Pore-scale modeling of particle filtration in porous media

Particle retention in porous media occurs in many natural and environmental settings, such as waste-water purification, contaminants dispersion, fines migration and more. In petroleum engineering, particle retention (e.g. drilling mud invasion, produced water re-injection, polymer retention) will induce permeability decline and formation damage. Existing macroscopic models often fail to be predictive without empirical adjustments. A predictive micro-scale model of particle filtration is of great significance to the control of formation damage and to the economical exploitation of hydrocarbon reservoirs. In this work, a Lagrangian pore network model has been developed for particle deposition. The model tracks the transport trajectory of each individual particle in porous media. It is able to capture the complex particle-surface interaction during deposition and has been validated against published experimental data. A new gravity number is developed to better scale the filtration coefficient. The particle size distribution is found to be one of the causes of hyperexponential deposition. The permeability decline not only depends on the volume of deposited particles, but also on the surface charge. In addition, an Eulerian pore network model has been developed for particle jamming in porous media. The probabilistic nature of jamming has been systematically studied using a Discrete Element Method (DEM). Based on the DEM simulations, a unified model for the jamming probability has been created, which is able to predict the effect of friction, pore/particle size ratio, and particle concentration on jamming. The numerical results achieved good agreement with direct CFD-DEM and particle flooding experiments. We then combine the Eulerian model with a deposition model to predict polymer adsorption and mechanical entrapment in porous media. The hydraulic conductivity of a fouled cylindrical tube is updated using models that are created based on CFD simulations. It is found that the longitudinal dispersivity is larger breakthrough curve broader than a Newtonian fluid for a power-law fluid with constant rheological properties. However, if the power-law parameters are functions of polymer concentration, the breakthrough curve is narrower than a Newtonian fluid because fluid is concentrated and thus more viscous in the fast flow paths. For particle retention, fluids with a high shear-thinning index result in more permeability reduction. For Bingham plastic fluids with concentration independent rheological properties, breakthrough occurs earlier as yield stress increases because the number of the dead-end or isolated pores increases. Compared with a Newtonian fluid, flow of a Bingham plastic fluid results in less jamming because particles are unable to enter the smaller pore throats that are closed to flow.