Flow through a saturated, granular, porous medium can lead to internal erosion,
preferential flow enhancement, and the formation of channels within the bulk of the medium. We
examine this phenomenon using a combination of experimental observations, continuum theory
and numerical simulations in a minimal setting. Our experiments are carried out by forcing water
through a Hele-Shaw cell packed with bidisperse grains. When the local flow-induced stress exceeds
a critical threshold, the smaller grains are dislodged and transported. This changes the porosity
of the medium, thence, the local hydraulic conductivity, and leads to the development of erosional
channels. Erosion is ultimately arrested due to the drop in the mean pressure gradient, while most
of the flow occurs through the channels. We describe this using a minimal multiphase description
of erosion where the volume fraction of the fluid, mobile, and immobile, grains change in space
and time. Numerical solutions of the resulting initial boundary value problem yield results for the
dynamics and morphology that are in qualitative agreement with our experiments. In addition to
providing a basis for channelization in porous media, our study highlights how heterogeneity in
porous media may arise from flow as a function of the erosion threshold.