COMPUTER SIMULATION OF AIR PRESSURE MODIFICATION IN RADON-LADEN SUB-FLOOR SOIL

2,1 Akis M.C., 1Stadtmann H., 2 Kindl P.

1ARC Seibersdorf research GmbH1, Division of Health Physics/Radiation Protection

A-2444 Seibersdorf, Austria 2 Graz University of Technology, Institute of Technical Physics

E.Mail: akis@chello.at

Abstract – The air pressure disturbance introduced at any point in the soil which propagates throughout the whole soil block and finally reaches a new equilibrium, is called the disturbance pressure distribution. This pressure distribution is independent of the static pressure distribution in soil. The resultant absolute pressure at a point (x,y,z) in the soil is simply the addition of static and disturbance pressure distributions. The pressure disturbance field p(x,y,z) in the soil due to airflow driven by a fan or by any kind of pressure disturbance, is given by the Laplace equation if the soil-permeability and the soil-gas dynamic viscosity are assumed to be constant. A standard finite elements software, ANSYS-Multiphysics 5.5 has been utilised for mesh generation and to solve the Laplace equation numerically in two dimensions, as well as to simulate the porous soil matrix; the active sub-floor depressurization (ASD) system; the pressure disturbance introduced to the sub-floor soil by the normal operation of private houses; simulation of pressure distribution in a sub-floor soil with rocky structure; and finally, air flow velocity-vector distribution in soil. Corresponding results are presented diagrammatically. 1. Introduction Air pressure modification in sub-floor areas of houses with elevated radon problem is done usually by means of active sub-slab depressurization (ASD) [1]. ASD is a highly efficient method in radon mitigation as long as it is engineered well, and applied correctly in accordance with different specific conditions of each single house under consideration. In this connection, simulation of ASD with different physical, structural and soil characteristics plays an important role to obtain high efficiency in reality. The mathematical modeling of ASD or a pressure disturbance introduced to sub-floor soil owing to the normal operation of houses is simple, and involves the equation (1) given below [2][3]:

0)( -. =���

�

���

�∇���

�

�∇ rp

k

µ (1)

If the soil-permeability k and the soil gas dynamic viscosity µ are assumed to be constant and and the fluid (air) is incompressible, then the equation (1) becomes simply the Laplace’s equation. In other words, the pressure field p must satisfy the following condition :

0)(2 =∇ rp or more explicitly, in two dimensions:

0),(),(

2

2

2

2

=∂

∂+∂

∂y

yxp

x

yxp (2)

2. Methods and Materials A standard finite elements package, namely ANSYS-Multiphysics rel.5.5 [4] was utilized to carry out the computational work. The equation (2) is an elliptic partial differential equation (PDE) satisfied by a single stationary function p(x,y) within some region of interest. Moreover this function has some predetermined behaviour on the boundary of the region. Therefore this is a boundary value problem and the goal of the applied software is somehow to converge to the correct solution everywhere in the region at once. All the conditions on a boundary value problem must be satisfied “simultaneously”, as a result large numbers of linear simultaneous algebraic equations are obtained. Hence the problem can be considered as being the solution of special, large sets of equations.

1 This work has been a part of a project supported by ARC Seibersdorf Research GmbH.

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2.1. Simulation with ANSYS

The package software ANSYS-Multiphysics 5.5.3, has many finite element analysis capabilities ranging from a simple, linear, static analysis to a complex, non-linear, transient dynamic analysis. ANSYS-Multiphysics offers nearly 100 different types of elements . Among these elements only two, namely “Thermal SOLID-55” and “Thermal SOLID-70” were used in this work since ANSYS-Multiphysics / thermal analysis program solves the Laplace’s equation for steady state heat conduction without heat generation and assuming constant thermal conductivity [5][6].

“Thermal SOLID-55” with 4-nodes and “Thermal SOLID-70” [7] with 8-nodes, give the possibility to model porous flow (seepage flow) in two and in three dimensions respectively, so they have two and three-dimensional thermal conduction capability. These elements have a single degree of freedom that is, temperature, at each node, and they are applicable to two and three-dimensional, steady-state or transient thermal analysis. These elements can also compensate for mass transport heat flow from a constant velocity field.

An option exists that allows the elements to model non-linear steady-state fluid flow through a porous medium. With this option, the thermal parameters are interpreted as analogous fluid-flow parameters. In other words, the temperature degree of freedom becomes equivalent to pressure degree of freedom. For example, with the element “Thermal SOLID-70”, the nonlinear porous-flow option can be selected with KEYOPT(7). For this option, temperature is interpreted as pressure and the absolute permeabilities of the medium are input as material properties KXX, KYY, and KZZ. Properties DENS and VISC are used for the mass density and viscosity of the fluid respectively.

The software ANSYS-Multiphysics 5.5.3 has a comprehensive graphical user interface (GUI) that gives users interactive access possibility to program functions, commands, documentation, and reference material. An intuitive menu system helps users navigate through the ANSYS program. Users can input data using a mouse, a keyboard, or a combination of both. If the nonlinear porous-flow option has been selected using KEYOPT(7) with “Thermal SOLID-70” (and via KEYOPT(9) with “Thermal SOLID-55”), then, the temperature boundary conditions entered by means of GUI, are interpreted as pressure boundary conditions, and heat flow boundary conditions are interpreted as mass flow rate (mass/time).

3. Results

The numerical values of pressure p(x,y) on the boundaries were determined carefully to obtain correct and realistic results. In addition to the pressure boundary conditions, the properties like dynamic viscosity (µ =1.8� 510− Pa.sec) and density (ρ=1.1774 kg/m³ ) [8] of soil-gas (� air), and permeability (k) of soil were input as isotropic material properties. High soil permeability is defined as k � 1.0� 1210− m² and low soil permeability is defined as k � 1.0� 1210− m² [3].

Operation of private houses introduce usually a negative pressure into indoor areas with respect to atmospheric pressure [9]. This is simply because of the increased indoor-air temperature as a result of the daily activities inside the building like, heating, cooking etc. Under normal conditions, such a negative indoor air pressure can be in between ~5 to ~20 Pa with -5 Pa being a typical value in most of the cases. The software ANSYS has been utilized to simulate such cases considering 1210− m² or

1010− m² of soil permeability to air, 5Pa or 20Pa of indoor negative pressure with respect to atmospheric pressure, 0.3 m of wall width, and with a crack of 0.001 m width in the concrete floor. A result is given Figure 1, graphically. The 0.001 m width is typical for a crack which might happen to exist on a concrete floor. The air pressure difference in between the soil-crack interface and atmospheric pressure is chosen as minus 5 Pa, as one of the pressure boundary conditions. The atmospheric pressure was normalized to zero Pascal on the boundary in between the soil and atmospheric air, hence all the numerical figures characterizing the pressure in the results are not absolute, but relative to atmospheric pressure.

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According to the simulation results, -5 Pa in the crack, with a soil permeability of 1010− m², induced about -2 Pa at a distance of ~0.3 m in radial direction away from the crack (Figure 1). At ~0.8 m away from the crack, the air pressure increases until about -1 Pa. Figure 1, introduces the pressure gradient around the crack which has been generated by the software.

ANSYS 5.5.3 NOV 23 200323:18:40

1

-6 -5.333 -4.667 -4 -3.333 -2.667 -2 -1.333 -.666667 0

6 m

5 m

3.2

m

4 m

concrete slab

wal

l

Figure 1. Sub floor pressure field distribution generated by 5 Pa of a negative pressure with respect to atmospheric air pressure, at the crack soil interface. The position of the crack is on the corner connecting the concrete floor and the wall (The numerical figures are in Pascals). Here the soil permeability is 1010− m², the width of the walls is 0.3 m.

The air-flow velocity vector field which corresponds to the pressure gradient around the crack with 1210− m² of soil permeability is presented in Figure 2. The 5 Pa of indoor negative air pressure

compared with atmospheric pressure, is a quite small driving force as regards air flow through the 0.001 m wide crack, towards indoor areas. Therefore magnitude of air flow velocity at the crack entrance (Figure 3) has been calculated as ~0.4�

410− m/s, by the software. This is a rough figure and has to be utilized only as order of magnitude estimation.

3.1. Consideration of Transported Activity

The product of radon activity concentration in the soil gas by air-flow velocity in the crack, gives the radon-flux at the soil-crack interface. If the radon flux is multiplied by the area of the crack, then the radon entry rate per time, through the crack (Bq/s in SI units) is obtained.

The radon contents in the soil gas (� air) are typically in between 20 kBq/m³ and 50 kBq/m³, but in uranium-rich earth the radon level may be as high as 250 kBq/m³, whereas in earth types that have a high content of alum-shale, the radon activity concentration may be more than 1000 kBq/m³ [10] [11].

Provided that the radon content in the sub-floor soil is 50 kBq/m³, soil permeability is 1210− m², and indoor air pressure is 5 Pa lower than the atmospheric pressure, moreover, if the air flow velocity is taken as calculated above by the software (i.e. 0.4�

410− m/s), then, the activity transport from the sub-floor soil into indoor areas is calculated as 7.2 Bq/h through the crack with a length 1 m and of typical width (0.001 m). If such a crack, which happen to exist on a concrete slab, has a total length of 10 m, the transported activity per hour becomes 72 Bq/h.

4

1

0.3m

Figure 2. The air-flow velocity vector field which corresponds to the pressure gradient around the crack. The arrows show the direction of flow.

ANSYS 5.5.3 JAN 7 200422:41:36 MIN=.485E-12 MAX=.129E-03

1

.485E-12

.143E-04

.287E-04

.430E-04

.574E-04

.717E-04

.860E-04

.100E-03

.115E-03

.129E-03

0.001 m

0.00

6 m

Figure 3. The air-flow velocity2 distribution which corresponds to the pressure gradient at the soil crack interface. The speed of air flow at the crack entrance has been calculated about ~0.4� 410− m/s, with soil permeability of 1210− m², and 5 Pa indoor negative pressure with respect to atmospheric air pressure (The numerical figures are in m/s).

We assumed also the case that the indoor air pressure is 20 Pa lower than the atmospheric pressure, instead of 5 Pa. Keeping all the other parameters unchanged (with permeability 1210− m²) , the magnitude of air flow velocity at the crack entrance was calculated by the software as ~0.2�

310− m/s (Figure 4). Provided that the radon content in the sub-floor soil is again 50 kBq/m³, then the activity

2 The velocity figure 0.48� 1210− m/s, corresponds to the lowest (zero) pressure zone lying along soil to atmospheric air boundary, which is not visible in figure 3.

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transport from the sub-floor soil towards indoor areas was determined roughly as ~36 Bq/h through the crack with a length of 1m and of typical width (0.001 m). However, the same argument as above is also considered with a radon rich area of 250 kBq/m³ typical radon content in soil. Under 5 Pa of negative indoor air pressure, the activity transport from the sub-floor soil towards indoor areas was determined roughly again as ~36 Bq/h, nevertheless the same quantity was determined as ~180 Bq/h with 20 Pa of relative indoor pressure drop. In Table.1 below, the effect of soil permeability on air flow velocity at the soil-crack interface and on resultant radon-activity transport can be seen. As expected, the higher the permeability, the higher the air-flow velocity therefore the higher radon-activity transport towards indoor areas.

ANSYS 5.5.3 JAN 10 200402:20:17 MIN=.485E-12 MAX=.490E-03

1

.485E-12

.545E-04

.109E-03

.163E-03

.218E-03

.272E-03

.327E-03

.381E-03

.436E-03

.490E-03

0.001m

0.01

0 m

Figure 4. The air-flow velocity distribution which corresponds to the pressure gradient at the soil crack interface. The speed of air flow at the crack entrance has been calculated about ~0.2� 310− m/s, with 1210− m² of soil permeability and 20 Pa indoor negative pressure with respect to atmospheric air pressure. The numerical figures corresponding to colors are in m/s.

Soil Permeability(m²)

Flow Velocity at Soil-CrackInterface (m/s)

Rn Activity Transport(Bq/h)

Table 1. Effect of soil permeability on air-flow velocity* at the crack-soil interfaceand on the resultant radon-activity transport* towards indoor area

*Numerical figures are obtained by using ANSYS, considering a crack of 0.001 m widthand 1 m length, as well as 5 Pa of indoor pressure drop and 50 kBq/m³ soil radon content.

1010−

1210−

1410−

3104 −⋅4104.0 −⋅6104.0 −⋅

720

7.20.072

3.2 Active Sub-Slab Depressurization

Here, the results of a computer modelling of two distinct cases are graphically introduced. In the first case the sub-floor soil is assumed to have a normal homogenous structure (Figures 5&6). and in the second case the soil under the floor was assumed to have a rocky structure (Figures7&8). In both of the cases, either homogenous or rocky structure, soil permeability to air was assumed to be 1010− m².

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ANSYS 5.5.3 JAN 19 200415:12:47

1

MN

-120 -106.667 -93.333 -80 -66.667 -53.333 -40 -26.667 -13.333 0

4.6 m

3.12

5 m

Figure 5. Sub floor pressure field distribution generated by ASD system, with -120 Pa of a negative pressure with respect to atmospheric air pressure. The white arrow on the left hand side symbolizes the ASD system. The numerical figures corresponding to colors are in Pascals. Here the soil permeability is 1010− m².

ANSYS 5.5.3 JAN 19 200415:34:30 MIN=.907E-08 MAX=.001906

1

.907E-08

.212E-03

.424E-03

.635E-03

.847E-03

.001059

.001271

.001482

.001694

.001906

3.12

5 m

4.5 m

Figure 6. The air-flow velocity [m/s] vector field which corresponds to the pressure gradient generated by ASD system shown in figure 5. The arrows show the direction of flow.

The Active Sub-Slab Depressurization (ASD) sytem has been represented by a semicircular area under the concrete slab on the left hand side (Figure 5). The semicircular area is the suction-pit of radius 0.1m, in two dimensions. The existence of a suction-pit increases the surface area of the applied pressure reduction (-120 Pa) by the fan, and therefore modulates the sub slab area pressure distribution constructively.

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ANSYS 5.5.3 JAN 19 200416:25:54

1

MN

-120 -106.667 -93.333 -80 -66.667 -53.333 -40 -26.667 -13.333 0

5 m

5 m

Figure 7. Simulation of pressure distribution generated by ASD system (-120 Pa) in two dimensional sub-floor soil with rocky structure. Here the deviation from a smooth pressure distribution is the major characteristic.

ANSYS 5.5.3 JAN 19 200416:17:26 MIN=0 MAX=.001162

1

0 .129E-03 .258E-03 .387E-03 .516E-03 .645E-03 .774E-03 .904E-03 .001033 .001162

5 m

4.40

m

Figure 8. Air flow velocity-vector diagram corresponding to the pressure distribution depicted above in Figure 6. The simulation generated increasing air speeds through the narrow passages between the rocks. The numerical values are in [m/s]. In the case with the sub-floor soil was assumed to have a simple homogenous structure, the negative pressure induced by the ASD effect was distributed smoothly (Figures 5) under the whole floor-slab. Such a smooth pressure distribution increases the efficiency of active sub-slab depressurization (ASD), so that even with low power electric-fans quite satisfactory results can be obtained. In the other case the sub-floor soil was assumed to have a complex, rocky structure, the sub floor pressure

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distribution has been no longer so smooth as in the first case (Figure 7).Such a deterioration in the pressure field might well be the result of sudden variations in air-flow velocity (Figure 8) through the tunnel like passages between rocks. In figure 8 above, air flow velocity-vector diagram corresponding to the rocky soil structure is introduced. The abrupt variations in the air-flow velocity between the rocks correspond to the orange and blue coloured arrows. When an ASD system is needed for a house with radon problem, and if the sub-floor soil has a rocky structure, the sub-floor pressure field may not be modified as desired. To remedy this situation, more powerful fan or fans with a few different suction-pipe connections to the sub-floor area, may be needed.

4. Discussion The distinctive character of the present work has been to introduce the use of a standard finite elements software (ANSYS/multiphysics) in radon problem as regards sub-floor area pressure modification, and prediction of radon activity transport through a crack towards indoor areas. The software was utilised by means of a quite ordinary PC with 800 MHz CPU speed and ~400 MB workspace. To determine air flow velocity at the soil-crack interface is essential to calculate the transported radon activity per unit time, through the crack. In view of this fact, the velocity of air flow at the soil-crack interface has been calculated about ~0.4�

410− m/s, with 1210− m² of soil permeability and 5 Pa indoor negative pressure with respect to atmospheric air pressure. As an order of magnitude ~0.4�

410− m/s seems to be in good agreement with a similar figure (~0.7 410−⋅ m/s) from existing literature [3]. With -20 Pa indoor pressure drop as well, the air flow velocity has been calculated as ~0.2�

310− m/s, being again in good agreement with the corresponding figure (~0.3� 310− m/s) from the literature [3]. The nature of air flow in soil was determined through the Reynolds number (Re) for the cases modelled in the present work. The Reynolds number for flow through porous media is given as Re=u.d/ν [12], where u {m/s} is speed of fluid (air) flow, d {m} is characteristic dimension of soil grains, and ν {m²/s} is the kinematic viscosity of the fluid (for air ν=15.7 610−⋅ m²/s at 300 K). Moreover, soil grain diameters range from 0.06 310−⋅ m to 2 310−⋅ m [13]. Therefore, if as characteristic grain dimension 0.1 310−⋅ m, and as air flow velocity ~0.2� 310− m/s are taken, then the Reynolds number becomes 1.2� 410− , indicating laminar flow. Because, a safe upper limit for laminar flow is given when Re<1, and a safe lower limit for turbulent flow corresponds to Re>10 [14], whereas in between, there is transition region from laminar to turbulent flow. This is the range of Reynolds Number for turbulent flow which is valid for flow in packed soil or gravel beds, although, for flow inside tubes and ducts, turbulent flow occurs at Reynolds numbers of several thousands. In general, houses are so constructed that the concrete floor-slab lies on a gravel bed which is built above soil. Because of high porosity and grain size, the permeability of a gravel bed is usually much higher than that of the soil below. Under these conditions the efficiency of an Active Sub-Slab Depressurization (ASD) system gets better and the nature of the flow can be turbulent (Re>10) under effect of ASD system, as show in one of our previous papers [15]. In the present work, a gravel bed is not included in the modelling stage, and ASD suction (-120 Pa) has been applied through a semicircular suction-pit, directly to the soil of permeability 1010− m². Therefore, maximum air flow velocity has been about ~1.5� 310− to ~2� 310− indicating a laminar flow regime, considering again the characteristic dimension of soil grain is 0.1� 310− m. In the final model, sub-floor soil was assumed to have a complex, rocky structure (Figures 7&8). This has been done by subtracting randomly, about 45-50 pentagon shaped areas of various dimensions and orientations from the modelling plane, and then by meshing the remaining area. The pentagons correspond to rocks and stones embedded in the soil, and among them there exist randomly distributed many narrow passages. Because of this structure, the suction (-120 Pa) applied by ASD was not able to establish a smooth pressure and air-flow velocity distribution underneath the concrete slab. If this is the case, usually it is somewhat more difficult to remedy the elevated indoor radon level.

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References 1. U.S. Environmental Protection Agency, Office of Research and Development. Radon-Resistant Construction Techniques for new Residential Construction. EPA / 625 / 2-91 / 032 (1991).

2. Loureiro C. d O., Simulation of the Steady-State Transport of Radon From Soil into Houses under Constant Negative Pressure. Dissertation; The University of Michigan, (1987). 3. Middelman S., An Introduction to Fluid Dynamics: Principles of Analysis and Design, John Wiley & Sons Inc., ISBN 0-471-18209-5, (1998) . 4. ANSYS Basic Analysis Procedures Guide 001086 3rd Ed. ANSYS Release 5.5. ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317. 5. ANSYS Verification Manual 001095, 3rd Ed, ANSY Release 5.5, Groundwater Seepage, p.163. ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317. 6. Moaveni S., Finite Element Analysis, Theory and Application with ANSYS. Prentice-Hall, ISBN 0-13-785098-0, (1999). 7. ANSYS Elements Reference 001084, 10th Ed, ANSYS Release 5.5. ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317. 8. Holman J. P., Heat Transfer 7th ed. in SI Units. McGraw-Hill Book Co, ISBN 0-07-112644-9, (1992). 9. Zürcher, C., Frank, T., Bauphysik / Bau und Energie /Leitfaden für Planung und Praxis. vdf, Hochsch.-Verl. AG an der ETH Zürich ISBN 3-7281-1822-2 , (1998). 10. Clavensjö B., Åkerblom G., The Radon Book; Measures Against Radon. The Swedish Council for Building Research, DA: 1994, ISBN 91-540-5649-7, Stockholm (1994). 11. Nero A. V., Nazaroff W .Characterizing the Source of Radon Indoors. Radiation Protection Dosimetry Vol. 7 No. 1-4 p. 23-39, (1984). 12. Bear, J., Dynamics of Fluids in Porous Media, Dover Publicat. Inc. ISBN 0-486-65675-6 13. Nazaroff W.W. (Editor), Nero A. V. (Editor). Radon and its Decay Products in Indoor Air. A Wiley Interscience Publication, ISBN: 0-471-62810-7, John Wiley & Sons Inc. (1988). 14. Reddy, T. A., Sextro, R. G., Modelling Air Flow Dynamics in Radon Mitigation Systems, J. Air Waste Manage. Assoc., Vol. 41 No.11 pp.1476-1482, (1991). 15. Akis M. C., Stadtmann H., Kindl P., Experimental Analysis of an Active Sub-Slab Depressurization System, Developed for a Radon Test-House. Proceedings of the IRPA Regional Symposium: “Radiation Protection in Neighbouring Countries of Central Europe”, Prague, 8-12 September (1997), pp.72-75.