Relative permeability and capillary pressure are important parameters in reservoir engineering calculations and numerical simulation of reservoir performance. Heterogeneities are often avoided during core-plug screening and selection for relative permeability and capillary pressure measurements. However sandstone rocks in many depositional environments show significant small-scale laminations that affect the measured relative permeability. This report demonstrates the length-scale dependence of relative permeability data that results from centimeter- to millimeter-scale rock laminations and patterns of initial and final oil-saturation distribution in laminated core. It shows quantitatively the capillary trapping of water in low-permeability laminae during primary drainage and of oil in high-permeability laminae during water imbibition. Steady-state water/oil imbibition relative permeability data and unsteady-state drainage and imbibition data were collected with linear X-ray and X-ray CT scanning for in-situ fluid-saturation measurement. Numerical simulations of the corefloods show that relative permeabilities and capillary pressures that are correlated with small-scale differences in porosity and permeability ability are necessary to reproduce the observed saturation distributions. Thus, the relative permeability length-scale dependence, combined with anisotropy data, implies that scaled-up effective relative permeability must account properly for heterogeneity. Assignment of core-plug relative permeability to simulator gridblocks may not capture the correct effective fluid flow performance in rocks that are heterogeneous with correlation length greater than the plug dimensions, leading to erroneous fluid flow performance predictions.