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HydrogeologyFrom Wikipedia, the free encyclopedia

This article includes a list of references, but its sources remain unclear because it has

insufficient inline citations. Please help to improvethis article by introducing more precise

citations. (September 2007)

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 auifers)! "he term geohydrology is often used interchangeably!

#ome make the minor distinction between a hydrologist or engineer  applying themselves to

geology (geohydrology), and a geologist applying themselves to hydrology (hydrogeology)!

"ypical auifer cross$section

Contents

  [hide]

1 Introduction

2 Hydrogeology in relation to other fields

!efinitions and material properties

o .1 Hydraulic head

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o .2 Porosity

o . "ater content

o .# Hydraulic conductivity

o .$ %pecific storage and specific yield

o .& 'ontaminant transport properties

.&.1 Hydrodynamic dispersion

.&.2 (olecular !iffusion

.&. )etardation by adsorption

# *overning e+uations

o #.1 !arcys -a

o #.2 *roundater flo e+uation

$ 'alculation of groundater flo

o $.1 /nalytic methods

o $.2 0umerical methods

$.2.1 *eneral properties of gridded methods

$.2.2 /pplication of finite difference models

$.2. /pplication of finite element models

$.2.# /pplication of finite volume models

$.2.$ ther methods

& %ee also

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)eferences

3 4urther reading

o 3.1 *eneral hydrogeology

o 3.2 0umerical groundater modeling

o 3. /nalytic groundater modeling

5 67ternal lin8s and sources

%edit&ntroduction

Hydrogeology is an interdisciplinary subect it can be difficult to account fully for

the chemical, physical, biological and even legal interactions

between soil, water , nature and society! "he study of the interaction between groundwater

movement and geology can be uite comple*! +roundwater does not always flow in the subsurface

down$hill following the surface topography groundwater followspressure gradients (flow from highpressure to low) often following fractures and conduits in circuitous paths! "aking into account the

interplay of the different facets of a multi$component system often reuires knowledge in several

diverse fields at both the e*perimental and theoretical levels! "he following is a more traditional

introduction to the methods and nomenclature of saturated subsurface hydrology, or simply

hydrogeology!

%edit&Hydrogeology in relation to other fields

Hydrogeology, as stated above, is a branch of the earth sciences dealing with the flow of water

through auifers and other shallow porous media (typically less than -. m or /,-.. ft below the

land surface!) "he very shallow flow of water in the subsurface (the upper 0 m or /. ft) is pertinent

to the fields of soil science, agriculture and civil engineering, as well as to hydrogeology! "he

general flow of fluids (water, hydrocarbons, geothermal fluids, etc!) in deeper formations is also a

concern of geologists, geophysicists and petroleum geologists! +roundwater is a slow$

moving, viscous fluid (with a1eynolds 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 #tokes flow (viscosity and pressureterms, but no inertial term)!

"he mathematical relationships used to describe the flow of water through porous media are

the diffusion and 2aplace euations, which have applications in many diverse fields! #teady

groundwater flow (2aplace euation) has been simulated using electrical, elastic and heat

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conduction analogies! "ransient 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!

"raditionally, 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)! 3s the field of hydrogeology matures, the strong interactions between

groundwater, surface water , water chemistry, soil moisture and even climate are becoming more

clear!

For e*ample4 3uifer drawdown or  overdrafting and the pumping of  fossil water  increases the total

amount of water within the hydrosphere subect to transpiration and evaporation processes,

thereby causing accretion in water vapour  and cloud cover, the primary absorbers

of infrared radiation in the earth's atmosphere! 3dding water to the system has a forcing effect on

the whole earth system! 3n accurate estimate of the climatic forcing effect due to this

hydrogeological fact is yet to be uantified!

%edit&5efinitions and material properties

Main article: Aquifer 

6ne of the main tasks a hydrogeologist typically performs is the prediction of future behavior of an

auifer system, based on analysis of past and present observations! #ome hypothetical, but

characteristic uestions asked would be4

7an the auifer support another subdivision8

Will the river  dry up if the farmer doubles his irrigation8

5id the chemicals from the dry cleaning facility travel through the auifer to my well and

make me sick8

Will the plume of effluent leaving my neighbor's septic system flow to my drinking water

well8

9ost of these uestions can be addressed through simulation of the hydrologic system (using

numerical models or analytic euations)! 3ccurate simulation of the auifer system reuires

knowledge of the auifer properties and boundary conditions! "herefore a common task of the

hydrogeologist is determining auifer properties using auifer tests!

n order to further characteri:e auifers and auitards some primary and derived physical

properties are introduced below! 3uifers are broadly classified as being either confined or

unconfined (water table auifers), and either saturated or unsaturated the type of auifer affects

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what properties control the flow of water in that medium (e!g!, the release of water from storage for

confined auifers is related to the storativity, while it is related to the specific yield for unconfined

auifers)!

%edit&Hydraulic head

Main article: Hydraulic head 

7hanges in hydraulic head (h) are the driving force which causes water to move from one place to

another! t is composed of pressure head (ψ ) and elevation head (z )! "he head gradient is the

change in hydraulic head per length of flowpath, and appears in 5arcy'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 auifers), and z  can be measured relative

to a surveyed datum (typically the top of the well casing)! 7ommonly, in wells tapping unconfined

auifers the water level in a well is used as a pro*y for hydraulic head, assuming there is no

vertical gradient of pressure! 6ften only changes in hydraulic head through time are needed, so the

constant elevation head term can be left out ( Δh = Δψ )!

 3 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!

%edit&Porosity

Main article: Porosity 

;orosity (n) is a directly measurable auifer property it is a fraction between . and / indicating the

amount of pore space between unconsolidated soil particles or within a fractured rock! "ypically,

the maority of groundwater (and anything dissolved in it) moves through the porosity available to

flow (sometimes called effective porosity)! Permeability is an e*pression 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)!

 3n e*ample of this phenomenon is pumice, which, when in its unfractured state, can make a poor

auifer!

;orosity does not directly affect the distribution of hydraulic head in an auifer, but it has a very

strong effect on the migration of dissolved contaminants, since it affects groundwater flow

velocities through an inversely proportional relationship!

%edit&Water content

Main article: ater content 

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Water content (! ) is also a directly measurable property it is the fraction of the total rock which is

filled with liuid water! "his is also a fraction between . and /, but it must also be less than or eual

to the total porosity!

"he water content is very important in vadose :one hydrology, where the hydraulic conductivity is a

strongly nonlinear  function of water content this complicates the solution of the unsaturated

groundwater flow euation!

%edit&Hydraulic conductivity

Main article: Hydraulic conducti"ity 

Hydraulic conductivity (# ) and transmissivity ($ ) are indirect auifer properties (they cannot be

measured directly)! $  is the #  integrated over the vertical thickness (b) of the auifer

($=#b when #  is constant over the entire thickness)! "hese properties are measures of an auifer 's

ability to transmit water ! ntrinsic permeability (% ) is a secondary medium property which does not

depend on theviscosity and density of the fluid (#  and $  are specific to water) it is used more in

the petroleum industry!

%edit&Specific storage and specific yield

Main article: &pecific storage

#pecific storage (&s) and its depth$integrated euivalent, storativity (&=&sb), are indirect auifer

properties (they cannot be measured directly) they indicate the amount of groundwater released

from storage due to a unit depressuri:ation of a confined auifer! "hey are fractions between . and

/!

#pecific yield (&y ) is also a ratio between . and / (&y  < porosity) and indicates the amount of water

released due to drainage from lowering the water table in an unconfined auifer! "he value for

specific yield is less than the value for porosity because some water will remain in the medium

even after drainage due to molecular forces! 6ften the porosity or effective porosity is used as an

upper bound to the specific yield! "ypically &y  is orders of magnitude larger than &s!

%edit&Contaminant transport properties

6ften we are interested in how the moving groundwater water will move dissolved contaminants

around (the sub$field of contaminant hydrogeology)! "he contaminants can be man$made

(e!g!, petroleum products, nitrate or  7hromium) or naturally occurring (e!g!, arsenic, salinity)!

=esides needing to understand where the groundwater is flowing, based on the other hydrologic

properties discussed above, there are additional auifer properties which affect how dissolved

contaminants move with groundwater!

%edit&Hydrodynamic dispersion

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Hydrodynamic dispersivity (>2, >") is an empirical factor which uantifies how much contaminants

stray away from the path of the groundwater which is carrying it! #ome of the contaminants will be

?behind? or ?ahead? the mean groundwater, giving rise to a longitudinal dispersivity (> 2), and some

will be ?to the sides of? the pure advective groundwater flow, leading to a transverse dispersivity

(>")! 5ispersion in groundwater is because each water ?particle?, passing beyond a soil particle,

must choose where to go, whether left or right or up or down, so that the water ?particles? (and their 

solute) are gradually spread in all directions around the mean path! "his is the ?microscopic?

mechanism, on the scale of soil particles! 9ore important, on long distances, can be the

macroscopic inhomogeneities of the auifer, which can have regions of larger or smaller

permeability, so that some water can find a preferential path in one direction, some other in a

different direction, so that the contaminant can be spread in a completely irregular way, like in a

(three$dimensional) delta of a river!

5ispersivity is actually a factor which represents our lac' of information about the system we are

simulating! "here are many small details about the auifer which are being averaged when using

amacroscopic approach (e!g!, tiny beds of gravel and clay in sand auifers), they manifest

themselves as an apparent  dispersivity! =ecause of this, > is often claimed to be dependent on the

length scale of the problem @ the dispersivity found for transport through / mA of auifer is

different than that for transport through / cmA of the same auifer material! %/&

%edit&Molecular Diffusion

5iffusion is a fundamental physical phenomenon, by which Einstein e*plained =rownian motion,

which describes the random thermal movement of molecules and small particles in gases and

liuids! t is an important phenomenon for small distances (it is essential for the achievement of

thermodinamic euilibria), but, as the time necessary to cover a distance by diffusion is

proportional to the suare of the distance itself, it is ineffective for spreading a solute over

macroscopic distances! "he diffusion coefficient, 5, is typically uite small, and its effect can oftenbe considered negligible (unless groundwater flow velocities are e*tremely low, as they are in clay

auitards)!

t is important not to confuse diffusion with dispersion, as the former is a physical phenomenon and

the latter is an empirical factor which is cast into a similar form as diffusion, because we already

know how to solve that problem!

%edit&Retardation by adsorption

"he retardation factor is another very important feature that make the motion of the contaminant to

deviate from the average groundwater motion! t is analogous to the retardation

factor  of chromatography! Bnlike diffusion and dispersion, which simply spread the contaminant, the

retardation factor changes its global a"erage "elocity , so that it can be much slower than that of

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water! "his is due to a chemico$physical effect4 the adsorption to the soil, which holds the

contaminant back and does not allow it to progress until the uantity corresponding to the chemical

adsorption euilibrium has been adsorbed! "his effect is particularly important for less soluble

contaminants, which thus can move even hundreds or thousands times slower than water! "he

effect of this phenomenon is that only more soluble species can cover long distances! "he

retardation factor depends on the chemical nature of both the contaminant and the auifer!

%edit&+overning euations

%edit&Darcy's La

Main article: (arcy)s la 

5arcy's law is a 7onstitutive euation (empirically derived by Henri 5arcy, in /C-D) that states the

amount of groundwater  discharging through a given portion of  auifer  is proportional to the cross$

sectional area of flow, the hydraulic head gradient, and the hydraulic conductivity!

%edit&!roundater flo e"uation

Main article: *roundater flo equation

+eometry of a partially penetrating well drainage system in an anisotropic layered auifer 

"he groundwater flow euation, in its most general form, describes the movement of groundwater

in a porous medium (auifers and auitards)! t is known in mathematics as the diffusion euation,

and has many analogs in other fields! 9any solutions for groundwater flow problems were

borrowed or adapted from e*isting heat transfer  solutions!

t is often derived from a physical basis using 5arcy's law and a conservation of mass for a small

control volume! "he euation is often used to predict flow towells, which have radial symmetry, so

the flow euation is commonly solved in polar  or  cylindrical coordinates!

"he "heis euation is one of the most commonly used and fundamental solutions to the

groundwater flow euation it can be used to predict the transient evolution of head due to the

effects of pumping one or a number of pumping wells!

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"he "hiem euation is a solution to the steady state groundwater flow euation (2aplace's

Euation) for flow to a well! Bnless there are large sources of water nearby (a river or lake), true

steady$state is rarely achieved in reality!

=oth above euations are used in auifer tests (pump tests)!

"he Hooghoudt euation is a groundwater flow euation applied to subsurface drainage by

pipes, tile drains or ditches!%&  3n alternative subsurface drainage method is drainage by wells for

which groundwater flow euations are also available!%0&

%edit&7alculation of groundwater flow

1elative groundwater travel times!

"o use the groundwater flow euation to estimate the distribution of hydraulic heads, or the

direction and rate of groundwater flow, this partial differential euation (;5E) must be solved! "he

most common means of analytically solving the diffusion euation in the hydrogeology literature

are4

2aplace, Hankel and Fourier  transforms (to reduce the number of  dimensions of the ;5E),

similarity transform (also called the =olt:mann transform) is commonly how the "heis

solution is derived,

separation of variables, which is more useful for non$7artesian coordinates, and

+reen's functions, which is another common method for deriving the "heis solution @

from the fundamental solution to the diffusion euation in free space!

o matter which method we use to solve the groundwater flow euation, we need both initial

conditions (heads at time (t ) G .) and boundary conditions(representing either the physical

boundaries of the domain, or an appro*imation of the domain beyond that point)! 6ften the initial

conditions are supplied to a transient simulation, by a corresponding steady$state simulation

(where the time derivative in the groundwater flow euation is set eual to .)!

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"here are two broad categories of how the (;5E) would be solved

either analytical methods, numerical methods, or something possibly in between! "ypically, analytic

methods solve the groundwater flow euation under a simplified set of conditions e+actly , while

numerical methods solve it under more general conditions to an appro+imation!

%edit&#nalytic methods

 3nalytic methods typically use the structure of mathematics to arrive at a simple, elegant solution,

but the reuired derivation for all but the simplest domain geometries can be uite comple*

(involving non$standard coordinates, conformal mapping, etc!)! 3nalytic solutions typically are also

simply an euation that can give a uick answer based on a few basic parameters! "he "heis

euation is a very simple (yet still very useful) analytic solution to the groundwater flow euation,

typically used to analy:e the results of an auifer test or slug test!

%edit&$umerical methods

"he topic of  numerical methods is uite large, obviously being of use to most fields

of engineering and science in general! umerical methods have been around much longer

than computers have (n the /.s 1ichardson 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! 3 uick 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

?+roundwater model?!

"here are two broad categories of numerical methods4 gridded or discreti:ed methods and non$

gridded or mesh$free methods! n the common finite difference method and finite element

method (FE9) the domain is completely gridded (?cut? into a grid or mesh of small elements)!

"he analytic element method (3E9) and the boundary integral euation method (=E9 @

sometimes also called =E9, or =oundary Element 9ethod) are only discreti:ed at boundaries or

along flow elements (line sinks, area sources, etc!), the maority of the domain is mesh$free!

%edit&!eneral properties of gridded methods

+ridded 9ethods like finite difference and finite element methods solve the groundwater flow

euation by breaking the problem area (domain) into many small elements (suares, rectangles,

triangles, blocks, tetrahedra, etc!) and solving the flow euation 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)! "his results in a system which overall appro*imates the

groundwater flow euation, but e*actly matches the boundary conditions (the head or flu* is

specified in the elements which intersect the boundaries)!

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Finite differences are a way of representing continuous differential operators using discrete

intervals ( Δ+  and Δt ), and the finite difference methods are based on these (they are derived from

a "aylor series)! For e*ample the first$order time derivative is often appro*imated using the

following forward finite difference, where the subscripts indicate a discrete time location,

"he forward finite difference appro*imation is unconditionally stable, but leads to an implicit

set of euations (that must be solved using matri* methods, e!g! 2B or  7holesky

decomposition)! "he similar backwards difference is only conditionally stable, but it is e*plicit

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)! 1ather than the

finite difference method, sometimes the +alerkin FE9 appro*imation is used in space (this is

different from the type of FE9 often used instructural engineering) with finite differences still

used in time!

%edit&#pplication of finite difference models

965F26W is a well$known e*ample of a general finite difference groundwater flow model! t

is developed by the B# +eological #urvey as a modular and e*tensible simulation tool for

modeling groundwater flow! t is free software developed, documented and distributed by the

B#+#! 9any 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! 9any other models have been developed to work with 965F26W 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 965F26W!

%edit&#pplication of finite element models

Finite Element programs are more fle*ible in design (triangular elements vs! the block

elements most finite difference models use) and there are some programs available (#B"13, 

a 5 or 05 density$dependent flow model by the B#+# Hydrus, a commercial unsaturated

flow model FEF26W, a commercial modeling environment for subsurface flow, solute and

heat transport processes and 769#62 9ultiphysics (FE923=) a commercial general

modeling environment), but unless they are gaining in importance they are still not as popular

in with practicing hydrogeologists as 965F26W is! Finite element models are more popular

in university and laboratory environments, where speciali:ed models solve non$standard forms

of the flow euation (unsaturated flow, densitydependent flow, coupled heat and groundwater

flow, etc!)

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%edit&#pplication of finite volume models

"he finite volume method is a method for representing and evaluating partial differential

euations as algebraic euations %2eIeue, .. "oro, /&! #imilar 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! n the finite volume method,

volume integrals in a partial differential euation that contain a divergence term are converted

to surface integrals, using the divergence theorem! "hese terms are then evaluated as flu*es

at the surfaces of each finite volume! =ecause the flu* entering a given volume is identical to

that leaving the adacent volume, these methods are conservative! 3nother advantage of the

finite volume method is that it is easily formulated to allow for unstructured meshes! "he

method is used in many computational fluid dynamics packages!

P%R&L%W software package is a comprehensive mathematical model for simulation of

+round Water Flow and uclear Waste 9anagement developed by 3nalytic J 7omputational

1esearch, nc!, 371i& 371i

"he &HM software package is available free from 2os 3lamos ational 2aboratory and can

be accessed at the FEH9 Website! "his versatile porous flow simulator includes capabilities to

model multiphase, thermal, stress, and multicomponent reactive chemistry! 7urrent work using

this code includes simulation of methane hydrate formation, 76 seuestration, oil shale

e*traction, migration of both nuclear and chemical contaminants, environmental isotope

migration in the unsaturated :one, and karst formation!

%edit&%ther methods

"hese include mesh$free methods like the  3nalytic Element 9ethod (3E9) and the =oundary

Element 9ethod (=E9), which are closer to analytic solutions, but they do appro*imate the

groundwater flow euation in some way! "he =E9 and 3E9 e*actly solve the groundwater

flow euation (perfect mass balance), while appro*imating the boundary conditions! "hese

methods are more e*act and can be much more elegant solutions (like analytic methods are),

but have not seen as widespread use outside academic and research groups yet!