10.3. Homework assignment

Question

Given the above geochemical conditions above and the physical flow and transport given in lesson 8, please set up the 2D Mixed and One-zone magnesite dissolution columns. Please answer the following questions:

1. Effects of flow rates:
   1. At the average flow velocity of 3.6 m/day, please
      1. compare the spatial profiles of Mg(II) in the two columns at the residence time of 3.0.
      2. draw the Mg(II) breakthrough curves using the equation for C_Mg(II),out,. Note that similar to the example in lesson 8, you will need to do this calculation for multiple time points. Which column dissolves magnesite faster under steady state conditions? By how much? Please show steps of calculation.
   2. At the average flow velocity of 0.36 m/day,please answer the same two questions as in question 1).
   3. At the average flow velocity of 36.0 m/day, please answer the same two questions as in question 1).
   4. Please summarize your observations from questions 1) to 3). What are the effects of flow velocities on the column-scale dissolution rates? Why are rate differences between the two columns similar under some flow conditions, and more different under other conditions?
2. (optional) Effects of transverse dispersivity a_T: If you increase or decrease the transverse dispersivity a_T, what difference does it make for the column-scale dissolution rates and spatial patterns of Mg(II) ? Do you think a_T is important in controlling column-scale dissolution rates? If so, why?