Upscaling and multiscale simulation by bridging pore scale and continuum scale models
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Many engineering and scientific applications of flow in porous media are characterized by transport phenomena at multiple spatial scales, including pollutant transport, groundwater remediation, and acid injection to enhance well production. Carbon sequestration in particular is a multiscale problem, because the trapping and leakage mechanisms of CO2 in the subsurface occur from the sub-pore level to the basin scale. Quantitative and predictive pore-scale modeling has long shown to be a valuable tool for studying fluid-rock interactions in porous media. However, due to the size limitation of the pore-scale models (10-4-10-2m), it is impossible to model an entire reservoir at the pore scale. A straightforward multiscale approach would be to upscale macroscopic parameters (e.g. permeability) directly from pore-scale models and then input them into a continuum-scale simulator. However, it has been found that the large-scale models do not predict in many cases. One possible reason for the inaccuracies is oversimplified boundary conditions used in this direct upscaling approach. The hypothesis of this work is that pore-level flow and upscaled macroscopic parameters depends on surrounding flow behavior manifested in the form of boundary conditions. The detailed heterogeneity captured by the pore-scale models may be partially lost if oversimplified boundary conditions are employed in a direct upscaling approach. As a result, extracted macroscopic properties may be inaccurate. Coupling the model to surrounding media (using finite element mortars to ensure continuity between subdomains) would result in more realistic boundary conditions, and can thus improve the accuracy of the upscaled parameters. To test the hypothesis, mortar coupling is employed to couple pore-scale models and also couple pore-scale models to continuum models. Flow field derived from mortar coupling and direct upscaling are compared, preferably against a true solution if one exists. It is found in this dissertation that pore-scale flow and upscaled parameters can be significantly affected by the surrounding media. Therefore, using arbitrary boundary conditions such as constant pressure and no-flow boundaries may yield misleading results. Mortar coupling captures the detailed variation on the interface and imposes realistic boundary conditions, thus estimating more accurate upscaled values and flow fields. An advanced upscaling tool, a Super Permeability Tensor (SPT) is developed that contains pore-scale heterogeneity in greater detail than a conventional permeability tensor. Furthermore, a multiscale simulator is developed taking advantage of mortar coupling to substitute continuum grids directly with pore-scale models where needed. The findings from this dissertation can significantly benefit the understanding of fluid flow in porous media, and, in particular, CO2 storage in geological formations which requires accurate modeling across multiple scales. The fine-scale models are sensitive to the boundary conditions, and the large scale modeling of CO2 transport is sensitive to the CO2 behavior affected by the pore-scale heterogeneity. Using direct upscaling might cause significant errors in both the fine-scale and the large-scale model. The multiscale simulator developed in this dissertation could integrate modeling of CO2 physics at all relevant scales, which span the sub-pore or pore level to the basin scale, into one single simulator with effective and accurate communication between the scales. The multiscale simulator provides realistic boundary conditions for the fine scales, accurate upscaled information to continuum-scale, and allows for the distribution of computational power where needed, thus maintaining high accuracy with relatively low computational cost.