Upscaling of Fractured Oil Reservoirs Using Homogenization Including Non-equilibrium Capillary Pressure

摘要

Recovery in incompletely water-wet fractured reservoirs can be extremely low. In the laboratory, these systems are often mistaken for oil-wet reservoirs, because imbibition only starts after removal of the oil layer, which originally covers the grains. The long time required to remove the oil film will be referred to as delay time. There are two theories that describe the delay time necessary for removal of an oil film, leading to a capillary pressure that depends on time. One of the theories is developed by Barenblatt et al. and it modifies both the capillary pressure and the relative permeabilities. The other theory is developed by Hassanziadeh et al. and it only deals with the non-equilibrium effect for the capillary pressure. No attempt has yet been made to model non-equilibrium effects in fractured reservoirs for a field-scale problem and this is an innovative aspect of this paper. To examine whether the non-equilibrium effect has any effect on larger-scale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the non-equilibrium effects are included. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use the simulation to determine the range of delay times for which discernable effects occur in terms of oil recovery.