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Verified Commit 12ca5541 authored by Lars Bilke's avatar Lars Bilke
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[web] Use page bundle resource in img shortcode.

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...@@ -15,7 +15,7 @@ project = "Parabolic/T/3D_deep_BHE/3D_deep_BHE_CXA.prj" ...@@ -15,7 +15,7 @@ project = "Parabolic/T/3D_deep_BHE/3D_deep_BHE_CXA.prj"
## Problem description ## Problem description
In recent years, Borehole Heat Exchangers (BHE) are very widely utilized to extract geothermal energy for building heating. For coaxial type of BHEs, an inner pipe is installed inside of an outer pipe, allowing the downward and upward flow to be separated. In some projects, very long coaxial BHEs are installed down to a 2-km depth, in order to extract more energy from the deep subsurface (Kong et al., 2017). Based on the flow directions, there are two types of coaxial BHEs. When downward flow is located in the inner pipe, it is called Coaxial-Centred (CXC) type. On the countary, if the inflow is introduced in the annular space, it is called a CXA type. Detailed schematization of the CXA-type BHE system is shown in Figure 1. In this benchmark, the numerical model in OGS-6 has been tested for the 2 coaxial types of BHEs. The simulation results are compared with previous OGS-5 results and also the analytical solution proposed by [Beier et al. (2014)](../Analytical_coaxial_BHE.zip). In recent years, Borehole Heat Exchangers (BHE) are very widely utilized to extract geothermal energy for building heating. For coaxial type of BHEs, an inner pipe is installed inside of an outer pipe, allowing the downward and upward flow to be separated. In some projects, very long coaxial BHEs are installed down to a 2-km depth, in order to extract more energy from the deep subsurface (Kong et al., 2017). Based on the flow directions, there are two types of coaxial BHEs. When downward flow is located in the inner pipe, it is called Coaxial-Centred (CXC) type. On the countary, if the inflow is introduced in the annular space, it is called a CXA type. Detailed schematization of the CXA-type BHE system is shown in Figure 1. In this benchmark, the numerical model in OGS-6 has been tested for the 2 coaxial types of BHEs. The simulation results are compared with previous OGS-5 results and also the analytical solution proposed by [Beier et al. (2014)](Analytical_coaxial_BHE.zip).
{{< img src="coaxial_deep_BHE.png" width="200">}} {{< img src="coaxial_deep_BHE.png" width="200">}}
......
...@@ -40,7 +40,7 @@ where ${\mathop q\nolimits_k }$ is a sequence of heat extraction pulses at t =1, ...@@ -40,7 +40,7 @@ where ${\mathop q\nolimits_k }$ is a sequence of heat extraction pulses at t =1,
= \sum\limits_{l = 1}^m {\sum\limits_{k = l}^n {\frac{{\mathop q\nolimits_{k,l} }}{{4\pi L\lambda }}} } \left( {E_1\left[ {\frac{{{{\left( {i - \mathop x\nolimits_k } \right)}^2} + {{\left( {j - \mathop y\nolimits_k } \right)}^2}}}{{4\alpha \left( {\mathop t\nolimits_m - \mathop t\nolimits_{l - 1} } \right)}}} \right] - E_1\left[ {\frac{{{{\left( {i - \mathop x\nolimits_k } \right)}^2} + {{\left( {j - \mathop y\nolimits_k } \right)}^2}}}{{4\alpha \left( {\mathop t\nolimits_m - \mathop t\nolimits_l } \right)}}} \right]} \right). = \sum\limits_{l = 1}^m {\sum\limits_{k = l}^n {\frac{{\mathop q\nolimits_{k,l} }}{{4\pi L\lambda }}} } \left( {E_1\left[ {\frac{{{{\left( {i - \mathop x\nolimits_k } \right)}^2} + {{\left( {j - \mathop y\nolimits_k } \right)}^2}}}{{4\alpha \left( {\mathop t\nolimits_m - \mathop t\nolimits_{l - 1} } \right)}}} \right] - E_1\left[ {\frac{{{{\left( {i - \mathop x\nolimits_k } \right)}^2} + {{\left( {j - \mathop y\nolimits_k } \right)}^2}}}{{4\alpha \left( {\mathop t\nolimits_m - \mathop t\nolimits_l } \right)}}} \right]} \right).
\end{split}\end{equation} \end{split}\end{equation}
where ${\mathop q\nolimits_{k,l} }$ is the heat extraction of the k-*th* BHE at time step *l*. The equation (3) will be used to calculate the analytical solution of the overall temperature change in this model for validating the numerical results. It is written in python code and can be found [here](../bhe_array_analytical_solver.py). where ${\mathop q\nolimits_{k,l} }$ is the heat extraction of the k-*th* BHE at time step *l*. The equation (3) will be used to calculate the analytical solution of the overall temperature change in this model for validating the numerical results. It is written in python code and can be found [here](bhe_array_analytical_solver.py).
## Numerical model setup ## Numerical model setup
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...@@ -38,5 +38,3 @@ shown in the following figure. ...@@ -38,5 +38,3 @@ shown in the following figure.
Comparison with 2D setup yields identical results (up to numerical differences Comparison with 2D setup yields identical results (up to numerical differences
in order of 1e-15): in order of 1e-15):
TODO: Image missing! TODO: Image missing!
<!-- {{< img src="single_fracture_3D_vs_2D.png" >}} -->
...@@ -83,4 +83,4 @@ Over time, opposed concentration fronts for educts and Product d evolve. ...@@ -83,4 +83,4 @@ Over time, opposed concentration fronts for educts and Product d evolve.
Both, OGS-6 and OGS-5 simulations yield the same results in the 1d as well as 2d scenario. Both, OGS-6 and OGS-5 simulations yield the same results in the 1d as well as 2d scenario.
For instance, the difference between the OGS-6 and the OGS-5 computation for the concentration of Product d expressed as root mean squared error is 1.76e-7 mol kg$^{-1}$ water (over all time steps and mesh nodes, 1d scenario); the corresponding median absolute error is 1.0e-7 mol kg$^{-1}$ water. For instance, the difference between the OGS-6 and the OGS-5 computation for the concentration of Product d expressed as root mean squared error is 1.76e-7 mol kg$^{-1}$ water (over all time steps and mesh nodes, 1d scenario); the corresponding median absolute error is 1.0e-7 mol kg$^{-1}$ water.
This verifies the implementation of OGS-6--IPhreeqc. This verifies the implementation of OGS-6--IPhreeqc.
{{< img src="../KineticReactant2.gif" title="Simulated component concentrations over domain length for different time steps (1d scenario) .">}} {{< img src="KineticReactant2.gif" title="Simulated component concentrations over domain length for different time steps (1d scenario) .">}}
...@@ -66,7 +66,7 @@ The temporal evolution of the concentration profiles of the chosen mineral combi ...@@ -66,7 +66,7 @@ The temporal evolution of the concentration profiles of the chosen mineral combi
On the other hand, the enormous difference between sorbing and non-sorbing reactive transport is evident from the resulting concentration profiles. Therefore, we highlight the importance of considering the impact of sorption in the transport of radionuclides, as this is paramount for the safety assessment in the design of nuclear waste repositories. Finally, the CPU time of the simulation taking into account surface complexation is roughly double of the simulation with only aqueous speciation. This posses the necessity of choosing a good compromise between accuracy (large number of reactions and chemical parameters) and performance. On the other hand, the enormous difference between sorbing and non-sorbing reactive transport is evident from the resulting concentration profiles. Therefore, we highlight the importance of considering the impact of sorption in the transport of radionuclides, as this is paramount for the safety assessment in the design of nuclear waste repositories. Finally, the CPU time of the simulation taking into account surface complexation is roughly double of the simulation with only aqueous speciation. This posses the necessity of choosing a good compromise between accuracy (large number of reactions and chemical parameters) and performance.
{{< img src="../Fig2.gif" title="Time evolution of mineral combination 2 (albite/hematite) in comparison to the results obtained with the ESTRAL database. The green dotted line shows the temporal evolution of U(IV) as a non-sorbing radionuclide.">}} {{< img src="Fig2.gif" title="Time evolution of mineral combination 2 (albite/hematite) in comparison to the results obtained with the ESTRAL database. The green dotted line shows the temporal evolution of U(IV) as a non-sorbing radionuclide.">}}
{{< data-link >}} {{< data-link >}}
...@@ -76,4 +76,4 @@ Parkhurst, D.L., Appelo, C.A.J., 2013. Description of Input and Examples for PHR ...@@ -76,4 +76,4 @@ Parkhurst, D.L., Appelo, C.A.J., 2013. Description of Input and Examples for PHR
Noseck, U., Britz, S., Fricke, J., Gehrke, A., Fluegge, J., Brendler, V., ... & Lampe, M. (2018). Smart K d-concept for long-term safety assessments. Extension towards more complex applications (No. GRS--500). Gesellschaft fuer Anlagen-und Reaktorsicherheit (GRS) gGmbH. Noseck, U., Britz, S., Fricke, J., Gehrke, A., Fluegge, J., Brendler, V., ... & Lampe, M. (2018). Smart K d-concept for long-term safety assessments. Extension towards more complex applications (No. GRS--500). Gesellschaft fuer Anlagen-und Reaktorsicherheit (GRS) gGmbH.
Thoenen, T., Hummel, W., Berner, U., & Curti, E. (2014). *The PSI/Nagra Chemical Thermodynamic Database 12/07*. Thoenen, T., Hummel, W., Berner, U., & Curti, E. (2014). *The PSI/Nagra Chemical Thermodynamic Database 12/07*.
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...@@ -98,7 +98,7 @@ For instance, the difference between the OGS-6 and the OGS-5 computation for the ...@@ -98,7 +98,7 @@ For instance, the difference between the OGS-6 and the OGS-5 computation for the
The relatively high error may be associated with the missing transport or charge in the OGS-6 simulation, which affects computations by Phreeqc. The relatively high error may be associated with the missing transport or charge in the OGS-6 simulation, which affects computations by Phreeqc.
Please note that due to the long computation time of the simulation (~13 h), the corresponding test (Wetland_1d.prj) is reduced to the first four time steps (28800 s). Please note that due to the long computation time of the simulation (~13 h), the corresponding test (Wetland_1d.prj) is reduced to the first four time steps (28800 s).
{{< img src="../Wetland_1d.gif" title="Fig. 3: Simulated concentrations of solutes (left) and bacteria (right). Solid lines represent solutions by OGS-5; dashed lines represent solution by OGS-6.">}} {{< img src="Wetland_1d.gif" title="Fig. 3: Simulated concentrations of solutes (left) and bacteria (right). Solid lines represent solutions by OGS-5; dashed lines represent solution by OGS-6.">}}
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