Exercises
49
2.3. List the dimensions of all parameters mentioned in Section 2.1.2.
2.4. Write the convection-diffusion equation (2.3.10) in Cartesian coordinates (1-0, 2-0,3-0).
2.5. Explain why the convection-diffusion equation cannot be used directly
to study the contaminant transport in porous media.
2.6. Prove that 8()y/8t =
2.8. Derive the advection-dispersion equation (2.4.23) from equation (2.4.31)
using Green's formula.
2.9. What is the scale dependence problem of the dispersivity coefficient?
2.10. Under what conditions can we use Eq. (2.5.14) to calculate the dispersion coefficients?
2.11. Derive Eq. (2.6.17).
2.12. What is the governing equation when radioactive decay and adsorption both exist?
2.13. Present the mathematical model for the two-dimensional experiment
described by Example 1 in Section 2.2.1.
2.14. Present the mathematical model for the one-dimensional experiment
described by Example 2 in Section 2.2.1.
2.15. Write the steady state flow model for Examples 1 and 2 in Section 2.6.3.
2.16. Assume that clean water C = 0 is injected into a homogeneous confined aquifer at rate Q from a single well and a steady radial flow is
formed. Then, the concentration ofinjected water is changed to Co> o.
Present an advection-dispersion model to describe this experiment.
49
2.3. List the dimensions of all parameters mentioned in Section 2.1.2.
2.4. Write the convection-diffusion equation (2.3.10) in Cartesian coordinates (1-0, 2-0,3-0).
2.5. Explain why the convection-diffusion equation cannot be used directly
to study the contaminant transport in porous media.
2.6. Prove that 8()y/8t =
2.8. Derive the advection-dispersion equation (2.4.23) from equation (2.4.31)
using Green's formula.
2.9. What is the scale dependence problem of the dispersivity coefficient?
2.10. Under what conditions can we use Eq. (2.5.14) to calculate the dispersion coefficients?
2.11. Derive Eq. (2.6.17).
2.12. What is the governing equation when radioactive decay and adsorption both exist?
2.13. Present the mathematical model for the two-dimensional experiment
described by Example 1 in Section 2.2.1.
2.14. Present the mathematical model for the one-dimensional experiment
described by Example 2 in Section 2.2.1.
2.15. Write the steady state flow model for Examples 1 and 2 in Section 2.6.3.
2.16. Assume that clean water C = 0 is injected into a homogeneous confined aquifer at rate Q from a single well and a steady radial flow is
formed. Then, the concentration ofinjected water is changed to Co> o.
Present an advection-dispersion model to describe this experiment.