Efficient Data-Driven Simulations of Subsurface Phenomena

Delineation of geological features from limited hard and/or soft data is crucial to predicting subsurface phenomena. Ubiquitous sparsity of available data implies that the reliability of any delineation effort is inherently uncertain. We present probabilistic support vector machines (pSVM) as a viable method for both lithofacies delineation from sparse data and quantification of the corresponding predictive uncertainty. Our numerical experiments demonstrate an agreement between the probability of a pixel classifier predicted with pSVM and indicator Kriging. While the latter requires manual inference of a variogram (two-point correlation function) from spatial observations, pSVM are highly automated and less data intensive. We also investigate the robustness of pSVM with respect to its hyper-parameters and the number of measurements. The deep learning methodology is also considered to solve a similar problem. Convolutional Neural Network (CNN) is applied to obtain an accurate geobodies segmentation from underground data given sparse labeling of geobodies in a 3D seismic volume. Augmenting the CNN model with the semi-supervised learning approach allows us to leverage the limited training dataset in this niche field while improving upon naive, baseline results.

After the geological structure is understood, reservoir simulation is performed to determine the productivity of the field. This portion of the thesis concerns the numerical solution of the underground fluid flow system, which is inherently stiff. Applying an explicit numerical scheme on a stiff system is proven to be challenging as the required time step could be so small that it is infeasible to compute. Even though stiff systems are common in several engineering and science fields, particularly when complex physics is modeled, it remained difficult to solve until recently. This paper discusses one of the best performance schemes called exponential time differencing. Such a scheme takes advantage of the natural separation of the problem as a linear stiff term and non-linear non-stiff term by solving the first portion analytically and solve the second part numerically. Such natural separation, however, is not found in multiphase flow in oil and gas reservoir simulation. This thesis demonstrates the way to reformulate the problem to a simple stiff equation so exponential time differencing can be applied. Numerical experiments demonstrate that the best scheme considering time step size is the combination of exponential time differencing and fourth-order Rung-Kutta scheme.

Dendumrongsup, Nutchapol and Tartakovsky, Daniel M. (2019). EFFICIENT DATA-DRIVEN SIMULATIONS OF
SUBSURFACE PHENOMENA. Stanford Digital Repository. Available at: https://purl.stanford.edu/bd016zd6593