Fine-scale models that represent first-principles physics are challenging to represent at larger scales of interest in many application areas. In nanoporous media such as tight-shale formations, where the typical pore size is less than 50 nm, confinement effects play a significant role in how fluids behave. At these scales, fluids are under confinement, affecting key properties such as density, viscosity, adsorption, etc. Pore-scale Lattice Boltzmann Methods (LBM) can simulate flow in complex pore structures relevant to predicting hydrocarbon production, but must be corrected to account for confinement effects. Molecular dynamics (MD) can model confinement effects but is computationally expensive in comparison. The hurdle to bridging MD with LBM is the computational expense of MD simulations needed to perform this correction. Here, we build a Machine Learning (ML) surrogate model that captures adsorption effects across a wide range of parameter space and bridges the MD and LBM scales using a relatively small number of MD calculations. The model computes upscaled adsorption parameters across varying density, temperature, and pore width. The ML model is 7 orders of magnitude faster than brute force MD. This workflow is agnostic to the physical system and could be generalized to further scale-bridging applications. Multi-scale physics problems are found in all scientific disciplines. Prominent examples can be found in material science 1-3 , biology 4 , chemistry 5-9 , and geosciences 10-12. Typically, information from computationally intensive fine-scale models have to be translated or upscaled into faster coarse-scale models to solve the problem at the scale of interest. A problem of great scientific and economic interest is the flow of hydrocarbon in nanoporous shale. Traditional porous media approaches such as the LBM allow for complex pore geometries but need to be provided with effective properties that account for nanoconfinement effects in order to accurately simulate mass transport at the continuum scale 13. Atomistic simulations such as Molecular Dynamics (MD) capture nanoconfinement effects accurately, but are limited to a few pores as they are computationally intractable to simulate for mesoscopic pore geometries. There is a need for approaches that efficiently bridge these two scales without compromising accuracy. Recently, Machine Learning (ML) has shown great promise in accelerating physics-based models that makes it feasible to build a scale-bridging framework 14-16. The applications include fracture propagation in brittle materials 17 , computational fluid dynamics 18 and molecular dynamics 19. On another dimension, Machine Learning

Abstract:In porous media, pore geometry and wettability are determinant factors for capillary flow in drainage or imbibition. Pores are often considered as cylindrical tubes in analytical or computational studies. Such simplification prevents the capture of phenomena occurring in pore corners. Considering the corners of pores is crucial to realistically study capillary flow and to accurately estimate liquid distribution, degree of saturation and dynamic liquid behavior in pores and in porous media. In this study, capillary flow in polygonal tubes is studied with the Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM). The LB model is first validated through a contact angle test and a capillary intrusion test. Then capillary rise in square and triangular tubes is simulated and the pore meniscus height is investigated as a function of contact angle θ. Also, the occurrence of fluid in the tube corners, referred to as corner arc menisci, is studied in terms of curvature versus degree of saturation. In polygonal capillary tubes, the number of sides leads to a critical contact angle θ c which is known as a key parameter for the existence of the two configurations. LBM succeeds in simulating the formation of a pore meniscus at θ > θ c or the occurrence of corner arc menisci at θ < θ c . The curvature of corner arc menisci is known to decrease with increasing saturation and decreasing contact angle as described by the Mayer and Stoewe-Princen (MS-P) theory. We obtain simulation results that are in good qualitative and quantitative agreement with the analytical solutions in terms of height of pore meniscus versus contact angle and curvature of corner arc menisci versus saturation degree. LBM is a suitable and promising tool for a better understanding of the complicated phenomena of multiphase flow in porous media.