A New Mathematical Formulation for Estimating Flow Capacity and Phase Mobility in Oil-Water Segregated Flow Systems

A new analytical procedure is introduced for the interpretation of pressure-transient data in oil producers with pronounced water production. The new mathematical model is applicable to flow conditions where segregated flow dominates the displacement process in the reservoir. Here, formation flow capacity and individual magnitudes of oil- and water-phase mobility are also determined, allowing accurate reservoir characterization under such complex flow conditions. Segregated flow is very common in natural porous rocks and is characterized by a sharp interface between oil and water. Hence, our new mathematical model mimics the dynamics of this flow mechanism by taking into consideration the individual contributions of oil and water from each reservoir zone. This novel mathematical model is utilized to extract formation flow capacity and mobility for both phases. An average fluid saturation can also be determined with a reasonable accuracy. The reservoir system in hand is represented by a two-layer model with no crossflow between the different zones in the reservoir. Because of gravity effects, oil is produced from the top layer while water is produced from the bottom one. Each reservoir layer has its own distinct static and dynamic properties, such as porosity, permeability, thickness, and petrophysical properties. A case study based on synthetic reservoir data is presented to demonstrate the application of the mathematical model in characterizing formation rocks. It is observed that conventional well-testing methods could produce inaccurate results when applied to reservoir systems influenced by segregated flow. Using the new model, a correction factor is derived to estimate absolute permeability values from the conventional well-testing analysis, producing a one-to-one transformation between dispersed and segregated flow. The conventional way of interpreting pressure-transient data for two-phase flow displacements under segregated conditions is based on an equivalent single-phase flow model that might produce inaccurate results and invalid estimates of flow capacity and phase mobility. Our new approach, therefore, is more representative for the system under consideration and captures the flow mechanism more robustly.