Tag: Hysteresis

Stable Propagation of Saturation Overshoots for Two-Phase Flow in Porous Media

Post author By R Hilfer
Post date March 21, 2017

M. Schneider, T. Köppl, R. Helmig, R. Steinle, R. Hilfer

Transport in Porous Media 121, 621-641 (2018)
https://doi.org/10.1007/s11242-017-0977-y

submitted on
Tuesday, March 21, 2017

Propagation of saturationovershoots for two-phaseflow of immiscible and incompressible fluids in porous media is analyzed using different computational methods. In particular, it is investigated under which conditions a given saturation overshoot remains stable while moving through a porous medium. Two standard formulations are employed in this investigation, a fractional flow formulation and a pressure–saturation formulation. Neumann boundary conditions for pressure are shown to emulate flux boundary conditions in homogeneous media. Gravity driven flows with Dirichlet boundary conditions for pressure that model infiltration into heterogeneous media with position-dependent permeability are found to exhibit pronounced saturation overshoots very similar to those seen in experiment.

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Tags 2018, Hysteresis, saturation overshoot

fluid flow Porous Media Simulations Two-Phase Flow

Hysteresis in relative permeabilities suffices for propagation of saturation overshoot: A quantitative comparison with experiment

Post author By R Hilfer
Post date December 21, 2016

R. Steinle, R. Hilfer

Physical Review E 95, 043112 (2017)
https://doi.org/10.1103/PhysRevE.95.043112

submitted on
Wednesday, December 21, 2016

Traditional Darcy theory for two-phase flow in porous media is shown to predict the propagation of nonmonotone saturation profiles, also known as saturation overshoot. The phenomenon depends sensitively on the constitutive parameters, on initial conditions, and on boundary conditions. Hysteresis in relative permeabilities is needed to observe the effect. Two hysteresis models are discussed and compared. The shape of overshoot solutions can change as a function of time or remain fixed and time independent. Traveling-wave-like overshoot profiles of fixed width exist in experimentally accessible regions of parameter space. They are compared quantitatively against experiment.

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Tags 2017, Hysteresis, saturation overshoot

fluid flow Porous Media Two-Phase Flow

Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media

Post author By R Hilfer
Post date October 16, 2015

S. Schlüter, S. Berg, M. Rücker, R. Armstrong, H.-J. Vogel, R. Hilfer, D. Wildenschild

Water Resources Research 52, 2194-2205 (2016)
https://doi.org/10.1002/2015WR018254

submitted on
Friday, October 16, 2015

The macroscopic description of the hysteretic behavior of two-phase flow in porous media remains a challenge. It is not obvious how to represent the underlying pore-scale processes at the Darcy-scale in a consistent way. Darcy-scale thermodynamic models do not completely eliminate hysteresis and our findings indicate that the shape of displacement fronts is an additional source of hysteresis that has not been considered before. This is a shortcoming because effective process behavior such as trapping efficiency of CO 2 or oil production during water flooding are directly linked to pore-scale displacement mechanisms with very different front shape such as capillary fingering, flat frontal displacement, or cluster growth. Here we introduce fluid topology, expressed by the Euler characteristic of the nonwetting phase, as a shape measure of displacement fronts. Using two high-quality data sets obtained by fast X-ray tomography, we show that the Euler characteristic is hysteretic between drainage and imbibition and characteristic for the underlying displacement pattern. In a more physical sense, the Euler characteristic can be interpreted as a parameter describing local fluid connectedness. It may provide the closing link between a topological characterization and macroscopic formulations of two-phase immiscible displacement in porous rock. Since fast X-ray tomography is currently becoming a mature technique, we expect a significant growth in high-quality data sets of real time fluid displacement processes in the future. The novel measures of fluid topology presented here have the potential to become standard metrics needed to fully explore them.

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Tags 2016, Hysteresis

Porous Media Two-Phase Flow

Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

Post author By R Hilfer
Post date May 31, 2015

O. Hönig, P. Zegeling, F. Doster, R. Hilfer

Transport in Porous Media 114, 309-340 (2016)
https://doi.org/10.1007/s11242-015-0618-2

submitted on
Sunday, May 31, 2015

Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. All boundary resp. limit value problems of the travelling wave ansatz, which lead to smooth travelling wave solutions, are systematically explored. A complete, visually and computationally useful representation of the five-dimensional manifold connecting wave velocities and boundary resp. limit data is found by using methods from dynamical systems theory. The travelling waves exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is given to the non-monotonic profiles. The stability of the travelling waves is studied by numerically solving the full system of the partial differential equations with an efficient and accurate adaptive moving grid solver.

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Tags 2016, Hysteresis, saturation overshoot

fluid flow Porous Media Two-Phase Flow

Inﬂuence of Initial Conditions on Propagation, Growth and Decay of Saturation Overshoot

Post author By R Hilfer
Post date November 24, 2014

R. Steinle, R. Hilfer

Transport in Porous Media 111, 369-380 (2016)
https://doi.org/10.1007/s11242-015-0598-2

submitted on
Monday, November 24, 2014

A sequence of drainage and imbibition shocks within the traditional theory of two-phase immiscible displacement can give rise to shallow non-monotone saturation profiles as shown in Hilfer and Steinle (Eur Phys J Spec Top 223:2323, 2014). This phenomenon depends sensitively on model parameters and initial conditions. The dependence of saturation overshoot on initial conditions is investigated more systematically in this article. The results allow to determine regions in the parameter space for the observation of saturation overshoot and to explore limitations of the underlying idealized hysteresis model. Numerical solutions of the nonlinear partial differential equations of motion reveal a strong dependence of the overshoot phenomenon on the boundary and initial conditions. Overshoot solutions with experimentally detectable height are shown to exist numerically. Extensive parameter studies reveal different classes of initial conditions for which the width of the overshoot region can decrease, increase or remain constant.

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Tags Hysteresis, saturation overshoot