Nanoparticles applications in the petroleum industry have grown significantly recently especially for EOR, and waterfloding. Although the nanoparticles are small, they can be retained in the porous media by different mechanisms (i.e. surface deposition, and plugging of pore throat either by single or multi-particles). The objective of this paper is to develop a mathematical model capable of capturing the different damage mechamisms and the associated permeability impairment. We introduce a mathematical model that combines Darcy and convection-diffusion equation to describe fluid flow, and nanoparticles transport and interaction in porous media. Pore throat size distribution is used to characterize pore-scale heterogeneity. Permeability field is generated as a function of the pore throat size distribution. Pore throat size and permeability distributions are dynamic functions of nanoparticles deposition and plugging. The mathematical model is solved on a two-dimensional domain using finite difference. The model was matched with experimental data to obtain the model parameters. The model shows that each of the three damage mechanisms can be dominant at specific conditions. The preliminary numerical results demonstrate that concentration and injection rate are the key factors that control the degree of formation damage. These parameters should be optimized to reduce the formation damage associated with nanoparticles transport in porous media. Mathematical modeling along with experimental studies can help to optimize the nanoparticles systems to minimize formation damage.

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