4. Experimental determination of material parameters and transfer properties91
4.2. B RICK PROPERTIES
4.2.4. Saturated permeability
The saturated permeability of ceramic brick is assumed to be an invariant material property. Averaged values for the bulk material are determined for the two different bricks, series ‘A’ and ‘B’. A large difference in permeability is noticed. Additionally, the influence of cracks on the saturated permeability is investigated.
4.2.4.1. Saturated permeability of uncracked brick material
Three different experimental methods are used to determine the saturated permeability of ceramic brick: (1) a steady state air flow experiment on dry samples; (2) a water permeability cell test using a variable pressure head; (3) a water permeability test with constant water head. On bricks ‘A’ techniques (1) and (2) are performed, while technique (3) is applied on brick ‘B’. The relation between both the air and water permeability is given by equation (3.19) with kr,l
( )
Sl =kr,g( )
Sl =1:. . ρ η
= ρ ηl a
l a
a l
K K (4.4)
where Klis the water permeability of the water saturated material, Kais the air permeability of the dry material, ρl is the water density (= 997.54 kg/m³ at 23°C), ρais
the air density (1.2 kg/m³) and the air and water viscosity are assumed to be constant and equal to 17.3x10-6 Pa.s respectively 1x10-3 Pa.s.
4.2.4.1.1 Steady state air flow experiment (for bricks ‘A’)
By means of a pressure pump and valves a constant airflow is created over a sample.
The sample is mounted in a sample holder and is at one side in contact with the atmospheric pressure. The flow and the pressure drop over the sample are measured (Fig. 4.6) using a flow meter and a pressure meter. All tested samples have diameters between 25 and 91 mm and thicknesses vary between 9 and 17 mm. The applied pressure differences range from 2 till 18 kPa for the large samples and until about 230 kPa for the small ones.
0.000 0.002 0.004 0.006 0.008 0.010 0.012
0 200000 400000 600000 800000 1000000
Δ Pa / width (kg/(s².m²)) Ga (kg/(s.m²))
Ka = 1.73x10-8 s pressure
pump flow meter pressure meter sample Patm
P [Pa] v [m²/s]
Fig. 4.6 Results of an air permeability measurement on a sample with a diameter of 91 mm and a thickness of 10 mm
Based on the following expression the air permeability Ka can be determined:
. .
a a
a a
r
P P
G K
V d d
Δ Ω Δ
= = (4.5)
where Ga is the air flow (kg/(s.m²)), ΔPa is the applied pressure difference, Ω is the surface of the sample, Vr is the flow resistance (m³/s) and d indicates the thickness of the sample (m).
Both the measured Kaand theKl determined using equation (4.4)) are given in Table 4.2.
Table 4.2: Air and liquid permeability data based on an air permeability test on dry samples.
Parameter Mean value Minimum value Maximum value
Ka (s) 1.76x10-8 1.06x10-8 2.63x10-8
Kl (s) 2.53x10-7 1.52x10-7 3.79x10-7
The results in Table 4.2 are of the same order of magnitude as the saturated water permeability found in literature [CAR-99] measured on the same series of bricks, namely 1.3x10-7 s.
4.2.4.1.2 Cell test with variable water head (for bricks ‘A’)
The cell test consists of two reservoirs with distilled water with in between a water saturated sample. Over the sample an initial water height difference of 3 cm is created.
Based on the liquid flow an indirect determination of the permeability resulted in a value of 0.7x10-7 s.
0 2 4 6 8 10 12 14 16
0 200 400 600
Time (min) Change of water heigth (mm)
Measured data Kl = 2.4x10-7s Kl = 1.0x10-7s Kl = 0.7x10-7s Kl = 0.5x10-7s Kl↓
Kl
Kl
Kl
Kl
2.4x10-7 s 1.0x10-7 s 0.7x10-7 s 0.5x10-7 s
Fig. 4.7 Fitting the measured height changes in a cell test with initial water head of 3 cm resulting in a permeability value.
4.2.4.1.3 Water permeability test with constant water head (for bricks ‘B’) The assumed isotropic liquid permeability of the uncraked brick of series ‘B’ is measured by performing a water permeability test. A constant pressure gradient ΔP dl/ (kg/s².m²)
is imposed on a saturated specimen by the use of a reservoir with an overflow. The resulting liquid flow
, 2 m H O
q (kg/s.m²) is measured. The permeability is determined by
2 2
H O
l H O
K K q
Pd
= =
Δ (4.6)
Two samples of 60 x 28 mm² and a height of 37 mm are submitted to a pressure head of 1.56 m. After a transitional stage, due to the starting up of the experiment and the initial presence of air bubbles, a permeability of about 5x10-9 s was obtained (Fig. 4.8). As mentioned before this is a large difference in permeability with the results for the bricks
‘A’ (Table 4.2 and Fig. 4.7). This difference can be explained by the fact that both bricks belong to a different fabrication set.
0.E+00 1.E-08 2.E-08
0 2 4 6 8 10
Time (days) Kl (s)
Fig. 4.8 Evolution of the permeability towards a constant value of 5x10-9 s.
4.2.4.2. Saturated permeability of cracked material
Cracks in the material will considerably increase the overall permeability. Darcian flow in cracks is modelled using the cubic law. If a parallel crack with aperture wcrack is filled with liquid, the permeability Kl crack, is given by [VAN-02a, BEA-93]:
2 ,
. 12.
l crack l crack
l
K ρ w
= η (4.7)
where ρl is the density of the liquid dependent on salt the concentration, ηl is the dynamic viscosity of the salt solution (mPa.s) considered independent of the concentration.
The liquid permeability of a crack can be determined based on the crack width according to equation (4.7). As a first estimation of the crack width, a crack meter can be used to determine the crack width at the surface of the specimen. Due to crumbling of the edges of the crack surface, the measurement of the crack width at the surface is very place dependent and usually results in an overestimation of the crack width. A more accurate estimation of the crack permeability can be obtained by measuring the total permeability of the cracked sample (equation (4.8)).
( )
, ,
, , _
_ _
2 ,
_ _
. .
. . . .
12.
ρ η
Ω + Ω
= Ω
Ω +
= Ω
l brick brick l crack crack l tot brick crack
tot brick crack l crack
l brick brick crack crack
l tot brick crack
K K
K
K w l w (4.8)
where Kl tot brick, , _crack is the total permeability of a parallel cracked brick (s), Ωcrackis the total surface of the crack (m²) with lcrack the length of the crack (m) see Fig. 4.9 and
_ _
tot brick crack
Ω is the total surface of the cracked part including the two brick pieces (m²).
Knowing the permeability of the (uncracked) brick material Kl brick, and the dimensions of the uncracked part Ωbrick, the average crack width wcrack can be determined. Note that all these permeability tests are performed with H2O. Further it is also assumed that the cracked surfaces have a parallel configuration and that the crack and the material have negligible influence one on the other.
Samples with cracks having parallel surfaces are created by joining two pieces brick, with a slice of micrometer paper in between (Fig. 4.9). Different crack widths were realized, by varying the thickness of the micrometer paper. When pulling out the paper, after having fixed the two parts together with epoxy resin, some material may be removed from the inner surfaces of the crack. Therefore, the crack width of these samples is determined based on the water permeability test. Table 4.3 gives the comparison between the surface measurement technique and the permeability based values for two cracked bricks of series ‘B’, using a micrometer paper of 100 and 200 µm.
micrometer paper micrometer
paper right brick
left brick
epoxy length of
the crack, Lcrack
right brick left brick
epoxy length of
the crack, Lcrack
right brick left brick
epoxy length of
the crack, Lcrack
Fig. 4.9 On the right side a brick sample with a crack. The preparation using micrometer paper is shown on the left side.
Table 4.3: Comparison between two measurement techniques, the surface crack meter versus the permeability measurement, for the determination of the crack width (µm)
µm-paper of 200 µm µm-paper of 100 µm Surface crack meter
Front 233 372
Back 267 296
Mean value 250 334
Permeability test
Mean value 266 212
Note that the values of the crack width found using a µm-paper of 100 µm are even larger than those found using µm-paper of 200 µm.