Diffuse Source Transmissibility Upscaling

Static high resolution three dimensional geological models are routinely constructed to provide an integrated description of a reservoir which includes seismic, well log and core data, and which characterize the reservoir heterogeneity at multiple scales. These models also represent the structure and stratigraphy of the reservoir within the design of the modeling grid, which may include faults, fault blocks, pinch-outs, layering and cross bedding. Numerical simulation of these high resolution static models remains a challenge even with the rapid growth of computational resources since both geological and flow simulation models have increased in size. 50 million cell geologic models are routine, while simulation models are typically one or two orders of magnitude coarser. Also, multiple simulations should be performed to optimize among various recovery or well placement scenarios for subsurface uncertainty assessment which is not possible to carry out on fine scale models. Hence, upscaling of the geologic models for flow simulation remains part of the subsurface workflows.

The industry also faces new reservoir engineering challenges. Unconventional reservoirs (tight gas / shale oil / shale gas) have low permeabilities ranging from micro to nano Darcy. The time for pressure transients are no longer measured in hours or days, but instead are measured in decades or longer for unconventional systems. The separation between transient testing and steady state reservoir management is no longer applicable. Historically, our upscaling algorithms have relied upon steady state concepts of flow, which are no longer applicable to unconventional reservoirs.

In the current study, a novel diffuse source transmissibility upscaling approach is described. It applies pressure transient concepts to the calculation of the effective transmissibility between coarse cell pairs. Unlike the usual steady state upscaling algorithms, it is a completely local calculation and is not dependent upon knowledge of, or assumptions about, global reservoir flow patterns. The concept of diffusive time of flight is utilized to calculate the drainage volume at the inter-cell face and remove the fine cells disconnected from the drainage volume.

The approach is validated at field scale using an onshore US tight gas reservoir model and is shown to reduce simulation run times by up to two orders of magnitude without significance loss of accuracy in performance prediction.