Prof. Marios S. Valavanides
University of West Attica, Egaleo, Athens, Greece
Title of the paper: Beyond Saturation-Dependent Relative Permeabilities: A Mechanistic Framework for Immiscible Two-Phase Flow in Porous Media
Abstract: Immiscible two-phase flow in porous media is ubiquitous in energy and environmental
applications. At the continuum scale, this process is commonly described by the extended
Darcy law, in which the fractional flow rates of the two immiscible phases are governed by
their relative permeabilities under different flow conditions. Conventionally, relative
permeabilities are expressed as functions of saturation, which quantifies the volumetric
fraction of the pore space occupied by each fluid. However, the applicability of this classical
modelling framework remains limited to a relatively narrow range of flow conditions.
Recent research, combining experimental investigations with theoretical and analytical
developments, has made substantial progress towards elucidating the underlying flow
mechanisms and establishing improved modelling approaches. A particularly promising
direction is the development of a flow-rate-dependent scaling law for relative permeabilities
in steady-state two-phase flow through pore networks. Rooted in the underlying physics of
multiphase flow, this approach retains the classical fractional-flow formulation while
extending its predictive capability beyond the conventional saturation-dependent
framework to encompass distinct flow regimes, including viscous–capillary and capillaritydominated
flows.
This plenary talk will provide an overview of the fundamental principles and recent
advances in this emerging framework, covering: (a) the theoretical foundations of the new
approach; (b) implications for energy efficiency; (c) extensive virtual experiments using the
DeProF hybrid mechanistic–stochastic model; (d) validation against systematic laboratory
experiments in two-fluid systems and pore-network configurations, including natural rock
cores and artificial microfluidic pore networks spanning a range of sizes, network
geometries, and physicochemical properties; (e) intrinsic system invariants, including critical
flow conditions and crossover relative permeabilities; (f) an improved, true-to-mechanism
definition of the effective capillary number; and (g) similarities and potential connections
with other flow phenomena.
Finally, the talk will highlight open questions and emerging research challenges, including
the role of flow history and the extent of hysteresis, the influence of boundary-induced end
effects, and the relationship between maximum energy efficiency and the maximum
entropy production principle.
Bio: Professor Marios S. Valavanides is a Professor of Hydraulics and Flow in Porous Media in the Department of Civil Engineering at the University of West Attica in Athens, Greece. He holds a PhD in Fluid Mechanics from the University of Patras, awarded in 1998, and a Diploma in Mechanical Engineering from the same university. His research focuses on fluid mechanics, multiphase flow in porous media, continuum mechanics, and composite materials. He is particularly known for his work on the DeProF theoretical framework, which advances the understanding and modelling of two-phase flow in porous structures. His research contributes to improved flow characterization, energy efficiency, and practical applications in porous media engineering."