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The Lorenz curve is used to estimate the heterogeneity of an oil reservoir. The corresponding permeability distributions in a series of concept reservoir models with a uniform average permeability but different heterogeneities are obtained and characterized by inverse calculation of the Lorenz curve. Then the development laws of a reservoir in relation to its heterogeneity are studied in method of numerical simulation. The results show that reservoirs with a Vk (permeability variation coefficient is defined in appendix) which characterizes the heterogeneity less than 0.2 have almost the same development rule. It is also found that the permeability profile is consistent with the water-cut profile in both positive and reverse rhythm reservoirs where injected water channels in high permeable layers. Furthermore, the water-cut profile of a reverse rhythm reservoir is more uniform than that of a positive rhythm reservoir. In addition, results also show an exponential relation between water-free recovery and variation coefficients in positive rhythm heterogeneous reservoirs. From the simulation results of reservoir models with different oil-water viscosity ratios, it is found that during the development process, the water-free recovery firstly decreases rapidly with an increasing oil/water viscosity ratio less than 30:1 before it decreases slightly. Besides, a modified logistic function is built to present the relation between ultimate recovery and variation coefficient for positive rhythm reservoirs. The ultimate recovery firstly decreases slightly before the permeability variation coefficient increases up to 0.4, and then decreases sharply. However, the inflexion of variation coefficient in a reverse rhythm one is 0.6. An algebraic equation is also built to describe the water cut change with the recovery factor of recoverable oil reserves. The water-free recovery is higher in a reverse rhythm reservoir than that in a positive rhythm reservoir especially in a reservoir with a relative small oil/water viscosity. However, the ultimate recovery of a reverse rhythm reservoir is higher than that of a positive rhythm reservoir. Also, during development process, the water-cut increases faster in a positive rhythm reservoir than in a reverse rhythm reservoir especially for medium heterogeneous reservoirs.

Quantitative Models of Development Laws for Heterogeneous Sandstone Reservoirs by Water Flooding