Borehole heat exchangers (BHE) are widely applied in Ground Source Heat Pump (GSHP) systems to explore geothermal energy for building heating and cooling purposes. There are more and more engineering companies starting to use simulation tools for the performance evaluation and design of GSHP projects.
For OGS6, it allows the users to simulate the subsurface and soil temperature evolution induced by BHE and operation performance of BHE coupled heat pump.
This part aims to give an explanation of the mathematical framework in configuring the Heat_Transport_BHE process provided in OpenGeoSys. The numerical method implemented in OGS6 is the socalled doublecontinuum finite element method (DCFEM
). This approach was originally proposed by AlKhoury et al. (2010) and extended by Diersch et al. (2011a; 2011b). It was then implemented in OpenGeoSys by Shao et al. (2016). This modelling approach has the following assumptions.
$$\begin{equation}\frac{\partial}{\partial t} \left[ \epsilon \rho_f c_f + ( 1\epsilon ) \rho_s c_s \right] T_s + \nabla \cdot \left( \rho_f c_f \mathbf{v_f} T_s \right)  \nabla \cdot \left( \Lambda_s \cdot \nabla T_s \right) = H_s, \end{equation}$$
Here, $\Lambda_s$ denotes the tensor of thermal hydrodynamic dispersion and $H_s$ represents the heat source and sink term.
In the configuration of Heat_Transport_BHE
process, it is generally configured as follows.
temperature_soil
and temperature_BHE1
. For multiple boreholes, the name temperature_BHE2
, temperature_BHE3
etc can be added.<name>HeatTransportBHE</name>
<type>HEAT_TRANSPORT_BHE</type>
<integration_order>2</integration_order>
<process_variables>
<process_variable>temperature_soil</process_variable>
<process_variable>temperature_BHE1</process_variable>
</process_variables>
The borehole < length > and < diameter > are defined here. The unit of these parameters are in $\mathrm{m}$. Here is an example of a borehole with 18 m in length and 0.13 m in diameter.
<borehole>
<length>18.0</length>
<diameter>0.13</diameter>
</borehole>
Currently there are 4 types of BHE available. Following the convention in Diersch et al. (2011a), they are named as 1U，2U，CXA and CXC types. In the OGS .prj file, it is defined as:
<type>2U</type>
Especially in CXA and CXC type, the direction of the borehole itself could be deviated by any angle, which is defined by mesh. The inflow direction will be in accordance with the direction of the line element (represents the BHE borehole) in the mesh. And the outlet direction is the opposite of the inflow direction.
The crosssections of these 4 types of BHEs are illustrated in the following figures.
The properties of the pipes are defined in this section. For different types of BHE, the pipes are also configured differently.
The units of these parameters are all in $\mathrm{m}$. Here is an example of a 2U type BHE. The inlet and outlet pipe are all made of highdensity polyethylene(HDPE).
<pipes>
<inlet>
<diameter> 0.0378</diameter>
<wall_thickness>0.0029</wall_thickness>
<wall_thermal_conductivity>0.42</wall_thermal_conductivity>
</inlet>
<outlet>
<diameter>0.0378</diameter>
<wall_thickness>0.0029</wall_thickness>
<wall_thermal_conductivity>0.42</wall_thermal_conductivity>
</outlet>
<distance_between_pipes>0.053</distance_between_pipes>
<longitudinal_dispersion_length>0.001</longitudinal_dispersion_length>
</pipes>
Four type of flow and temperature control patterns are provided in OGS.
The unit of < power > is in $\mathrm{W}$ and < flow_rate > is in $\mathrm{m^{3}/s}$. For heating applications, thermal energy is extracted from the subsurface, then a negative power value should be given. It is vice versa for cooling applications.
Further info:
For all the flow and temperature control options, OpenGeoSys calculates the inlet temperature of each BHE internally. For each BHE, temperature on its inlet pipe is always set as a Dirichlet type boundary condition. Depending on the choice of < flow_and_temperature_control >, the inflow temperature will be calculated dynamically in each time step and iteration to satisfy the given constrains.
Here is an example using TemperatureCurveConstantFlow
.
<flow_and_temperature_control>
<type>TemperatureCurveConstantFlow</type>
<flow_rate>2.0e4</flow_rate>
<temperature_curve>inflow_temperature</temperature_curve>
</flow_and_temperature_control>
For 2Utype BHE configuration, the flow rate in < flow_and_temperature_control > indicates the flow rate within each Upipe. When a fixed power or power curve is imposed on a 2Utype BHE, the given value in < flow_and_temperature_control > or in the related power curve should be specified with half of the user’s presumed entire borehole exchanger power.
The thermal properties of the grout material is defined here.
Here is an example how the typical parameters of borehole grout looks like.
<grout>
<density>2190.0</density>
<porosity>0.0</porosity>
<specific_heat_capacity>1735.1</specific_heat_capacity>
<thermal_conductivity>0.73</thermal_conductivity>
</grout>
The thermal properties of the circulating fluid is defined here. The parameters and their units are listed below.
Here is an example in which the circulating fluid is water at about 15 $^{\circ}$C.
<refrigerant>
<density>998</density>
<viscosity>0.0011375 </viscosity>
<specific_heat_capacity>4190</specific_heat_capacity>
<thermal_conductivity>0.6</thermal_conductivity>
<reference_temperature>22</reference_temperature>
/refrigerant>
[1] AlKhoury, R., Kölbel, T., Schramedei, R.: Efficient numerical modeling of borehole heat exchangers. Comput. Geosci. 36(10), 1301–1315 (2010).
[2] Diersch, H.J.G., Bauer, D., Heidemann, W., Rühaak, W., Schätzl, P.: Finite element modeling of borehole heat exchanger systems: part 1. Fundamentals. Comput. Geosci. 37(8), 1122–1135 (2011a).
[3] Diersch, H.J.G., Bauer, D., Heidemann, W., Rühaak, W., Schätzl, P.: Finite element modeling of borehole heat exchanger systems: part 2. Numerical simulation. Comput. Geosci. 37(8), 1136–1147 (2011b).
[4] Hein, P., Kolditz, O., Görke, U.J., Bucher, A., Shao, H.: A numerical study on the sustainability and efficiency of borehole heat exchanger coupled ground source heat pump systems. Appl. Therm. Eng. 100, 421–433 (2016).
[5] Shao, Haibing, Philipp Hein, Agnes Sachse, and Olaf Kolditz. Geoenergy modeling II: shallow geothermal systems. Springer International Publishing, 2016.
This article was written by Wanlong Cai, Haibing Shao. If you are missing something or you find an error please let us know.
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Last revision: September 7, 2022
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