Volumetric hydraulic conductance

It is obvious from Equation 14.14 that the most important parameter determining the volumetric air flow rate <2W is the intrinsic permeability K of soil. At this point it is important to stress the difference between water permeability (or hydraulic conductivity) k , air permeability ka, and intrinsic permeability K. In most cases, when permeability data are provided for a type of soil or geological formation, these data are based on hydraulic conductivity measurements and describe how easily the water can flow through this formation. However, the flow characteristic of a fluid depends greatly on its properties, e.g., density p and viscosity p. Equation 14.16 describes the relationship between permeability coefficient k and fluid properties p and p ... 

FIGURE 3.25 Graphs of hydraulic conductivity vs. volumetric water content showing characteristic curves for different sediments from the VOC-arid site integrated demonstration at the Hanford site. 

When comparing the kinematic limit of Eq. [21] with Eq. [24], we note similitude both derive from a conservation law and from a structural relation and both apply when gravity driven flow is dominant. But the first one is limited to macroscopic continuum media where the hydraulic conductivity is well defined everywhere. The other one is more general as the structural relation between the flux and the volumetric content is not dependent on the existence of a REV. Equation [24] does not account for waterfront dispersion, nevertheless dispersive effects have been experimentally observed for low input intensities (Di Pietro Lafolie,1991). 

Using an equation of equilibrium or motion, which determines the deformation of the solid skeleton, and (5.58), a system of differential equations for specifying the mean velocity v (i.e., the conventional consolidation problem) is achieved. Note that in (5.58)

total head excluding the velocity potential), k is the hydraulic conductivity tensor, p is the pore pressure of the fluid, g is the gravity constant, and is the datum potential. Thus by starting with the mass conservation laws for both fluid and solid phases, we can simultaneously obtain the diffusion equation and the seepage equation which includes a term that accounts for the volumetric deformation of the porous skeleton. 

Here a-j is the effective stress, which acts on the solid skeleton, p is the pore pressure, is the volumetric strain, ky is the hydraulic conductivity tensor, and Yw = Pg is the bulk weight of the liquid phase. It should be noted that the mass flux is described as q = —KVpjg, and the boundary condition is given by (6.42). We use a convention where a[j is positive for tension, and p is positive for compression. 

It is more complex to model water flow in the unsaturated zone than in the saturated zone because water flow in the vadose zone occurs only via water-filled pores, and the fraction of the pore spaces filled with water (the percent saturation) is highly variable. The water content 0 in a porous medium refers to the volumetric fraction that contains water it can range between zero and n, the porosity. The relationship between hydraulic conductivity and water content is complex and difficult to predict therefore, it is usually measured experimentally and expressed in the form of a K-6 curve, as shown in Fig. 3.21. One major complication in the K-6 relationship is hysteresis hydraulic conductivity differs depending on whether the porous media most recently have been dried or wetted to obtain a given moisture content. For dry material, regardless of its texture, hydraulic conductivity is low. 

Experiments without HMs were conducted using synthetic WW inoculated with 10% (v/v) acclimated seed MOs to twice their combined threshold concentration (that is, 10 mg/L Cu2+, and 60 mg/L Zn2+). The reactor was operated as a batch system for 48 h with the growth of new biomass. Then, continuous feeding of synthetic WW to the reactor at a desired volumetric flow rate (or desired residence time) was started. The system reaches steady state in about 12-44 days depending on the influent metal concentrations and the hydraulic residence time (HRT) effluent... 

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