We report the application of machine learning methods for predicting the effective diffusivity (De) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28–0.98), and effective diffusivity spanning more than one order of magnitude (0.1 ≲ De < 1), e.g., >95% of predicted De have truncated relative error of <10% when the true De is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with De < 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true De < 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.
The adsorption of multicomponent gas mixtures in shale formations and their recovery are of great interest to the shale gas industry. Here we report molecular dynamics simulations of the adsorption of methane/ethane mixtures in 2 and 4 nm-wide nanopores and their recovery from these nanopores. Surface adsorption contributes significantly to the storage of methane and ethane inside the pores, and ethane is enriched inside the nanopores in equilibrium with bulk methane–ethane mixtures. The enrichment of ethane is enhanced as the pore is narrowed but is weakened as the pressure increases due to entropic effects. These effects are captured by the ideal adsorbed solution (IAS) theory, but the theory overestimates the adsorption of both gases. Upon opening the mouth of the nanopores to gas baths with lower pressure, both gases enter the bath. The production rates of both gases show only weak deviation from the square root scaling law before the gas diffusion front reaches the dead end of the pores. The ratio of the production rate of ethane and methane is close to their initial mole ratio inside the nanopore despite the fact that the mobility of pure ethane is smaller than that of pure methane inside the pores. Scale analysis and calculation of the Onsager coefficients for the transport of binary mixtures of methane and ethane inside the nanopores suggest that the strong coupling between methane and ethane transport is responsible for the effective recovery of ethane from the nanopores.
Understanding the recovery of gas from reservoirs featuring pervasive nanopores is essential for effective shale gas extraction. Classical theories cannot accurately predict such gas recovery and many experimental observations are not well understood. Here we report molecular simulations of the recovery of gas from single nanopores, explicitly taking into account molecular gas-wall interactions. We show that, in very narrow pores, the strong gas-wall interactions are essential in determining the gas recovery behavior both quantitatively and qualitatively. These interactions cause the total diffusion coefficients of the gas molecules in nanopores to be smaller than those predicted by kinetic theories, hence slowing down the rate of gas recovery. These interactions also lead to significant adsorption of gas molecules on the pore walls. Because of the desorption of these gas molecules during gas recovery, the gas recovery from the nanopore does not exhibit the usual diffusive scaling law (i.e., the accumulative recovery scales as R ∼ t 1/2 but follows a super-diffusive scaling law R ∼ t n (n > 0.5), which is similar to that observed in some field experiments. For the system studied here, the super-diffusive gas recovery scaling law can be captured well by continuum models in which the gas adsorption and desorption from pore walls are taken into account using the Langmuir model. a Article accepted by Phys. Rev. Fluids †
This paper studies three-lane totally asymmetric simple exclusion processes (TASEP) with weak coupling under open boundary conditions. Here, particles can hop along each lane or hop to the adjacent lane. Besides, the lane-changing rates are inversely proportional to the system size L. Complemented by Monte Carlo simulations, mean-field analysis has been performed. The phase diagrams, density profiles and current profiles have been calculated. Moreover, the bulk-induced shock has been found in the system.
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