Quantitative Models of Development Laws for Heterogeneous SandstoneReservoirs by Water Flooding

摘要

The Lorenz curve is used to estimate the heterogeneity of an oil reservoir. The corresponding permeabilitydistributions in a series of concept reservoir models with a uniform average permeability but different heterogeneities areobtained and characterized by inverse calculation of the Lorenz curve. Then the development laws of a reservoir inrelation 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 almostthe same development rule. It is also found that the permeability profile is consistent with the water-cut profile in bothpositive and reverse rhythm reservoirs where injected water channels in high permeable layers. Furthermore, the water-cutprofile of a reverse rhythm reservoir is more uniform than that of a positive rhythm reservoir. In addition, results alsoshow an exponential relation between water-free recovery and variation coefficients in positive rhythm heterogeneousreservoirs. From the simulation results of reservoir models with different oil-water viscosity ratios, it is found that duringthe development process, the water-free recovery firstly decreases rapidly with an increasing oil/water viscosity ratio lessthan 30:1 before it decreases slightly. Besides, a modified logistic function is built to present the relation between ultimaterecovery and variation coefficient for positive rhythm reservoirs. The ultimate recovery firstly decreases slightly beforethe permeability variation coefficient increases up to 0.4, and then decreases sharply. However, the inflexion of variationcoefficient in a reverse rhythm one is 0.6. An algebraic equation is also built to describe the water cut change with therecovery factor of recoverable oil reserves. The water-free recovery is higher in a reverse rhythm reservoir than that in apositive rhythm reservoir especially in a reservoir with a relative small oil/water viscosity. However, the ultimate recoveryof a reverse rhythm reservoir is higher than that of a positive rhythm reservoir. Also, during development process, thewater-cut increases faster in a positive rhythm reservoir than in a reverse rhythm reservoir especially for mediumheterogeneous reservoirs.