Nanoparticles transport in heterogeneous porous media using continuous time random walk approach

Abstract

Abstract Reservoir heterogeneities and reactive processes strongly affect the fluid flow in porous media. The mechanism of transport and reaction of the fluid varies from pore-to core-scales, leading to the discrepancies between theoretical predictions and experimental observations, which are caused by the anomalous diffusion. Also, the reactive processes in porous media may alter reservoir properties in different spatial and temporal scale, varying subsequent transport and reaction behaviors. In this article, the coupled transport and reaction process in heterogeneous porous media is studied. The Continuous Time Random Walk (CTRW) framework incorporating particle tracking (PT) method is proposed to simulate the transport and reaction processes at pore-scale and show macroscopic behavior at core-scale. Utilizing the CTRW-PT approach, the motion of solute particles is described as a combination of random independent spatial and temporal increments in each walk step. The particle transition distance and time are chosen from a joint space-time probability density function by a stochastic process. The modeling of reaction is followed by the modeling of transport and updates the change of porous media with its effect on following transport and reaction. Simulations of non-reactive tracer and reactive nanofluid flow under different heterogeneity, injection flow rate and rate of reaction were performed. By adjusting the ensemble parameter β and t 2 the effects of the above factors on flow behavior are accounted. The concentration profiles with time are displayed to show the effect of heterogeneity, flow rate and rate of reaction on anomalous behavior. Higher level of heterogeneity, higher flow rate and rate of reaction are captured by smaller β and larger t 2 quantitatively, representing more anomalous flow behavior. The breakthrough curves from CTRW-PT simulation well match the experimental as well as Advection-Diffusion-Reaction Equation (ADRE) modeling results in most cases. The CTRW results also better match the experimental results than the ADRE as the anomalous behavior becomes significant. It is also found that CTRW-PT simulation as a statistical approach is more computationally efficient than solving the ADRE.