Attrition of Dolomitic Lime in a Fluidized-Bed Reactor at High
Temperature
Miloslav Hartman,* Karel Svoboda, Michael Pohořelý, Michal Šyc, and
Michal Jeremiáš
Institute of Chemical Process Fundamentals, Academy of Sciences of the
Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic
The results of an experimental study on the rate of attrition of lime
catalyst/sorbent in a high-temperature, turbulent fluidized bed with quartz
sand are presented. Batchwise measurements were conducted at 850 oC
in an electrically heated gasification reactor of an inner diameter of 5.1
cm with three sizes (450, 715, and 1060 µm) of high-grade, dolomitic
lime. In addition to the influence of the particle size, the effect of
operating (elapsed) time was investigated at different superficial gas
velocities. Assuming that the attrition rate decays exponentially with time,
a simple mechanistic model is presented which makes it possible to
correlate the measured experimental data. The course of the attrition of
lime particles is described as a function of the elapsed time, the excess
gas velocity, and the particle size. The present approach and the results
may be applicable to the attrition of high-grade, dolomitic lime,
particularly in fluidized gasification of biomass.
Keywords: Dolomitic lime; Attrition; Fluidized bed; Catalytic gasification
___________________________________________________________________
2
*Contact details for correspondence:
Tel.: +420 220 390 241 Fax: +420 220 920 661 E-mail: hartman@icpf.cas.cz
Introduction
As has been well-established, a fluidized bed with particles of an alkaline
solid, such as is produced by the calcination of limestone or dolomite, can effectively
remove unwanted acidic gases like SOx, HCl, H2S, and COS from the gaseous phase
at high temperature.1-10 It is apparent that under operating conditions typical of
fluidized-bed combustion, the carbonate rock first undergoes thermal decomposition
and then starts further reacting. During the processing, sorbent particles are subject
to thermal shock possibly causing their fragmentation and subsequent detrimental
elutriation out of the contacting bed. The continual and vigorous movement of the
fluidized solids11-13 causes their significant comminution (pulverization). Nevertheless,
this phenomenon may lead to the favorable removal of the very dense layer of the
reaction products, which are preferentially formed and accumulate at the outer
surface of particles in the course of sulfation.1,4,14-16
A promising route to reduce the direct use of fossil fuels is biomass
gasification.17,18 In this aspect, biomass is usually viewed as any organic material of
plant origin. Gasification involves the partial oxidation of biomass at a high
temperature by heating in the environment of air, oxygen, and/or steam. The
produced combustible gas can be burned to generate heat or electricity, or
processed into chemicals and various gaseous or liquid fuels. However, prior to any
use of the product (fuel) gas, a number of undesirable impurities, both inorganic and
3
organic, need to be removed from the gas (e.g., dust (ash), nitrogen compounds,
sulfur compounds, metal compounds, and tar).
Tar(s) can hardly be defined by a simple specific term. They are usually
taken as viscous, complex organic mixtures mainly composed, for example, of
(higher) aromatic hydrocarbons, heterocyclic compounds, phenolic compounds, and
other constituents. These tars are carcinogens, have corrosive effects, can plug the
pores of filters, and also reduce the overall efficiency of a process. In general, tars
can be eliminated from the fuel gas by a number of methods, for example, by
physical, thermal cracking, and catalytic tar removal processes.17,18 Catalytic
methods also impede the occurrence of methane in the product gas. Catalysts can
be used within (in situ) or outside the gasifier (downstream).
The main groups of catalysts for tar elimination are based on alkaline earth
metal oxides (CaO and/or MgO), alkali metals, and nickel.19 According to another
classification,20 based upon the catalyst production method, the catalysts fall into two
groups: relatively inexpensive minerals [e.g., (calcined) limestone, magnesites,
dolomites, olivine, clay minerals, and iron ores] and synthetic catalysts (e.g., char,
fluid catalytic cracking catalysts, activated alumina, and alkali metal- and transition
metal- based catalysts).
In our ongoing research into catalytic biomass gasification (in situ) in a
fluidized bed, we have been employing particulate (calcined) dolomite/limestone
rocks. Calcined dolomites are generally considered as very promising active catalysts
for tar elimination.21,22 Moreover, dolomite carbonates are inexpensive and abundant
rocks which can be, after use, disposed of without difficulty. However, a significant
problem with the use of dolomite/limestone calcines lies in their possible
friability/fragility. Their particles are quite soft and can have a tendency to break.
4
Characteristics and Terminology of Limestone and Magnesite Rocks.
Limestone is rather a general term for any rock containing more than 80% of calcium
carbonate and magnesium carbonate.23,24 Amongst their numerous minor (trace)
components (impurities), silica, alumina, iron oxides and alkali metals are the most
common. Many ways of classifying limestone rocks have been suggested to describe
their nature. Such classifications can be based, for example, on the average grain
size, the micro-structure, the texture, the principal impurities, or on the carbonate
content and the Ca/Mg ratio. The classification of limestone rocks based upon the
contents of their principal carbonate components is presented in Table 1.
By the term “calcination of limestone or magnesite”, it is routinely understood
its thermal conversion, usually under oxidizing conditions, into quicklime (CaO or
MgO), which is also often called more generally (burnt) lime or calcine. According to
their precursors, they may be classified into calcitic (high calcium), magnesian, or
dolomitic lime. All lime is crystalline or microcrystalline, although it usually appears to
be amorphous to the unaided eye. Both oxides possess virtually the same cubic
crystal lattice with one exception: the MgO crystals are slightly smaller, which
accounts for the somewhat higher true density of magnesian and dolomitic lime (3.5
– 3.6 g/cm3) compared to calcium oxide (3.2 – 3.4 g/cm3). Most commercial quicklime
has a hardness of 2 to 3 on the Mohs scale. The values for dolomitic lime lie in the
range between 3 and 4 – 5. The porosity (relative volume of pores) of quicklime
varies widely from 20 to 55% depending on the parent carbonate rock and the
process conditions of calcination. The temperature at which the dissociation pressure
of CO2 above CaCO3 reaches 101.325 kPa is a value between 898 and 902 oC.9 The
corresponding decomposition temperature for MgCO3 is between 400 – 550oC.25,26
5
Experience indicates that all dolomitic rocks decompose at higher temperatures than
magnesium carbonate.
Comminution (Pulverization) Phenomena: Scope and Terminology. Catalyst
attrition (scouring) and solid particle fragmentation were recognized as important
problems in the design and operation of many fluidized bed contacting units some
years ago.27-30 Different terms have been employed to describe the phenomena by
which solids undergo comminution/pulverization in fluidized beds.31-33 “Primary
fragmentation” occurs as a consequence of thermal stresses caused by rapid heating
of the particles and/or of internal pressure of the gases evolved by chemical reaction
(e.g., thermal decomposition). Both coarse and fine fragments can be generated in
this way. “Attrition by abrasion” yields fine, readily elutriable particulates due to
surface wear and collisions/contact with other particles and reactor internals. It
reflects the resistance of the bed particles to surface wear. “Percolation
fragmentation” is brought about by loss of connectivity in the very porous particle
texture. “Secondary fragmentation” occurs due to particle-particle collisions or particle
impacts against the reactor walls or internals and generates coarser, mostly
nonelutriable fragments. All the comminution phenomena manifest themselves in
changes of the particle size distribution of bed solids and in unwanted elutriation of
the generated fines from the system. The extent as well as the sort of dominant
pulverization mechanism depends on the complex interplay (balance) between
particle mechanical strength and particle morphology and disruptive forces acting on
the particles in suspension. Aside from the chemical and thermal stresses (caused,
for example, by cyclic heating and cooling of the bed solids), fluid-dynamic-induced
disruptive forces must always be taken into consideration. The primary difficulty is
6
that the behavior of the bulk of particulate materials under actual operating conditions
depends strongly upon the origin, formation and whole history of the particles.
Although different attrition/fragmentation models are available in the
literature,14,30,33,34 there is no generally accepted description of particle breakage. Its
precise mechanism is still a matter of disagreement amongst researchers. As can be
expected, the particle hardness provides a general measure of the particle’s ability to
resist wear and to its susceptibility to fracturing. There is a relation between the
particles’ tendency to fracture and the energy needed to break the particles. Similarly,
the extent of attrition, expressed as the size or weight reduction of particles, can be
related to the energy input into the given system. In general, spherical (and smooth)
particles are less likely to attrit than those irregularly shaped (and with a rough
surface). It is believed that porous particles (but not those very fragile) attrit less than
nonporous particles thanks to their higher resilience. Yao et al. 16 confirmed that
fragmentation and attrition of limestone are strongly influenced by the hydrodynamic
forces in suspension and by the inventory of inert bed material. The results of Ayazi
Shamlou et al.30 indicate the attrition of bed material occurs in the core (bulk) of the
bed rather than in the grid (distributor) region. In case of excessive linear velocities of
gas exiting into the bed, attrition in the jetting zone should be also considered.
Dolomites are considered as the most promising inexpensive catalysts for tar
elimination from the fuel gas. The catalytic activity of these materials is higher than
that of calcite and magnesite calcines.20 However, only a small amount of knowledge
is available on comminution of dolomitic limes in the fluidized bed. This work
embodies the authors’ efforts to narrow such a gap. The aim of this experimental
study is to explore and describe the rate of attrition of a particulate dolomitic lime in
the turbulent fluidized bed at high temperature.
7
Methods and Materials
Aside from chemical analyses and textural measurements of dolomitic lime
particles, two different sorts of experiments were carried out: (1) The point of
minimum fluidization was determined for the lime particles as well as for the inert,
abrasion-resistant bed material (quartz sand) at an elevated temperature. (2) At an
elevated temperature, batch experiments were conducted in order to explore attrition
kinetics for precalcined samples originated from high-grade, dolomitic limestone rock.
Apparatus. The experiments were performed in a turbulent fluidized-bed reactor
constructed of heat-resistant stainless steel. The apparatus was primarily designed
and made for experimental studies on biomass and plastic gasification. The benchscale unit is schematically shown in Figure 1. The fluidized-bed reactor was
constructed of a heat-resistant, stainless tube, 50 cm high and 5.1 cm in inner
diameter. The upper part (freeboard) was built with a heat-resistant stainless pipe 9.9
cm ID and 160 cm high. The fluidization gas distributor was a set of interchangeable
perforated plates 0.8 cm thick of different free area with orifices 0.49 mm in diameter
disposed on a triangular pitch. A linear air velocity through each opening was in the
range 25-30 m/s at 500 oC. The reactor was heated by means of several cylindrical
segments of electrical elements; its internal temperature was measured with the aid
of a series of Pt-PtRh thermocouples located throughout the height of reactor and
kept constant by a PID controller. The maximum operating temperature was as high
as 1000oC. The flow rate of the fluidization air was measured and controlled by mass
flow controllers. Batches of bed material could be introduced into the reactor through
a feeding port at the top of the freeboard. A high-efficiency cyclone and sintered
brass filter separated elutriated fines from the fluidization gas (air). The particulate
8
samples could be withdrawn from both the bed and the separating devices in order to
measure the mass and particle size changes in the course of fluidization.
Materials. A high-grade, commercially available carbonate rock was employed in
the present work. This rock is a crystalline, high purity carbonate (according to Table
1) containing 37.5 wt.% CaO and 15.6 wt.% MgO whose loss on ignition (calcination)
at 900oC amounts to 46.5 wt.%. As it contains 32.7 wt.% MgCO 3, it may be
considered dolomitic limestone in light of Table 1.
The hand-picked stones from a commercial quarry, which contained no
visible inclusions, were crushed and sieved. The fractions investigated in this study
comprised three narrow size ranges: 400 – 500 µm (đp = 450 µm), 630 – 800 µm (
đp = 715 µm), and 1000 – 1120 µm (đp = 1060 µm). Microscopic examination
showed that the particles were sharp-edged and of irregular shape. The dolomitic
lime was prepared by thermal decomposition of the carbonate at 900oC in a bed
fluidized with air. Such mild conditions of calcination tend to inhibit both primary
fragmentation and unwanted sintering of the calcined particles. No significant
fragmentation of the decomposing solids was found when the conversion to lime was
complete. The calcined particles were sieved again and the narrow fractions of lime
were maintained in airtight containers. The irregular shape of the particles remained
practically unchanged by the calcination process. The chemical and physical
characteristics of the lime particles are presented in Tables 2 and 3. According to the
generally accepted classification of carbonate rocks in Table 1, our lime can be taken
as dolomitic one. A slightly different term follows from the classification of calcined
rocks based on the CaO/MgO weight ratio20: calcitic dolomite lime in which CaO/MgO
= 2.40. We prefer to adhere to the first term.
9
Round quartz sand was employed as an inert and attrition-resistant bed
material. Its particles were nearly isometric and fairly spherical. Basic physical
properties of the sand particles are shown in Table 3.
Procedures. The point of minimum fluidization of our particulate materials was
determined by the standard procedure from the dependence of bed pressure drop on
air flow with the air velocity gradually reduced from a well-fluidized state to packed
(static) bed.35,36
The parent lime sample in this experiment was high-grade, reactive lime
formed by calcining high-purity dolomitic limestone so that all the carbon dioxide was
liberated and all moisture removed. Attrition experiments were conducted in the
fluidized-bed reactor using the sieved, very narrow fractions of lime with a mean
particle size of 450, 715, and 1060 µm. Quick estimates of the terminal velocities37,38
of the lime and sand particles showed that no elutriation of such particles could occur
in our fluidization experiments. Therefore, the mass reduction of bed materials and
the amount of fines elutriated from the reactor (and captured by means of the cyclone
and the filter) are considered as a practical measure of the extent of attrition. Tests
repeated under the same operating conditions indicated that the extent of attrition
could be determined with good reproducibility within the range of 3 – 5%. It was also
found that the attrition of quartz sand in our experiments was not significant. To
prevent hydration and recarbonation of the lime particles in ambient air, the dried
fluidization air was used; the collected samples were cooled down in dessicators and
weighed as quickly as possible.
10
In a typical attrition/gasification experiment, the reactor was preloaded with 1
kg of sand which was fluidized under the preset gas flow rate and heated to the
desired temperature until a steady state was attained. Then, the 0.5 kg lime sample
was introduced into the bed. By collecting and weighing the elutriated fines, the
course of attrition was measured.
Results and Discussion
Incipient Fluidization at Elevated Temperature. The experimental measurements
were conducted with three fractions of lime and with the particles of sand (450, 715,
1060, and 305µm) at temperatures of 25 oC and 850oC. In this temperature interval,
the air density changes by a factor of 0.2655, whereas its viscosity changes by a
factor of 2.40. The sets of experimental data are shown in Table 4 and demonstrate
that the minimum fluidization velocity appreciably decreases with an increasing
operating temperature at ambient pressure. These results indicate that the viscous
energy losses in the bed predominate over the kinetic energy losses. 39 In other
words, the decrease of Umf with an increasing temperature demonstrates that the
increasing viscosity of the fluidizing gas is the controlling factor under the flow
conditions that have been employed (Remf = 0.07 – 21).
Attrition Experiments. Analysis of the particle-size distributions of fresh and
fluidized-for-an-hour lime indicated that no significant primary fragmentation of the
particles occurred. This is also consistent with our results from the microscopic
examinations of such solids. Thus, it may be inferred that comminution of lime
particles in this work was a consequence of the attrition by abrasion rather than that
of gross fragmentation.
11
Attrition tests were performed at 850oC in a batch mode with 450, 715, and
1060 µm particles of dolomitic lime to explore the fluid energy-induced tendency
towards attrition. As is known, in the core of the fluidized bed, usually rapid particle
motion is governed by the flow of gas and bulk circulation of the bed material. The
excess gas air velocities (U – Umf) were varied in the range from 0.85 to 1.74 m/s. In
a recent work of ours40 we developed a method that quite objectively determines the
points of transition between different flow (hydrodynamic) regimes of the fluid bed
(bubbling/slugging/ turbulent/fast (dilute) bed). This method is based upon the
concept of symmetry of the sampled pressure fluctuating signal within the bed.
Having employed this procedure, we determined with a fair accuracy that our bed
was operated in the regime(s) of intermediate or full turbulence (turbulent bed).
Unfortunately, it was hard to determine unequivocally the point of transition between
these two turbulent (sub)regimes. The operating time (elapsed time of attrition) was
varied between ten minutes and four hours. Statistical analysis was performed on the
basis of 75 experimental data points amassed with different particle sizes at different
excess gas velocities and at varying elapsed time of attrition.
Figure 2 presents a typical course of the relative mass of parent lime
remaining in the bed as a function of elapsed time. As can be seen, the lime mass
decreases most rapidly in the initial phases and the rate of decline gradually slows
down with elapsed time. It appears that rounding off (dislodgement) of originally
sharp-edged lime solids considerably enhances attrition in the early stages of this
batch process. Nevertheless, the attrition process is not likely to cease entirely. Very
small bed weight reductions were still detected even after 15 hours of continuous
fluidization. In light of this experimental finding, the concept of an asymptotic
12
minimum weight of parent solids remaining in a bed, which some researchers14,34 use
in their attrition models, needs to be unequivocally defined.
Particles with different extents of attrition were also examined with the aid of
a microscope. The results indicate that the original sharp edges of lime particles are
rounded off at first. Then, the attrition by abrasion due to collisions and surface wear
gains ground. While the sharp edges gradually disappear, the generally round shape
of particles does not change with time and their surface remains or becomes
somewhat rough, possibly due to frequent collisions. A limited number of samples of
the fines elutriated from the bed, and collected by the cyclone and filter, were
subjected to particle-size characterization. Findings indicate that the large majority of
such particles is below 80 µm, which is in general agreement with the corresponding
results in the literature.31
Three different sizes of parent lime particles (đp = 450, 715, and 1060 µm)
were employed to investigate the course of attrition at excess gas velocities in the
range between 0.85 and 1.74 m/s. A representative sample of the experimental
measurements is shown in this article in the graphical form, by way of illustration.
However, all the amassed experimental data were included in our effort to describe
the measured results by means of the proposed model. Figures 2 and 3 show lime
weight (mass) loss for various attrition times due to continuing particle attrition. As
follows from the comparison of Figures 2 and 3 and also as expected, the mass
losses are considerably greater when the superficial gas velocity is significantly
increased. As also shown in Figures 2 and 3, weight losses of smaller particles are
moderately higher than those of larger particles under comparable operating
conditions.
13
It should be noted that the origin and structure (texture) of original (fresh)
particles can strongly affect the course and extent of comminution. The breakage
process of the suspended particles can be viewed as an intricate interplay between
mechanical (material) properties of the solid and fluid-dynamic-induced disruptive
forces within the bed. As pointed out in the literature,16,31 the course of attrition of
sulfated lime (a mixture of CaSO4 and CaO) is similar to that of fresh lime, but its
attrition rate is an order of magnitude smaller than that of lime. On the other hand, the
weight loss occurs much more rapidly when the lime particles are wetted. Shattering
and the soft surface of the hydrated lime are most likely the cause of such enhanced
attrition.
Mechanistic Model of Attrition. All the measured data suggest an exponential
decline of the mass of attrited solids with the elapsed time of fluidization. The rate of
attrition (ra) can be defined as
ra = -
1
dw
___
_____
w
d
for w > 0
(1)
where w = m/mo is the relative mass of sample particles at a given instant of time ()
and dw/d is the rate of relative mass decrease of the sample at the same . In light
of the two-phase theory, all gas in excess above Umf passes through the bed in the
form of “bubbles” and these ascending gas pockets (tongues) can be viewed as a
driving engine keeping the suspended solids in more or less intensive continuous
motion. The rate of such excess energy supply to the bed by the gas above the
condition of minimum fluidization is given by
14
Eexc = Apb (U - Umf)= m g (U - Umf )
(1a,b)
Thus, the excess gas velocity (U – Umf) is a useful measure of the energy being
introduced through the moving heterogeneities into the suspension.11,30
Assuming that the rate of attrition is directly proportional to the excess gas
velocity, we can describe the course of attrition as follows
dw
_____
= - Ka (U – Umf) d 
(2)
w
where Ka is the overall (effective) attrition rate constant. It is apparent that Ka
depends strongly upon a number of important material properties of solids such as
impact strength, wear hardness, particle size and particle shape, texture, and surface
roughness. The excess gas velocity (U – Umf) accounts for the influence of fluiddynamic-induced forces on attrition.
Early experience indicated that Ka displays a tendency to decay exponentially
with the duration of fluidization experiments. Presuming that
Ka = a exp (- b )
(3)
and on substituting eq. 3 into eq. 2 we get
dw
_____
= - a (U – Umf) [ exp (- b ) ] d 
(4)
w
Integration of eq. 4 with the boundary condition
w=1
at
=0
(5)
15
gives the fractional amount of a parent sample remaining in the bed (w) as
a
ln w = ____ (U – Umf) { [ exp (- b ) ] – 1 }
b
(6)
and the rate of sample attrition (ra)
ra = a (U – Umf) exp (- b )
(7)
as functions of time.
Symbols a and b in eq.s 3, 4, 6, and 7 represent by this time the unknown
parameters. The available measured data are the time series of values of w() for
different particle sizes and excess gas velocities. The parameters a and b were
determined by a nonlinear least-squares procedure which minimizes the sum of
squares of the residuals. Modified simplex minimization, which had proved successful
in our previous work,41 was employed as the optimization method.
The computational results of the nonlinear regression fitting, and the
statistical evaluation based upon the Student’s t analysis are presented in Table 5.
The particle size is a relevant operating variable rather than a material property.
Thus, we believe that any practical model of attrition should make it possible to
account for this quantity. In attempt to extend the model also in this direction, the rate
parameters given Table 5 were regressed with respect to the particle size. The
available data were correlated by means of linear algebraic equations with the aid of
a least-squares procedure:
a=-4.032x10-8 dp + 1.036x10-4
(8)
b=1.645x10-7 dp + 7.018x10-5
(9)
16
The particle size is given in m and the respective regression factors (R2 ), amount to
0.993 and 0.986, respectively.Figures 2 and 3 visualize a good correlation between
the model predictions and the experiments.
With respect to always-present differences in the operating conditions and
particularly in light of the varying origins (and consequently the properties) of the
parent carbonate or lime, it is not easy to compare the results of different
researchers. Thus, any comparison should be taken as approximate. Using a high
calcium lime, Lee et al.14 explored the rate of attrition at high superficial velocities in a
similar manner to us. For 903 µm particles fluidized with air for 2 h at U = 2 m/s, the
authors14 found by experiment that the relative mass of particles decreased (from
unity) to w = 0.78. The authors’ empirical model estimates for these operating
conditions a relative mass as large as w = 0.83. The corresponding prediction of our
model amounts to w = 0.69. In view of the fact that the authors’ bed did not contain
any hard particles (in contrast to ours), our somewhat higher rate of attrition appears
to be understandable. Therefore, we believe that our findings are in general
agreement with those of Lee et al.14 and the predictions of our model can be
considered as realistic.
It should be noted that attrition models available in the literature 14,34 include
as an important quantity, the minimum mass of solids below which attrition may be
neglected. Undoubtedly, this is a helpful attrition parameter, but its rigorous definition
and its determination by experiment are not unambiguous.
Of course, the attrition model developed in this work has the usual
constraints and should be applied with caution outside the range of the operating
conditions for which it was educed. Nevertheless, the model offers some practical
features. For example, it provides, in combination with suitable solids feeders, 42,43
17
essential background information for the control of the amount of catalyst present
within the bed during fluidized gasification with effective limestone/dolomite-based
catalysts. The model parameters depend only on the material properties of solids and
can be determined in simple tests.
Model Predictions. As can be seen in Figures 2 and 3, the original (initial) size of
parent lime particles significantly affects the course of the attrition curves. This
influence embraces variation of the minimum fluidization velocity with size of bed
solids on one side and variation of the external particle surface, exposed to attrition
by abrasion, with solids size on the other side. While the specific external particle
surface is proportional to dp-1, the dependence of Umf on dp is more involved.35 Under
the conditions of laminar flow, for small Reynolds numbers, we have
Umf  dp2
(for Remf < 1)
(10)
In highly turbulent flow, for large Reynolds numbers, it holds
Umf  dp0.5
(for Remf > 1000)
(11)
In the flow regime transition conditions, the minimum fluidization velocity is
proportional to the solids diameter (dp) raised to a power in the range between 2 and
0.5:
Umf  dp2 to dp0.5
(for 1 < Remf > 1000)
(12)
18
The attrition rate parameters a and b for different particles can be estimated by eq.s 8
and 9. As follows from eq. 7, a greater value of a for the smaller particles indicates
their more rapid initial attrition than that of the larger solids at the same excess gas
velocity. Furthermore, a lesser value of b for the smaller particles demonstrates that
their attrition rate decays with time more slowly than that of the larger ones.In order
to take a different look at our results, we carried out systematic computations of the
attrition rates. Some of the results are plotted in Figures 4 and 5. As visualized, the
rate of attrition diminishes rapidly as the attrition process progresses.
The presented curves also illustrate how the rate of attrition depends on the
excess gas velocity and particle size. The curves are very similar in shape to the
lines describing an entirely different process: the rate of sulfation of calcined
limestone particles. As we reported some years ago, 5 the sulfation rate also
diminishes rapidly with the increasing conversion of CaO to CaSO 4. It is necessary to
add that this is because of the formation of a dense product shell (CaSO4 + CaO) on
the particle surface. It was observed that the attrition rate of the sulfation product is
an order of magnitude smaller than that of lime (CaO) under similar operating
conditions.
Conclusions
The attrition rate of dolomitic lime in a turbulent fluidized bed with quartz sand can
be described in terms of a simple model. This mechanistic model is based upon
experimental observations that the rate of particle attrition decays exponentially with
the elapsed time of fluidization. Assuming a first-order dependency with respect to
the excess gas velocity, the model includes two rate constants: one of which (a)
reflects the initial rate of attrition, while the other (b) indicates how rapidly the attrition
19
rate may decay with time. Particle size has a significant effect on both rate constants,
and therefore is also accounted for in the model. The proposed model can be
employed for batch and continuous processes with fluidized beds in which attrition of
dolomitic lime particles (mainly by surface abrasion) and subsequent elutriation of
fines out of the bed occur. In any application, possible differences in mechanical
properties of the solid (the nature of the parent material) must always be borne in
mind.
20
Nomenclature
Abbreviation
wt
= weight
Symbols
a
= fitted attrition rate parameter given by eqs. 3 and 8, 1/m
A
=cross – sectional area of bed, cm2, m2
b
= fitted decay parameter given by eqs. 3 and 9, 1/s
dp
= diameter of spherical particle, µm, m
đp
= mean particle size determined by sieving, µm, m
dw/d
= rate of change of the relative mass of lime particles, 1/s
Eexc
=power input in excess of minimum fluidization, W, m2kg/s3
g
=acceleration due to gravity, cm/s2, m/s2
Ka
= effective attrition rate constant given by eq. 2, 1/m
m
= mass of lime particles in the bed at a given moment of time, g, kg
mo
= initial mass of lime particles in the bed (i.e., at  = 0), g, kg
ms
= mass of sand in the bed, g, kg
ra
= rate of attrition defined by eq. 1, 1/s
Remf = Umf đp f / µf = Reynolds number at the onset of fluidization
T = t + 273.15 = thermodynamic temperature, K
t
= Celsius temperature, oC
U
= superficial gas velocity, m/s, cm/s
Umf
= minimum fluidization velocity, m/s, cm/s
U - Umf
= excess gas velocity / flow, m/s, cm/s
21
w = m/mo
= relative mass of lime particles in the bed at a given moment of time
Greek Letters
pb
=pressure drop acros the bed, Pa, kg/(ms2)
µf
= fluid viscosity; µair = (4.261 x 10-7) T0.66, kg/(m s), Pa s
f
= fluid density; air = 352.8 / T (at ambient pressure), kg/m3

= elapsed time of fluidization/attrition, s
Other Symbols
e
= base of natural system of logarithms; e = 2.7183
exp x
= ex
ln
= base e or natural logarithm
log
= base 10 or common (Briggsian) logarithm
dx
= differential of x
22
Acknowledgments
The authors gratefully acknowledge the financial support for this research awarded
by the Grant Agency of the Academy of Science of the Czech Republic through Grant
No. IAA 400720701. Thanks are also due to the Research Fund for Coal and Steel of
the EC for the support through Grant No. RFCR-CT-2010-00009.
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26
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Table 1. Classification of Limestone Rocks Based on the Contents of Their
Principal Components / Carbonates23,24
___________________________________________________________________
rock
amount (wt %)
___________________________________________________________________
high calcium or chemical-grade
limestone
> 95 % CaCO3
high purity carbonate
> 95 % (CaCO3 + MgCO3)
calcitic limestone
< 5 % MgCO3
magnesian limestone
5 – 20 % MgCO3
dolomitic limestone
20 – 40 % MgCO3
(high magnesium) dolomite
40 – 46 % MgCO3 a
aThe
stoichiometric value for CaMg(CO3)2 amounts to 45.72 wt % MgCO3, i.e., 21.86
wt % MgO.
27
Table 2. Chemical Properties of Dolomitic Lime Samples
___________________________________________________________________
chemical
component
chemical
(wt %)
components
(wt %)
___________________________________________________________________
CaO
70.1a
Fe2O3
0.054
MgO
29.2a
Cl
0.040
SiO2
0.29
K2O
0.028
Al2O3
0.24
SO3
0.024
aOn
the basis of these values, the parent carbonate rock can be viewed as a high
purity carbonate and/or dolomitic limestone.
28
Table 3. Physical Properties of Dolomitic Limea and Quartz Sand
Samples
___________________________________________________________________
sample
quantity
lime
lime
quartz sand
___________________________________________________________________
sieve particle size (µm)
400 – 500
1000 – 1120
250 – 360
mean particle size (µm)
450
1060
305
true solid density (kg/m3)
2946
particle density (kg/m3)
1150
2941
2530
1148
2530
pore volume (m3/kg)
5.301 x 10-4
5.311 x 10-4
0
fractional particle porosity
0.6096
0.6097
0
11.6
11.3
-
specific BET surface
area (m2/g)
aCalcination
took place in a fluidized bed at 900oC and in an oxidizing atmosphere
with a weight loss of 46.5 wt %. True and particle densities were determined by
helium and mercury displacement. The textural data for 630 – 800 m particles occur
between the presented values.
29
Table 4. Experimental Minimum Fluidization Velocities (Umf) of Lime and Sand
Samples in Air at Different Temperature (t) and Ambient Pressurea
___________________________________________________________________
material
lime
mean particle size (µm)
450
715
sand
1060
305
___________________________________________________________________
t (oC)
Umf (cm/s)
___________________________________________________________________
24-25
7.29
16.28
29.43
7.53
848-852
3.33
8.21
17.32
3.38
aPhysical
properties of the solids are presented in Table 3.
30
Table 5. Effective Rate Parameters for Attrition of Dolomitic Lime in Turbulent
Fluidized Beda at 850oC (eqs 3, 4,6, and 7)
___________________________________________________________________
mean particle size, đp (µm)
quantity
450
715
1060
______________________________________________________________
a x105 (1/m)
8.631
7.402
6.147
95 % confidence intervalb
+ 1.19 x 10-6
1.02 x 10-6
1.11 x 10-6
b x104(1/s)
1.428
1.897
2.442
95 % confidence intervalb
+ 1.36 x 10-6
+ 1.62 x 10-6
+1.50 x 10-6
no. of exptl. points
25
26
24
aThe
bed inventory was made up of silica sand (1050 g; dp = 250 – 360 µm) and lime
(559 g in the initial state ( = 0)).
bBased
upon the Student's t distribution.
31
List of Figures
Figure 1: Schematic diagram of a fluidized-bed reactor for the gasification and
attrition experiments. (1) container; (2) screw feeder; (3) motor with gear box; (4)
pneumatic transport; (5) cooler; (6) inlet of a gasification medium; (7) fluidized bed;
(8) electric heating; (9) freeboard region; (10) thermocouples; (11) gas sample
withdrawal; (12) cyclone; (13) container; (14) gas outlet; (15) feeding of the bed
material.
Figure 2: Decrease of the relative mass of dolomitic lime samples (w)
as a function
of elapsed time of attrition (). The symbols represent experimental data points
measured at 850oC and excess gas velocity U – Umf = 1.74 m/s: initial mass of lime,
mo = 559 g; mass of sand, ms = 1050 g. (O) Experimental data points measured with
450 µm lime particles, (●) experimental data points measured with 1060 µm lime
particles. The solid lines show the values predicted by the model.
Figure 3: Decrease of the relative mass of dolomitic lime samples (w) as a function
of elapsed time of attrition (). The symbols represent experimental data points
measured at 850oC and excess gas velocity U – Umf = 0.85 m/s: initial mass of lime,
mo = 558 g; mass of sand, ms = 1051 g. (O) Experimental data points measured with
450 µm lime particles, (●) experimental data points measured with 1060 µm lime
particles. The solid lines show the values predicted by the model.
Figure 4: Rate of attrition [ (-1/w)(dw/d) ] as a function of the relative mass of lime
particles in the bed (w). The lines show the model predictions for the respective lime
fractions and for the operating conditions as in Figure 2.
Figure 5: Rate of attrition [ (-1/w)(dw/d) ] as a function of the relative mass of lime
particles in the bed (w). The lines show the model predictions for the respective lime
fractions and for the operating conditions as in Figure 3.
32
33