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Gravity drainage is one of the essential recovery mechanisms in naturally fractured reservoirs. Several mathematical formulas have been proposed to simulate the drainage process using the dual-porosity model. Nevertheless, they were varied in their abilities to capture the real saturation profiles and recovery speed in the reservoir. Therefore, understanding each mathematical model can help in deciding the best gravity model that suits each reservoir case. Real field data from a naturally fractured carbonate reservoir from the Middle East have used to examine the performance of various gravity equations. The reservoir represents a gas&ndash, oil system and has four decades of production history, which provided the required mean to evaluate the performance of each gravity model. The simulation outcomes demonstrated remarkable differences in the oil and gas saturation profile and in the oil recovery speed from the matrix blocks, which attributed to a different definition of the flow potential in the vertical direction. Moreover, a sensitivity study showed that some matrix parameters such as block height and vertical permeability exhibited a different behavior and effectiveness in each gravity model, which highlighted the associated uncertainty to the possible range that often used in the simulation. These parameters should be modelled accurately to avoid overestimation of the oil recovery from the matrix blocks, recovery speed, and to capture the advanced gas front in the oil zone.

A post-fracturing evaluation is essential to optimize a fracturing design for a multi-stage fractured well located in unconventional reservoirs. To accomplish this task, a production logging tool (PLT) can be utilized to provide the oil production rate of each fracturing stage. In this research, a practical method is proposed to integrate PLT and surface production data into a reservoir model. It applies the ensemble smoother for history-matching to integrate various kinds of dynamic data. To investigate the validity of the proposed method, three cases are designed according to the frequency of PLT surveys. Each fracture half-length calibrated by PLT data is similar to the true value, and the dynamic behavior also has the same trend as true production behavior. Integration with PLT data can reduce error ratios for fracture half-length down to 48%. In addition, it presents the applicability of reserve prediction and uncertainty assessment. It has been proven that the more frequently PLTs are surveyed, the more accurate the results. By sensitivity analysis of PLT frequency—a cost-effective strategy—a combination of only one PLT survey and continuous surface production data is employed to demonstrate this proposed concept.