Observations of the impact of rock heterogeneity on solute spreading and mixing

Abstract

Rock heterogeneity plays an important role in solute spreading and mixing in hydrogeologic systems. Few observations, however, have been made that can spatially resolve these processes in 3-D, in consolidated rocks. We make observations of the spatially resolved steady state concentration of a sodium iodide solute while flowing brine through cylindrical rock cores using X-ray CT imaging. Three rocks with an increasing level of heterogeneity are chosen: a Berea sandstone, a Ketton carbonate, and an Indiana carbonate. The impact of heterogeneity on solute transport is analyzed by: (1) quantifying spreading and mixing using metrics such as the transverse dispersion coefficient, the dilution index, the reactor ratio, and the scalar dissipation rate and (2) visualizing and analyzing flow structures such as meandering, flow-focusing, and flow-splitting using isoconcentration contour maps. The transverse dispersion coefficient, D t , and the variation in D t throughout the rock core, increases with Pecl et number (Pe) and rock heterogeneity. The reactor ratio indicates that mixing is Fickian for the Berea sandstone and Ketton carbonate, but diverges for the Indiana carbonate. The temporal evolution of the scalar dissipation rate, a measure of the mixing rate, remains close to that of Fickian mixing for the Berea and Ketton rocks but not for the Indiana. Heterogeneous rock features are observed to cause meandering, focusing, or splitting of the plume depending on Pe.

Measuring, imaging and modelling solute transport in a microporous limestone

“…As shown in Figure 15, for Ketton Limestone (d P ≈ 600 µm), we obtain σ = 2.5 from the fitted longitudinal dispersivity (α L = 0.15 cm). This value is roughly one order of magnitude larger than the measured transverse dispersivity in Ketton Limestone [46], and compares favourably with estimates reported in the literature for various rocks, including Berea Sandstone (α L = 0.1 − 0.3 cm) [19], Indiana Limestone (α L = 0.38 cm) [54] and, most significantly, Ketton Limestone (α L = 0.16 cm using m = 1 in Eq. 22) [15].…”

“…D eff can be determined from the molecular (bulk) diffusion coefficient, D, through a correction factor, (D eff = D/X with X > √ 2 [13]), so as to accounts for the obstructions presented to diffusion in a tortuous pore space [1]. Transverse dispersivity (α T ) is considered to be negligible in this study, as it is about one order of magnitude smaller than the corresponding value in the longitudinal direction, according to the results reported in the literature for beadpacks (α L /α T ≈ 30 [45]) and Ketton Limestone (α L = 0.16 cm [15] vs. α T = 0.013 cm [46]). We also note that the Fickian treatment implies that the injected tracer pulse has evolved into a Gaussian plume on a length-scale that is smaller than the length of the rock sample.…”

“…In our study, m = 1 and we attribute this behaviour to the cancellation, upon flow reversal, of the distortion of the solute plume caused by the presence of permeability heterogeneity. This distortion cannot be smoothed out by the effect of transverse dispersion alone, because the latter is limited in Ketton (α T /α L ≈ 0.1 [46]) and the length scale of the heterogeneities is significant (∼ length of the sample, L). A large portion of these 'spreading' effects can however be eliminated upon flow reversal (again, due to the limited action of transverse dispersion) and the echo breakthrough curve appears therefore more diffusive.…”

Calibration of astigmatic particle tracking velocimetry based on generalized Gaussian feature extraction

“…For easier processing, the resulting images were inversed, causing the particles to appear bright and the background dark. The inverted images were smoothed by four different 2D median filters of sizes [3,5], [5,3], [1,3] and [3,1] pixels. The filters were applied separately and the results were averaged.…”

“…The area of flow in porous media relates to many processes which are driven by pore-scale velocities. Prominent examples are dispersion 1,2 reactive transport 3,4 and mass transfer 5,6 . Conventional measurement techniques used for the investigation of flow in porous media, such as X-ray computer tomography and positron emission tomography, achieve frame rates of <1 frame per second.…”