Ground Water Models Scientific and Regulatory Applications (1990) / Chapter Skim
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3 FLOW PROCESSES
3 FLOW PROCESSES
Pages 79-112
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From page 79... ...
For example, predictions of the economic yield of an aquifer, or of the impacts of new or increased pumping on existing wells, or of ground water recharge below irrigated agriculture, all require an understanding and prediction of ground water head and flow. Second, ground water flow models are a crucial component of all analyses of contaminant transport because of the need to define the ground water velocity field.
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From page 80... ...
This chapter summarizes the committee's sense of the state of the art of ground water flow modeling and of the issues related to the current and future use of flow models in decisionmaking. SATURATED CONTINUUM FLOW As mentioned in the introduction to this chapter, the earliest models of ground water were saturated continuum flow models.
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From page 81... ...
This is especially true for problems of contaminant transport below the water table. For such problems, the role of ground water flow modeling is to provide an estimate of the flow velocities.
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From page 82... ...
The mathematical properties of the governing partial differential equation for fully saturated continuum ground water flow (Equation t2.5~) are well understood.
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From page 83... ...
The nature of the parameters appearing in the various forms of the fully saturated ground water flow equation ~ reasonably well understood. Both the hydraulic conductivity and the specific storage are empirical parameters that arise from the simplifications leading to Darcy's law and a workable statement of continuity (see discussion on ground water flow in Chapter 2~.
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From page 84... ...
In most applications of ground water flow models, parameter values are obtained via calibration using some type of "inverse technique," leavened by well test estimates and geologic knowledge. Parameter values are chosen that yield satisfactory predictions of observed head at selected observation points (usually few in number)
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From page 85... ...
The next few paragraphs summarize the most important issues that must be addressed in applying saturated continuum flow models to practical ground water problems, given the current state of the art. Spatial Dimensionality Many ground water flow problems may be successfully addressed by assuming that flow occurs in only one or two dimensions, i.e., in a single direction or in a plane.
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From page 86... ...
No matter how complex the model, proper application will always depend on a knowledgeable, trained user working with data that have been collected in such a way as to shed light on boundary conditions. Transient Versus Steady State Another valuable assumption in the application of saturated continuum flow models ~ that of steady state, i.e., that conditions remain constant over time.
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From page 87... ...
Velocity Computation More and more problems of saturated continuum flow focus on the prediction of ground water flow velocities. As noted earlier, the accurate prediction of head gradients, on which velocities directly depend, is much more difficult than the accurate prediction of head alone.
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From page 88... ...
Parameter evaluation will remain a challenging task demanding education, experience, skill, and wisdom. FLOW IN THE: UNSATURATED ZONE This report is primarily devoted to a discussion of various issues related to modeling water flow and contaminant transport in the saturated zone.
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From page 89... ...
If a porous medium can be thought of as a random network of capillary tubes of varying sizes, it can be seen that the suction force with which water is held in different pore sequences varies inversely
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From page 90... ...
, has a maximum value, called the saturated hydraulic conductivity (Ke) , in a completely saturated soil and decreases dramatically with decreasing soil water content.
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From page 91... ...
Some of these are listed in Tables 3.1 and 3.2. CONCEPTS OF WATER FLOW IN THE UNSATURATED ZONE As in a saturated soil, the rate and the direction of water flow in an unsaturated soil also depend upon the magnitude of the soil hydraulic conductivity (Kth]
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From page 92... ...
A detailed treatment of unsaturated water flow is beyond the scope of the present discussion, the reader is referred to several textbooks on the topic (e.g., Campbell, 1985; Hanks and Ashcroft, 1980; Hillel, 1980a,b; Koorevaar et al., 1983) for a thorough analysis of is
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From page 93... ...
For infiltration into a "dry" soil, the infiltration rate is initially large because the large hydraulic potential gradients can sustain a large soil water flux. However, as the soil becomes saturated and the wetting front penetrates deeper, the potential gradient driving water flow decreases, and the infiItration rate asymptotically approaches the saturated conductivity (K,)
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From page 94... ...
is hydraulic conductivity at (a; E) is volumetric water content; h is hydraulic potential (and has negative values)
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From page 95... ...
different, although the physical principles that govern flow are the same. The capacity of the soil profile to take in water is initially large enough such that the infiltration rate is equal to the application rate Steak.
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From page 96... ...
The foregoing scenario, simplified for the present discussion, should illustrate that transient water flow in the unsaturated zone, particularly in the top several meters, is episodic as determined by water input events at the ground surface (see Figure 3.5~. Each of these episodes, in turn, has at least three extinct phases where the soil water content and soil water flux vary considerably.
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From page 97... ...
As noted in Chapter 2, by coupling Darcy's law with the conservation of mass principles, the governing differential equation for transient water flow can be derived; this equation is known as the Richards equation. FRACTURE: FLOW The term fracture is a general one referring to the various types of discontinuities that can break a medium into blocks (Torsaeter et al., 1987~.
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From page 98... ...
The important feature of conduit flow, when it is able to develop, is the integration of the drainage network (QuinIan and Ewers, 1985~. In many ways, the network is analogous to a river system with smaller tributaries supplying water to a succession of TABLE 3.4 Major Differences Between Saturated arid Transient Unsaturated Water Flow in Porous Media Parameter Saturated ~ = Os H = h + z (h 2 0)
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From page 99... ...
Many of the fundamental principles developed in the previous sections of this chapter need to be extended to deal with fractured media. The first major question of how one conceptualizes flow in a single fracture can be addressed with the help of the so-called parallel plate mode!
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From page 100... ...
the stress coupling to hydraulic conductivity. In representing the hydraulic conductivity of a fractured medium, it must be considered that two systems of porosity are present.
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From page 101... ...
Recently, there has been interest in formulating and modeling multiphase flow in fractured media. A significant motivation is the assessment of the fractured and unsaturated Yucca Mountain turf in Nevada as a potential host rock for nuclear waste (Evans and Nicholson, 1987~.
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From page 102... ...
A few books and papers (LeGrand and Stringfield, 1973; Milanovic, 1981; White, 1969) treat ground water flow in karst and provide a starting point for readers interested in this fascinating topic.
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From page 103... ...
Mathematically then, one flow equation is written for the fractures and one for the blocks, with the equations coupled by the source-sink terms. Thus a loss in fluid from the fracture represents a gain in fluids in the blocks (Shapiro, 1987~.
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From page 104... ...
The representative elemental volume is a sample volume for which the hydraulic conductivity is independent of sample volume or averaging volume. In other words, the representative elemental volume exists when a small change in the sample volume does not result in a change in hydraulic conductivity.
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From page 105... ...
and the mean hydraulic conductivity will be zero no matter how large the averaging volume (Schwartz and Smith, 1987~. Thus in modeling a fractured system, simply choosing a large volume of rock for a cell will not necessarily guarantee that the assumption of a representative elemental volume is met.
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From page 106... ...
SOURCE: Schwartz and Smith, 1987. Computational Constraints on Discrete Network Models Modeling fluid flow in a network of discrete fractures does not require that the fractures behave as a continuum.
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From page 107... ...
However, so little work has been conducted on natural systems that it will require years to fully assess how uncertain predictions in fractured rock systems might be. Adequacy of Modeling Technology In most practical problems involving saturated flow in fractured media, there has never been much hesitation in applying continuumtype models.
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From page 108... ...
Again, the committee would consider the capability of modeling to exist but without the theoretical and practical experience with the models to consider these applications in any sense routine. As was the case with unsaturated flow modeling in fractured media, limitations in the data provide
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From page 109... ...
1987. Definition of Boundary and Initial Conditions in the Analysis of Saturated Ground-Water Flow Systems An Introduction, Book 3, Chapter Be, Techniques of WaterResources Investigations of the United States Geological Survey.
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From page 110... ...
1958. Some steady-state solutions to the unsaturated flow equation with application to evaporation from a water table.
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From page 111... ...
1985. Ground water flow in limestone terrains: Strategy, rationale, and procedures for reliable efficient monitoring of ground water quality in karat areas.
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From page 112... ...
1979a. Stochastic analysis of steady state groundwater flow in a bounded domain, 1.
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