Bridging element-free Galerkin and pluri-Gaussian simulation for geological uncertainty estimation in an ensemble smoother data assimilation framework

The facies distribution of a reservoir is one of the biggest concerns for geologists, geophysicists, reservoir modelers, and reservoir engineers due to its high importance in the setting of any reliable decision-making/optimization of field development planning. The approach for parameterizing the facies distribution as a random variable comes naturally through using the probability fields. Since the prior probability fields of facies come either from a seismic inversion or from other sources of geologic information, they are not conditioned to the data observed from the cores extracted from the wells. This paper presents a regularized element-free Galerkin (R-EFG) method for conditioning facies probability fields to facies observation. The conditioned probability fields respect all the conditions of the probability theory (i.e. all the values are between 0 and 1, and the sum of all fields is a uniform field of 1). This property achieves by an optimization procedure under equality and inequality constraints with the gradient projection method. The conditioned probability fields are further used as the input in the adaptive pluri-Gaussian simulation (APS) methodology and coupled with the ensemble smoother with multiple data assimilation (ES-MDA) for estimation and uncertainty quantification of the facies distribution. The history-matching of the facies models shows a good estimation and uncertainty quantification of facies distribution, a good data match and prediction capabilities.