PNG 550
Reactive Transport in the Subsurface

4.4 Homework Assignment

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Question 1 (an extension of example 4.1):

As an extension of the example 4.1, we can look at different parameters and understand how they change the cation concentrations on the exchange site. Please include all Cl- and OH- aqueous complexes as in example 4.1. Please calculate the major cation concentrations on the exchange site (K, Na, Ca, Mg, Ba, Sr) by changing only the parameter discussed in each sub-question, with all other parameters being the same as those in example 4.1. For each sub questions, please plot major cation concentrations on the exchange site as the changing parameter.

  1. Specific surface area: 1.39, 13.9, and 139.0 m2/g;
  2. CEC: 10.0, 100, and 1,000 meq/kg;
  3. pH of the Marcellus water: 7.02, 8.00, 12.0. (Note that at pH=12.0, you need to use the Cl- concentration you got from pH = 8.0 and put Na+ as "charge" species)

For each question, calculate the mole fraction of each species on the exchange site, and the mole fraction of each species compared to its own original total mass. Please make a table and a figure comparing different species. Which one has the largest percentage of its own mass on exchange sites? Why?

Which parameter(s) have the largest impact on ion exchange reactions? In lesson 3 we learned that pH is important for surface complexation reactions. Does it make a difference for ion exchange reactions?

Click here for HW4 solution. 

Question 2 (optional): This is part of problem 6.7 in chapter 6, A&P.

Read the paper (Valocchi et al., 1981). Native groundwater in the injection test of this paper had the composition of $Na^+=\ 86.5,\mathrm{\ Mg}^{2+}=18.2,\text{ and }\mathrm{Ca}^{2+}=11.1\mathrm{\ mmol}/\mathrm{L}$. Injected water has 14.66 meq Cl-/L. Selectivity coefficient were (Gaines and Thomas convention, activity = molal concentration) $\mathrm{K}_{\text{Na\Mg}}=0.54\text{ and }\mathrm{K}_{\text{Na\Ca}}=0.41$. Sediment $\mathrm{CEC}=750\mathrm{\ meq}/\mathrm{L}$ pore water. Calculate

  1. the composition of the exchange complex of native groundwater.
  2. the composition of water after the salinity jump, in equilibrium with the original exchange complex (compare with Figure 6.16).
  3. the composition of the exchange complex in equilibrium with injected water (cf. example 6.11