Velocity seepage

The minus sign results from the definition of Ap, which is equal to p2 - Pi, a negative quantity. The term q is known as the seepage velocity and is equivalent to the velocity of approach v , which is also used in the definition of the Reynolds number. 

If the liquid uniformly passes through all the pores in the soil, then the effective and total porosities are equal. However, if the flow takes place in only a small percentage of the total pore space, for example, through fractures or macropores, the effective porosity will be much lower than the total porosity. Judging the effective porosity is one of the problems in estimating seepage velocities. 

So we deduce that only one DMB molecule out of 11 will be in the moving ground-water at any instant (Fig. 9.6). This result has implications for the fate of the DMB in that subsurface environment. If DMB sorptive exchange between the aquifer solids and the water is fast relative to the groundwater flow and if sorption is reversible, we can conclude that the whole population of DMB molecules moves at one-eleventh the rate of the water. The phenomenon of diminished chemical transport speed relative to the water seepage velocity is referred to as retardation. It is commonly discussed using the retardation factor, Rfi, which is simply equal to the reciprocal of the fraction of molecules capable of moving with the flow at any instant, ff (see Chapter 25). 

The model under consideration incorporates seven independent fields, namely the solid displacement us = x — Xs, the seepage velocity wj =... 

Both last terms on the right side of (11) denotes the friction influence on each of the fluids in relation to their seepage velocities wp = — x . The... 

Typical aquifer porosities are in the range of 0.2 to 0.4. The rate at which nonsorbing chemicals move in the groundwater is equal to the seepage velocity, defined as... 

To estimate the travel time for a dissolved chemical across square B, the groundwater seepage velocity in square B must first be estimated using Eq. [3-5] ... 

In an aquifer, the total Fickian transport coefficient of a chemical is the sum of the dispersion coefficient and the effective molecular diffusion coefficient. For use in the groundwater regime, the molecular diffusion coefficient of a chemical in free water must be corrected to account for tortuosity and porosity. Commonly, the free-water molecular diffusion coefficient is divided by an estimate of tortuosity (sometimes taken as the square root of two) and multiplied by porosity to estimate an effective molecular diffusion coefficient in groundwater. Millington (1959) and Millington and Quirk (1961) provide a review of several approaches to the estimation of effective molecular diffusion coefficients in porous media. Note that mixing by molecular diffusion of chemicals dissolved in pore waters always occurs, even if mechanical dispersion becomes zero as a consequence of no seepage velocity. 

If the Fickian transport coefficient is known, it is possible to predict the distribution of the tracer at any time and location after it is introduced into the column. At the time of injection of the tracer (t = 0), the concentration is high over a short length of column. At a later time tL, the center of the mass of tracer has moved a distance equivalent to the seepage velocity multiplied by q, and the mass has a broader Gaussian, or normal, distribution see Eq. [2-6]. The solution to Eq. [1-5] for this one-dimensional situation gives the concentration of the tracer as a function of time and distance,... 

Equation [3-17] does not hold at very low seepage velocities because mechanical dispersion no longer dominates Fickian mass transport. When the mechanical dispersion coefficient becomes less than the effective molecular diffusion coefficient, the longer travel times associated with lower velocities do not result in further decreases in Fickian mass transport. 

A column experiment is set up in the laboratory. Sand with a mean grain size of approximately 0.5 mm is packed into a cylindrical column, 1.5 m in length and 10 cm in diameter water flows through the column with a seepage velocity of 1 m/hr. Porosity is 0.3. Five milligrams of salt are injected into the column (a pulse injection). 

If groundwater seepage velocity is 600 ft/year, how fast will the plume migrate ... 

First, an estimate of the travel time is needed. Estimate the seepage velocity using Eq. [3-5], but use the water-filled porosity 6 instead of porosity, n ... 

Groundwater contains 10 ppm of ethyl acetate, CH3COOC2H5, under a landfill. If the seepage velocity is 1 m/day, what is the maximum distance downgradient at which a concentration in excess of 0.2 ppm could be expected Answer for a water pH of (a) 4 and (b) 10. 

Let us return to two waters separated by a partition, with their composition different on the accoimt colorant i present only in one of them. When the partition is removed during flow, imaginary boundary between the waters (the place of the partition) is also moving at a rate equal to the seepage velocity of water flow... 

It turned out that the mechanical dispersion may be formally described by the same Pick s laws if the diffusion coefficient is replaced with mechanical dispersion coefficient This is a proportionality coefficient between value of a deflection of component i migration rate from the average seepage velocity on the one hand, and the component concentration gradient between mixed waters, on the other. In a case of unidimensional and bidimensional fluxes this correlation by analogy with the first Pick s law has the following format... 

Experiments showed that mechanical dispersion coefficients are directly proportionate with filtration (flow) average seepage velocity, i.e.,... 

Hydrodynamic dispersion is a summary effect of two mixing processes whose relative contribution depends on the seepage velocity and groimd... 

As a consequence of mixing different composition waters the rate of migration components in these waters may substantially differ from the seepage velocity of flow per se, which shows up in their dispersion. Such migration of individual components in ground water composition accompanied by... 

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