Modeling of gas flow in confined formations at different scales

Gas flow in fractured nano-porous shale formations is complicated by a hierarchy of structural features, ranging from nanopores to hydraulic fractures, and by several transport mechanisms that differ from standard viscous flow used in reservoir modeling. The use of accurate simulation techniques that honor the physical complexity of these reservoirs and capture the associated dynamics of nanopores is required. However, these simulations often necessitate a large amount of computational resources for field scale models and therefore require upscaling. Usually, the upscaling techniques are based on idealizations that do not reflect the discrete features of the reservoir. In this work, we first incorporate the physics model that describe dynamics of shale gas into a numerical Discrete Fracture and Matrix (DFM) model. The formulation of our DFM model 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 Embedded DFM upscaling, relies on a structured Cartesian coarse grid. The second method, which we call the Multiple Sub-Regions (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 using numerical homogenization of the underlying discrete fracture model. An accurate comparison with the fine-scale representation indicates an existence of an additional transient phenomenon at coarse scale. To account for this effect, the transmissibility of both types of coarse models is related to the pressure in our approach. Both upscaling methods are applied to simulate a shale-gas flow in 2D fractured reservoir models and are shown to provide results in close agreement with the underlying fine-scale model and with a considerable reduction in the computational time.