Modeling and Upscaling of Shale Gas with a Discrete Fracture Model

Gas flow in fractured nano-porous shale formations is complicated by a hierarchy of structural features, ranging from nanopores to microseismic and hydraulic fractures, and by several transport mechanisms that differ from standard viscous flow used in reservoir modelling. In small pores, self-diffusion becomes more important than advection, also slippage effect and Knudsen diffusion becomes relevant at this scal

The characteristics and properties of the fracture networks plays a major role in the performance of shale gas reservoirs, therefore the use of accurate simulation technique that honor the complexity of these reservoirs and capture the associated dynamics of nanopores is strongly required. However, these accurate simulations often necessitate a large amount of computations for field scale models and therefore require upscaling. Yet the upscalling techniques generally in use are based on idealizations that do not reflect the discrete features of the reservoir.

In this work, we first incorporate the formulations of a statistical bundle of dual tube model to describe the dynamics of shale gas into a discrete fracture model. The formulation of the DFM model we use applies an unstructured control volume finite difference approach with a two point flux approximation. We then propose to upscale these detailed descriptions using two different techniques, with the major difference in their coarse grid geometry. The first approach, referred to as EDFM upscaling, relies on a structured Cartesian coarse grid. While the second method, which we call the multiple subregion (MSR) upscaling, introduces a flow based coarse grid to replicate the diffusive character of the pressure in the matrix. The required parameters for the coarse scale model in both methods and the geometry of the subregions in the second method are determined efficiently from global single-phase flow solution using the underlying discrete fracture model.

The methods are applied to simulate single-phase gas flow in 2D fractured reservoir models, and are shown to provide results in close agreement with the underlying DFM and with considerable reduction in the computational time. We notice that in order to account for the prevailing transient effects in low permeability shale, the upscaled transmissibility need to be related to pressure for better results.

Finally, we consider the EDFM upscaling we propose as an easier approach in its implementation, while the MSR technique as a more accurate method. 

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