Dispersion water flow velocity

For soil systems contaminated with Na+, kinematic viscosity is not significantly affected, thus the components controlling water flow velocity are the hydraulic gradient (A< >/AX) and soil permeability (k). The latter component (k) is influenced by clay dispersion, migration, and clay swelling. These processes may cause considerable alteration to such soil matrix characteristics as porosity, pore-size distribution, tortuosity, and void shape. 

In a final example, we consider a similar problem in two dimensions. Water containing 1 mg kg-1 benzene leaks into an aquifer for a period of two years, at a rate of 300 m3 yr-1. Once in the aquifer, which is 1 m thick, the benzene migrates with the ambient flow, sorbs, and biodegrades. We model flow and reaction over 10 years, within a 600 m x 60 m area, assuming a dispersivity ay along the flow of 30 cm, and a-y across flow of 10 cm. All other parameters, including the flow velocity, remain the same as in the previous calculation. 

Datametrics Model lOOVT Air Flow Meter. Measurements were taken at various locations above the soil or water surface at a height of 0.8 cm, where the laminar air flow velocity was greatest. Depending on the probe location relative to the air dispersion tube, the measured wind speed varied from 0.5 to 1.5 m/s, with an average of 1 m/s. At greater heights above the surface, the air flow rate was much lower and the air flow patterns were unknown. 

The spreading results from a combination of two processes, (1) Fickian horizontal diffusion with scale-independent diffusivity Eb, and (2) dispersion by velocity shear in the direction of the mean flow. The process of dispersion is discussed in Section 22.4. It is related to the flow velocity difference (called velocity shear ) between adjacent streamlines. Since water parcels traveling on different streamlines (e.g., at different depth) have different velocities, a tracer cloud is elongated along the direction of the mean flow (see figure below). 

Once the mathematical description of dispersion has been clarified, we are left with the task of quantifying the dispersion coefficient, Eiis. Obviously, Edh depends on the characteristics of the flow field, particularly on the velocity shear, dvx/dy and dvx /dz. As it turns out, the shear is directly related to the mean flow velocity vx. In addition, the probability that the water parcels change between different streamlines must also influence dispersion. This probability must be related to the turbulent diffusivity perpendicular to the flow, that is, to vertical and lateral diffusion. At this point it is essential to know whether the lateral and vertical extension of the system is finite or whether the flow is virtually unlimited. For the former (a situation typical for river flow), the dispersion coefficient is proportional to (vx )2 ... 

Figure 24.5 (a) Streamlines at a bend are asymmetrically distributed across the river, (b) Contour lines of equal velocity in a cross section indicate that flow velocities strongly vary laterally as well as from the water surface to the bottom. Such variations are responsible for longitudinal dispersion. 

You are responsible for the safe operation of a drinking-water supply system that gets its raw water from a well located close to a river. From tracer experiments you know that the effective mean flow velocity is u =3 m d l and that the distance along the streamline from the point of infiltration to the well is x = 18 m. The dispersivity of the aquifer for this distance of flow is aL = 5 m. In order to be prepared for a possible pollution event in the river you are interested in the following questions ... 

Because of greatly contrasting low tritium levels before thermonuclear tests and because of the distinct peak tritium levels that occurred in the atmosphere during 1962-1965, tritium has been used as an environmental tracer in the studies on surface water budgets, groundwater age and flow velocities, groundwater recharge, and dispersion and diffusion in aquifers. A 1989 study detailed the distribution of tritium... 

FIGURE 1-7 Fickian transport by dispersion as water flows through a porous medium such as a soil. Seemingly random variations in the velocity of different parcels of water are caused by the tortuous and variable routes water must follow. This situation contrasts with that of Fig. 1-6, in which turbulence is responsible for the random variability of fluid paths. In this case as well as in the previous one, Fickian mass transport is driven by the concentration gradient and can be described by Fick s first law. The mass transport effect arising from dispersion can be further visualized in Fig. 3-17. There, a mass initially present in a narrow slice in a column of porous media is transported by mechanical dispersion in such a way as to form a wider but less concentrated slice. At the same time, the center of mass also is transported longitudinally in the direction of water flow. 

Equation (3.4.34) can be altered by making assumptions as to the influence of molecular diffusion and rate of water flow. For example, if the molecular diffusion is negligible and the dispersion carries with the pore-water velocity,... 

A 500 ppm dispersion of silica (Cab-O-Sil, EH-5, Calbot Corp.), 8 liters in volume, was prepared by dilution of a 2 g/1 dispersion idiich had been sonicated for 40 min. in a Bransonic ultrasonic bath. The turbidity of the final solution was 24 NTU. With the permeate valve closed, the cross-flow velocity and formation pressure were set. Timing for a total of 30 min. was begun idien the permeate was opened, and readings of permeate flow rate and turbidity were taken at periodic intervals. After formation, and without allowing system shut-down, the silica solution was flushed out with DI water and replaced with the Pazomus B oil emulsion. (Emulsion concentrations are % vol/vol, e.g., 3% represents 30 cc/1 of the commercial mixture.)... 

The convection-dispersion equation (CDE) is the most widely used of the velocity distribution models. For steady state, one-dimensional water flow, the CDE for a nonreactive solute can be written as (Fried Combarnous, 1971),... 

Soil structure, antecedent soil moisture and input flow rate control rapid flow along preferential pathways in well-structured soils. The amount of preferential flow may be significant for high input rates, mainly in the intermediate to high ranges of moisture. We use a three-dimensional lattice-gas model to simulate infiltration in a cracked porous medium as a function of rainfall intensity. We compute flow velocities and water contents during infiltration. The dispersion mechanisms of the rapid front in the crack are analyzed as a function of rainfall intensity. The numerical lattice-gas solutions for flow are compared with the analytical solution of the kinematic wave approach. The process is better described by the kinematic wave approach for high input flow intensities, but fails to adequately predict the front attenuation showed by the lattice-gas solution. 

Solute Diffusion-Dispersion Coefficient. In these studies D was assumed to be constant and not a function of flow velocity. For low flow velocities this assumption seems reasonably valid (23). For the natural rainfall conditons of these studies the flow velocities were generally quite low. In lieu of actual measured D values on the two Maui soils, an estimate of D obtained on a somewhat similar soil on Oahu bv Khan (24) was used in this study. An average value of D = 0.6 cm /hr was measured in the field with a steady water flux of 10 cm/ day. 

In this context, Griffiths reported in 1911 the interactions of an aqueous plug with a chemically inert carrier stream flowing through a narrow, straight tube [53]. He carried out the first experimental work demonstrating the essence of the dispersion process and concluded (without a mathematical treatment) that "a tracer injected into a water stream spreads out in a symmetrical manner about a plane in the cross section that moves with the mean flow velocity" [54], He also pointed out the establishment of a fully developed laminar flow regime. 

When water flows through the porous medium, the deviation of the local scale advection velocities around the mean advection velocity v induces hydrodynamic dispersion. At the pore scale, streamline density increases from the pore wall to the pore center. For real and irregularly shaped soil pores however, this within pore variability will be more pronounced, as streamline densities change between pore bodies and pore necks. The heterogeneous pore size distribution with larger flow velocities in larger pores leads to an important additional variability of velocities (Fig. 6). 

Figure 17. Effect of dispersion on the H- He age in a system dominated by vertical water movement. A input function typical for the north-eastern United States was used and a vertical flow velocity of 1 m yr assumed. The calculation was conducted for the year 1992. Similar one-dimensional models were published by Schlosser et al.

CFCs, and Kr were studied in a sandy, unconfined aquifer on the Delmarva Peninsula in the eastern USA by Ekwurzel et al. (1994). H and H+ He depth-profiles show peak-shaped curves that correspond to the time series of H concentration precipitation, smoothed by dispersion (Fig. 18a). The peak occuring at a depth of about 8m below the water table therefore most likely reflects the H peak in precipitation that occurred in 1963 (Fig. 6). The H- He ages show a linear increase with depth, reaching a maximum of about 32 years. The H- He ages are also supported by CFC-11, CFC-12, and Kr tracer data (Fig. 18b). The latter tracers are used here as dyes and their concentrations are converted into residence times by using the known history of the atmospheric concentrations and their solubility in water. From the vertical H- He age profile at well nest 4 at the Delmarva site, the vertical flow velocity can be... 

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