Directional hydraulic conductivity

Darcy s law applied to a soil liner shows the rate of flow of liquid q directly proportional to the hydraulic conductivity of the soil and the hydraulic gradient, a measure of the driving power of the fluid forcing itself through the soil and the cross-sectional area A of the liner (see Figure 26.9). 

The tests do not directly measure the hydraulic conductivity k of the soil. Instead they measure the infiltration rate / for the soil. Since hydraulic conductivity is the infiltration rate divided by the hydraulic gradient i (see equations in Figure 26.14), it is necessary to determine the hydraulic gradient before k can be calculated. The following equation (with terms defined in Figure 26.14) can be used to estimate the hydraulic gradient ... 

In addition to direct effects on the plant, benzylamine may induce hydrophobic (water repellent) conditions in soil (Figure 4)-These data indicate a linear increase in moisture content as benzylamine content increases, attributable to the development of a lower unsaturated hydraulic conductivity in the surface soil, which thus became less able to transfer water from depth in response to evaporative demand. McGhie (50) suggests that poor germination of crop and pasture plants may be related to the development of hydrophobic conditions, the affected soil being unable to supply water to the germinating seed. 

The toxicity of the degradation products may exceed the toxicity of the parent compounds. Heavy metals are converted to less soluble forms they are not removed from the subsurface. Heterogeneities in the subsurface may cause the uneven distribution of nutrients during direct-injection applications. Injection may be slower in formations with low hydraulic conductivities. Smaller reactive zones may also form in areas with low hydraulic conductivities. 

The physics of thermal conduction and storage are, in fact, directly analogous to those of groundwater flow. Thermal conductivity (kT) and hydraulic conductivity (k) are analogous, as are heat capacity and storage coefficient and temperature (7) and hydraulic head (h). Indeed, heat flow (H) is estimated by an analogous equation to Darcy s Law ... 

Figure 20.2 The apparent hydraulic conductivity (Kapp) in fibrosarcomas at different perfusion pressures. The curve labeled with 1-D was obtained during one-dimensional perfusion of tumor slices. The curve labeled with 3-D was obtained during direct infusion into a tumor chunk via a 23G needle. The perfusion pressure varied between 20 cmH20 and 163 cmH20. The threshold pressures in 1-D and 3-D experiments are indicated by arrow-head and arrow, respectively. The symbols and error bars represent mean and SD, respectively. The number of tumors for each data point was six in 1-D experiments and three or four in 3-D experiments. Reprinted with permission (Zhang et al., 2000).

The physical factors include mechanical stresses and temperature. As discussed above, IFP is uniformly elevated in solid tumors. It is likely that solid stresses are also increased due to rapid proliferation of tumor cells (Griffon-Etienne et al., 1999 Helmlinger et al., 1997 Yuan, 1997). The increase in IFP reduces convective transport, which is critical for delivery of macromolecules. The temperature effects on the interstitial transport of therapeutic agents are mediated by the viscosity of interstitial fluid, which directly affects the diffusion coefficient of solutes and the hydraulic conductivity of tumor tissues. The temperature in tumor tissues is stable and close to the body temperature under normal conditions, but it can be manipulated through either hypo- or hyper-thermia treatments, which are routine procedures in the clinic for cancer treatment. 

Hydraulic conductivity decreases in less permeable soils resulting in flow that is horizontal in direction this is called interflow and may represent a substantial amount of the total runoff. The reservoir of groundwater is balanced by newly infiltrated waters and the baseflow, which discharges into a stream. 

The time required for sampling depends directly on the actual unsaturated hydraulic conductivity (k) of a soil. Soil pore water will be extracted when k > 10-3 m day-1 and when there is a good hydraulic contact between the soil and the sampler. 

Table 3-1 presents approximate values of hydraulic conductivity that can be expected for different types of porous material. These values are assumed to be the same no matter in which direction the flow is occurring. In reality, the hydraulic conductivity of aquifer materials may not be isotropic (the same in all directions) anisotropic media have hydraulic conductivities that vary with direction (Fig. 3-7). Anisotropy is often a result of the way in which nonspherical particles are deposited, with their long axes oriented in a horizontal direction. Anisotropy can occur in small samples, but is especially common in sand and gravel aquifers containing horizontal clay lenses that... 

FIGURE 3-7 Anisotropy in a porous material. Hydraulic conductivity is higher in the horizontal direction than in the vertical direction because the long axes of the nonspherical particles become oriented in a horizontal direction during deposition. 

Two monitoring wells are located 150 m apart in an unconfined sandy aquifer. The second well is directly downgradient of the first well. The hydraulic head in the first well is 20 m and in the second well is 19 m the hydraulic conductivity is estimated using a pump test as 10 3 cm/sec. What is the specific discharge in the aquifer Given that the porosity is 0.2, what is the rate at which nonsorbing chemicals dissolved in the groundwater will move between the wells ... 

Note that the slope of the water table in the radial direction, given by the gradient ds/dr, is proportional to the rate at which the well is pumped the slope is inversely proportional to hydraulic conductivity, distance from the well, and aquifer thickness. 

The sensitivity of the hydraulic conductivity and other transport properties of discontinua (fractured media) to normal stress is typically substantially greater than that of continua (unfractured media). The stress-sensitivity has been demonstrated in numerous studies of fracture flow (e.g.. Gale, 1982). Natural fractures are a suspected cause of anisotropic water-flooding with a maximum rate of flood front advance approximately in the direction of the maximum horizontal stress (Heffer and Dowokpor, 1990). Natural fractures were recognised as significantly contributing to Clair well productivity (Coney et al., 1993). These fractures are aligned with the present day direction of the maximum horizontal stress in at least one of the wells in the Clair Field. 

As a final note to the flow equation, it should be evident that porous media properties can vary with location. In this case, the medium is considered heterogenous with respect to the property of interest (as opposed to homogenous media where the porous media property of interest does not vary with location). Likewise, the medium is characterized as either anisotropic or isotropic depending on whether the property is a function of direction or independent of direction, respectively. For example, if the vertical hydraulic conductivity is less than the horizontal conductivity (as is typically the case in aquifers because of sedimentation processes), the medium is considered to be anisotropic. Simplification of the flow equations will depend on the heterogeneity and the anisotropic nature of the porous media. 

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