During coreflooding under stationary conditions, permeability is determined by the Darcy formula; thus, the apparent permeability is determined, which characterizes the average hydraulic conductivity of the core, but does not take into account the processes occurring at the microlevel. Transient processes during fluid injection regime change are important for understanding the evolution of permeability and underlie such phenomena as permeability degradation and its hysteresis. Our paper presents the coreflooding methodology and the results showing that during changes in injection conditions, the permeability of samples can significantly decrease due to the migration of colloids. In the developed methodology, coreflooding conditions exclude the influence of other factors on permeability, such as creep, the chemical reactions of rocks and fluids, and chemical mobilization of colloids. It has been established that the decrease in permeability occurs only when fluid is injected through the core, which is indirect evidence of pore blockage by colloids. The article also attempts to evaluate the effect of pore pressure on the sensitivity of the porous medium permeability to the amount of injected fluid. A decrease in pore pressure leads to a more intense decrease in permeability during injection, which most likely indicates additional mobilization of colloids, while the narrowing of pore channels does not affect permeability. Analysis of coreflooding results showed that porous media with lower permeability are more sensitive to colloid migration and pore pressure changes. It has also been found that the sensitivity of porous media to colloid migration is greatly affected by the pore pressure gradient, while media with higher permeability are less sensitive to colloid migration.