A three-dimensional particle tracking model for colloid transport in porous media was developed that predicts colloid retention in porous media in the presence of an energy barrier via two mechanisms: (1) wedging of colloids within grain to grain contacts; (2) retention of colloids (without attachment) in flow stagnation zones. The model integrates forces experienced by colloids during transport in porous media, i.e., fluid drag, gravity, diffusion, and colloid-surface Derjaguin-Landau-Verwey-Overbeek interactions. The model was implemented for a fluid flow field that explicitly represented grain to grain contacts. The model utilized a variable time stepping routine to allow finer time steps in zones of rapid change in fluid velocity and colloid-surface interaction forces. Wedging was favored by colloid: collector ratios greater than about 0.005, with this threshold ratio increasing with decreasing fluid velocity. Retention in flow stagnation zones was demonstrated for colloid: collector ratios less than about 0.005, with this threshold decreasing with increasing fluid velocity. Both wedging and retention in flow stagnation zones were sensitive to colloid-surface interaction forces (energy barrier height and secondary energy minimum depth). The model provides a mechanistic basis for colloid retention in the presence of an energy barrier via processes that were recently hypothesized to explain experimental observations.