This paper examines an application of the method of characteristics (MOC) to evaluate the effectiveness of nanoparticles to mitigate fines migration in porous media. The positive contribution of nanoparticles to mitigate fines migration was characterized by the increase of maximum retention concentration of fines particles on rock grains through two reactions described in this paper: (1) adsorption of nanoparticles onto the fines/grain surface and (2) increased retention of fines attachment on the pore surface by means of reducing the surface potential between grains and fines. We develop semianalytic MOC solutions for two different scenarios of nanoparticle application to control fines migration: (1) coinjection of nanoparticles with fines suspension into 1D permeable medium and (2) precoating porous medium with nanoparticles before fines injection to evaluate the enhanced capability of porous medium to capture unsettled fines by success of nanoparticle application.

A nanoparticle adsorption front, a suspended fines front, and an attached fines front occur in our analytic solution, depending on conditions. The mitigation index (MI) is introduced to evaluate the success of nanoparticles to control fines migration. In addition, the proposed approach provides a fast and reliable method to optimize nanoparticles treatment (nanoparticles concentration and the required amount) to control fines migration. Through quantitative comparison of effluent history and concentration-profile plots, we verify the accuracy of the analytical solutions with both numerical simulations and experimental results. In practice, our analytical approach provides valuable insights into how nanoparticle application can help reduce fines migration in reservoirs suffering from fines-migration problems.

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