What is Induced Calcite Precipitation (ICP)?

Microbes change the chemistry in a way that promotes the precipitation of calcite.

What is ICP?

Credit: James Connolly, Montana State University.

What is ICP?

Results of ICP

Segmented CT image of a glass-bead column mineralized by ICP

Credit: Johannes Hommel, University of Stuttgart

Why investigate ICP?

Why investigate ICP?

Applications in which a porous medium should be cemented in-situ, e.g. sealing, leakage mitigation, creating subsurface barries, reducing erosion, or stabilizing soil.

Main desired effects of ICP in those applications are:

• reduce flow (reduce \(K\) and \(k_r\), increase \(p_c\))
• increase mechanical strength

Model concept: Relevant processes

Model concept: Relevant processes

Model concept: Relevant processes

Model concept: Relevant processes

MICP: Main reactions

Here: Ureolytic microbes produce the enzyme urease (MICP) \[ \mathrm{CO(NH_2)_2 + 2 H_2O + Ca^{2+} \rightarrow 2 NH_4^+ + CaCO_3} \]

Different reactions in detail:

\[ \begin{array}{lr} \mathrm{CO(NH_2)_2 + 2 H_2O \rightarrow 2 NH_3 + H_2CO_3} \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! & \text{ureolysis} \\ \mathrm{H_2CO_3 \rightleftharpoons HCO_3^- + H^+} & \text{dissociation of carbonic acid} \\ \mathrm{HCO_3^- \rightleftharpoons CO_3^{2-} + H^+} & \text{dissociation of bicarbonate ion} \\ \mathrm{2 NH_4^+ \rightleftharpoons 2 NH_3 + 2 H^+} & \text{dissociation of ammonia} \\ \mathrm{Ca^{2+} + CO_3^{2-} \rightleftharpoons CaCO_3 \downarrow} & \text{calcite precipitation/dissolution} \end{array} \]

Model concept: Relevant processes

Model concept: Relevant processes

Balance Equations

Overall procedure of implementing chemical reactions in DuMu\(^\mathsf{x}\):

1. Chemical equation calculate equilibrium/kinetic reaction rate e.g. \(r_\text{urea}\)
2. Reaction rate set component source/sink term e.g. \(q^\varphi\) depending on and chemical reaction

Sources & Sinks:

For this exercise:

• Neglecting microbial growth and decay, attachment and detachment as we assume a fixed biofilm for simplicity!
• We also assume that the rate of precipitation is equal to the rate of ureolysis, saving the work of detailed geochemistry calculations for the sake of both simplicity and faster run times.

Sources & Sinks:

\[ \begin{aligned} &\text{Urea:} & q^{\text{urea}} &= -r_\text{urea} \\ &\text{Calcium:} & q^{\mathrm{Ca}^2+} &= -r_\text{precip} \\ &\text{Total carbon:}& q^{\mathrm{C}_\text{tot}^+} &= r_\text{urea} - r_\text{precip} \\ &\text{Calcite:} & q^{\mathrm{C}} &= r_\text{precip} \end{aligned} \]

Sources & Sinks:

\[ \begin{aligned} \qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \text{Precipitation rate:} \\ r_\text{precip} &= f\; \left( A_\text{interface}, \Omega = \frac{\left[\mathrm{Ca}^{2+}\right]\left[\mathrm{CO_3}^{2-}\right]}{K_\text{sp}}, T \right) \\ \qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \text{For this exercise:} \\ r_\text{precip} &= r_\text{urea} \\ \qquad\qquad & \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \!\!\!\!\!\! \text{Ureolysis rate:} \\ r_\text{urea} &= k_\mathrm{urease}^\mathrm{m} k_{\mathrm{urease}, \text{biofilm}} \left(\rho_\text{biofilm} \phi_\text{biofilm}\right) \frac{m_\text{urea}}{K_\text{urea} + m_\text{urea}} \end{aligned} \]

Supplementary Equation:

• Updating porosity and permeability

\[ \begin{aligned} \phi &= \phi_0 - \Sigma_\varphi \phi_\varphi \\ K &= K_0 \left(\frac{1-\phi_0}{1-\phi}\right)^2 \left(\frac{\phi}{\phi_0}\right)^3 \\ \text{or}& \\ K &= K_0 \left( \frac{\phi}{\phi_0} \right)^\eta \end{aligned} \]

Specific Implementations

• Implement reactive sources and sinks, calling a seperate chemistry file

#include "chemistry/simplebiominreactions.hh" // chemical reactions
…
using Chemistry = typename Dumux::SimpleBiominReactions<NumEqVector,
                                                        VolumeVariables>;
…

Specific Implementations

• Implement reactive sources and sinks, calling a seperate chemistry file

NumEqVector source(const Element& element,
                   const FVElementGeometry& fvGeometry,
                   const ElementVolumeVariables& elemVolVars,
                   const SubControlVolume& scv) const
{
    NumEqVector source(0.0);
    Chemistry chemistry;

    const auto& volVars = elemVolVars[scv];
    chemistry.reactionSource(source, volVars);

    return source;
}

Specific Implementations

• Update porosity in dumux/material/fluidmatrixinteractions/porosityprecipitation.hh

…
auto priVars = evalSolution(element, element.geometry(),
                            elemSol, scv.center());
Scalar sumPrecipitates = 0.0;

for (int solidPhaseIdx = 0; solidPhaseIdx < numSolidPhases; ++solidPhaseIdx)
    sumPrecipitates += priVars[numComp + solidPhaseIdx];

using std::max;
return max(minPoro, refPoro - sumPrecipitates);
…

Specific Implementations

• Update permeability in /material/fluidmatrixinteractions/permeabilitykozenycarman.hh

template<class Scalar>
PermeabilityType evaluatePermeability(PermeabilityType refPerm,
                                      Scalar refPoro,
                                      Scalar poro) const
{
    using std::pow;
    auto factor = pow((1.0 - refPoro)/(1.0 - poro), 2)
        * pow(poro/refPoro, 3);
    refPerm *= factor;
    return refPerm;
}

Exercise

Exercise tasks

1. Get familiar with the code
2. Implement the simplified chemical reactions
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

First step: Go to https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/tree/master/exercises/exercise-biomineralization and check out the README