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

Abstract

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 AD for designing effective acoustically assisted experiments in the laboratory.

Effects of Acoustic Stimulation on Fluid Flow in Porous Media

“…18 In miscible displacements, the local velocity variations can accelerate mass transfer between the stagnant and mobile regions and change the dispersion coefficient and mixing indices. 19 The latter changes in mixing were also reported for ultrasonic treatments. 20 Such enhancements in the mixing between two phases can increase the reaction rate by reducing the mass-transfer resistance.…”

“…This range of capillary numbers is above the maximum capillary number of 10 –5 , which triggers capillary fingering effects at very small injection rates . Such instabilities at a low capillary number might complicate the study of sonication effects on recovery enhancements since a acoustic wave can change breakthrough time as well …”

“…73 Such instabilities at a low capillary number might complicate the study of sonication effects on recovery enhancements since a acoustic wave can change breakthrough time as well. 19 The effects of adsorbed acoustic energy by the medium can be evaluated by the fraction of wave energy transformed to heat averaged over a wave cycle, which is known as the inverse quality factor (Q −1 ). 74 Q −1 is a measurable quantity in the lab and accounts for the ratio of damped energy to the total input wave energy in the system.…”

“…Wettability alteration can occur under excitation by collapsing or reducing the thin wetting film which is formed once a nonwetting phase enters a saturated medium . In miscible displacements, the local velocity variations can accelerate mass transfer between the stagnant and mobile regions and change the dispersion coefficient and mixing indices . The latter changes in mixing were also reported for ultrasonic treatments .…”

“…For example, coupling sound waves to the frame of the medium would direct more energy to the fast-compressional wave that has significantly smaller energy attenuation than that of the slow waves . In addition to the positive reported effects of sonication in Table , negative effects of excitation, including decreasing rock permeability and an early breakthrough, were also reported in the literature. Explaining when and why excitation may have adverse impacts on recovery depends on associated mechanisms in a specific scenario.…”