Abstract Understanding of high viscous fluid flow in porous media is very important in the accurate development plan for heavy oil reservoirs. Viscous fingering and effects of unstable flow are phenomenon that must be considered during displacements of heavy oil by water in reservoirs. Experimental problems in rock tests with high viscous fluids (due to exaggerated increases in pressure differential, early breakthrough times, large differences in mobility ratios) are some of the technical difficulties showed during the acquisition of relative permeability curves by unsteady state in heavy oil reservoirs. At the same way, difficulties in conventional interpretation (JBN interpretation is supposing uniform displacement) are challenges that numerical interpretations must be try to solve for modeling accurately what is happening inside rock. This paper presents a number of "best practices" for defining a reliable relative permeability curve in heavy oil reservoirs related to numerical modeling and experimental modeling. Description of phenomenon in a Colombian heavy oil reservoir field are shown for three petrophysical quality rocks (less than 500 mD, around 5000 mD and larger than 10000 mD). Capillary pressure effects are included in the modeling and its importance in the displacement is analyzed. Finally, results of sensibilities to different mobility ratios in crudes with different viscosities (5, 25, 100 and 1000 cp) are presented in the same group of rocks mentioned previously. The results of this study help to understand the influence of viscosity and its impact in total recovery.