Slurry-handling problems in the process industries

Slurry-handling problems in the process industries

C h a p t e r 12 Slurry-handling problems in the process industries A. W. Etchells III D u P o n t Engineering Newark Delaware USA 12.1 Introduction...

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C h a p t e r 12

Slurry-handling problems in the process industries A. W. Etchells III D u P o n t Engineering Newark Delaware USA

12.1 Introduction T h e following sections are an overview of some of the problems encountered in the handling of solids-liquid mixtures or slurries in the process industries. T h e importance of such slurries and the experience of manufacturing plants handling t h e m is discussed, followed by some typical process concerns and a review of some of the most important problems. T h e point of view is that of the design engineer who needs to design and build a reliable plant and of the operations engineer who needs to keep such a plant running. Not all problems are included. In such a review, one will always miss someone's favourite slurry problem. Industrialists must rely to a large extent on academics doing research at universities to develop the knowledge and the correlations for the design of slurry plants. T h e many academics doing excellent work in these areas will be pleased to know that their work is known and appreciated even if not directly cited. Some academics may view these problems as beneath their consideration, or as already studied. If they look deeper they will find many areas of research interest and many challenging research problems where an improved understanding can benefit industry and society significantly. Many areas have been explored but have not been civilized enough so that we can build safe and reliable slurry-handling manufacturing plants.

12.2 Solids processing plants In the process industries, steps involving solids are becoming more c o m m o n . In the past, solvents were used for many reactions and formulations. T h e high cost of solvents, the environmental and the health hazard concerns associated with many previously common organic solvents have all driven industry to handle solids in slurry form rather than solution form. T h e process industries have been aided by advances m a d e in physical and surface chemistry associated with stabilizing agents and the ability to p r o d u c e custom-designed particles and particle distributions. The develop310

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m e n t of coal slurry fuels, water-based paints, finishes, pigment slurries, and water-based slurry agrichemicals are some of the most noticeable developments in the field. T h e renewed emphasis on improved environmental facilities has increased the need for well-designed solidshandling systems. T w o studies by Merrow (1986, 1988) have shown that these solids steps have brought new problems with t h e m . Forty solids processing plants in the U S A were studied. Plants processing solids anywhere in the main process train perform p o o r e r than plants that process only liquids and gases. This poor performance costs the economy considerably. In addition, plants built recently perform no better than plants built in the 1960s. In particular, start-ups were m o r e troublesome than fluids-only start-ups and there were frequent disasters. A fluids-only plant could start-up in three months while those handling solids varied between nine and eighteen m o n t h s . These start-up times were typically three times longer than predicted. E v e n after start-up only about 6 0 % of the plants achieved their desired rates, as contrasted with 9 0 % for a fluids-only plant. W h e t h e r the feed was a raw or refined solid had a significant effect, as did the n u m b e r of innovative process steps. Some of the difficulties in start-up were due to erosion and corrosion but transport problems occurred in three-quarters of the start-ups. Flow meters and sampling systems were frequent problems. T h e most frequent serious equipment failures were in p u m p s , followed closely by valves. Pumps often had seal problems and valves tended to leak. D r y e r s , compressors, agitators and conveyors were all lesser culprits. T h e major difficulty would often be that the solids were unlike those for which the equipment was designed or that solids went where solids were not expected. In one of these studies Merrow (1986) shows that little attention is given to solids processing in the Research and Development stages of new processes. Research and D e v e l o p m e n t tends to emphasize chemistry and chemical conditions rather than the physics of the process. Chemical and mechanical engineers typically design process plants. Their education emphasizes single-phase fluid p h e n o m e n a and says little about the solids state. This, despite the estimate in one chemical company that engineers have an 8 0 % probability of working on a process involving solids in their first assignment. T h e neglect of two-phase flow concepts in engineering education (Etchells and Tilton, 1989) is probably a cause of this bias, which results in much financial waste.

12.3 Industrial goals In process design, the chief interest is in transporting and storing the slurry. Often the slurry is an intermediate in the process. O n occasion, the slurry is the final product. A major objective is to transport and store or hold the slurry without plugging or settling. T h e goal is trouble-free operation. The operation may be continuous, batch or occasional operation. It is preferred that the transport and storage be d o n e at low cost; however with many of the high-value-in-use materials handled as slurries, the cost of pumping is small compared to the cost of not pumping and the down-time associated

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with non-operation. This is not true of other industries such as coal but it is true of most of the process industries and it influences design and the requirements of design methods. T h e key design parameters to be determined are the minimum transport velocities or agitator speeds to give operation free of plugging and settling, given flow rates and physical properties and equipment configuration and layout. T h e cost in terms of pressure drop or power can be computed from these minimum values and if found to be high the process can be iterated, changing the various equipment parameters. Pilot-scale tests are very expensive and often impractical at processing conditions. Even when a pilot plant is considered it must often be of a size so large as to be impractical. Very little information of use in slurry transport design can come from laboratory transport tests. Typically, to demonstrate the p h e n o m e n a and to determine conditions to be run on a -1 scale is required. Experience shows that a large scale, a size close 3 to that unit of less than 0.30 m h r will not accurately reflect p h e n o m e n a on a small scale that would be seen on a large scale, and even worse, would be subject to small-scale problems that would not occur on the large scale. T h e equipment design must be obtained with the minimum amount of information and limited basic data such as physical properties and only simple observations or experiments. H e n c e the emphasis should be on developing relations based on easily determined physical properties that can be used to predict large-scale behaviour reliability, and the development of key experiments to determine the interaction between the slurry of interest and key process equipment. Thus erosion and corrosion, attrition and fouling may need to be measured in model equipment rather than in laboratory equipment. This requires a better understanding of the p h e n o m e n a and the basic principles behind t h e m , since in many cases simple 'scale-up' cannot be made.

12.4 Typical processing steps It might prove useful to consider some typical solid processing steps that might occur in a chemical plant. Consider a process to m a k e a high-value-in-use solid particulate. T h e first step is a reaction, usually a precipitation. T h e reactor consists of a stirred tank, to which are added, in a semibatch m a n n e r , several liquid, solid or gas ingredients. The reactor is agitated with a mechanical top-entering agitator. A n initial charge of liquid is present and the reactants are added over time. Some solids are added as solids and some as a slurry. Some solids dissolve, while the product solid is formed by reaction. T h e requirement of the agitator is to blend the ingredients and k e e p the solids involved in the reaction. Thus the solid feed and products must be kept suspended off the bottom. If the fluid is non-Newtonian, then the task of the agitator is to avoid stagnation anywhere in the vessel. If there is considerable additional growth during the whole precipitation it may be necessary to keep the solids uniformly distributed throughout the whole vessel height. A s the precipitation occurs, the nature of the fluid will change. Solids will be formed that might

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settle or float or be so fine as to cause the systems to thicken and form a non-Newtonian fluid. A recirculation loop may be used for cooling or for ingredient injection, or for sampling or continuous measurement. This stream must come from the reactor and return to the reactor and be representative of the reactor contents. In the recirculation loop there can be a heat exchanger. It may be single-pass double-pipe or a shell and t u b e , or other variety. This slurry may be supersaturated with solids and fouling would be of great concern. Obviously, pluggage of the recirculation system must be avoided. Once the reaction is over the slurry may be p u m p e d to a separations step or to a hold-up tank subsequent to use in another step as initial feed or reactant. It is often necessary to p u m p the reaction mass, solids and liquid, from the reactor directly to a filter or centrifuge or, m o r e likely, to an intermediate hold-up tank. Agitation must take place to avoid settling and to keep the mass h o m o g e n e o u s . For stable separation the feed should be as uniform as possible. A recirculation line from the storage tank to the separation device and back is likely to allow semicontinuous operation. Thus the slurry is kept continuously in motion even when the separation device, filter or centrifuge, is not in operation. O n c e filtered, the particles can be dried and sold 'as is' or perhaps even reslurried for sale as a slurry product. T h e act of pumping and transport should not cause attrition which could adversely affect product properties or the separation step. Specification for the product is based on chemical composition but often the particle size, size distribution and morphology are important product characteristics. Even with intermediate products the particle size and distribution often set the size and cost of the separation step. T h e r e are an infinite variety of similar processes, including continuous, but all have similar requirements for transport and mixing. These will give the reader some ideas of the concerns of those involved in process design of slurry-handling equipment in the process industries.

12.5 Slurry characterization - fast- and slow-settling T h e r e are two general types of slurries recognized in the process industries: fast-settling and slow-settling. Many other names are used for these types of fluids but these are the most descriptive to the average reader. Words such as 'dispersion', 'emulsion', and 'slurry' have multiple meanings and can b e confusing if applied too tightly. Fast-settling materials are those that settle visibly over a short period of time and consist of large particles of dense material at relatively low concentrations where hindered settling effects are minor. A simple test is to shake a jar of slurry and if it settles in one minute or less, then it is fast settling. Slurries that settle in less than fifteen minutes are also probably fast settling. Slow-settling slurries are those that take a long time to settle. They typically consist of fine particles at high concentrations so that hindered settling and steric interference have become important. Often, rather than settling, these systems form a clear fluid layer on t o p . Typically, the settled volume is over 6 0 % of the original volume. Some slurries are such that

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they d o not show visual evidence of settling at all, such as paints and emulsions. Invariably, these materials appear to have viscosities considerably higher than that of the clear fluid. T h e steric effect of close-packed particles, which decreases settling, also increases viscosity. A n interesting article by C h e n (1980) discusses such similarities between viscous and settling behaviour. In addition to being viscous (thick), these fluids often show non-Newtonian behaviour and, typically, they are Bingham plastic or yield stress materials. Some fluids that have the characteristic of both have b e e n observed but they appear to b e , fortunately, rare. N o t e that to determine the type of slurry a direct observation is required. Usually, physical properties of the solids and liquid separately and theory are not enough, due to the major effects of subtle differences in physical chemistry. T o characterize such slurries, certain basic data are required. For fast-settling slurries it is necessary to know the density and particle-size distribution of the solids. T h e required density is the solid or crystal or chemical density, not the bulk density, which is only a measure of solids packing. T h e viscosity of the clear fluid is also required. For most situations the particle size of the largest fraction determines equipment design. In measuring particle size, the size of agglomerates must also therefore be known. E l a b o r a t e particle-size distributions are not required for transport and storage but may be necessary for other equipment design, such as filtration or centrifugation. Careful micrography and size measurements which take into account the possible existence of agglomerates are very important. Settling rate as a function of concentration is also useful and can serve as a check of the particle-size determination. For thicker slurries, rheology is required over the range of shear rates of interest. Typical process equipment has shear rates that range between 10 and 1000 s . Rheology equipment should be absolute, giving a relation between shear stress and a well-defined shear rate. This usually means coaxial cylinder (couette) devices, pipeline or capillary devices or cone and plate. Unfortunately, the quick, simple devices readily available at most plant sites are inadequate for producing quality data of engineering usefulness. They measure at low shear rates which give false high apparent viscosities which often mislead. Some of these units are quite useful for product reproducibility control. T h e cone and plate and couette devices have an advantage over the capillary or pipe-line devices in that it is easier to observe time-dependent effects and the tests are faster. During the m e a s u r e m e n t of rheology the system should be checked for hysteresis. By hysteresis we m e a n that the shear stress-shear rate characteristic relation is different with increasing shear rate than with decreasing shear rate. This suggests a time-dependency. Hysteresis may be due to structure or to settling. Similarly, shear thickening or dilatancy can be detected. Rheology versus concentration is almost always useful. The relations are often highly non-linear. Many industrial fluids are yield stress materials possessing a rather high yield stress and a low infinite shear viscosity. They have the appearance of wall paint or foodstuffs such as ketchup or t o m a t o

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3

Table 12.1 Yield stresses for non-Newtonian slow-settling slurries. Infinite shear viscosity of 100 m Pa s, or less; density about 1000-2000 kg m Yield stress (Pa s)

Description

Less than 10

Easy to pour, like milk

10-20

Thick, pours easily, thin milkshake, conventional liquid designs will work

30-40

Thick, hard to pour, forms peaks, can write name on surface, difficult to flow to pump suction

40-100

Flows poorly, may need to push into pump suction, will cleave to walls under gravity

Greater than 100

Can build with it, must be moved by positive devices, will cleave to top of jar

sauce. Table 12.1 gives some typical properties and their observable behaviour. A useful additional laboratory test is to allow a sample to settle over a long period of time and check the ease of resuspension. Slurries typically settle into hard-cake and soft-cake systems, and this determines how hard it will be to resuspend and the a m o u n t of stagnation or down-time allowable in a design. T h e characterization of a slurry is not a routine determination to be d o n e by a plant control laboratory, but should be d o n e by those familiar with the m a n y types of p h e n o m e n a that can be exhibited and who are also skilled observers. Direct careful observation and testing is required. Often, a variety of tests are chosen to duplicate conditions that the fluid would experience.

12.6 Slurry transport T h e r e has b e e n much work in the field of slurry transport. T h e proceedings of the eleven B H R A Hydrotransport Conferences (e.g. 1988) cover many aspects of the problems and some design m e t h o d s along with several industrial examples. Most of the information reported in these Conferences has concentrated on the coal and mineral industries but some is applicable to the process industries. Slurries of the fast-settling type are typically transported in turbulent flow. In laminar flow, settling would cause eventual pluggage of the line with untransported solids. T h e r e is some evidence of slurry transport of settling slurries in laminar flow. A high shear stress may cause settled solids to lift. This typically requires a high-viscosity m e d i u m . With low-viscosity liquid if the flow is laminar, and there are solids present, the line will invariably plug. In a typical slurry plant both horizontal and vertical lines exist but most are horizontal. In vertical flow, transport is easy since a velocity higher than the settling velocity is easily obtained. For horizontal flow, vertical gravity must be

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overcome by the turbulence of the horizontal flow. Settling slurries need fluid turbulence to pick up and transport solids with the flow. There are several flow regimes for slurries transported in horizontal lines. In the process industry the fully suspended regime is the most common. Operation with a bed of settled solids, even though moving, can cause problems in short pipes with lots of turns. Fully uniform flow is not required in most circumstances. T h e r e is a minimum fluid velocity that must be maintained to transport slurries horizontally. W h e n these systems are restarted it takes a slightly higher velocity to resuspend the settled solids. This latter velocity is defined as the minimum transport velocity. Defining this minimum transport velocity is a key design criterion. Its dependence on fluid and solid density, particle size, concentration and other factors is critical. -1 no basis for a criterion seems to exist. Typically, For slow-settling fluids a minimum of 0.3 m s is used, but lower values may work just as well. T h e r e does not seem to be a major problem. With fast-settling slurries the minimum transport velocity is critical. Of the various transport regimes the most popular seems to be that of fully suspended but non-uniform flow. Usually, the volumetric or weight flow rate is specified and the pipe diameter determined from the transport velocity. A velocity that is too low will cause pluggage. A velocity that is too high results in wasted energy, erosion and attrition of the particles. A delicate balance is required in suction lines to p u m p s where high velocities can lead to pumping problems and cavitation. Charles et al. (1981) showed that equations of the D u r a n d form seem to work fairly well for the mineral industry. Similar equations have been used in the process industry, probably giving higher than required velocities. W h e n rating a pipeline for a new slurry such equations may not be sufficiently precise. Once the velocity and pipe size are determined it is necessary to calculate the pressure drop required, for p u m p sizing. Again high precision is not required and conservatism costs little with the short lines common in the process industries. Most of the existing equations are very empirical and those based on pseudo-homogeneous flows with a solids correction effect multiplier seem to work best for velocities higher than the minimum transport velocity. A n important, but seldom expressed, criterion is that the pipe size must be large compared to the maximum particle size. Typically, the empirical rule that pipe diameter should be six to ten times the maximum particle size is invoked to avoid blockage. Systems can be designed that do not follow that rule but many which break it have pluggage problems. A particular problem exists when small flows of fast-settling slurries must be transported long distances. Such systems occur in full-size plants handling slurry catalysts and in pilot-plant units. O n occasion, the line size is too small for good design practice. T h e line size is too small to pass the particles or the flow becomes laminar. In such cases a large recirculation flow is used from the tank to the take-off point running about ten times the delivered flow, and the delivered flow is taken off in a modest size line, usually as a vertical takeoff. Clear design rules do not exist for such systems.

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For slow-settling non-Newtonian slurries the pressure drop can be calculated from the rheology if good rheology is obtained. If the data are obtained from capillary or pipeline rheometry, then the scale-up is more reliable. Pipeline pressure drops predicted from couette rheometry pose some theoretical questions. Concern is often expressed over slippage at the wall due to clear liquid films, and extensive pilot pipeline testing might be required if small-scale tests indicate such anomalies. For slow-settling slurries the transition from laminar to turbulent flow is not simply defined. Reynolds n u m b e r s and other groups based on rheology must be used. Experience indicates that with yield stress materials such a transition occurs at m o d e r a t e velocities and can occur in process lines. M o r e theory backed by data in this area would be useful. Even for fast-settling slurries it is often necessary to have an estimate of viscosity to determine transition to turbulent flow and for mass transfer and, particularly, heat transfer correlations. Use of viscosities measured under low shear conditions as an estimate of what the effective viscosity near a wall at a high shear rate seems unnnecessarily conservative. A n o t h e r problem in horizontal flow is slip, the tendency for the solids to lag the liquid and therefore for the in situ concentration to be higher than the input concentration. Correlations have been developed based on experimental data by Spedding and Chen (1990) and Viswanathan and Mani (1984). This holdup or slip p h e n o m e n o n can cause pluggage and give false interpretations to concentration instruments. A typical concentration or density instrument measures total mass in a fixed volume. Thus it senses in situ concentration and if the flow is not uniform across the pipe diameter the value will d e p e n d upon the direction of sensing. This error can be as high as 1 0 - 1 5 % . Instrument manufacturers will often advise mounting such instruments in a vertical position where these problems are minimized but not eliminated. This is often not practical with large or long pipelines. With better slip-holdup correlations the magnitude of the problem can be better estimated and appropriate corrections m a d e . T h e holdup p h e n o m e na has b e e n m o r e thoroughly studied in the gas-liquid literature.

12.7 Pumps Much has been written about pumps for slurries. T h e most popular for slurries seems to be the centrifugal p u m p . Often, centrifugal pumps with elastomeric internals to minimize erosion or with thicker walls for extended life are called 'slurry p u m p s ' . In the process industries p u m p s designed and used for clear fluid service are used for slurries with no modifications. Despite all this literature there are some major areas which need m o r e understanding. With fast-settling slurries theory suggests that the extra energy required to accelerate the solids would lower the efficiency of such p u m p s . Some data support this, some do not. A clearer definition of what physical properties of the solids control this efficiency loss is required. It would seem logical that in systems with low slip between the solids and the liquid the p u m p efficiency would be unaffected. For non-Newtonian fluids the confusion is worse. Most vendors recommend using the Hydraulic Research Institute nomographs on the effect of

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viscosity. These are old empirical correlations and the base data seems lost. In addition, this correlation was developed for Newtonian fluids. W h a t , then, is the viscosity to use in a shear-thinning fluid? W h a t is the effective shear rate in a p u m p turning at 1800 rpm? The work by Walker (1984) in which efficiency is related to Reynolds n u m b e r is a start in bringing order to this topic but m o r e work needs to be done. Positive displacement pumps are often used but there are so many designs that the problems associated with them become very equipmentspecific. Flow through check valves of both kinds of slurries can affect p u m p performance. G a p s are often small and may not pass the particles. Some positive displacement pumps allow slippage of the fluid backwards. These p u m p s are commonly used with viscous fluids where the high viscosity reduces the slippage. With shear-thinning slurries the slippage can be quite high if the shear rate is high. Methods for calculating the shear rates are required. A most c o m m o n problem with all types of pumps is cavitation due to reduced pressures in the suction line and within the p u m p internals. Fine particles can trigger cavitation boiling. T h e net positive suction head ( N P S H ) criteria for avoiding cavitation are based on p u m p testing with clear water. Experience shows that, with slurries, the N P S H values should be increased significantly to take into account the presence of solids which nucleates vaporization. T h e amount of this increase is empirical. A n o t h e r problem associated with both kinds of p u m p is attrition, the breakage of particles by particle-particle or particle-equipment interaction. N o well-established theory exists. Some of the work in crystallizers suggests that turbulence mechanisms could be used as a guide line. O t h e r work suggests that elastomers can reduce attrition. Attrition seems worse in areas where there is much wasted energy (turbulence) such as valves, elbows, pumps running far from the best efficiency point and the like. A n important tool would be the development of small-scale tests that would indicate if erosion or attrition would be problems. Such questions as the relative hardness of particle to equipment, effect of particle size and concentration need to be determined, and tied into a general theory so that scale-up and extrapolation can be done with confidence. Closely tied into attrition is the question of erosion, the damage to equipment occurring during the transport and pumping of particles.

12.8 Mixing for slurries Almost all slurry processes have processing or storage tanks or other vessels. If these vessels are unagitated, then the solids will either settle or become stagnant depending on the type of slurry. Thus mechanical agitators are often used to keep the solids moving. A n extensive literature exists on mixing and the reader is referred to the books by Oldshue (1983) and H a r n b y , Nienow and Edwards (199^) for more detail. In this discussion it will be assumed that the agitator is a top-entering unit with vertical shaft turning one or more impellers with baffles in the tank where a p p r o p r i a t e . T h e r e is a wide variety of impellers. T h e basic data required for mixing is identical with that required and useful for transport since both

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are basically fluid dynamic p h e n o m e n a . E v e n the form of several of the key equations are similar since they are derived from similar turbulence principles. T h e most commonly desired mixing process results are solids suspension and tank activity or blending. O t h e r process results such as heat transfer, gas-liquid contacting and reaction also frequently occur but the above are t h e most c o m m o n . For fast-settling slurries the two basic criteria are off-bottom suspension and uniform suspension. In off-bottom suspension the solids rest only a short time on the b o t t o m of the vessel and are then swept u p into the bulk motion. A b o v e t h e level of the agitator impeller t h e concentration of the solids changes with height. A large volume of liquid free of solids can exist above the impeller. Uniform suspension is when the volume above the impeller approaches the average solids concentration. T h e power necessary to achieve uniform suspension is often several times higher than that for off-bottom suspension. T h e speed of a specific impeller to achieve these conditions is often discussed and studied. Studies have shown that the mass transfer rate shows little improvement with increasing agitator speed once the solids are in off-bottom suspension. Below this off-bottom criterion the settled solids occlude volume and slow down the transport. A b o v e this criterion the solids are exposed and mass transfer is controlled chiefly by the solids properties and only slightly affected by the increased speed and turbulence. Thus for many operations such as dissolving and chemical reaction it is only necessary to achieve off-bottom suspension. Bulk-mixing of the entire liquid volume keeps the process going without uniformity of the solids. For other processes, such as crystallization and some forms of precipitation, it may be necessary to k e e p all of the solids uniform throughout the vessel to obtain uniform t r e a t m e n t of all the particles. W h e n storage tanks act for semibatch feeds for subsequent processes, a uniform solids suspension is required over a wide range of levels in the mixed vessel. W h e n operation is continuous the position of the outlet affects the solids distribution. Inlet and outlet concentrations must be equal at steady state but the average concentration may be very different from the exit concentration if the tank is not completely uniform. This can give the effect of having longer average residence times for the solids in a stirred tank than for liquid. This is analogous to the slip p h e n o m e n a in pipeline transport. T h e current state of knowledge in the field of mixing of fast-settling slurries is that the criteria for off-bottom suspension seem well established for a n u m b e r of impeller configurations. All of these are similar to the correlation of Zweitering (1958). For uniform suspension there are uniformity criteria such as coefficient of variation over the height as a function of agitator speed or power. T h e existing criteria disagree and are not soundly based on theory. M o r e work needs to be d o n e in this area. T h e question of semibatch feeding and uniformity has only been lightly touched upon. Some interesting experimental data have been obtained on continuous operation by wash-out studies, but m o r e needs to b e d o n e . For slow-settling non-Newtonian slurries in mechanically agitated tanks, the p h e n o m e n a observed is one of tank activity. W h e n such slurries are

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mixing, zones of turbulence appear alongside zones of stagnation. In the stagnant zones little or no motion is detected and settling, though slow, can be measured as a thick, high-concentration sludge layer building u p on the b o t t o m . T h e purpose of the mixer is to keep all the tank in motion. W h e t h e r the tank is to be used for storage or reaction or feeding, the criterion is motion throughout the vessel. Observations by Elson, C h e e s m a n and Nienow (1986), Elson (1988), and Etchells, Ford and Short (1987) have shown that for yield stress fluids there are two zones: an active zone or cavern around the impeller of ovoid shape and a stagnant outer zone. T h e size of this active zone or cavern depends on a balance between the yield stress of the slurry and the forces exerted on the boundary by the impeller flow measured by the tip speed. Equations have been developed for predicting cavern size and the active volume when the cavern reaches the wall. A n u m b e r of different impellers have been studied including multiple impellers. T h e m e t h o d seems to work fairly well for well-defined yield stress fluids with low infinite shear viscosity. More work is required to generalize the work to other types of high-viscosity Newtonian and non-Newtonian slurries.

12.9 Miscellaneous H e a t transfer can be an occasional problem with both fast-settling and slow-settling slurries. All turbulent heat transfer equations contain viscosity in the Prandtl number. In turbulent flow the viscosity to use is not clear. A p p a r e n t slurry viscosity is often a steric effect and perhaps should not be used. T h e viscosity of the clear fluid makes some sense if turbulence damping can be ignored. For settling slurries in laminar flow the slurry can be treated as a non-Newtonian viscous fluid, like a polymer, and polymer heating and cooling techniques m a k e sense. Since yield stress materials can be in turbulent flow at relatively low velocities it is important to have good criteria for the laminar turbulent transition. T h e design of single-tube heat exchangers is relatively straightforward for fast-settling slurries, but multitube and multipass devices present problems in designing heads to avoid settling and stagnation. It would appear that vertical units have advantages over horizontal. Fouling, the forming of a layer at the wall of a t u b e , is common with slurries, particularly those with high solubility in the conveying fluid. Relatively cool spots can cause precipitation and pluggage. Such problems are c o m m o n with crystallizers which run near saturation. Chemical fouling, due to precipitations or surface reaction, will often plaque solids-handling plants. Stagnant areas will often collect solids which, under certain conditions, will grow together forming large masses which then break off and plug lines and equipment. E v e n simple devices, such as fittings, elbows and valves, present special problems when solids are present. Fittings and valves must be free of stagnation volumes where solids can build u p . Valves must be able to pass particles, even when the opening is small, to control flow. Small radius elbows are p r o n e to buildup and often long sweeps of radius of 3 - 5 diameters are used.

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12.10 Conclusions In this chapter an overview of the types of industrial slurry problems has been given. In some cases progress has been m a d e in developing the design equations and m e t h o d s needed by industry and based on sound theory. In others, empirical information can be used with caution because it is backed u p by some theory. In many cases some framework exists for understanding the p h e n o m e n a , but m o r e is required. T h e n u m b e r of unsolved problems of slurry handling in industry is still large. This is a field of continuing research by universities and research institutions. Much of this work needs to be drawn together to be turned into the structures industry requires. A l o n e it is of interest. Combined with other work and checked on a variety of scales it becomes the basis for designs. U n d o u b t e d l y , some of the reader's favourite problems have been missed and some good research work may have been neglected, but, given the immense a m o u n t of information, such omissions are unavoidable.

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