Fracture dissolution: simulations and microfluidic experiments


Figure 1: Dissolution of a gypsum chip: After several days the dissolution front shows a pronounced fingering instability (left panel). The contours of the (three-dimensional) front can be measured in situ from the optical intensity, as illustrated by a false color plot of the largest finger (center). The optical measurement can be confirmed by profilometry measurements at the end of the experiment (right). These experiments were made by Filip Dutka and Piotr Szymczak.

Figure 2: Simulation of fracture dissolution. The gypsum surface is viewed from below and is the negative of the experimental image.

Recent microfluidic experiments [1] have allowed for direct visual observation of the instabilities that can occur during fracture dissolution. Deionized water is injected at constant flow rate over a thin (0.5mm) chip of gypsum (38mm x 33mm), replacing the initially saturated solution. Dissolution of gypsum occurs mostly near the fresh water inlet, where the solution is least saturated. After about 48 hours the gypsum near the inlet has dissolved fully, as can be seen from the empty region near the inlet in the left panel of Figure 1. The irregular dissolution front indicates an instability [2], which is driven by a coupling between fluid flow and dissolution. Small perturbations in surface of the gypsum (of the order of 5-10 micron) generate fluctuations in the flow field and enhanced dissolution in regions where the flow is larger. This feedback mechanism causes an exponential growth of sinusoidal perturbations, of which a single mode is preferred because it has the highest growth rate [2]. The predicted wavelength agrees well with the early stages of dissolution of the gypsum chip [1].

Numerical simulations [3] have been used to model gypsum dissolution within the same microfluidic geometry. The fingering pattern is similar to the experimental observations (Figure 1). In particular we note the typical competition between the growing fingers that leads to patterns of hierarchical growth [4]. A further point of contact is in the development of the partially dissolved region ahead of the tip of the fully dissolved finger. This can be seen most easily in the profilometry image (Figure 1, right panel), but it is also visible in the simulation (Figure 2).

References

  1. F. Osselin et al.. Geophys. Res. Lett., 43:6907-6915, 2016.
  2. P. Szymczak and A. J. C. Ladd, EPSL, 201:424-432, 2011.
  3. V. Starchenko, and A. J. C. Ladd. Water Resources Res., In Press, 2018.
  4. V. Upadhyay, P. Szymczak, and A. J. C. Ladd. J. Geophys. Res., 120:6102-6121, 2015.

Collaborators

Vitaliy Starchenko
Piotr Szymczak




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