Water and Groundwater

Properties of water

• water is a very unusual substance because of the hydrogen bonds it forms (Fig)
• qualitative Summary of the most importnat properties (Fig)
• details on properties of water can be found here

Global water budget

• Earth's water inventory (Fig)
• groundwater in the hydrologic cycle (Fig)
• hydrological cyclereservoirs and fluxes (Fig)
• there is significant uncertainty in some of these numbers (Fig)
• residence times
  
• atmosphere: 2 weeks
• surface waters: 4 years
• groundwater: 20,000 years

Groundwater

• groundwater is the water in the saturated zone (Fig) (Fig)
  
• recharge is the water entering the saturated zone
• in many parts of the world, groundwater is the only source of fresh water
• 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
• Water use in the US (Fig)
• 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
• management of catchment areas  requires understanding of groundwater flow
• many environmental issues involve groundwater

Conceptual model of groundwater flow

the flow of water through a porous medium (Fig 6.1)

water flows tortuous paths

geometry of channels is very complex

frictionles flow is totally meaningless!

conceptual model of flow through a porous medium is flow through a bundle of very small (capillary) tubes of different diameters (Fig 6.2)

the flow (Q) through a horizontal tube can be described as: Q = -p*D⁴/(128*m)*dp/dx (Poiseuille's law)

=> size of the capillary tubes is important!

Darcy's law

• what drives groundwater flow?
• water flows from high elevation to low elevation and from high pressure to low pressure, gradients in potential energy drive groundwater flow
• two ways how to derive the potential energy:
• 1: Bernoulli
• Bernoulli equation said: u²/(2*g) + z +p/(r*g) = constant, means: velocity head + elevation head + pressure head = total head
• in groundwater flow, we cannot make the assumption that there is no friction, therefore the  head is not constant
• also u is so small that that term can be typically neglected
• 2: direct determination of potential energy
• lifting up a parcel of water: W₁=m*g*z
• creating space for it in the groundwater system: W₂=p*V
• total work/m = g*z + p/r or h =  z + p/rg
• groundwater flows from high to low  head
• how do you measure the head or potential? => drill an observation well, the elevation of the water level in the well is a measure of the potential energy at the opening of the well: h=z + p/rg = z + F/(Arg) ......
• in 1856, a French hydraulic engineer named Henry Darcy published an equation for flow through a porous medium that today bears his name (Fig. 6.3)
• Q = KA (h₁-h₂)/L or q = Q/A = -K dh/dl, h: hydraulic head, h = p/rg + z
• q = Q/A is the specific discharge [L/T], dh/dl is the hydraulic gradient
• K is the hydraulic conductivity [L/T]
• the law is very similar to Ohm's law for electrical curcuits I = 1/R * U (current = voltage divided by resistance)
• the orginal Darcy experiment yielded these data (Fig 6.4)
• the analogy between Darcy's law and Poiseulle's law suggests that K = (const*d²)*rg/m
• the first term (const*d²) is k, the intrinsic permeability [L²], summarized the properties of the porous medium, while rg/m describe the fluid
• hydraulic conductivities and permeabilities vary over many orders of magnitude (Fig 6.5)

Example: calculation of a typical hydraulic gradient of 1/100 in a salt formation with a hydraulic conductivity of 10^-10 m s^-1 will produce a specific discharge of 10^-12 m s-1, or less than 1 mm per 30 years!
• specific discharge has the dimension of a velocity, but it is not the velocity at which the water flows in the porous medium, the water has to squeeze through the pores
•  tagged parcels that are averaged together, will appear to move through a porous medium at a rate that is faster than the specific discharge
• porosity is the fraction of a porous material which is void space f = V_void/V_total
• the mean pore water velocity is then: v = q/f (Fig)
• Darcy's law has been found to be invalid for high values of Reynolds number and at very low values of hydraulic gradient in some very low-permeability materials, such as clays.
• example :
• 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*f)=q/f, f 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

Water in natural formations

• an aquifer is a saturated geological formation that contains and transmits "significant" quantities of water under normal field conditions (=> gravel, sand, volcanic and igneous rocks, limestone) (Fig 6.6) (Fig)
  
• an aquiclude is a formation that may contain water but does not transmit significant quantities (clays and shales)
• an aquitard is a formation with relatively low permeability
• confined and unconfined (water-table) 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
• the height to which water rises in a well defines the piezometric or potentiometric surface
• 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 (Fig 6.5)

Resources

Freeze, R.A. and Cherry, J.A. (1979) Groundwater. Prentice Hall, 604p.

Hornberger, G.M., Raffensberger, J.P., Wiberg, P.L., and Eshleman, K.N. (1998) Elements of physical hydrology. Johns Hopkins University Press,  Baltimore, 302p.

see also BC 3025 Hydrology class