Ground Water Models Scientific and Regulatory Applications (1990) / Chapter Skim
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2 MODELING OF PROCESSES
2 MODELING OF PROCESSES
Pages 28-78
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From page 28... ...
Subsurface movement- whether of water, contaminants, or heat is affected by various processes. These processes can be related to three different modeling problems: ground water flow, multiphase flow (e.g., soil, water, and air; water and gasoline; or water and a dense nonaqueous-phase liquid (MAPLE, and the flow of contaminants dissolved in ground water.
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From page 29... ...
In some simple situations, the direction of ground water flow is perpendicular to these equipotential lines, as shown in Figure 2.~. The actual distribution of hydraulic head observed for an area depends mainly on two factors, how much and where water is added and removed, and the hydraulic conductivity distribution that exists in the subsurface.
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From page 31... ...
Pilirf~r! - WAter Ts~hl I ~11 | I K = lo ~I j 11 ~71 S 1 ~: o RELATIVE BASIN LENGTH S FIGURE 2.3 Dependence of the pattern of ground water flow on the hydraulic conductivity distribution.
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From page 32... ...
Readers wishing a more detailed explanation of this parameter and aspects of ground water flow should see Freeze and Cherry (1979~. M~tiphase Flow Multiphase flow occurs when fluids other than water are moving ~ the subsurface.
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From page 33... ...
As the pressure head becomes smaller (more negative) , the soil becomes drier and the hydraulic conductivity decreases.
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From page 34... ...
The progress of a wetting front moving into a dry soil can be described in terms of either potentials or volumetric water content, 0.14 t _ ~ MOISTURE CONTENT FIGURE 2.5 The distribution of water in the unsaturated zone can be described in terms of pressure head and moisture content. Results presented for a combined saturated and unsaturated flow system illustrate how pressure head in particular is continuous across the water table (from Freeze, 1971b)
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From page 35... ...
Thus, if the volume of spilled liquid ~ small and the unsaturated zone is relatively thick, no free liquid may reach the water table. Of course, free liquid may reach the water table over extended periods of time, and dissolved organic liquid may be conducted by water flow.
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From page 36... ...
1 t..~ :! ~ CHC Phase Unsaturated Zone Capillary Fringe K2 K1 CHC Dissolved in Water Saturated _ _ _ _ _ _ _ _ ' Zone l _ I_ ~////////////////////////////////////////i/////~, FIGURE 2.6 The flow of a nonaqueous-phase liquid that is (a)
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From page 37... ...
Expressing the distribution of fluids in terms of relative saturation is analogous to expressing the moisture content in terms of unsaturated flow. Dissolved Contanunant Passport One of the reasons why problems involving dissolved contaminants are so difficult to model is the number and complexity of controlling processes.
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From page 38... ...
Chemical mass transfer 4. Radioactive decay 5.
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From page 39... ...
The close relationship between advective transport and ground water flow means that the factors considered for flow, the location and quantity of the inflow and outflow to the flow system, the hydraulic conductivity distribution, and the presence of pumping/injection wells also play a major role in determining where contarn~nants migrate. Indeed, the process of advection is often so dominant that the mean velocity predicted by flow models can be used to estimate patterns of contaminant transport with surprising accuracy.
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From page 40... ...
There are situations, mainly in fractured rock settings and low-permeability units, where diffusive mass transport is of primary importance and needs to be considered. Dispersion Dispersion refers generally to phenomena that cause fluid mixing.
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From page 41... ...
this variability may be caused by velocity variations within a pore or by subtle changes in the flow network that cause the mass to spread out or finger into adjacent pores of the pore network. At the macroscopic scale, the variability can be due to heterogeneities in the hydraulic conductivity distribution (Smith and Schwartz, 1980)
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From page 42... ...
b Macroscale Dispersion Mixing in a Pore Network (from Cherry et al., 1975) 5 m .~` 5 m Mixing Caused by Variability in Hydraulic Conductivity (from Schwartz, 1984)
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From page 43... ...
Because the radioactive isotopes of concern in the environment undergo other chemical reactions in addition to radioactive decay, many years of research will be required before their behavior can be modeled with confidence, even though radioactive decay is well understood. When the half-life for radioactive decay is of the same magnitude or smaller than the residence time of the contaminant in the subsurface, decay significantly affects contaminant migration.
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From page 45... ...
Another major class of contaminants, noncharged organic molecules, sorb mainly onto solid organic material. The force that drives the exchange in this case is the hydrophobic (water hating)
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From page 46... ...
gives exa~nples of precipitation of dissolved contaminants in ground water caused by reactions with other dissolved species, hydrolysis, and reduction or oxidation. Examples of contaminants that could be reduced to lower concentrations in ground water through the formation of precipitates include arsenic (by reaction with iron, aluminum, or calcium)
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From page 47... ...
For this reason, sophisticated mass transport models often need to include reactions related to the CO2water system, one of the dominant controls of the pH of ground water. Comp le x at ion The process of complexation is the combination of simple cations and anions into more complex aqueous species.
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From page 48... ...
This relatively straightforward treatment enables the concentration of the individual complexes in water to be easily calculated. In terms of mass transport, complexation reactions are important mainly because of the role they play in increasing the mobility of metals.
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From page 49... ...
Kinetic rate laws for hydrolysis/substitution reactions can be complex. However, in some cases, they can be approximated as first-order reactions or, in other words, reactions like radioactive decay that can be described simply in terms of a half-life.
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From page 50... ...
Much research is needed to identify which redox reactions can be modeled as reversible reactions and which are irreversible and should not be included in an equilibrium model. Biological Transformations When organic and some inorganic compounds are present as contaminants, biological transformation can be an important process, because the original contaminant is destroyed.
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From page 51... ...
To generate energy the electron donor must donate its electrons to an electron acceptor, making available the energy for cell synthesis. Following is an example of a biologically mediated redox reaction in which an organic compound typified as CH2O is oxidized to simpler compounds: (1/4)
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From page 52... ...
As an example of the steps in modeling, consider a ground water flow problem (Figure 2.~. Information that needs to be provided to describe a real system (Figure 2.12a)
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From page 53... ...
Hydraulic Conductivity 3. Boundary Conditions a Model Control Parameters ~Or | Governing | I Equation I Output: Predicted Hydraulic Head K = ~ it_ FIGURE 2.11 The components of a model: input data, a governing equation solved in the code, and the predicted distribution, which for this example is hydraulic head.
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From page 54... ...
54 E ~n o 7:, a, 3 o (n m cl5 3 ~ O a, m ~o ~ ~ ~q C~ C _ .o ~c C E _ ,= W C C ~ ~ W ~ il., o' D .m E ~ :, _ I,o ,C Cd w ~ ~4,, _ n W cC {D ~ C W ~Q C W ~a ~ o' m ~5 3 O cn m 1 0 0 ° O 0 ~_ - CM (I S w ~ I)
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From page 55... ...
Next, some of the different methods available to solve flow and transport equations are discussed. Governing Equations The development of the flow and contaminant transport equations is relatively straightforward because all of the flow problems of interest here ground water flow, multicomponent flow, and dissolved contaminant transport are developed from the same fundamental principle, namely, the conservation of fluid or dissolved mass.
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From page 56... ...
. For ground water flow, the step involves replacing specific discharge by using the well-known Darcy equation.
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From page 57... ...
However, for multicomponent flow problems, one continuity equation is required for each flowing fluid. Tables 2.4 and 2.5 summarize the development of basic equations for unsaturated ground water flow and two-component liquid flow (organic liquid and water)
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From page 58... ...
Right-hand side has been expanded and small terms removed, with (A = em'. Substitute the Darcy equation for unsaturated flow in which hydraulic conductivity K is a function of pressure head ¢.
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From page 59... ...
59 to s Q + ~ ~o - ~ -- - 51 -~ Cal o .~ Ct :: CQ o 3 3 ~ lo: o Em .= C C ~ O ~ O .
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From page 60... ...
60 'a 11 i oc 3 Q I ant 1 + i1 ~ 3 3 Q l ~3 =1 X it so VO in, ~ O ·Cd ~ O O ~ Cal a' 3 o V) o 4- ~ Cd ~ o cram at, o o o Cd ;> ~ Cd ~ ,3 .b ~ U)
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From page 61... ...
are replaced by more detailed expressions describing the processes. The mass transport of a dissolved species is controlled by three processes: advection, diffusion, and dispersion.
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From page 62... ...
All that is required to come up with one form of a simplified contaminant transport equation ~ to substitute {2.161 into {2.151 to Rive s2c Do [$2 Vat [X ~_ (2.17)
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From page 63... ...
into (2.15) provides the governing mass transport equation, or 82C [C Ka [C [C D2 -- v ~ -- Paq -- = Rearranging terms yields Do [s C _ in [sC = [C t1 + Palm (2.20)
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From page 64... ...
To illustrate these ideas, consider a problem involving the application of a steady-state ground water flow mode} to the field (Figure 2.12~. At the particular site shown in Figure 2.12, glacial till overlies sandstone and shale bedrock.
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From page 65... ...
are required to solve each mass transport equation applied to the domain. The water table boundary is an example of a specified-value
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From page 66... ...
With this information, it would be possible to simulate the changing conditions of hydraulic head not only as a function of space but also as a function of time. The discussion of the three preparatory steps to Cudgeling is related particularly to a simple problem of ground water flow.
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From page 67... ...
For the example problem, values of hyciraulic head are calculated at the nodes, located at the center of ceils, with one algebraic equation written for each node. Hydraulic conductivity values are supplied for each rectangular cell.
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From page 68... ...
In one approach the entire system of equations is solved simultaneously with direct methods, providing a solution that is exact, except for machine round-off error. In the second approach, iterative methods obtain a solution by a process of successive approximation, which involves making an initial guess at the matrix solution and then improving this guess by some iterative process until an error criterion is satisfied.
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From page 69... ...
69 o EM cat cat cd a' c°~ cat ._ cd 3 o .= o cat o o cat .
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From page 70... ...
70 s is in He o au o 4 o .
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From page 71... ...
71 Go - ~ oo To 'x ~ - ~ ~ -= .= - ~ ~ c == ^ 3 E hi, ~ ~ 0 ~ ~ O ~ ~ ~ ~ m ~ ~ of; ._ ._ ct v, so .
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From page 72... ...
compared the efficiency of 17 different iterative methods for the solution of the nonlinear three-dimensional ground water flow equation. He concluded that, in general, the conjugate gradient methods did the best.
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From page 73... ...
1979. Using models to simulate the movement of contaminants through ground water flow systems.
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From page 74... ...
Pp. 3-27 in Finite Elements in Water Resources, Proceedings of the 6th International Conference, Lisbon, Portugal.
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From page 75... ...
1987. A comparison of iterative methods as applied to the solution of the nonlinear three-dimensional groundwater flow equation.
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From page 76... ...
1986. Water flow and solute transport processes in the unsaturated zone.
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From page 77... ...
1986. A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process.
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From page 78... ...
1980. FEMWATER: A Finite-Element Model of Water Flow Through Saturated-Unsaturated Porous Media.
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