The broad objective of this study is to determine the limitations of the three-phase relative permeability estimation technique by using the experimental approach. In order to achieve this goal, three-phase relative permeability experiments were conducted on a Berea sandstone core plug by using brine, hexane and nitrogen gas. An unsteady-state analytical technique and a numerical technique where a black oil simulator was coupled with a global optimization algorithm in a least squares manner was used to compute three-phase relative permeabilities. It has been found that basic assumptions of linear flow and monotonic saturation changes, required for three-phase extensions of two-phase Johnson-Bossler-Nauman (JBN) theory, are violated in the displacement experiments, leading to errors in computed relative permeabilites even at high rates.