Non-uniqueness and uncertainty quantification of relative permeability measurements by inverse modelling

Abstract

Abstract Relative permeability is traditionally obtained in core flooding experiments from production data and pressure drop either using analytical methods or inverse modelling. In most cases the inverse modelling is performed manually, which does, however, not provide a realistic estimate of the resulting uncertainty. Here we provide a framework for a consistent uncertainty assessment of relative permeability measurements. We find that extracting relative permeability from experimental core flooding measurements by inverse modelling with the numerical solution of the 2-phase Darcy equations is an ill-posed problem for which the non-uniqueness, correlation of matching parameters and non-Gaussian errors are observed. We also show that the assisted history matching strategy where the two-phase immiscible displacement modelling of the 2-phase Darcy equations in 1D is coupled with a Levenberg-Marquardt based optimization scheme and using an adequate representation of relative permeability and capillary pressure-saturation functions leads to a realistic description of the data and the associated uncertainty which is – depending on conditions – significantly smaller than error of a manual interpretation with tabulated relative permeability. These findings suggest that the resulting does depend to some extent on the choice of relative permeability parameterization which are either too restrictive or have too many (correlated) parameters.