Buildings.Fluid.Geothermal.Boreholes
Package with borehole heat exchangers
Information
This package contains models for borehole heat exchangers.
Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).
Package Content
Name | Description |
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Single U-tube borehole heat exchanger |
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Example files for borehole heat exchanger |
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Base classes for Borehole |
Buildings.Fluid.Geothermal.Boreholes.UTube
Single U-tube borehole heat exchanger
Information
Model of a single U-tube borehole heat exchanger. The borehole heat exchanger is vertically discretized into nseg elements of height h=hBor⁄nseg. 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 rbor ≤ r ≤ rext. In the radial direction, the spatial domain is discretized into nhor 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 rext, is computed using a power-series solution to a line-source heat transfer problem. This temperature boundary condition is updated every tsample seconds.
The initial far-field temperature Text,start, which is the temperature of the soil at a radius rext, is computed as a function of the depth z > 0. For a depth between 0 ≤ z ≤ z0, the temperature is set to Text,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 ≤ hbor, the temperature is computed as
Tiext,start = Text,0,start + (zi - z0) dT ⁄ dz
with i ∈ {1, ..., nver}, 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 Text,0,start replaced with Tfil,0,start, and Tiext,start replaced with Tifil,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.
Extends from Buildings.Fluid.Interfaces.PartialTwoPortInterface (Partial model transporting fluid between two ports without storing mass or energy), Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters (Parameters for flow resistance for models with two ports), Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes).
Parameters
Type | Name | Default | Description |
---|---|---|---|
replaceable package Medium | PartialMedium | Medium in the component | |
Radius | rBor | 0.1 | Radius of the borehole [m] |
Nominal condition | |||
MassFlowRate | m_flow_nominal | Nominal mass flow rate [kg/s] | |
PressureDifference | dp_nominal | Pressure difference [Pa] | |
Soil | |||
Generic | matSoi | redeclare parameter Building... | Thermal properties of soil |
Radius | rExt | 3 | Radius of the soil used for the external boundary condition [m] |
Integer | nHor | 10 | Number of state variables in each horizontal layer of the soil |
Time | samplePeriod | Sample period for the external boundary condition [s] | |
Borehole | |||
Generic | matFil | redeclare parameter Building... | Thermal properties of the filling material |
Height | hBor | Total height of the borehole [m] | |
Integer | nVer | 10 | Number of segments used for discretization in the vertical direction |
Length | xC | 0.05 | Shank spacing, defined as the distance between the center of a pipe and the center of the borehole [m] |
Real | B0 | 17.44 | Shape coefficient for grout resistance |
Real | B1 | -0.605 | Shape coefficient for grout resistance |
Tubes | |||
Radius | rTub | 0.02 | Radius of the tubes [m] |
ThermalConductivity | kTub | 0.5 | Thermal conductivity of the tube [W/(m.K)] |
Length | eTub | 0.002 | Thickness of a tube [m] |
Assumptions | |||
Boolean | allowFlowReversal | true | = false to simplify equations, assuming, but not enforcing, no flow reversal |
Advanced | |||
MassFlowRate | m_flow_small | 1E-4*abs(m_flow_nominal) | Small mass flow rate for regularization of zero flow [kg/s] |
Boolean | homotopyInitialization | true | = true, use homotopy method |
Diagnostics | |||
Boolean | show_T | true | = true, if actual temperature at port is computed |
Flow resistance | |||
Boolean | computeFlowResistance | false | =true, compute flow resistance. Set to false to assume no friction |
Boolean | from_dp | false | = true, use m_flow = f(dp) else dp = f(m_flow) |
Boolean | linearizeFlowResistance | false | = true, use linear relation between m_flow and dp for any flow rate |
Real | deltaM | 0.1 | Fraction of nominal flow rate where flow transitions to laminar |
Dynamics | |||
Equations | |||
Dynamics | energyDynamics | Modelica.Fluid.Types.Dynamic... | Type of energy balance: dynamic (3 initialization options) or steady state |
Dynamics | massDynamics | energyDynamics | Type of mass balance: dynamic (3 initialization options) or steady state |
Real | mSenFac | 1 | Factor for scaling the sensible thermal mass of the volume |
Initialization | |||
AbsolutePressure | p_start | Medium.p_default | Start value of pressure [Pa] |
Temperature | T_start | Medium.T_default | Start value of temperature [K] |
MassFraction | X_start[Medium.nX] | Medium.X_default | Start value of mass fractions m_i/m [kg/kg] |
ExtraProperty | C_start[Medium.nC] | fill(0, Medium.nC) | Start value of trace substances |
ExtraProperty | C_nominal[Medium.nC] | fill(1E-2, Medium.nC) | Nominal value of trace substances. (Set to typical order of magnitude.) |
Initial temperature | |||
Soil | |||
Temperature | TExt0_start | 283.15 | Initial far field temperature [K] |
Temperature | TExt_start[nVer] | {if z[i] >= z0 then TExt0_st... | Temperature of the undisturbed ground [K] |
Filling material | |||
Temperature | TFil0_start | TExt0_start | Initial temperature of the filling material for h = 0...z0 [K] |
Temperature | TFil_start[nVer] | TExt_start | Temperature of the undisturbed ground [K] |
Temperature profile | |||
Height | z0 | 10 | Depth below which the temperature gradient starts [m] |
Real | dT_dz | 0.01 | Vertical temperature gradient of the undisturbed soil for h below z0 [K/m] |
Connectors
Type | Name | Description |
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FluidPort_a | port_a | Fluid connector a (positive design flow direction is from port_a to port_b) |
FluidPort_b | port_b | Fluid connector b (positive design flow direction is from port_a to port_b) |