Modeling of Chemical Tracers for Two-Phase Flow in Advective-Dominated Porous Media at Core Scale

Chemical tracer modeling in porous media plays a key role in subsurface applications including oil recovery, aquifer remediation, and geothermal energy production. In oil reservoirs, chemical tracers are critical to quantifying the remaining oil saturation in porous media after displacing processes, enabling the correct evaluation of the sweep efficiency of recovery methods at the field scale. Even though the transport of solutes under single-phase flow has been modeled extensively with numerous solutions, there are no existing mathematical approaches to examine the displacement of solutes in two-phase flow conditions. Therefore, we present in this research work the first analytical solutions derived to model the transport of ideal and partitioning tracers in porous media with mobile water and oil phases. The models presented are derived from the classic study of fluid displacement by viscous forces and the analysis of dynamic phase distribution in porous media, where key transformation variables are introduced to simplify the nonlinear advection-dispersion equation (ADE) into a conventional partial differential expression. In our derivation process, it is recognized that the dispersion effect can be superimposed onto an ideal concentration front via a singular perturbation expansion, resulting in practical solutions that do not require complex numerical calculations or inversion methods. The solutions derived are verified with numerical simulations and validated with experimental data under different flow conditions for the transport of ideal and partitioning tracers, demonstrating that the complex mechanisms of hydrodynamic dispersion, partitioning, and adsorption are accurately modeled under two-phase flow. Thus, our solutions can be used to rapidly evaluate tracer transport under the existing flow conditions in porous media, significantly reducing the number of experiments and simulations to characterize and select the correct tracer to be used in field applications.