A lattice Boltzmann simulation on the gas flow in fractal organic matter of shale gas reservoirs

The gas flow in the organic matter with multiple flow regimes is critical to the shale gas production from shale gas reservoirs, but simultaneously simulating the full flow regimes of shale gas in the nanopores of the fractal shale organic matter is still unavailable. This paper presents a modified lattice Boltzmann model with effective relaxation time to simulate the shale gas micro-flow behaviors in fractal organic matter for permeability prediction. Firstly, some fractal shale organic matters are reconstructed by the quartet structure generation set (QSGS) algorithm, and the structural parameters such as fractal dimension, lacunarity and average pore diameter are calculated to characterize the complexity of the fractal shale organic matter. Secondly, effective viscosity and Knudsen layer are introduced into the effective relaxation time to formulate a modified lattice Boltzmann model. Thirdly, this modified lattice Boltzmann model is verified by comparing with the theoretical permeability models for the gas flow in the body centered cubic (BCC) arrays. Finally, a series of gas flow simulations in reconstructed fractal shale organic matter are conducted to explore the effects of structure parameters on permeability. Numerical simulations show that the modified lattice Boltzmann model can simulate the full gas flow regimes and predict the permeability of the fractal shale organic matter. The logarithm of permeability is negatively linearly correlated with fractal dimension and positively linearly correlated with lacunarity of the shale organic matter. This permeability exponentially increases with the increase of average pore diameter and a power law is observed between the fractal dimension and average pore diameter of these fractal shale organic matters. The anisotropic structures have great impacts on the directional permeability of shale organic matter. The permeability k x in the horizontal direction increases first and then decreases with the increase of anisotropic ratio (AR) and reaches the peak when AR is about 20. The permeability k y in the vertical direction monotonically decreases with the increase of AR.