SERVICIOS DE ATENCION AL USUARIO

Chapter 5 presents the solution for the flow rate into a ‘house’ with a bare soil floor and footing walls with width and depth, using the conformai mapping of the solution found in chapter 4. Then chapter 6 discusses an experiment carried out by the author, with

colleagues at BRE, on the flow rate into a hut with a suspended timber floor. The geometry corresponded to the previous solution, allowing a comparison of the two; this is the subject of this chapter.

Chapter 5 equation (5.25) gives a theoretical expression for the flow rate into the radon pit as

Flow = 14x10®. k (mV^) = 5x10'® . k (m'h-'>

where k is the permeability of the sand in the radon pit.

Since the flow rate was measured (see Chapter 6) as 14 ± 6 m^h ' using this in equation (5.25) suggests the permeability of the sand to be

k s a n d -p it“ 2 . 8 X 1 0

but with the 90% confidence interval based on the uncertainty in the flow measurement being

1.6 X 10*®

< ksand-pit < 5.2 x 10'® m^.

This is typical for sands [Mowris 86] and is close to that measured for the sand in the laboratory,

K an d -lab “

1 X 10 '®

The cause of the difference is likely to be one of the following:

1) Neglecting the corner effects in calculating the theoretical flow rate into the hut.

The fact that the model assumes infinitely long walls means that the flow per metre is under predicted near a comer. This is because it only considered flow in two dimensions, and this is not true near the comer. The effect of this is difficult to calculate, but could be significant.

2) The leakiness of the subfloor walls of the hut has been neglected in the theory.

This means that all of the flow measured going through the fan has not necessarily come through the sand as has been assumed here. Hence the real flow through the sand at a given pressure will be lower than that measured here, although the amount of the difference is hard to estimate.

3) Leaks from the pipes used to measure the sand permeability in the laboratory.

When the permeability of the sand was measured in the laboratory it is possible that some leakage occurred. This would suggest a greater rate of flow through the sand than actually occurs, resulting in a predicted permeability higher than the correct value. This is perhaps indicated by the fact that the NRPB

measurement mentioned in chapter 6 gave a result slightly lower than that carried out at BRE. The NRPB test used a metal container that was more air tight than that used in the BRE test.

4) Uncertainty in the compaction and water content of the sand in the laboratory.

The degree of compaction of a material, and its moisture content affect the resulting permeability. In general a more compacted material has less air space within it, and so allows less flow through it for a given pressure. Hence in measuring the permeability of a sample of sand it is necessary to consider the degree of packing, and how this compares to conditions in the ground. It is likely

that any sample of sand will be less compacted in the laboratory than in the ground, so that the laboratory will give a value of permeabihty higher than the ‘real’ one.

However sand is relatively less prone to packing effects because of the small size of the particles, so that the effect due to compaction will be less than in some other materials. This topic is returned to in the part of this thesis on high pressure flows.

The moisture content also has an impact, with a high moisture content expected to reduce permeability by occupying the air space through which gas moves. If the tested sample is too dry it would be expected to give a high result, but if it is too wet it would probably be too low.

Both 1 and 2 would cause the calculated permeability to be reduced from the 3 x 10'^^ m^ predicted, while 3 would reduce the laboratory measured permeability. Point 4 could affect the permeability in either direction, and deserves further investigation. It is likely however that the first two effects will be larger than the others, which would reduce the prediction of permeability to closer to the laboratory result.

Overall the result is clearly very encouraging, and shows good agreement between the two methods of finding the permeability, well within the considerable experimental errors involved in the experiments.

Comparing the two theoretical results

It is also interesting to compare the results of the simple analytical result of chapter 3 and the more advanced solution of chapters 4 and 5. Carrying out the flow rate calculation using equation (3.2), with the factors m and n being 1.07 and 1.65 respectively for the radon pit hut, the flow rate per metre run of wall is given by

Flow = 1.5x10^® . k (m^h'^ per metre run of wall).

As before there are 4.28 metres of wall, so that the full result is

Row = 6.4x10^°. k (m^h'^).

This result is higher than that predicted for the more advanced theory which with the measured flow rate of 14 (m^h’O then predicts a slightly lower permeability of

k s a n d -p it“ 2 . 1

X

m l

The simpler theory is expected to produce a higher flow rate because it has neglected the depth of the footing walls, so this difference is as expected. However it is interesting to note that the difference is comparatively small. Further, the simpler theory has given a result closer to the laboratory test for the sand permeability. This is probably due to the reasons given above for the difference between the theory and the experiment, all of which still apply to the simpler theory.

Nevertheless, given the errors in the experimental data, it is not clear that the extra effort involved in the more advanced solution is justified, since the simpler solution has given a similar result. However it is only possible to observe this by calculating both, and extra insight is gained by the process. In addition, as the footing walls become deeper, the difference would become larger.