When a roll moves over a partially fluid filled porous layer, the degree of saturation in the porous layer will change in an a priori unknown area which is affected by the roll. In this work, a mathematical model is developed that describes the saturation dynamics in the porous layer for moderate rolling velocities. The model is based on two-phase flow equations in one dimension. It can be expressed as a nonlinear second order convection-diffusion equation that can be solved by standard (upwind) finite volume techniques. The size of the area affected by the roll, and within this area the degree of saturation, fluid pressures, and fluid velocities, can be predicted. An example is studied where a fully saturated zone evolves between the rolls when the rolling velocity is increased beyond some critical value.