Phase-Field Modeling of Wormhole Formation and Growth in Carbonate
Matrix Acidizing
- Kenji Furui,
- Tatsuro Abe,
- Takahiro Watanabe,
- Keita Yoshioka
Keita Yoshioka
Department of Environmental Informatics, Helmholtz Centre for Environmental Research - UFZ
Author ProfileAbstract
Acidic fluid flow in geologic formations leads to mineral dissolution
and, under certain circumstances, to localized dissolution forming a
dendritic pattern, known as wormhole. Such patterns of conduits and
caves are often observed in karstic aquifer and deliberately engineered
in oil and gas well stimulation with acid injection. Experimental
studies suggest that various parameters such as fluid velocity or
material heterogeneity control the wormhole formation. While many
numerical and experimental studies found the acid flow velocity to play
a controlling role, most models need to randomly seed material
heterogeneities to induce wormholes. Here we show that a phase-field
approach, which diffuses a sharp interface in a continuous manner, is
capable of simulating wormhole without random seeds by accounting for
the energy expenditure in the dissolution topology. We verified the
model against the sharp interface counterpart in one-dimensional
simulations. We then performed the two-dimensional simulations to
qualitatively validate wormhole formation and growth patterns against
acid injection experiments on carbonate rocks under radial flow
conditions. The simulation results indicate that the injected acid is
rapidly consumed near the acid entry point at low injection rates while
the live acid becomes available at the tip of the dissolved cavity under
high rates and thus wormhole starts to grow resulting in much faster
acid breakthrough.