Summer School on Porous Media

Udine, JULY 11, 2022 to JULY 15, 2022


This course is organised at CISM (Udine, Italy) and coordinated by Prof. Chris. MacMinn (University of Oxford) and me. All the details about the course are available here. You can download the flyer here.

Flow and transport in porous media are relevant for many geophysical, industrial, and biological applications, including carbon sequestration, glacial drainage, papermaking, transport across vascular walls, and bacteria motility. Predicting the evolution of these systems is difficult because of the interplay between different physical features, such as complex flow patterns, convection and reaction, and transformation of the porous matrix through deformation and phase change. In addition, flow and transport in porous media are governed by physical processes that span a wide range of length and time scales. Rapidly increasing computational power has recently enabled threedimensional, high-resolution and time-dependent simulations of these flows at both the pore-scale and the Darcy-scale, producing an entire branch of flourishing research into multiphase flow in porous media. Experimental progress has also been substantial, thanks to improved measurement techniques inboth 2D and 3D. Therefore, it is now useful to review the many studies on the subject to provide an overview of the current state of the art, and to put future research paths in perspective.
This course will provide an overview of the most up-to-date modelling approaches, numerical simulations, and experimental methods used to study the dynamics and properties of porous media flows characterized by convection and deformation.

Schematic representation of CO2 dissolution in saline aquifers

Fundamentals of transport in porous media will be presented, including upscaling techniques, thermodynamics of two-phase mixtures, Lagrangian interpretations, fractional diffusion, non-locality and memory.

Time-dependent evolution of convection-driven flows in different configurations will be analyzed, with reference to geophysical and industrial applications and with particular attention to the dynamics and structures of convection, effect of porous media properties on convection and transition from 2D to 3D convection. An overview of experimental and numerical techniques for convective flows in porous media will be presented and reviewed.

Principles of the coupling between flow, transport, and deformation in porous media will be presented. The small-deformation limit and classical linear poroelasticity will be discussed in the context of subsurface flows. Large-deformation poromechanics will be discussed in the context of polymeric hydrogels (including swelling and drying phenomena), paper-pulp suspensions (including viscoelasticity and plasticity), and granular media (including friction and rearrangement).
The implications of deformation for the dispersion and mixing of solutes will be considered. Two-phase flows will be considered, including capillary and wettability effects. Phase-field approaches will be introduced in the context of multiphase solidification problems (including ice, methane clathrates, and lava) and applied to the growth and migration of gas bubbles in soft porous media.

The course is addressed to graduate students and researchers in applied mathematics, physics and chemical/mechanical engineering.
The advanced topics and the presentation of current progress in this very active field will also be of considerable interest to senior researchers and industrial practitioners having a strong interest in understanding the multiscale complex behavior of such multiphase flows.



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the begin of the Summer School