We utilize a modified form of the theory of invasion percolation in a gradient (IPG) in pore networks to simulate numerically immiscible displacement and reaction (solid formation and precipitation) in porous media. We examine the two-dimensional invasion patterns that result, as well as the change in prosity due to the solid precipitation and the subsequent pore blocking and how they depend on various parameters including the solid formation kinetics and the strength of the percolation gradient. This work clearly demonstrates that for two-dimensional systems it is not the overall change of porosity in the system that controls the ability of the porous medium to accommodate flow, but its transverse average. This is because localized pore blocking occurring in narrow zones perpendicular to the invasion front can completely eliminate flow.