A lattice model for gas production from hydrofractured shale
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Natural gas production from US shale and tight oil plays has increased over the past 10 years, currently constitutes more than half of the total US dry natural gas production, and is projected to provide the US with a major energy source in the next several decades. The increase in shale gas production is driven by advances in hydraulic fracturing. Recent studies have shown that gas production from hydraulically fractured shales has to come from a network of connected hydraulic and natural fractures, and that if one takes the shale permeability to be 10 nD, then the characteristic spacing of the fracture network will be about 1.5 − 3 m. The precise nature of the characteristic spacing, as well as other production and formation properties of the fracture network, are questions which motivated the present dissertation. This dissertation studies (1) the topology of the fracture network, (2) the mechanics of how the fracture network evolves in time during injection and (3) how fracture network geometry affects production. We use percolation theory to study fracture network topology. Fracture are placed on the bonds of a two–dimensional square lattice and follow a power law length distribution. We analytically obtain the scaling of connectivity for power law fracture networks, and numerically compute the percolation threshold as a function of the exponent. We develop a hydrofracture model which makes it possible to simulate initiation and propagation of hydraulic fractures, as well as the interaction between hydraulic and natural fractures. The model uses the Reynolds lubrication approximation to describe fluid flow through the fractures and relies on analytical estimates to predict the stress response. We develop a diffusion model to compute gas production from hydraulically fractured shales. The model uses a random walk algorithm and takes the fracture network as the absorbing boundary to the gas transport equation. We show that scaling the cumulative production versus time data from the diffusion model with respect to characteristic scales of production maps the production versus time plots onto a single scaling curve. Using the model, we identify, or define, characteristic spacing for fracture networks.
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