Basic Theory and Ground Properties
Deng (2004) introduced a theoretical background on underground thermal energy systems in his dissertation on standing column wells. The contents in this chapter are mainly based on Deng's (2004) dissertation.
- PDF / 844,720 Bytes
- 32 Pages / 439.37 x 666.142 pts Page_size
- 24 Downloads / 252 Views
Basic Theory and Ground Properties
Deng (2004) introduced a theoretical background on underground thermal energy systems in his dissertation on standing column wells. The contents in this chapter are mainly based on Deng’s (2004) dissertation.
3.1 Basic Physical Mechanism Above the water table lies the unsaturated zone, where voids or pores between rocks are usually only partially filled with water, the remainder being occupied with air. Water is held in the unsaturated zone by molecular attraction, and it will not flow toward or enter a well. In the saturated zone, which lies below the water table, all the openings in the rocks are full of water that may move through the aquifer to streams, springs, or wells from which water is being withdrawn (see Fig. 3.1). The energy transport in the ground outside of the well is through a porous media called an aquifer. An ‘‘aquifer’’ is defined as a geologic formation, group of formations, or part of a formation that contains sufficient saturated permeable material to yield economical quantities of water to wells and springs. The aquifer can be considered as a porous medium that consists of a solid phase and an interconnected void space totally filled with groundwater. Transport of groundwater occurs only through the interconnected voids. Heat is transported both in the solid matrix and in the void system, forming a coupled heat transfer process with conduction and advection by moving groundwater. The governing steady-state, one-dimensional equations for heat and fluid flow are given by Fourier’s law and Darcy’s law, which are identical in the form: Fourier’s law: q ¼ k
dT dx
K. S. Lee, Underground Thermal Energy Storage, Green Energy and Technology, DOI: 10.1007/978-1-4471-4273-7_3, Springer-Verlag London 2013
ð3:1Þ
27
28
3 Basic Theory and Ground Properties
Fig. 3.1 Occurrence of groundwater in rocks (http://capp.water.usgs.gov/GIP/gw_gip/how_ occurs.html)
where q is heat flux (W/m2); k is the thermal conductivity of the ground (W/m K). Darcy’s law: u ¼ K
dh dx
ð3:2Þ
where u is the specific discharge or Darcy flux (volume flow rate per unit of crosssectional area) (m/s); K is the hydraulic conductivity of ground (m/s); h is the hydraulic head (m). The specific discharge u is related to average linear groundwater velocity v by: v¼
u n
ð3:3Þ
where n is the porosity, which, for a given cross-section of a porous medium, is the ratio of the pore area to the cross-sectional area.
3.1.1 Hydrological Flow in the Aquifer The first fundamental law governing groundwater flow is the continuity equation, which expresses the principle of mass conservation (De Smedt 1999). Consider the flow of groundwater through an elementary control volume of porous medium around a point with Cartesian coordinates (x, y, z) as shown in Fig. 3.2. The principle of mass conservation on the control volume implies that the net result of inflow minus outflow is balanced by the change in storage versus time.
3.1 Basic Physical Mechanism
29
Fig. 3.2 Mass conservation in a reference ele
Data Loading...
