PNG 550
Reactive Transport in the Subsurface

5.5 Homework Assignments

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Problem 5.1

In addition to the chemicals and biomass specified in example 5.1, assume there is also sulfate in the water at the concentration of 3.0 mmol/L. The initial sulfate reducing bacteria has the concentration of 1.0×10-6 mol-biomass/L.

Sulfate reduction (Fs = 0.08 and Fe = 0.92) goes as follows:

$\begin{array}{l}
0.125 \mathrm{SO}_{4}^{2-}+0.13525 \mathrm{CH}_{3} \mathrm{COO}^{-}+0.004375 \mathrm{NH}_{4}^{+}+0.0065 \mathrm{H}^{+} \rightarrow \\
0.004375 \mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}_{S R B}+0.250 \mathrm{HCO}_{3}^{-}+0.013 \mathrm{H}_{2} \mathrm{O}+0.125
\end{array}$

Sulfate reduction rate parameters are specified in Table 2. Note that it has two inhibition terms because it has both O2 and NO3 above in the redox ladder.

Table 1. Kinetic parameters of microbe-mediated reactions*
Reactions $\mu_{\max }(\mathrm{mol} / \mathrm{mol}-\mathrm{biomass/yr})$ $\begin{array}{l} K_{m, \text { acceptor }} \\ \text { (mol/kgw) } \end{array}$ $\begin{array}{c} K_{m, \text { donor }} \\ \text { (molkgw) } \end{array}$ $\begin{array}{c} K_{I, O 2(a q)} \\ \text { (molkgw) } \end{array}$ $\begin{array}{c} K_{I, \mathrm{NO} 3(a q)} \\ (\mathrm{molkgw}) \end{array}$
Sulfate reduction 35000 1.25x10-3 1.25x10-3 1.00x10-6 1.00x10-3

*Range of relevant parameters is from Cheng et al., 2016; Li et al., 2010.

Questions:
  1. What are the types of the reactions and the order of reactions in this system?
  2. Plot out the additional sulfate concentration evolution, together with other chemicals in the example;
  3. Increase both KI,NO3 and KI,O2(aq) values by a factor of 2 for the sulfate reduction reaction, what difference do you see in the time evolution figures.
  4. Initial O2(aq): Simulate one more case with no O2(aq) concentration. What are the differences in the concentration evolution of different species? And why are the differences?

Problem 5.2

Extension: In Problem 1, we mainly discuss how O2(aq) affects the microbe-mediated reactions. Other thermodynamics and kinetic parameters, including maximum biomass grow rate, half saturation of the electron donor and acceptor, and the concentrations of electron donor and acceptor, also affect the biomass reactions. Please use the input and database files from Problem 1 as the base case to do the following analysis comparing N2(aq) and sulfide evolution:

  1. How does the growth rate of NRB (maximum grow rate of nitrate reducing biomass μmax,NO3) change the evolution? The μmax,NO3 value in the base case is 20,000 mol/mol-biomass/yr. Simulate two more cases with μmax,NO3 of 40,000 and 60,000 mol/mol-biomass/yr.
  2. How does the half saturation of the electron donor for the nitrate-reducing reaction (e.g., Km,acetate) influence the evolution? The Km,acetate value in the base case is 1.0 mmol/kgw. Simulate two more cases using Km,acetate being 0.2 and 5.0 mmol/kgw.
  3. How does the abundance of electron donor (acetate) affect the evolution? The initial concentration of acetate Cinitial,acetate in the base case is 5.0 mmol/L. Simulate two more cases by increasing and decreasing Cinitial,acetate by an order of magnitude.