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This text book presents validation, diagnostics and field application of new physics based data analytics techniques to quantify communication between injection and production wells in a reservoir based on temporal fluctuations in rates. Such knowledge of reservoir heterogeneities and discontinuities is particularly important to optimize water flooding performance and eventually maximize oil recovery in water injection projects. These techniques combine a nonlinear signal processing model and multiple linear regression (MLR) to provide information about permeability trends and the presence of flow barriers. The new methods were tested in synthetic fields using rates generated by a numerical simulator and then applied to producing fields in Argentina, the North Sea, Texas, and Wyoming. The results indicate significance of these methods to provide better insight into the well-to-well connectivities. The applications to numerically simulated fields and then to real fields indicate that the methods are also capable of identifying whether the connectivity of an injector-producer well pair is through fractures, a high-permeability layer, or through partially completed wells.