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[web] Fixed header syntax.

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bilke committed Mar 4, 2020
1 parent a6925de commit 7237de99200909d888029a941103a00c7ca37152
Showing with 10 additions and 14 deletions.
  1. +10 −14 web/content/docs/benchmarks/liquid-flow/buildup_test.pandoc
@@ -13,8 +13,8 @@ project = "/Parabolic/LiquidFlow/BuildupTest/buildup_test.prj"

{{< data-link >}}

Problem description {#problem-description .unnumbered .unnumbered}
===================
## Problem description


The pressure buildup test is performed by shutting in a producing well
at time $t=t_p$, after which a smooth rise of the well head pressure can
@@ -26,8 +26,7 @@ the model, a time dependent nodal source term was set up to represent
the shut-in operation. The simulated pressure profile is then verified
against the analytical solution.

Model Setup {#model-setup .unnumbered .unnumbered}
===========
## Model Setup

This benchmark represents a scenario in which the well had been
producing geothermal brine for $118\ \mathrm{h}$ at a rate of
@@ -70,8 +69,7 @@ which corresponds to the infinite shut-in time $(\Delta t)$. This leads to
an extrapolated pressure $p_0$ of $67.5~\mathrm{kPa}$, which is the
undisturbed reservoir pressure .

Input files {#input-files .unnumbered .unnumbered}
===========
## Input files

The benchmark project is defined in the input file `buildup_test.prj`. It defines the process to
be solved as "LiquidFlow" and the primary variable is hence pressure.
@@ -85,8 +83,7 @@ conditions, and source term can be found in `line_1000_axi.gml` file.
The mesh is specified in `line_1000_axi.vtu`, which is stored in the
VTK format and can be directly visualized in Paraview.

Analytical solution {#analytical-solution .unnumbered .unnumbered}
===================
## Analytical solution

The pressure buildup test is comparable to a pumping recovery test as
the extraction rate is first kept constant at $Q$, and then becomes zero
@@ -101,8 +98,8 @@ $$\Delta p=\rho g \frac{-Q}{4\pi T}W\left(\frac{r^2S}{4Tt}\right)$$ and
for $t>t_p$,
$$\Delta p=\rho g \frac{-Q}{4\pi T}W\left(\frac{r^2S}{4Tt}\right)+\rho g \frac{Q}{4\pi T}W\left(\frac{r^2S}{4T(t-t_p)}\right)$$

Results and evaluation {#results-and-evaluation .unnumbered .unnumbered}
======================
## Results and evaluation


The pressure evolution is simulated throughout the domain and the result
is compared with the analytical solution at $r=10.287\ \mathrm{m}$. In
@@ -121,12 +118,11 @@ Figure 2: OGS 6 result compared with analytical solution

Figure 3: Absolute and relative error

References {#references .unnumbered .unnumbered}
========
## References

[1] RN Horne. Characterization, evaluation, and interpretation of well data. In: R DiPippo, editor,Geothermal Power Generation, chapter 6, pages 141–163.Elsevier, 2016.

Appendix {#appendix .unnumbered .unnumbered}
========
## Appendix

\centering
| $\Delta t$ (h) | $\Delta p$ (bar) | $\Delta t$ (h) | $\Delta p$ (bar) |

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