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SOIL PHYSICS

Dense Gas Flow in Volcanic Ash Soil: Effect of Pore Structure on Density-Driven Flow

^a Dep. of Biological and Environmental Eng., Graduate School of Agric.and Life Sci., Univ. of Tokyo, 1-1-1 Yayoi Bunkyo-ku, Tokyo, 113-8657, Japan
^b Dep. of Global Agricultural Sciences, Graduate School of Agric. and Life Sci., Univ. of Tokyo, 1-1-1 Yayoi Bunkyo-ku, Tokyo,113-8657, Japan

^* Corresponding author (S07de004{at}mail.saitama-u.ac.jp).

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Unique physical properties of volcanic ash soils characterize the soil gas transport parameters of gas diffusivity and air permeability. Air permeability controls the density-driven flow that has been recognized as one of the important phenomena for subsurface dense gas. In this study, one-dimensional column experiments were conducted to investigate the effects of the pore structure of a volcanic ash soil on the density-driven flow of a dense gas (isohexane). The results showed that the overall horizontal gas movement in Tachikawa loam (volcanic ash soil) and Toyoura sand (sand) used as reference materials was expressed by Fick's diffusion law. On the other hand, the vertical downward gas movements in Tachikawa loam were considerably enhanced by the occurrence of density-driven flow, especially at high air contents (30–40%). Pore size distribution and pore structure analysis based on the tube model suggest that a greater volume of large pores (>0.01 cm) and a more continuous pore network led to the greater density-driven flow in Tachikawa loam than in Toyoura sand.

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Volcanic ash soils exhibit unique soil properties such as high water retention, large total porosity due to noncrystalline materials like allophane, and good drainage, all of which are favorable for plant root growth (Shoji et al., 1993; Moldrup et al., 2003a). The texture is often classified as light clay or clay loam due to high clay contents (Fujikawa and Miyazaki, 2005). Those unique soil properties are closely related to a well-developed soil structure with the existence of aggregates (Shoji et al., 1993).

Highly developed soil structure in volcanic ash soil strongly affects the gas transport parameters of gas diffusivity and air permeability. Air permeability controls an advective (pressure gradient induced) gas transport, while gas diffusivity controls gas transport under a natural system where diffusive gas transport is typically dominating (Moldrup et al., 2003b). Moldrup et al. (2003a) observed a sudden increase in air permeability in undisturbed volcanic ash soils under dry conditions (around –10³ cm H₂O), which was explained by a highly connected pore network, although such a sudden increase was not apparent in the gas diffusivity. Moldrup et al. (2003a) also showed that the gas diffusivity as a function of air content was well predicted by the Campbell soil water characteristic model (Moldrup et al., 2003c), while a corresponding model for air permeability could not reproduce its sudden increase. Those differences between the gas diffusivity and the air permeability in volcanic ash soil may result from their different dependency on soil properties: while the gas diffusivity is mainly controlled by air-filled pore space and pore size distribution, air permeability is governed by pore configuration such as pore connectivity (Moldrup et al., 2003a). Nagata (1987) reported that air permeability measurements obtained from volcanic ash soils and non-volcanic-ash soils reflected the difference in soil structures and could be used as an index of aggregate structure. Several researchers have investigated soil structure (pore connectivity and continuity) on the basis of air permeability or gas diffusivity measurements (Ball et al., 1988; Schjønning et al., 1999; Moldrup et al., 2001; Schjønning et al., 2002).

The transport of gaseous chemicals is driven mainly by diffusion, advection, and dispersion (Lenhard et al., 1995). Studies on the transport of gases such as CO₂ in soils have investigated the transport in terms of diffusive movement because diffusion has been considered the main transport mode (Jury et al., 1983; Baehr, 1987; Cook et al., 1998; Plummer et al., 2004); however, several researchers have reported that density-driven flow, which is a kind of advective flow, might be an important transport phenomenon for a dense gas with a high molecular weight (Falta et al., 1989; Mendoza and Frind, 1990a,b; Lenhard et al., 1995). Density-driven flow occurs where the spatial difference in gas phase densities is caused by gravity. Lenhard et al. (1995) showed the occurrence of density-driven flow of trichloroethylene in two-dimensional cell experiments in sand and suggested that the vapor-density effects of volatile organic compounds (VOCs) on gas movement in soil should be considered. Altevogt et al. (2003) investigated the transport of freon-113 through air-dried sand in a one-dimensional laboratory column experiment with three flow directions (horizontal, vertically upward, and vertically downward) and high source densities. They reported that gas movement in the downward direction was enhanced compared with the horizontal direction due to the occurrence of density-driven flow. Falta et al. (1989) and Mendoza and Frind (1990b) showed by numerical simulations of VOC gas movement that the magnitude of the density-driven flow was strongly affected by a soil's physical properties, such as air permeability, the saturated vapor pressure, and the molecular weight of the gas. Hence, it is reasonable to suppose that the unique physical properties of volcanic ash soils may affect the density-driven flow of a dense gas. Further information about dense gas transport in volcanic ash soils is needed for remediation strategies for VOCs, such as soil vapor extraction or natural attenuation, and risk assessment of the contaminants.

The objective of this study was to examine the effect of the pore structure of a volcanic ash soil on dense gas transport, with emphasis on density-driven flow. One-dimensional laboratory column experiments were conducted to observe the movement of a dense gas, isohexane (2-methylpentane), in both a volcanic ash soil and a sandy soil. The column experiments were conducted with two different flow directions, horizontally and vertically downward, in an attempt to isolate the effect of gravity on density-driven flow, as shown in Altevogt et al. (2003). The pore structures of the volcanic ash soil were investigated from the aspects of gas diffusivity, air permeability, and the water retention curve.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Physical Properties of the Soil Sample
Two disturbed soils, Tachikawa loam (volcanic ash soil) and Toyoura sand (sand), were used in all of the experiments in this study. Tachikawa loam to depths of 70 cm was collected from an agricultural field in the Field Production Science Center at The University of Tokyo. Both soils were sieved to 2-mm mesh to obtain homogeneous physical properties. The disturbed soils were repacked uniformly at bulk densities of 0.50 Mg m^–3 for the Tachikawa loam and 1.50 Mg m^–3 for the Toyoura sand.

The physical properties of the soil samples are shown in Table 1 . From the measurement of the grain size distribution, Tachikawa loam and Toyoura sand were classified as clay loam and sand, respectively. The water retention curve of Tachikawa loam, repacked in 40-cm³ soil cores (5.0 cm i.d., 2.0 cm long) with bulk densities of 0.50 Mg m^–3, was measured by the hanging water column method from –10 to –100 cm H₂O and the pressure plate method from –10 to –1.0 x 10⁴ cm H₂O (Dane and Hopmans, 2002a,b). The water potentials of the air-dried samples of Tachikawa loam with three different soil water contents (0.60, 0.43 and 0.3 kg H₂O kg^–1 soil) were measured with a Dewpoint Potential Meter (WP4, Decagon Devices, Pullman, WA). The water retention curve of Toyoura sand was measured from –10 to –100 cm H₂O by using the hanging water column method and the pressure plate method (Dane and Hopmans, 2002a,b). Figure 1 shows the water retention curves of Tachikawa loam and Toyoura sand. The water retention curve for Tachikawa loam showed the two water drop ranges (pF 1–1.5 and >2.5), indicating the two pore systems of the volcanic ash soil due to the existence of aggregate structure, as shown in previous studies about volcanic ash soils in Japan (Iwata et al., 1995; Miyamaoto et al., 2003). The saturated hydraulic conductivity was measured with 100-cm³ soil cores (5.0 cm i.d., 5.1 cm long) by the falling head method (Reynolds and Elrick, 2002). Total specific surface area was determined by the ethylene glycol monoethyl ether method (Pennell, 2002).

View larger version (15K): [in this window] [in a new window]   Fig. 1. Water retention curves of Tachikawa loam and Toyoura sand fitted by the Durner's bimodal pore size distribution model (Durner, 1994) and the van Genuchten model (van Genuchten, 1980), respectively. The pF equals log(–) in centimeters of H2O, where is the soil-water matric potential.

The air permeability was measured by blowing pure air through a 100-cm³ core (5.6 cm i.d., 4.05 cm long) at three flow rates (each flow rate falling within 0.2–2.3, 1.7–10.3, and 5.7–60 dm³ min^–1, respectively) for each soil sample (Iversen et al., 2001). The procedure of repacking and the method of obtaining the different air contents for each soil sample were the same as the gas diffusivity measurements. The air permeability was calculated based on Darcy's equation by using the difference in the pressure across the core and the viscosity of the air (1.86 x 10^–5 Pa s) (Iversen et al., 2001).

Isohexane Gas Transport Experiments
One-dimensional laboratory column experiments were conducted in an apparatus consisting of a stainless steel column packed with either Tachikawa loam or Toyoura sand attached to an inlet chamber and a flux chamber (Fig. 2 ). The experiments were conducted in two experimental configurations: horizontally and vertically downward (inlet at the top). We performed three replicates for each air content in both configurations and both soils. A similar experimental setup and measurement procedure were shown in Altevogt et al. (2003). The column was 30 cm long with an inner diameter of 5.0 cm. The volumes of the inlet chamber and the flux chamber were 9.4 and 1.0 L, respectively, and they were constructed of 2.0-mm-thick stainless steel. After the soil was packed into the entire length of the column, one end of the column was connected to the edge of the inlet chamber (Fig. 2). The other end of the column was kept open to the atmosphere. Either Tachikawa loam or Toyoura sand was packed into the column with three different air contents: 40, 30, and 20%. The different air contents in the soil column were obtained by the same procedure as the measurement of the gas diffusivity. The flux chamber was connected to the right end of the column (Fig. 2) when the effluent gas flux from the column was measured. The inlet chamber and flux chamber were vented with Teflon tubing (1.0-m length and 2.0-mm inner diameter) to prevent the pressure gradients from being affected by external influences. The atmospheric pressure was confirmed by air pressure manometers that were attached to both of the chambers. Leakage of the entire system was checked by putting the experimental setup into water.

View larger version (12K): [in this window] [in a new window]   Fig. 2. Schematic diagram of the experimental setup.

[1]

where (m³ m^–3) is the air content, _g (kg m^–3) is the gas density of the isohexane, R is the retardation factor, D_p (m² s^–1) is the gas diffusivity of the soil, t (s) is time, and z (m) is length (Altevogt et al., 2003). In this study, Eq. [1] was analytically solved with an initial condition of _g = 0 kg m^–3 at t = 0 s and boundary conditions of _g = 0.71 kg m^–3 at z = 0 m and _g = 0 kg m^–3 at z = 0.3 m. The gas diffusivities of isohexane for both soils at 40, 30, and 20% air contents were calculated by relative gas diffusivity at each air content estimated from the approximated curves of measured relative gas diffusivity and gas diffusivity of isohexane in air (7.7 x 10^–6 m² s^–1) (Fuller et al., 1996).

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Gas Diffusivity and Air Permeability
Figure 3a shows the measured relative diffusion coefficient (D_p/D₀) in both soils and its predicted values by the Porosity Enhanced (POE) model proposed to predict the gas diffusivity for repacked soils (Moldrup et al., 2005). The POE model is described as

[2]

where (m³ m^–3) is the total soil porosity.

View larger version (11K): [in this window] [in a new window]   Fig. 3. (a) Gas diffusivity and (b) air permeability of Tachikawa loam and Toyoura sand as a function of air content. The solid and dotted lines in gas diffusivity represent the predicted curves of the Porosity Enhanced (POE) model (Moldrup et al., 2005) against measured data of both soils. The solid and dotted lines in air permeability indicate the approximations of measured data by the soil-water-characteristic-based model (Moldrup et al., 2003a) for both soils. Bars show the standard error of measured data (n = 5).

Figure 3b shows the measured air permeability and its predicted curves based on a soil-water-characteristic-based model (Moldrup et al., 2003a). Moldrup et al. (2003a) established the prediction model for air permeability with a reference point as

[3]

where k_a (µm²) is the air permeability, k_a,–10kPa (µm²) is the air permeability at –10kPa, _–10kPa (m³ m^–3) is the air content at –10 kPa, and is the tortuosity–connectivity parameter. Based on Moldrup et al. (2003a), we tested the tortuosity–connectivity parameter as = 1 + (b/20), where b is the Campbell pore size distribution parameter (Campbell, 1974), which is shown in the following equation:

[4]

where (cm H₂O) is the soil water matric potential, _e is the soil water matric potential at the air-entry point, (m³ m^–3) is the volumetric soil water content, and _s (m³ m^–3) is the saturated volumetric soil water content. In this study, the following values were applied to predict air permeability: k_a,–10kPa = 34.5 µm² for Tachikawa loam and 48.0 µm² for Toyoura sand, and _–10kPa = 0.41 m³ m^–3 for Tachikawa loam and 0.20 m³ m^–3 for Toyoura sand. Approximations of the Campbell model (Eq. [4]) to the measured water retention data up to 40% air content (equivalent to up to pF 4.0 for Tachikawa loam and pF 2.0 for Toyoura sand) gave Campbell b values of 14.8 for Tachikawa loam and 0.8 for Toyoura sand.

The air permeability of both soils increased as air contents increased (Fig. 3). The air permeability was significantly higher in Tachikawa loam at high air content than in Toyoura sand (three times higher at 40% air content). The values predicted by the soil-water-characteristic-based model agreed well with the measured values for both soils.

Several researchers have pointed out that air permeability is related to the pore size distribution, especially the volume of large pores (Blackwell et al., 1990; McCarthy and Brown, 1992). Table 1 shows the pore size fractions in Toyoura sand and Tachikawa loam at an air content of 40%. The equivalent pore radius r (cm) can be calculated from the fitted water retention curves (Fig. 1) as r = 0.15/| (–cm H₂O)| (Schjønning et al., 1999). For large pores (here large pores are defined as pores >0.01 cm, Schjønning et al., 1999), Tachikawa loam had greater volumes (15.9%) than Toyoura sand (6.8%), presumably because of the existence of interaggregate pores. This may explain the air permeability of Tachikawa loam being higher than Toyoura sand. In addition, Tachikawa loam may have a wider pore size distribution than Toyoura sand due to the existence of aggregates. For Tachikawa loam, the pores <0.005 cm in size were dominant (61.5%), whereas for Toyoura sand, more than half of the air-filled volume (53.0%) was restricted to pores ranging from 0.01 to 0.005 cm.

Isohexane Gas Transport with Horizontal Flow Direction
The Validity of Fick's Diffusion
The gas density profiles at 40% air content in the horizontal experiments are shown in Fig. 4a for Tachikawa loam and Fig. 4b for Toyoura sand. The plots in Fig. 4 represent the average of the three replicates. The solid lines in Fig. 4a and 4b show the Fickian model predictions, assuming that there was no gas adsorption onto soils (i.e., R = 1.0). The dashed lines in Fig. 4a indicate the Fickian model predictions when gas adsorption is considered (R = 2.0). In this study, only gas density profiles at an air content of 40% are shown because the trend of the gas density profiles at other air contents was similar to that at 40% air content. All the experiments showed that the gas density reached a quasi-steady state in 250 min, at which time the temporal deviation of observed gas density was <1%.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Gas density profiles for gas samples taken at 5, 15, and 25 cm from the column inlet of (a) Tachikawa loam and (b) Toyoura sand at 40% air content in horizontal experiments. The plots show the average of three replicates. The solid and dashed lines show the Fickian model predictions (Eq. [1]) with retardation factor R = 1.0 (no gas adsorption) and R = 2.0, respectively. Coefficient of variation of three replicates at each plot was <5%.

The calculated gas fluxes based on Fick's law in a steady state (Tachikawa loam: 4.4 x 10^–4 mg s^–1 cm^–2, Toyoura sand: 3.7 x 10^–4 mg s^–1 cm^–2) were comparable to the measured values (Tachikawa loam: 4.6 x 10^–4 mg s^–1 cm^–2, Toyoura sand: 3.8 x 10^–4 mg s^–1 cm^–2). The same agreement was also found in the other experiments (30 and 20% air contents) in both soils. These results indicate that the overall gas movement in the horizontal experiments can be expressed well by gas diffusion governed by Fick's law.

The Effect of Gas Adsorption on Isohexane Gas Transport
For Tachikawa loam, the gas densities at the 15- and 25-cm ports at early stages (0–100 min) showed a better agreement when gas adsorption was taken into consideration (Fig. 4a), while for Toyoura sand, a good agreement was found between the measured and the predicted gas densities at R = 1.0 (i.e., no adsorption). A large specific surface area of Tachikawa loam (more than two orders of magnitude larger than that of Toyoura sand, Table 1) might be responsible for the adsorption effect.

Isohexane Gas Transport with Vertical Downward Flow Direction
The Effect of Density-Driven Flow on Isohexane Gas Transport
Table 3 shows the measured effluent gas fluxes of the column experiments and the values predicted by Fick's law under the steady-state condition at three different air contents. In the vertical downward direction, the measured gas fluxes of both soils were significantly higher than those in the horizontal direction, and higher as well than Fickian model estimations. This clearly reveals the enhancement of gas transport in the vertical downward direction with the occurrence of density-driven flow. The effluent gas fluxes at 40% air content were higher than those at the other air contents in all the experiments. This might be attributed to the existence of more pore space available for the gas movement at 40% air content.

View larger version (13K): [in this window] [in a new window]   Fig. 5. Gas density profiles for gas samples taken at 5, 15, and 25 cm from the column inlet of (a) Tachikawa loam and (b) Toyoura sand at 40% air content in vertical downward experiments. The plots show the average of three replicates. The solid and dashed lines show the Fickian model predictions (Eq. [1]) with retardation factor R = 1.0 (no gas adsorption) and R = 2.0, respectively. Coefficient of variation of three replicates at each plot was <5%.

To investigate the causes for the greater density-driven flow in Tachikawa loam, the pore characteristics of both soils were investigated by applying the tube model of Millington and Quirk (1961) and Ball (1981). Millington and Quirk (1961) assumed soil pores to be uniform tortuous and unjointed tubes of similar diameter and expressed the tortuosity (L/L_s, the ratio of tube length L to sample length L_s) and the equivalent pore diameter d (cm), the effective diameter of the drained pores active in leading air through the sample, by combining Fick's law and Poiseuille's law as

[5]

[6]

The tortuosity L/L_s and the equivalent pore diameter d as a function of air content were calculated by Eq. [5] and [6] using the measured gas diffusivity and air permeability.

Figure 6a shows the relationship between calculated tortuosity and air content. The tortuosity decreased as air content increased for both soils, although the data for Tachikawa loam appeared to be decreasing linearly, whereas it decreased rapidly from 20 to 30% air content in Toyoura sand. Except for the lowest air content (around 20%), similar values of tortuosity were observed as this result could be implied from the results of gas diffusivity (Fig. 3a). The larger tortuosity for Toyoura sand at low air content may be explained by a greater water-induced disconnectivity of soil pores than in Tachikawa loam (Schjønning et al., 2002). The small pores filled with water in Toyoura sand may reduce the diffusion pathway through larger pores.

View larger version (10K): [in this window] [in a new window]   Fig. 6. (a) Tortuosity and (b) equivalent pore diameter of Tachikawa loam and Toyoura sand calculated from Eq. [5] and [6], respectively. The data sets of the averaged gas diffusivity and air permeability at each air content (Fig. 2 and 3) were used for the calculation.

From the estimated pore characteristics, it can be shown that density-driven flow, which is an advective gas flow, occurred mainly through the continuous large pores in Tachikawa loam. Moldrup et al. (2001) showed that continuity and the size of pores have little effect on gas diffusivity but have dramatic effects on air permeability. Hence, the more pronounced density-driven flow in Tachikawa loam than Toyoura sand can be attributed to the greater continuity and connectivity of the large pores, which were inferred from the results of the pore structure analysis.

	CONCLUSIONS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
For horizontal gas movement, the gas density profiles and the effluent gas fluxes were well described by Fick's diffusion model in both Tachikawa loam and Toyoura sand. In the vertical downward experiments, enhancement of the gas movement was clearly found in both soils, suggesting the occurrence of density-driven flow. The degree of the enhancement was, however, much greater in Tachikawa loam than in Toyoura sand. Pore structure analyses indicated that the existence of large interaggregate pores and the more continuous pore network enabled Tachikawa loam to have higher air permeability, which in turn led to the occurrence of greater density-driven flow in the downward gas movement.

	ACKNOWLEDGMENTS

 
We wish to express gratitude to Hiromi Imoto, Univ. of Tokyo, for his technical assistance during the laboratory experiments.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
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Received for publication February 19, 2007.

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