Abstract: An example system for obtaining relative permeability from unsteady state saturation profiles is described herein. The system can include a pressure source configured to inject a first fluid into a core, and a nondestructive test (NDT) device configured to measure a saturation profile of a second fluid along the core. The saturation profile of the second fluid can be measured at each of a plurality of times. The system can also include a processor and a memory in operative communication with the processor. The processor can be configured to estimate one or more parameters related to conditions of the core directly from the respective saturation profiles, and calculate the relative permeability using the one or more parameters.