A numerical method has been developed to simulate the dissolution of a rough fracture of known topography, for which experimental dissolution patterns were available [1]. At high Peclet numbers (high flow velocity) the under-saturated fluid penetrates deep inside the fracture and the dissolution tends to be uniform throughout the sample, but at lower flow rates the erosion is slower and much more inhomogeneous, with a clearly visible dissolution front. This front becomes unstable with respect to fingering instabilities [2], since an increase in permeability within a channel enhances solute transport, leading to faster growth of the channel. As the dissolution proceeds, the channels compete for flow and the growth of the shorter channels eventually ceases. At the end of the experiment, the flow is focused in a few main channels while most of the pore space is bypassed.
Sample dissolution patterns obtained by simulation [3] and experiment are shown below at a Peclet number Pe = 216 (upper) and Pe = 54 (lower). Here we define the Peclet number Pe = Uh/D in terms of the mean flow velocity, U, the initial value of the mean fracture aperture,h, and the molecular diffusion coefficient, D. The experimental and numerical dissolution patterns are strikingly similar. The dominant channels develop at the same locations in the simulation and experiment, despite the strongly nonlinear nature of the dissolution front instability. While there are differences in the length of the channels, relatively small changes (of the order of 10%) in the diffusion constant or reaction rate can lead to comparable differences in the erosion patterns. Our results suggest that the simulations are capturing the effects of the complex topography of the pore space quite faithfully, despite the coarse aperture resolution of the flow solver.
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Aperture growth due to dissolution of a KDP fracture. The figures show patterns of aperture growth (in mm) at Pe = 216 (upper) and Pe = 54 (lower). The experimental results [1] are shown on the left and the corresponding simulation results [3] are on the right. The flow direction is from left to right. |
The time evolution of the flow in the fracture is illustrated in this video clip 5.8MByte AVI (Cinepac CODEC).