A Pore-Scale Model for Dispersion and Mass Transfer during Acoustically Assisted Miscible Displacements in Porous Media

Enhancing flow and transport in porous media by acoustic stimulation has been investigated for the past several decades. Most studies focused on the effect of sound propagation in immiscible displacements. Much less emphasis has been given to understand the beneficial mechanisms during miscible displacements. In this work, a pore-scale model is developed to study the influence of acoustic excitation on dispersion and mass transfer in porous media. The modeling involves first solving for the single-phase fluid flow without the acoustic field, then calculating an external acoustic pressure field across a stationary saturated medium, and finally evaluating the interaction between the acoustic field and the flowing fluid. Simulations are run at different injection velocities, wave frequencies, and acceleration amplitudes. Concentration profiles of the pore-scale model show that the mass transfer between the mobile and immobile regions is accelerated under the sonication. In addition, the dispersion coefficient is increased due to the enhanced effective diffusivity and the additional acoustically induced velocity. To quantify the enhancement in transport, dispersion and mass transfer coefficients are calculated by matching the analytical solutions of the continuum transport model with effluent concentration profiles obtained by pore-scale simulations. At lower injection rates, dispersion coefficient is more affected by acoustic excitation compared to mass transfer coefficient. Lower frequencies and higher acceleration amplitudes of the propagated waves increase the enhancements in dispersion and mass transfer coefficients. The results at higher viscosity ratios indicate that low-frequency excitation could be a promising technique for improving miscible displacements. The effects of controlling parameters are summarized in a proposed dimensionless group of A(D) for designing effective acoustically assisted experiments in the laboratory.