A coupled permeability thresholding with effective medium theory upscaling technique for highly heterogeneous reservoirs

Abstract

Reservoir simulations are performed with fine grid geological models as primary input into the reservoir simulators. These fine grid geological models contain ten million to one hundred million cells while current serial reservoir simulators can only handle one hundred thousand to one million cells. This disparity in scales prohibits direct input of fine grid geological models into serial simulators. However, traditional upscaling techniques are unable to reproduce the fine-scale dynamic flow behavior at the coarse-scale and up-scaled permeability values are dependent on the applied boundary conditions. The problem is exacerbated if isolated flow units are present. These problems motivated the need to couple the permeability thresholding and effective medium theory (EMT) approaches to develop a practical and accurate quasi-global single-phase permeability upscaling technique that uses the reservoir simulator in the upscaling process. The workflow involves identifying and making the no-flow cells slightly permeable. This is followed by defining two models for each region to be scaled up, one of which includes the heterogeneous permeability field in the region and the other the upscaled value. Also, a fine-scale gridded ring is constructed around the target region. Then the upscaled value of the permeability is resolved by minimizing the difference between the well water production rates (WWPR) of the two runs. The technique is shown to mimic the channel fine-scale permeability distribution at the coarse-scale. It is also shown to reproduce the physics of flow for two-phase flow problems as evident in the well oil production rate, injection well pressure and pressure distribution profile. Sensitivity analyses on different scale-up factors, well locations and sequentially active wells show the superiority of the novel technique over the upscaling and downscaling with effective medium theory (UDEMT) and local upscaling techniques - albeit at the cost of more CPU time. The new method takes more CPU time than local upscaling method but the accurate results justifies the extra CPU time. Our workflow should be extended to three dimensions and fractured reservoirs as well as coupled with existing upscaling techniques for near wellbore and relative permeability upscaling.