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There are a number of challenges associated with the determination of relative permeability and capillary pressure. It is difficult to measure both parameters simultaneously on the same sample using conventional methods. Instead, separate measurements are made on different samples, usually with different flooding protocols. Hence, it is not certain that the pore structure and displacement processes used to determine relative permeability are the same as those when capillary pressure was measured. Moreover, at present, we do not use pore-scale information from high-resolution imaging to inform multiphase flow properties directly. We introduce a method using pore-scale imaging to determine capillary pressure from local interfacial curvature. This, in combination with pressure drop measurements, allows both relative permeabilities and capillary pressure to be determined during steady state coinjection of two phases through the core. A steady state waterflood experiment was performed in a Bentheimer sandstone, where decalin and brine were simultaneously injected through the core at increasing brine fractional flows from 0 to 1. The local saturation and the curvature of the oil-brine interface were determined. Using the Young-Laplace law, the curvature was related to a local capillary pressure. There was a detectable gradient in both saturation and capillary pressure along the flow direction. The relative permeability was determined from the experimentally measured pressure drop and average saturation obtained by imaging. An analytical correction to the brine relative permeability could be made using the capillary pressure gradient. The results for both relative permeability and capillary pressure are consistent with previous literature measurements on larger samples.