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[en] Multiscale schemes for transferring information from fine to coarse scales are typically based on homogenization techniques. Such schemes smooth the fine scale features of the underlying fields, often resulting in the inability to accurately retain the fine scale correlations. In addition, higher-order statistical moments (beyond mean) of the relevant field variables are not necessarily preserved. As a superior alternative to averaging homogenization methods, a wavelet-based scheme for the exchange of information between a reactive and diffusive field in the context of multiscale reaction-diffusion problems is proposed and analyzed. The scheme is shown to be efficient in passing information along scales, from fine to coarse, i.e., upscaling as well as from coarse to fine, i.e., downscaling. It incorporates fine scale statistics (higher-order moments beyond mean), mainly due to the capability of wavelets to represent fields hierarchically. Critical to the success of the scheme is the identification of dominant scales containing the majority of the useful information. The dominant scales in effect specify the coarsest resolution possible. The scheme is applied in detail to the analysis of a diffusive system with a chemically reacting boundary. Reactions are simulated using kinetic Monte Carlo (kMC) and diffusion is solved by finite differences (FDs). Spatial scale differences are present at the interface of the kMC sites and the diffusion grid. The computational efficiency of the scheme is compared to results obtained by averaging homogenization, and to results from a benchmark scheme that ensures spatial scale parity between kMC and FD
[en] Highlights: ► In small-scale CAES there are no robust guidelines in choosing an operational pressure for the vessels. ► Through the stress analysis of the vessel, an optimum pressure at minimum cost can be determined. ► One contribution is in determining the optimum pressure is small-scale CAES. ► Another contribution is in determining the shape size, and number of vessels in small-scale CAES designs. - Abstract: The paper reports guidelines for the efficient design and sizing of Small-Scale Compressed Air Energy Storage (SS-CAES) pressure vessels, including guidelines for pressures that should be used in the SS-CAES system to minimize the cost of the pressure vessel. Under a specified energy storage capacity and specified maximum and minimum operating pressures in CAES, the volume of the vessel(s) can be evaluated. The present study provides guidelines for choosing appropriate shape and size for the vessels that minimize material and manufacturing cost for cylindrical vessels. The two main contributions of the paper are that it provides a methodology to determine: (a) an optimum pressure; (b) the shape, size, and number of vessel to be used in a particular application. Results suggest that pressure vessels with a length to diameter ratio of roughly three are the most economical, and that a system should be designed for a pressure of roughly three times the minimum pressure of the expansion device.