diff --git a/slides/biomin.md b/slides/biomin.md index ac68768d3c47c07f481743647e988d9a77a4f7ad..05e43c58ec79025e28d3ba2bee5598d9b25d9c2d 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 @@ $$ \begin{aligned} \qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \text{Precipitation rate:} \\ -r_\text{precip} &= f\; \left( A_\text{interface}, \Omega = \frac{\left[\mathrm{Ca}^{2+}\right]\left[CO_3^{2-}\right]}{K_\text{sp}}, T \right) +r_\text{precip} &= f\; \left( A_\text{interface}, \Omega = \frac{\left[\mathrm{Ca}^{2+}\right]\left[\mathrm{CO_3}^{2-}\right]}{K_\text{sp}}, T \right) \\ \qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \text{For this exercise:} \\ @@ -266,7 +266,7 @@ K &= K_0 \left(\frac{1-\phi_0}{1-\phi}\right)^2 \left(\frac{\phi}{\phi_0}\right) \\ \text{or}& \\ -K &= K_0 \left( \frac{1-\phi_0}{1-\phi} \right)^\eta +K &= K_0 \left( \frac{\phi}{\phi_0} \right)^\eta \end{aligned} $$ @@ -305,6 +305,8 @@ NumEqVector source(const Element& element, ## Specific Implementations * Update porosity in dumux/material/fluidmatrixinteractions/porosityprecipitation.hh + +<section style="font-size: 0.9em"> ```cpp … auto priVars = evalSolution(element, element.geometry(), elemSol, scv.center()); @@ -317,6 +319,8 @@ using std::max; return max(minPoro, refPoro - sumPrecipitates); … ``` +</section> + ## Specific Implementations * Update permeability in /material/fluidmatrixinteractions/permeabilitykozenycarman.hh @@ -344,10 +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%} @@ -359,12 +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