Polymer solutions are used commonly in oil-recovery applications to reduce water production. While the polymer treatment is known to modify the permeability of the rock, the mechanism by which this occurs is poorly understood, and, hence, the ability to optimize either the polymer solution or its application is restricted. In this work, the pulsed-gradient spin-echo nuclear magnetic resonance technique is used to determine displacement propagators (distributions) for brine solution flowing through a Bentheimer sandstone rock core, both before and after treatment of the rock core with a polyacrylamide polymer solution. A novel simulation strategy employing the lattice–Boltzmann method is then proposed to interpret the differences in these propagators in terms of the location of polymer retained within the pore structure of the rock following treatment. The results suggest that the polymer is preferentially trapped in comparatively low permeability pores.