Estimation of sub-core permeability statistical properties from coreflooding data

Knowledge of sub-core permeability is necessary for accurate numerical modeling of coreflooding experiments and for investigation of sub-core flow phenomenon. A new method for estimating sub-core permeability geometric mean (k_G) and log-permeability variance (σ_y ²) is presented. The method is based on matching coreflooding experiment measurements of wetting phase relative permeability with semi-analytical calculations of effective relative permeability. The semi-analytical solution is formulated assuming log-normal permeability (k), steady state and capillary-limit conditions. It is based on the geometric mean and log-phase-permeability variance for isotropic k and power law averaging for anisotropic correlations. The solution is validated on synthetic k realizations by comparison with numerical calculations. Then, the estimation method is tested on synthetic data assuming various types of core capillary pressure relationships, relative permeability functions and k anisotropies. Results demonstrate high accuracy in almost all of the cases except for small anisotropy ratios l_h/l_v between horizontal (l_h) and vertical (l_v) dimensionless correlation lengths, where flow is in the horizontal direction, and when σ_y ² is large. The method is also validated using data from CO₂-brine coreflooding experiments conducted on two different cores. It is found that the estimation method remains accurate in these realistic settings, however, accuracy of k_G is reduced when the core permeability departs from a log-normal distribution.