Hydrogeology (
hydro- meaning water, and
-geology meaning the study of the
Earth) is the area of
geology
that deals with the distribution and movement of
groundwater in the
soil and
rocks of the Earth's
crust, (commonly in
aquifers). The term
geohydrology is
often used interchangeably. Some make the minor distinction between
a
hydrologist or
engineer applying themselves to geology
(geohydrology), and a
geologist applying
themselves to
hydrology
(hydrogeology).
Typical aquifer cross-section
Introduction
Hydrogeology (like most
earth
sciences) is an interdisciplinary subject; it can be difficult
to account fully for the
chemical,
physical,
biological and even
legal
interactions between
soil,
water,
nature and
society. The study of the interaction between
groundwater movement and geology can be quite complex. Groundwater
does not always flow in the subsurface down-hill following the
surface topography; groundwater
follows
pressure gradients (flow
from high pressure to low) often following fractures and conduits
in circuitous paths. Taking into account the interplay of the
different facets of a multi-component system often requires
knowledge in several diverse fields at both the
experimental and
theoretical levels. This being said, the following is
a more traditional (
reductionist
viewpoint) introduction to the methods and nomenclature of
saturated subsurface hydrology, or simply hydrogeology.
Hydrogeology in relation to other fields
Hydrogeology, as stated above, is a branch of the earth sciences
dealing with the flow of water through aquifers and other shallow
porous media (typically less than 450
m or 1,500
ft
below the land surface.) The very shallow flow of water in the
subsurface (the upper 3 m or 10 ft) is pertinent to the fields of
soil science,
agriculture and
civil engineering, as well as to
hydrogeology. The general flow of
fluids
(water,
hydrocarbons,
geothermal fluids, etc.) in deeper
formations is also a concern of geologists,
geophysicists and
petroleum geologists. Groundwater is a
slow-moving,
viscous fluid (with a
Reynolds number less than unity);
many of the empirically derived laws of groundwater flow can be
alternately derived in
fluid
mechanics from the special case of
Stokes flow (viscosity and
pressure terms, but no inertial term).
The
mathematical relationships used to describe
the flow of water through porous media are the
diffusion and
Laplace equations, which have applications
in many diverse fields. Steady groundwater flow (Laplace equation)
has been simulated using
electrical,
elastic and
heat conduction analogies. Transient
groundwater flow is analogous to the diffusion of
heat in a solid, therefore some solutions to
hydrological problems have been adapted from
heat transfer literature.
Traditionally, the movement of groundwater has been studied
separately from surface water,
climatology, and even the chemical and
microbiological aspects of hydrogeology (the
processes are uncoupled). As the field of hydrogeology matures, the
strong interactions between groundwater,
surface
water,
water chemistry, soil
moisture and even
climate are becoming more
clear.
Definitions and material properties
One of the main tasks a hydrogeologist typically performs is the
prediction of future behavior of an aquifer system, based on
analysis of past and present observations. Some hypothetical, but
characteristic questions asked would be:
- Can the aquifer support another subdivision?
- Will the river dry up if the farmer
doubles his irrigation?
- Did the chemicals from the dry
cleaning facility travel through the aquifer to my well and
make me sick?
- Will the plume of effluent leaving my neighbor's septic system
flow to my drinking water well?
Most of these questions can be addressed through simulation of the
hydrologic system (using numerical models or analytic equations).
Accurate simulation of the aquifer system requires knowledge of the
aquifer properties and boundary conditions. Therefore a common task
of the hydrogeologist is determining aquifer properties using
aquifer tests.
In order to further characterize aquifers and
aquitards some primary and derived physical
properties are introduced below. Aquifers are broadly classified as
being either confined or unconfined (
water
table aquifers), and either saturated or unsaturated; the type
of aquifer affects what properties control the flow of water in
that medium (e.g., the release of water from storage for confined
aquifers is related to the
storativity,
while it is related to the specific yield for unconfined
aquifers).
Hydraulic head
Changes in hydraulic head (
h) are the driving force which
causes water to move from one place to another. It is composed of
pressure head (
ψ) and elevation head (
z). The
head gradient is the change in hydraulic head per length of
flowpath, and appears in
Darcy's law as
being proportional to the discharge.
Hydraulic head is a directly measurable property that can take on
any value (because of the arbitrary datum involved in the
z term);
ψ can be measured with a pressure
transducer (this value can be negative,
e.g., suction, but is positive in saturated aquifers), and
z can be measured relative to a surveyed datum (typically
the top of the
well casing). Commonly, in
wells tapping unconfined aquifers the water level in a well is used
as a proxy for hydraulic head, assuming there is no vertical
gradient of pressure. Often only
changes in hydraulic head
through time are needed, so the constant elevation head term can be
left out (
Δh = Δψ).
A record of hydraulic head through time at a well is a
hydrograph or, the changes in hydraulic head
recorded during the pumping of a well in a test are called
drawdown.
Porosity
Porosity (
n) is a directly measurable aquifer property; it
is a fraction between 0 and 1 indicating the amount of pore space
between unconsolidated
soil particles or within
a fractured rock. Typically, the majority of groundwater (and
anything dissolved in it) moves through the porosity available to
flow (sometimes called effective porosity).
Permeability is an expression of the connectedness
of the pores. For instance, an unfractured rock unit may have a
high
porosity (it has lots of
holes between its
constituent grains), but a low
permeability (none of the
pores are connected). An example of this phenomenon is
pumice, which, when in its unfractured state, can
make a poor aquifer.
Porosity does not directly affect the distribution of hydraulic
head in an aquifer, but it has a very strong effect on the
migration of dissolved contaminants, since it affects groundwater
flow velocities through an inversely proportional
relationship.
Water content
Water content (
θ) is also a directly measurable property;
it is the fraction of the total rock which is filled with liquid
water. This is also a fraction between 0 and 1, but it must also be
less than or equal to the total porosity.
The water content is very important in
vadose zone hydrology, where the
hydraulic conductivity is a strongly
nonlinear function of water content; this
complicates the solution of the unsaturated groundwater flow
equation.
Hydraulic conductivity
Hydraulic conductivity (
K) and transmissivity (
T)
are indirect aquifer properties (they cannot be measured directly).
T is the
K integrated over the vertical thickness
(
b) of the aquifer (
T=Kb when
K is
constant over the entire thickness). These properties are measures
of an
aquifer's ability to transmit
water.
Intrinsic
permeability (
κ) is a secondary medium property which
does not depend on the
viscosity and
density of the fluid (
K and
T are specific to water); it is used more in the petroleum
industry.
Specific storage and specific yield
Specific storage (
S_{s}) and its depth-integrated
equivalent, storativity (
S=S_{s}b), are indirect
aquifer properties (they cannot be measured directly); they
indicate the amount of groundwater released from storage due to a
unit depressurization of a confined aquifer. They are fractions
between 0 and 1.
Specific yield (
S_{y}) is also a ratio between 0
and 1 (
S_{y} ≤ porosity) and indicates the amount
of water released due to drainage from lowering the water table in
an unconfined aquifer. Typically
S_{y} is orders
of magnitude larger than
S_{s}. Often the
porosity or effective porosity is used as an upper
bound to the specific yield.
Contaminant transport properties
Often we are interested in how the moving groundwater water will
move dissolved contaminants around (the sub-field of contaminant
hydrogeology). The contaminants can be man-made (e.g.,
petroleum products,
nitrate or
Chromium) or naturally occurring (e.g.,
arsenic,
salinity).
Besides needing to understand where the groundwater is flowing,
based on the other hydrologic properties discussed above, there are
additional aquifer properties which affect how dissolved
contaminants move with groundwater.
Dispersivity (α
_{L}, α
_{T}) is an
empirical factor which quantifies how much contaminants stray away
from the path of the groundwater which is carrying it. Some of the
contaminants will be "behind" or "ahead" the mean groundwater,
giving rise to a longitudinal dispersivity (α
_{L}), and
some will be "to the sides of" the pure advective groundwater flow,
leading to a transverse dispersivity (α
_{T}).
Dispersivity is actually a factor which represents our
lack of
information about the system we are simulating. There are many
small details about the aquifer which are being averaged when using
a
macroscopic approach (e.g., tiny beds
of gravel and clay in sand aquifers), they manifest themselves as
an
apparent dispersivity. Because of this, α is often
claimed to be dependent on the length scale of the problem — the
dispersivity found for transport through 1 m³ of aquifer is
different than that for transport through 1 cm³ of the same
aquifer material.
Hydrodynamic dispersion (D) is a positive physical
parameter which describes the molecule-scale movement of solute
away from the mean flow; it is a result of
Brownian motion. This is the same mechanism
as dye uniformly spreading out in a still bucket of water. The
dispersion coefficient is typically quite small (typically orders
of magnitude smaller than α), and can often be considered
negligible (unless groundwater flow velocities are extremely low,
as they are in clay aquitards).
It is important not to confuse hydrodynamic dispersion with
dispersivity, as the former is a physical phenomenon and the latter
is an empirical factor which is cast into a similar form as
dispersion, because we already know how to solve that
problem.
Governing equations
Darcy's Law
Darcy's law is a
Constitutive
equation (empirically derived by
Henri
Darcy, in 1856) that states the amount of
groundwater discharging through a given portion
of
aquifer is proportional to the
cross-sectional area of flow, the hydraulic head gradient, and the
hydraulic conductivity.
Groundwater flow equation
The groundwater flow equation, in its most general form, describes
the movement of groundwater in a porous medium (aquifers and
aquitards). It is known in mathematics as the
diffusion equation, and has many analogs
in other fields. Many solutions for groundwater flow problems were
borrowed or adapted from existing
heat
transfer solutions.
It is often derived from a physical basis using
Darcy's law and a conservation of mass for a
small control volume. The equation is often used to predict flow to
wells, which have radial symmetry, so the
flow equation is commonly solved in
polar or
cylindrical coordinates.
The
Theis equation is one of the most
commonly used and fundamental solutions to the groundwater flow
equation; it can be used to predict the transient evolution of head
due to the effects of pumping one or a number of pumping
wells.
The
Thiem equation is a
solution to the steady state groundwater flow equation (Laplace's
Equation). Unless there are large sources of water nearby (a river
or lake), true steady-state is rarely achieved in reality.
Calculation of groundwater flow
Relative groundwater travel
times.
To use the groundwater flow equation to estimate the distribution
of hydraulic heads,or the direction and rate of groundwater flow,
this
partial differential
equation (PDE) must be solved. The most common means of
analytically solving the diffusion equation in the hydrogeology
literature are:
No matter which method we use to solve the
groundwater flow equation, we need
both initial conditions(heads at time (
t) = 0) and
boundary conditions
(representing either the physicalboundaries of the domain, or an
approximation of the domain beyond thatpoint). Often the initial
conditions are supplied to a transientsimulation, by a
corresponding steady-state simulation (where the timederivative in
the groundwater flow equation is set equal to 0).
There are two broad categories of how the (PDE) would be solved;
either
analytical methods,
numerical methods, or something
possibly in between. Typically, analytic methods solve the
groundwater flow equation under a simplified set of conditions
exactly, while numerical methods solve it under more
general conditions to an
approximation.
Analytic methods
Analytic methods typically use the structure of
mathematics to arrive at a simple, elegant
solution, but the required derivation for all but the simplest
domain geometries can be quite complex (involving non-standard
coordinates,
conformal mapping, etc.). Analytic
solutions typically are also simply an equation that can give a
quick answer based on a few basic parameters. The
Theis equation is a very simple
(yet still very useful) analytic solution to the
groundwater flow equation,
typically used to analyze the results of an
aquifer test or
slug
test.
Numerical methods
The topic of
numerical methods is
quite large, obviously being of use to most fields of
engineering and
science
in general. Numerical methods have been around much longer than
computers have (In the 1920s
Richardson developed some of the
finite difference schemes still in
use today, but they were calculated by hand, using paper and
pencil, by human "calculators"), but they have become very
important through the availability of fast and cheap
personal computers. A quick survey of the
main numerical methods used in hydrogeology, and some of the most
basic principles is shown below and further discussed in the
article "
Groundwater model".
There are two broad categories of numerical methods: gridded or
discretized methods and non-gridded or mesh-free methods. In the
common
finite difference method
and
finite element method
(FEM) the domain is completely gridded ("cut" into a grid or mesh
of small elements). The
analytic
element method (AEM) and the boundary integral equation method
(BIEM — sometimes also called BEM, or Boundary Element Method) are
only discretized at boundaries or along flow elements (line sinks,
area sources, etc.), the majority of the domain is mesh-free.
General properties of gridded methods
Gridded Methods like
finite
difference and
finite element
methods solve the groundwater flow equation by breaking the problem
area (domain) into many small elements (squares, rectangles,
triangles, blocks,
tetrahedra, etc.) and
solving the flow equation for each element (all material properties
are assumed constant or possibly linearly variable within an
element), then linking together all the elements using
conservation of mass across the
boundaries between the elements (similar to the
divergence theorem). This results in a
system which overall approximates the groundwater flow equation,
but exactly matches the boundary conditions (the head or flux is
specified in the elements which intersect the boundaries).
Finite differences are a way of
representing continuous
differential operators using discrete
intervals (
Δx and
Δt), and the finite difference
methods are based on these (they are derived from a
Taylor series). For example the first-order
time derivative is often approximated using the following forward
finite difference, where the subscripts indicate a discrete time
location,
- \frac{\partial h}{\partial t} = h'(t_i) \approx \frac{h_i -
h_{i-1}}{\Delta t}.
The forward finite difference approximation is unconditionally
stable, but leads to an implicit set of equations (that must be
solved using matrix methods, e.g.
LU or
Cholesky decomposition). The similar
backwards difference is only conditionally stable, but it is
explicit and can be used to "march" forward in the time direction,
solving one grid node at a time (or possibly in
parallel, since one node depends only on
its immediate neighbors). Rather than the finite difference method,
sometimes the Galerkin
FEM
approximation is used in space (this is different from the type of
FEM often used in
structural
engineering) with finite differences still used in time.
Application of finite difference models
MODFLOW is a well-known example of a general
finite difference groundwater flow model. It is developed by the
US Geological Survey as a
modular and extensible simulation tool for modeling groundwater
flow. It is
free software developed,
documented and distributed by the USGS. Many commercial products
have grown up around it, providing
graphical user interfaces to its
input file based interface, and typically incorporating pre- and
post-processing of user data. Many other models have been developed
to work with MODFLOW input and output, making linked models which
simulate several hydrologic processes possible (flow and transport
models,
surface water and
groundwater models and chemical reaction
models), because of the simple, well documented nature of
MODFLOW.
Application of finite element models
Finite Element programs are more flexible in design (triangular
elements vs. the block elements most finite difference models use)
and there are some programs available (
SUTRA, a 2D or 3D density-dependent flow model by the
USGS;
Hydrus, a commercial
unsaturated flow model;
FEFLOW, a commercial
modeling environment for subsurface flow, solute and heat transport
processes; and
COMSOL
Multiphysics (FEMLAB) a commercial general modeling
environment), but unless they are gaining in importance they are
still not as popular in with practicing hydrogeologists as MODFLOW
is. Finite element models are more popular in
university and
laboratory environments, where specialized models
solve non-standard forms of the flow equation (
unsaturated flow,
density
dependent flow, coupled
heat and
groundwater flow, etc.)
Application of finite volume models
The finite volume method is a method for representing and
evaluating partial differential equations as algebraic equations
[LeVeque, 2002; Toro, 1999]. Similar to the finite difference
method, values are calculated at discrete places on a meshed
geometry. "Finite volume" refers to the small volume surrounding
each node point on a mesh. In the finite volume method, volume
integrals in a partial differential equation that contain a
divergence term are converted to surface integrals, using the
divergence theorem. These terms are then evaluated as fluxes at the
surfaces of each finite volume. Because the flux entering a given
volume is identical to that leaving the adjacent volume, these
methods are conservative. Another advantage of the finite volume
method is that it is easily formulated to allow for unstructured
meshes. The method is used in many computational fluid dynamics
packages.
PORFLOW software package is a comprehensive
mathematical model for simulation of Ground Water Flow and Nuclear
Waste Management developed by Analytic & Computational
Research, Inc., ACRi]
ACRi
The
FEHM software package is
available free from Los Alamos National Laboratory and can be accessed at the FEHM Website.
This versatile porous flow simulator includes capabilities to model
multiphase, thermal, stress, and multicomponent reactive chemistry.
Current work using this code includes simulation of methane hydrate
formation, CO
_{2} sequestration, oil shale extraction,
migration of both nuclear and chemical contaminants, environmental
isotope migration in the unsaturated zone, and karst
formation.
Other methods
These include mesh-free methods like the
Analytic Element Method (AEM) and
the Boundary Element Method (BEM), which are closer to analytic
solutions, but they do approximate the groundwater flow equation in
some way. The BEM and AEM exactly solve the groundwater flow
equation (perfect mass balance), while approximating the boundary
conditions. These methods are more exact and can be much more
elegant solutions (like analytic methods are), but have not seen as
widespread use outside academic and research groups yet.
Further reading
General hydrogeology
- Domenico, P.A. & Schwartz, W., 1998. Physical and
Chemical Hydrogeology Second Edition, Wiley. — Good book for
consultants, it has many real-world examples and covers additional
topics (e.g. heat flow, multi-phase and unsaturated flow). ISBN
0-471-59762-7
- Driscoll, Fletcher, 1986. Groundwater and Wells, US
Filter / Johnson Screens. — Practical book illustrating the actual
process of drilling, developing and utilizing water wells, but it
is a trade book, so some of the material is slanted towards the
products made by Johnson Well Screens. ISBN 0-9616456-0-1
- Freeze, R.A. & Cherry, J.A., 1979. Groundwater,
Prentice-Hall. — A classic text; like an older version of Domenico
and Schwartz. ISBN 0-13-365312-9
- de Marsily, G., 1986. Quantitative Hydrogeology:
Groundwater Hydrology for Engineers, Academic Press, Inc.,
Orlando Florida. — Classic book intended for engineers with
mathematical background but it can be read by hydrologists and
geologists as well. ISBN 0-12-208916-2
- Porges, Robert E. & Hammer, Matthew J., 2001. The
Compendium of Hydrogeology, National Ground Water Association,
ISBN 1-56034-100-9. Written by practicing hydrogeologists, this
inclusive handbook provides a concise, easy-to-use reference for
hydrologic terms, equations, pertinent physical parameters, and
acronyms
- Todd, David Keith, 1980. Groundwater Hydrology Second
Edition, John Wiley & Sons. — Case studies and real-world
problems with examples. ISBN 0-471-87616-X
- Fetter, C.W. Contaminant Hydrogeology Second Edition,
Prentice Hall. ISBN 0137512155
- Fetter, C.W. Applied Hydrogeology Fourth Edition,
Prentice Hall. ISBN 0130882399
Numerical groundwater modeling
- Anderson, Mary P. & Woessner, William W., 1992 Applied
Groundwater Modeling, Academic Press. — An introduction to
groundwater modeling, a little bit old, but the methods are still
very applicable. ISBN 0-12-059485-4
- Chiang, W.-H., Kinzelbach, W., Rausch, R. (1998): Aquifer
Simulation Model for WINdows - Groundwater flow and transport
modeling, an integrated program. - 137 p., 115 fig., 2 tab., 1
CD-ROM; Berlin, Stuttgart (Borntraeger). ISBN 3-443-01039-3
- Elango, L and Jayakumar, R (Eds.)(2001) Modelling in
Hydrogeology, UNESCO-IHP Publication, Allied Publ., Chennai, ISBN
81-7764-218-9
- Rausch, R., Schäfer W., Therrien, R., Wagner, C., 2005
Solute Transport Modelling - An Introduction to Models and
Solution Strategies. - 205 p., 66 fig., 11 tab.; Berlin,
Stuttgart (Borntraeger). ISBN 3-443-01055-5
- Rushton, K.R., 2003, Groundwater Hydrology: Conceptual and
Computational Models. John Wiley and Sons Ltd. ISBN
0-470-85004-3
- Wang H. F., Theory of Linear Poroelasticity with Applications
to Geomechanics and Hydrogeology, Princeton Press, (2000). Good
introduction to fundamentals of poroelasticity.
- Waltham T., Foundations of Engineering Geology, 2nd Edition,
Taylor & Francis, (2001). General introduction.
- Yang X. S., Mathematical Modelling for Earth Sciences, Dunedin
Academic Press, (2008). Good introduction to mathematical and
numerical techniques in flow in porous media.
- Zheng, C., and Bennett, G.D., 2002, Applied Contaminant
Transport Modeling Second Edition, John Wiley & Sons — A
very good, modern treatment of groundwater flow and transport
modeling, by the author of MT3D. ISBN 0-471-38477-1
Analytic groundwater modeling
- Haitjema, Henk M., 1995. Analytic Element Modeling of
Groundwater Flow, Academic Press. — An introduction to
analytic solution methods, especially the Analytic element method (AEM). ISBN
0-12-316550-4
- Harr, Milton E., 1962. Groundwater and seepage, Dover.
— a more civil engineering view on
groundwater; includes a great deal on flownets. ISBN 0-486-66881-9
- Lee, Tien-Chang, 1999. Applied Mathematics in
Hydrogeology, CRC Press. — Great explanation of mathematical
methods used in deriving solutions to hydrogeology problems (solute
transport, finite element and inverse problems too). ISBN
1-56670-375-1
- Liggett, James A. & Liu, Phillip .L-F., 1983. The
Boundary Integral Equation Method for Porous Media Flow,
George Allen and Unwin, London. — Book on BIEM (sometimes called
BEM) with examples, it makes a good introduction to the method.
ISBN 0-04-620011-8
See also
External links and sources