From a957e61c4b5f0fa222eab76baea1d05080fa9913 Mon Sep 17 00:00:00 2001
From: Mathis Kelm <mathis.kelm@iws.uni-stuttgart.de>
Date: Fri, 31 Mar 2023 19:57:36 +0300
Subject: [PATCH] [slides][biomin] fixup formatting, power law, tasks
---
slides/biomin.md | 37 ++++++++++++++++++-------------------
1 file changed, 18 insertions(+), 19 deletions(-)
diff --git a/slides/biomin.md b/slides/biomin.md
index f16bd050..05e43c58 100644
--- a/slides/biomin.md
+++ b/slides/biomin.md
@@ -122,10 +122,10 @@ Neglecting microbial growth and decay, attachment and detachment
- Urea hydrolysis
$$
\begin{aligned}
-\underset{\text{urea}}{CO(NH_2)_2} + 2 H_2O
+\underset{\text{urea}}{\mathrm{CO(NH_2)_2}} + 2 \mathrm{H_2O}
\overset{\text{urease}}{\rightarrow}
\\
-\underset{\text{ammonia}}{2NH_3} + \underset{\text{carbonic acid}}{H_2CO_3}
+\underset{\text{ammonia}}{\mathrm{2NH_3}} + \underset{\text{carbonic acid}}{\mathrm{H_2CO_3}}
\end{aligned}
$$
:::
@@ -135,7 +135,7 @@ $$
Here: Ureolytic microbes produce the enzyme urease (MICP)
$$
-CO(NH_2)_2 + 2 H_2O + Ca^{2+} \rightarrow 2 NH_4^+ + CaCO_3
+\mathrm{CO(NH_2)_2 + 2 H_2O + Ca^{2+} \rightarrow 2 NH_4^+ + CaCO_3}
$$
Different reactions in detail:
@@ -144,12 +144,12 @@ Different reactions in detail:
$$
\begin{array}{lr}
-CO(NH_2)_2 + 2 H_2O \rightarrow 2 NH_3 + H_2CO_3 \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\!
+\mathrm{CO(NH_2)_2 + 2 H_2O \rightarrow 2 NH_3 + H_2CO_3} \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\!
& \text{ureolysis} \\
-H_2CO_3 \leftrightarrow HCO_3^- + H^+ & \text{dissociation of carbonic acid} \\
-HCO_3^- \leftrightarrow CO_3^{2-} + H^+ & \text{dissociation of bicarbonate ion} \\
-2 NH_4^+ \leftrightarrow 2 NH_3 + 2 H^+ & \text{dissociation of ammonia} \\
-Ca^{2+} + CO_3^{2-} \leftrightarrow CaCO_3 \downarrow & \text{calcite precipitation/dissolution}
+\mathrm{H_2CO_3 \rightleftharpoons HCO_3^- + H^+} & \text{dissociation of carbonic acid} \\
+\mathrm{HCO_3^- \rightleftharpoons CO_3^{2-} + H^+} & \text{dissociation of bicarbonate ion} \\
+\mathrm{2 NH_4^+ \rightleftharpoons 2 NH_3 + 2 H^+} & \text{dissociation of ammonia} \\
+\mathrm{Ca^{2+} + CO_3^{2-} \rightleftharpoons CaCO_3 \downarrow} & \text{calcite precipitation/dissolution}
\end{array}
$$
@@ -166,7 +166,7 @@ $$
$$
\mathrm{
\underset{\text{calcium}}{Ca^{2+}} + \underset{\text{carbonate}}{CO_3^{2-}}
-\leftrightarrow \underset{\text{calcite}}{CaCO_3 \downarrow}
+\rightleftharpoons \underset{\text{calcite}}{CaCO_3 \downarrow}
}
$$
:::
@@ -242,7 +242,7 @@ $$
\begin{aligned}
\qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\!
\text{Precipitation rate:} \\
-r_\text{precip} &= f\; \left( A_\text{interface}, \Omega = \frac{\left[\mathrm{Ca}^{2+}\right]\left[CO_3^{2-}\right]}{K_\text{sp}}, T \right)
+r_\text{precip} &= f\; \left( A_\text{interface}, \Omega = \frac{\left[\mathrm{Ca}^{2+}\right]\left[\mathrm{CO_3}^{2-}\right]}{K_\text{sp}}, T \right)
\\
\qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\!
\text{For this exercise:} \\
@@ -266,7 +266,7 @@ K &= K_0 \left(\frac{1-\phi_0}{1-\phi}\right)^2 \left(\frac{\phi}{\phi_0}\right)
\\
\text{or}&
\\
-K &= K_0 \left( \frac{1-\phi_0}{1-\phi} \right)^\eta
+K &= K_0 \left( \frac{\phi}{\phi_0} \right)^\eta
\end{aligned}
$$
@@ -348,10 +348,10 @@ Academic problem setup
* 2 aquifers with sealing aquitard
* Upper aquifer: "drinking water"
- * Lower aquifer: "$CO_2$ storage"
+ * Lower aquifer: "$\mathrm{CO_2}$ storage"
* Problem:
* Leakage pathway
- * Stored $CO_2$ would migrate to drinking water aquifer!
+ * Stored $\mathrm{CO_2}$ would migrate to drinking water aquifer!
* Biomineralization injection could "seal" the leakage pathway
:::
::: {.column width=55%}
@@ -363,12 +363,11 @@ Academic problem setup
1. Get familiar with the code
2. Implement the simplified chemical reactions
- * Add kinetic reaction rates to chemistry-file
- * Use source()-function to link chemistry-file to problem
-3. Vary parameters, so that leakage pathway is "sealed" (porosity <0.07)
-4. Implement new boundary condition for $CO_2$-injection in lower aquifer
-5. Exchange the permeability law from Kozeny-Carman to a Power Law
-6. Use tabulated values for $CO_2$
+3. Use source()-function to link chemistry-file to problem
+4. Vary parameters, so that leakage pathway is "sealed" (porosity $<0.07$)
+5. Implement new boundary condition for $\mathrm{CO_2}$-injection in lower aquifer
+6. Exchange the permeability law from Kozeny-Carman to a Power Law
+7. Use tabulated values for $\mathrm{CO_2}$
## Exercise
--
GitLab