Theoretical Modeling of Reinfiltration Process in Naturally Fractured Reservoirs: A Comparative Study on Traveling Liquid Bridges and Continuum Film Flow Approaches

Abstract

Abstract Most of the Iranian oil reservoirs are naturally fractured. Reinfiltration is a key process which controls oil flow from the upper to the lower matrix block. However, theoretical modeling of fracture aperture as well as fracture dip angle effects on flow rate of drained oil during reinfilteration process remains a topic of debate in the literature. Moreover, there is no reported experience in the literature that compared the oil velocity predicted by traveling oil bridges and continuum film flow approaches. In this work reinfiltration process is modeled through two different approaches: discrete traveling liquid elements and continuum film flow along inclined fractures. For a case study reported in the literature, the oil velocity at various fracture aperture as well as fracture dip angle was predicted and compared using both approaches. The results of this work confirmed that the geometry of fractures between matrix blocks plays a crucial role on drained oil during reinfiltration process. By decreasing fracture aperture or fracture dip angle the oil velocity modeled by liquid film flow approach decreases, it might be due to more time available, for the droplets and film to be adsorbed on lower block; therefore reinfiltration effect increases. It has been observed that the velocity of traveling liquid bridges is maximized for fracture aperture close to 0.5 mm. A surprising result, for the case studied here, is that there are critical values for fracture aperture and fracture dip angle, close to 1 mm and 15 degree respectively, in which after those the velocity of traveling liquid elements is higher than that predicted by liquid film flow approach. The results of this work might help to obtain an independent transfer function for dual permeability model incorporating the interaction between matrix blocks which might improve the reliability of simulators for evaluation of naturally fractured reservoirs. 1. Introduction Warren & Root (1963) have presented an analytical solution for a single-phase, unsteady state and radial flow regime in naturally fractured reservoirs. They also presented an experision for the shape factor of parallele piped matrix blocks within an orthonormal fracture system of one, two or three dimensions. Their double porosity model assumes a continuous uniform fracture network oriented parallel to the principal axes of the permeability. The matrix blocks occupy the same physical space as the fracture network and are assumed to have no interaction between the matrix blocks. However in reality there exists some degree of block to block interaction, the interaction between the matrix blocks has strong effect on the ultimate recovery as well as the oil flow rate in fractured porous media, which must be accounted in order to have a reliable prediction of the reservoir performance (Saidi 1987). Later Saidi et al. (1979) questioned the single-block concept in the simulation of fractured petroleum reservoirs. The single-block concept assumes that the matrix blocks drain independently. Hence the performance of stack blocks is equal to the performance of a single block multiply by the number of individual blocks. This assumption is valid for the oil flow rate as well as ultimate oil recovery from naturally fractured reservoirs. The number of individual blocks can be estimated from either outcrop or well logging data (Dejam 2008).