Petro-physical Properties Bias Around Uncertain Facies Boundary - Analysis, Correction by Conditional Property Interface Filler (CoPIF) and Impact on Ensemble-based Assisted History Match

With the advent of Ensemble methods for Assisted History Matching of reservoir models, it has become increasingly common to use initial ensembles of reservoir models consisting of a fixed (certain) grid geometry and variable (uncertain) 3D facies distributions and 3D petro-physical property distributions conditional upon facies. In such process, 3D facies realizations are often derived by modifying facies boundary locations around certain known 3D features (often from seismic interpretation).

In the context of a fixed grid, distributions of petro-physical parameters are biased because all the models in the initial ensemble are such that facies boundaries are located at grid boundary locations; in reality, the facies boundary can be located anywhere, and the petro-physical properties of cells containing facies boundaries differ from strictly facies-dependent statistics. The bias results, typically, in excessive variance of petro-physical parameters in initial ensembles in cells which possibly belong to different facies. Such variance bias has detrimental consequences on iterative inversion processes, incrementally introducing a cumulative error on the match term.

A 3D Facies Boundary Filter has been developed to statistically correct this bias over ensembles of initial models. The filter relies on the construction of a refined grid and simple averaging of petro-physical properties and is based on a hypothesis of piecewise linearity of facies boundaries between cell centres. In any ensemble approach, a filtered ensemble would be used to compute unbiased updates and such updates applied upon un-filtered ensembles. The filter helps obtain better matched models (closer to initial ensemble and/or, in synthetic cases, the truth) and ultimately determines better performance forecast. The bias will be illustrated through a simple 1D example, a 3D synthetic dataset and a real 3D field model. The principle of the filter will be detailed. The impact of the filter on the petro-physical statistics will be illustrated as well as its impact within the context of EnKF Assisted History Match.