Attrition of Dolomitic Lime in a Fluidized-Bed Reactor at High
Temperature
Miloslav Hartman,* Karel Svoboda, Michael Pohořelý, Michal Šyc, Michal Jeremiáš
Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic,
Rozvojová 135,165 02 Prague 6-Suchdol, Czech Republic
Corresponding author: Miloslav Hartman, e-mail: hartman@icpf.cas.cz
Received
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 850oC 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
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
(Hartman & Couhlin, 1976; Hartman & Svoboda, 1985; Hartman & Trnka, 1993, 2002;
Hartman et al., 1979, 1988, 1991, 1994a, 2000, 2002). 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 continuous and vigorous movement of the fluidized
solids (Yates, 1983; Kunii & Levenspiel, 1991; Gupta & Sathiyamoorthy, 1999) 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 (Hartman &
Couhlin, 1976; Hartman et al., 1988; Lee et al., 1993; Scala & Salatino, 2010; Yao et al.,
2010).
A promising route to reduce the direct use of fossil fuels is biomass gasification
(Knoef 2005; Higman & Burgt, 2008). 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 organic, need to be removed from the gas (e.g.,
dust (ash), nitrogen compounds, sulfur compounds, metal compounds, and tar).
3
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 (Knoef, 2005; Higman & Burgt, 2008). 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 (Sutton et al., 2001). According to
another classification (Abu El-Rub et al., 2004), 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 (Gil et al.,
1999; Corella et al, 2002). 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 (Boynton, 1980; Oates, 1998). 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 cm-3) 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 902oC (Hartman & Trnka,
2002). The corresponding decomposition temperature for MgCO3 is between 400 – 550oC
5
(Hartman & Svoboda, 1985; Hartman & Martinovský, 1992). 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 (Forsythe & Hertwig, 1949; Lin et al., 1980; Arena et al., 1983; Ayazi Shamlou et
al., 1990). Different terms have been employed to describe the phenomena by which solids
undergo comminution/pulverization in fluidized beds (Scala et al., 1997, 2007; Chen et al.,
2008). “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
6
consideration. The primary difficulty is 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 (Lee et
al., 1993; Ayazi Shamlou et al., 1990; Chen et al., 2008; Cook et al., 1996) 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. (2010) 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.
(1990) 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 (Abu El-Rub et al., 2004). 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
7
explore and describe the rate of attrition of a particulate dolomitic lime in the turbulent
fluidized bed at high temperature.
Experimental
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 bench-scale unit is schematically shown in
Fig. 1.
8
Fig. 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.
9
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 2530 m s-1 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 highefficiency cyclone and sintered brass filter separated elutriated fines from the fluidization gas
(air). The particulate 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.%.
10
Table 1. Classification of limestone rocks based on the contents of their principal components /
carbonates (Boynton, 1980; Oates, 1998)
Rock
Amount /(wt %)
High calcium or chemicalgrade 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*
*
The stoichiometric value for CaMg(CO3)2 amounts to 45.72 wt % MgCO3, i.e., 21.86 wt %
MgO.
As it contains 32.7 wt.% MgCO3, 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 sharpedged 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.
11
Table 2. Chemical properties of dolomitic lime samples
Chemical
(wt %)
component
Chemical
(wt %)
component
CaO
70.1*
Fe2O3
0.054
MgO
29.2*
Cl
0.040
SiO2
0.29
K2O
0.028
Al2O3
0.24
SO3
0.024
*
On the basis of these values, the parent carbonate rock can be viewed as a high purity
carbonate and/or dolomitic limestone.
Table 3. Physical properties of dolomitic lime* and quartz sand samples
Sample
Guantity
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 m-3)
2946
2941
2530
Particle density/(kg m-3)
1150
1148
2530
Pore volume/(m3 kg-1)
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-1)
*
Calcination 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 µm particles occur between the
presented values.
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 ratio (Abu El-Rub et al., 2004): calcitic
dolomite lime in which CaO/MgO = 2.40. We prefer to adhere to the first term.
12
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 (Hartman & Coughlin,
1993; Hartman et al., 2007).
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 velocities (Hartman & Yates, 1993; Hartman et al., 1994) 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.
13
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.
Table 4. Experimental minimum fluidization velocities (Umf) of lime and sand samples in air
at different temperature (t) and ambient pressure*
Material
Mean particle size/(µm)
Lime
450
t/(oC)
Sand
715
1060
305
Umf/(cm s-1)
24-25
7.29
16.28
29.43
7.53
848-852
3.33
8.21
17.32
3.38
*
Physical properties of the solids are presented in Table 3.
These results indicate that the viscous energy losses in the bed predominate over the
kinetic energy losses (Hartman & Svoboda, 1986). In other words, the decrease of Umf with an
14
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.
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-1. In a recent work of ours (Hartman et al.,
2009) 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.
15
1
w
0.8
0.6
0.4
0
1
2
3
4
 h
Fig . 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 ms-1: 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.
Fig. 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 decrease 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
16
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 minimum weight of parent solids remaining in a bed, which some researchers (Lee
et al., 1993; Cook et al., 1996) 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 (Scala et al., 1997).
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-1. 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. Figs. 2 and 3 show lime weight (mass) loss for various attrition times due to
continuing particle attrition.
17
1
w
0.9
0.8
0.7
0
1
2
3
 h
4
Fig. 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 ms-1: 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.
As follows from the comparison of Figs. 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 Figs. 2 and 3, weight losses of smaller particles are moderately higher than those of
larger particles under comparable operating conditions.
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 (Yao et al., 2010; Scala et al., 1997), 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
18
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 twophase 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
Eexc = AΔpb (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 (Yates, 1983; Ayazi Shamlou et al.,
1990).
Assuming that the rate of attrition is directly proportional to the excess gas velocity,
we can describe the course of attrition as follows
dw
_____
w
= - Ka (U – Umf) d 
(2)
19
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 fluid-dynamic-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)
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)
20
as functions of time.
Symbols a and b in Eqs. (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 (Hartman
et al., 2010), 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.
Table 5. Effective rate parameters for attrition of dolomitic lime in turbulent fluidized bed a at
850oC [Eqs. (3), (4), (6), and (7)]
Mean particle size, đp/(µ m)
Quantity
450
715
1060
a x105/m-1
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/s-1
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
The bed inventory was made up of silica sand (1050 g; dp = 250 – 360 µm) and lime (559 g
a)
in the initial state ( = 0)). b)Based upon the Student's t distribution.
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:
21
a=-4.032x10-8 dp + 1.036x10-4
(8)
b=1.645x10-7 dp + 7.018x10-5
(9)
The particle size is given in μm and the respective regression factors (R2), amount to 0.993
and 0.986, respectively. Figs. 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. (1993) 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-1, the authors Lee et al. (1993) 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. (1993) and the predictions of our model can be
considered as realistic.
It should be noted that attrition models available in the literature (Lee et al., 1993;
Cook et al.,1996) 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
22
combination with suitable solids feeders, (Zheng et al., 1982; Pohořelý et al., 2004) 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 Figs. 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 (Hartman & Coughlin, 1993). 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:
23
Umf  dp2 to dp0.5
(for 1 < Remf < 1000)
(12)
The attrition rate parameters a and b for different particles can be estimated by Eqs. (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 Figs. 4 and 5. As visualized, the rate of attrition diminishes rapidly as the
attrition process progresses.
-3.5
-4.0
log ra
450 m
-4.5
1060 m
-5.0
-5.5
0
0.2
0.4
1-w
0.6
Fig . 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 Fig. 2.
24
-4.0
-4.5
450 m
log ra
-5.0
1060 m
-5.5
-6.0
0
0.1
0.2
0.3
1-w
Fig . 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 Fig. 3.
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 (Hartman et al., 1991), the sulfation rate also diminishes rapidly with the
increasing conversion of CaO to CaSO4. 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.
25
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 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.
Acknowledgements. 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.
26
Symbols
a
fitted attrition rate parameter given by Eqs. (3) and (8)
m-1
A
cross – sectional area of bed
cm2, m2
b
fitted decay parameter given by Eqs. (3) and (9)
s-1
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
s-1
Eexc
power input in excess of minimum fluidization
W
g
acceleration due to gravity
cm s-2, m s-2
Ka
effective attrition rate constant given by Eq. (2)
m-1
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)
s-1
Remf
Reynolds number at the onset of fluidization (= Umf đp f / µf )
T
thermodynamic temperature
K
t
Celsius temperature
o
U
superficial gas velocity
m s-1, cm s-1
Umf
minimum fluidization velocity
m s-1, cm s-1
U - Umf excess gas velocity / flow
w
C
m s-1, cm s-1
relative mass of lime particles in the bed at a given moment of time (= m/mo)
Greek Letters
Δpb
pressure drop acros the bed
Pa, kg m-1 s-2
27
µf
fluid viscosity; µair = (4.261 x 10-7) T0.66
Pa s
f
fluid density; air = 352.8 / T (at ambient pressure)
kg m-3

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
dx
differential of x
wt
weight
References
Abu El-Rub, Z., Bramer, E. A. & Brem, G. (2004). Review of catalysts for tar elimination in
biomass gasification processes. Ind. Eng. Chem. Res., 43, 6911-6919. DOI:
10.1021/ie0498403.
Arena, V., D´Amore, M. & Massimilla, L. (1983). Carbon attrition during the fluidized
combustion of a coal. AIChE J., 29, 40-49.
Ayazi Shamlou, P., Liu, Z. & Yates, J. G. (1990). Hydrodynamic influences on particle
breakage in fluidized beds. Chem. Eng. Sci., 45, 809-817.
Boynton, R. S. (1980). Chemistry and Technology of Lime and Limestone, 2nd ed., Wiley:
New York.
28
Chen, Z., Grace, J. R. & Jim Lim, C. (2008). Limestone particle attrition and size distribution
in
a
small
circulating
fluidized
bed.
Fuel,
87,
1360-1371.
DOI:
10.1016/j.fuel.2007.06.012.
Cook, J. L., Khang S. J., Lee, S. K. & Keener, T. C. (1996). Attrition and changes in particle
size distribution of lime sorbents in a circulating fluidized bed absorber. Powder Technol.,
89, 1-8. DOI: 10.1016/S0032-5910(96)03115-4.
Corella, J., Toledo, J. M. & Aznar, M. P. (2002). Improving the modeling of the kinetics of
the catalytic tar elimination in biomass gasification. Ind. Eng. Chem. Res., 41, 3351-3356.
DOI: 10.1021/ie0110336.
Forsythe, Jr. W. L. & Hertwig, W. R. (1949). Attrition characteristics of fluid cracking
catalysts: laboratory studies. Ind. Eng. Chem., 41, 1200-1206.
Gil, J., Caballero, M. A., Martin, J. A., Aznar, M. P. & Corella, J. (1999). Biomass
gasification with air in a fluidized bed: effect of the in-bed use of dolomite under different
operating conditions. Ind. Eng. Chem. Res., 38, 4226-4235. DOI: 10.1021/ie980802r.
Gupta, C. K. & Sathiyamoorthy, D. (1999). Fluid Bed Technology in Materials Processing,
CRC Press: Boca Raton, FL.
Hartman, M., & Coughlin, R. W. (1976). Reaction of sulfur dioxide with limestone and the
grain model. AIChE J., 22, 490-498. DOI: 10.1002/aic.690220312.
Hartman, M., Hejna, J. & Beran, Z. (1979). Application of the reaction kinetics and dispersion
model to gas-solid reactors for removal of sulfur dioxide from flue gas. Chem. Eng. Sci.,
34, 475-483. DOI: 10.1016/0009-2509(79)85092-7.
Hartman, M. & Svoboda, K. (1985). Physical properties of magnesite calcines and their
reactivity with sulfur dioxide. Ind. Eng. Chem. Process Des. Dev., 24, 613-621. DOI:
10.1021/i200030a016.
29
Hartman, M. & Svoboda, K. (1986). Predicting the effect of operating temperature on the
minimum fluidization velocity. Ind. Eng. Chem. Process Des. Dev., 25, 649-654. DOI:
10.1021/i200034a009.
Hartman, M., Svoboda, K., Trnka, O. & Veselý, V. (1988). Reaction of sulfur dioxide with
magnesia in a fluidized bed. Chem. Eng. Sci., 43, 2045-2050. DOI: 10.1016/00092509(88)87082-9.
Hartman, M., Svoboda, K. & Trnka, O. (1991). Unsteady-state retention of sulfur dioxide in a
fluidized bed with continual feeding of lime and limestone. Ind. Eng. Chem. Res., 30,
1855-1864. DOI: 10.1021/ie00056a027.
Hartman, M. & Martinovský, A. (1992). Thermal stability of the magnesian and calcareous
compounds for desulfurization processes. Chem. Eng. Comm., 111, 149-160. DOI:
10.1080/00986449208935985.
Hartman, M. & Trnka, O. (1993). Reactions between calcium oxide and flue gas containing
sulfur dioxide at lower temperatures. AIChE J., 39, 615-624. DOI: 10.1002/aic.690390410
Hartman, M. & Yates, J. G. (1993). Free-fall of solid particles through fluids. Collect. Czech.
Chem. Commun., 58, 961-982. DOI: 10.1135/cccc19930961.
Hartman, M. & Coughlin, R. W. (1993). On the incipient fluidized state of solid particles.
Collect. Czech. Chem. Commun., 58, 1213-1241. DOI: 10.1135/cccc19931213.
Hartman, M., Trnka, O. & Svoboda, K. (1994). Free settling of nonspherical particles. Ind.
Eng. Chem. Res., 33, 1979-1983. DOI: 10.1021/ie00032a012.
Hartman, M., Trnka, O. & Veselý, V. (1994a). Thermal dehydration of magnesium hydroxide
and
sintering
of
nascent
10.1002/aic.690400314.
magnesium
oxide.
AIChE
J.,
40,
536-542.
DOI:
30
Hartman, M., Trnka, O. & Svoboda, K. (2000). Fluidization characteristics of dolomite and
calcined dolomite particles. Chem. Eng. Sci., 55, 6269-6274. DOI: 10.1016/S00092509(00)00409-7.
Hartman, M., Svoboda, K., Trnka, O. & Čermák, J. (2002). Reaction between hydrogen
sulfide and limestone calcines. Ind. Eng. Chem. Res., 41, 2392-2398. DOI:
10.1021/ie010805v.
Hartman, M. & Trnka, O. (2002). Comments on „Proposal for regenerative high-temperature
process for coal gas cleanup with calcined limestone“. Ind. Eng. Chem. Res., 41, 62076208. DOI: 10.1021/ie020193u.
Hartman, M., Trnka, O. & Pohořelý, M. (2007). Minimum and terminal velocities in
fluidization of particulate ceramsite at ambient and elevated temperature. Ind. Eng. Chem.
Res., 46, 7260-7266. DOI: 10.1021/ie0615685.
Hartman, M., Trnka, O. & Svoboda, K. (2009). Use of presure fluctuations to determine
online the regime of gas-solids suspensions from incipient fluidization to transport. Ind.
Eng. Chem. Res., 48, 6830-6835. DOI: 10.1021/ie900055x.
Hartman, M., Trnka, O., Pohořelý, M. & Svoboda, K. (2010). High-temperature reaction in
the freeboard region above a bubbling fluidized bed. Ind. Eng. Chem. Res., 49, 2672-2680.
DOI: 10.1021/ie901760f .
Higman, Ch. & van der Burgt, M. (2008). Gasification, 2nd ed., Elsevier: Amsterdam.
Knoef, H. A. M. (Ed.) (2005). Handbook of Biomass Gasification, BTG biomass technology
group: Enschede, The Netherlands.
Kunii, D. & Levenspiel, O. (1991). Fluidization Engineering, 2nd ed.: ButterworthHeinemann: Boston.
31
Lee, S. K., Jiang, X., Keener, T. C. & Khang, J. (1993). Attrition of lime sorbents during
fluidization in a circulating fluidized bed absorber. Ind. Eng. Chem. Res., 32, 2758-2766.
DOI: 10.1021/ie00023a044.
Lin, L. W., Sears, J. T. & Wen, C. Y. (1980). Elutriation and attrition of char from a large
fluidized bed. Powder Technol., 27, 105-115. DOI: 10.1016/0032-5910(80)85045-5.
Oates, J. A. H. (1998). Lime and Limestone: Chemistry and Technology, Production and
Uses, Wiley-Vch: Weinheim.
Pohořelý, M., Svoboda, K. & Hartman, M. (2004). Feeding small quantities of particulate
solids. Powder Technol., 142, 1-6. DOI: 10.1016/j.powtec.2004.03.005.
Scala, F., Cammarota, A., Chirone, R. & Salatino, P. (1997). Comminution of limestone
during batch fluidized-bed calcination and sulfation. AIChE J., 43, 363-373. DOI:
10.1002/aic.690430210.
Scala, F., Montagnaro, F. & Salatino, P. (2007). Attrition of limestone by impact loading in
fluidized beds. Energy & Fuels, 21, 2566-2572. DOI: 10.1021/ef0700580.
Scala, F. & Salatino, P. (2010). Limestone fragmentation and attrition during fluidized bed
oxyfiring. Fuel, 89, 827-832. DOI: 10.1016/j.fuel.2009.03.024.
Sutton, D., Kelleher, B. & Ross, J. R. H. (2001). Review of literature on catalysts for biomass
gasification. Fuel Process Technol., 73, 155-173. DOI: 10.1016/S0378-3820(01)00208-9.
Yao, X., Zhang, H., Yang, H., Liu, Q., Wang, J. & Yue, G. (2010). An experimental study on
the primary fragmentation and attrition of limestones in a fluidized bed. Fuel Process.
Technol., 91, 1119-1124. DOI: 10.1016/j.fuproc.2010.03.025.
Yates, J. G. (1983). Fundamentals of Fluidized-Bed Chemical Processes, Butterworths:
London.
32
Zheng, J., Yates, J. G. & Rowe, P. N. (1982). A model for desulfurization with limestone in a
fluidized coal combustor. Chem. Eng. Sci., 37, 167-174.
2509(82)80151-6.
DOI: 10.1016/0009-