Geostatistical Modeling of Transmissibility for 2D Reservoir Studies

Abstract

Summary: A geostatistical approach is used to characterize reservoir transmissibility with the aim of assigning simulator parameters in 2D models. Transmissibility is represented as a spatial random function where heterogeneity is described by the probability distribution and the variogram of sample values. The key element of the geostatistical model is the definition of block transmissibilities as spatial geometric averages. Published analytical results have shown that the effective transmissibility of infinite, statistically isotropic flow fields is equal to the ensemble geometric mean. Numerical results presented here show that a spatial geometric average is an excellent approximation of effective transmissibility in such finite fields as simulator gridblocks. The geostatistical model for transmissibility is used to show that the mean and variance of block-averaged values depend on the averaging area. As the averaging area is increased, mean block transmissibility decreases toward the ensemble geometric mean while the block variance decreases to zero. The geostatistical model is also used to investigate the kriging of block transmissibilities from well data. The current method of correcting bias in kriged values is found to cause artifacts of gridblock size in flow simulation results. The simpler, uncorrected kriging estimator is shown to preserve overall flow-field transmissibility, regardless of gridblock size.