modelUTube

Information

Model of a single U-tube borehole heat exchanger. The borehole heat exchanger is vertically discretized into n_seg elements of height h=h_Bor⁄n_seg. Each segment contains a model for the heat transfer in the borehole, for heat transfer in the soil and for the far-field boundary condition.

The heat transfer in the borehole is computed using a convective heat transfer coefficient that depends on the fluid velocity, a heat resistance between the two pipes, and a heat resistance between the pipes and the circumference of the borehole. The heat capacity of the fluid, and the heat capacity of the grout, is taken into account. The thermal resistance and capacity network inside the borehole is computed according to Bauer et al., (2011).

The heat transfer in the soil is computed using transient heat conduction in cylindrical coordinates for the spatial domain r_bor ≤ r ≤ r_ext. In the radial direction, the spatial domain is discretized into n_hor segments with uniform material properties. Thermal properties can be specified separately for each horizontal layer.

The far-field temperature, i.e., the temperature at the radius r_ext, is computed using a power-series solution to a line-source heat transfer problem. This temperature boundary condition is updated every t_sample seconds.

The initial far-field temperature T_ext,start, which is the temperature of the soil at a radius r_ext, is computed as a function of the depth z > 0. For a depth between 0 ≤ z ≤ z₀, the temperature is set to T_ext,0,start. The value of z₀ is a parameter with a default of 10 meters. However, there is large variability in the depth where the undisturbed soil temperature starts. For a depth of z₀ ≤ z ≤ h_bor, the temperature is computed as

Tⁱ_ext,start = T_ext,0,start + (zⁱ - z₀) dT ⁄ dz

with i ∈ {1, ..., n_ver}, where the temperature gradient dT ⁄ dz ≥ 0 is a parameter. As with z₀, there is large variability in dT ⁄ dz ≥ 0. The default value is set to 1 Kelvin per 100 meters. For the temperature of the grout, the same equations are applied, with T_ext,0,start replaced with T_fil,0,start, and Tⁱ_ext,start replaced with Tⁱ_fil,start. The default setting uses the same temperature for the soil and the filling material.

Assumptions and limitations

The vertical heat flow is assumed to be zero and hence there is no heat flow from the ground surface to the soil that could be used to regenerate the soil temperature.

There is no ground water flow.

Implementation

Each horizontal layer is modeled using an instance of Buildings.HeatExchangers.Fluid.Boreholes.BaseClasses.BoreholeSegment. This model is composed of the model Buildings.Fluid.Geothermal.Boreholes.BaseClasses.HexInternalElement which computes the heat transfer in the pipes and the borehole filling, of the model Buildings.HeatTransfer.Conduction.SingleLayerCylinder which computes the heat transfer in the soil, and of the model Buildings.Fluid.Geothermal.Boreholes.BaseClasses.SingleUTubeBoundaryCondition which computes the far-field temperature boundary condition. The thermal resistor and capacitor network is computed in Buildings.Fluid.Geothermal.Boreholes.BaseClasses.singleUTubeResistances.

References

D. Bauer, W. Heidemann, H. Müller-Steinhagen, and H.-J. G. Diersch. Thermal resistance and capacity models for borehole heat exchangers . International Journal Of Energy Research, 35:312–320, 2011.

Parameters

Connectors

Components

Revisions

• March 7, 2022, by Michael Wetter:
  Set final massDynamics=energyDynamics.
  This is for #1542.
• April 14, 2020, by Michael Wetter:
  Changed homotopyInitialization to a constant.
  This is for IBPSA, #1341.
• December 23, 2015, by Michael Wetter:
  Updated documentation and added section about model assumptions and limitations.
• October 8, 2013, by Michael Wetter:
  Removed parameter show_V_flow.
• September 27, 2013, by Michael Wetter:
  Added missing each in propagation of material properties.
• August 2011, by Pierre Vigouroux:
  First implementation.