| Abstract: | The aim of this thesis is to explore and develop proxy models for a petroleum reservoir numerical simulator based on scientific machine learning methods. Numerical reservoir simulation is an essential tool used in all stages of petroleum reservoir exploitation. Several technical studies are performed using these simulations, supporting many business decisions. These simulations are computationally expensive, and the complexity of the analysis may require thousands of simulations. An active research area is searching for a proxy model which could estimate the simulation outputs with a fraction of its computational cost. We developed the Embed to Control and Observe method based on a convolutional autoencoder and the control system approach with physical loss functions. We showed our proxy model⁰́₉s potential by applying it to three reservoir models. The last two models contained non-active grid blocks, which most real reservoir simulation models also have. To overcome this, we introduce the use of partial convolutional layers in reservoir simulation applications. The error obtained on our application are considerably low, so a reliable proxy can be obtained by applying the proposed method. Physics Informed Neural Network has emerged as a powerful scientific machine learning tool. We developed a partial differential equation solver for hyperbolic problem that can automatically handle discontinuities. Our method can learn and localize the application of artificial viscosity during the neural network training procedure. We solved the Inviscid Burger⁰́₉s equation and the Buckley-Leverett problem. The method can potentially be applied to solve other hyperbolic PDE systems. We also formulate a two-dimensional two-phases reservoir simulation PDE set of equations to be used on the Physics Informed Neural Network framework. The significance of this study is that it shows the development and application of machine learning techniques associated with physical knowledge of the fluid flow phenomenon. These techniques have the potential to provide an inexpensive and reliable prediction of essential reservoir simulation outputs for the petroleum industry. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/197910 |
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