Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
EXPERIMENTAL SETUP FOR MEASURING DIFFUSIVE AND ADVECTIVE TRANSPORT
OF RADON THROUGH BUILDING MATERIALS
M. van der Pal1, E.R. van der Graaf2, R.J. de Meijer2, M.H. de Wit1, N.A. Hendriks1
1
Department of the Physical Aspects of the Built Environment, Faculty of Architecture, Building and
Planning, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The
Netherlands.
2
Nuclear Geophysics Division, Kernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA, Groningen,
The Netherlands.
This study describes an approach for measuring and modeling diffusive and advective transport of radon
through building materials. Goal of these measurements and model calculations is to improve our
understanding concerning the factors influencing the transport of radon through building materials. To
reach this goal, a number of experiments has to be conducted. These experiments, including
measurements in a large cylinder for creating diffusive and advective transport of radon under controlled,
‘dwelling-like’ conditions, are described here and the initial results are presented. A better understanding
about the transport of radon through building materials will lead to more effective ways to decrease or to
prevent the entrance of radon into dwellings.
Keywords: Radon, exhalation, building materials, aerated concrete, diffusion, advective flow, modeling.
INTRODUCTION
In The Netherlands, unlike many other countries, the main source of indoor radon is the building
materials. With a contribution of 20 Bq m-3 of radon, building materials contribute about 70% of the
total indoor radon concentration. This was concluded from the results of the last Dutch national radon
survey (Stoop et al. 1998) where radon concentrations and ventilation rates were measured in Dutch
dwellings, newly built between 1985 and 1994. However, these results cannot be matched with the
results from various radon exhalation measurements of building materials (Put and Van der Graaf
1996, Van der Graaf et al. 1998) showing considerable lower radon exhalation rates than expected from
the estimated contribution of 70%.
In addition, measurements of the diffusion length of radon in concrete also yield conflicting results.
Radon exhalation measurements on two different sized concrete cubes of 0.15 and 0.20 meter
respectively (Bosmans, 1997) showed no significant difference in radon exhalation rate when
expressed on base of mass, indicating a large diffusion length (of at least 10 cm). On the other hand,
recent measurements at KVI on (sealed) concrete cylinders show a much smaller diffusion length
(Cozmuta and Van der Graaf, 1999).
A probable cause of these differences might the assumed driving force of radon transport, diffusion.
The radon exhalation measurements are based on maximizing diffusive transport. A vessel containing
the sample is continuously flushed with nitrogen, resulting in a low radon concentration in the vessel.
The low radon concentration leads to maximum diffusive transport and the calculated radon exhalation
rate is considered the maximum exhalation. Because the measured exhalation rates can not be matched
23
Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
with the results from the Dutch National Survey, other transport processes, such as advective transport
of radon, should be considered.
An advective flow can be created by pressure- or temperature gradients in a building material. In the
light of the recent measurements, the assumption that advective transport would be very small
compared to the diffusive transport and therefore could be neglected, should be reconsidered. An
approach to investigate the importance of advective transport of radon through building materials via
modeling and measurement of radon transport under various conditions is described in this paper.
Therefore, an experimental setup is developed at the Eindhoven University of Technology to measure
diffusive and advective transport of radon through building materials. Advective transport can be
created by setting a pressure-gradient or a temperature gradient over a building material sample.
Furthermore, the humidity (gradient) can be set. The ranges in parameters settings are chosen in such a
way that conditions in dwellings can be simulated with a larger degree of control than possible with the
‘regular’ radon exhalation setups. This paper will describe the experimental setup together with a
model for combined diffusive and advective transport of radon.
MODEL CALCULATIONS
Rogers and Nielson (1991, 1993) developed a formalism to describe the diffusive and advective multiphase transport of radon in porous materials. Van der Spoel (1998) successfully verified this model for
dry and (partly) wetted sand via experiments.
This formalism includes four processes that determine the (change in) radon concentration; diffusion,
advective flow, radon production and radon decay. The time-dependent partial differential equation is
given by equation 1.
β
∂C a
K
= ∇(D∇C a ) + ∇Pa ⋅ ∇C a − βλC a + S
∂t
µ
(1)
where
β
Ca
D
K
µ
Pa
λ
S
= multiphase-corrected porosity
= radon concentration in air-phase (Bq m-3)
= bulk diffusion coefficient (in m2s-1)
= intrinsic permeability (m2)
= dynamic viscosity of air (Pa s)
= air pressure (Pa)
= decay constant of radon (=2.1.10-6s-1)
= radon production rate per unit bulk volume (Bq m-3s-1)
Effects of absorption of radon are accounted for via the multiphase-corrected porosity, β:
β = ε a + Lε w + ρ b k a
(2)
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
where
εa
εw
L
ka
ρ
004
= air-filled porosity
= water-filled porosity
= Ostwald coefficient for radon (0.26 at 293 K)
= surface adsorption coefficient for radon (m3kg-1)
= density of the porous medium (kg m-3)
For solving this time-dependent, partial differential equation in more than one dimension, a numerical,
finite-element has been developed and validated. The deviations between model calculations and
measurements of diffusive and advective transport of radon were well within 15% for dry sand and
between 15% and 40% for (partly) wetted sand (Van der Spoel 1998). For building materials, this
model has never been experimentally validated.
EXPERIMENTAL SETUP
To validate the radon-transport model for building materials, measurements on radon transport will be
conducted under well-defined and controlled conditions. For this purpose, an experimental setup was
built. The experimental setup, shown in Fig 1, consists of a large cylindrical cylinder with inlets and
outlets to allow air to flow in and out of the cylinder. The cylinder is made of stainless steel, weighs
500 kg and has an effective diameter of 1000 mm. The lid is 30 mm thick, has a diameter of 1015 mm
and weighs 400 kg. In the cylinder, a cylinder of building material with an inner and outer diameter of
>500 mm and <800 mm respectively can be placed on the bottom plate via a removable ring of
stainless steel. The top of the cylinder of building material is closed with a lid of stainless steel.
Aerated concrete has been chosen as initial building material for the measurements because it cures fast
and so possible effects due to aging are excluded, exhales measurable amounts of radon and is quite
homogeneous and isotropic. The aerated concrete cylinder was made out of a 1 m-side cube, specially
made for this purpose by Ytong (Meppel) in The Netherlands. More complex building materials such
as concrete and gypsum will be considered after measurements with aerated concrete are found to
correspond with model calculations.
The aerated concrete cylinder is sealed to the lid (inside) and the inner ring with glue (Sickaflex). This
way, two compartments are created in the cylinder, which are separated by the aerated concrete
cylinder. In addition, radon transport between the two compartments (through the aerated concrete
cylinder) is reduced to one dimension (only radial transport).
Furthermore, the following parameters can be set and/or measured in the cylinder:
-
Temperature: The temperature is measured with four Kelatron K431 four wired PT100 temperature
sensors that can measure in a range of 0-100 oC with an uncertainty of 0.1 oC. Two temperature
sensors are placed in the inner compartment and two in the outer compartment. The air temperature
can be set via heating the incoming air. Presently, the type of heaters to be used, is still under
discussion.
25
Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
-
-
-
-
Pressure: The barometric pressure is measured with a Setra type 276 pressure sensor that can
measure in a range of 0.8-1.4 bar with an uncertainty of 0.5 mbar. The pressure difference between
the inner and outer compartment is measured with two Setra type 264 differential pressure-sensors
for a range of 0-100 Pa with an uncertainty of 0.2 Pa. The pressure in each compartment can be set
by opening (for a decrease in pressure) or closing (for an increase in pressure) of the two
Bronckhorst type F-004AC-LU-22-V control valves which are connected to the inner and outer
compartment-outlets. The pressure difference can be set by opening or closing of one of the control
valves.
Ventilation rate: The ventilation rate is measured for each compartment with a Bronckhorst type F102D-FA-22-V mass flow meter, for a range of 0-20 Ln N2 per minute and an uncertainty of 0.2%
FS. The ventilation rate can be set for each compartment with two Bronckhorst type F201C-FA-22V mass flow controllers.
Relative humidity; To set the relative one mass flow controller is connected to an air-humidifier,
producing nearly 100% humid air, while the other mass flow controller supplies dry air. By
adjusting the ratio between these two mass flow controllers, the humidity can be set. Earlier
experiments at KVI (Van der Graaf et al. 1998) and at the Eindhoven University of Technology
(Brocken 1998) have shown that this system functions very well. Presently, the type of humidity
meters to be used is still under discussion.
Radon concentration: The radon concentration is measured with α-counting two quasi-continuous
radon meters (Stoop and Aldenkamp, 1994). The radon meters have a detection limit of 10 Bq m-3
for a measuring time of 30 minutes.
An overview of the devices is given in Fig 2. A Pentium-166MHz computer with a Keithley
DAS1802HC data-acquisition board and a Keithley PD-ISO8 relays switchboard is used to collect the
data and to control the set conditions.
PLANNED EXPERIMENTS
The conditions in the two compartments of the cylinder can be altered and set to ‘dwelling-like’
conditions, giving the possibility to simulate various realistic conditions and to examine the effect of
various parameters on the radon concentration. The following experiments will be conducted:
-
The influence of an advective flow can be investigated by setting a temperature and/or pressuredifference between the two compartments.
The influence of the humidity (gradient) on radon generation and transport can be studied by setting
the ratio between dry and 100% humid air via the mass flow controllers.
The influence of high radon concentration in cavity walls of dwellings on the indoor radon
concentration can be studied by placing a radon source in the outer compartment.
In addition, the effectiveness of radon-reduction measures, such as ventilation of cavity walls, can be
tested.
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
ADDITIONAL EXPERIMENTS
To model the experiments in the cylinder, various properties of the aerated concrete and other model
parameters have to be measured in separate experiments. A selection of these additional experiments is
given below.
To determine the effective radon production, the effective radon diffusion length and the effective
porosity for radon of the aerated concrete, a ‘multiple-volume’ measurement will be conducted; A
sample of aerated concrete is placed in a closed compartment that is connected with a gas tap to a
second compartment. The radon equilibrium concentration is measured with the gas tap closed and
opened. This measurement is repeated with a calibrated radon source in the first compartment and the
sample in the second. From these measurements, the radon production, diffusion length and porosity
can be derived.
The radon exhalation rate of aerated concrete was measured at KVI via a flush and adsorb experiment.
The density, total porosity and open porosity for water of the aerated concrete were measured at the
Eindhoven University of Technology.
Permeability of the aerated concrete will be calculated from measurements in the cylinder whereby the
cylinder will be closed off while a pressure-difference over the aerated concrete cylinder is created and
the change in pressure-difference measured in time. From this measurement, the permeability can be
derived. Porosity will be measured on large samples with a specially designed setup based on the gas
expansion method. Furthermore, the possibilities of using image-analysis for determining parameters
such as porosity and tortuosity, will be explored.
To assure that radon is mainly transported through the aerated concrete and not through the Sickaflex
connection, the possibility of transport of radon through the Sickaflex has to be assessed. This is done
by glueing a cylinder of building material with Sickaflex with one side on a steel plate. The other side
of the cylinder is glued with Sickaflex on a steel lid sealing a closed compartment, thereby creating two
compartments separated from each other by the glue and the aerated concrete as shown in Figure 3. The
inner compartment is filled with a high radon concentration by connecting it to a radon source while
the outer compartment is flushed with nitrogen at an accurately known ventilation rate, setting a radongradient over the building material. The radon concentration in the outer compartment is measured in
equilibrium. Thereafter, the cylinder is removed and sawn in two equal parts and glued together again
with Sickaflex, and the radon concentration is measured until equilibrium has been reached. If a large
part of the radon is transported through the Sickaflex connection, this will result in a large difference
between the radon concentration before and after the sawing.
SENSITIVITY ANALYSIS
The influence of uncertainties in the various model parameters on the radon concentrations calculated
with the finite-element model is determined with the following numerical procedure;
First, an estimation of the average values of the various parameters and the achievable accuracy was
made from information from literature. Secondly, a set of 24 parameter values was created by a
random-number generator according to a normal distribution with an expectation value and standard
27
Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
deviation equal to the estimated value and uncertainty of the model parameters. Using these values, 24
radon (equilibrium) concentration-profiles were calculated with the finite-element model.
Subsequently, the average value for and the deviation in the radon concentration were calculated for
both compartments and the building material. This procedure was conducted for every individual
parameter to get a better understanding of the influence of the various model parameters on the radon
concentration. In addition, a set of numbers was generated to calculate the influence of all parameters
together on the radon equilibrium concentration. The values and conditions used for the sensitivity
analysis are shown in Table 1.
RESULTS, DISCUSSION AND CONCLUSIONS
The values and accuracy’s of the parameter values found in literature and measured at KVI or the
Eindhoven University of Technology (TUE) are shown in Table 2. The values of some parameters, e.g.
the radon exhalation, depend on the relative humidity. For these parameters, the estimated value is
given for a relative humidity of 50% although this condition was not always well defined in literature.
In comparison with ‘regular’ concrete, aerated concrete has a very high porosity. This is probably the
most important reason for the relative high values for the diffusion coefficient and the relative low
values for the density and the radium content of aerated concrete.
The influence of the uncertainty in model parameter on the variance in the resulting radon
concentration is given in Table 3 as R, the ratio between the maximum relative standard deviation in
radon equilibrium concentration in the inner compartment and the relative standard deviation in
parameter value;
R=
σ Rn
(3)
σ Parameter
where
σRn
σparameter
= maximum relative standard deviation in radon equilibrium concentration
= relative standard deviation in parameter value
The total influence of the uncertainties in all parameters on the variance in the equilibrium radon
concentration is shown in Fig 4. It can be concluded that the radon equilibrium concentration can be
calculated with a relative standard deviation of less than 2% for the inner compartment and of less than
5% for the outer compartment for the conditions given in Table 1. Although for other conditions the
sensitivity analysis has not yet been conducted, it seems that experimental results and model
calculations can be compared with an accuracy of less than 10%. In the light of the large differences
between the calculations based on radon exhalation rates and measurement of the indoor radon
concentrations, this can be considered as accurate enough.
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
ACKNOWLEDGEMENTS
This research is funded by the Centre of Technology for Sustainable Development (TDO) of the
Eindhoven University of Technology. Also, the authors are grateful to Ytong Nederland who specially
made for us the king-sized cubes of aerated concrete.
REFERENCES
[1]
Bosmans G, Optionele maatregelen ter reductie van de stralingseigenschappen van praktijkbeton, Intron
report 96173, 1997 (in Dutch).
[2]
Brocken HJP, Moisture and Salt transport in porous building material, PhD-thesis, PhD-thesis, Eindhoven
University of Technology, 1998.
[3]
Cozmuta I, Van der Graaf ER, Methods for measuring diffusion coefficients of radon in building
materials, Paper presented at ERRICCA workshop ‘Radon in the Living Environment’, 1999.
[4]
Darcy HPG, Les Fontaines Publiques de la Ville de Dijon. Librarie de Corps Imperiaux des Ponts et
Chausses et de Mines, Paris, 1856 (in French).
[5]
Folkerts KH, Keller G, Muth H, Experimental Investigations on Diffusion and Exhalation of
220
Rn from Building Materials, Radiation Protection Dosimetry, 7, 41-44, 1984.
[6]
Put LW, Van der Graaf ER, Invoerparameters voor radontransportmodellen: een literatuurstudie, KVI
report R 92, 1996 (in Dutch)
[7]
Rogers VC, Nielson KK, Generalized Source Term for the Multiphase Radon Transport Equation, Health
Physics, 64, 324-326, 1993.
[8]
Rogers VC, Nielson KK, Multiphase radon generation and transport in porous materials, Health Physics,
60, 807-815, 1991.
[9]
Stoop P, Aldenkamp FJ, Sources and Transport of Indoor Radon - Measurements and mechanisms, PhD
thesis, University of Groningen, 1994.
222
Rn and
[10] Stoop P, Glastra P, Hiemstra Y, de Vries L, Lembrechts J, Results of the second national survey on radon
in dwellings, RIVM report 610058006, 1998.
[11] Van der Graaf ER, Cozmuta I, Van der Spoel WH, de Meijer RJ, Calibration of the KVI instrument to
measure radon exhalation rates from building materials under controlled conditions, KVI report R 99,
1998.
[12] Van der Spoel WH, Radon Transport in Sand, A Laboratory Study, PhD-thesis, University of Groningen,
1998.
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
Table 1. Settings of model calculations for sensitivity analysis.
Parameter
Inner
Aerated concrete
compartment
Outer
compartment
Inner radius
0m
0.3 m
0.4 m
Outer radius
0.3 m
0.4 m
0.5 m
(1.00 ± 0.04) h-1
0
0
---
(700 ± 7) kg m-3
---
1
(0.50 ± 0.02) m3 m-3
1
Emanation factor
---
(0.30 ± 0.01) Bq Bq-1
---
Radium content
---
(15.0 ± 0.5) Bq kg-1
---
1.10-3 m2 s-1
(0.62 ± 0.02).10-6 m2 s-1
1.10-3 m2 s-1
Ventilation rate
Density
Multi-phase
corrected
porosity
Bulk diffusion coefficient
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
Table 2. Overview of values for various properties of aerated concrete from literature and
measurements at the KVI and Eindhoven University of Technology (TUE).
Parameter
Value
Source
Density
(560 ± 6) kg m-3
TUE
Total porosity
(0.73 ± 0.03) m3 m-3
TUE
Water-filled Porosity
(0.42 ± 0.04) m3 m-3
TUE
Radon production
(2.01 ± 0.06).10-6 Bq kg-1 s-1
KVI
Radium content
(11.52 ± 0.19) Bq kg-1
KVI
Bulk diffusion coefficient
0.62 .10-6 m2 s-1
Folkerts et al. (1984)
Table 3. Results of sensitivity analysis, influence of deviation of parameter on radon concentration
given as ratio between its relative standard deviation and the resulting maximum relative
standard deviation in radon concentration.
Parameter
Value
R
(1 ± 0.04) h-1
0.98
(700 ± 7) kg m-3
1.00
Effective porosity
(0.50 ± 0.02) m3 m-3
0.10
Emanation factor
(0.30 ± 0.01) Bq Bq-1
1.00
Radium content
(15.0 ± 0.5) Bq kg-1
1.00
(0.62 ±0.02).10-6 m2 s-1
0.70
Ventilation rate inner compartment
Density
Effective diffusion coefficient
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
air out
lid (outside)
air out
to radon monitor 2
from radon monitor 2
outer com partm ent
lid (inside)
PT 100
T
T
pressure transducer
P
P
T
T
P
P
from radon monitor 1
to radon monitor 1
building material
inner com partm ent
diffusion- box
air in
air in
Figure 1. Schematic cross-section of the radon cylinder
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
MFC
MFC
H2O
Radon
Source
004
Humidity
Meter
Heater
T P
Humidity
Meter
Air
MFC
H2O
Humidity
Meter
valve
∆P
∆T
MFC
Flow
Meter
T P
Heater
Humidity
Meter
Flow
Meter
valve
MFC = Mass Flow Controller
Figure 2. Flow diagram of the experimental setup: an overview of the devices for measuring and
controlling various parameters in the radon cylinder (the radon cylinder is represented by the
large block divided in the middle by the building material)
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
Radon
source
Radon
source
Radon
meter
MFC
MFC
Aerated Concrete
Sickaflex
Figure 3. Experimental setup for measuring transport of radon through Sickaflex-connection:
34
Radon
meter
Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
70
-3
radon concentration (Bq m )
80
60
50
average
+1 std
-1 std
40
30
20
10
0
0.2
0.3
0.4
0.5
radius (m)
Figure 4. Average Radon concentration, represented by the solid line, ± 1 standard deviation caused by
estimated uncertainties in model parameters, represented by the dotted lines. The aerated
concrete is placed between the vertical dotted lines.
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Radon in the Living Environment,
19-23 April 1999, Athens, Greece
004
36