Powder Flow

Executive Summary

Many industries produce, or encounter during processing, dry powders having mean sizes in the range 20-150pm; others, notably the petroleum and petrochemical industries, deliberately choose such powders as catalysts for use in fluided bed reactors. These Group A powders, as they are known, are, on the whole, aeratable; that is, they retain gas in the interparticle voids, and this property gives them to a greater or lesser extent good flowability. However, flowability and other related properties are influenced by interparticle forces (IPFs) and hydrodynamic forces (HDFs) which in turn are affected by the physical and physico-chemical properties of the gas and particles. It is believed that it is the balance of these which determines the behaviour of fine powders in a fluidized bed and in powder flow and handling operations.

The overall objectives of this research programme were to understand better (a) the nature of these forces and their relative importance and, in particular (b) the influence which temperature, addition of fine particles, and the gas itself have on them.

Experiments were carried out in 152 mm diameter columns with cracking catalyst (a spherical alumino-silicate) to which much finer catalyst particles were added. These were fluidized at temperatures up to SOOC with air, argon, neon, carbon dioxide, and freon-12. Measurements were made of bubble sizes, bed expansion, and collapse times using specially developed purged pressure probes.

The results show that the behaviour of Group A powders is caused by a combination of IPFs and HDFs, and that their relative magnitudes change with mean particle size. For cracking catalyst HDFs dominate above about 70 urn and IPFs below about 60 l.t m. Strongly adsorbing gases such as CO2 can increase the IPFs at temperatures below about 1OOC so that even relatively coarse powders may exhibit cohesive behaviour. Dimensional analysis shows that the fluidization behaviour can be characterized by a Cohesion number, and the Galileo and Density numbers. As yet it is not possible to make predictions of the Cohesion number a priori because it depends on the Van der Waals forces which in turn depend on the size of the asperities, and on the Hamaker constant, i.e. on the nature of the material from which the particle is formed. For FCC-FCC contact, particles can be treated as smooth when the asperities are smaller than 0.01 l.trn; however, the interactions between the asperities begin to dominate the IPFs rather than the parent particles when the asperities are larger than 0.1 l,trn. This critical size could be as large as 10 pm for FCC-polymer contacts because the polymer particles are soft and deform easily. For FCC-FCC the theoretical predictions agree well with our experimental results and those of other researchers. Although the Cohesion number cannot readily be predicted for most powders in Group A, other parameters which are relatively easy to measure can be used to characterize their fluidized behaviour, notably the ratio of minimum bubbling to minimum fluidization velocity, and the standardized collapse time. The influence of temperature on these parameters has been measured and has been incorporated into new and existing correlations. Measurements of bubble size confirm that there is an equilibrium size which is sensitive to particle size, but virtually independent of bed level and gas velocity. It appears to change relatively little with increasing temperature.

The presence of small amounts of fine particles influences strongly the behaviour of aerated and fluidized Group A powders, and the percentage present in powders used in any given industrial process may increase due to attrition of coarser components, or may reduce as elutriation occurs. In either case the performance of the process may be affected adversely.

The purpose of this state-of-the-art review is to survey the literature on inter-particle forces in dry powder systems - in particular their origin and their known influence on powder processing operations - and current research that indicates to what extent these forces can be measured directly.

Chapter headings include:

• Introduction and background
• Types of force acting between solid surfaces
• Contact mechanics (deformation associated with adhesive forces and with friction)
• Surface-electrical parameters and forces
• Recommendations for future lans (the potential most fruitful research objectives)

Results of current research lead to a number of relevant conclusions:

1. (i) while macroscopic concepts (plasticity, viscoelastic deformation, etc.) appear in general to hold at the level of a single interaction between two particles, it will become clear that there is an urgent need for more direct force measurements to be made with individual particles, where the variable effects of surface condition and topography are especially hard to predict.
2. (ii) Using proximal-probe technology, it is possible to derive useful quantitative information that relates to contact area and the nano-mechanical and adhesive properties of model particles (atomic force microscope tips) or actual particles.
3. (iii) Relatively little detail is known about changes to the van der Waals interaction that are induced by the presence of an adsorbed layer of permittivity different to that of the material of the underlying particle.
4. (iv) Examples of processes in which inter-particle forces are strongly influenced by surface-electrical properties include electrostatic precipitation, powder coating, fibre filtration, xero raphy, particle collection, and separation by means of triboelectrification. Within the general area of contact electrification, there remain many other complications, unsolved problems, and recent intruiging findings. For instance, van der Waals forces (in experiments with model particles of high curvature) are masked by a longer-range attraction. A “patch charge” model gives the most romising ex lanation and the best fit to the data, but analysis of patch charge effects arising from inhomogeneities in work function is in its infancy. An explosion of activity in proximal probe work on surface-electrical properties of surfaces in general at the nanometre level is taking place. So far, there have been few attempts to extend these techniques to work on actual particles. This now calls out to be done.

In recommending possible forward plans, a final chapter identifies two broad fundamental research objectives as being potentially the most fruitful, and involving measurements at the level of an individual particle-particle contact, but geared to the requirements of powder technology. The two topics recommended are:

• (i) study of energy-dissipative contact processes (as measured, for example, by force curve hysteresis) that underlie dynamic and frictional recesses
• (ii) a proper characterisation of surface-electrical roperties of particles and the factors that influence them. For example, what are the individual sites on the surface of a particle of photoreceptor material, that allow it to retain positive or negative charge? How may polymer powders be designed specifically for electrostatic deposition, with a view to improving the proportion of sufficently charged particles in a particular process? There is always hysteresis in the loading/unloading cycle of an individual particle-particle contact - what is the role of this hysteresis in determining the dynamic and frictional behaviour of particles?

These are just three of the many situations in which selective application of the “individual particle” experimental methods would help to answer specific questions of importance in particulate technology.

Executive Summary

• The object of this paper is to review studies of gas-solid fluidization at elevated temperatures and pressures and to draw conclusions from them that enable reliable extrapolations to be made from one set of operating conditions to another.
• Following a brief introduction the survey begins with the low velocity end of operations in the region between minimum fluidization velocity and minimum bubbling velocity and shows how correlations established at ambient temperature and pressure for these two quantities may be used to calculate their values at superambient conditions. The application of purely hydrodynamic fluid-bed stability criteria to account for the transition from the non-bubbling to the bubbling state is described and compared with the expected effect of interparticle forces on this transition.
• The effects of temperature and pressure on the dynamics of gas bubbles in powders of Groups A, B and D are considered next and areas of uncertainty in current theories of bubble motion are highlighted.
• Correlations for jet penetration are then discussed and recommendations made as to the most reliable of these.
• Circulating fluidized beds (CFB’s) operated at high velocity are then considered and it is shown that many of the observed effects in these systems at superambient conditions can be accounted for in terms of changes in the value of the terminal fall velocity, ut, of the bed particles. The effects of changes in ut on entrainment, elutriation and choking are also considered.
• The effect of increased pressure in enhancing bed-to-surface heat transfer coefficients in beds of Group A powders is shown to be due to the suppression of bubbling while in beds of Group B materials the enhancement is through an increase in the gas convective component of the transfer coefficient. The small amount of work carried out on heat transfer in CFB combustors is reviewed.
• Pressure effects on the combustion of char in bubbling beds are considered in terms of an established two-phase theory model and it is concluded that the increased rate of solids bum-out at high pressures is due to an increase in the value of the local Sherwood number thereby increasing the rate of mass transfer of oxygen to the surface of the burning particle.
• The important question of sintering leading to defluidization at elevated temperatures is then examined and attention drawn to the current lack of broadly based mechanical models to account for and predict the phenomenon.
• The state of the art in the area of scaling relationships is reviewed and it is shown that while the scaling laws for bubbling beds are by now reasonably well established the same is not so for CFB’s indicating a major area for further work. Finally conclusions are drawn and suggestions made for three projects worthy of funding support.

EXECUTIVE SUMMARY

OBJECIVES . . . The objectives of this paper are to give an overview of chaotic time series analysis and to survey studies of application of chaos theory in gas-solids fluidization in order to identify the potentials of chaos theory in improving fluidized bed design and operation.

OVERVIEW . . .

The review begins with a brief introduction to chaos theory and gas-solids fluidization and follows with a discussion of the gamut of practical methods for the analysis of nonlinear, chaotic dynamical systems. It is described that chaos theory is a relatively new branch of science that is being developed as the nonlinear counterpart of classical linear signal processing.

Practical aspects of chaotic time series analysis are then discussed and recommendations are made as to the requirements for the measurement system, the optimum data-acquisition settings and standardized methods of data analysis.

Chaos studies in the field of bubbling and slugging fluidization were initiated about five years ago. These studies are considered next and it is shown that dynamical invariants such as correlation dimension and Kolmogorov entropy are able to quantitatively characterize the fluidized bed’s dynamics. Other analysis techniques such as principal component analysis and chaotic trajectory decomposition are then described and shown to be able to uniquely characterize different modes of dynamical bed behavior. It is found that these studies are merely prelimiiry in the sense that only specific examples are shown while so far only one study gives a more detailed impression about the dependency of chaotic invariants on varying fluidization conditions.

It is shown further that the dynamics of bubbling and slugging beds are spatially extended in the sense that the number of degrees of freedom (dimension) and the level of predictability (entropy) vary with the location in the bed. Novel methods are discussed that quantify this spatio-temporal behavior of fluidized beds in terms of the degree of dynamical coupling between different locations in the bed and of the level of predictability per unit of length.

Since two years also chaos studies in circulating fluidized beds (CFBs) operated at high gas velocity have been carried out and these have shown that Kolmogorov entropy can be used, for example, to quantify the turbulence level of flowing gas-solids suspensions as a function of fluidizing conditions in CFBs. These chaos studies of CFBs have been performed at a wide range of riser diameter and fluidizing conditions.

Two simple one-dimensional, ‘learning’ fluidized bed models that exhibit chaotic behavior are then examined. The first model describes single bubbles and bubble-to-bubble interactions and the second model is based on single particles and particle-to-particle interactions. The latter model is compared with experimental data about the dependence of entropy and dimension on gas velocity and is very well able to qualitatively reproduce the chaotic dependencies that were observed in the measurements.

OUTLOOK AND CONCLUSIONS ...

An outlook is presented on two practical applications of chaos theory in the areas of design and operation of gas-solids fluidized beds.

First, it is proposed to include the chaoticness of fluidized beds in reactor scale-up. Two different routes are considered: the first route, proposes to include chaotic similarity as an additional requirement in dimensionless scaling laws for fluidized beds, and the second route is based on establishing (empirical) scaling correlations that relate the chaoticness of the fluidized bed to bed size, fluidizing conditions and particle properties.

Secondly, it is suggested that the concepts of chaos control that have recently been developed in the literature may also be applied to interactively control the dynamics of fluidization in order to, for example, enhance conversion and selectivity by influencing gas flow and bubble size distributions.

Conclusions are drawn that focus on general observations and suggestions for further work.

SUGGESTED PROJECTS..

Finally outlines are presented for four projects that may be considered for funding by IFPRI. In these outlines it is proposed to support chaos research in the following areas:

• (A) dimensionless scaling of bubbling fluidized beds using the concept of chaotic similarity;
• (B) scaling of bubbling fluidized beds based on empirical correlations that relate chaotic dynamics to bed size and operating conditions;
• (C) chaos analysis of flow regimes in high velocity, circulating fluidized bed;
• (D) development of a chaos control technique for bubbling fluidized beds.

Executive Summary

Simulation models of gas-solid flows are classified into two kinds; one is the continuum model and the other is the discrete particle model. The present principal investigator has been using the discrete particle model for predicting gas-solid flows from dilute to dense phase. The purpose of this report is to compare results based on the discrete particle model with those based on the continuum model concerning flows in the riser of circulating fluidized bed. Trajectories of particles are calculated by the Newtonian equations of motion in the discrete particle model. In this report, methods and techniques used by the present principal investigator are described in detail, particularly about the DSMC (Direct Simulation Monte Carlo) method which is a powerful means for calculating particle motion under the effects of collision. Calculation based on a small number of sampled particles is possible owing to the DSMC method.

Results for comparison are those calculated by Tsuo and Gidaspow( 1990 ) who used the two fluid model. Following Tsuo and Gidaspow, parametric studies were conducted, and effects of gas velocity, solids mass flux, particle size and duct size on flow patterns were studied. Quantitatively large difference is observed between the results of the discrete particle model and the two fluid model. For instance, cluster population is much larger in the discrete particle model than the two fluid model. Qualitatively both results show the same tendencies in most cases. However, concerning the effect of duct size, results are different even qualitatively; the discrete particle model shows that as the duct size increases, clusters are formed not only near the wall but also in the center part of the duct, while the two fluid model shows that clusters disappear in the wide duct. The present principal investigator neglects fluid viscosity and thus the results are not satisfactory near the wall. Fluid viscosity must be taken into account in the future work.

To classify the characteristics of Geldart-A powders in bubbling fluidized beds utilizing electric fields, we have developed the electric field operation map for bubble control relating three variables: electric field strength, frequency and superficial velocity. The map includes regions of expanded bubble control, bed freezing, and elutriation control. These deliniations define our goals for the development of a uniBed theory of bubble control for ac and dc fields.

Perturbation theory and interparticle force theory have led to the evaluation of a powder modulus of elasticity. Results for 3 types of FCC and glass powders are reported. Early discrepancies in utilizing perturbation theory appear to have been resolved. Future studies will include the effects of particle diameter, relative humidity, and high temperatures.

In this reprt we continue our development of a unified theory of bubble control utilizing continuum and particle theories. Studies are reported at the frozen bed limits for ac and dc field and for bubble stabilization based on our extension of the Davidson bubble model. Van der Waals forces are now being incorporated in our ac and dc models. Scaling parameters are being developed and reported for our future work with large beds.

Our new high temperature facility is now operational and continues to be developed. A problem remains with the quartz sinter used for gas distribution in the bed. Our preliminary data from this facility indicate that:

• Bubble control remains effective at elevated temperatures depending on the increase in electrical conductivity of the material; for example, fresh Zeolitic FCC was successfully tested up to 465 “C for bubble control.
• The bed modulus of elasticity decreases with increasing temperature for fresh Zcolitic F C C.
• The bed modulus of elasticity increases approximately linearly with electric field strength for 3 kinds of FCC’s tested and for glass.

The strong influence of electric fields in controlling elutriation is now established for both ac and dc fields. This year a specially designed electrode-from-below fluidized bed was developed for these studies that is capable of measuring both particle charge and elutriation constants. Some first results on naturally occurring and induced particle charging within the bed are presented indicating significant particle charging -lOa C/kg for 8.66 pm sand fines. Particle charge remains an important variable for our interparticle force theory relating to elutriation control.

The work performed by our group during the previous IFPRI contract period focussed on fully developed, turbulent flow of gas-particle mixtures in vertical pipes, A K-E model for the fully developed flow was formulated and used to explain the mechanism responsible for the nonuniform distribution of particles over the pipe cross section (please refer to last year’s annual report, FRR 09-15, for a detailed description). In the present contract period is work will be extended to developing flow problems in an effort to understand (1994-97), th’ how the flow evolves in risers and standpipes, and get an appreciation for the length scales associated with various regimes of flow development.

We first derive the time-smoothed equations for a 2D, developing, turbulent gas- particle flow. The coordinate system used for this purpose is shown in Figure 1: x and y denote the axial and transverse coordinates, respectively. A Cartesian coordinate system is used rather than a cylindrical one so that asymmetric inlet conditions can eventually be analyzed. The vertically upward flow in a slit (Figure la) should have characteristics similar to those of flow in a riser so, henceforth, this geometry will be referred to as riser flow. By a similar token, the flow corresponding to Figure lb will be called a standpipe flow. The equations take the form of eight coupled partial differential equations ‘representing two mass balances, four momentum balances (two axial, two transverse) and balances for turbulent kinetic energy and its dissipation rate per unit volume of suspension. As in the case of the fully developed flow equations derived in FRR 09-15, separate transport equations for K and E are not required for the two phases, since, for the solid mass fluxes being considered, the inertia associated with the gas is negligible when compared to that of the solids. A full fledged analysis of developing flow in vertical ducts on the basis of this K-E model, taking into account the entrance and exit effects and the possibility of internal recirculation of particles and gas, is a very large-scale computational problem.

The axial development of the flow of gas-particle suspension in vertical ducts is characterized by a number of distinct zones. The pariticles are initially accelerated by a high-velocity gas stream (acceleration zone), where large changes in the particle concentration, pressure gradient, etc. take place over very small axial distances. Accurate numerical computations in this zone will necessarily require a very fibe axial mesh. Following the acceleration, the particle concentration and velocity fields slowly evolve to their fully developed states over a relatively larger distances (transition zone). This is followed by a fully-developed zone, after which is an end zone where the flow patterns change again to conform to the exit geometry. If the riser is not “sufficiently tall,” the fully developed zone may be absent and exit and entrance zones will interact strongly. A general purpose computational code that allows for all these regions will require large computer resources. It is therefore of interest to identify simplifications which will make the problem computationally more tractable.

In the present annual report, we have derived the time-averaged equations of motion for steady developing flow and simplified the resulting system of equations through a scaling 1 analysis (see Section 2). This analysis led to a system of equations containing only the first derivatives of dependent variables in the axial (vertical) direction, and the first and second derivatives in the transverse direction, This form allows us to view the developing flow problem as an initial value problem (as opposed to a boundary value problem) and compute the solution by marching form the inlet to the exit. It should be noted that the existence of a solution for such an initial value problem is not guaranteed. For example, when the flow develops an internal recirculation, such an approach will necessarily fail; however, in case no recirculation develops, this approach will yield the entire solution. Nevertheless, it is useful to solve the initial value problem and get a feel for the developing flow, largely because of the tremendous computational advantages it offers over the boundary value problem. With this in mind, we performed a number of calculations and these are described in Sections 3 and 4.

Section 3

which is devoted to a laminar flow model, that neglects the effect of tur-bulent fluctuations, shows that the entrance length in two-phase flow is considerably larger than that in a comparable single-phase flow, and this is a consequence of the particle seg- regation in the acceleration zone.

Section 4

results based on laminar and turbulent flow models are compared to demonstrate that the initial segregation of particles to the tube wall in the acceleration zone in purely a continuity effect, and the turbulent fluctuations, which come into play only in the transition zone, are solely responsible for causing segregation of particles in fully developed flow The main findings of the study are summarized in Section 5.

This project focuses on the fluid dynamics of vertical gas-solid risers. Its principal objective is to produce data for evaluating theories elaborated by Professors Sundaresan and Jackson at Princeton. Thus in this report, we review Cornell activities in the area of gas-solid suspension flows.

At Cornell, we possess a unique facility with the ability to recycle - rather than discard - fluidization gases of adjustable composition to a vertical riser of 20cm diameter and 7m height. This allows us to simulate the fluid dynamics of industrial units (atmospheric and pressurized coal-burning circulating fluid beds, catalytic crackers) in a cold, atmospheric riser by matching the dimensionless parameters that govern the flow. The facility is equipped with capacitance, optical fiber and pressure instrumentation that records solid concentration profiles in the vertical and radial directions.

In the first year of the award, we have established that, under typical industrial conditions, dense gas-solid flows are nearly independent of gas density in the fully-developed region of the riser. This observation of a viscous flow regime suggests that particle clusters dominate the exchange of momentum between the two phases. It further suggests that extrapolations of flow behavior from atmospheric to pressurized conditions should be more straightforward than previously envisaged.

To inform closure of theories elaborated at Princeton, we have also carried out simultaneous measurements of pressure fluctuations and local wall volume fraction. Here we have shown that, because gas pressure reflects fluctuations originating throughout the vessel, they are not closely correlated with local solid volume fractions.

In addition, we have begun a study of cyclone performance under conditions of high gas density and solid loading, which have not yet received much attention despite their importance for a new generation of high efficiency coal gasifiers and other dense gas-solid processes operating at high pressures.

In 1996, we have also made progress in the area of instrumentation, which is often of interest to industry. In particular, we have designed an uncooled capacitance instrument capable of recording instantaneous solid volume fraction near the wall of an industrial vessel operating up to 950°C and 15 bar. In addition, we have completed a technology review of instrumentation for dense gas-solid suspensions to be presented at an upcoming IFPRI meeting.

A sensor with 12 sensing electrodes and 24 driven guard clcctrodes has been constructed. This provides an increase of 80% in the measured capacitances and enables narrower cross sectional slices to be imaged.

A series of experiments on both bubbling and fast fluidization flow regimes were conducted at University of Bradford. The tomographic data were compared with measurements taken with an existing mass flux probe as well as pressure transducer measurements. The results showed that for a bubbling fluidization the data obtained from ECT measurements agreed very well with the data obtained from the pressure drop measurements. A satisfactory correlation of the tomographic data was obtained for a fast fluidization flow regime.

A new method for setting the system measurement range has been incorporated into our Windows software to measure a mean solid concentration in the range 2 to 10%. This method allows more accurate measurement of low solid concentrations (up to 5% by volume).

To order to study the dynamic behaviour of a fluidized bed by using Deterministic Chaos Theory it is necessary to calculate statistical invariants from hundreds of thousands of data points. Our existing software has been modified to carry out such an analysis. The application of a singular value decomposition technique combined with the data from an ECT system is presented (Dyakowski et al, 1996).

AVS software has been used to visualize the movement of a bubble chain through a fluidized bed. In the future we intend to use this software to visualise slugging and turbulent flow regimes.

Introduction

Our research, funded by IFPRI, has concentrated on developing physical models for the rapid flow of particles and gas, and exploring the consequences of these models for fully developed and developing flow of the two phases in both vertical and inclined ducts. Experimental studies have shown that solid particles transported by a gas in vertical pipes, such as those encountered in riser reactors, are distributed non-uniformly over the cross section (Bader et al., 1988). Consequently, neither quantitative nor qualitative features of the overall behavior can be represented correctly by one-dimensional flow models, which take into account the presence of the pipe walls only through empirically introduced friction factors. The origin of this segregation has been investigated by us and others over the last decade.

During the past twelve months, we have focused our efforts on understanding the various routes to formation of clusters in rapid flow of gas-particle mixtures. It was apparent from the reactions of some of the industrial representatives during the annual meeting in Nancy that the connection between this work and riser flow modeling is not entirely obvious. Therefore, we begin this report with a discussion of this connection (section 2), then highlight some of the results (section 3) and finally conclude with a summary of the anticipated course of research for the next year (section 4).