Permeability spatial variability

As noted in Table I, average surface radium concentrations appear to vary by about a factor of 20. This can also be seen from the distributions from the NARR data. Soil permeabilities, on the other hand, have much larger variations, and thus, in principle, may have a greater influence on the spatial variations in average indoor radon concentrations that have been observed. As with the case of surface radium concentrations, the spatial variability of air permeabilities of soils is an important element in developing a predictive capability. 

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

As the permeability and framework mineralogy are spatially variable, cementation in general is expected to show spatial variability and an initial tendency to produce heterogeneous lithification. In particular, when dependent on fluid flow, the effect of textural and compositional heterogeneities is expected to prevail during diagenesis. When diage-netic processes are dependent solely on diffusion, these effects are less distinct as diffusion is less dependent on permeability. 

Two methods are developed for calculating gridblock-scale stress-permeability relationships. Although the first method is developed by assuming identical properties for individual hactures and spatially variable fracture densities, it can be mathematically shown that the model is also valid for individual fractures with different aperture parameters (e.g., b, and bmu) as long as Rb is the same for individual fractures. 

Vogel, T. Gerke, H. H. Zhang, R. van Genuchten, M. T. (2000) Modelling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties,... 

The derivation of the conjugated or unconjugated reciprocity theorems requires two distinct electromagnetic situations one characterized by refractive-index profile n, current density J and electric and magnetic fields E and H while the other is characterized by n, J, E and H. All vector quantities contain the implicit time dependence exp( — iwt), where (o is the angular frequency. The refractive-index profiles n and n may depend on all three spatial variables, but the permeability is taken to have the free-space value Po unless otherwise stated. 

The system states (dependent variables) are the pressure, p, and the superficial (Darcy) velocity, v. The density, p, and viscosity, p, are fluid properties, and g is the acceleration of gravity. The porosity, < )(z), and permeability, fc(z), represent the macroscopic properties of the media. Both are spatially dependent and are represented as continuous functions of position z, as explicitly noted. While the per-... 

In contrast to Chapter 1, we have explicitly introduced q(x,y,x,t), representing the local source volume flow rate per unit volume produced by any infinitesimal element of a general well. It is a three-dimensional, point singularity that applies to both injector and producer applications. For example, when q is a semi-infinite line, cylindrical radial flow is obtained over most of the source distribution, while spherical flow effects apply at the tip. In other words, partial penetration and spherical flow are modeled exactly. In this section, subscripts are used in three different contexts. First, they represent partial derivatives for example, Px is the partial derivative of p(x,y,z,t) with respect to the spatial coordinate x. Second, they are used as directional markers for example, ky (x,y,z) is the anisotropic permeability in the y direction. Finally, subscript indexes (i,j,k) in pijrepresent the centers of grid block volumes used in our finite difference discretizations. As usual. Ax, Ay, Az, and At are used to denote grid sizes for the independent variables x, y, z, and t. 

As the precipitation of carbonates from the pore water is very sensitive to variables like porosity, permeability, texture and composition of the fill mass, the water depth, temperature and chemistry of the pore water and the burial depth, the resulting cementation may be highly variable as well, both in terms of strength and in terms of spatial distribution (vertical and lateral extent). 

The simulation results demonstrate that Brinkman s equations extend Darcy s law to include a term that accounts for the viscous transport in the momentum balance and introduce the velocities in the spatial directions as dependent variables. This approach seems to be more robust than Darcy s law, since it is valid over a wider range of flow rates, and for different permeabilities of the porous media. 

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