Porous-Medium Scaling of CO$_2$ Plume Footprint Growth

TL;DR

This paper compares analytical solutions with seismic data to understand CO₂ plume growth in porous media, deriving models for plume structure and growth under different conditions, and providing a baseline for future extensions.

Contribution

It introduces a physically transparent model for CO₂ plume growth, linking analytical solutions with field data, and offers a foundation for incorporating non-local effects via fractional derivatives.

Findings

Effective plume-growth exponents align with porous-medium scaling.

Derived expressions for plume edge, core radius, and layer thickness.

Model predicts different plume behaviors under shut-in and constant injection.

Abstract

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.