Characterization of wormhole dissolution in different fractal dimensionless fractures

Wormhole dissolution is a key phenomenon in various underground geo-engineering applications, such as carbon dioxide sequestration, contaminant migration in groundwater and petroleum reservoirs stimulation. It can create conductive channels for fluid flow and significantly enhance the permeability of fractured reservoirs. Fractal dimension is an important parameter to characterize the fracture surface topography. We employ a Fourier-transformation based approach to generate different fractal dimension fracture surfaces, and two mated surfaces with a specified aperture can form artificial fractured 3D rocks. We use the lattice Boltzmann method to simulate the wormhole dissolutions in 3D fractured rocks by varying Péclet and Damköhler numbers. We analyze the permeability evolutions and aperture spatial distributions under different Pe and Da conditions. Our simulations indicate that the fractal dimension has a non-linear effect on permeability change. It implies that, for a given fractured rock, the permeability evolution rate increases as both Pe and Da numbers increase; for the same Pe and Da conditions, when Pe and Da are both small, the permeability evolution rate decreases as the fractal dimension increases; however, when Pe and Da are both large, the permeability evolution rate increases as the fractal dimension increases. Based on the aperture spatial distribution analysis, we find that when the ratio of Da to Pe is large, the inlet regions are almost completely dissolved, which would slow down the rate of permeability increase.