Capillary hysteresis and gravity segregation in two phase flow through porous media

We study the gravity driven flow of two fluid phases in a one dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken into account. In the hyperbolic limit, solutions of such systems satisfy the Buckley-Leverett equation with a non-monotone flux function. However, solutions for the hysteretic case do not converge to the classical solutions in the hyperbolic limit in a wide range of situations. In particular, with Riemann data as initial condition, stationary shocks become possible in addition to classical components such as shocks, rarefaction waves and constant states. We derive an admissibility criterion for the stationary shocks and outline all admissible shocks. Depending on the capillary pressure functions, flux function and the Riemann data, two cases are identified a priori for which the solution consists of a stationary shock. In the first case, the shock remains at the point where the initial condition is discontinuous. In the second case, the solution is frozen in time in at least one semi-infinite half. The predictions are verified using numerical results.

The Modeling for Coupled Elastoplastic Geomechanics and Two-Phase Flow With Capillary Hysteresis in Porous Media

We study new constitutive relations employing the fundamental theory of elastoplasticity for two coupled irreversible processes: elastoplastic geomechanics and two-phase flow with capillary hysteresis. The fluid content is additively decomposed into elastic and plastic parts with infinitesimal transformation assumed. Specifically, the plastic fluid content, i.e., the total residual (or irrecoverable) saturation, is also additively decomposed into constituents due to the two irreversible processes: the geomechanical plasticity and the capillary hysteresis. The additive decomposition of the plastic fluid content facilitates combining the existing two individual simulators easily, for example, by using the fixed-stress sequential method. For pore pressure of the fluid in multi-phase which is coupled with the geomechanics, the equivalent pore pressure is employed, which yields the well-posedness of coupled multi-phase flow and geomechanics, regardless of the capillarity. We perform an energy analysis to show the well-posedness of the proposed model. And numerical examples demonstrate stable solutions for cyclic imbibition/drainage and loading/unloading processes. Employing the van Genuchten and the Drucker Prager models for capillary and the plasticity, respectively, we show the robustness of the model for capillary hysteresis in multiphase flow and elastoplastic geomechanics.

Reversible and Irreversible Processes in Drying and Wetting of Soil

In this article, we provide a detailed description of a modeling technique for the capillary hysteresis in a soil-like porous material based on a Generalized Preisach Model. The identification of the reversible and irreversible Preisach distributions was performed with the first-order reversal curve (FORC) diagram technique, which is very popular now in magnetism and in other areas of science to give a fingerprint of the studied system. A special attention was given to the evaluation of the reversible component. In this case, we used a set of data published in 1965 by Morrow and Harris which has been used as a reference by many other researchers since. The advantage of this approach is that the experimental FORC distributions can be described with analytical functions and easily implemented in the mentioned Preisach-type model. Our research is also focused on the development of a characterization tool for the soil using the soil-moisture hysteresis. The systematic use of scanning curves provides a (FORC) diagram linked to the physical properties of the studied soil. The agreement between the experimental data and the Preisach model using the set of parameters found through the FORC technique is really noticeable and gives a good practical option to the researchers to use a method with a strong predictive capability.

LABORATORY DIAGNOSTIC SYSTEM FOR WATER-PHYSICAL SOIL PROPERTIES

Actuality of the problem. Irrigation has become a determining factor in the formation of bioproduction processes of new agricultural crop varieties and hybrids due to global climate change for all soil-climatic zones of Ukraine. Moreover, irrigation efficiency is determined to a significant degree by the reliability of the soil water-physical properties. The purpose of comprehensive hydrophysical studies was to determine the basic soil water-physical properties and constants necessary to create favorable soil regimes of reclaimed lands, and to do the mathematical modeling of the soil water regime. Complex laboratory hydrophysical tests of soil samples of undisturbed structure make it possible to determine hydrophysical functions for each soil sample: water holding capacity, water conductivity and water-physical constants of full and minimum moisture capacity, wilting moisture and maximum hygroscopic moisture, which can be determined on the same soil sample located on the same soil desorption curve from full moisture capacity to maximum hygroscopic humidity. The primary saturation of the soil sample under vacuum to full moisture capacity provides a single curve of water retention capacity taking into account structural macroporosity, which is the main feature of this technique. The resulting capillary hysteresis loop has the algorithm: fast nonequilibrium desorption from full moisture capacity and slow equilibrium sorption enables to build a differential curve of the distribution of pore volume over radii, characterizing the structure of the soil pore space. These structural characteristics are sensitive to soil processes, which determine the direction of epigenetic changes in the structure of the soil pore space and the direction of evolution of the soil matrix. The threshold of structural soil macroporosity formation is established from the loop of capillary hysteresis by the ratio of meniscus radii exceeding . Conclusions. The proposed system of soil laboratory diagnostics has advantages over the existing diagnostic methods and significantly increases the information content of complex hydrophysical tests, provides qualitatively new information on soils and provides mathematical modeling with the necessary parameters of mass transfer processes in moisture-saturated soils of the aeration zone.

Capillary hysteresis in sloshing dynamics: a weakly nonlinear analysis

The sloshing of water waves in a vertical cylindrical tank is an archetypal damped oscillator in fluid mechanics. The wave frequency is traditionally derived in the potential flow limit (Lamb, Hydrodynamics, Cambridge University Press, 1932), and the damping rate results from the combined effects of the viscous dissipation at the wall, in the bulk and at the free surface (Case & Parkinson, J. Fluid Mech., vol. 2, 1957, pp. 172–184). Still, the classic theoretical prediction accounting for these effects significantly underestimates the damping rate when compared to careful laboratory experiments (Cocciaro et al., J. Fluid Mech., vol. 246, 1993, pp. 43–66). Specifically, theory provides a unique value for the damping rate, while experiments reveal that the damping increases as the sloshing amplitude decreases. Here, we investigate theoretically the effects of capillarity at the contact line on the decay time of capillary–gravity waves. To this end, we marry a model for the inviscid waves to a nonlinear empiric law for the contact line that incorporates contact angle hysteresis. The resulting system of equations is solved by means of a weakly nonlinear analysis using the method of multiple scales. Capillary effects have a dramatic influence on the calculated damping rate, especially when the sloshing amplitude gets small: this nonlinear interfacial term increases in the limit of zero wave amplitude. In contrast to viscous damping, where the wave motion decays exponentially, the contact angle hysteresis can act as Coulomb solid friction, thus yielding the arrest of the contact line in a finite time.