Algorithms for numerical modeling and inversion of multi-phase fluid flow and electromagnetic measurements

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Alpak, Faruk Omer

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The focus of this dissertation is the estimation of petrophysical properties of rock formations based on the combined use of electromagnetic and fluid-flow measurements. Traditionally, borehole electromagnetic measurements are interpreted independently in terms of spatial variations of electrical resistivity. The estimated spatial variations of electrical resistivity are subsequently interpreted in terms of variations of fluid saturation and porosity. Such a strategy can lead to erroneous conclusions concerning the petrophysical evaluation of rocks because the spatial distribution of electrical resistivity is often governed by the interplay between salt concentration, absolute permeability, relative permeability, and capillary pressure. To date, no consistent effort has been advanced to use the physics of multi-phase fluid flow as the leading phenomenon in the interpretation of borehole electromagnetic measurements. This dissertation develops several efficient nonlinear inversion algorithms that quantitatively combine borehole electromagnetic and fluid-flow phenomena. These inversion algorithms also provide a measure of uncertainty and non-uniqueness in the presence of noisy and imperfect measurements. The combined use of electromagnetic and fluid-flow measurements drastically reduces non-uniqueness and uncertainty of the estimated petrophysical parameters and, therefore, increases the accuracy of the estimates. Specific problems considered in this dissertation are the estimation of spatial distributions of porosity, permeability, and fluid saturation, as well as the estimation of relative permeability and capillary pressure. Joint and independent nonlinear inversions are performed for large-scale petrophysical properties from in-situ permanent sensor data and near-borehole scale petrophysical variables of rock formations from wireline formation tester and electromagnetic induction logging measurements. For cases where fluid-flow related measurements are absent, the coupled dual-physics inversion strategy allows quantitative interpretation of electromagnetic measurements consistent with the physics of fluid flow. It is conclusively shown that the simultaneous use of fluid-flow and electromagnetic data sets reduces non-uniqueness in the inverted petrophysical model.