www.elsevier.com/locate/powtec

Powder Technology 138 (2003) 93–117

Characterization of bulk solids to assess dense phase pneumatic conveying

Luis Sancheza, Nestor Vasqueza, George E. Klinzinga,*, Shrikant Dhodapkarb

aUniversity of Pittsburgh, 826 CL, Pittsburgh, PA 15260, USAbDow Chemical Company, Freeport, TX, USA

Received 22 October 2002; received in revised form 20 August 2003; accepted 26 August 2003

Abstract

This work concentrates on being able to predict the feasibility of conveying particles in the dense phase mode by exploring some of the

basic characteristics of the particles in an assembly. The various suggested methods in the literature are reviewed and comparisons made with

new and existing data. Measurement of the permeability and de-aeration time of the particles are key parameters to providing a predictive

model. A multi-regression analysis has been carried out to provide a model determining the ability of particles to be conveyed in dense phase

pulsed piston operation.

D 2003 Elsevier B.V. All rights reserved.

Keywords: Bulk solids; Dense phase pneumatic conveying; Multi-regression analysis

1. Introduction

One of the most challenging issues in solids handling is

being able to predict ahead of time whether a powder or

granular material will convey in a dense phase plug format.

Until now, we have had to rely on conducting almost full-

scale testing on the material to ascertain if it will convey in

this mode. Other investigators have been asking this same

question and have proposed a number of techniques to

address the question. In general, measurements usually are

made on the material using table-top tests and the resulting

values are correlated to the actual large-scale testing or

inferred from known operating systems. Thus, one sees the

terms of bulk density, permeability factor and de-aeration as

being the most common properties measured and analyzed.

Previous researchers have made progress in the prediction of

dense phase capabilities of materials. The predictive meth-

ods, in our opinion, should be able to use properties of the

conveyed materials without extraordinary devices and

designs. Employing the unique methods is too specialized,

and generalizations are almost impossible to state.

In previous studies, little standardization was developed

on how the experiments should be conducted. As with many

0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2003.08.061

* Corresponding author. Tel.: +1-412-624-9630; fax: +1-412-624-

9639.

E-mail address: klinzing@provost.pitt.edu (G.E. Klinzing).

measurements on particulate systems, if standardization is

not followed, a variety of results can be obtained. One

example is the shear stress measurements employed by the

Jenike shear tester and others. These shear stress behavior

values are imperative in designing a bin or hopper, but they

are dependent on how the experiment is carried out and the

experience of the person who carries out the experiment.

For the tests of permeability factor and de-aeration, this

study has described the process for construction of the

experimental unit as well as the procedures for carrying

out the tests. This does not mean that former researchers

made errors, only that different conditions and equipment

that were utilized made it difficult to find consistency in the

results across investigators. This study will provide detailed

guidelines on the procedure and process. As time goes on,

these methods certainly can be modified and improved so

that a final consistent analysis can be carried out in all

laboratories.

1.1. Particle size, size distribution and shape

The particle size, size distribution and shape are crucial

parameters to assess whether materials will be conveyed in

dense phase flow. Dense phase flow can be construed to

mean two types of flow, the pulsed piston flow and the

wave-like motion flow of solids. Both of these flow types

can deliver large quantities of materials at lower velocities

than the dilute phase flow condition because of the higher

L. Sanchez et al. / Powder Technology 138 (2003) 93–11794

solids concentrations. It should be mentioned that it is

difficult to make broad statements about the ability to

convey materials in dense phase since innovative mechan-

ical designs probably can ensure that most material can flow

in dense phase. The amount of mechanical design needed

increases with the smaller-size material.

Generally speaking, if the particle size falls within in the

Geldart D classification—that is, in the 1- to 5-mm diameter

range—and the density is light, there is a natural tendency

for the particles to move in the pulsed piston fashion.

Larger-density materials such as iron oxide also have been

made to convey in the dense phase piston mode. These

materials have narrow particle size distributions which

generate very permeable plugs. If the particle size distribu-

tion is broad for the Geldart D material with considerable

fines, the permeability factor is significantly reduced. Using

mechanical devices, plugs can produce piston flow, but their

ability to reform into new plugs, once the plugs are broken

apart, is much reduced.

The Geldart D materials also can be conveyed in a wave-

like fashion forming easily into full plugs covering the total

cross-section of the pipe. Having a higher degree of fines

can provide ease in producing wave-type motion.

The shape of the particles is another parameter that must

not be forgotten. Generally, if particles have an interlocking

tendency, it will be easy to maintain the plug’s integrity than

if the particles are more spherical in shape.

Looking at Geldart C materials presents us with finer,

more cohesive materials. Since these materials are fine to

begin with, the size distribution is not as extreme. The

particle shape is less important in these materials, since the

surface forces dominant and adhesion is high, whether due

to moisture or electrostatics. Generally, using mechanical

methods can create a dense phase piston flow. Any degra-

dation in the piston presents a challenging problem to restart

the piston in the same format. Interlocking shapes can

increase the integrity of the plug. Geldart type C material

also has a tendency to form wave-like motion easily.

Cement and fly ash are notorious for this wave-like motion

of finer materials.

Geldart B materials are usually rather heavy in density

and medium in particle size, which makes them less likely to

form plugs on their own. Similarly, these materials probably

will not move in a wave-like fashion. If the shape of these

materials is interlocking, the plug probably can be formed,

but any degradation of the plug will present problems on

reformation of the plugs.

Type A Geldart materials are considered the best type of

free-flowing materials for dilute phase flow. Certainly, these

materials can form plugs, although using a mechanical

design to enhance the formation is desired.

1.2. Permeability

This parameter depends on particle size, size distribution

and shape and offers extremes, from a uniform-sized Geldart

D material with a large permeability factor to a cohesive C

material with low permeability factor. Generally, as the

permeability factor of the material decreases, the formation

of self-forming pistons decreases. For the finer material, one

will have to design systems to form the plug initially.

However, if the plug experiences degradation in the flow

process, reformation of these C materials into plugs will

prove difficult. The low-permeability-factor materials will

have a greater tendency to convey in a dense phase wave

fashion. The Geldart type A and B materials have perme-

ability factor between the Geldart type D and C limits.

1.3. De-aeration

The finer the material, the more difficult the experiment

and its reproducibility is. Air bubbles can be entrapped in

the materials which will cause surges and in the de-aeration

process. Large particles have short de-aeration times; denser

material reduces de-aeration time even further. Finer materi-

als settle more slowly, but present problems in the visual

observation. Fine materials often have a tendency to retain

the air longer than coarser materials. This tendency makes

them ideal candidates for transporting in a dense wave-like

fashion. Having very dense materials such as, iron oxide and

urania definitely would cause de-aeration to occur faster

than the cement and fly ash and would present a challenge

to the wave-like transport.

1.4. Surface characteristics (adhesion, moisture, cohesive-

ness, electrostatics)

All surface characteristics have the tendency to make

particles stick together more. Once formed in a piston or

plug, materials with large surface characteristics will keep

the plug’s integrity. As the particle size increases, these

forces tend to decrease and thus are less controlling to the

plug’s behavior. The smallest particles are dominated by the

surface forces, which usually present problems in one’s

overall ability to handle the material. Often times in pro-

cessing fine materials, the process will call for an agglom-

eration step to form the particles into large sizes for ease in

handling. This technique can be used to form fine particles

into Geldart D-like materials that would ease transport in

plug format.

1.5. Elasticity

Large particles that are elastic in nature have unique

properties. These particles can bounce and rebound differ-

ently than inelastic particles. They also have the tendency to

stick to the pipe surface and to themselves. If this stickiness

is dominant, conveying pneumatically is indeed a challenge.

Mechanical modes of transport probably would be preferred

for these materials. The stickiness can assist in the formation

of a plug and provide the glue to increase the integrity of the

plug. This stickiness also can increase wall friction, requir-

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 95

ing more force and thus more pressure to move the plug.

Smaller particles that are flexible probably can be com-

pressed more as the additional force is applied, which may

again make it more attractive to find another mode of

transport rather than pneumatic, since higher energy would

be required for transport in this mode. These elastic materi-

als probably will not be good candidates for wave-like

motion flow.

1.6. Temperature sensitivity

Except for ceramic-type material, most particles have a

low temperature limit that must be obeyed in pneumatic

conveying. Blowers are notorious for producing hot gases

and thus subjecting solids to high temperatures and the

risk of softening during conveying. In food processing,

this temperature limit is crucial to produce a saleable

product. Generally, dense phase conveying does not re-

quire cool transport air, since low velocities are experi-

enced. High velocities can generate significant impacts

that will cause point temperature increases and local

melting of the material. These impacts can lead to an

overall stickiness to the pipe wall that may cause total

blockage. One question that must be asked before consid-

ering conveying both dilute and dense is: what is the

softening temperature of the material? Design of a system

that will maintain a lower temperature that the softening

point is essential. Even with fine material such as coal,

one can experience impact temperature increasing build up

of material on the wall of the pipeline, eventually causing

blockages with time.

Fig. 1. Geldart Classification for Fluidizati

2. Review of existing efforts on characterization for

dense phase conveying

The potential to classify bulk solids to determine the

feasibility of conveyance has been of interest to many

researchers. While previous investigators carried out experi-

ments consistently, their individual work does present differ-

ences. A review of their studies presents their findings.

Geldart [1] classified materials based on the particle size and

density was first employed in assessing the fluidizing

characteristics of materials (Fig. 1). Dixon [2] used the

Geldart classification as a beginning and looked at these

systems under increasing external pressures. He used the

criteria of naturally slugging. His findings lined up rather

well with the Geldart classification. The work of Mainwar-

ing and Reed [3] measured the permeability factor and the

de-aeration of particles to assess the potential for dense

phase conveying. As stated, table-top experiments to pro-

vide this information would be very useful for the designer

and engineer. Two plots were developed by these research-

ers, one having the permeability factor vs. the pressure drop

per unit length and the other with the de-aeration factor and

the pressure drop per unit length. Jones and Mills [4] noted

that the Geldart classification is too broad to assess the

conveying properties of materials. They also noted that,

according to their studies, several materials from the Geldart

and Dixon classification group appear in the wrong classi-

fication for conveyability. These researchers used vibrations

to eliminate the influence of external vibrations on the

particle behavior. Pan [5] addressed the minimum superfi-

cial air velocity needed to transport solids in slug flow. An

on, with the data used in this study.

L. Sanchez et al. / Powder Technology 138 (2003) 93–11796

experimental unit was employed that passed air through a

fixed volume of solids suspended between two porous

plates. A linear expression was used to present the data of

the pressure drop with the air flow rate. Fargette et al. [6]

concentrated on bench-scale tests that could provide insight

into pneumatic conveying behavior. Using data on de-

aeration time and permeability factor, they found that

Geldart Types C and D powders are acceptable for convey-

ing in dense phase slugs. Pan et al. [7] used a similar

apparatus as Pan [5] to explore the plug velocity, using a

pressure drop expression across a plug developed by Mi [8],

under Wypych’s direction. Pan et al. [9] carried out a similar

study to that of Pan [5] with similar results. Chambers et al.

[10] developed a dimensionless parameter to distinguish

modes of transport in pneumatic conveying. This parameter

multiplies the ratios of the particle density by the perme-

ability factor, then divides the total by the de-aeration time

constant. In exploring the de-aeration phenomenon, Ken-

nedy [11,12] determined the de-aeration rate of air for a bulk

solid from a fluidized state followed an exponential decay

format. The extrapolation of the rate to a zero plenum

chamber condition was employed along with a normaliza-

tion technique to account for varying bed heights. Pan [15]

considered the concept of a loosely poured bulk density and

the mean particle size as a technique to characterize materi-

Fig. 2. Permeability factor tester—

als for determining the appropriate modes of pneumatic

conveying. Three groupings of solids were defined. The

modes of transport were established by the author and other

investigators. In an analysis by Pan et al. [9], they followed

the original work of Pan [5] and the follow-up articles by

Pan et al. [7] on measuring the properties of the slug in an

aerated state. Similar conclusions were reached in this work

as in the previous two works.

3. Experimental setup for characterization of particles

The permeability factor of a bulk material can be defined

as the rate with which air can permeate through a fixed bed

of bulk materials. In this study, our fluidization equipment

was also employed to measure the permeability factor, but

of course, at much reduced velocity. The permeability factor

also can be determined with a commercial permeameter.

3.1. The permeameter

The equipment to measure permeability factor in this

study was the same as the equipment used to measure the

de-aeration parameter and consisted of a rather standard

Fluid Bed Test columns. The columns were constructed in

15.24-cm diameter column.

Fig. 3. Relation between superficial velocity and pressure drop per unit length for various experiments of polystyrene (D-1).

L.Sanchez

etal./Powder

Tech

nology138(2003)93–117

97

Fig. 4. Permeability factor average and standard deviation obtained for various experiments of polystyrene (D-1).

L.Sanchez

etal./Powder

Tech

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98

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 99

different sizes, from a 5.08-, 10.16- and 15.24-cm diameter

clear plastic (Plexiglas tube). For the permeability factor

measure, the experimental values obtained were found to be

the same for the 5.08- and 10.18-cm columns. Thus, these

determinations were not carried out on the 15.24-cm col-

umn. The column had a Dynapore screen made of com-

pressed metal that functioned as the distributor plate. The

pore size (28 Mesh or 595 Am and 400 Mesh or 37 Am)

permitted a good distribution of air through the bed. The

pore size used for the distributor plates for three columns

depended on the diameter of the particles being studied. For

instance, for materials with mean diameter of 100 Am, a

pore size of 50 Am or 400 mesh also is required.

Fig. 2 shows the schematic with the dimensions of the

apparatus for the studies of the 15.24-cm diameter column.

The plenum chambers for the columns were made

deliberately small in order to reduce the escape time and

resistance for the de-aeration tests. For the 15.24-cm col-

umn, the plenum volume was 463 cm3, reduced with the

volume of Raschig rings to assist with the distribution of air

to the bed.

3.1.1. Auxiliary equipment

The airflow to the column came from the house air

compressor. The airflow was regulated by needle valves

before the air rotameter (Brooks Serial Number 6806-47428

Table 1

Summary of materials characteristics

Properties of the materials for this study

CODE Name Density

(kg/m3)

particle

dp, Particle

mean (Am)

P

f

(

A-1 Alumina (NW) 3400 82.9 0

A-2 Alumina (Tabular A-3500) 3600 13.58 0

A-3 Alumina (Tabular 60-325) 3700 52.6 0

A-4 Glass bead 2500 67.5 0

A-5 Glass bead 2500 45.8 0

A-6 Titanium Dioxide 4100 44.28 1

C-1 Alumina (Tabular 64-20) 2500 26.7 N

C-2 Glass bead 2500 10.81 0

C-3 HDPE Powder 1100 7.67 0

C-4 Dolomite 2910 19.5 1

D-1 Polystyrene 912 5409 1

D-2 Polyester (Green Particle) 1400 3275 0

D-3 Polyethylene High Density 922 4000 1

D-4 Polyethylene Low Density 923 5412 1

D-5 Glass bead 2500 1000 N

D-6 Alumina (Tabular 64-1428) 3600 852 N

D-7 LDPE Pellet 998 2000 N

D-8 Polyester Polymer Green 1300 3275 N

D-9 Polyester (spherical) 1300 1000 0

B-1 Alumina (Pitt) 3800 486 0

B-2 Alumina (Tabular 64-2848) 4170 562 0

B-3 Alumina (Tabular 64-100) 4350 150 0

B-4 Glass bead 2500 203 0

B-5 Glass bead 2500 115 N

B-6 Glass bead 2400 450 0

B-7 Sand (NW) 2800 250 0

B-8 Sand (Pitt) 2700 100 0

with maximum flow of 42 SCFM at 70 jF and 30 psig.) and

measured by digital mass flowmeter (Micro Motion Model

IFT9701). The pressure in the delivery line was measured

with a wide range of differential pressure transducers

(Omega PX140, 162 and 164 models), depending on the

pressure drop range of the materials. Knowing the pressure

and the room temperature, the volumetric flow rate at

standard condition can be determined. The computer and

A/D convertor had the following specifications:

� Computer—Gateway Pentium III 500 MHz� Data acquisition (Series AT-AI-16-30)� LabView National Instruments (NI-DAQ)

3.1.2. Analysis and considerations

The permeability factor of a material may be expressed

as the relationship between the superficial air velocity and

the pressure drop of a gas passing through a fixed bed. The

permeability factor can be determined by using the follow-

ing equation:

Pf ¼DPA

LQð1Þ

From this expression, one can construct the plots of the

pressure drop across the bed with the gas flow rate, as the

example of polystyrene (D-1) shown in Fig. 3. The slope of

ermeability

actor, average

m2/bar�s)

umf (m/s) (DP/DL)c(mbar/m)

Shape

.39 0.048 9.4 Hexagonal

.05 0.12 9.5 Hexagonal

.005 0.008 15 Hexagonal

.13 0.021 13.4 Spherical

.07 1.0 12.5 Spherical

.06 0.06 35 N/A

/A N/A N/A Hexagonal

.11 0.006 48.5 Spherical

.236 0.014 35 N/A

.26 0.1 70 N/A

.72 1.2 62.5 Amorphous

.732 0.86 97.5 Cubic

.38 0.95 65.5 Spherical

.56 1.58 53 Elliptical—2/1 D ratio

/A N/A N/A Spherical

/A N/A N/A Hexagonal

/A N/A N/A Elliptical—2/1 D ratio

/A N/A N/A Cubic

.73 0.8 90 Spherical

.059 0.23 190 Hexagonal

.23 0.85 150 Hexagonal

.0051 0.0085 152.5 Hexagonal

.2 0.031 135 Spherical

/A N/A N/A Spherical

.0725 0.12 135 Spherical

.0239 0.032 131 N/A

.125 0.36 140 N/A

L. Sanchez et al. / Powder Techn100

this plot is related to the permeability factor. For each test,

the standard deviation of the slope could be determined.

Multiple experiments permitted an average value of the

permeability factor for each material to be found with its

associated standard deviation, as shown in Fig. 4. The plot

of the data of pressure loss per unit length with gas flow rate

utilized only the central section of the plot eliminating the

end conditions. The values within the middle 80% of the

plots were analyzed. These permeability factor values were

reported at 95% confidence levels.

3.1.3. Results

The permeability factor of the powders and granular

materials tests is summarized in Table 1 which also has

the following physical properties: particle density, size, de-

aeration factor, permeability factor, velocity of minimum

fluidization, quasi-steady pressure drop per unit length, and

shape.

3.2. Determination of de-aeration factor

The de-aeration factor of a bulk material can be defined

as the characteristics of the materials to allow them to retain

air. According to this definition, the de-aeration factor can

be expressed in different formats between the time and

pressure drops.

Fig. 5. Pressure decay curve obtained for 50-Am alum

3.2.1. The equipment

The equipment to measure the de-aeration factor is also

the Fluid Bed Test Column described previously. The

addition of a solenoid valve for the system is necessary to

have quick action when the air is shut off.

3.2.2. Analysis details

The slopes of the pressure and height of the column with

time were presented as the base data for the de-aeration

studies. Several experimental runs were performed to obtain

the average values of the de-aeration rate, presenting the

standard deviations of the data. Each test has its own slope

and standard deviation while multiple testing provided an

analysis of the reproducibility of the results. The mid-range

of the data was employed for the analysis, representing 10%

at the beginning of the test and at 20% before the end of the

test. Fig. 5 shows an example of a de-aeration test for

various experimental tests with 50-Am alumina.

We found that for Type C material, the time between

consecutive experiments should be short to avoid bed

agglomeration. Reproducing the test with Geldart Type C

materials proved challenging. It was necessary to run

several experiments, selecting the test where no air pockets

existed in the bed. The air pockets were seen visually or

indicated by pressure spikes over the average pressure drop

signal from the transducer.

ology 138 (2003) 93–117

ina (A-1) to de-aeration factor, for various tests.

Fig. 6. Regression analysis for linear (Mainwaring and Reed) and exponential (this work) models to de-aeration factor, for test of 50-Am alumina (A-1).

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 101

The analyses of the de-aeration times (see Fig. 6) were

those presented by Mainwaring and Reed [3], Jones and

Mills [4], and this study (2001).

4. Analyses of results

In analyzing the data obtained in this work, only the past

studies and models that had a relevant bearing were

employed. It should be noted that Section 2 contains a

complete review of the literature that exists in this area.

This research studied 175 different materials, covering

a wide range of bulk solid properties in an effort to asset

the ability of the materials to be conveyed in a pulsed-

piston format. In the process of exploring different

classifications, other modes of transport were also sug-

gested. A number of researchers have been able to carry

out experiments both in the classification manner as well

as performance conveying tests to establish the transport

conditions. Our study did a limited number conveying

tests.

The de-aeration data presented in this analysis are given

in three formats or definitions for the de-aeration factor:

Mainwaring and Reed [3], Geldart and Wong [13] and

Kwauk [14], and this work.

4.1. Analysis with Geldart’s1 approach

This classification of materials based on the particle size

and density was first employed in assessing the fluidizing

characteristics of materials. Some researchers have tried to

employ this information to predict pneumatic transport abil-

ities. Some believe that Geldart Type B particles that are

mostly sand-like in nature will not convey in dense phase

plug flow. Light Group D powders, of which plastic pellets

are a good example, naturally form dense phase plugs in

transport. Both Types A and Cmaterials can be transported in

dense phase plugs with varying degrees of difficulty often

with help from mechanical devices. Fig. 1 shows the Geldart

classification for the data used in this study.

Over the years, this diagram has been enhanced and

explored to establish a more detailed analysis of the regions

defined as A/C and B/D where the transition between the

various regions is not clear cut. The use of the Geldart

diagram to predict the flow regimes in pneumatic conveying

also has been proposed and considerable success has been

L. Sanchez et al. / Powder Technology 138 (2003) 93–117102

achieved in this realm. Table 2 is a listing of the principal

characteristics according to the Geldart classification for

both the fluidization process and for the pneumatic convey-

ing operation. Particular note should be made of the prop-

erties of permeability factor and de-aeration properties as

being important properties needed for the pneumatic con-

veying analysis. Fig. 7 is a graphical representation of all the

particles that have been studied in this work, as well as the

work of Mainwaring and Reed [3], Chambers et al. [10],

Pan [5], Jones and Mills [4], and Fargette et al. [6]. The

material from this study is indicated as the Pitt material [16].

It should be noted that the present study covered all particles

with the Geldart classifications of A through D, with a

number that span the A/C and B/D ranges. The Geldart

diagram is divided to four areas A, B, C and D. These four

groups have a similar flow capability and can give some

indication of the potential conveyability and mode of flow.

Also, we have to emphasize that an important amount of

materials are in the boundary of each group, such as:

A/C A/B B/D

. Pulverized Fuel

Ash (20 Am)

. Coal (degraded)

(146 Am)

. Slate dust (500 Am)

. Coal (20 Am) . Sugar (157 Am) . Alumina (435 Am)

. Cement (14 Am) . Copper ore

(55 Am)

. Granular

Sugar (720 Am). Some kind of

alumina (50, 60 Am)

. Polyethylene

Powder (825 Am). Pulverized fuel

ash (700 Am)

4.2. Analysis with Mainwaring and Reed’s3 approach

Mainwaring and Reed generated a diagram for the

potential of dense phase conveying according to the

Table 2

Principal properties of Geldart classification

Properties Group A Group B

Type of material Powder Coarse

Mean diameter, Am 20 to 50–100 50–100 to 500–1000

Density, kg/m3 1000 to 4000 1000 to 5000

Fluidization Considerable bed

expansion before Vmf

Naturally occurring

bubbles start at Vmf ;

bed expansion is small

Pressure drop at

minimum fluidization,

mbar/m

< 50 > 80

Permeability factor,

m2/bar s

0.1 0.01–0.1 to 1

De-aeration Collapses slowly Collapses very rapidly

Type of flow in a

conventional system

Moving bed Not likely to convey in

dense phase

Examples Fly ash, pulverized coal,

flour, PVC powder,

alumina, sugar, etc.

Sand, granular sugar, alu

semolina, PVC granules,

minerals powder, glass b

permeability factor of material and the pressure drop per

unit length at minimum fluidization. This plot is seen in

Fig. 8. In general, they defined two different areas: the

data points above the line of constant minimum fluidizing

velocity (50 mm/s) are noted as those that could be

conveyed in a dense phase plug flow. These materials

have a high permeability factors; while the other data

points below the line as that can be conveyed in a moving

bed format or not in dense phase flow. According to Fig.

8, the materials Geldart Type D and some B can be

conveyed in dense phase plug flow, while the A, C and

some B materials cannot be recommended for the dense

phase pulsed piston conveying.

Fig. 8 notes that there is overlap between the Geldart

classifications using this classification process. Some mate-

rials are in the boundary of regions A/C and B/D such as

granular sugar, coal, certain kinds of sand, fly ash, certain

types of alumina and glass beads. This plot also contains the

data of Mainwaring and Reed [3], Chambers et al. [10], Pan

[5]; Jones and Mills [4], Fargette et al. [6], Mi (1990) and

the data from this study.

Mainwaring and Reed also generated a plot using the de-

aeration data (according to their linear model) from the

process of de-aeration of materials from their fluidized state

as a function of the pressure drop per unit length at minimum

fluidization as shown in Fig. 9. They found that materials

that exhibited high values of the results of de-aeration

divided by the particle density can be conveyed in a moving

bed flow while other materials below the demarcation line

are best conveyed in the plug-type flow or cannot be

conveyed in dense phase flow at all. In this region, one finds

the Geldart B, C and D materials. The line of demarcation in

this figure dividing the two regimes is the line of constant

X = 0.001 m3 s/kg. Fig. 9 shows the dominant areas for the

materials of different Geldart classifications. The legend in

Group C Group D

Cohesive fine powder Granular

< 20 > 600–1000

> 2000 < 3000

Normal fluidization is

very difficult

Naturally occurring

bubbles start at Vmf. Bed

expansion is small. High

flow forms plugs.

50–130 5–150

0.1 to 1 > 1

Collapses slowly,

good air retention

Collapses very rapidly

Can be conveyed in dense

phase but can be troublesome

Possibly candidates for

plug or slug flow

mina,

eads, etc.

Cement, Dolomite, pulverized

coal, titanium dioxide, fly ash,

aluminum powder, etc.

Plastic pellets, polyethylene,

wheat, glass beads, coarse

sand, seeds, etc.

Fig.7.Geldartclassification.

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 103

Fig. 8. Permeability factor vs. pressure drop per unit length.

L. Sanchez et al. / Powder Technology 138 (2003) 93–117104

Fig. 9 indicates the different materials used for comparison

as well as the data from this study.

The permeability factor data and the de-aeration data

were plotted against each other in Fig. 10. This figure

attempts to explore the division of the flow regimes using

the base properties of permeability factor and de-aeration

Fig. 9. De-aeration factor vs. pre

(according to Mainwaring and Reed model). The data from

this study should be reviewed first. All of the data points

indicated by a letter from the Geldart classification are from

this study. The points not preceded by a letter come from

other studies, for instance, A-1 for Alumina (83 Am) is from

this study. Two distinct regions seem to be present in the

ssure drop per unit length.

Fig.10.De-aerationfactorvs.thepermeabilityfactor.

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 105

L. Sanchez et al. / Powder Technology 138 (2003) 93–117106

overall comparison process. Analyzing the plot of the de-

aeration factor vs. the permeability brings out some general

conclusions but a degree of uncertainty throughout. Gener-

ally, Geldart Type A materials with low permeability factor

and high de-aeration factor values can convey in a moving

bed mode. Geldart Type D materials with lower de-aerations

than Type A and high permeability factors are conveyed in

plug type flow. Geldart Type B materials fall into the dilute

phase, dense phase (high solids concentration flows). Gel-

dart Type C fall in all three regions of designated flow.

4.3. Analysis with Pan’s15 approach

Pan classified the facility of the materials conveyed in

dense phase as a function of loosely poured bulk density

and median particle diameter. In general, Pan developed a

flow mode diagram classifying the products into three

groups (PC1, PC2 and PC3). The lines noted in Fig. 11

were set by Pan. Pan showed that materials in the group

PC1 can be transported smoothly and gently from dilute

to fluidized dense phase, usually fine powders. According

to this research, the materials in the PC1 category are

Geldart Types A and C, and some materials in the

boundary A/B.

Fig. 11 indicates this behavior with the data designated

by regions A, B, C, and D for the different references used

in this study.

Materials in group PC2 usually light and free-lowing

granular materials can be transported in the dilute phase or

slug-low.

According to this research, the materials that have these

properties are some types of Geldart B and D materials with

a true density of less than 2000 (kg/m3) and loosely poured

densities of less than 1000 (kg/m3). Fig. 11 indicates the

data points with (area B) and (area D) from the references

used in this study.

Materials in group PC3, consisting usually of heavy

granular and/or crushed products, can be conveyed in dilute

phase only. Also, some light, fibrous and/or spongy materi-

als fall into this category. According to this research, the

materials that have these properties are some types of

Geldart B and D with true density larger than 2000 (kg/

m3) and loosely poured density greater than 1000 (kg/m3).

As shown in Fig. 11, some data points with from different

studies are noted in this region PC3.

4.4. Analysis with Chambers et al. [10] approach

In this study, a characterizing dimensionless parameter

was developed to distinguish modes of transport in pneu-

matic conveying. This parameter multiplies the ratios of the

particle density by the permeability factor, then divides the

total by the de-aeration time constant, Nc = qsqf/tda.

These researchers performed their parameter analysis

using modes of transport observations from various

investigators.

In addition, these investigators developed a dimension-

less expression to establish boundaries for various types of

transport. For dense phase flow, the expression below is

shown by the following inequality being greater than 0.04.

mpu½gDfqp=qi � 1g0:5

ðFrpÞ�0:1ðdp=DÞ1=6 > 0:04 ð2Þ

The data of Martinussen [17] was used extensively in this

analysis.

Chambers introduced a pneumatic flow parameter, Nc,

defined as:

Nc ¼qsPf

tdað3Þ

According to Chambers, Nc can indicate the feasibility of

conveying the materials in either of the following three flow

modes:

(i) dense phase slugging mode;

(ii) lean phase mode;

(ii) dense phase moving bed mode.

The materials that can be conveyed in a dense phase

mode also can be conveyed in a lean phase.

To compare different data with the Chambers analysis, it

is necessary to define the type of de-aeration factor used in

the calculations. For instance, Chambers used Martinussen

data [17], where the de-aeration time, tda, was determined by

fitting the expression DL/DL0f exp (� t/tda) with the data,

where tda is a parameter of correlation, DL is the decrease in

bed height after t s, and DL0 is the bed height at t= 0 s.

However, Fargette et al. [6] estimated the de-aeration time as

the time (expressed in seconds) between when the valve is

shutoff and the pressure drop reaches zero. The definition of

the de-aeration time is defined in our present work using the

expression DP/DL0f exp (� t/tda) in correlating the data.

According to Chambers, large Nc values (0.01) generally

suggest that the material is a good candidate for slugging

dense phase conveying, whereas low Nc values (0.001)

indicate that the material is a good candidate for a dense

phase conveying in a moving bed flow. However, moderate

Nc values (0.01>Nc>0.001) indicate that the material can be

conveyed only in a lean phase mode.

It should be noted that Nc is affected by the values of tda,

which can depend on the size of a plenum chamber and

column being tested.

4.5. Chambers et al. analysis with Martinussen data

Fig. 12 portrays the determination of Nc for the Marti-

nussen data. According to Chambers et al., the materials that

can be conveyed in slugging dense phase are Geldart Type

D materials and some materials in the Geldart boundary B/

Fig. 11. Flow mode of bulk solid materials in pneumatic conveying in function of mean diameter and loose-poured bulk density.

L.Sanchez

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107

Fig. 12. Nc for a range Geldart classification, with tda according to Chambers.

L. Sanchez et al. / Powder Technology 138 (2003) 93–117108

D. The materials that can be conveyed in dense phase

moving bed are Geldart Types B materials and some

materials in the boundary A/B along with one Geldart Type

C material. The materials that can be conveyed in lean phase

mode are Geldart boundary A/B.

Martinussen data are sparse, this presents difficulties in

establishing a definitive general conveying mode.

4.6. Chambers et al. analysis with data of Kennedy [12]

and Sanchez

An attempt was made to use the data of Kennedy [12]

and Sanchez to test the Chambers classification. This was

challenging since permeabilities needed to be assumed and

de-aeration times were measured with different techniques.

First, we assume the permeability parameters

Geldart Type A pf = 0.1 (m2/bar�s)Geldart Type B pf = 0.1 (m2/bar�s)Geldart Type C pf = 0.001 (m2/bar�s)Geldart Type D pf = 10 (m2/bar�s)

Then employing the de-aeration times designated by each

researcher, we observed two grouping of data for Nc: one for

Nc less than 0.1, which generally is a lean phase mode of

conveying: and the second for Nc greater than 1.0, which are

dense phase slugging mode conveying. The latter materials

are of the Geldart type D, which are well known to be

conveyed in this mode of transport. This analysis generally

shifts the Chambers values for Nc higher than the original

projection. This procedure was not successful in incorporat-

ing data outside the data used by Chambers for a general

interpretation.

4.7. Chambers et al. analysis with data from various

researchers

Our finding were analyzed using the Chambers et al.

analysis and the data of Mainwaring and Reed; Jones and

Mills; Fargette et al.

The wide range of data show that there are some overall

trends to predict the feasibility of the materials conveying in

pneumatic modes, but by no means are they definitive. It

should be noted, however, that the Mainwaring and Reed

data, with the different modes of conveying, fit the Cham-

bers prediction of Nc very well.

4.8. Analysis with Kennedy’s [11,12] approach

Kennedy classified the conveyability of the materials in

dense phase as a function of the de-aeration time constant

(DTC). This de-aeration time constant was determined by

the rate of decay in pressure drop across a de-aerating bulk

solid at minimum fluidization. Using a decay rate function

to represent the data, the DTC was determined.

Kennedy proposed a classification based on his experi-

ments with the pneumatic transport of a range of materials.

Using the de-aeration time constant, he established the

following classifications for predicting the mode pneumatic

conveying:

DTC < 5: DTC of less than 5 represents either coarse

heavy materials or fine cohesive materials. The coarse

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 109

materials may be suitable for lean phase conveying, slug

flow, or low-velocity plug flow with rounded and non-

interlocking particles. The fine cohesive materials are

likely to be difficult to handle by pneumatic conveying,

thus resisting fluidization and entrainment in the air

stream. Fig. 13 shows that the predominance of materials

in the Geldart Type B, boundary A/B and some Type C

materials belong to this category. It should be noted that

Chambers assumed Type D materials had a value of DTC

of 1.

DTC 5–15: These materials are difficult to convey,

particularly in dense phase and at low velocity. Severe

pipe vibrations and blockages are likely under these

conditions. These materials may perform well in bypass

systems and are suitable for handling by air slides. Fig.

13 shows that these materials are Geldart Types C, A, B

and A/B.

DTC 15–25: This region is a transition range which

includes some materials that may be expected to perform

satisfactorily in pneumatic conveying systems and others

that likely are to require bypass systems or secondary air

injection. Fig. 13 shows that Geldart Type C, and A/B

materials are in the range. It should be noted that there is

a limited amount of data in this narrow range.

DTC >25: These materials have good air retention

characteristics (plastic pellets) and likely are to be the

most suited for dense phase pneumatic conveying,

particularly as the normalized time constant exceeds 40

s/m. Fig. 13 shows that materials of Geldart Type C and

some D as well as the boundary region A/C fall in this

range.

Fig. 13. Normalized de-aeration time for a range o

Overall, one notes that the Kennedy classification

appears to be a more reliable method to predict pneumatic

conveying modes than the Geldart or Dixon’s classifica-

tions. In order to refine the prediction of pneumatic con-

veying modes, one should utilize additional tests such as

fluidization, permeability factor, and de-aeration time.

4.9. Fargette et al. [6]

Fargette et al. classified the conveyability of the materials

in dense phase as a function of permeability factor, air

retention characteristics and cohesion of powders. Their

research concentrated on powders used for the manufacture

of steel.

They introduced the following pneumatic flow parame-

ter, which depends on gas diffusion properties:

X ¼ tda=Pfqb ð4Þ

According to Fargette et al., X can indicate the conveyability

of the material in any of the following three flow modes:

(i) dense phase plug flow;

(ii) dense phase moving bed;

(iii) dilute phase.

They first studied the relationship between the permeability

factor and the de-aeration time. They found five different

ranges of permeability factor:

� very high, over 4 (m2/bar�s);� high, between 2 and 4 (m2/bar�s);

f Geldart classification—Kennedy’s analysis.

L. Sanchez et al. / Powder Technology 138 (2003) 93–117110

� intermediate, between 0.2 and 2 (m2/bar�s);� low, between 0.07 and 0.2 (m2/bar�s);� very low, under 0.07 (m2/bar�s).

They also found three different ranges of de-aeration time:

� high, over 70 s;� intermediate, between 5 and 70 s;� low, under 5 s.

According to the ranges previously defined, five areas

emerged, as seen in Fig. 14.

Area I: The powders are very fine, cohesive, have a very

low permeability factor with high de-aeration times and

can be conveyed in a dense phase flow. Fargette et al.

proposed that if the materials in this region are not too

cohesive, they will be suitable for dense phase in a

moving-bed type flow. Materials in this area are Geldart

Types C and boundary A/C.

Area II: The powders are very coarse bulk materials,

characterized by a very high permeability factor and very

small de-aeration time, which also can be suitable for

dense phase, but in plug flow. Materials in this area are

Geldart Types D.

Area III: These powders have a slightly lower

permeability factor than Geldart D powders and exhibit

little or no air retention. These materials are considered

to have intermediate pneumatic conveying performance.

Materials in this area are Geldart Types B and

boundary B/D.

Areas IV and V: Materials in these Areas mostly are

Geldart A and B powders, which have intermediate

permeability factors. Materials in Area IV have larger de-

aeration times than materials in Area V that exhibit little

or no air retention. No straightforward conclusion in

terms of pneumatic conveying performances can be

drawn for the materials in Areas IV and V. It seems that

extra parameters need to be taken into account to

determine the potential conveyability of these materials.

For the two Areas (IV and V), Fargette et al. proposed

considering other parameters to reach a conclusion in terms

of pneumatic conveying. One parameter could be a measure

of the cohesion of the material.

Fig. 15 shows the distribution of the dimensional

number, X proposed by Fargette et al. for a range of

Geldart classification. This parameter, combined with the

cohesion, can allow the classification of the materials in

terms of pneumatic conveying performance. According to

these authors, at low values of X (under 0.1) and low values

of cohesion, the materials can be conveyed in plug flow. At

high values of X (over 190) and high values of cohesion, the

materials can be conveyed in a moving bed type flow. Small

values of X (around 0.5) and small cohesion values are

expected to have an intermediate pneumatic conveying

performance. This also holds true for powders with inter-

mediate values of X and cohesion.

4.10. Dimensional analysis

A number of different dimensionless groups were

explored to find a correlation that would allow one to

take the basic data of particle characteristics, permeability

factor and de-aeration factors and establish if a plug flow

would occur.

Previously, we reviewed the work of various researchers

who were trying to establish different correlations between

the principal properties of the materials and the plug flow

mode. In the following analysis, the relationship between

the principal material properties for each Geldart classifica-

tion was explored, such as:

� Particle density (qp)� Bulk density (qb)� Minimum fluidization velocity (umf)� Quasi-steady pressure drop (DP/DLc)� De-aeration time-Jones (tda-Jones)� De-aeration time-Sanchez (tC)� Mean particle size (dp)� Permeability factor ( pf)

The analysis was performed in terms of the four Geldart

classifications (A, B, C and D) and three boundaries (A/B,

A/C and B/D). Specific Geldart classification information

was not available for Fargette et al.’s data, although the data

are known to comprise mainly Type A, C and some B.

These data are therefore plotted only in terms of their values

without type classification. The analysis of all parameters

was performed to find a relationship for two and three

dimensions.

From Fig. 16, we can observe that the data tend to

form a cluster for each Geldart classification material.

Table 3 summarizes the range values of the parameter

studied for each cluster and the principal characteristics

observed in the flow mode according to different

researchers.

It can be concluded, therefore, that the permeability

factor, de-aeration, mean particle size, and density can be

inter-correlated. This provides us with a method to predict

one parameter while measuring only a limited number of

the others. The process then permits us to employ the

other predictive techniques for modes of flow to assess if

the flow should be dense phase or otherwise. For exam-

ple, since the de-aeration parameters are the most chal-

lenging to measure, knowledge of the permeability factor

and prediction of the de-aeration time can then permit us

to go to the methods of Mainwaring and Reed, Kennedy

[11,12], Chambers and Fargette et al. to determine the

flow transport mode. Taking into consideration the anal-

ysis of the different parameters in the previous section

and the relationship between each parameter, dimension-

Fig. 14. tda vs. permeability factor for a range Geldart classification.

L.Sanchez

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111

Fig. 15. Dimensional number (X) vs. tda for a range Geldart classification.

L.Sanchez

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112

Fig. 16. Analysis of permeability factor as a function of tda-Jones and dp. All data including this work.

L.Sanchez

etal./Powder

Tech

nology138(2003)93–117

113

Table 3

Summary of the range parameters analyzed

Parameter (DP/DL)c, mbar/m Pf, m2/bar s qs, kg/m

3 qb, kg/m3 dp, Am umf, m/s tda-Jones, s tc, s

A Min. 4.0 0.005 800.0 100.0 13.6 0.0003 0.70 0.115

Max. 140.0 1.063 4100.0 1660.0 200.0 1.0000 300.00 56.818

Average 44.9 0.156 2262.7 756.5 78.0 0.0826 60.51 5.379

B Min. 9.5 0.005 990.0 400.0 64.0 0.0024 0.38 0.101

Max. 200.0 4.200 5710.0 2778.0 825.0 0.8500 65.00 3.125

Average 101.1 0.718 2812.7 1167.0 371.7 0.1278 19.31 0.978

C Min. 35.0 0.007 1060.0 368.0 7.7 0.0003 0.40 0.012

Max. 130.0 1.260 4250.0 1590.0 26.7 0.1000 500.00 5.577

Average 78.2 0.226 2438.9 769.0 16.7 0.0174 112.65 0.500

D Min. 3.0 2.300 834.0 458.0 782.0 0.0920 0.08 0.020

Max. 130.0 42.000 4655.0 1540.0 5412.0 1.5800 4.40 0.231

Average 69.2 12.661 1379.9 703.1 3080.2 0.8748 1.12 0.073

Jones Min. 1.3 0.028 0.0 26.0 – – 4.47 –

Max. 110.7 3.623 2950.0 1475.0 – – 200.00 –

Average 61.0 0.431 1118.1 724.7 – – 38.26 –

L. Sanchez et al. / Powder Technology 138 (2003) 93–117114

less relationship was probed. The dimensionless numbers

were defined independently as follows:

NC ¼ qsPf

tcð5Þ

X ¼ qbPf

tcð6Þ

RateðqÞ ¼qp

qb

ð7Þ

Fr ¼ umfffiffiffiffiffiffiffidpg

p ð8Þ

Fig. 17. Analysis of dimensionless num

qs;b ¼qs � qb

qs

ð9Þ

qs;g ¼qs � qg

qg

ð10Þ

Grt ¼lg

dpðqs þ qg=2Þtc ð11Þ

P* ¼Pfqs

ffiffiffiffiffiffiffigdp

p

dpð12Þ

tc = de-aeration time, according to Jones or Sanchez.

ber, P* as a function of Grt(tda).

Table 5

Parameters obtained from multiple regression analysis

Equation a b c R

P*(Gr,Fr) 10.0 � 3.0 1.1366 0.6

X(Fr,Gr) 0.002 � 0.326 0.7085 0.81

X(qs,g, qs,b) 1.094E6 � 1.1168 � 1.6005 0.83

X (qs,g, Fr) 2.154 � 0.5429 0.2784 0.52

X(qs,b,Gr) 0.6234 10.223 0.5308 0.88

Technology 138 (2003) 93–117 115

4.11. Probing the dimensionless groupings

The analysis shows that materials with similar Geldart

classifications tend to form regional clusters on the two-

dimensional figures developed. One should note that in

analyzing the dimensionless numbers’ inter-relationships,

some pairs of dimensionless numbers show a linear or

exponential relationship. In other cases, the dimensionless

numbers tend to cluster in different regions according to

Geldart classifications. Fig. 17 shows, for example, the

linear relationship between P* and Grt.

Therefore, it can be concluded that some dimensional

numbers can give an indication of the mode flow of the

material to be conveyed by noting former analyses about

flow modes and Geldart classifications.

Fig. 17 shows that some materials do not fall neatly into

the clusters that are typical for their Geldart classification

types. This could be explained by the cohesiveness, adhe-

sion, moisture, or electrostatics of the materials. It should be

noted that this also could be due to different techniques in

the measurement or methodology used.

In the same way that two-dimensional analysis was

performed, the three-dimensional analysis shows that

materials with similar Geldart classifications tend to

form regional clusters on the three dimensional graphs.

The result of this analysis is shown as range values in

Table 4.

For the three-dimensional analysis, the expression is

Grt ¼ aðFrÞbðP*Þc ð13Þ

where a and b are correlation parameters.

The best correlation in this study was obtained with Grt

as a function of P* and Fr. Table 5 summarized the best

parameter found for each correlation and the statistical

analysis.

It can be concluded, therefore, that some dimensionless

numbers can be predicted as a function of others. One then

L. Sanchez et al. / Powder

Table 4

Summary of the range value for dimensionless numbers

Dimension-less number Nc X� 103 Rate (q)?

A Min. 0.000003 0.069 1.6

Max. 0.062 909. 8.0

Average 0.0035 193. 3.4

B Min. 0.000003 0.313 1.7

Max. 0.017 1045 6.1

Average 0.0026 68 2.7

C Min. 0.000001 0.046 2.3

Max. 0.0917 1700 6.4

Average 0.012 352 3.4

D Min. 0.0234 0.001 1.2

Max. 1.96 0.085 6.1

Average 0.675 0.022 2.0

Jones Min. 0.0 0.404 2.0

Max. 0.004953 9615 2.0

Average 0.000304 944 2.0

can employ the same procedure as suggested previously to

explore and predict the modes of flow.

5. Conclusions

Dense phase conveying can be applied to a wide range of

products. This study was primarily concerned with which

parameters could be considered the best predictors of

material conveyability.

� The four Geldart classifications can give some

indication of the potential conveyability and mode of

flow. This classification is very useful for quick

estimation of the mode flow of certain materials.

Unfortunately, this classification alone is unsuitable for

predicting the potential conveying of material in a

dense phase mode.� The Dixon classification also is useful for quick

estimation of the flow modes, but it is still imprecise

for an accurate estimation.� The Mainwaring and Reed analysis, based on the

permeability factor and the de-aeration factor, provides

a more reliable predictive method of flow modes than the

Geldart and Dixon approaches. Using this analysis, this

work related their findings to four dominant regions of

the Geldart classification.

Fr kg/m3 qp kg/m3 qb Grt� 104 P*

0.000007 666 379 15.49 0.0015

11.5 3416 875 18380 0.177

1.42 1885 661 2243 0.035

0.087 824 400 0.076 0.008

11.9 4757 837 380 3.67

1.89 2343 568 46.1 0.58

0.026 882 568 64.3 0.0008

7.23 3541 844 90790 2.01

1.38 2031 680 31410 0.25

0.636 694 194 0.0005 3.23

9.34 3878 835 0.163 83.16

4.99 1149 444 0.031 25.54

– 42.3 500 – –

– 2457 500 – –

– 1207 500 – –

L. Sanchez et al. / Powder Technology 138 (2003) 93–117116

� Jones and Mills noted that the Geldart classification is

too broad to assess the conveying properties of

material. They also classified the suitability of material

for dense phase conveying as a function of perme-

ability factor and de-aeration factor. They have defined

three groups with different characteristics for the

conveyability of the materials. Since these researchers

used vibrations in the methodology in determining the

de-aeration factor, comparison with other data was not

possible.� Pan classified the ability of the materials to be

conveyed in dense phase as a function of loosely

poured bulk density and median particle diameter.

This analysis was compared with the findings of

Geldart, Dixon and Mainwaring and Reed and showed

agreement.� Chambers introduced a pneumatic flow parameter that

can indicate the feasibility of conveying material. With

the data Chambers analyzed, it is difficult to establish a

definitive conveying mode, but by using the de-aeration

factor defined in this study, good agreement was found

with the three flow modes of conveying.� Kennedy [11,12] classified the conveyability of the

materials as a function of a de-aeration time constant.

Three regions were defined in this analysis, and the data

evaluated by this present study had a good agreement

with the three flow modes.� Fargette et al. classified the conveyability of the materials

as a function of permeability factor, air retention

characteristics and cohesion of powders. In the analysis

of permeability factor vs. de-aeration factor, five areas

were defined. The analysis of the data considered in the

present work had very good agreement with the

definition for each area and the conveying characteristics

of the material. It also should be noted that the results of

this research agree with the work of Geldart, Dixon, and

Mainwaring and Reed.� Determining the dense phase conveyability of materials,

depends on the materials properties: The Primary Parameters: particle size and size

distribution; shape; particle and bulk density;

permeability factor; de-aeration factor; fluidizability;

cohesiveness. The Secondary Parameters: Adhesion, moisture,

electrostatics, elasticity, temperature sensitivity.� Parameters such as particle and bulk density, perme-

ability factor and de-aeration factor, mean particle size,

and minimum fluidization properties can indicate the

flow mode of the material studied. It was observed that

the data studied tend to form clusters according to

Geldart classification.� The two-dimensional analysis showed that some pairs of

dimensionless numbers are inter-related in a linear or

exponential manner. By measuring the parameters which

are more easily determined experimentally (permeability

and minimum fluidization velocity), the more challeng-

ing parameter of de-aeration can be predicted. The flow

modes then can be determined with the methods

suggested by other researchers who employed these

parameters in their analyses.� The three-dimensional analysis also showed success in

correlating the physical parameters of the materials

studied. Again, the easier measurement parameters could

predict the parameters that were more challenging to

measure.� The analyses show that some materials do not fall

neatly into the clusters in line with their Geldart

classification types. This most likely can be explained

mostly likely because of the secondary parameter

properties of materials (such as cohesion, moisture,

etc.), which can affect the flow modes of the

materials.� The best correlation found in this study was obtained

using the dimensionless numbers that are a function of

permeability factor (P*), de-aeration factor (Grt), and

minimum fluidization velocity (Fr).

Nomenclature

A cross-sectional area of the bed

Af de-aeration factor =DP/L*tdaa constant in the pressure drop equation

b constant in the pressure drop equation

D diameter of the bed

dp particle diameter

Frp Froude number—ut/(gdp)0.5

Fr Froude number based on minimum fluidization

velocity,umfffiffiffiffiffidpg

pg gravity constant

Grt dimensionless number, aðFrÞbðP*Þc¼ðlg=½dpðqpþqg=2ÞÞtc

L length of the bed

mf mass flow rate of gas

Nc dimensionless number, (qpPf)/tcP pressure

P* dimensionless number—Pfqp

ffiffiffiffiffiffiffigdp

p ��=dp

pf permeability constant

Q volumetric flow rate

tda de-aeration time

tc de-aeration time

umf velocity at minimum fluidization

umb velocity at minimum bubbling

u, usp superficial gas velocity

upu pickup velocity

Greek

qb bulk density

qs density of the particle

Rate(q) dimensionless number (qs/qb)

qp;b dimensionless number (qs–qb)/qpqp;g dimensionless number (qs–qg)/qgX dimensionless number of Kennedy [13]—tda/Pf �qb

lg viscosity of the gas

L. Sanchez et al. / Powder Technology 138 (2003) 93–117 117

References

[1] D. Geldart, Powder Technology 7 (1973) 285–292.

[2] G. Dixon, Proceeding of Int. Conf. on Pneumatic Conveying, 16–18

January, Cafe Royal, London, 1979.

[3] N.J. Mainwaring, A.R. Reed, Permeability and air retention character-

istics of bulk solid materials in relation to modes of dense phase

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