New dynamic permeability upscaling method for flow simulation under depletion drive and no-crossflow conditions

The main purpose of upscaling in reservoir simulation is to capture the dynamic behavior of fine scale models at the coarse scale. Traditional static or dynamic methods use assumptions about the boundary conditions to determine the upscaled properties. In this paper, we show that the upscaled properties are strongly dependent on the flow process observed at the fine scale. We use a simple nocrossflow depletion drive process and demonstrate that an upscaled property is not a constant value. Instead, if the goal is to match the performance of the fine scale model, the upscaled permeability changes with time. We provide an analytical solution to determine the upscaled permeability and present the value of upscaled permeability under limiting conditions. Our equation suggests that it is possible that upscaled value can fall outside the range of fine scale values under certain conditions. We show that for pseudo steady state flow, using common averaging methods like arithmetic or even geometric averaging methods can lead to optimistic results. We also show that the no-crossflow solution is significantly different than crossflow solution at late times. We validate our method by comparing the results of the method with flow simulation results in two and multi-layered models.