Boundary conditions aquifers

Modeling of the transport of the long-lived nuclides, especially U, require knowledge of the input at the water table as a boundary condition for aquifer profiles. There are few studies of the characteristics of radionuclides in vadose zone waters or at the water table. Significant inputs are likely to occur to the aquifer due to elevated rates of weathering in soils, and this is likely to be dependent upon climatic parameters and has varied with time. Soils may also be a source of colloids and so provide an important control on colloidal transport near recharge regions. 

Figure 2 was constructed by contouring of values calculated from the flow net of figure 1. Much more complex diagrams are possible provided sufficient information concerning the aquifer and fluid-flow conditions can be obtained. For simple boundary conditions and homogeneous aquifers, a direct analytical solution for isochronal surfaces is available [2]. 

Wilson and Liu showed that both location and travel time probabilities can be calculated directly, using a backward-in-time version of traditional continuum advection-dispersion modeling. In addition, they claimed that by choosing the boundary conditions properly, the method can be readily generalized to include linear adsorption with kinetic effects and 1st order decay. An extension of their study for a 2D heterogeneous aquifer was reported in Liu and Wilson [39]. The results for travel time probability are in very close agreement with the simulation results from traditional forward-in-time methods. 

At the aquifer scale, the most important contribution of age tracers is probably reduction in the nonuniqueness of numerical models. Lack of uniqueness stems, among other things, from inadequate knowledge of the distribution of hydraulic properties within groundwater systems and from poor constraints on boundary conditions (Konikow and Bredehoeft, 1992 Maloszewski and Zuber, 1993). Commonly, groundwater flow... 

There are two schools of thought about the time of the initial As mobilization either (i) it is recent and has been induced by man s activities [there are proponents of this who support both the pyrite oxidation hypothesis and the iron oxide reduction hypothesis (Acharyya et al., 2000)], or (ii) it occurred much earlier and is therefore dominantly a natural process. While we believe that an early release date, (ii) above, is the more likely, this is not to imply that man s recent activities have not had, or will not have, any impact on the extent of the groundwater arsenic problem. For example, recent changes in land use such as irrigation will not only alter the groundwater flow patterns but could also affect the boundary conditions for oxygen diffusion into the aquifer and so could also affect its redox status (Bhattacharya et al., 1997). 

Figure 1. Initial and boundary conditions for the model problem. Undersaturated flow enters from the left, causing the reaction front to migrate gradually downstream. Shaded portion of the aquifer contains 5% reactive cement, resulting in a porosity of 5% and a permeability of 1 millidarcy. Upstream of the reaction front the porosity is 10% and the permeability is 10 millidarcies.

This quite arbitrary method of two-dimensional transport ignores the components of vertical flow and thus underestimates the transversal dispersion thereby induced. On the other hand we tested a simple non-reacting case with the same hydraulic conditions against an analytical solution and found that the longitudinal dispersion is not influenced by numerical dispersion, whereas the numerical solution overestimates the transversal dispersion by approximately 10 %. The influence of the boundary conditions for top and bottom of the aquifer (no gradient, no flux) is more important in terms of an increased transversal dispersion for these cells. All these effects are negligible compared to the influences of inhomogeneities of hydraulic conductivities onto the modelled transversal dispersion. 

There are three reasons the complexity of boundary conditions and the aquifer medium, which will take water inflow errors. selecting the applicable formulas the Dupuit equation is the steady flow of groundwater, but using the analytical method to predict water inflow in mines, the drawdown range from tens of meters to several hundred meters, is not a slowly varying flow. errors from selecte impact radius, impact radius in mines is impossible symmetrical. 

Equation (6) states that if both h, and h are found aquifer s velocity can be determined. To find and h, two flow equations (3) and (4) need to be invoked. For given boundary and initial conditions, h can be found from the transient flow equation (3). Similarly, for given boundary conditions, can be solved from the steady flow equation (4) (or the Laplace equation). Thus, the field of aquifer s velocity can be determined from (6). Moreover, the field of aquifer displacement u, can be further found using the following relation ... 

The concentration profile c(x) of the pollutant in the liner is divided into different ranges (Fig. 7.1) Cq is the concentration of the substance in the leachate, which remains constant, C x) is the concentration profile in the geomembrane and C2(x) in the mineral liner, the concentration beneath the liner is assumed always to be zero. One may imagine a highly permeable aquifer under the liner where a very rapid dilution takes place. These steady-state diffusion conditions are surely an extreme assumption which might, in practice, be the case only at very unfavourable locations. Thus these boundary conditions also represent a worst case scenario. 

In this section, we discuss numerical solutions to Laplace s equation for the pressure P(x,y), with and without wells and fractures, using both aquifer boundary conditions specifying pressure, and solid wall conditions assuming zero normal flow. We consider, for purposes of exposition, the Cartesian form... 

Certain factors must, however, be considered in choosing the appropriate analytical solution unconsolidated vs. consolidated conditions, fully vs. partially penetrating wells, variable discharge rules, delayed yield, and aquifer boundaries. Most methods are best suited for unconsolidated aquifers with well-defined overlying and underlying boundaries, whereas with consolidated aquifers, the effective aquifer thickness is uncertain. A pumping well that fully penetrates a confined aquifer (i.e.,... 

Aquifers may be classified as unconfined or confined. Although unconfined aquifers usually have sediments or soils between them and the surface, the geologic materials are sufficiently permeable so that unconfined aquifers are rapidly influenced by atmospheric conditions, including pressure and precipitation events (Figure 3.5). The upper boundary of an unconfined aquifer is the water table. A confined aquifer is located between two aquitards ((Freeze and Cherry, 1979), 48). At least one aquitard occurs between a confined aquifer and the surface. That is, a confined aquifer is substantially insulated from conditions on the Earth s surface. 

A two-dimensional example problem is also developed to demonstrate the advective control model. The example problem is solved for both confined and unconfined conditions and the solutions are compared. In this example problem, the aquifer is homogeneous and isotropic, with no flow conditions imposed at the top and bottom boundaries and constant head conditions along the left and right boundaries. The head on the constant head boundaries slopes downward toward the bottom of the domain. The domain is 3100 m by 3100 m and is discretized into 49 rows and 58 columns. A river runs through the domain as shown in Figure 6. 

Eq. [3-10b] assumes that the aquifer is horizontally isotropic (i.e., K is the same in both x and y directions). Solutions to the preceding differential equations under appropriate boundary and initial conditions describe the time-varying hydraulic head, i, in two dimensions. Several solutions are given by Carslaw and Jaeger (1959). More complicated boundary and initial conditions are treated by Hantush (1964), Reed (1980), and Wang and Anderson (1982). Note that in Eq. [3-1 Ob] the quantity (Kb) could be replaced by T, the aquifer transmissivity. 

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