Numerical and dimensional analysis of nanoparticles transport with two-phase flow in porous media

•A general mathematical model is developed for the nanoparticles transport in porous media.•Numerical simulation of countercurrent imbibition in a small-scale is considered.•Dimensional analysis is introduced to examine contributions of each term of the model.•Several dimensionless numbers such as Da, Ca, Bo, and Sc are examined.•Variations of the fluids and solid properties due to nanoparticles addition are monitored.

In this paper, a mathematical model and numerical simulation are developed to describe the imbibition of nanoparticles–water suspension into two-phase flow in a porous medium. The flow system may be changed from oil-wet to water-wet due to nanoparticles (which are also water-wet) deposition on surface of the pores. So, the model is extended to include the negative capillary pressure and mixed-wet relative permeability correlations to fit with the mixed-wet system. Moreover, buoyancy and capillary forces as well as Brownian diffusion and mechanical dispersion are considered in the mathematical model. An example of countercurrent imbibition in a core of small scale is considered. A dimensional analysis of the governing equations is introduced to examine contributions of each term of the model. Several important dimensionless numbers appear in the dimensionless equations, such as Darcy number Da, capillary number Ca, and Bond number Bo. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles using numerical experiments.