1. 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

2. 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.

3. Mean temperature of groundwater (  C) at a depth of 10m. Annual variation is 5 - 10  C.

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

5. For constant density, K is larger at warmer temperatures. 3.98  C K = k  g /  K = hydraulic conductivity (L/T) k = permeability (L)  = density  = viscosity g = acceleration

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

7. Head Temperature (with advection of groundwater) Conduction only If temperature is a variable, we need to couple the groundwater flow model to a heat transport model. groundwater flow Heat flow

8. Specified head; specified temperature No flow; No heat flux No flow; specified heat flux No flow; No heat flux Cross section through a groundwater basin Boundary conditions for a coupled groundwater flow and heat flow model Heat

9. Head - Shallow Basin Results from SHEMAT

10. Head – Deep Basin Results from SHEMAT

11. Temperature - Shallow Basin 10 – 18  C Results from SHEMAT

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

13. 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.