Rock particles can easily become mobile and migrate in poorly cemented sandstone in a heavy-oil reservoir because of their higher density and viscosity. Deposition of the solid particles clog and bridge the pores and pore throats, leading to increased filtration resistances in the reservoir and decreased well output. In this work, we studied the process of particle migration and pore blockage under a microscope using an unconsolidated sandstone model. We studied the mechanism for migration of fine particles and their effect on the percolation capacity of a porous medium by monitoring the dynamic permeability in a poorly cemented sandstone sample, containing a mixture of particles of different sizes. We have shown that the change in permeability with particle migration depends on the size and type of the mobile particles and pore throats, the concentration of the migrating particles, the total number of particles, the pressure drawdown or fluid flow velocity, and the reduction in maximum permeability, while the clogging transition time is determined by the minimum size of the bridging particles. As an example of field application, we consider a strategy for oil production with sand control.