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This book provides the details of the study done for Ph.D. dissertation. It serves as both a study guide and a foundation for the probable future works. In this study a hybrid Pore Network (PN) model that simulates water-oil drainage and imbibition mechanisms was developed. This model produces Nuclear Magnetic Resonance (NMR) T2 relaxation times using correlations available in the literature. The PN was calibrated using experimental relative permeability data obtained for Berea Sandstone, Kuzey Marmara Limestone, Yenikoy Dolostone and Dolomitic Limestone core plugs. PN body and throat parameters were obtained from serial computerized tomography scans and thin section images. It was observed that the PN model can be used to model different displacement mechanisms. By using the synthetic data obtained from PN model, an Artificial Neural Network (ANN) model was developed and tested. It has been observed that the ANN tool can be used to estimate water-oil relative permeability data very well given a T2 signal. It was finally concluded that the developed tools can be used to obtain multiphase flow functions directly from an NMR well log such as Combinable Magnetic Resonance (CMR).