To gain insight in relationships among capillary pressure, interfacial area, saturation, and relative permeability in two-phase flow in porous media, we have developed two types of pore-network models. The first one, called tube model, has only one element type, namely pore throats. The second one is a sphere-and-tube model with both pore bodies and pore throats. We have shown that the two models produce distinctly different curves for capillary pressure and relative permeability. In particular, we find that the tube model cannot reproduce hysteresis. We have investigated some basic issues such as effect of network size, network dimension, and different trapping assumptions in the two networks. We have also obtained curves of fluid-fluid interfacial area versus saturation. We show that the trend of relationship between interfacial area and saturation is largely influenced by trapping assumptions. Through simulating primary and scanning drainage and imbibition cycles, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (P c -S w -a nw ) points as well as to relative permeability, saturation, and interfacial area (k r -S w -a nw ) points. The two fitted three-dimensional surfaces show very good correlation with the data points. We have fitted two different surfaces to P c -S w -a nw points for drainage and imbibition separately. The two surfaces do not completely coincide. But, their mean absolute difference decreases with increasing overlap in the statistical distributions of pore bodies and pore throats. We have shown that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure-saturation (P c -S w ) and the relative permeability-saturation (k r -S w ) curves.
[1] Domains composed of a porous part and an adjacent free-flow region are of special interest in many fields of application. So far, the coupling of free flow with porous-media flow has been considered only for single-phase systems. Here we extend this classical concept to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region. The mathematical modeling of flow and transport phenomena in porous media is often based on Darcy's law, whereas in free-flow regions the (Navier-) -Stokes equations are used. In this paper, we give a detailed description of the employed subdomain models. The main contribution is the developed coupling concept, which is able to deal with compositional (miscible) flow and a two-phase system in the porous medium. It is based on the continuity of fluxes and the assumption of thermodynamic equilibrium, and uses the Beavers-Joseph-Saffman condition. The phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail. Our model can account for evaporation and condensation processes at the interface and is used to model evaporation from soil influenced by a wind field in a first numerical example.
Abstract. Analytical methods and numerical experiments are used to study salinization of groundwater in response to sea level rise. The system that is studied involves a saturated porous medium with an inclined upper surface. The upper surface is progressively inundated during sea level rise to simulate transgression, the landward migration of the shoreline. Four "modes" of seawater intrusion are distinguished: (1) horizontal intrusion for slow transgression and a relatively high-permeability (sand/silt) substrate, (2) vertical intrusion by seawater fingering for fast transgression and a sand/silt substrate, (3) vertical intrusion by diffusion for fast transgression and a low-permeability (clay) substrate, (4) vertical intrusion by combined diffusion and low-salinity fingering for fast transgression and a clay layer at the seafloor overlying an aquifer. These four modes are characterized by the development of very distinctive transition zones between the fresh and salt groundwater domains. An analytical expression is derived for the critical transgression rate which separates horizontal (mode 1) from dominantly vertical (modes 2-4) intrusion. For modes 3 and 4, salinization significantly lags behind sea level rise. The results are consistent with observations of fossil fresh/brackish groundwater beneath many continental shelves and shallow seas.
Because natural organic matter (NOM) can act as a carrier for contaminants, it is of great importance to understand its dynamic adsorption/desorption behavior. NOM is a mixture of organic molecules that vary both in chemical and physical properties. The adsorption/desorption behavior of a NOM mixture to the solid matrix cannot be adequately described using simple equilibrium sorption isotherms, like the Langmuir isotherm. Often adsorption/desorption hysteresis is found or “adsorption maxima” keep increasing slowly. In this paper a relatively simple model is developed to describe the kinetic adsorption/desorption of NOM. The model is calibrated using experimental data. Model simulations of experimental data show that adsorption/desorption hysteresis is an inherent property of a heterogeneous mixture of molecules. The composition and thus the properties of the mixture vary with the total amount of NOM added and with surface/volume ratios. Therefore the relationship between the overall adsorption and the overall solution concentration is nonunique and thus a nonthermodynamic isotherm. Although adsorption in terms of mass of carbon seems to reach equilibrium relatively fast, the distribution of individual components can still be far from equilibrium. This indicates that the composition of the NOM mixture may vary with time as well.
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