A New Model to Calculate Oil-Water Relative Permeability of Shaly Sandstone

Oil-water relative permeability curves are the basis of oil field development. In recent years, the calculation of oil-water relative permeability in sandstone reservoirs by resistivity logging data has received much attention from researchers. This article first analyzed the existing mathematical models of the relationship between relative permeability and resistivity and found that most of them are based on Archie formula, which assumes the reservoir is clean sandstone. However, in view of the fact that sandstone reservoir is commonly mixed with shale contents, this research, based on the dual water conductivity model, Poiseuille’s equation, Darcy’s law, and capillary bundle model, derived a mathematical model (DW relative permeability model) for shaly sandstone reservoir, which calculates the oil-water relative permeability with resistivity. To test and verify the DW relative permeability model, we designed and assembled a multifunctional core displacement apparatus. The experiment of core oil-water relative permeability and resistivity was designed to prove the effectiveness of the DW relative permeability model in shaly sandstone reservoirs. The results show that the modified Li model can well express the transformational relation between resistivity and relative permeability in sandstone reservoir with low clay content. Compared with the modified Li model and the Pairoys model, the DW relative permeability model is more helpful to collect better results of relative permeability in shaly sand. These findings will play a significant role in the calculation of oil-water relative permeability in reservoirs based on resistivity logging data and will provide important data and theory support to the shaly sandstone reservoir characterized oil field development.