Reservoir modelling with feature selection: A kernel learning approach

Geological realism is an increasingly important aspect of automated history matching and uncertainty quantification. While there are many algorithms that can automate the process of generating multiple history matched reservoir models, there is no guarantee that the changes made to the reservoir description to achieve a history match preserve geological characteristics. This paper proposes a novel data-driven approach to modelling the spatial distribution of petrophysical properties in reservoirs. The proposed approach applies an advanced kernel-based approach - Multiple Kernel Learning (MKL) - to integrate multiscale geological features. Measured reservoir properties and prior knowledge are fused in an intelligent way in order to improve the realism of reservoir models. We show how we can use MKL to combine prior geological knowledge with seismic data. Geologically tailored features (e.g. large scale continuous fluvial sand bodies, small scale heterogeneity, spatial variability around facies boundaries, etc.) are identified from delta using convolution filters to capture changes in gradients, orientations, sizes of geological bodies. Such spatial features are then used as separable input patterns for the MKL model to compute petrophysical reservoir properties through regression in high-dimensional kernel Hilbert space. MKL derives the internal model relations from data without enforcing predefined dependencies by optimising a weighted combination of kernels to fit to the conditioning data. We used Multiple Kernel Learning to achieve realistic reproduction of geological properties of a complex fluvial reservoir system. It provides flexible control over the model properties by kernel weighting of spatial patterns, which reflect different geological features and data interpretations. MKL is also able to maintain the right balance between model complexity and goodness of fit, yielding robust history matched models. Finally, Multiple Kernel Learning was integrated into a Bayesian uncertainty quantification framework for a synthetic reservoir to obtain uncertain production forecasts based on the ensemble of multiple history matched models. Copyright 2011, Society of Petroleum Engineers.