# Groundwater flow

### Environments and definitions

• groundwater is the water in the saturated zone (Fig)
• recharge is the water entering the saturated zone
• in the US about 10% of the rainfall becomes groundwater eventually. This amount equals the annual use of water in the US, about 3 inch per year
• residence time = reservoir/flux = ~4000 m / 3 inch/year = 50,000 y! This is a very rough estimate.
• water may stay in the groundwater reservoir between several days and thousands of years. We will discuss tracer techniques that may be used to derive residence times later in the class

### What drives groundwater flow?

• gravity is the dominating driving force
• water flows from high elevation to low elevation and from high pressure to low pressure, gradients in potential energy drive groundwater flow
• recharge and discharge
• in recharge areas water is added to groundwater
• in discharge areas water is lost from groundwater
• recharge occurs from the unsaturated zone or from surface waters
• groundwater discharge occurs into rivers, lakes, springs, or by evapotranspiration
• examples:
• "Puszta" in Hungary: groundwater is discharging in the low lands of the Great Hungarian Plain and leaves the dissolved salts behind -> reduction of soil quality -> bad conditions for agriculture
• example: evaporation in the Sahara, loss of valueable groundwater resources that were recharged in the last ice age (loss may be up to a few 10's inches per year)
• example springs, e.g. at Grand Canyon
• driving force for GW flow: gravity => pressure and elevation
• you can determine the energy needed to move a parcel of water from a reference surface to a location in the aquifer: E/m=g*y + p/rho => h=E/m/g=y+P/rho/g
• how do you measure the potential? => drill an observation well, the elevation of the water level in the well is a measure of the potential energy, this elevation is also termed 'hydraulic head'
• thought experiment: hydraulic head distribution in a lake
• if these measurements are taken at several locations, a contour map may be reconstructed and flow directions can be determined
• Darcy's law
• Darcy's laboratory apparatus (Fig)
• Q=-A*k*(h2-h1)/L
• Q is the flow rate, A the surface area, h the hydraulic head, L the distance between the two places where the hydraulic head has been measured, and k the hydraulic conductivity
• Q/A=q (specific discharge)
• the law is very similar to Ohm's law for electrical curcuits I = 1/R * U (current = voltage divided by resistance)
• hydraulic conductivity values vary over a wide range
• gravel: 10-2 - 1 m/s, clean sands: 10-5 - 10-2 m/s, clayey sands, fine sands: 10-8 - 10-3 m/s
• example for Darcy's law: k= 10-5 m/s, h2-h1 = 100m, L = 10km, A = 1m2 > Q = 3.15 m3/y; the K value above is typical for a sandstone aquifer
• the actual flow velocity v may be calculated with the following formula: v=Q/(A*n)=q/n, n is the porosity, and q the specific discharge
• n is the porosity, and q the specific discharge. If the porosity n is 30%, the flow velocity in the example above is 10.5 m/y
• Student excercise: determination of the hydraulic head of the 'groundwater model' (Fig)
• establish a flow from left to right in the model
• put dye into three wells tapping the upper (thick) aquifer and measure the hydraulic head relative to the bench as a function of distance from the recharge area, which is the left boundary of the sand in the box.
• after establishing a continuous flow in the model, let the discharge flow into a (weighted) beaker for approximately 10 minutes. Weigh the beaker afterwards and determine Q.
• A is the average cross sectional area of the sand perpendicular to the flow of the water, thickness * width
• plot the hydraulic head as a function of distance, and describe the function that you obtain
• calculate k using Darcy's law by using the hydraulic head measurements on both ends of the model
• what simplifying assumptions are we making here?
• Student excercise: determination of the porosity of the top part of the 'groundwater model' (Fig)
• inject some dye into one of the wells tapping the sand on the left side of the model
• while the model is running, determine the velocity at which the plume is moving
• use the above formula (n = q/v) to determine the porosity

### Aquifers ("bearing water")

• aquifers: geologic formations that are porous and permeable and yield significant amounts of water to springs or wells; aquitards, aquicludes: formations that allow little flow (aquitards) or no flow (aquicludes)
• geology of aquifers (show examples)
• unconsolidated sediments: loose granular deposit, particles are not cemented together (e.g.: Long Island)
• consolidated sediments, most important: sandstone, porosity varies depending on the degree of compaction (e.g. Zion, Bryce, and Grand Canyon National Parks)
• limestone: composed mainly of calcium carbonate, CO2 rich water dissolves limestone, e.g.: limestone caves, karst (e.g. Floridan aquifer)
• volcanic rock
• basalt lava, fractures (e.g.: Hawaii, Palisades)
• crystalline rocks: igneous and metamorphic rocks, e.g. Granite, have often very low porosity, flow through fractures
• porosities and hydraulic conductivities of different aquifer rocks
• confined and unconfined aquifers
• an unconfined aquifer has a water table (water table aquifer)
• a confined aquifer does not have a water table. If you drill a well, water will rise (in the well) above the top of the aquifer
• perched groundwater is groundwater sitting on top of a poorly permeable layer with an unconfined aquifer underneath

### Storage of groundwater in aquifers

• in many areas of the world the hydraulic head is declining with time because a lot of water is pumped out of the aquifer, example from the southern San Joaquin valley
• storage in unconfined and confined aquifers is different
• in unconfined aquifers the water pumped stems from drained void space
• in confined aquifers the water stems from decompression of the water and the sediments.
• the same change in water table represents a larger amount of water if taken from an unconfined aquifer as compared to a confined aquifer
• definition of the storage coefficient: yield per unit area and unit change in hydraulic head
• unit: m3/m/m2 (-> dimensionless)
• in unconfined aquifers the storage coeff. = porosity
• in confined aquifer much smaller ~10-6
• where is water being stored in confined aquifers? -> compressibility of water and change in aquifer structure
• land subsidence as a result of overpumping
• examples:
• the Dakota artesian basin: flowing artesian wells (hydraulic head above surface) are wells in which the water level is higher than the surface. A lot of wells were drilled into the Dakota basin, in South Dakota about 15000 wells. Most of them do not flow anymore
• New Mexico, where an old school well was still flowing when visited, why did it break?

### What information can be drawn from the hydraulic head?

• where the water is flowing (flownets, give examples)
• how fast it is flowing
• how much water there is -> storage coefficient

### How to measure hydraulic head and hydraulic conductivity?

• hydraulic head: install a well open to the aquifer only over a small distance (short screen), measure the level of the water in the well relative to a reference surface, for example sea level
• hydraulic conductivity: pumping tests
• shape of depression cone
• how does this cone look like in different geol. environments?
• quantification (Theis equation)

Student excercise: the 'groundwater model' (Fig)

• inject different dyes into one of the wells on the left into all three injection wells
• discussion of the elements of the model
• recharge and discharge areas, aquifers, pumping wells, artesian well, piezometers, land fill, river,.....
• springs may originate in artesian aquifers
• water table
• wells draw water from all directions
• cone of depression
• drawing water from a well can interfere with the ability of neighboring wells to produce water (they go dry!)
• groundwater is related to surface waters, use the lake as discharge area, by draining it, dye should show the movement of water; after closing the drain, lake should fill up again
• relation between confined and unconfined aquifers: pumping on one aquifer has not a big effect on the other one
• however, there is water moving through the confining bed
• texture of material affects flow rate: gravel has higer conductivity almost confined conditions, water should move upward! Also other plumes in sand should spread more slowly
• inhomogeneities in the aquifers affect flow

### Resources

• Manning, J.C. (1997) Applied Principles of Hydrology. Prentice Hall, third edition, 276p.
• Freeze, R.A. and Cherry, J.A. (1979) Groundwater. Prentice Hall, 604p.