Transport with Steady-State Water Flow Exercises

 

1. A chemical solution is being added to a soil at a constant rate (flux density) of 1.2 cm per day. The concentration of the inflowing solution is 100 micrograms per ml. This solution is allowed to flow into the soil for 1 day. After that, pure water continues to enter the soil at the same rate. The chemical is not adsorbed on the soil surfaces. The soil has a volumetric water content of 0.3 m³ m^-3. The chemical is not undergoing degradation. The dispersivity of the chemical in this soil is 0.5 cm.

a.      What is the pore water velocity for this flow system? (Recall that the pore water velocity is the flux density divided by the volumetric water content.)

b.      Describe the location and shape of the pulse of chemical 2, 4, 8, and 16 days after flow begins.

2.      Repeat exercise 1 for a flux density of 2.4 cm per day. Compare these results with those in that exercise. Compare the positions of the curves, their shapes, and the areas under them.

3.      Describe the effect of pore water velocity upon the shape of the curves at these times. Experiment with additional pore water velocities as needed.

4.      Consider again the soil described in exercise 1. This time the chemical solution is allowed to enter the soil for 100 days.

a.      At what times will the concentration reach one half of its maximum value (or 50 micrograms per ml) for positions 10, 20, 40, and 80 cm from the inlet?

b.      Do the times required depend upon the dispersivity value? Examine this for positions near the inlet as well as far from it. Summarize your findings.

c.      Consider the time required to reach 50 micrograms per ml concentration at 80 cm. How much solution has entered into the soil by this time?

d.      How much water is stored in the pores of the soil from the soil surface to the 80-cm depth? Compare this amount with the amount found in part c. Does the same relationship hold for positions of 10, 20, and 40 cm?

5. Use the retain line features of the software to compare the curves 4 hours after application with a flux density of 2.4 cm per hour with the curve for 8 hours after application with a flux density of 1.2 cm per hour. What do you find? Can you adjust a parameter to make these 2 curves coincide? If so, how?
6. Another experiment was conducted with a pesticide as the chemical. This product was adsorbed somewhat on the soil surfaces. In fact it had a retardation factor of 2. All other parameters were the same as those in exercise 1.
1. Describe the location and shape of the pulse of chemical 2, 4, 8, and 16 days after flow begins
2. Compare these curves with those for the non-adsorbed material in exercise 1. What similarities and differences do you observe?
3. Since the flow rate and the concentration of chemical in the inflowing solution in this case were the same as those used in exercise 1, the amount of chemical entering the soil was the same as in exercise 1. Why then is the concentration much less in this case? Hint: What concentration is being shown on these graphs? 
7. Simulate flow for several additional chemicals with larger retardation factors. Draw a graph of the position of the center of the pulse 10 days after flow begins for different retardation factors. How does the retardation factor influence the position of the pulse?
8. Consider a soil with an initial concentration of 100 micrograms per ml. Pure water enters the soil with a pore water velocity of  2.0 cm/day. At what time will the concentration of chemical at 30 cm equal one half its initial value? At what time will the concentration at 40 cm be one half its initial value? Does the answer to this question depend upon the dispersivity? At what time will the value at 200 cm be one-half its original value?