Porous-Medium Scaling of CO$_2$ Plume Footprint Growth
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| Format: | Preprint |
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2026
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| author | Alonso-Marroquin, Fernando Tantardini, Christian |
| author_facet | Alonso-Marroquin, Fernando Tantardini, Christian |
| contents | Building on porous-medium-type nonlinear diffusion, we compare analytical Barenblatt-type similarity solutions with plume's radii from digital analysis of published seismic monitoring images, to quantify field-scale CO$_2$ plume-footprint growth. Using an area-based equivalent radius extracted from time-lapse plume maps at Sleipner, Aquistore, and Weyburn--Midale, we obtain effective plume-growth exponents that are broadly compatible with slow porous-medium scaling in axisymmetric geometry. We then interpret the plume as a vertically segregated CO$_2$ layer of thickness $b(r,t)$ within an aquifer of thickness $H$, and derive closed-form expressions for the normalized thickness $b(r,t)/H$, the compact-support plume edge $R(t)$, and a transient inner core radius $a(t)$ that marks the region where the plume occupies the full aquifer thickness. In the shut-in case, the core radius decreases with time and eventually vanishes, after which the plume recovers the pure Barenblatt regime; under constant injection, the model predicts an injection-controlled core and a plume edge that grows with the square-root law. This framework provides a physically transparent baseline for comparing plume-radius evolution, internal plume structure, and core development across sites, and establishes a consistent route for incorporating non-local effects by fractional derivatives in future extensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Porous-Medium Scaling of CO$_2$ Plume Footprint Growth Alonso-Marroquin, Fernando Tantardini, Christian Fluid Dynamics Building on porous-medium-type nonlinear diffusion, we compare analytical Barenblatt-type similarity solutions with plume's radii from digital analysis of published seismic monitoring images, to quantify field-scale CO$_2$ plume-footprint growth. Using an area-based equivalent radius extracted from time-lapse plume maps at Sleipner, Aquistore, and Weyburn--Midale, we obtain effective plume-growth exponents that are broadly compatible with slow porous-medium scaling in axisymmetric geometry. We then interpret the plume as a vertically segregated CO$_2$ layer of thickness $b(r,t)$ within an aquifer of thickness $H$, and derive closed-form expressions for the normalized thickness $b(r,t)/H$, the compact-support plume edge $R(t)$, and a transient inner core radius $a(t)$ that marks the region where the plume occupies the full aquifer thickness. In the shut-in case, the core radius decreases with time and eventually vanishes, after which the plume recovers the pure Barenblatt regime; under constant injection, the model predicts an injection-controlled core and a plume edge that grows with the square-root law. This framework provides a physically transparent baseline for comparing plume-radius evolution, internal plume structure, and core development across sites, and establishes a consistent route for incorporating non-local effects by fractional derivatives in future extensions. |
| title | Porous-Medium Scaling of CO$_2$ Plume Footprint Growth |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2603.26169 |