Relative Permeability Homogenization by a Regression Technique

Geological and geophysical expertise coupled to numerical simulation allow the petroleum industry to build increasingly detailed reservoir models. These models integrate the whole set of available data but involve geostatistics and stochastic approach. A large number of simulations is required to estimate hydrocarbon reserves and optimize oil recovery. Geoscientists begin by building a geological model respecting the real geometry of the reservoir and containing possibly million of cells. A reservoir model containing less cells is then built in order to ensure that numerical simulation is feasible within a reasonable time. Upscaling is the link between the geological model and the reservoir model. Multiphase flows upscaling is still an actual issue. In particular, relative permeability curves are characteristic of twophase flow equations. Upscaled relative permeabilities are called pseudo-functions. These functions are often computed for each different case, assuming special flow conditions. The purpose here is to propose a homogenization method for relative permeability by an optimization approach. Non-linear regression analysis can also generate pseudo-relative permeabilities. Such a method is here adopted. Production curves are to be matched by an optimization algorithm in order to generate a homogenized relative permeability model.