The governing equation for groundwater flow can be written using total head (h) or pressure (p). Why do we typically use head (h) as the dependent variable?

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Presentation transcript:

The governing equation for groundwater flow can be written using total head (h) or pressure (p). Why do we typically use head (h) as the dependent variable?  = density of water h = z + p/  g Total head (h) = elevation head + pressure head

K = k  g /  K = hydraulic conductivity (L/T) k = permeability (L)  = density  = viscosity g = acceleration Hydraulic conductivity is dependent on density and viscosity of water. Density and viscosity are dependent on temperature of water.

Mean temperature of groundwater (  C) at a depth of 10m. Annual variation is  C.

Rule of thumb: The average groundwater temperature at around 10 m below surface is 1 to 2  C warmer than the average air temperature.

For constant density, K is larger at warmer temperatures  C K = k  g /  K = hydraulic conductivity (L/T) k = permeability (L)  = density  = viscosity g = acceleration

Isotherms showing a plume of “hot” water in the aquifer (Winslow 1962)

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Head – Deep Basin Results from SHEMAT

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Temperature - Deep Basin 10 – 28  C Results from SHEMAT

In applications of groundwater models to shallow problems in freshwater aquifers, we typically assume groundwater has a constant temperature and density and viscosity of water are constants. Therefore, we can use total head, h, as the dependent variable and hydraulic conductivity, K. Furthermore, density is not constant when brines are present or in coastal aquifers where sea water is present. A governing equation that allows for variation in density is used in these applications as well. In applications of groundwater models to geological problems (e.g., earthquakes, fluid movement along deep-seated faults, plate tectonics), temperature is an important variable and the governing equation is written in terms of pore pressure, p, allowing density and viscosity to vary. Permeability, k, is used instead of K. The flow model is coupled to a heat transport model that calculates temperatures.