An Inverse Source Problem for Focusing Wave Energy To Targeted Subterranean Formations

Abstract eng:
I discuss a PDE-constrained optimization approach for constructing optimal excitations capable of imparting a maximal outcome to a target underground formation, by steering the focusing of the excitation energy to the formation. The motivation stems from the possibility of “shaking” sufficiently strongly (via ground, wellbore, or other sources) a target reservoir zone to increase oil mobility. However, the applications are not limited to Enhanced Oil Recovery (EOR) purposes. The method leads formally to an inverse source problem, where the tempo-spatial characteristics of the source are sought in order to maximize the kinetic energy, or the acceleration field, or other mobility metrics, in the targeted formation, subject to the physics of the associated wave propagation problem. The inverse source problem is resolved on a PML-truncated finite computational domain using a hybrid method (a conventional single-field coupled with a mixed) that is dealt with numerically using finite elements. I report numerical experiments in idealized heterogeneous formations, which show robustness of the optimization scheme (Fig. 1). I also discuss practical strategies for optimal illumination of the targeted formations. f(t) 2.5 m

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