COMPARISON STUDY BETWEEN ARONOFSKY AND LAMBERT W FUNCTIONS TO PREDICT OIL RECOVERY BY GAS GRAVITY DRAINAGE

Free-fall gas gravity drainage is an important oil recovery mechanism in fractured reservoirs. For decades, the Aronofsky single parameter fit exponential expression has been used as a simple tool to predict oil recovery by this process. In this expression the only fitting parameter is called rate constant. In some recent works it has been claimed that the Lambert W function is able to capture oil recovery data very well better than the widely used Aronofsky function. The main objective of this study is to check the validity of this claim using several sets of oil recovery data. Basic rock and fluid properties along with gas-oil relative permeability and capillary pressure data belonging to some Iranian fractured oil reservoirs were used as input to a reservoir simulator to generate twenty cases of oil recovery by gravity drainage. The input data were chosen such that they covered a wide range of rock properties. The Aronofsky and Lambert W functions were then fitted to the oil recovery curves and best fits were obtained and compared. Results of this study show the studied cases can be classified into two categories based on the fitting behaviour of different expressions. In some cases the Aronofsky expression yields the perfect fit to the oil recovery data at all times (early and late times). For these cases the Lambert W function overestimates and underestimates recovery at, respectively early and late times. When it comes to the remaining cases, the Aronofsky expression overestimates recovery at late times. For these cases the Lambert W function overestimates recovery at early times

کلیدواژه ها:

Fractured reservoirs ، porous media ، gravity drainage ، simulation ، Aronofsky ، Lambert W function