AixLib.Fluid.Geothermal.Borefields.UsersGuide

# .AixLib.Fluid.Geothermal.Borefields.UsersGuide

User's Guide

## Information

This package contains borefield models. These models can simulate any arbitrary configuration of vertical boreholes with equal lengths with both short and long-term accuracy with an aggregation method to speed up the calculations of the ground heat transfer. Examples of how to use the borefield models and validation cases can be found in AixLib.Fluid.Geothermal.Borefields.Examples and AixLib.Fluid.Geothermal.Borefields.Validation, respectively.

The following major features and configurations are supported:

- User-defined borefield characteristics and geometry (borehole radius, pipe radius, shank spacing, etc.), including single U-tube, double U-tube in parallel and double U-tube in series configurations.
- The resistances Rb and Ra are either automatically calculated using the multipole method, or the resistance Rb can be directly provided by the user. In this case, the resistances Rb and Ra are still evaluated internally, but their values are weighted so that the borehole resistance matches the specified value.
- User-defined vertical discretization of boreholes are supported. However, the borehole wall temperature is identical for each borehole, as the ground temperature response model only computes the average borehole wall temperature for all boreholes combined.
- Borefields can consist of one or many boreholes. Each borehole can be positioned at an arbitrary position in the field using cartesian coordinates.
- The resolution and precision of the load aggregation method for the ground heat transfer can be adapted.
- The thermal response of the ground heat transfer is stored locally to avoid having to recalculate it for future simulations with the same borefield configuration.
- Pressure losses are calculated if the `dp_nominal` parameter is set to a non-zero value.

The model is limited to the simulation of borefields with boreholes connected in parallel, as shown on the figure below for a single U-tube configuration. All boreholes have the same length `hBor`, the same radius `rBor`, and are buried at the same depth `dBor` below the ground surface (also known as the inactive borehole length).

#### How to use the borefield models

##### Borefield data record

Most of the parameter values of the model are contained in the record called `borFieDat`. This record is composed of three subrecords: `filDat` (containing the thermal characteristics of the borehole filling material), `soiDat` (containing the thermal characteristics of the surrounding soil), and `conDat` (containing all others parameters, namely parameters defining the configuration of the borefield). The structure and default values of the record are in the package: AixLib.Fluid.Geothermal.Borefields.Data. The `borFieDat` record can be found in the AixLib.Fluid.Geothermal.Borefields.Data.Borefield subpackage therein. Examples of the subrecords `conDat`, `filDat` and `soiDat` can be found in AixLib.Fluid.Geothermal.Borefields.Data.Configuration, AixLib.Fluid.Geothermal.Borefields.Data.Filling and AixLib.Fluid.Geothermal.Borefields.Data.Soil, respectively.

It is important to make sure that the `borCon` parameter within the `conDat` subrecord is compatible with the chosen borefield model. For example, if a double U-tube borefield model is chosen, the `borCon` parameter could be set to both a parallel double U-tube configuration and a double U-tube configuration in series, but could not be set to a single U-tube configuration. An incompatible borehole configuration will stop the simulation.

##### Ground heat transfer parameters

Other than the parameters contained in the `borFieDat` record, the borefield models have other parameters which can be modified by the user. The `tLoaAgg` parameter is the time resolution of the load aggregation for the calculation of the ground heat transfer. It represents the frequency at which the load aggregation procedure is performed in the simulation. Therefore, smaller values of `tLoaAgg` will improve the accuracy of the model, at the cost of increased simulation times due to a higher number of events occuring in the simulation. While a default value is provided for this parameter, it is advisable to ensure that it is lower than a fraction (e.g. half) of the time required for the fluid to completely circulate through the borefield, as increasing the value of `tLoaAgg` beyond this will result in non-physical borehole wall temperatures.

The `nCel` parameter also affects the accuracy and simulation time of the ground heat transfer calculations. As this parameter sets the number of consecutive equal-size aggregation cells before increasing the size of cells, increasing its value will result in less load aggregation, which will increase accuracy at the cost of computation time. On the other hand, decreasing the value of `nCel` (down to a minimum of 1) will decrease accuracy but improve computation time. The default value is chosen as a compromise between the two.

Further information on the `tLoaAgg` and `nCel` parameters can be found in the documentation of AixLib.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.GroundTemperatureResponse.

##### Other parameters

Other parameters which can be modified include the dynamics, initial conditions, and further information regarding the fluid flow, for example whether the flow is reversible. It is worth noting that regardless of the `energyDynamics` chosen, the `steadyState` parameter can be set to `true` in the data record for the filling material to remove the effect of the thermal capacitance of the filling material in the borehole(s). The `nSeg` parameter specifies the number of segments for the vertical discretization of the borehole(s). Further information on this discretization can be found in the "Model description" section below.

##### Running simulations

When running simulations using the borefield models, the `tmp/temperatureResponseMatrix` directory within the current directory will be checked to see if any of the borefield configurations used in the simulation have already had their ground temperature response calculated previously If the data doesn't exist in the `tmp/temperatureResponseMatrix` folder, it will be calculated during the initialization of the model and will be saved there for future use.

#### Model description

The borefield models rely on the following key assumptions:

- The thermal properties of the soil (conductivity and diffusivity) are constant, homogenous and isotropic.
- The conductivity, capacitance and density of the grout and pipe material are constant, homogenous and isotropic.
- There is no heat extraction or injection prior to the simulation start.
- All of the boreholes in the borefield have uniform dimensions (including the pipe dimensions).
- Inside the boreholes, the non-advective heat transfer is only in the radial direction.

The borefield models are constructed in two main parts: the borehole(s) and the ground heat transfer. The former is modeled as a vertical discretization of borehole segments, where a uniform temperature increase or decrease (due to heat injection or extraction) is superimposed to the far-field ground temperature to obtain the borehole wall temperature. The thermal effects of the circulating fluid (including the convection resistance), of the pipes and of the filling material are all taken into consideration, which allows modeling short-term thermal effects in the borehole. The borehole segments do not take into account axial effects, thus only radial (horizontal) effects are considered within the borehole(s). The thermal behavior between the pipes and borehole wall are modeled as a resistance-capacitance network, with the grout capacitance being split in the number of pipes present in a borehole section. The capacitance is only present if the parameter `steadyState` of the filling material data record is `false`, which is the default setting. The figure below shows an example for a borehole section within a single U-tube configuration.

The second main part of the borefield models is the ground heat transfer, which shares a thermal boundary condition at the uniform borehole wall with all of the borehole segments. The heat transfer in the ground is modeled analytically as a convolution integral between the heat flux at the borehole wall and the borefield's thermal response factor.

The model uses a load aggregation technique to reduce the time required to calculate the borehole wall temperature changes resulting from heat injection or extraction.

The ground heat transfer takes into account both the borehole axial effects and the borehole radial effects which are a result of its cylindrical geometry. The borefield's thermal response to a constant load, also known as its g-function, is used to calculate the thermal response in the simulation. This g-function is stored in the `tmp/temperatureResponseMatrix` subdirectory, as discussed previously in the "How to use the borefield models" section. Further information on the ground heat transfer model and the thermal temperature response calculations can be found in AixLib.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.GroundTemperatureResponse and AixLib.Fluid.Geothermal.Borefields.BaseClasses.HeatTransfer.ThermalResponseFactors.gFunction.

#### References

D. Picard, L. Helsen. Advanced Hybrid Model for Borefield Heat Exchanger Performance Evaluation; an Implementation in Modelica Proc. of the 10th Intertional ModelicaConference, p. 857-866. Lund, Sweden. March 2014. https://lirias.kuleuven.be/retrieve/270880.

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