Prediction of CO2 injection performance in deep subsurface porous media relies on the ability of the well to maintain high flow rates of carbon dioxide during several decades typically without fracturing the host formation or damaging the well. Dynamics of solid particulate suspensions in permeable media are recognized as one major factor leading to injection well plugging in sandstones. The invading supercritical liquid-like fluid can contain exogenous fine suspensions or endogenous particles generated in situ by physical and chemical interactions or hydrodynamic release mechanisms. Suspended solids can plug the pores possibly leading to formation damage and permeability reduction in the vicinity of the injector. In this study we developed a finite volume simulator to predict the injectivity decline near CO2 injection wells and also for production wells in the context of enhanced oil recovery. The numerical model solves a system of two coupled sets of finite volume equations corresponding to the pressure–saturation two-phase flow, and a second subsystem of solute and particle convection–diffusion equations. Particle transport equations are subject to mechanistic rate laws of colloidal, hydrodynamic release from pore surfaces, blocking in pore bodies and pore throats, and interphase particle transfer. The model was validated against available laboratory experiments at the core scale. Example results reveal that lower CO2 residual saturation and formation porosity enhance CO2-wet particle mobility and clogging around sinks and production wells. We conclude from more realistic simulations with heterogeneous permeability spanning several orders of magnitude that the control mode of mobilization, capture of particles, and permeability reduction processes strongly depends on the type of permeability distribution and connectivity between injection and production wells.