Browsing by Author "Doyle, Bryan"

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    A Hybrid Numerical Scheme for Immiscible Two-Phase Flow
    (2020-05-05) Doyle, Bryan; Riviere, Beatrice
    This thesis proposes a hybrid numerical scheme for immiscible, two-phase flow in porous media, for two separate partial differential equation (PDE) formulations. Discontinuous Galerkin (DG) methods are a commonly used numerical scheme in such applications due to their local mass conservation and ability to handle discontinuous coefficients. Another popular choice are fi nite volume (FV) methods, which are computationally cheaper than their DG counterparts but are only first order accurate and struggle when discontinuous coefficients are introduced. The proposed hybrid numerical scheme uses the DG method in areas of the domain where accuracy is important or around regions where coefficients are discontinuous, and the FV method in all other areas. Preliminary numerical results show that such a hybrid method produces similar results to the standard DG and FV methods in cases of homogeneous and heterogeneous fluid flow, at a fraction of the computational cost. Applications of this work include simulating the quarter- five spot validation test and the channel-flow problem.
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    Numerical Error Quantification of Agent-Based Models as Applied to Oil Reservoir Simulation
    (2018-01-05) Doyle, Bryan; Riviere, Beatrice
    Agent-based models (ABMs) provide a fast alternative to traditional oil reservoir models by applying localized inexpensive simulations, rather than solving a partial differential equation at every time-step. However, while there have been theoretical and numerical results obtained with ABMs in social science applications, the accuracy of ABMs has not been analyzed in the context of oil reservoir modeling. My project quantifies the accuracy of a specific ABM by comparing its results to a widely accepted reservoir model, based on Darcy's law. I show that while modeling single phase flow with a variety of reservoir scenarios, this ABM matches results given by the traditional simulator with less than 5.4% difference. I propose extensions of my work, including modeling two and three phase flow, and obtaining an accurate correlation between the ABM and traditional simulator parameters; such results would provide significant motivation in the extended use of ABMs in oil reservoir modeling.