@@ -5,5 +5,5 @@ title = "Ehlers plastic-damage coupled model"

## Introduction

We implemented and isotropic damage evolution law coupled to Ehelers plastic theory. The yield surface is formulated in the effective stress space and damage grows as a function of plastic strain.

We implemented an isotropic damage evolution law coupled to Ehlers plastic theory. The yield surface is formulated in the effective stress space and damage grows as a function of plastic strain.

For detailed reference, refer to the implementation manual.

@@ -19,7 +19,7 @@ This is one of the benchmark examples with analytical solutions presented

A detailed description about this benchmark can be found in section 10.1 of

the book

[Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking From Benchmarking to Tutoring](https://www.opengeosys.org/books/bmb-4/),

one of the ogs Benchmark books (see the reference list below).

one of the OGS Benchmark books (see the reference list below).

<!--

These benchmark examples test the implementation of

@@ -58,7 +58,7 @@ As of now a small portion of possible inputs is implemented; one can change:

The geometries used to specify the boundary conditions are given in the [square_1x1.gml](https://gitlab.opengeosys.org/ogs/ogs/-/blob/master/Tests/Data/Elliptic/square_1x1_SteadyStateDiffusion/square_1x1.gml) file.

The input mesh `square_1x1_quad_1e2.vtu` is stored in the VTK file format and can be directly visualized in Paraview for example.

The input mesh `square_1x1_quad_1e2.vtu` is stored in the VTK file format and can be directly visualized in ParaView for example.

## Running simulation

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...

@@ -68,7 +68,7 @@ To start the simulation (after successful compilation) run:

ogs square_1e2_neumann.prj

```

It will produce some output and write the computed result into the `square_1e2_neumann.vtu` for visualization with Paraview.

It will produce some output and write the computed result into the `square_1e2_neumann.vtu` for visualization with ParaView.

The output on the console will be similar to the following one (ignore the spurious error messages "Could not find POINT..."):

@@ -52,13 +52,13 @@ All the other parameters adopted in the model is same as the ones used in the sc

For the benchmark a FEFLOW model is presented.

The mesh used in the OGS model is directly converted from the FEFLOW model mesh, to ensure that there is no influence to the comparison results from the mesh side.

Both the FEFLOW and ogs model mesh can be found in the ogs GitLab (<https://gitlab.opengeosys.org/ogs/ogs/-/merge_requests/3426>).

Both the FEFLOW and OGS model mesh can be found in the OGS GitLab (<https://gitlab.opengeosys.org/ogs/ogs/-/merge_requests/3426>).

## FEFLOW Input Files

## Results

The computed resutls from scenario by adopting the fixed inflow boundary condition are illustracted in Figure 1 and Figure 2.

The computed results from scenario by adopting the fixed inflow boundary condition are illustrated in Figure 1 and Figure 2.

The OGS numerical outflow temperature over time was compared against results of the FEFLOW software as shown in the Figure 1. And the vertical distributed temperature of circulating water was presented in Figure 2 after operation for 3300 s.

The comparison figures demonstrate that the OGS numerical results and FEFLOW results can match very well and the biggest absolute error of outflow temperature is 0.20 $^{\circ}$C after 360 s' operation, while such error decreases to 0.037 $^{\circ}$C after 3600 s' operation. The maximum relative error of vertical temperature is 0.019 \% after operation for 3300 s.

...

...

@@ -67,7 +67,7 @@ The comparison figures demonstrate that the OGS numerical results and FEFLOW res

Figure 2: Comparison of vertical temperature distribution from scenario by adopting the fixed inflow boundary condition

Figure 3 shows the vertical distributed temperature of circulating fluid after operation for 3300 s by adopting different power boundary conditions in OGS and FEFLOW models.

Compared to the resutls computed from the OGS model with using a fixed power boundary condition (illustrated as the blue and green line), A 0.18 $^{\circ}$C difference is found for the averaged vertical temperature from the FEFLOW model (illustrated as the dotted line).

Compared to the results computed from the OGS model with using a fixed power boundary condition (illustrated as the blue and green line), A 0.18 $^{\circ}$C difference is found for the averaged vertical temperature from the FEFLOW model (illustrated as the dotted line).

The reason to the results difference is due to the different power boundary condition type adopted in the two software.

In FEFLOW the power boundary condition is based on the outlet temperature calculated from the last time step (non-iterative).

Compared to it, the default power boundary condition adopted in the OGS `Heat_Transport_BHE` process is based on the outlet temperature calculated from the current time step (with-iterative).

@@ -69,7 +69,7 @@ Two different pipe network setup were constructed for this benchmark.

* A one-way pipe network (see Figure 1a)

In this setup, the refrigerant mass flow rate is given in $kg/s$, as this is the default setting in the TESPy model (see ./pre/3bhes.py).

In this setup, the refrigerant mass flow rate is given in $kg/s$, as this is the default setting in the TESPy model (see `./pre/3bhes.py`).

After being lifted by the pump, the refrigerant inflow will be divided into 3 branches by the splitter and then flow into each BHEs.

Because of this configuration, the inflow temperature on each BHE will be the same.

The refrigerant flowing out of the BHEs array will be firstly mixed at the merging point and then extracted for the heat extraction through the heat pump.

...

...

@@ -107,9 +107,9 @@ In this figure, the difference between the total heat extraction rate of all BHE

In comparison to the one-way setup, the closed-loop network shows a slightly different behaviour.

The evolution of inflow refrigerant temperature and flow rate entering the BHE array is shown in Figure 5.

With the decreasing of the working fluid temperature over the time, the system flow rate dereases gradually.

With the decreasing of the working fluid temperature over the time, the system flow rate decreases gradually.

Figure 6 depicts the thermal load shifting phenomenon with the closed-loop model.

Except for the thermal shifiting behavior among the BHEs, the averaged heat extraction rate of all BHEs (black line) increases slightly over the time.

Except for the thermal shifting behavior among the BHEs, the averaged heat extraction rate of all BHEs (black line) increases slightly over the time.

This is due to the fact that additional energy is required to compensate the hydraulic loss of the pipe.

{{<imgsrc="Soil_temperature.png"width="200">}}

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@@ -134,8 +134,12 @@ Figure 6: Evolution of the heat extraction rate of each BHE with close loop netw

## References

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[1] Diersch, H. J., Bauer, D., Heidemann, W., Rühaak, W., & Schätzl, P. (2011). Finite element modeling of borehole heat exchanger systems: Part 1. Fundamentals. Computers & Geosciences, 37(8), 1122-1135.

[2] Francesco Witte, Ilja Tuschy, TESPy: Thermal Engineering Systems in Python, 2019. URL: <https://doi.org/10.21105/joss.02178>. doi:10.21105/joss.02178.

[3] Webpage of the High-Level Interface in CoolProp. URL: <http://www.coolprop.org/coolprop/HighLevelAPI.html>.