Flows through porous media can carry suspended and dissolved materials. These sediments may deposit inside the pore space altering its geometry. In return the changing pore structure modifies the preferential flow paths resulting in a coupling between structural modifications and transport characteristics. Here we compare two different models that lead to channel obstruction as a consequence of subsequent deposition. The first model randomly obstructs pores across the porous medium, while in the second model the pore with the highest flow rate is always obstructed first. By subsequently closing pores, we find that the breakdown of the permeability follows a power law scaling, whose exponent depends on the obstruction model. The pressure jumps occurring during the obstruction process also follow a power law distribution, but in the case of random obstructions we observe a crossover between an initial regime and the clogging transition. This clogging transition is characterized by a universal scaling which follows the avalanche distribution of invasion percolation for both models.