Full text of DOI:10.1111/j.1151-2916.2001.tb00715.x

J. Am. Ceram. Soc., 84 [3] 645–47 (2001)
journal
Permeability of Refractory Castables at High Temperatures
Murilo D. M. Innocentini,† Maur´ıcio G. Silva,† Bruno A. Menegazzo,‡ and Victor C. Pandolfelli*,†
Departamento de Engenharia de Materiais, Universidade Federal de Sa˜o Carlos, 13565–905 Sa˜o Carlos, Sa˜o Paulo, Brazil; and
ALCOA Alum´ınio S.A., 05804–900 Sa˜o Paulo, Sa˜o Paulo, Brazil
Temperature is an important factor affectng the permeation of
fluids in refractory castables. Because of experimental difficul-
ties, however, permeability parameters are usually obtained at
room temperature and then extrapolated to the temperature of
interest, with no concern regarding porous structure modifi-
cation (thermal expansion, etc.). In this work, an apparatus
has been developed to evaluate the air-flow permeability of
refractory castables at temperatures up to 800°C. The objec-
tive is to investigate modifications in the permeability con-
stants obtained by Forchheimer’s equation to provide a more
realistic relationship with castable processing and molten-
metal corrosion parameters.
velocity (determined by dividing the exiting volumetric flow rate
(Q) by the total free-flow area (A)), L the sample thickness, ␮ the
fluid viscosity, and ␳ the fluid density (calculated for Po).
Constants k1 and k2 are known, respectively, as Darcian (viscous)
permeability and non-Darcian (inertial) permeability.
For tests conducted at high temperatures, the changes in the
fluid properties must be considered for the evaluation of perme-
ability constants. Air density and air viscosity can be corrected
with temperature (T) according to the following equations:
Tr P
␳ ͑T͒ ϭ ␳
(2)
(3)
air
r
T Pr
1.5
T
398
I. Introduction
␮ ͑T͒ ϭ 1.73 ϫ 10Ϫ5
ͩ ͪ ͩ ͪ
air
273
T ϩ 125
MONG the parameters affecting the drying process and chem-
where ␳r is the gas density at the temperature Tr and pressure Pr of
reference. (In this work, ␳r ϭ 1.29 kg/m3 at Tr ϭ 273 K and Pr ϭ
1.013 ϫ 105 Pa). Equation (3) is referred in the literature as the
Sutherland equation.9
A
ical attack of refractory castables, permeability is one of the
most important.1–3 The literature, however, has related the castable
permeability to simplified equations that do not consider ade-
quately the interactions between the percolating fluid and the
porous medium. Permeability constants, obtained at ambient condi-
tions, are assumed to be constant with temperature increase, which, in
fact, may not occur. In this sense, there has been a lack of more-
accurate information to help the understanding and the optimization
of drying schedules and performances of refractory castables.3–7
In this work, an apparatus has been developed to evaluate the
permeability of refractory castables at temperatures ranging from
ambient to 800°C. The objective is to verify and quantify the
dynamic changes in structure with thermal treatment, allowing a
more realistic correlation between permeability and castable prop-
erties. Cement-free high-alumina self-flow refractory castable
samples have been used in the tests.
Because the air velocity (vso) is measured only at room
temperature (Tamb) and ambient pressure (Patm), the actual velocity
at the sample exit at the test temperature is calculated by
T Patm
vs͑T͒ ϭ vso
(4)
Tamb
P
Equations (1)–(4) can be applied to estimate the variation in the
pressure-drop curve of castables as the temperature increases.
However, even without experimental evidence, permeability con-
stants have been usually assumed in the literature to be invariable
with temperature.
(2) Permeameter Developed
II. Materials and Methods
The permeameter is comprised of two cylindrical chambers
(140 cm3 each) made of refractory stainless-steel SS-310S (service
temperature up to 870°C). A cylindrical sample holder made of a
special alloy with low thermal-expansion coefficient is fixed
between the chambers by stainless-steel bolts. Sample size is
typically 7.5 cm in diameter (4 cm exposed to air flow and 3.5 cm
for sample support) and 2–3 cm in thickness. Air is supplied by a
2 horsepower (1.5 kW) compressor through a 6 mm outside
diameter stainless-steel SS-316L tube directly to the bottom
chamber. Pressure measurements (0–10 bar (0–1 MPa)) are
conducted at the entrance and exit chambers using electronic
pressure transducers. The entire system (chambers and sample
holder) is set within an electric furnace (7.5 kW) controlled by a
proportional integral derivative (PID) system, which allows pro-
gramming up to 10 heating rates and 10 temperature plateaus. Air
is preheated in a 2 m long metal coil within the furnace chamber
before reaching the sample. Temperature is measured with K-type
thermocouples placed at the entrance and exit chambers. J-type
thermocouples are used to monitor the air temperature near the
pressure transducers and before entering into the flowmeter de-
vices. The exit temperature is applied for calculations of air density
(1) Permeability Modeling
Permeability of compressible fluids (gases and vapors) flowing
through rigid and homogeneous porous media can be well de-
scribed according to Forchheimer’s equation,5–8 expressed as
P2i Ϫ P2o
␮
␳
ϭ
vs ϩ v2s
(1)
2PoL
k1
k2
where Pi and Po are, respectively, the absolute fluid pressures at
the entrance and at the exit of the sample, vs the superficial fluid
B. R. Marple—contributing editor
Manuscript No. 188516. Received May 31, 2000; approved October 30, 2000.
Supported by FAPESP, Brazil.
Presented at the 102nd Annual Meeting of The American Ceramic Society, St.
Louis, MO, May 2, 2000 (Refractory Ceramics Division, paper No. R-018–00).
*Member, American Ceramic Society.
645

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Communications of the American Ceramic Society
Vol. 84, No. 3
and viscosity. Air-flow-rate measurements are conducted by rota-
meters (0–40 L/min) and soap-bubble flow meters (0–10 L/min).
Figure 1 shows details about the permeameter developed in this work.
Tests are conducted using the steady-state permeametry tech-
nique.6–8 The sample is tightly fixed in the sample holder using
heat-resistant O-rings to avoid leakage. The temperature is in-
creased to the desired value, and air is allowed to flow upward
through the sample with a constant pressure Pi. When the steady-
state regime is reached (constant T, Pi, and Po), the volumetric
flow rate Q is measured at the sample exit. Three flow-rate
measurements are conducted for each pressure setting at a given
temperature. After the collection of at least 10 pairs of pressure and
flow-rate data, the temperature is increased and the entire proce-
dure is repeated.
3°C/min up to the final temperature) to prevent mechanical
damage of the porous structure.
III. Results and Discussion
Figure 2 shows typical pressure-drop–velocity curves at various
testing temperatures for the refractory sample previously sintered
at 1650°C. The resistance to flow increased continuously from
ambient to 696°C, indicating changes in fluid properties and
possibly in the castable structure. Air density, ␳air, was 30% lower
at 696°C (0.33 kg/m3) compared with the value at room temperature
(1.08 kg/m3), whereas air viscosity, ␮air, increased 127% in the same
temperature range (from 1.83 ϫ 10Ϫ5 to 4.20 ϫ 10Ϫ5 Pa⅐s).
Figure 2 also confirms that experimental data follow the
parabolic trend proposed by Forchheimer’s equation rather than
the linear relationship between pressure drop and fluid velocity
stated by Darcy’s law.5 The intensity of the quadratic term clearly
increases at higher temperatures, showing that the inertial term
(␳v2s/k2) must not be disregarded in permeability analysis. Such
results indicate that the use of Darcy’s law, common in the
literature on refractory castables, must be avoided, especially for
prediction of fluid flow at high temperatures.10
Experimental values of Pi, Po, Q, and T are used in Eqs. (2)–(4)
for calculation of vs, ␮air, and ␳air. Equation (1) is finally used to
fit permeability constants k1 and k2 through the least-squares method.
(3) Sample Preparation
Cement-free high-alumina self-flow refractory castable samples
were prepared following Andreasen’s model for particle-size
distribution (q ϭ 0.21). Samples were molded as cylinders 7.5 cm
in diameter and 2.5 cm in thickness. The composition consisted of
a mixture of a fine matrix (Ͻ100 ␮m) and coarse aggregates (Յ4.7
mm) with 98 wt% of alumina. Hydratable alumina (2 wt%;
commercially known as Alphabond 300, Alcoa Industrial Chem-
icals, Pittsburgh, PA) was used as binding agent and water (4.12
wt%) was added to the castable mixing. All the white-fused
alumina (AEB) used as aggregates and the calcined alumina
(A1000 SG, A3000 FL, APC3017 SG) was supplied by Alcoa,
Brazil, and Alcoa, United States. Castables exhibited self-
flowability of 90% just after mixing. Drying was conducted at
110°C for 24 h, and thermal treatment was conducted at 900°,
1200°, 1500°, and 1650°C with a dwell time of 12 h. Heating rates
were slow (1°C/min up to 600°C, 2°C/min up to 900°C, and
In Fig. 3, the comparison between the actual curve obtained at
696°C and the one collected at room temperature but in which ␳
air
and ␮air have been corrected to 696°C, both for the sample treated
at 1650°C, clearly shows that variations in fluid properties do not
completely explain changes in permeability. Below 10 mm/s, the
actual resistance to flow at 696°C is lower than the resistance to
flow resulting from ␳ and ␮ corrections in the room-temperature
curve. Above 10 mm/s, however, the trend is inverted, and the actual
curve increases more intensely, which indicates that, in fact, other
factors are contributing to the increase the fluid pressure drop.
Figure 4 confirms such a hypothesis, showing changes in k1 and
k2 with the temperature increase. Considering that all samples have
been prepared according to the same composition (water content
and particle-size distribution) and thermally treated above the
temperature for permeability tests, then all changes observed in k1
and k2 can be associated only with reversible physical modifica-
tions in the porous structure as the air temperature increases.
However, although common sense suggests that the thermal
expansion due to the temperature increase would lead to an
increase in the flow path and, consequently, in permeability,
results in this work reveal an opposite behavior.
The overall rearrangement of the porous structure caused by
sample heating leads to a reduction in the pore diameter, decreas-
ing k1 and k2. The greater decrease in the non-Darcian constant k2,
shown in Fig. 4, indicates the generation of a preferentially
more-tortuous flow path, in which inertia is more important to
Fig. 2. Pressure-drop curves at various temperatures for the refractory
sample pretreated at 1650°C for 12 h. Lines for each curve represent data
fitted according to Forchheimer’s equation (Eq. (1)).
Fig. 1. Schematic of permeameter developed in this work.

March 2001
Communications of the American Ceramic Society
647
overestimated if changes only in fluid properties are taken into
account in the permeability analysis. In fact, the microstructure is
altered in a way to reduce its open and permeable porosity, mainly
because of the pore morphology generated during the previous
thermal treatment.
The equipment developed may also be a valuable tool for
evaluation of irreversible changes that occur during the elimination
of hydration and mixing water of refractory castables. Because the
equipment allows the simultaneous heat treatment and permeabil-
ity testing of green castables up to 800°C, a very careful analysis
of constants k1 and k2 obtained during elimination of water may
reveal why and how the water-vapor pressure builds up inside the
pores and how this affects the refractory explosion, mainly for
castables containing hydratable alumina as a binding phase.
Finally, with regard to permeability, this work has shown that
Forchheimer’s equation is a more realistic model to describe the
fluid dynamic behavior of gases and liquids in refractories at high
temperatures. Permeability changes occur preferentially in the
inertial range, making the parabolic term more important as the
testing fluid temperature increases. Such phenomena cannot be
fully understood if Darcy’s law is applied, because it considers
only the viscous interactions during the fluid flow.
Fig. 3.
Comparison of pressure-drop curves of sample previously
sintered at 1650°C ((e) actual curve, obtained at 696°C, and (F) curve that
resulted from corrections of viscosity and density (␳ and ␮ at 696°C)
in the pressure drop-curve obtained at 24°C).
air
air
IV. Conclusions
The objective of this work was to introduce an apparatus for
evaluating the permeability of refractory castables at high temper-
atures. Results showed that changes only in fluid properties do not
explain the variation in permeability constants. The non-Darcian
constant k2 was significantly decreased with temperature com-
pared with the Darcian constant k1. The overall effect was an
increase in the pressure-drop curve, with the intensification of
inertial effects. Tests from ambient to 700°C showed that thermal
expansion was the cause of reversible reduction in channel
diameter and, consequently, in permeability.
Results inferred that, concerning the physical aspects, the
infiltration of corrosive fluids may be overestimated if changes in
the castable structure are not expected to occur with increasing
temperatures. The equipment developed and the modeling pro-
posed for high-temperature permeability may also be important
tools for evaluating the structural changes that occur during the
drying process and for helping to provide insights regarding the
explosion tendency in refractory castables.
Acknowledgments
Fig. 4. Influence of test temperature on (a) Darcian permeability, k1, and
(b) non-Darcian permeability, k2.
The authors are grateful to the Brazilian research funding institutions FAPESP and
CNPq and to Alcoa for their support of this work. Authors also thank Arturo R. F.
Pardo for his help in the experiments.
fluid pressure drop. The causes of this behavior are not yet
understood, but seem to be related to the pore pattern generated
during the previous thermal treatment from 900° to 1650°C, as
discussed by Innocentini et al.7 and Pardo.10
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