Editorial: physics of porous media

Editorial on the Research Topic
Physics of Porous Media

The physics of porous media is, when taking a broad view, the physics of multinary mixtures of immiscible solid and fluid constituents. Its relevance to society echoes in numerous engineering disciplines such as chemical engineering, soil mechanics, petroleum engineering, groundwater engineering, geothermics, and fuel cell technology. It is also at the core of many scientific disciplines ranging from hydrogeology to pulmonology.

Perhaps one may affix a starting point for the study of porous media as the year 1794 when Reinhard Woltman introduced the concept of volume fractions when trying to understand mud [ 1 ]. In 1856, Henry Darcy published his findings on the flow of water through sand packed columns and the first constitutive relation was born [ 2 ]. Wyckoff and Botset proposed in 1936 a generalization of the Darcy approach to deal with several immiscible fluids flowing simultaneously in a rigid matrix [ 3 ]. This effective medium theory assigns to each fluid a relative permeability, i. e., a constitutive law for each fluid species. It remains to this day the standard framework for handling the motion of two or more immiscible fluids in a rigid porous matrix even though there have been many attempts at moving beyond it.

When the solid constituent is not rigid, forces in the fluids and the solid phase influence each other. von Terzaghi realized the importance of capillary forces in such systems in the thirties [ 4 ]. An effective medium theory of poroelasticity was subsequently developed by Biot in the mid fifties [ 5 ]. Biot theory remains to date the state-of-the art for handling matrix-fluid interactions when the deformations of the solid phase remain small. For large deformations, e. g., when the solid phase is unconsolidated, no effective medium theory exists.

The situation today in porous media research is a patchwork of domains, some of which are advancing at high speed, whereas other domains remain where they have been for decades. For example, pore scale visualization techniques together with advances in numerical techniques and hardware have today reached a level of refinement that makes it possible numerically to reproduce the motion of immiscible fluids and their interfaces in complete detail at the pore level. On the other hand, to derive effective equations at the large-scale continuum level based on what happens at the pore scale the upscaling problem remains a rather stagnant endeavor as proven by the popularity of the 80-year old relative permeability theory of Wyckoff and Botset.

It is the aim of any physical theory to join experimental observations into a common framework reducing the field to solving mathematical problems. Here is an example. The flow of Newtonian fluids remained a catalog over experimental observations until the advent of the Navier-Stokes equations. Afterwards, the problem became solving these equations with the proper boundary conditions. The fact that it is extremely difficult to solve these equations in the majority of instances is a different story. The science of porous media is still at the catalog stage with no general theory of porous media flow in existence nor in sight.

This Research Topic attempts to present a snapshot of the state-of-the-art in some of the domains that constitute the physics of porous media. The physics of porous media is of course far too wide to make it possible to give a comprehensive picture of the field. Interdisciplinarity is a key word.

The paper by Xu et al. studies the dissolution of plaster by water in a two-dimensional Hele-Shaw cell. The water is drained from the center of the cell which has a radial geometry. This causes fingers to grow inwards from the surface of the plaster. There has been a number of numerical studies of similar phenomena, but the experimental work is sparse—in spite of the importance of this process in geological settings.

In another experimental and numerical study, Xu et al. inject a reactive fluid into an open fracture with the result that the fracture surface is modified locally by creating a ramified structure around the injection point. A tracer is then injected and the influence of the modified fracture surface on stability of dispersion front is studied.

2. Darcy HPG. Les Fontaines publiques de la ville de Dijon. Exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau. Paris: Victor Dalamont (1856).

3. Wyckoff RD, Botset HG. The flow of gas-liquid mixtures through unconsolidated sands. Physics.(1936)7: 325–45. doi: 10. 1063/1. 1745402

4. von Terzaghi K. Auftrieb und Kapillardruck an betonierten Talsperren. Die Wasserwirtschaft.(1933)26: 397–9.

5. Biot MA. Theory of deformation of a porous viscoelastic anisotropic solid. J Appl Phys.(1956)27: 459–67. doi: 10. 1063/1. 1722402