PrintPlease pick one of the following for homework assignments.
1) Chemical Weathering (Example 9.1 extension, total 60 points, 15 points each):
assess the role of dissolution rates, dissolution kinetics, rainwater chemistry, and rainwater abundance.
Continuing along example 1, please analyze the role of different parameters/conditions in determining chemical weathering rates and profile. In each of the questions below, please compare the base case in the example to two more cases with different parameter values. In each question, please keep all other parameters and conditions the same so we can fully focus on the effects of the changing parameter. In each question, draw the depth profiles of porosity, volume fractions of Quartz, K-Feldspar, and Kaolinite, and $\tau$ figures at 100,000 years:
- 1.1) Effects of K-Feldspar dissolution rates: K-Feldspar rate 10 and 100 times slower;
- 1.2) Effects of K-Feldspar equilibrium constants: 1 order of magnitude larger or 1 order of magnitude smaller;
- 1.3) Effects of rainwater composition: change the total inorganic carbon (HCO3-) concentration by 2 times larger or 2 times lower, to represent changing CO2 content in rainwater;
- 1.4) Effects of annual rainfall (flow velocity): increase and decrease by 2 times.
Click here for CrunchFlow Solutions.
2) Calcite dissolution in a 1D homogeneous column (short time scale, total 60 points).
In a homogeneous column at the length of 10.0 cm and diameter of 2.5 cm, calcite and sand grains are uniformly distributed in the column. Detailed physical and geochemical properties are in Table 2.
| Parameters | Values |
|---|---|
| Calcite (gram) | 14.62 |
| Quartz (gram) | 76.10 |
| Grain Size Calcite ($\mu m$) | 225-350 |
| Grain Size Quartz ($\mu m$) | 225-350 |
| BET SSA of Calcite (m2/g) | 0.115 |
| BET SSA of Quartz (m2/g) | 0.41 |
| AT Calcite (m2) | 1.68 |
| $\phi \text { ave }$ | 0.40 |
| $k_{e f f}\left(x 10^{-13} m^{2}\right)$ | 8.20 |
| Local longitudinal dispersivity $a_{L}(\mathrm{~cm})$ | 0.20 |
The initial and inlet solution conditions are listed in Table 3. Flushing through experiments were carried out at flow velocities of 0.1, 0.3, 3.6, 7.2 and 18.5 m/d at pH 4.0. Prior to dissolution experiments, each of the columns was flushed with 10-3 mol/L NaCl solution at pH 8.8 at 18.0 m/d to flush out pre-dissolved Ca(II) for a relatively similar starting point.
| Species | Initial Concentrations (mol/L, except pH) | Inlet Concentrations (mol/L, except pH) |
|---|---|---|
| pH | 8.8 | 4.0 for all columns and 6.7 only for Kratio,Ca/Qtz at 0.5 (in dissolution experiment) 8.8 (in tracer experiment) |
| Total Inorganic Carbon (TIC) | 1.0x10-3 (Approximate, close to equilibrium with calcite) | 1.0x10-10 to 1.0x10-5 (depending on experimental conditions, some contain CO2 bubbles) |
| Ca(II) | Varies between 1.0x10-5 to 1.5x10-4 depending on experimental conditions | 1.0x10-20 |
| Na(I) | 1.0x10-3 | 1.1x10-3 |
| Cl(-I) | 1.0x10-3 | 1.0x10-3 |
| Br(-I) | 1.0x10-20 | 1.2x10-4 |
| Number | Kinetic reactions | Log Keq | kCa (mol/m2/s) |
|---|---|---|---|
| (1) | $\mathrm{CaCO}_{3}(s)+\mathrm{H}^{+} \Leftrightarrow \mathrm{Ca}^{2+}+\mathrm{HCO}_{3}^{-}$ | 1.85 | 1.0x10-2 |
| (2) | $\mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{CO}_{3}^{0} \Leftrightarrow \mathrm{Ca}^{2+}+2 \mathrm{HCO}_{3}^{-}$ | -- | 5.60x10-6 |
| (3) | $\mathrm{CaCO}_{3}(s) \Leftrightarrow \mathrm{Ca}^{2+}+\mathrm{CO}_{3}^{2-}$ | -- | 7.24x10-9 |
Reaction (1) dominates when pH<6.0; reaction (3) dominates at higher pH conditions: reaction (2) are important under CO2- rich conditions.
Please do the following:
2.1) Calculate the pore volume (total volume of pore space), residence time $\tau_{a}$, and Peclet number (Pe) at each flow velocity;
2.2) Set up simulation for each flow velocity, and plot the breakthrough curves (BTCs, concentrations as a function of $\tau_{a}$) under each flow condition for Ca(II), IAP/Keq, and pH; plot one figure for each (Br, Ca(II), IAP/Keq, and pH) so you have all BTCs under different flow conditions in the same figure; comment on the role of flow in determining calcite dissolution and why; Here breakthrough curve is defined as concentrations vs time at the last grid block of the column.
2.3) Calculate the steady-state column-scale rates under each flow velocity by R = Q(Ceffluent – Cinfluent). Note that Q (volume/time) = u * Ac, where u is the Darcy flow velocity, Ac is the cross-sectional area of the column; Also note that "steady-state conditions" means the conditions under which concentrations in each grid do not change with time any more.
2.4) Calculate the DaI and DaII (again, under steady state) for each flow velocity;
2.5) Make a table of v, R, $\tau$, Pe, and Da numbers at each flow velocity. Plot R as a function of Pe and DaI and DaII.