**Hydrogeology** (*hydro-* meaning water, and *-geology* meaning the study of rocks) is the part of hydrology 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). ## Introduction
Hydrogeology (like most earth sciences) is an interdisciplinary subject; it can be difficult to account fully for the the chemical, physical, biological and even legal interactions between soil, water, nature and man. Although the basic principles of hydrogeology are very intuitive (e.g., water flows "downhill"), the study of their interaction can be quite complex. 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 formations (typically less than 450 metre -or roughly 1,500 feet- 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 (Reynolds number much less than 1). Therefore, the foundations of hydrogeology were taken from the fields of fluid dynamics and mechanical engineering. The mathematical relationships used to describe the flow of groundwater 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 transient diffusion of heat in a solid and some solutions to hydrological problems have borrowed solutions from the heat transfer literature. Traditionally, the movement of groundwater has been studied separately from surface water, climatology, andeven 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 In order to further characterize aquifers and aquitards some primary and derived physical properties are introduced.
### Hydraulic Head "Diagram illustrating relation between heads in hydrostatic state" **Click to Enlarge.** "Diagram illustrating relation between heads for downward flow" **Click to Enlarge.** *Pressure head*, *elevation head*, and *hydraulic head* (ψ, z and h) are directly measurable state properties, (the word *head* means that the quantity is expressed in terms of a depth of water - 1.0 m of head is equivalent to 52 kPa or 1 ft of head is approximately equal to 2.3 psi of pressure). It is convention to use gauge pressure (pressure measured greater than atmospheric pressure), when speaking of pressure (unless absolute pressure is explicitly specified). *Pressure head* is the gauge pressure at a point. *Elevation head* is the relative amount of potential an object has due to its vertical position, compared to an arbitrary datum (it always increases 1:1 with elevation). *Hydraulic head* is the sum of pressure and elevation heads; it is the actual driving force which makes groundwater flow from one place to another (if the flow were not slow {if the Reynolds number were larger than unity}, a velocity head would need to be included in the total head as well.) h = ψ + z The first figure illustrates these how these three heads relate for a hydrostatic case (no flow). The top of the hydrostatic column is a water table (atmospheric, or zero pressure head), while a tube or hose connected to the outlet of the bottom is held at the same height as the top of the collumn. Hydraulic head is constant (no hydraulic head gradient), elevation head increases 1:1 (as it always does), and typically pressure head is determined as the difference of the two. The second figure illustrates the same three heads when there is steady-state flow through the column, due to ahydraulic head gradient (red line). The pressure head is still zero at the top of the column (water table conditions), but the tube connected to the outflow from the bottom of the column is held at an elevation of 0.75 m, which produces a net hydraulic head gradient of , (gradient = (h_{a} - h_{b}) / length). This gradient is positive (increasing) upward, and Darcy's law indicates that flow would be out the bottom valve on the column (water flows from high head to low head).
### Porosity Porosity (n) is a directly measurable property; it is the fraction of the volume of porous media which is not solid material (typically filled with the fluids air and water); it is a fraction between 0 and 1, typically ranging from less than 0.01 for solid granite to more than 0.5 for peat and clay. *Effective porosity* refers the fraction of the total volume in which fluid flow is effectively taking place (this excludes dead-end pores or non-connected cavities). Porosity is indirectly related to hydraulic conductivity; for two similar sandy aquifers, the one a higher porosity will typically have a higher hydraulic conductivity (more open area for the flow of water), but there are many complications to this relationship. Clays, which typically have very low hydraulic conductivity also have very high porosities (due to the structured nature of clay minerals), which means clays can hold a large volume of water per volume of bulk material, but they do not release water very quickly. "Diagram illustrating porosities of well and poorly sorted materials" **Click to Enlarge.** Well sorted (grains of approximately all one size) materials have higher porosity than poorly sorted materials (where smaller particles fill the gaps between larger particles). The following table lists some ranges of values of total porosity for common earth materials.
**Porosity (n) values found in nature**
**material** | **typical n range (fraction)** | well sorted sand or gravel | 0.25-0.40 | moderately sorted sand or; gravel | 0.15-0.30 | poorly sorted sand or gravel | 0.05-0.15 | clay | 0.30-0.50 | fresh granite | 0.001-0.20 | fractured granite | 0.20-0.45 | ### Water Content Water content (θ) is also a directly measurable property; it is either the volumetric or gravimetric 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 the total porosity. Saturated conditions occur when the porosity and the water content are equal, (*saturation* is a fraction ranging between 0 and 1, indicating the percentage of porosity filled with water.) Unsaturated conditions are everything other than this case, and they make up the subject of vadose zone hydrogeology. One of the main complications in the vadose zone, is the fact that hydraulic conductivity is a function of the water content of the material. As a material dries out, the connected wet pathways through the media become smaller, the hydraulic conductivity decreasing with lower water content in a very non-linear fashion.
### Hydraulic Conductivity Hydraulic Conductivity, Transmissivity and Intrinsic Permeability (k, T and κ) are indirect or secondary properties, they cannot be directly measured. Hydraulic conductivity is the proportionallity constant in Darcy's law, which relates the amount of water which will flow through a unit cross-sectional area of aquifer under a unit gradient of hydraulic head. It is analagous to the thermal conductivity of materials in heat conduction, or 1/resistivity in electrical circuits. The hydraulic conductivity (k - the English letter kay) is specific to the flow of a certian fluid (typically water, sometimes oil or air); intrinsic permeability (κ - the Greek letter kappa) is a parameter of a porous media which is independent of the fluid. The two are related through the following equation Where ρ is the density of water (with units of kg/m³), g is the acceleration of gravity (units of m²/s), μ is the dynamic viscosity of water (units of Ns/m²), and κ is the intrinsic permeability (units of m² or the oil industry unit of the Darcy). A sand or gravel aquifer would typically have a high k value, and a clay or unfractured granite would have a low k value. Transmissivity is simply a vertically averaged form of k (for situations with two-dimensional flow), which for a uniform aquifer or aquitard would be the material's k times its thickness (b). Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and gal/(day/ft²) ); transmissivity then has units with dimensions of length squared per time. The following table gives some typical ranges (illustrating the many orders of magnitude which are likely) for k values. Hydraulic conductivity (k) is the most complex and important of the hydrogeologic aquifer properties; values found in nature: - range over many orders of magnitude (often considered to be randomly spatially distributed, or stochastic in nature),
- are directional (k is a tensor; it has different values in different directions), and
- are scale dependent (testing a m³ of aquifer will generally produce different results than a similar test on only a cm³ sample of the same aquifer).
- must be determined indirectly through field pumping tests, laboratory flow tests or inverse computer simulation.
**Hydraulic conductivity (k) and intrinsic permeability (κ) values found in nature** - adapted from Bear, 1972
Hydraulic Conductivity: k (cm/s) | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 | 0.0001 | 10^{−5} | 10^{−6} | 10^{−7} | 10^{−8} | 10^{−9} | 10^{−10} | Permeability | Pervious | Semi-Pervious | Impervious | Aquifer | Good | Poor | None | Unconsolidated Sand & Gravel | Well Sorted Gravel | Well Sorted Sand or Sand & Gravel | Very Fine Sand, Silt, Loess, Loam | | Unconsolidated Organic | | Peat | Layered Clay | Fat / Unweathered Clay | Consolidated Rocks | Highly Fractured Rocks | Oil Reservoir Rocks | Fresh Sandstone | Fresh Limestone, Dolomite | Fresh Granite | Intrinsic Permeability: κ (cm²) | 0.001 | 0.0001 | 10^{−5} | 10^{−6} | 10^{−7} | 10^{−8} | 10^{−9} | 10^{−10} | 10^{−11} | 10^{−12} | 10^{−13} | 10^{−14} | 10^{−15} | Intrinsic Permeability: κ (milli Darcies) | 10^{+8} | 10^{+7} | 10^{+6} | 10^{+5} | 10,000 | 1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 | 0.0001 | ### Specific Storage and Specific Yield Specific storage, Storativity and Specific yield (S_{s}, S and S_{y}) are also indirect or secondary properties, they cannot be directly measured. *Specific storage* the amount of water which a given volume of aquifer will produce, provided a unit change in hydraulic head is applied to it (while it still remains fully saturated); it has units of dimension length^{-1}. Storativity is the vertically averaged specific storage value for an aquifer or aquitard. For a homogeneous aquifer or aquitard they are simply related by *S* = *S*_{s} * *b*. Storativity is a dimensionless quantity.
*Specific yield* is a ratio between 0 and 1 indicating the volumetric fraction of the bulk aquifer volume that a given an aquifer will yield when all the water is allowed to drain out of it under the forces of gravity. Roughly, this is the effective porosity, but there are several subtle things which make this value more complicated than it seems. Some water always remains in the formation, even after drainage; it clings to the grains of sand and clay in the formation. Also, the value of specific yield may not be fully realized until very large times, due to complications caused by unsaturated flow. the following table gives some typical ranges for S_{y}. Specific storage is associated with confined aquifers, while specific yield is associated with unconfined (water table) aquifers.
**Specific Yield (S**_{y}) values found in nature
**material** | **typical S**_{y} values (fraction) | gravel | 0.23 | coarse sand | 0.25 | medium sand | 0.28 | fine sand | 0.23 | clay | 0.03 | fresh granite | 0.05 | fractured granite | 0.15 | ## Governing Equations ### Darcy's Law see Darcy's law article
### Groundwater Flow Equation A mass balance must be performed, along with Darcy's law, to finally arrive at the transient groundwater flow equation. This balance is analogous to the energy balance used in heat transfer to arrive at the heat equation. It is simply a statement of bookkeeping, that for a given control volume, aside from sources or sinks, mass cannot be created or destroyed. The conservation of mass states that for a given increment of time (Δ t</math>) the difference between the mass flowing in across the boundaries, the mass flowing out across the boundaries, and the sources within the volume, is the change in storage. Mass can be represented as density times volume, and under most conditions, water can be considered incompressible. The mass flux rates then become volume flux rates (as are found in Darcy's law). Using Taylor series to represent the in and out flux terms across the boundaries of the control volume, and using the divergence theorem to turn the flux across the boundary into a flux over the entire volume, the final form of the groundwater flow equation (in differential form) is: This mathematical statement indicates that the change in head with time (left hand side) equals the negative divergence of the flux (q) and the source terms (G). This equation has both head and flux as unknowns, but Darcy's law relates flux to hydraulic heads, so substituting it in for the flux (q) leads to Now if hydraulic conductivity (k) is homogeneous (constant in space, so it can be taken out of the gradient operation), this leads to Typically we deal with Cartesian coordinates, so the Laplacian operator becomes (for three-dimensional flow) -
This equation is the fundamental equation in groundwater flow, but to arrive at this point requires considerable simplification. Some of the main assumptions which went into this form of the equation are: - the aquifer material is incompressible (loading doesn't affect water levels)
- the ground water is flowing slowly (Reynolds number << 1)
- the hydraulic conductivity (k) is homogeneous and isotropic
Despite these large assumptions, the groundwater flow equation does a good job of representing the distribution of heads in aquifers due to a transient distribution of sources and sinks.
## Calculation of Groundwater Flow 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. To solve it we need both initial conditions (heads at time t=0) and boundary conditions (representing either the physical boundaries of the domain, or an approximation of the domain beyond that point). Often the initial conditions are supplied to a transient simulation, by a corresponding steady-state simulation (where the time derivative 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 conformal mapping, etc.). Analytic solutions typically are also simply an equation, which 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. The Theis equation was adopted by C.V. Theis (working for the US Geological Survey) in 1935, from heat transfer literature, for two-dimensional radial flow to a point source in an infinite, homogeneous aquifer. It is simply
- ,
where s is the drawdown (change in hydraulic head at a point since the beginning of the test), u is a dimensionless time parameter, Q is the pumping rate of the well (m³/s), T and S are the transmissivity and storativity of the aquifer around the well (m²/s and unitless), r is the distance from the pumping well to the point where the drawdown was observed (m), t is the time since pumping began (s), and W(u) is the "Well function" (called the Exponential integral in non-hydrogeology literature). Typically this equation is used to find the average T and S values near a pumping well, from drawdown data collected during an aquifer test. This is a simple form of inverse modeling, since the result (s) is measured in the well, r, t and Q are observed, and values of T and S which best re-produce the measured data are put into the equation until a best fit between the observed data and the analytic solution is found. As long as none of the additional simplifications which the Theis solution requires (above those required by the groundwater flow equation) are violated, the solution should be very good. The assumptions required by the Theis solution are: - homogeneous, isotropic, confined aquifer
- well is fully penetrating (open to the entire thickness of aquifer)
- aquifer is infinite in radial extent
- horizontal (not sloping), flat, impermeable top and bottom of aquifer
Even though these assumptions aren't always met, depending on the degree to which they are violated (e.g., if the boundaries of the aquifer are well beyond the part of the aquifer which will be tested by the pumping test) the solution may still be useful. The interpretation of the Theis equation, and the many other related pumping test methods (which are more specific cases of the Theis equation) was the main task of the practicing hydrogeologist, before the proliferation of cheap computing resources. Now most hydrogeology is done using numerical models of aquifer systems, but analytic methods have not lost their usefulness; they are the necessary first step, back of the envelope calculation which must be done to get an understanding of a situation before moving on to more powerful (and more complex) methods.
### 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, 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 below. There are two broad categories of numerical methods: gridded or discretized methods and non-gridded or mesh-free methods. The common finite difference and finite element method (FEM) both are gridded methods. The analytic element method (AEM) is a completely mesh-free method, while the boundary integral equation method (BIEM) is somewhere in between these two endmembers.
**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, then linking together all the elements using conservation of mass between the elements. This results in a system which overall approximates the groundwater flow equation, but exactly matches the boundary conditions (they are specified in the elements which intersect them). MODFLOW is a well-known example of a general finite difference groundwater flow model. It was developed by the US Geological Survey (USGS) in 1988 as a modular and extensible simulation tool for modeling groundwater. 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 text 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 and groundwater models and chemical reaction models), because of the simple, well documented nature of MODFLOW. 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 density-dependant flow model by the USGS, Hydrus, a commercial unsaturated flow model; and FEMLab a commercial general modeling environment), but they are 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 dependant flow, coupled heat and groundwater flow, etc.)
**Other Methods** include mesh-free methods like the Analytic Element Method (AEM) and the Boundary Integral Equation Method (BIEM), which are closer to analytic solutions, but they do approximate the groundater flow equation in some way. The BIEM 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.
## See also **Texts on the subject of Hydrogeology** - Anderson, Mary P. & Woessner, William W., 1992
*Applied Groundwater Modeling*, Academic Press. -- A good introduction to groundwater modeling, a little bit old, but the methods are still very applicable. ISBN 0120594854 - Bear, Jacob, 1972.
*Dynamics of Fluids in Porous Media*, Dover. -- A very mathematical, rigorous treatment of the subject, and an inexpensive Dover book. ISBN 0486656756 - 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 0471597627 - Driscoll, Fletcher, 1986.
*Groundwater and Wells*, US Filter / Johnson Screens. -- Practical book illustrating the actuall 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 Johnons Well Screens. ISBN 0961645601 - Fetter, C.W., 2001.
*Applied Hydrogeology* Fourth Edition, MacMillian. -- Probably most common hydrogeology textbook found in introductory college courses on the subject. It has an associated website (*http://www.appliedhydrogeology.com/*). ISBN 0130882399 - Freeze, R.A. & Cherry, J.A., 1979.
*Groundwater*, Prentice-Hall. -- A classic text; a bit older, but very thorough. ISBN 0133653129 - Haitjema, Henk M., 1995.
*Analytic Element Modeling of Groundwater Flow*, Academic Press. -- Good introduction to analytic solution methods, especially the Analytic Element Method (AEM). ISBN 0123165504 - Liggett, James A. & Liu, Phillip .L-F., 1983.
*The Boundary Integral Equation Method for Porous Media Flow*, George Allen and Unwin, London. -- Good book on BIEM (sometimes called BEM), good examples, makes a good introduction to the method. ISBN 0046200118 - Todd, David Kieth, 1980.
*Groundwater Hydrology* Second Edition, John Wiley & Sons. -- More info about wells, well construction and application, with examples. ISBN 047187616X - 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 0471384771 ## External links - Hydrogeology basics (
*http://www.epa.gov/seahome/groundwater/src/geo.htm*) by the Environmental Protection Agency (EPA) - EPA drinking water standards (
*http://www.epa.gov/safewater/*) - a primer on groundwater flow (
*http://www.uwsp.edu/water/portage/undrstnd/gwmove2.htm*) with illustrations. - US Geological Survey water resources homepage (
*http://water.usgs.gov/*) -- a good place to find free data (for both surface water and groundwater) and free groundwater modeling software like MODFLOW. - US Geological Survery TWRI index (
*http://water.usgs.gov/pubs/twri/*) -- a series of instructional manuals covering common procedures in hydrogeology. They are freely available online as .pdf files - International Ground Water Modeling Center (IGWMC) (
*http://typhoon.mines.edu/*) -- an educational repository of groundwater modeling software which offeres support for most software, some of which is free. |