Update example with optimal coaxial BHE, with figure of COP over time and...

The power yield that follows from the simulation is shown in Fig. 3.

![Fig. 3](images/COAX_optimization_A_T_SRtimeplot_Q_b.png)

![Fig. 3](images/COAX_optimization_A_T_SR_timeplot_Q_b.png)

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Fig. 3: Power yield during a year of constant operation of the coaxial BHE with an optimized flow rate and pipe insulation design.

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The COP of the fluid circulation pump during the simulated period is shown in Fig. 4. The last value of this time-variable

COP is used to test the COP constraint in the optimization process (see [Theory section](../../theory/theory.md)).

![Fig. 4](images/COAX_optimization_A_T_SR_timeplot_COP.png)

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Fig. 4: COP of the fluid circulation pump during a year of constant operation of the coaxial BHE with an optimized flow 

rate and pipe insulation design.

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### Optimal flow rate and radius of the inner pipe

In the second simulation, the radius of the inner pipe in the coaxial BHE is optimized for the maximum power yield, for which

the result is shown in Fig. 4. The inner pipe has a radius of 36 mm.

the result is shown in Fig. 5. The inner pipe has a radius of 36 mm.

![Fig. 4](images/COAX_optimization_rout_A_T_bhdesign.png){width="500"}

![Fig. 5](images/COAX_optimization_rout_A_T_bhdesign.png){width="500"}

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Fig. 4: Cross-section of the BHE design in the second optimization simulation for maximum power yield of the system.

Fig. 5: Cross-section of the BHE design in the second optimization simulation for maximum power yield of the system.

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Here, the flow rate and the radius of the inner pipe are optimized under the condition of a minimum COP of the circulation

pump of 20 and an imposed pumping pressure of 1.7 bar.

The lack of insulation in the outlet is clearly reflected by the heat loss in the working fluid during upward transport

in the inner pipe of the BHE (see Fig. 5).

in the inner pipe of the BHE (see Fig. 6).

![Fig. 5](images/COAX_optimization_rout_A_T_SR_temperature_depth_4500.0.png)

![Fig. 6](images/COAX_optimization_rout_A_T_SR_temperature_depth_4500.0.png)

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Fig. 5: Fluid and borehole wall temperatures after half a year of operation of the coaxial BHE with an optimized flow 

Fig. 6: Fluid and borehole wall temperatures after half a year of operation of the coaxial BHE with an optimized flow 

rate and radius of the inner pipe.

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The power yield that follows from the simulation is shown in Fig. 6.

The power yield that follows from the simulation is shown in Fig. 7.

![Fig. 6](images/COAX_optimization_rout_A_T_SRtimeplot_Q_b.png)

![Fig. 7](images/COAX_optimization_rout_A_T_SR_timeplot_Q_b.png)

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Fig. 6: Power yield during a year of operation of the coaxial BHE with an optimized flow rate and radius of the inner pipe.

Fig. 7: Power yield during a year of operation of the coaxial BHE with an optimized flow rate and radius of the inner pipe.

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