Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13The governing equation for groundwater flow can be written usingtotal head (h) or pressure (p).Why do we typically use head (h) as the dependent variable? = density of waterh = z + p/gTotal head (h) = elevation head + pressure headK = k g /  K = hydraulic conductivity (L/T)k = permeability (L) = density = viscosityg = 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 5 - 10 C.Rule of thumb: The average groundwater temperature at around10 m below surface is 1 to 2 C warmer than the average air temperature.For constant density,K is larger at warmer temperatures.3.98 CK = k g /  K = hydraulic conductivity (L/T)k = permeability (L) = density = viscosityg = accelerationIsotherms showing a plume of “hot” water in the aquifer(Winslow 1962)HeadTemperature(with advectionof groundwater)Conduction onlyIf temperature is a variable, we needto couple the groundwater flow modelto a heat transport model.groundwaterflowHeat flowSpecified head; specified temperatureNo flow;No heat fluxNo flow; specified heat fluxNo flow;No heat fluxCross section through a groundwater basinBoundary conditions for a coupled groundwater flow and heat flow modelHeatHead - Shallow BasinResults from SHEMATHead – Deep BasinResults from SHEMATTemperature - Shallow Basin10 – 18 CResults from SHEMATTemperature - Deep Basin 10 – 28 CResults from SHEMATIn applications of groundwater models to shallow problemsin freshwater aquifers, we typically assume groundwater hasa constant temperature and density and viscosity of waterare constants. Therefore, we can use total head, h, as the dependentvariable and hydraulic conductivity, K.Furthermore, density is not constant when brines are presentor in coastal aquifers where sea water is present. A governing equationthat 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 thegoverning equation is written in terms of pore pressure, p, allowingdensity and viscosity to vary. Permeability, k, is used instead of K.The flow model is coupled to a heat transport model that