Incorporating mm-m scale capillary pressure heterogeneity into upscaled numerical models is key to the successful prediction of low flow potential plume migration and trapping at the field scale. Under such conditions, the upscaled, equivalent relative permeability incorporating capillary pressure heterogeneity is far from that derived conventionally at the viscous limit, dependent on the heterogeneity structure and flow rate, i.e. dependent on the capillary number. Recent work at the SCA 2017 symposium (SCA2017-022) demonstrated how equivalent functions can be obtained on heterogeneous rock cores from the subsurface under drainage conditions; going beyond traditional SCAL. Experimental observations using medical CT scanning can be combined with numerical modelling so that heterogeneous subsurface rock cores can be directly characterized and used to populate field scale reservoir models. In this work, we extend this characterization approach by incorporating imbibition cycles into the methodology. We use a Bunter sandstone core with several experimental CO 2 -Brine core flood datasets at different flow rates (2x drainage, 1x imbibition and 2x trapping) to demonstrate the characterization of hysteretic multiphase flow functions in water-wet rocks. We show that mm-m scale experimental saturations and equivalent, low flow potential relative permeabilities can be predicted during drainage and imbibition, along with trapping characteristics. Equivalent imbibition relative permeabilities appear as a function of capillary number, as in the drainage cases. We also find that the form of capillary pressure function during imbibition has a large impact on the trapping characteristics, with local heterogeneity trapping reduced (or removed), if the capillary pressure drops to zero, or below at the residual saturation.