered is to recirculate the feed to the centrifuge or filter back to the feed tank so that flow back to the tank is maintained at all times.
2. How variable is the particle size distribution? Many designs are based on the largest particles and fail to account for particle distribution. Fine particles can get into the boundary layer of the flow, increasing the shear rate and overall pressure drop. Particles also may settle in the boundary layer and sluff off, disrupting the laminar layer or turning laminar flow into turbulent flow. While the resulting pressure drop may decrease, the return of laminar flow may cause solids to separate and become a slugging or erratic flow. This may turn a non-settling slurry into a settling slurry, where different design rules apply. Large concentrations of fine particles also can turn a normal non-settling slurry into a settling slurry due to hindered settling effects. The lower drag from local turbulence causes fine particles to cluster and act as a much larger particle.
3. What are the consequences of poor suspension? Most crystallizers will still make an acceptable product even without fully suspended solids. Attempts to mix the suspension further may not be desirable due to attrition or power consumption. It may be more inexpensive to install several re-suspension points on a long pipeline rather than take the chance that a change in the particle size distribution may cause a problem. Can fluid injection along the line or in a vessel return a plugged system to operational? If so, it may be more inexpensive to plan for blockages than to try to design around them. When faced with a new system or a large scale-up situation, this may be the best course of action.
4. What experimental data are needed for design? If you don’t have an existing slurry system to draw from, the design will be developed from physical property data and hydraulic models. It will be important to determine the settling characteristics of the slurry and determine to what extent it can be treated as a non-settling slurry. These data are needed in addition to the physical properties and the rheology (Newtonian, shear-thinning, shear-thickening, or Bingham plastic) of the slurry. More effort must go into defining the viscosity, particle size, and variability of the slurry than in scaling up an existing system. However, scale-up of an existing system must insure that settling of the slurry is properly handled, such as accounting for the effect of larger diameter pipe on saltation.
5. How will the system (pipeline, agitation, etc.) be controlled? While not a focus of this article, there have been many improvements in on-line instrumentation for slurries (see sidebar); these should be a major part of the design. Many chemical plants lack adequate instruments for solids or slurry flow because these were expensive, unreliable, and the need wasn’t well understood many years ago. Slurry density can be controlled more precisely and blockages eliminated through simple non-intrusive flow meters or velocity sensors.  At a minimum, sample ports must be provided to allow for determination of slurry characteristics after the design is installed. The experimental work should have identified and incorporated some key process variables (shear rate, density, and particle size) into the overall control strategy.

Succeed with slurries

Designing reliable slurry-handling systems starts with an understanding of the slurry properties, especially settling rates, viscosity and density. It is rare that physical properties can be obtained from empirical correlation or existing databases, as may be the case for single-phase liquid mixtures; testing is required before design. Even scale-up from an existing installation may be difficult due to the variability of settling characteristics. However, an existing installation is often a better source for design than a theoretical design using standard viscometric design methods.

With the correct attention to obtaining the physical properties, consideration of adequate instruments, and an understanding of the principles of slurry design, there is little reason that operators should have problems handling slurries.

References:

1. Brown, N.P. and N.I. Heywood, eds. “Slurry Handling: Design of Solid-Liquid Systems,” Kluwer Publications, Dordrecht, The Netherlands (1991).
2. Govier, G.W. and K. Aziz, “The Flow of Complex Mixtures in Pipes,” Van Nostrand Reinhold (1972).
3. Heywood, N.I., “Pipeline Design, Slurry Systems,” in “Encyclopedia of Chemical Processing and Design,” 36, pp. 363-399, Marcel Dekker, New York (1991).
4. Heywood, N.I., “Stop Your Slurries from Stirring Up Trouble,” CEP, pp. 21-41, (September, 1999).
5. Worster, R.C. and D.F. Denny, “Transport of Solids in Pipes,” Proc. I. Mech. E., 169, pp. 463-486 (1955).
6. Allsford, K.V. and N.I. Heywood, “Pipeline Design for Slurries and Pastes, State-of-the-art Review,” Wet Solids Handling Report 6, AEA Technology, Oxford, U.K. (1985).
7. Cheng, D.C.-H. and W. Whittaker, “Paper C2,” Hydrotransport 2 (1972).
8. Zwietering, T.N., “Suspending of Solids in Liquids by Agitators,” Chem. Eng. Sci., 8, pp. 244-253 (1958).
9. Gates, L.E. et al., “Selecting and Agitator to Suspend Solids in Liquids,” Chem. Eng., pp 144-150 (May, 1976).
10. Zenz, F.A. and D.F. Othmer, “Fluidization and Fluid-Particle Systems,” Figure 10.9, Reinhold Chemical Engineering Series, p. 328 Van Nostrand Reinhold, New York (1960).
11. Brown, N.P. and N.I. Heywood, “The Right Instrumentation for Slurries,” Chem. Eng., pp 106-113 (September, 1992).

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Thomas R. Blackwood is director of technology forHealthsite Associates, Ballwin, Mo.; E-mail him at trblac@att.net. He also serves as the solids processing guru in the Ask the Experts.