FRR - Final Report
ABSTRACT
When a fine material is loaded into a bunker, air can become trapped between the particles and is gradually expelled as the material consolidates. Two effects need to be considered when analysing the deaeration process; the changing density of the gas as the pressure falls and the changing voidage of the material as it consolidates.
If only the first factor is important and the voidage of the material in the bunker uniform, the theoretical analysis of the deaeration process is straightforward. For modest initial pressures, the pressure at the base of the hopper decays with a half-life of about 0.3H2E/k pa, where k is the Darcy's Law constant, H the height of the fill, E the void fraction and pa is atmospheric pressure.
When consolidation is important, the calculations are very much more difficult due to the changing height of the top surface. A detailed numerical analysis has been performed and the predicted values of the half-life of the deaeration process are presented graphically for a number of cases.
A detailed description of the theoretical analysis and of the computer program is included for the benefit of those wishing to extend the work.
This report is concerned with one aspect of the problem of flooding, namely the deaeration of powders in bins. In chapter 2 we review the literature on flooding and conclude that the consensus of opinion links flooding with the aeration properties of the material. Most authors maintain that materials become aerated as a result of rapid filling or the collapse of an arch or rat-hole. It is important to determine for how long the material will remain in the aerated state.
Chapter 3
Chapter 3 contains a theoretical analysis of deaeration and a computer program has been written which enables detailed prediction of the half-life of the deaeration process. Also a simple formula is presented from which a rough estimate of the half-life can be found directly. The theory predicts that fine materials in industrial sized bins can remain aerated for periods of the order of days and thus present a flooding hazard.
Chapters 4 and 5
The details of the experiments performed to test the predictions and the nature of the materials used are given in chapters 4 and 5 and the experimental results are presented and analysed in chapter 6. It was found that of the eight materials investigated, the five coarsest obeyed the model whereas the finer materials deaerated more rapidly than predicted. The materials failing to obey the predictions were all Geldart type-C materials which are known to channel badly on fluidisation. It is therefore not surprising that the model, which assumed homogeneous behaviour, fails in these cases.
We conclude therefore that we are able to predict the aeration properties of a material/bin combination and thus assess its flooding potential for all but the finest (type-C) materials. This work, unlike most previous work on flooding, suggest that flooding does not depend only on the nature of the material, but that bin dimensions are also important.
EXECUTIVE SUMMARY
The long term objectives of the suspension rheology work of IFPRI were summarized by B. Yates in 1981 as: "The main long term aim is to be able to predict and manipulate the rheological behaviour of dispersed systems..."
The present project deals with two well defined but quite general aspects of this long term aim:
- The development of qualitative insight and possibly quantitative predictions for the rheological behaviour of stable colloidal suspensions;
- The generation of systematic data on weakly flocculated suspensions in order to elucidate the general pattern of their behaviour and to initiate their modelling.
The two classes of materials under consideration cover a large fraction of the industrial suspensions for which a specific rheology is required.
Systematic rheological measurements were performed on sterically stabilized colloidal suspensions. The following parameters were varied: particle size, concentration, temperature and the nature of the medium. The present set of data constitutes the most comprehensive study to date of the rheology of sterically stabilized systems. From the results a general procedure is derived which makes it possible to predict the rheological properties of sterically stabilized suspensions with a minimum number of experiments. Furthermore it is shown how oscillatory rheological measurements can be used to obtain information about suspension characteristics such as interparticle potential and particle diffusivity.
With respect to the second group, the weakly flocculated systems, two phenomena were investigated: yielding and thixotropy. The experiments on yielding indicate that stored energy models cannot be used here. A kinetically controlled mechanism must be introduced. Rheological and electric measurements were performed on thixotropic materials. Qualitative trends could be derived as well as a possible scheme for data reduction.
In conclusion it can be said that progress has been made along the following lines:
- Qualitative insight has been gained in the rheological behaviour of stable and flocculated suspensions;
- Experimental data have been collected which provide a basis for model assessment and model development;
- Practice oriented procedures have been suggested which can be used in industry for data reduction to predict rheological properties.
SUMMARY
The term "attrition" is taken to embrace any unwanted particle damage that can arise during processing. This damage may be evident as particle fragmentation due to bodily fracture or as the creation of fines due to the removal of surface layers. Attrition due to mechanical means may arise from the bulk strain of particulate solids and powders or due to particle impact on a wall.
An annular shear cell has been exploited in order to study in a controlled, systematic manner the influence of normal stress and strain on the bulk attrition of a number of bulk solids. No such work had been performed previously, reliance being placed upon arbitrary tests in which the key parameters were not known or controlled. The cell offers the possibility of comparing the tendency of materials to be subject to attrition. The work for IFPRI aimed to exploit this potential with a view to relating bulk attrition to particle characteristics with a view to improving process operation and to understanding particle design. To this end studies were performed on high density polyethylene granules and on alumina particles.
Various grades of high density polyethylene enabled the influence of polymer molecular weight and degree of branching to be examined. In this particular polymer system, bulk attrition was found to be reduced by increase in molecular weight and by the existence of branching.
Alumina extrudates were manufactured in accordance with a precise recipe. This enabled cylindrical particles with identical sizes but of significantly different strengths to be formed, these being assessed by a measurement of single particle crushing strength. Attrition experiments conducted with any of these extrudates at the same total breakage yielded the same product size distribution. Further experiments on one material at one stress enabled the behaviour of any other of the extrudates at any other stress to be predicted making use of the particle tensile failure stress, as deduced from the crushing tests, as a normalising parameter. It is logical to argue that a more fundamental property of the extrudates, the fracture toughness, should be employed to normalise the attrition results and therefore this was measured by casting the extrudates in the form of bars. However, this does not produce an improved means of correlating results, probably because it specifically excludes the flaw structure in the extrudates.
The attrition cell also offers the potential of providing guidance on the performance of operating equipment. Tests in a laboratory stirred vessel showed that the attrition rates were in the same order as those found in the cell and in the crushing tests but the relationship was not a linear one.
The studies have established that it is possible to relate simply and scientifically the bulk attrition of a material to particle properties and, although the predictions are not yet quantitative, to equipment performance.
EXECUTIVE SUMMARY
An experimental and theoretical study of the agglomeration phenomenon which causes destabilization of certain low and high temperature fluidized beds was performed. A theoretical model was proposed to determine the conditions under which defluidization occurs in fluidized beds in which cohesion forces between granules arise due to the presence of sticky fluids and/or high temperatures. Bonding mechanisms between particles such as solid-liquid bridges, viscoelastic flattening and high temperature sintering were all considered. The model, which predicts breakup of aggregates by bubble motion, was compared to limiting fluidization-defluidization (quenching) experiments performed by the authors and others. An experimental method to measure surface softening of small particles heated to high temperatures was developed by using a dilatometer to measure the surface viscosity of the particles from rate of deformation data. Experimental methods to determine the minimum sintering temperatures of a variety of granules were also presented. Lastly, experiments were performed to study the dynamic strength of a liquid bridge between two spheres coated with a liquid and moving away from one another. It was shown that the strength of the dynamic bridge was at least one order of magnitude larger than the corresponding strength of the static bridge between the two spheres. This result accounts for the relatively high gas velocities necessary to keep a bed of sticky particles in continuous fluidization.
SUMMARY
This report is the result of a research programme on the subject of particle attrition. Fox the purpose of the report we have taken to this mean the process of mechanical damage to particles which is undesired, since that is the topic which stimulated the IFPRI committee to set up the project. By the end of the project, the word attrition is taken to denote one of the mechanical breakage processes which may occur when particles are stressed, regardless of whether the breakage is required or not. The thesis of the report is that particle breakage is a complex process which can only be understood and modelled if the various mechanisms are identified.
The first chapter of the report concerns, then, the identification and definition of four different mechanisms which can occur within the total process of particle breakage. The first mechanism is fracture, the splitting of the particle into several smaller fragments and dust. The resistance to fracture is dependent upon the previous stress history of the particle and this is the mechanism of fatigue, the gradual weakening of the particle due to continuous stress loading.
These two mechanisms occur throughout the whole volume of the particle whereas the other two occur at the surface of the particle. Attrition is the gradual wearing away of the surface of the particle due to the very high compressive stresses at the points of contact. A much larger portion of the surface may be involved if the particle is rolling or rotating and this results in abrasion, a polishing of the contacted surface due mainly to the shearing stresses at the surface.
A quantitative assessment of the susceptibility of a sample of particles to these four mechanisms depends upon experimental tests and four levels of testing are defined and discussed. At the most theoretical level, a knowledge of the basic elastic constants of the particle material, combined with the use of a large computer, can make predictions on the breakage behaviour of particles. The major limitation to such calculations is pre-knowledge of the fatigue factor, the incidence of faults and flaws which is present. At the other extreme, a measurement of the breakage behaviour can be made in an actual plant and under actual conditions. Here, the limitation is that such tests are completely specific and expensive, impossible in fact if the process of interest has not yet been constructed. Between these two extremes lie two possibilities. In the first we carry out tests on a sample of particles individually and build up, thus, a statistical description of their strength characteristics. These tests are classified as single particle tests. The alternative is to test the whole sample simultaneously under conditions of stress and strain which are as closely controlled and uniform as possible. Such tests are bulk test. By classifying the sort of tests and the mechanisms which they must determine, the broad field of particle strength testing is defined. The relevence of the particular subject of this report, single particle impact testing, is thus clarified.
The second chapter gives some examples of the practical importance of particle breakage. The first example, lean phase pneumatic conveying is a case where particle impact is the predominant mechanism. Measurements of extreme fracture and attrition are reported. In the second example, fluidised beds, impact is not the only mechanism and may not be so violent but, nevertheless, it is still important. The third example is that of particles sliding against a boundary under compressive strength. Here, impact is not important at all. The three examples are thus chosen to illustrate the wide range of processes and conditions under which particle attrition may occur, dilute conditions with high velocity impact, packed beds with high compressive stresses or some intermediate condition. The theme of the chapter is to illustrate that, in all these cases, all the four mechanisms occur simultaneously and that they are interactive. Thus, particularly for fracture and attrition, the rate at which one occurs is affected by the rate of the other.
The third chapter is the heart of the report. In it we describe the single particle impact tests which are carried out and discuss their significance. The ostensible variables in the test are the velocity and angle of impact. In the chapter it is demonstrated, however, that the normal and tangential stresses which are generated by the impact are more truly the primary variables and that the link between the performance of particles in a test and in a process can be established by knowledge of the stresses in both cases. The measurement of stress during an impact, which has very short duration, still presents a challenging experimental problem. The chapter illustrates how the four breakage mechanisms can be assessed by the single particle tests, both by instantaneous and retrospective measurements. It is clearly demonstrated that a sample of particles may have a broad distribution of strength and that the parameter should be considered as a statistical distribution. It is also shown that the ranking of particles may not be the same fox the different mechanisms, that is that the sample which is most resistant to fracture is not necessarily that which is also resistant to attrition. It seems to be possible to define an "attrition constant" which relates the rate of attrition to the forces exerted. The most important implication of the chapter is the comparison of impact and compression tests. In this chapter we strongly imply that there is no fundamental difference between the two, rather do they represent extreme differences in the rate of loading. In future, this parameter should be considered to be an important variable in particle strength testing.
The concluding chapter is short, simply summarising the mechanisms, their interactive nature and the need for a unified impact and compression testing procedure.
This project was primarily an experimental project. Science follows a regular pattern of observation, hypothesis and confirmation. The experimental work in this thesis can be considered to have made some interesting observations but also to have lead to some positive if tentative hypotheses. They now require further confirmation.
The real conclusion is that the project is concluded but the work not.
ABSTRACT
The characterization, stability, rheology and flow of titanium dioxide, laterite, gypsum and silica flour suspensions have been studied. The flow experiments included the determination of the pressure drops for suspension flow in straight pipes, bends, fittings, valves and Venturi meters. The shear stress/shear rate/concentration dependence for the suspensions was determined using a capillary rheometer and rotational viscometer. This dependence was correlated using the Sisko model, which was then used as the basis of the friction factor/Reynolds number correlations for suspension flow through straight pipe in the laminar and turbulent regions, and for prediction of laminar-turbulent transition. The resistance coefficients for flow through bends, valves and sudden contraction and enlargement were found to vary inversely with the modified Reynolds number (based on the power-law parameter) for laminar flow, and to approach constant asymptotic values in turbulent flow. The results pertaining to the lami lami nar and turbulent regions can be used for design purposes. For the Venturi meters it was found that at high flow rates the discharge coefficients based on calibration using single phase flow are applicable to suspensions. The yield stresses of the suspensions were measured directly using the vane method. An empirical equation was used to correlate theyield theyield stress/concentration dependence, This equation provides a quantitative means for assessing the low and high concentration yielding behavior of the suspensions. The maximum packing solids volume fraction was used to provide a link between the stability and rheology. The results of the sedimentation, the yield stress measurements, and the Sisko model parameters were found to follow consistent trends. The data for our gyspum suspensions were used to compare the straight pipe-flow friction loss correlations established in this part using the rheologically-based, continuum approach with those using the multiphase flow aproach based upon solutions of the equations of continuity and motion. It was found that both methods do an excellent job job in the case of gypsum whose particle size overlaps the colloidal and noncolloidal ranges.
EXECUTIVE SUMMARY
The long term objectives of the Suspension Rheology project have been formulated as: "TO be able to predict and manipulate the flow behaviour of disperse systems from an understanding of their chemistry and composition." A complete theoretical solution of this problem is not expected in the near future. The approach which has been taken here consists in developing suitable characterization techniques and applying them to specifically designed model systems. In this manner the contributions from the various parameters can be isolated and evaluated. Applying suitable scaling principles and data reduction schemes efficient strategies can then be developed to predict the flow behaviour of real systems on the basis of a small number of experiments.
Two specific problems have been addressed in the present project. They refer respectively to stable colloidal suspensions and reversibly flocculated systems. Sterically stabilized suspensions are used for the first case. The possible applications of hard sphere scaling have been investigated in the previous period. The work has now been extended to include a procedure to handle the softness of the stabilizer barrier in monodisperse systems. This includes experimental techniques to characterize the deformability of the stabilizer barrier. The results agree quite well with a first theoretical estimate. As a next step the problem of particle size distribution has been tackled. A first series of data has become available. They indicate that the various characteristics of the viscosity curves are affected differently by size distribution. The results suggest some trends which will require confirmation from further experiments.
The rheology of reversibly flocculated suspensions is still poorly understood. Experimental techniques for characterizing yielding and time-dependent behaviour (i.e. thixotropy) have been investigated. The suitability of constant stress devices for this purpose could be demonstrated. Yielding in weakly flocculated systems turns out to be a complex phenomenon. Structural rearrangements before the final yielding complicate the development of a theory. Some of the reversibly flocculated materials display a behaviour which resembles that of the strongly flocculated systems, which might provide a starting point for theories.
Measuring the concentration dependence of yielding and the equilibrium moduli is a suitable procedure to analyse structure in flocculated systems. Data on two systems with similar components but different particle interactions seem to be in good agreement with some of the theories. However, earlier data on more open floe structures obey a different concentration law. The discrepancy has not been solved yet.
No suitable data handling procedures for thixotropy are available. Data on two different systems indicate that the time scale of the stress transients can be related to the initial stress levels in step strain rate experiments. With a constant stress device a recovery time can be easily determined from step stress experiments with a final stress level below the yield stress. This leads to a suitable technique to characterize thixotropic recovery.
It can be concluded that:
- for sterically stabilized suspensions procedures have been suggested to take into account the presence of a deformable stabilizer barrier and a start has been made with the analysis of the effect of particle size distribution;
- for reversibly flocculated systems the suitability of some experimental characterization methods for yielding and thixotropy has been demonstrated, it is shown that the combined measurement of yielding and equilibrium modulus as a function of concentration provides insight in the floe structure.
Executive Summary
The majority of previous granulation research has been of a mechanistic nature examining the effect of operating variables such as ‘fluid-bed excess gas velocity or spray characteristics on granule growth rate and morphology. Various mechanisms of granule growth have been identified and a general population balance similarity theory of granulation has been developed. However, little 4 m knowledge of granulation phenomena is provided by the above disparate, essentially macroscopic approaches alone, One must instead turn to a microscale consideration of interparticle cohesive forces in relation to the energetics of disruptive particle motion.
A brief description of the fluid-bed granulation process is presented in Chapter 2 with the aim of clarifying various competing mechanisms as well as establishing their respective controlling material parameters. Specifically, the present work seeks to explain differences in observed granulation morphology and growth rates in terms of the strength of a dynamically strained pendular bridge and differences in the viscous history of the involved binders. An extensive review of growth mechanisms, the effect of operating and material parameters, and granulation modeling has been given previously (Ennis et al., 1986).
Research emphasizing the importance of dynamic pendular bridge strength is outlined in Chapter 3. Completed results concerned with the strength of an axially strained bridge are given in Ennis et al.(1988). These as well as further preliminary results dealing with relative sphere shearing motion, surface roughness, and imperfect wetting are summarized in Chapter 4. An ad hoc solution of dynamic bridge strength based on the superposition of lubrication theory and circular approximation is presented. For small gap distance with sufficient bridge volume and in the limit of small Reynolds’ number, good agteemgnt between the experimental and present theoretical axial force response is observed indicating the importance of a capillary number Ca in determining pendular bridge strength. The present theoretical analysis is zeroeth order in capillary number and gap distance and hence, is expected to break down with increasing local inertial effects. Such inertial effects are governed by a modified Bond number and, in the limit of low Ca, lead to an increase in bridge strength due to an added mass effect, whereas in the limit of high Ca, lead to a reduced, shifted force response due to an insufficient rate of vorticity propagation. Preliminary investigations indicate that the present theoretical analysis extends to the cases of arbitrary (nearly touching) particle motion, imperfect solid wetting, and particles with only small scale surface roughness.
Initial granulation results and binder bridge measurements supporting the influence of viscosity are presented in Chapter 5. Typical industrial binder solutions such as 2.5 weight percent aqueous carboxymethylcellulose exhibit an exponential increase in pendular bridge strength due to solvent evaporation and, therefore, display a full range of capillary number behavior from an initial weak surface tension response to an extensive viscous reponse with an equivalent viscosity of the order of fifty poise. Liquid bridge measurements of binder solutions appear to adequately predict fluid-bed granule morphology indicating that growth is controlled by a combination of a viscous strengthening time constant and a final solid bridge strength. Such a time constant and final bridge strength are, in turn, related to the effect of binder concentration on solution viscosity and the molecular weight of the binder, respectively.
Lastly, a preliminary analysis of the competing processes of fluid-bed coalescence and breakage as well as an attempt at incorporating knowledge of these phenomona into a population balance framework is presented in Chapter 6. Two unknown cctnqtants related to coalescence and breakage should bear a fundamental relationship to the properities of the binder - namely, the viscous strengthening time constant and solid bridge strength, respectively.