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We consider periodic injection and extraction of a buoyant fluid into and, from a cone-shaped geological structure initially fully saturated with another fluid of different properties. To our knowledge, such geometry has not been analytically investigated before in a manner that reduces the problem from three dimensions to an effective one-dimensional problem while preserving the essential physics of segregation and dip-driven flow. Previous studies are largely limited to either dipping linear geometries [1,2] or non-periodic horizontal radial models [3]. Our goal is to develop a dimensionless model and scaling laws of practical importance for engineering design and simulation benchmarks. We limit the discussion to the non-restrictive case of injecting and producing a lighter, more mobile fluid into, and from a homogeneous medium motivated in particular by hydrogen storage in aquifers. The analytical model’s geometry is shown in Fig. (a). By combining symmetry with transverse equilibrium, we derive a dimensionless interface equation. The governing two-phase flow equation is a nonlinear diffusion-advection equation with embedded periodic boundary condition to represent injection-storage-extraction cycles in cone-shaped geological formations. The nondimensionalization of the governing PDE reveals the key controlling groups: the mobility ratio, the radial buoyancy number, the slope number, and the cyclicity number. We solve the dimensionless interface equation using the method of lines in MATLAB. We have also compared our numerical solution to a classical asymptotic analytical solution and obtained good agreement. The results of a representative case are shown in Fig. (c). Of particular importance for code verification, but also for physical understanding, is the equilibrium profile after a single injection period which is obtained by combining the steady-state form of the flow equation with mass conservation. Finally, we mention that the present study offers a theoretical framework for understanding buoyant flow dynamics in geological domes and is particularly useful for preliminary assessments.
| References | [1] Dudfield, P. & Woods, A.W. 2014 On the periodic injection of fluid into, and its extraction from, a confined aquifer. J. Fluid Mech. 755, 111–141. [2] Whelan, B. K., & Woods, A. W. (2025). The periodic injection and extraction of fluid in a porous medium for hydrogen storage. Journal of Fluid Mechanics, 1002, R2. doi:10.1017/jfm.2024.1094 [3] Nordbotten, J. M., & Celia, M. A. (2006). Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech., 561, 307–327. [4] Jamaludin, S.N.F., Pubellier, M. & Menier, D. Structural Restoration of Carbonate Platform in the Southern Part of Central Luconia, Malaysia. J. Earth Sci. 29, 155–168 (2018). |
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| Country | France |
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