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Gas Diffusion Measurement and Modeling in Coarse-Textured Porous Media

^a Dep. Plants, Soils and Biometeorology, Utah State University, Logan, UT 84322-4820
^b Civil and Environmental Engineering Department, University of Connecticut, Storrs, CT 06269-2037
^c Space Dynamics Laboratory, 1695 North Research Park Way, North Logan, UT 84341

View larger version (33K): [in a new window]   Fig. 1. Illustration of (a) a conventional soil core attached to a diffusion cell with a hypothetical coarse-textured water retention curve depicting the distribution of water content, , and difference, , between the core profile top and bottom. The relationship (b) between water retention, h(), and soil gas diffusion, Ds, is linked through air-filled porosity, . Similar to water content distribution in the sample profile, (c) Ds is also distributed within the sample thickness, where a thinner sample exhibits less variation in Ds.

View larger version (22K): [in a new window]   Fig. 2. Modeled substrate water characteristic curves for different particle size ranges of (a) sand (Schroth et al., 1996) and (b) calcined clay are plotted using Eq. [1]. In (b) both measured draining (filled symbols) and wetting (empty symbols) retention curves for the aggregate external (macropore) water are shown.

View larger version (52K): [in a new window]   Fig. 3. Gas diffusion chamber design showing source (O2) and sink (N2) chambers on either side of the substrate chamber, each of specified length assuming each with the same cross-sectional area as the substrate chamber. Each air chamber is equipped with a galvanic O2 sensor and dual solenoid valves for air and N2 priming. The substrate chamber is underlain by a porous stainless steel sheet providing water to the substrate and with a heat pulse moisture probe and tensiometer for matric suction determination.

View larger version (52K): [in a new window]   Fig. 4. Idealized aggregated substrate showing internal aggregate porosity, i, and external pore space, e, where the solid fraction, s, forms the aggregate and there is a distinct pore-size difference between the two regimes.

View larger version (21K): [in a new window]   Fig. 5. Modeled water retention for the calcined clay (0.25–0.85 mm plotted in Fig. 2) compared with the wetting and draining process measured by pumping and tensiometric readings showing the expected hysteresis in water retention. Order of measurement is indicated by numbers and pressure jumps arise from ambient air pressure changes during diffusion.

View larger version (18K): [in a new window]   Fig. 6. Concentration change of O2 (%) measured in the sink and source chambers of the diffusion cell showing both the gas priming stage and diffusing stage (note different time scales). The modeled diffusion coefficient was fit using Eq. [3] to the measured sink chamber concentration for 1 to 2 mm calcined clay with = 0.22 and the resulting value of Ds = 0.88 cm2 min-1.

View larger version (20K): [in a new window]   Fig. 7. Measured oxygen diffusion coefficients in (a) 1- to 2-mm aggregates using manual adjustment of sample water content and (b) 0.25- to 0.85-mm aggregates using automated control. The WLR model (Moldrup et al., 2000) assumes a total porosity of 0.37 (Eq. [8]) and models the external pore diffusion only. The M&S model (Millington and Shearer, 1971) describes the entire pore system including measurements made in the internal pore water domain using a conventional diffusion chamber where samples are pre-wet and repackaged for each measurement. Two identical diffusion cells were used for measurements in the external pore domain where wetting and draining indicate the process of addition or removal of water between measurements.

View larger version (26K): [in a new window]   Fig. 8. Sample thickness- and gravity-dependent gas diffusivities computed as the ratio of the integrated diffusion coefficient [Ds(1 g)] and the diffusion coefficient computed at the mean water content of the sample [Ds(0 g)]. Both the integration of Ds(1 g) and the integration of water content at which Ds(0 g) is computed are taken over the sample thickness, T, (e.g., 1.9 cm in the diffusion cell) using the draining retention curves shown in Fig. 2b. The relative water content, , at the sample base is 0.99 for each of the five media shown. Representative sample volume indicators described by ratios of ten times the mean particle diameter, d, to sample thickness (i.e., 10 x d x T-1) are plotted for d = 1.5 and 0.55 mm, representing the 1- to 2- and 0.25- to 0.85-mm particles, respectively.