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Heterogeneity of permeability is an important factor affecting the production of a carbonate reservoir. How to correctly characterize the heterogeneity of permeability has become a key issue for carbonate reservoir development. In this study, the reservoirs were categorized into four superimposed modes based on the actual logging data from a super-giant heterogeneous carbonate reservoir in the Middle East. A modified permeability formula in terms of the variogram method was presented to reflect the heterogeneity of the reservoirs. Furthermore, the models of oil production and water cut were established and the analytical solutions were obtained. The calculation results show that the present model can predict the productivity of wells with different heterogeneous layers more accurately and rapidly. The larger the varigoram value, the stronger the heterogeneity of the reservoirs, and the faster the decline of production owing to a quicker reduction of formation pressure. With the increase in variogram value, the relative permeability of the oil phase is smaller and the water phase larger, and the water cut becomes larger. This study has provided a quick and reasonable prediction model for heterogeneous reservoir

Production Characteristics with Different Superimposed Modes Using Variogram: A Case Study of a Super-Giant Carbonate Reservoir in the Middle East