Seeing Invisible Properties of Subsurface Oil and Gas Reservoir through Extensive Uses of Machine Learning Algorithms

Current geostatistical simulation methods allow generating multiple realizations that honor all available data, such as hard and secondary data under certain geological scenarios (e.g. 3D training image-based models, multi-Gaussian law, Boolean models). However, it is difficult to simulate large models that honor highly nonlinear response functions (e.g. remote sensing data, geophysical data or flow in porous media data). The large CPU cost to evaluate the response function imposes limitations on the size of the model. This is particularly the case when one desires to generate a sizeable set of realizations matching the same data. The objective of this study is to generate multiple realizations all of which honor all available data (hard and secondary data and especially the non-linear response function) under certain geological scenarios. First, we generate a large ensemble of possible realizations describing the spatial uncertainty for given hard and secondary data. Any fast geostatistical simulation methods can be used for generating these prior models. Secondly, using multidimensional scaling, we map these models into a low-dimensional metric space by defining a distance between these prior models. We propose to make this distance a function of the response function. Next, kernel principal component analysis is applied to the coordinates of realizations mapped in this metric space to create a kernel, or feature, space with linear/Gaussian type variability between the input realizations. In this space, we can apply optimization algorithms, such as gradient-based algorithms or ensemble Kalman filtering or gradual deformation method to generate multiple realizations matching the same data. A back-transformation, first from the kernel space, then to metric space and finally to the actual space of realizations allows then the generation of multiple geostatistical models that match all data, hard, secondary and non-linear response. We apply the proposed framework to generate a realistic model which honors geologic information and dynamic (time-varying) response data. A flow simulator is used as the non-linear response function and may require several hours of CPU-time per simulation. We show how this technique applies to non-Gaussian (e.g. multiple-point or Boolean) geostatistical models. We also demonstrate the importance of using a distance function tailored to the particular response function used in creating a low-dimensional parameterization of the ensemble of geostatistical model in feature space.