Initial conditions or emergence: What determines dissolution patterns in rough fractures?

Abstract

Dissolution of fractured rocks is often accompanied by the formation of highly localized flow paths. While the fluid flow follows existing fractures in the rock, these fissures do not, in general, open uniformly. Simulations and laboratory experiments have shown that distinct channels or “wormholes” develop within the fracture, from which a single highly localized flow path eventually emerges. The aim of the present work is to investigate how these emerging flow paths are influenced by the initial aperture field. We have simulated the dissolution of a single fracture starting from a spatially correlated aperture distribution. Our results indicate a surprising insensitivity of the evolving dissolution patterns and flow rates to the amplitude and correlation length characterizing the imposed aperture field. We connect the similarity in outcomes to the self‐organization of the flow into a small number of wormholes, with the spacing determined by the length of the longest wormholes. We have also investigated the effect of a localized region of increased aperture on the developing dissolution patterns. A competition was observed between the tendency of the high‐permeability region to develop the dominant wormhole and the tendency of wormholes to spontaneously nucleate throughout the rest of the fracture. We consider the consequences of these results for the modeling of dissolution in fractured and porous rocks.

Influence of Layering on the Formation and Growth of Solution Pipes

“…As observed, the pipes are now much more irregular and winding, but the overall patterns are very similar to those in Figure 7. This conclusion agrees with a more detailed analysis of Upadhyay et al [45] which shows that the statistical properties of the dissolution patterns are only weakly sensitive to the parameters governing the randomness in the initial porosity field. In the remainder of the paper, we focus on the low-noise regime, since a more regular geometry of the pipes in this case allows us to better discern the effects of the stratification of the porous matrix.…”

“…In a homogeneous system, the exponent α is close to unity [24,39,45]. Figure 8 shows the length distributions corresponding to the patterns presented in Figure 7.…”

“…As shown in a number of studies [24,39,45] a strong screening between the dissolution channels usually leads to the power-law distribution of their lengths,…”

“…This data has been subsequently re-analyzed in Ref. [45], which led to the conclusion that-if one discards the partially buried pipes the full length of which remain unknown-the length distribution is found to be consistent with a power-law. Such scale-invariant distributions are a characteristic feature of a large number of hierarchical growth processes [46], observed experimentally e.g., in some of the viscous fingering systems [47,48], dendritic sidebranches growth in crystallization [49] or crack propagation in brittle solids [50].…”

Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth

“…Competition and flow focusing are determinant for the final pattern of nonreactive finger growth (Pecelerowicz et al, ) and the dissolution of fractures in the genesis of karst (Hanna & Rajaram, ; Szymczak & Ladd, ). The important role of competition is also suggested by the observed decay of the number of wormholes with depth, which follows a power law with exponent close to 1 (Budek & Szymczak, ; Krug et al, ; Upadhyay et al, ).…”