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Numerical prediction of rock properties is a rapidly evolving area that has the potential to influence dramatically how core analysis is performed. In this paper, we investigate the numerical prediction of relative permeability from micro-computed tomographic images using pore network modeling. Specifically, we apply four different algorithms to a digital image of a reservoir sample that has been tested using traditional core analysis, and compare the results. The four algorithms are the following: quasi-static, unsteady-state, steady-state periodic, and steady-state non-periodic. They differ significantly in terms of the physics that they are designed to capture and their computational performance, but there is no published research quantifying how these differences affect the simulation of relative permeability. We show that the traditional quasi-static algorithm exhibits outstanding computational performance, but gives results that are the most different from the other three methods. The unsteady- and steady-state simulations give surprisingly similar results given the differences in how relative permeability is obtained. The two steady-state methods differ little under the conditions tested. This result is encouraging because the periodic simulation is significantly more computationally efficient. However, it raises questions about the ability to capture hysteretic behavior. Phase saturations are mapped from the network results onto the digital images of the pore space as a means to help interpret differences in the pore-scale behavior of the models. Finally, results are compared to relative permeabilities from laboratory corefloods.