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UBC Theses and Dissertations

Adaptive optimal experimental design and inversion of a coupled fluid flow and geophysical imaging model for reservoir monitoring Fohring, Jennifer


Imaging and prediction of fluid flow within the subsurface provides information crucial to decision making processes in fields such as groundwater management and enhanced oil recovery. The flow of a fluid through a reservoir depends primarily on the permeability of the subsurface rock; a quantity that is often unknown throughout the entire domain of the reservoir. One method for predicting flow is to estimate the permeability of the reservoir and simulate flow through a mathematical subsurface flow model. Given the model, flow data can be inverted to estimate the permeability. However, this inversion approach can lead to inaccurate results due to the sparse sampling of flow data, and thus inaccurate predictions. To acquire a higher sampling of data, geophysical survey techniques are applied in order to efficiently collect a higher density of data sampled at the surface. These data are sensitive to changes to the geophysical properties of the reservoir due to flow. Inversion of geophysical data then provides images of changes to the geophysical properties of the reservoir. In order to estimate the flow parameters using geophysical data, the two mathematical models require coupling. The thesis therefore proposes two approaches to improve the imaging and prediction of flow. First, a novel coupled inverse problem for estimating the fluid velocity field and the initial geophysical property model from geophysical data is developed. Second, a new method of optimally designing the geophysical survey for the coupled inverse problem is developed. The new adaptive design approach builds on traditional A-Optimal design methods such that historic data are included in the design algorithm. This produces designs that adapt with flow in the subsurface and reduce the collection of unnecessary data. Both the coupled inverse problem and adaptive survey design method are demonstrated using a seismic tomography geophysical survey and a tracer advection fluid flow model. Numerical examples show that the coupled approach yields an improved flow estimate as well as improved image quality, while the adaptive optimal designs provide sufficient geophysical data.

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