Hydraulic conductivity coefficient

Atterberg-limit tests determine the water content influence in defining liquid, plastic, semisolid and solid states of fine-grained soils. Permeability tests may be carried out in the laboratory or in the field. Such tests are used to determine the hydraulic conductivity coefficient k. ... 

LP is the hydraulic conductivity coefficient and can have units of m s-1 Pa-1. It describes the mechanical filtration capacity of a membrane or other barrier namely, when An is zero, LP relates the total volume flux density, Jv, to the hydrostatic pressure difference, AP. When AP is zero, Equation 3.37 indicates that a difference in osmotic pressure leads to a diffusional flow characterized by the coefficient Lo Membranes also generally exhibit a property called ultrafiltration, whereby they offer different resistances to the passage of the solute and water.14 For instance, in the absence of an osmotic pressure difference (An = 0), Equation 3.37 indicates a diffusional flux density equal to LopkP. Based on Equation 3.35, vs is then... 

LP (hydraulic conductivity coefficient) K (water permeability coefficient) Minor both indicate water permeability... 

K(0) = Water content-dependent hydraulic conductivity coefficient. 

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 26.9 illustrates Darcy s law, the basic equation used to describe the flow of fluids through porous materials. In Darcy s law, the coefficient k, hydraulic conductivity, is often called the coefficient of permeability by civil engineers. 

Transmissivity is simply the coefficient of permeability, or the hydraulic conductivity (k), within the plane of the material multiplied by the thickness (T) of the material. Because the compressibility of some polymeric materials is very high, the thickness of the material needs to be taken into account. Darcy s law, expressed by the equation Q = kiA, is used to calculate the rate of flow, with transmissivity equal to kT and i equal to the hydraulic gradient (see Figure 26.22) ... 

Model selection, application and validation are issues of major concern in mathematical soil and groundwater quality modeling. For the model selection, issues of importance are the features (physics, chemistry) of the model its temporal (steady state, dynamic) and spatial (e.g., compartmental approach resolution) the model input data requirements the mathematical techniques employed (finite difference, analytic) monitoring data availability and cost (professional time, computer time). For the model application, issues of importance are the availability of realistic input data (e.g., field hydraulic conductivity, adsorption coefficient) and the existence of monitoring data to verify model predictions. Some of these issues are briefly discussed below. 

It is often easy to measure the flux density, e.g., using a flowmeter, and then determine the hydraulic conductivity or diffusion coefficient by dividing the flux by the driving force. One of the most difficult problems is determining how to represent the driving force. The symbol V is called an operator, which signifies that some mathematical operation is to be performed upon whatever function follows. V means to take the gradient with respect to distance. For Darcy s law under saturated... 

Of course, more complicated situations and conditions will require more sophisticated mathematical treatment, especially for the driving force, but the basic flux relationships are similar for any liquid and gas migration through the subsurface. If the hydraulic conductivities and diffusion coefficients are known for the materials and each migrating fluid of interest, then predictive computer models can often handle the difficult calculations associated with multiple fluids, multiple pressures, and multiple types of materials. 

NAPL will migrate from the liquid phase into the vapor phase until the vapor pressure is reached for that liquid. NAPL will move from the liquid phase into the water phase until the solubility is reached. Also, NAPL will move from the gas phase into any water that is not saturated with respect to that NAPL. Because hydraulic conductivities can be so low under highly unsaturated conditions, the gas phase may move much more rapidly than either of the liquid phases, and NAPLs can be transported to wetter zones where the NAPL can then move from the gas phase to a previously uncontaminated water phase. To understand and model these multiphase systems, the characteristic behavior and the diffusion coefficients for each phase must be known for each sediment or type of porous media, leading to an incredible amount of information, much of which is at present lacking. 

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 ... 

In the literature the hydraulic conductivity is commonly designed by K here Kq is used to distinguish it from the various partition coefficients, Kd, Kom, etc. 

Figure 25.5 Permeability as a function of (mean) particle radius r for different aquifer porosity < >, which, in turn, depends on the sorting coefficient So = (r75 / r25)1,2, where r75 and r2S characterize the particle radii larger than, respectively, 75% and 25% of the radii of all the aquifer particles. The hydraulic conductivity Kq (right scale) refers to water at 20°C. Redrawn from Lerman (1979).

The conflicting results discussed above suggest that further studies are required for understanding mechanisms of convection. More specifically, it is important to investigate hydraulic conductivity, interstitial pressure, and retardation coefficient in different tumor tissues, and how these factors are coupled with infusion-induced tissue deformation. 

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. 

Parameswaran, S., Brown, L.V., Ibbott, G.S. and Lai-Fook, S.J. (1999) Hydraulic conductivity, albumin reflection and diffusion coefficients of pig mediastinal pleura. Microvasc. Res., 58, 114-127. 

The effects of aquifer anisotropy and heterogeneity on NAPL pool dissolution and associated average mass transfer coefficient have been examined by Vogler and Chrysikopoulos [44]. A two-dimensional numerical model was developed to determine the effect of aquifer anisotropy on the average mass transfer coefficient of a 1,1,2-trichloroethane (1,1,2-TCA) DNAPL pool formed on bedrock in a statistically anisotropic confined aquifer. Statistical anisotropy in the aquifer was introduced by representing the spatially variable hydraulic conductivity as a log-normally distributed random field described by an anisotropic exponential covariance function. 

Numerically evaluated average mass transfer coefficients, k, based on the average of 200 different realizations of the log-normal hydraulic conductivity, as a function of C,JC,X for several variances of Y=lnK (a =0.1,0.2,0.3,0.4, and 0.5) for a hydraulic gradient of dhldx=0.01 and mean log-transformed hydraulic conductivity of 7=0.8 are shown in Fig. 7a. The results indicate that for increasing C,JC,X there is a significant increase in k. Low values of the anisotropy... 

Fig. 7a, b Average mass transfer coefficient as a function of a aquifer anisotropy ratio for several variances of the log-transformed hydraulic conductivity distribution b variance of the log-transformed hydraulic conductivity distribution where open circles represent numerically generated data and solid lines represent linear fits. All model parameter values are identical with those used in Fig. 6... 

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