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.