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# Hydrogeology

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).

 Contents

## 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 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 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 (Reynolds number less than 1). Therefore, the analytical foundations of groundwater flow 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, 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

In order to further characterize aquifers and aquitards some primary and derived physical properties are introduced.

$h = \psi + z \,$

$\psi = \frac{p} {\gamma}$

In the definition of ψ, p is the pressure (units of force per area, kPa or psi), and γ is the specific weight of water (related to the density as γ = , units of force per volume, N/m³ or lbf/ft³). 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 a hydraulic 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 (which is defined as change in hydraulic head per length of flow path, or (hahb)/L),

$0.25 \mbox{ m} = \frac{1 \mbox{ m} - 0.75 \mbox{ m}}{1 \mbox{ m}}$.

This gradient is positive (increasing) upward, and Darcy's law indicates that flow would be out the bottom valve on the column (water flows "downhill", from high hydraulic head to low hydraulic head). Also note that water would flow upward in the second column if the hydraulic head gradient was "pointing" that way, even though that is "up" in the column.

Atmospheric Pressure
Even though it is convention to use gauge pressure in the calculation of hydraulic head, it is more correct to use total pressure (gauge pressure + atmospheric pressure), since this is truly what drives groundwater flow. Often detailed observations of barometric pressure are not available at each well through time, so this is often disregarded (contributing to large errors at locations where hydraulic gradients are low or the angle between wells is acute.)

The effects which changes in atmospheric pressure have water levels observed in wells has been known for many years. The effect is a direct one, an increase in atmospheric pressure is an increase in load on the water in the aquifer, which increases the depth to water (lowers the water level elevation). Pascal first qualitatively observed these effects in the 1600s, and they were more rigorously described by Buckingham using air flow models in the early 1900s.

### 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).

This article mostly pertains to porosity in unconsolidated alluvial sands and gravels; consolidated rocks (e.g. sandstone, shale, granite or limestone) potentially have more complex "dual" porosities. The rock itself may have a certain (low) porosity, and the fractures (cracks and joints), or dissolution features may create a second (higher) porosity. The interaction of these porosities is complex and often makes simple models highly inaccurate.

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.

Well sorted (grains of approximately all one size) materials have higher porosity than similarly sized poorly sorted materials (where smaller particles fill the gaps between larger particles). The graphic illustrates how some smaller grains can effectively fill the pores (where all water flow takes place), drastically reducing porosity and hydraulic conductivity, while only being a small fraction of the total volume of the material. For tables of common porosity values for earth materials, see references below.

### Water content

Water content (θ) is also a directly measurable property; it is either the volumetric (by volume) or gravimetric (by weight) 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. The water table (or more precisely the top of the capillary fringe above the water table) is the dividing line between saturated and unsaturated conditions.

Basically every point in the Earth's subsurface has a non-zero water content. Even in the driest places (e.g., deserts) have measurable amounts of soil moisture. The amount may be so low that it is physically impossible to remove it, but the classical view that saturation is effectively zero above the water table and 1 below the water table, only works as an approximation.

One of the main complications which arises in studying the vadose zone, is the fact that the unsaturated 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 analogous 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 certain 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. This means that, for example, k will go up if the water in a porous media is heated (reducing the viscosity of the water), but κ will remain constant. The two are related through the following equation

$k = \frac{\kappa \gamma}{\mu}$

Where γ is the specific gravity of water (with units of force per volume, N/m³ or lbf/ft³), μ is the dynamic viscosity of water (with units of pascal seconds (Pa·s), poise, or lbf·s/ft²) 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 k (for situations with two-dimensional flow), for a uniform aquifer T would be the material's k times its thickness (often called 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 (the distribution is often considered to be lognormal),
• change rapidly in space (sometimes considered to be randomly spatially distributed, or stochastic in nature),
• are directional (k is a tensor; vertical k values can be several orders of magnitude smaller than horizontal k values),
• 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 column flow tests or inverse computer simulation, (sometimes also from grain size analyses), and
• are very dependent (in a non-linear way) on the water content (this makes solving the unsaturated flow equation difficult). In fact, the variably saturated k for a single material varies over a wider range than the saturated k values for all types of materials (see chart below for an illustrative range of the latter).

Ranges of saturated hydraulic conductivity (k) values found in nature

 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 Relative 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 Clay & Organic Peat Layered Clay Fat / Unweathered Clay Consolidated Rocks Highly Fractured Rocks Oil Reservoir Rocks Fresh Sandstone Fresh Limestone, Dolomite Fresh Granite

Source: modified from Bear, 1972

### Specific storage and specific yield

Specific storage, storativity and specific yield (Ss, S and Sy) 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 inverse length (1/m). 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 = Ssb. Storativity is a dimensionless quantity.

In terms of basic physical properties, Specific Storage can be expressed as

Ss = γ(cb + ncw),

where γ is the specific weight of water (units of force per volume, N/m³ or lbf/ft³), n is the porosity of the material (a ratio between 0 and 1), cb is the compressibility of the bulk aquifer material and cw is the compressibility of water (compressibility has units of length squared per force, e.g., m²/N). The compressibility terms relate a given change in stress to a change in volume (a strain). These two terms can be defined as:

$c_b = -\frac{dV_t}{d\sigma_e}\frac{1}{V_t}$

$c_w = -\frac{dV_w}{dp}\frac{1}{V_w}$

These equations relate a change in total or water volume (Vt or Vw) per change in applied stress (effective stress — σe or pore pressure - p) per unit volume. The compressibilities (and therefore also Ss) can be estimated from laboratory consolidation tests (in an apparatus called a consolidometer), using the consolidation theory of soil mechanics (developed by Karl Terzaghi).

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. Tables can be found in the references which give typical ranges for Sy, Ss and S.

Specific storage is the primary mechanism for releasing water in confined aquifers, while specific yield is the primary mechanism for releasing water in unconfined (water table) aquifers.

## Governing equations

### Darcy's Law

see Darcy's law article

### Groundwater flow equation

Mass Balance
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 (Δt) 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.

$\frac{\Delta M_{stor}}{\Delta t} = \frac{M_{in}}{\Delta t} - \frac{M_{out}}{\Delta t} - \frac{M_{gen}}{\Delta t}$

Diffusion Equation (Transient Flow)
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:

$S_s \frac{\partial h}{\partial t} = -\nabla \cdot q - G$

This is known in other fields as the diffusion equation or heat equation, it is a parabolic partial differential equation (PDE). 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

$S_s \frac{\partial h}{\partial t} = -\nabla \cdot (-\nabla kh) - G$

Now if hydraulic conductivity (k) is a scalar, rather than a tensor, (same value in all directions) it can be taken out of the spatial derivatives, which simplifies the equation to

$S_s \frac{\partial h}{\partial t} = k\nabla^2 h - G$

Dividing through by the specific storage (Ss), puts hydraulic diffusivity (α = k/Ss or equivalently, α = T/S) on the right hand side. The hydraulic diffusivity is proportional to the speed at which a finite pressure pulse will propagate through the system (high α means fast propagation of signals). The groundwater flow equation then becomes

$\frac{\partial h}{\partial t} = \alpha\nabla^2 h - G$

Rectangular Cartesian Coordinates
Especially when using rectangular grid finite-difference models (e.g. MODFLOW), we deal with Cartesian coordinates. In these coordinates the general Laplacian operator becomes (for three-dimensional flow) specifically

$\frac{\partial h}{\partial t} = \alpha \left[ \frac{\partial^2 h}{\partial x^2} +\frac{\partial^2 h}{\partial y^2} +\frac{\partial^2 h}{\partial z^2}\right] - G$

Circular Cylindrical Coordinates
Another useful coordinate system is 3D cylindrical coordinates (typically where a pumping well is a line source located at the origin — parallel to the z axis — causing converging radial flow), where the above equation becomes (r being radial distance and θ being angle)

$\frac{\partial h}{\partial t} = \alpha \left[ \frac{\partial^2 h}{\partial r^2} + \frac{1}{r} \frac{\partial h}{\partial r} + \frac{1}{r^2} \frac{\partial^2 h}{\partial \theta^2} +\frac{\partial^2 h}{\partial z^2} \right] - G$

Polar Coordinates
For most generic radial flow problems, there is a symmetry in θ and if the pumping well is fully penetrating, then all flow is horizontal and radial, so the problem becomes 1D (assuming that the pumping well is at the origin). When switching from 3D to 2D (or here 1D) flow, the definition of α changes conceptually (but not in value), now becoming α = T/S (where T is thickness times k and S is thickness times Ss). This simplifies the problem to

$\frac{\partial h}{\partial t} = \alpha \left[ \frac{\partial^2 h}{\partial r^2} + \frac{1}{r} \frac{\partial h}{\partial r} \right] - G$

Assumptions
This equation represents 2D flow to a pumping well (a sink of strength G), located at the origin. Both this equation and the Cartesian version above are the fundamental equation in groundwater flow, but to arrive at this point requires considerable simplification. Some of the main assumptions which went into both these equations are:

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.

If the aquifer has recharging boundary conditions a steady-state may be reached (or it may be used as an approximation in many cases), and the diffusion equation (above) simplifies to the Laplace equation.

$0 = \alpha\nabla^2 h - G$

This equation has many analogs in other fields, and can be solved using various techniques. A common method for solution of this equations in civil engineering and soil mechanics is to use the graphical technique of drawing flownets.

## 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. The most common means of analytically solving the diffusion equation in the hydrogeology literature are:

• Laplace and Fourier transforms (to reduce the number of dimensions of the PDE),
• similarity transform (also called the Boltzmann transform, and is commonly how the Theis solution is derived),
• separation of variables, which is more useful for non-Cartesian coordinates, and
• Green's functions, which is another common method for deriving the Theis solution — from an instantaneous point source in 3D free space (no boundaries.)

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 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, typically used to analyze the results of an aquifer test.

The Theis equation was adopted by Charles Vernon Theis (working for the US Geological Survey) in 1935 (see references), from heat transfer literature (with the mathematical help of C.I. Lubin), for two-dimensional radial flow to a point source in an infinite, homogeneous aquifer. It is simply

$s=\frac{Q}{4\pi T}W(u)$

$u=\frac{r^2 S}{4Tt}$,

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 discharge (pumping) rate of the well (volume divided by time, or 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 or ft), t is the time since pumping began (minutes or seconds), and W(u) is the "Well function" (called the exponential integral, E1, 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 reproduce 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 (in addition to 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 (non-leaky) top and bottom boundaries 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 (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 below.

There are two broad categories of numerical methods: gridded or discretized methods and non-gridded or mesh-free methods. The common finite difference method and finite element method (FEM) are both gridded. 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 (see further reading section below for books on these subjects).

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). 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 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 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.

Apllication 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 density-dependent 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
These 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 groundwater 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.

## References

• Theis, Charles V., 1935. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage, Transactions, American Geophysical Union, 16, 519-524.
• 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

### 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 0471597627
• 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 Screen. ISBN 0961645601
• Freeze, R.A. & Cherry, J.A., 1979. Groundwater, Prentice-Hall. — A classic text; like a older version of Domenico and Schwartz. ISBN 0133653129
• Todd, David Kieth, 1980. Groundwater Hydrology Second Edition, John Wiley & Sons. — Case studies and real-world problems with examples. ISBN 047187616X

### 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 0120594854
• 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

### 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 0123165504
• Harr, Milton E., 1962. Groundwater and seepage, Dover. — a more civil engineering view on groundwater; includes a great deal on flownets. ISBN 0486668819
• 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 1566703751
• 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 0046200118