Effect of wind turbulence on gas transport in porous media: experimental method and preliminary results

We demonstrate a novel experimental arrangement for measuring wind turbulence‐induced gas transport in dry porous media under controlled conditions. This equipment was applied to assess the effect of wind turbulence on gas transport (quantified as a dispersion coefficient) as a function of distance to the surface of the porous medium exposed to wind. Two different strategies for the measurement of wind‐induced gas transport were compared. Experiments were carried out with O2 and CO2 as tracer gases with average vertical wind speeds of 0.02–1.06 m s−1. Oxygen breakthrough curves as a function of distance to the wind‐exposed surface of the porous medium were analysed numerically with a finite‐difference‐based model to assess gas transport. We showed that wind turbulence‐induced gas transport is an important transport mechanism that can be 20–70 times larger than molecular diffusion‐induced transport. Wind conditions and properties of the porous medium had strong controlling effects on this relationship. Importantly, we show that even though wind‐induced gas transport is greatest near to the wind‐exposed surface, it can have marked effects on the variation in gas concentration at much greater depths.


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Greenhouse gases play in important role in global warming. Soil is a source of some 47 greenhouse gases such as methane (CH4), carbon dioxide (CO2) and nitrous oxide 48 (N2O). Various soil properties affect soil gas emissions, such as humidity, 49 temperature, air pressure and vegetation (Oertel et al., 2016). Furthermore, the 50 emission of methane, which is an important greenhouse gas, can result from land 51 management such as from rice paddy soil and landfill sites that receive organic 52 matter (Topp & Pattey, 1997). Radon (Rn) is a radioactive gas that can move from 53 soil to the atmosphere with the potential to affect human health. Advective flow 54 controlled by wind and the difference between indoor and outdoor temperatures are 55 the main factors in the transport process of radon from soil to air and buildings 56 (Nazaroff, 1992). Oliver & Khayrat (2001) found that in addition to lithology, 57 4 factors such as elevation, soil depth and particle size can affect the spatial variation 58 in radon in the soil atmosphere. . 59 Wind action (high-frequency velocity or pressure fluctuations caused by wind 60 turbulence) has been shown in several cases to play an important role in the transport Woodruff (1958) found that the rate of water evaporation increased two to six times 71 for soil mulches and 10 to 15 times for gravel and straw when wind speed increased 72 from 0 to 40 km hour -1 . 73 Wind turbulence (gustiness) affects gas transport in porous media by inducing  Several studies have modelled the effect of the gustiness of wind on gas 80 transport in porous media in one, two and three dimensions (Farrell et al., 1966;81 Scotter & Raats, 1969; Kimball & Lemon, 1970;Colbeck, 1981 approaches showed that wind-induced gas transport in porous media is a multi-87 dimensional process, and that the use of sinusoidal functions to represent one-88 dimensional wind action generally underestimates gas transport. The above studies 89 show further that wind-induced gas transport decreases with increasing distance 90 from the surface exposed to wind action.

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In general, modelling of wind-induced gas transport has been done by simulating intensive simulations can be avoided, therefore, by modelling wind turbulence-103 induced gas transport as a purely dispersive process with a cumulative location-104 dependent dispersion coefficient, Dtot, that represents the sum of molecular diffusion, 105 Dm, and wind-induced mixing, Dw (Poulsen et al., 2001;Poulsen & Sharma, 2011).

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This approach, however, requires knowledge about the relation between Dw and 107 distance from the surface exposed to wind. Experimental investigations of Dw are 108 limited at present, however. The authors are aware of four earlier studies only that 109 focus on this property. Scotter & Raats (1968   This research had two main objectives, therefore. First, to measure the variation 124 in gas concentration of the porous medium in response to wind turbulence at 125 7 different distances from the surface exposed to wind, and second to use these 126 measurements to determine Dw as a function of distance to the surface exposed to 127 wind. Measurements were made by two different methods: (i) gas concentrations 128 were measured at both ends of a porous medium column, following the approach 129 used in previous research. To assess the effect of distance, columns of different 130 length were used with one end exposed to wind turbulence, and (ii) gas 131 concentrations were measured at several distances from the surface exposed to wind 132 simultaneously within the same column. The results are used to compare the two 133 methods of measurement and to assess the relation between the wind-induced 134 dispersion coefficient Dw and distance below the surface exposed to wind. (2) For a porous medium where gas concentration and wind conditions in the 149 atmosphere at its surface exposed to wind are uniform, net gas transport in the 150 porous medium is one-dimensional (Poulsen et al., 2001) and Equation (2) becomes: where z is the distance from the surface exposed to wind.
where ε is gas-filled porosity and ϕ is total porosity (assumed to be equal in media 157 with no liquid phase)

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Material characteristics 160 The dry porous medium used in this study was a crushed and polished, sub-rounded 161 marble rock with particle sizes that ranged between 6.3 and 14 mm. This material 162 was selected because it was very permeable to gas, which allowed the effects of 163 9 wind turbulence to penetrate deep into the medium. This also made it easier to 164 compare the methods to measure Dw and to assess the relation between Dw and 165 distance to the surface exposed to wind.

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Gas permeability in a porous medium, k, was determined by measurement of the 167 drop in pressure P across a sample of the medium with length L and cross-sectional 168 area As exposed to a gas flow Q, followed by the application of Darcy's law 169 (Kirkham, 1947), where  is the dynamic viscosity of the gas. Darcy's law was chosen because 171 relations between Q and P were approximately linear. Particle shape of the medium 172 was characterized by particle roundness, , given as (Russ, 2007)

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where Ap is the area of a two dimensional image of the particle and R is the major 175 axis of the best fitting ellipse to the area, Ap of the particle image. The roundness 176 was determined by analysing images of 459 randomly selected particles with ImageJ 177 (National Institutes of Health, Bethesda, MA, USA). An overview of the physical 178 characteristics of the porous medium is given in Table 1.   Figure 3 shows the six oxygen breakthrough curves for experiment B at wind 292 condition 3, which corresponds to the six oxygen sensors installed inside and below 293 the sample. Figure 3 shows the curves that represent the fitted numerical model.

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These show that it is possible to obtain models that fit well to the measured 295 concentration data. This was also the case for the remaining experiments, indicating 296 that Equation (3) can be used to describe wind-induced gas transport.

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Relation between wind-induced gas transport and distance to the surface exposed to  Table 2 are an indicator of the intensity of wind 351 turbulence) although the tendency is not fully consistent.
352 Figure 6a shows the breakthrough time (tb) as a function of depth for the 13 353 wind conditions. In this case breakthrough time is taken as the amount of time that 354 elapsed before the oxygen concentration at a given depth reaches 50% of its final 355 value (10.5 relative to 21% oxygen). As expected, tb increases with z ( Figure 6a).

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Although tb increases almost linearly with z for wind condition 0, the tb-z relation is  Table 2. suggests further that β also depends on wind conditions. A direct correlation between 397 β and wind characteristics, however, did not reveal any strong trends, which suggests 398 that this relation is possibly more complex. Furthermore, it is likely that the relations 399 in Figure 8 are specific to the type of porous material used, therefore, more data are 400 required to assess if this is the case. surface of the porous medium exposed to wind. In addition, we observed that 408 although wind turbulence affects gas dispersion close to the surface exposed to wind

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The results indicate further that measurements with deeper samples and with 416 multiple gas sensors placed inside the sample are more reliable than for a series of 417 thinner samples with the gas sensor placed at the bottom. Measurements with deeper 418 samples equipped with multiple gas sensors are also much more rapid to carry out, 419 therefore, we suggest that this approach should be adopted for the measurement of 420 wind turbulence-induced gas transport.  respectively,  is total porosity, k is air permeability and is particle roundness.   and curves are those that fitted best from Equation (10) to the measured data.  Note that the y-axis is reversed to represent measurement location better.