From 76d25f11a414c99c0e0b9b47cca6a2ca3c214eae Mon Sep 17 00:00:00 2001
From: Mathis Kelm <mathis.kelm@iws.uni-stuttgart.de>
Date: Mon, 3 Apr 2023 17:22:44 +0300
Subject: [PATCH] [biomin] fix formatting for chemistry in README
---
.../exercise-biomineralization/README.md | 32 +++++++++----------
1 file changed, 16 insertions(+), 16 deletions(-)
diff --git a/exercises/exercise-biomineralization/README.md b/exercises/exercise-biomineralization/README.md
index ab345a9f..91fe456f 100644
--- a/exercises/exercise-biomineralization/README.md
+++ b/exercises/exercise-biomineralization/README.md
@@ -4,10 +4,10 @@ The aim of this exercise is to get a first glimpse at the _DuMu<sup>x</sup>_ way
## Problem set-up
-The domain has a size of 20 x 15 m and contains a sealing aquitard in the middle. The aquitard is interrupted by a "fault zone" and thereby connects the upper drinking water aquifer and the lower CO2-storage aquifer. Initially, the domain is fully saturated with water and biofilm is present in the lower CO2-storage aquifer. Calcium and urea are injected in the upper drinking water aquifer by means of a Neumann boundary condition. The remaining parts of the upper boundary and the entire lower boundary are modelled with Neumann no-flow conditions, while on the right-hand side a Dirichlet boundary conditions is assigned, which fixes there the the initial values.
+The domain has a size of 20 x 15 m and contains a sealing aquitard in the middle. The aquitard is interrupted by a "fault zone" and thereby connects the upper drinking water aquifer and the lower CO<sub>2<sub>-storage aquifer. Initially, the domain is fully saturated with water and biofilm is present in the lower CO<sub>2<sub>-storage aquifer. Calcium and urea are injected in the upper drinking water aquifer by means of a Neumann boundary condition. The remaining parts of the upper boundary and the entire lower boundary are modelled with Neumann no-flow conditions, while on the right-hand side a Dirichlet boundary conditions is assigned, which fixes there the the initial values.
-Disclaimer: Please note, that this is not a realistic scenario. No one would think of storing gaseous CO2 in this subcritical setting.
+Disclaimer: Please note, that this is not a realistic scenario. No one would think of storing gaseous CO<sub>2<sub> in this subcritical setting.
@@ -60,13 +60,13 @@ $`\displaystyle Z_{urease,biofilm} = k_{urease,biofilm} * mass_{biofilm}`$
The last step is defining the source term for each component according to the chemical reaction equations:
-$`\displaystyle CO(NH_{2})_{2} + 2 H_{2}O -> 2 NH_{3} + H_{2}CO_{3}`$
+$`\displaystyle \mathrm{CO(NH_{2})_{2} + 2 H_{2}O \rightarrow 2 NH_{3} + H_{2}CO_{3}}`$
-$`\displaystyle Ca^{2+} + CO_{3}^{2-} -> CaCO_{3}`$
+$`\displaystyle \mathrm{Ca^{2+} + CO_{3}^{2-} \rightarrow CaCO_{3}}`$
Alternatively, it can be written in terms of the total chemical reaction equation, in which the appearance of inorganic carbon species cancels out:
-$`\displaystyle Ca^{2+} + CO(NH_{2})_{2} + 2 H_{2}O -> 2 NH_{4}^{+} + CaCO_{3}`$
+$`\displaystyle \mathrm{Ca^{2+} + CO(NH_{2})_{2} + 2 H_{2}O \rightarrow 2 NH_{4}^{+} + CaCO_{3}}`$
which, written in terms of our primary variables are:
@@ -78,11 +78,11 @@ Calcium ion + Urea + 2 Water → (2 Ammonium ions) + Calcite
Note that for the sake of having a simplified chemistry for this dumux-course example, the component Ammonium is not considered as part of the reaction. Thus, you cannot set its source term, even though it is produced in the real reaction.
Similarly, we only account for "Total Carbon", which is the sum of all carbon species
-($`CO_{2}`$, $`H_{2}CO_{3}`$, $`HCO_{3}^{-}`$, and $`CO_{3}^{2-}`$).
+($`\mathrm{CO_{2}}`$, $`\mathrm{H_{2}CO_{3}}`$, $`\mathrm{HCO_{3}^{-}}`$, and $`\mathrm{CO_{3}^{2-}}`$).
Further, we assume that the overall reaction has reached an equilibrium state, i.e. every mole of urea hydrolyzed will lead to a mole of Calcite precipitating, and thus the precipitation rate simplifies to $`\displaystyle r_{prec} = r_{urea}`$.
-In reality, the initial geochemistry might be far away from conditions at which Calcite precipitates, e.g. due to low pH values at which the "Total Carbon" is mainly present as bicarbonate, $`HCO_{3}^{-}`$, not taking part in the Calcite precipitation reaction.
+In reality, the initial geochemistry might be far away from conditions at which Calcite precipitates, e.g. due to low pH values at which the "Total Carbon" is mainly present as bicarbonate, $`\mathrm{HCO_{3}^{-}}`$, not taking part in the Calcite precipitation reaction.
To reach the overall reaction's equilibrium state, the pH value needs to be increased first by ureolysis.
-However, to calculate the detailed precipitation rate of Calcite, we would first need to determine how much of the aggregate species "Total Carbon" is present in the form of each of its sub species, $`CO_{2}`$, $`H_{2}CO_{3}`$, $`HCO_{3}^{-}`$, and $`CO_{3}^{2-}`$.
+However, to calculate the detailed precipitation rate of Calcite, we would first need to determine how much of the aggregate species "Total Carbon" is present in the form of each of its sub species, $`\mathrm{CO_{2}}`$, $`\mathrm{H_{2}CO_{3}}`$, $`\mathrm{HCO_{3}^{-}}`$, and $`\mathrm{CO_{3}^{2-}}`$.
Further, we would need to account for all involved complex aqueous geochemistry to be able to determine the activities of both Calcium and Carbonate ions, which also impact the precipitation rate.
We feel that this very specific chemistry goes beyond what is necessary for this dumux-course exercise and simplify the chemistry also with the motivation to save on the run time, which accounting for the detailed, complex geochemistry would increase significantly.
The assumption of the overall reaction being at an equilibrium is used in many models for biomineralization.
@@ -135,18 +135,18 @@ make exercisebiomin
-### 5. CO2 injection to test aquitard integrity
+### 5. CO<sub>2</sub> injection to test aquitard integrity
-Now, the sealed aquitard is tested with a CO2-Injection into the lower CO2-storage aquifer.
+Now, the sealed aquitard is tested with a CO<sub>2<sub>-Injection into the lower CO<sub>2<sub>-storage aquifer.
__Task:__
-Implement a new boundary condition on the left boundary, injecting CO2 from 2 m to 3 m from the bottom. Make sure, that the injection time for the calcium and urea is finished. You can use the predefined value `gasFlux` directly and divide it by the molar mass of CO2.
+Implement a new boundary condition on the left boundary, injecting CO<sub>2<sub> from 2 m to 3 m from the bottom. Make sure, that the injection time for the calcium and urea is finished. You can use the predefined value `gasFlux` directly and divide it by the molar mass of CO<sub>2<sub>.
Run two simulations and compare them side by side by creating two input files, or overwriting the input file in the command line:
```bash
./exercise_biomin -Problem.Name biominNoUrea -Injection.ConcUrea 0
```
-The result for the biomineralization process during the CO2 injection should look like this:
+The result for the biomineralization process during the CO<sub>2<sub> injection should look like this:
@@ -196,19 +196,19 @@ Note: As both the Kozeny-Carman and the Power-Law relation use the same paramete
}
```
-What is the effect of the exchanged permeability calculation on the results, especially the leakage of CO2? What if the exponent would be smaller, e.g. $`\displaystyle \eta=2`$, which would mean that the precipitation is less efficient in sealing the leakage?
+What is the effect of the exchanged permeability calculation on the results, especially the leakage of CO<sub>2<sub>? What if the exponent would be smaller, e.g. $`\displaystyle \eta=2`$, which would mean that the precipitation is less efficient in sealing the leakage?
You can again run two simulations and compare them side by side by creating two input files, or overwriting the input file parameter in the command line:
```bash
./exercise_biomin -Problem.Name biominPowerLawExponent2 -PowerLaw.Exponent 2.0
```
-### 7. Use tabulated CO2 values instead of SimpleCO2
+### 7. Use tabulated CO<sub>2</sub> values instead of SimpleCO2
-So far we have been using a simplified component for CO2, which is based on the ideal gas law. Due to the conditions present in this exercise this is not too inaccurate, but for real applications of CO2 storage changes to the model are required. We use tabulated data for density and enthalpy of CO2, accessed through `GeneratedCO2Tables::CO2Tables` and `Components::CO2` from DuMu<sup>x</sup>.
+So far we have been using a simplified component for CO<sub>2</sub>, which is based on the ideal gas law. Due to the conditions present in this exercise this is not too inaccurate, but for real applications of CO<sub>2<sub> storage changes to the model are required. We use tabulated data for density and enthalpy of CO<sub>2<sub>, accessed through `GeneratedCO2Tables::CO2Tables` and `Components::CO2` from DuMu<sup>x</sup>.
__Task:__
-The CO2 component is used in the fluidsystem, which is defined in `properties.hh`. Replace the component `SimpleCO2` with `CO2` defined in `dumux/material/components/co2.hh`, with a CO2 table as an additional template parameter. Use the the table defined in `dumux/material/components/defaultco2table.hh`, noting the different namespace. Take care to include the appropriate headers.
+The CO<sub>2<sub> component is used in the fluidsystem, which is defined in `properties.hh`. Replace the component `SimpleCO2` with `CO2` defined in `dumux/material/components/co2.hh`, with a CO<sub>2<sub> table as an additional template parameter. Use the the table defined in `dumux/material/components/defaultco2table.hh`, noting the different namespace. Take care to include the appropriate headers.
```c++
#include <dumux/material/components/co2.hh> //!< CO2 component for use with tabulated values
--
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