Fundamentals of Groundwater Flow(Flow in the Natural Environment)

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Types of Aquifers:Confined versus Unconfined

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Definition of a confined aquifer: A horizontal permeable zone with impermeable zones above and below. By definition the fluid in a confined aquifer is at higher-than-atmospheric pressure, so that its water will rise in any well or borehole penetrating it.

© John F. Hermance

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Our representation of a confined aquifer.

Definition of an “unconfined” or a “watertable” aquifer.

An unconfined aquifer is one that is substantially unbounded above by impermeable zones. Accordingly, the surface of the saturated zone is at atmospheric pressure.

Our representation of an unconfined aquifer.

Creating coupled unconfined and confined aquifers.

Operationally defining “confined” and“unconfined” aquifers.

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First, operationally define a “confined” aquifer.

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We operationally define a confined aquiferby drilling.

Defining a confined aquifer “operationally”.

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Water “streams”back up thewell-bore.

Definitely a confined, artesian orover-pressured aquifer.

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We operationally define an unconfined aquiferby drilling.

Looking closely:Unconfined (Watertable) Aquifer.

Looking closely:Unconfined (Watertable) Aquifer.

Looking closely:Confined (Artesian) Aquifer.

Looking closely:Confined (Artesian) Aquifer.

(No water in well even though it is significantly deeper than the local piezometric surface.)

Looking closely:Confined (Artesian) Aquifer.

(At some depth, the drill intercepts an aquifer andwater rises to the local piezometric surface.)

Flow in a Confined (or Artesian) Aquifer(A Qualitative View)

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Elements of a Confined Aquifer

Definition of a confined aquifer: A horizontal permeable zone with impermeable zones above and below. By definition the fluid in a confined aquifer is at higher-than-atmospheric pressure, so that its water will rise in any well or borehole penetrating it.

This confined aquifer is supplied by two sources of equal head.

The hydraulic head is everywhere the same;no gradient in h no flow.

Here, a difference in hydraulic head causes flow;a gradient in h causes flow (for finite K).

The piezometric (or potentiometric) surface invertical section.

Flow in an Unconfined (or Watertable) Aquifer(A Qualitative View)

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An “unconfined” aquifer under no flow conditions.

This unconfined aquifer is supplied by two sources of equal head.

If the surface of the water table is level, there is no groundwater flow.

Here h1 and h2 are the same.

The hydraulic head is everywhere the same;no gradient in h, no flow.

An “unconfined” aquifer under flow conditions

If there is a difference in the elevation of the watertable, groundwater will flow down-gradient, from higher

elevations of the watertable to lower.

Quantitative Modeling of Subsurface Flow

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What do we mean by 3D, 2D and 1D models?

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The earth is basically 3D.

But when a set of processes are dominant in some plane, we might

invoke a 2D model.

In some cases, we can get insight into one or more processes using

a 1D model.

Here the hydraulic head along a 1D “profile” can “map” inflow and outflow; or water sources and sinks.

Water injected into the core of a 1D aquifer causes an inflation or mounding of the watertable.

A fundamental relation in groundwater flow.

A local representation of a volumetric groundwater source.

Such volumetric water sources are an essential feature of this conservation condition.

How can we simplify the simultaneous simulation of the hydraulic head in 3D [h(x,y,z)] and

q(x,y,z) = (qx(x,y,z), qy(x,y,z), qz(x,y,z)) ?

The Basic Model and Boundary Conditions

Quantitative Modeling of Confined Flow

The Basic Model and Boundary Conditions

This is the general solution of the problem.Works in all cases meeting assumptions.

Piezometric surface for confined flow.

Quantitative Modeling of Unconfined Flow

A Volumetric Element in Unconfined Flow

This is the general solution of the problem.Works in all cases meeting assumptions.

The Basic Model and Boundary Conditions

Application 1: Watertable on an elongated island.

Application 2: Flow relations across a topographic (& watertable) divide.

The concept of “transmissivity” as ahydrogeological parameter

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A Common Parameter in Hydrogeology:

A vertical section through a hypothetical aquifer.

We desire an efficient way to represent the spatialcharacteristics of the aquifer.

We would like to do so in a computationallyefficient manner.

It is invariably computationally efficient ($$), instead ofmodeling the geologic detail of an aquifer, to invoke the

following mathematical idealization.

The conceptual consequence of this representation is that all flow is in a thin sheet lying in the horizontal plane.

Using color to represent lateral variations in transmissivity

As before, the conceptual consequence of this representation is that all flow is in a thin sheet lying in the horizontal plane.

For the example shown here, there are interesting implications for the direction of flow. (Recall that horizontal flow is down-gradient,

with the implications shown here.)

What are the implications of such a pattern for the presence of sources and sinks for the fluid?

Comparing Groundwater Levels for Confinedand Unconfined Aquifers

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Piezometric surface for confined flow.

Piezometric surface for unconfined flow.

Compare piezometric surfaces for unconfined andconfined flow.

Alert: A consequence of these results is that the transmissivity of this unconfined aquifer - even though it has uniform properties - is constantly changing along the direction of flow, whereas the transmissivity of the confined aquifer is constant.

Alert: A consequence of these results is that the transmissivity of this unconfined aquifer - even though it has uniform properties - is constantly changing along the direction of flow, whereas the transmissivity of the confined aquifer is constant.

An Example of a Transmissivity “Map”:The Palmer River Watershed

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