By Adam Szymkiewicz
The booklet makes a speciality of matters concerning mathematical and numerical modelling of circulate in unsaturated porous media. within the first half numerical answer of the governing equations is mentioned, with specific emphasis at the spatial discretization of hugely nonlinear permeability coefficient. the second one half offers with huge scale movement in heterogeneous porous media of binary constitution. Upscaled versions are built and it's proven that the presence of fabric heterogeneities can give upward push to extra non-equilibrium phrases within the governing equations or to hysteresis within the averaged constitutive relationships.
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Extra info for Modelling Water Flow in Unsaturated Porous Media: Accounting for Nonlinear Permeability and Material Heterogeneity
Sample text
Numerical experiments [73] showed that the agreement between results obtained from the Richards equation and from the twophase model is less than perfect for the water-to-air viscosity ratio smaller than 100. In natural conditions the viscosity of air can be expected to be only about 50 to 60 times smaller than the mobility of water. It should be noted that the phase mobility depends not only on its viscosity, but also on the relative permeability. Thus, further decrease in the mobility ratio can be expected if the relative permeability of air is much smaller than the permeability of water, which occurs as the air saturation approaches the residual value.
1 Fundamental Concepts 19 capillary pressure head h c . Transition to the pressure head based form is straightforward and requires only that the parameters pe and pg are replaced by the corresponding pressure heads. 2 to 5. Large values of n b correspond to a rapid decrease of the saturation above the entry pressure, which is typical for media having uniformly sized pores. Smaller values of n b characterize media with non-uniform pore size distributions. This model is useful for porous media having a distinct air entry pressure and relatively uniform pore sizes, however it cannot reproduce the inflection point in the capillary function, characteristic for many finely textured soils [41].
Therefore, from the pore scale point of view, the water pressure is lower than the air pressure in pendular rings or in capillary tubes, but it is higher 16 2 Mathematical Models of Flow in Porous Media than the air pressure in the thin water layers around spherical solid grains, or around occluded air bubbles. However, in each of these situations the Darcy-scale capillary pressure is defined as a nonnegative value. g. [58]. Indeed, the values of the water pressure potential at low saturations, measured with respect to the atmospheric pressure, are often well below −100 kPa, which would indicate negative absolute pressures.