SCAL3D Exploring Scaling Laws for Drainage in 3D Porous Media

Duration
15.04.2026–14.04.2027

Project goal illustration. In 2D porous media, drainage can be adequately represented by percolation models, which leads to the formulation of simple scaling laws for the front width η and phase saturation Snw according to the flow conditions. Images (a), (b), and (c) represent, respectively, 2D drainage experiments in Hele-Shaw cells [25], IP simulation results, and the theoreticalnumerical-experimental agreement. In 3D, we will test the ability of simple percolation models to represent drainage in naturally occurring/engineered porous media. With this, we will corroborate our theoretical model for η [29] and propose a model for Snw. Image (d) represents 3D drainage visualization experiments [9], (e) IP simulations on 3D ideal lattices, and (f) the theoretical models proposed and tested with SCAL3D

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About the project

Flow and transport in porous media play a central role in a range of environmental, geological, and engineering applications. Yet, our current understanding of these processes is, to a great extent, shaped by studies using two-dimensional models. Recent advances in experimental and computational capabilities have allowed the discovery of new behaviors in three-dimensional porous-media flows that challenge previously established knowledge.

With SCAL3D, we intend to substantiate our new theoretical model for drainage fronts in 3D porous media, which radically contrasts with conventional scaling laws derived for flow in two dimensions. This represents a first and necessary step toward a more ambitious project involving a joint theoretical, numerical, and experimental approach to develop predictive models for drainage in 3D porous media

Project Summary

The displacement of gases and liquids in porous media is present in several everyday circumstances, such as water soaking into a dry paper towel or water leaving the fabric of drying clothes. These apparently simple situations conceal complex flow phenomena at the microscale, as the interface between the immiscible fluids – such as air and water, or water and oil – moves through the tiny void spaces of a permeable material. Similar flows also take place in many industrial and natural processes of scientific/economic interest. Displacement flows in porous media occur when a liquid contaminant is spilled into soil, when CO2 is injected into an aquifer for storage, or when oil/gas is extracted from a reservoir. In all these cases, it is important to understand how much fluid is displaced and what the interface configuration is during the flow.

Historically, scientific investigation of such flows has been largely carried out using simplified two-dimensional models of porous media. This means approximating a complex 3D structure of interconnected pores by a planar network of flow paths, akin to a maze, that can be more easily visualized and understood. Studies of displacement flows in 2D or quasi-2D porous media have led to crucial advances in understanding porous media flows, which are now applied to hydrology, environmental engineering, and energy and materials sciences.

Recent advances in experimental techniques and computational capabilities have allowed, however, the discovery of behaviors in three-dimensional porous-media flows not well described in the previously established knowledge. In this context, with SCAL3D we intend to substantiate our new theoretical model for the interface between fluids during drainage in 3D porous media, which contrasts with conventional models developed for flow in two dimensions.

Outcomes and impacts

The main expected outcome of the project is the development and consolidation of new theoretical models of displacement flows in three-dimensional porous media, which can be readily used in a range of practical applications.

The current understanding of the scientific community of displacement flows in three-dimensional porous media is relatively limited, when compared to flows in 2D domains. Yet, most drainage processes of societal interest occur in natural or engineered porous materials of three dimensions. For instance, drainage in 3D porous media occurs when a CO2 plume migrates through an aquifer during subsurface carbon storage; when air infiltrates a wet soil after rain or a liquid contaminant spill; and in enhanced oil recovery when a gas is injected to push liquid hydrocarbons out of a reservoir.

In this context, the results of SCAL3D can benefit the understanding and prediction of such processes, for which typical 2D scaling laws fail

Participants

Published Sep. 24, 2026 11:38 AM - Last modified Sep. 25, 2026 2:42 PM