A fractal model to describe the evolution of multiphase flow properties during mineral dissolution

• We present a physically-based theoretical model of a fractal porous medium.
• The model describes porosity, permeability, saturation, and diffusion coefficient.
• The model calculates the evolution of these properties during rock dissolution.
• Under simplifying conditions the expressions are equivalent to empirical relations.

Understanding the changes in multiphase flow parameters caused by mineral dissolution-precipitation is required for multiple applications ranging from geological storage of CO2, enhanced geothermal energy production or ground water pollution. We present a physically-based theoretical model for describing the temporal evolution of porosity, saturated and relative permeabilities, retention curve and diffusion coefficient during rock dissolution by reactive fluids. The derivation of the model is based on the assumption that the pore structure of the rock can be represented by an ensemble of capillary tubes with fractal tortuosity and cumulative pore size distribution. Therefore, the model depends only on the minimum and maximum pore radii, the size of the representative elementary volume and the fractal dimensions of pore size and tortuosity, but do not need any other fitting parameters. Using this fractal description and known physical properties, we obtain analytical expressions for the hydrodynamic properties required by continuum (i.e., Darcy scale) multiphase flow models. Further, assuming periodic fluctuations in the radius of the pores, it is also possible to represent constrictivity and hysteresis. Finally, assuming a constant rate dissolution reaction it is possible to derive closed-form analytical expressions for the time evolution of porosity, retention curve, saturated and relative permeabilities and diffusion coefficient.