Abstract

Fracture dissolution in carbonate rocks is of great interest for the applications of CO2 geological storage and formation of conduits and caves in karst reservoirs. Taking into account the fracture roughness and interporosity fluid exchange between the fracture and the porous host rock, the classical cubic law for parallel-plate channels or Poiseuille's flow for tubes cannot describe the flow within the fracture's opening. The Reynolds number increases along the fracture as a result of the influx crossing the fracture walls. The wavy, irregular, nonparallel-plate shape of the boundaries affects the overall flow regime and the average flow model. The velocity field on the fracture boundaries possesses a slip and a normal component. The nonzero fluid velocity maintains the concentration gradient near the porous host rock and provides a fresh source of the solvent that facilitates dissolution. The aim of this work is to point out the role of fracture roughness and the influx of fluid from the porous host rock on fracture dissolution. The effective model of flow in a single fracture with permeable wavy walls is coupled to transport of dissolved calcite. The asymptotic solutions of the steady-state Navier-Stokes equations with slip boundary condition are used to determine the velocity field in the fracture opening. Two cases of axisymmetric and parallel-plate wavy fractures are considered. The inflow through the walls increases the Reynolds number along the fracture and results in local flow instabilities and formation of reverse flow. The local instabilities arise in relatively higher Reynolds numbers in parallel-plate wavy fractures than in cylindrical wavy fractures. The averaged pressure drop along the fracture is represented as quadratic and cubic corrections to the linear law. The corrections result from the effect of the inflow through the walls and the irregular geometry of channel. Asymptotic solutions to the reactive transport of the dissolved calcite in the acidified brine are derived for rate-limited reactions with a low Damkohler number and high Peclet number. The role of the fracture's walls corrugations, fractures aspect ratio, porous host rock permeability, and the interporosity fluid exchange between the fracture and host rock on the fracture dissolution is investigated.