Abstract
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. The conventional model for calculating permeability is derived from Darcy's law, which is valid only for continuum flow in porous rocks. We discussed the feasibility of simulating methane transport characteristics in the organic nano-pores of shale through the Lattice Boltzmann method (LBM). As a first attempt, the effects of high Knudsen number and the associated slip flow are considered, whereas the effect of adsorption in the capillary tube is left for future work. Simulation results show that at small Knudsen number, LBM results agree well with Poiseuille's law, and flow rate (flow capacity) is proportional to the square of the pore scale. At higher Knudsen numbers, the relaxation time needs to be corrected. In addition, velocity increases as the slip effect causes non negligible velocities on the pore wall, thereby enhancing the flow rate inside the pore, i.e., the permeability. Therefore, the LBM simulation of gas flow characteristics in organic nano-pores provides an effective way of evaluating the permeability of gas-bearing shale.
Highlights
Permeability is a key parameter for investigating the flow ability of sedimentary rocks
The production of shale gas largely depends on the flow ability of natural gas, which is affected by several inherent characteristics of gas shale, such as gas composition, organic richness, the geometry structure of the nano-pores, bedding and micro fractures, and more fundamentally, the deviation of the gas flow from the description of continuum fluid mechanics because of the considerable effects of high Knudsen numbers
Relaxation time t can be uniquely determined by the Reynolds number according to the relationship between t and viscosity when Lattice Boltzmann method (LBM) simulation is used for macroscopic flow
Summary
Permeability is a key parameter for investigating the flow ability of sedimentary rocks. It’s very expensive computationally and highly noisy at small Mach numbers[7] In addition these methods have great difficulties in simulating fluid systems with mixed fluid phase interfaces and are generally unsuitable for the complex flow problem of shale gas. Toschi et al[17] introduced a virtual wall collision concept into the bounce-back and diffuse scattering boundary conditions All these previous developments have made the LBM a very competitive technology for shale gas simulations. Gas flow characteristics under the influences of the slip effect and high Knudsen numbers in organic nano-pores capillaries are simulated with LBM. Permeability equation which is added a coefficient is provided to model the effect of high Knudsen number and slip
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