Upscaling hydraulics

The review is organized as follows first, we discuss aspects of the unitary approach for combining adsorptive and capillary contributions, and present the new pore scale model of Tuller et al. (1999). The upscaling scheme of Or and Tuller (1999) for representing sample scale retention properties will be presented, followed by illustrative examples with measured characteristic data and a discussion of critical soil parameters. The role of liquid-vapor interfacial area will be highlighted by comparisons of model predictions with limited measurements. Finally, we introduce hydrodynamic considerations of unsaturated flow in films and comers leading to prediction of hydraulic conductivity of rough rock surfaces and unsaturated porous media. 

Upscaling From Pore- to Sample Scale Hydraulic Conductivity... 

In an attempt to derive closed-form expressions for unsaturated hydraulic conductivity, we were forced to fix the shape of the gamma distribution by using a constant distribution parameter = 2. This led to a reduced flexibility, especially for soils with narrow pore size distribution. In Fig. 1-15 we show improved predictions of AXp) when the distribution parameter , is left as a free parameter (using a numerical scheme for the upscaling). The dashed line in Fig. 1—15b represents the numerically evaluated relative saturation curve ( , = 6) that is almost indistinguishable from the VG-Mualem model. A summary of resulting parameters is listed in Table 1-6. 

An extensive examination of the fracture network and mechanical data has been undertaken to determine models of the fracture characteristics of the three formations, the uncertainties in the parameterisation of the models, and the sensitivity of the upscaled flow properties to the underlying parameter variations. The methodology used to calculate effective hydraulic conductivity values and their sensitivity to the small-scale model is described in Blum el al. (2003). The study undertaken to obtain the effective hydraulic conductivity under different stress conditions and presented in Blum et al. (2003) revealed that the important parameters in modelling HM processes in the fractured rock mass are the fracture density, the mechanical (M) properties and the M property variations through the rock mass. 

Given that the mean hydraulic conductivities for the faults were too similar to those of the formations, it was decided to increase in two orders of magnitude the conductivities for the fault in the Formation Type I, and four orders of magnitude in the fault in Formation Type 2. It was also decided to make a sensitivity analysis of the upscaling procedure as a function of the standard deviation of logioAT, so the parameters in Table I were modified as indicated in Table 2. 

The block of 10 by 10 cells to be upscaled is isolated along with a skin. The flow equation is solved using the boundary conditions shown in the Figure. These boundary conditions force flow in four different directions. Then, a simple least-square procedure is used to determine the single conductivity tensor that is able to reproduce best the flows crossing the block for all four boundary conditions. The result is a full hydraulic conductivity tensor with arbitrary principal directions, not necessarily parallel to the Cartesian axes. In Figure 4, the diagonal components of the... 

Ohman, J. and Niemi, A. 2003a. Upscaling of Fracture Hydraulics by Means of an Oriented Correlated Stochastic Continuum Model, Water Resourc. Res. (Accepted). 

Upscaling of Hydraulic and Hydrogeochemical Aquifer Parameters Using an Approach Based on Sedimentologieal Facies... 

Upscaling of Hydraulic and Hydrogeo chemical Aquifer Parameters... 

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