Multiphase flow in porous media is found in a variety of engineering problems, including those technologies focused on satisfying the energy needs of an expanding global population whilst minimizing the effects of human activity on climate change. The lattice Boltzmann method (LBM), a kinetics-based method, has displayed potential in simulating multiphase flow in geometrically complex porous media. In this work, the stability and accuracy of three popular collision models within the LBM will be investigated using standard single-phase benchmark tests. In the context of porous media, the permeability of a defined flow will also be determined using the three collision models. Higher stability limits and accuracy are observed for the multiple relaxation time collision model over the two other collision models investigated due to the ability to separately relax the moments corresponding to the problem physics.