Acta Polytechnica


doi:10.14311/AP.2014.54.0052
Acta Polytechnica 54(1):52–58, 2014 © Czech Technical University in Prague, 2014

available online at http://ojs.cvut.cz/ojs/index.php/ap

THE INFLUENCE OF SIZE FRACTION ON THE
COMPRESSIBILITY OF PINE SAWDUST AND THE

EFFECTIVENESS CRITERION FOR DENSIFICATION

Miloš Matúš∗, Peter Križan, Monika Kováčová, Juraj Beniak

Slovak University of Technology in Bratislava, Faculty of Mechanical Engineering, Namestie slobody 17, 812 31
Bratislava, Slovak Republic

∗ corresponding author: milos.matus@stuba.sk

Abstract. Particulate matter from biomass, e.g. wood sawdust, is very diverse. The basic parameter
describing the densification process of particulate matter is its compressibility, quantified by the
coefficient of compressibility. Knowing this coefficient for a specific material is a basic prerequisite for
the application of compressibility equations describing the densification process, and for calculating the
workload in the production process of high-grade solid biofuel. This paper deals with a methodology for
determining the compressibility factor for sawdust on the basis of experiments to quantify pine sawdust.
The experiments were performed in two stages. The first stage was an experimental investigation of the
influence of size fraction on the final compressibility of pine sawdust. The results show the behaviour
of the pressure load when the parameters of the particulate matter are changed. In the second stage,
the experiments are evaluated and optimized to achieve minimum energy input of the process and a
maximum degree of densification. The research results will be used to develop new technologies and
machinery for biomass densification to achieve a high-grade solid biofuel.

Keywords: biomass, solid biofuel, compressibility, densification of biomass, effectiveness criterion,
briquetting.

1. Particulate matter from
biomass

For industrial compaction of biomass into the form a
fuel, it is necessary to disintegrate the material into
a homogeneous, fine fraction. Raw material (dendro-
mass or phytomass) treated in this way has properties
similar to those of particulate matter. For research
purposes, the raw material will be further considered
as referred to here as sawdust.
Particulate matter from biomass consists of solid

particles in contact with each other (solid phase), as
well as liquid and gaseous phases. The solid phase
consists of wooden mass (sawdust), the liquid phase
is water, and the gaseous phase is air. The liquid
and gaseous phases fill skeletal pores formed by solid
particles. The amount of liquid can be very small, and
may consist solely of water vapour absorbed on the
surface of solid particles. Because the solid particles of
biomass are highly porous, surface pores of particles
(open) and internal pores (closed) also coexist with
these external pores. The surface pores widen the sur-
face of the solid phase, while the internal pores affect
some basic physical properties, e.g. density, strength,
etc.
The solid particles come into contact with each

other. The existence of contacts restricts the freedom
of movement of the solid particles, i.e. their motion
autonomy, and thus determines the strength and stiff-
ness of the particulate matter. This depends on the
number and the strength of the contact bonds which

affect the size, shape, roughness and tensile strength of
the particle, the character of the interaction between
the phases, and the state of the particulate matter.
All the factors covered by the structure and its het-
erogeneity (alternation of films of finer and thicker
particles, particles of different composition, different
shape and orientation) are referred to as the texture,
sometimes called the macrostructure. The most im-
portant feature of particulate matter in general is
its transformation by the mutual movement of solid
particles (intergranular transformation). The degree
of motion autonomy of sawdust in the deformation
process varies according to the stress. With increasing
stress, the degree of physical autonomy decreases, un-
til the stress exceeds the ultimate strength of the solid
particles (sawdust) and leads to their disintegration.

Wood sawdust is particulate matter from biomass,
and can also be considered as a “consolidated ma-
terial”. Consolidated materials are solids that are
formed by joiningsolid particles into structural ele-
ments (by bonding or by consolidating them). For
wood sawdust, the consolidation process involves inter-
lacing, compacting and pressing the particles, which
are flat. Particulate matter from wood mass suitable
for direct compression usually has high porosity and
is in the state of loose powder, see Figure 1. The
porosity increases in proportion to the grain size and
larger fractions. The bulk density of the particulate
matter and its pressing is derived from this property
of the material.

52

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vol. 54 no. 1/2014 The Influence of Size Fraction on the Compressibility of Pine Sawdust

Figure 1. Particulate matter from wood mass suit-
able for direct compression.

2. Compressibility of particulate
matter from biomass, and a
methodology for determining
the coefficient of
compressibility

The compressibility of particulate matter from bio-
mass is a significant property that occurs during stor-
age, transport, compaction of bulk materials, and
a number of other technological operations. When
particulate matter is compressed, it densifies. The re-
duction in the volume of the particulate matter causes
a significant increase in the bulk density, and a reduc-
tion in porosity. There are two steps in compressing
bulk and non-cohesive materials. In the first step,
there is a significant change in density as the pores
between the particles are filled. Smaller particles fill
the spaces between larger particles, and the porosity
of the particulate matter is reduced. The size of the
pores is approximately equal to the size of the solid
particles. The motion autonomy of the particles de-
creases with reduced porosity until it is completely
eliminated. In the second step of compression a fur-
ther volume change takes place, but is significantly
smaller than in the first step. The second change is
due to filling of the pore cavities, which are smaller in
size than the primary particles. Hard particles there-
fore become deformed. When the material is exposed
to high pressure, the porosity can be reduced to zero.
In this case, the system will continuously form solid
contacts between particles and particulate matter.
The compressibility of particulate matter is mea-

sured by an instrument called an oedometer. A cylin-
drical sample of particulate matter of height h0 and
diameter D0 is placed in a ring that is loaded by
axial compaction force FZ through the piston (Fig-
ure 2). When it is sufficiently rigid, it is assumed that
the transverse expansion of the sample is zero, and
there is only volumetric reshaping of the particulate
matter in the direction of the ring axis. This is uni-
axial compression. The oedometer test determines
the compressibility curve of particulate matter, which
expresses the dependence of compacting force FZ on
the displacement of the oedometer piston h, i.e. the
compression of the sample.
The compacting force acting on the piston is cre-

Figure 2. Scheme of the function of an oedometer.

ated by movement of the crossbeam in the hydraulic
press. Compression is carried out at constant speed
and displacement. The increase in the force of com-
paction depending on the movement of the piston is
recorded graphically. Data for evaluating particulate
compressibility is obtained by the dependence of the
compacting force on the displacement of the piston of
the oedometer. Values from the compressibility curve
for a specific interval of pressure are transformed into
the resulting graph as log σ

σ0
depending on log ρ

ρ0
,

which is approximately linear. The coefficient of com-
pressibility K is determined by the slope of this line.

3. Experimental determination of
the coefficient of
compressibility of sawdust

Experiments were performed to determine the coeffi-
cient of compressibility of a material used for produc-
ing solid biofuels complying with European standard
EN 14961. The material was pine sawdust with vari-
ous fraction sizes: 0 to 0.5mm, 0.5 to 1.0mm, 1.0 to
2.0mm, 2.0 to 4.0mm and moisture 15.5%. For each
size fraction, seven densification experiments were car-
ried out at a constant pressing temperature of 20°C.
The arithmetic average of the measured values is used
in order to obtain the most relevant results. In the
experiments, measurements were made of the values
of compacting force FZ and the displacement of the
oedometer piston h. The compressibility curve shown
in Figure 4 was measured on the basis of the data.
The dimensions of the cylindrical pressing cham-

ber of the oedometer were: diameter D0 = 20mm,
height h0 = 229mm. Solid biofuels (wood briquettes,
wood pellets) made from sawdust are produced under
pressure from 90–130MPa, but at a high temperature.
In determining the compressibility of sawdust, the

53



M. Matúš, P. Križan, M. Kováčová, Juraj Beniak Acta Polytechnica

Figure 3. The oedometer used in the experiment.

Figure 4. Compressibility curve of pine sawdust of various fraction sizes (relative moisture 15,5%; pressing
temperature 20 °C).

interval from 1.9–159MPa was therefore considered.
The lower value of this interval was determined as the
lowest pressure at which no measurement errors are
caused by the piston entering the pressing chamber.

For a mathematical description of the uniaxial com-
pressibility of sawdust in the oedometer, we used the
simplified model of the Balshin formula for compress-
ibility:

σ

σ0
= A

( ρ

ρ0

)K
, (1)

where σ is the compressive stress at the calculated
point, σ0 is the initial compressive stress (at the start-
ing point of the measurement), ρ is the density of the
particulate matter at the calculated point, ρ0 is the
initial density of the particulate matter (at the start-
ing point of the measurement), K is the coefficient
of compressibility of particulate matter, and A is a

constant regulating the form of a function.
After modification, Equation (1.1) takes the form

of a slope equation for a line, where K represents the
slope of the line and its value is equal to the tangent of
the angle between the line and the positive direction
of the x axis. The coefficient of compressibility is
simply determined by the slope of this line:

log σ

σ0
= K logA+K log ρ

ρ0
. (2)

Calculating the coefficient of compressibility K on the
dependence of log σ

σ0
to log ρ

ρ0
, it was first necessary to

construct a dependence diagram of load σ (pressure)
on density ρ. Particular values of load σ at points of
the chart were calculated as the ratio of the forces
acting at each point and the constant circular surface
of the oedometer chamber with diameter do = 20mm.

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vol. 54 no. 1/2014 The Influence of Size Fraction on the Compressibility of Pine Sawdust

Movement of the oedometer piston h (mm) : Density ρ (kgm−3)
Fraction size (mm) 0.0–0.5 0.5–1.0 1.0–2.0 2.0–4.0

Sample weight m0 (kg) 0.0128 0.0104 0.0096 0.0066
Compacting Compacting h ρ h ρ h ρ h ρ
force FZ (kN) pressure p (MPa)

0.0 0.0 0.00 178 0.00 145 0.00 134 0.00 92
0.6 1.9 84.00 281 81.67 225 35.00 158 20.00 101
1.6 5.1 102.67 323 107.67 273 110.67 258 113.67 182
2.5 8.0 109.67 341 115.33 291 124.33 292 124.67 201
4.4 14.0 119.67 373 124.33 316 133.00 318 133.33 220
6.4 20.3 125.50 394 130.00 334 137.00 332 137.33 229
11.5 36.6 131.83 419 135.83 355 140.83 347 142.33 242
16.4 52.2 135.33 435 138.50 366 143.00 355 144.67 249
26.4 84.0 138.83 452 141.50 378 145.17 365 147.17 257
36.5 116.0 140.67 461 143.17 386 146.33 370 148.17 260
48.0 152.6 142.33 470 145.00 394 147.17 373 149.50 264
50.0 159.0 142.67 472 145.33 396 147.33 374 149.67 265

Table 1. Measured and calculated values obtained for densification of sawdust.

The loads at particular points of the chart were
calculated from the following relationship:

σ = FZ

S0
. (3)

Similarly, the density of the particulate matter at
different points of the chart was calculated from the
relationship:

ρ = m0

V0
, (4)

where m0 was the weight of pine sawdust for various
fraction sizes in the initial compressed volume V0 =
7.18885 · 10−5 m3. All measured and subsequently
calculated values are shown in Table 1. Then the chart
showing the dependence of load ratio σ

σ0
on density

ratio ρ
ρ0

was created. In the chart, the values σo and
ρo are initial values, i.e. the lowest load and density
value determined by measuring with the oedometer
(Figure 5).

Finally, the resulting curve relating log σ
σ0

and
log ρ

ρ0
was replaced by a standard linear approxima-

tion (Figure 5), the slope of which represents the
desired coefficient of compressibility K. It should be
mentioned that a linear approximation can be used
in cases where the shape of this curve is almost lin-
ear. For fraction sizes 0.0–0.5mm and 0.5–1.0mm the
curve is very similar to a line. The curve of this depen-
dence changes gradually from linear to exponential as
the fraction size increases. Since we want to compare
values while using the same method, we consider the
linear approximation.

Fraction Coefficient of
size (mm) compressibility (–)
0.0–0.5 7.97
0.5–1.0 7.09
1.0–2.0 4.07
2.0–4.0 3.60

Table 2. Coefficient of compressibility values. Bound-
ary conditions: particular matter — pine sawdust;
Relative moisture — 15.5%; Pressing temperature —
20 °C; Compacting pressure — 1.9–159.0MPa.

4. Results
Based on experiments on densification of pine sawdust
with a constant relative moisture content of 15.5%,
and a constant temperature of 20 °Cwith a compres-
sion pressure range from 1.9 to 159.0MPa (corre-
sponding to the compression force range from 0.6 to
50.0 kN), it can be concluded that the coefficient of
compressibility decreases with increasing fraction size
for this type of particulate matter. The resulting
compressibility coefficient approximation depends on
the mean of the examined fraction size ranges for the
boundary conditions shown in Figure 6. A summary
of the experimental results is presented in Table 2.
The evaluated experiments also introduce a sec-

ond output — a comparison of various sawdust frac-
tion sizes and the differences in their density during
compression. Figure 7 and Figure 8 show that the
difference in density of wood sawdust, at the same

55



M. Matúš, P. Križan, M. Kováčová, Juraj Beniak Acta Polytechnica

Figure 5. Dependence of log σ
σ0

on log ρ
ρ0

and linear approximation.

Figure 6. Resulting character of approximated coefficient of compressibility values, depending on the mean of the
fraction size ranges.

compacting pressure, increases as the fraction size
decreases. This fact has a big impact on the energy
efficiency of the whole densification process. The com-
pacting pressure is the input energy required for the
densification process. Determining its effect on the
density difference is of great benefit for the economy
of the densification process, and for the process of
solid biofuel production.
In order to compare the minimum energy input

for the process and the maximum degree of densifica-
tion for the four size fractions at a specific pressure
value, the Effectiveness Criterion for Densification was
created and calculated according to the relationship:

ECDi = ρi − ρi−1

pi
(kgm3/MPa). (5)

This criterion represents the ratio of the density dif-
ference per unit of pressure (kgm−3/MPa). A higher

value of the criterion for a specific pressure value in-
dicates higher energy efficiency of the densification
process. As is shown in Figure 7 and Figure 8, the Ef-
fectiveness Criterion for Densification increases as the
fraction size of the sawdust decreases, which means
higher energy efficiency of densification.
Wood sawdust is a “living” material. Therefore,

while it is being pressed, there is a difference in the
coefficient of compressibility not only due to the dif-
ferences in fraction size, but also due to the changes
in the pressing temperature and moisture content. It
should also be noted that in practical production of
solid biofuel by densification of wood sawdust, the raw
material is of varying fractional composition, i.e. it
does not have a uniform fraction size. The fractional
composition of the raw material has a major impact
on its compressibility. This will be a topic for future
research on biomass compressibility.

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vol. 54 no. 1/2014 The Influence of Size Fraction on the Compressibility of Pine Sawdust

Figure 8. Effectiveness Criterion for Densification of sawdust — detail.

Figure 7. Effectiveness Criterion for Densification of
sawdust — whole area.

5. Utilizing the coefficient of
compressibility for sawdust in
practical applications

The coefficient of compressibility for wood sawdust
is a very important parameter that describes the be-
haviour of this particulate matter during the densifica-
tion process into the form of a high-grade solid biofuel.
There are many biomass densification technologies
that are used for producing solid biofuels. On the
basis of the mathematical model describing these tech-
nologies, and on the basis of knowing the coefficient
of compressibility for a specific type of biomass, it
is possible to calculate the exact pressing forces, the
torques and the complex pressure ratios of the den-
sification process. This data is needed for designing
and optimizing the structure of compacting machines
and their functional components. With this data, it
will be possible to optimize machine design in terms
of strength, energy and minimizing production costs.

Acknowledgements
The research presented in this paper is an outcome of the
project “Research of the process of biomass densification
into the form of solid biofuel and experimental verification
of a mathematical model as an algorithm for the adaptive
control system of compacting machines”, supported by the
Program in Support of Young Researchers, funded by the
Slovak University of Technology in Bratislava.

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58


	Acta Polytechnica 54(1):52–58, 2014
	1 Particulate matter from biomass
	2 Compressibility of particulate matter from biomass, and a methodology for determining the coefficient of compressibility
	3 Experimental determination of the coefficient of compressibility of sawdust
	4 Results
	5 Utilizing the coefficient of compressibility for sawdust in practical applications
	Acknowledgements
	References