Optimization Loop Algorithm for Adsorbed Natural Gas Storage Systems

== Abstract ==

In the past few years, the development of inverse design and optimization methods has opened up new possibilities. The so-called Adjoint method is of great significance in that context, since it permits high fidelity to flow-physics at comparatively low computational costs. The present work is a sequel of a previous one presented in WCCM2018, called 'On the use of the Adjoint Method to evaluate sensitivities in adsorbed natural gas storage systems'. where one have developed and validated an Adjoint based approach to computing sensitivity derivatives for adsorbed natural gas (ANG) storage systems. The main goal of this work is to, by using the approach to compute sensitivities presented before, obtain and validate a basic structure of an optimization loop algorithm (OLA) for optimization of natural gas storage systems. Both flow and Adjoint solvers, which were previously developed, are assembled in FREEFEM++ platform. The OLA consists on solving sequential problems to achieve an optimal configuration of parameters that maximize/minimize an objective functional. It starts by solving the primal problem (flow solver), which consists in a physics flow solution, followed by the dual problem, based on the Adjoint Method. With both solutions, the OLA receives the sensitivity derivatives with respect to parameters and, if the configuration is not the optimal, a new values of parameters is obtained and the cycle restarts. To validate the OLA, we make use of the inverse design optimization, defining the objective functional as the mean square error, MSE, of the actual density of adsorption distribution q, with respect to an user--defined target distribution, qt. The strategy is generated a target distribution with a known filling flow curve and the OLA, starting the optimization cycles with other flow curve, minimizing the functional,

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