Abstract

Traditionally, multiphase flow in porous media is described by the so-called extended Darcy’s Law, which is based on the original Darcy’s Law by including the relative permeability. The driving force in the horizontal direction is only the pressure gradient, which means that flow will cease without a pressure gradient. However,
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this is contradicted by experimental evidence (Kona, 1997). Hassanizadeh and Gray (1993b) found that the actual driving force for the horizontal flow of a phase is the gradient in the Gibbs free energy, which itself is a function of saturation, specific interfacial area, and fluid pressure. Thus, in addition to the pressure gradient, gradients in saturation and the specific interfacial area also appear in the generalized Darcy’s law. This means that in principle it is possible to maintain gradients in pressure and saturation under no flow conditions. Since few studies of the generalized formula exist, in this thesis we only consider the saturation gradient as a new driving force in order to reduce uncertainties in the estimation of parameters. In addition to the generalized Darcy’s law, the constitutive relationship between capillary pressure and saturation is fundamental to characterizing unsaturated flow in soils. Traditionally, capillary pressure, defined as the difference in fluid pressures, is assumed to be a function of saturation. Rather than resorting to a hysteretic relationship, Hassanizadeh and Gray (1993b) have suggested that non-uniqueness in the capillary pressure-saturation relationship can be modelled by introducing the air-water specific interfacial area into the formulation. The main objective of this research is to provide an increased understanding of the advanced theories of two-phase flow presented above. To achieve this objective, experiments, numerical simulations, and mathematical analyses have been performed. Specific objectives are as follows: simulating an existing horizontal redistribution experiment, to test the validity of the generalized Darcy’s law; designing, performing and simulating well-defined horizontal redistribution experiments, to have a better understanding of the generalized Darcy’s law; simulating an existing downward infiltration experiment, including dynamic capillarity effects; analysing the dynamic capillarity effect term mathematically, in order to gain insights in its effect on the solutions; designing and performing well-defined experiments to quantify the dynamic capillarity effect.
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