For this question you should read sections 2.1 to 2.5 in Fetter (1993) and it will be helpful to refer to the publication by Ogata and Banks (1961). Using the Ogata-Banks analytical solution to the advection- dispersion equation (see attached Excel spreadsheet), answer the questions below. Read Section 2.2 to understand the characteristics of the complimentary error function. Plot the results with concentration (C) on the Y axis and Time on the X axis. This form of plot is known as a breakthrough curve. Conceptual Model An unlined waste disposal site is located some distance L from a pristine river system. The waste disposal site is built on a sandy aquifer that has a relatively high permeability and the groundwater velocity varies seasonally from 0.2 to 0.8 m/day. The groundwater flow direction is from the waste disposal site toward the adjacent river. 2.2 Assume that the waste disposal site was built on top of a 1 m thick low permeability clay liner that eliminates downward advection through the liner. a) Show how the Ogata-Banks solution is modified to eliminate advection. b) Calculate the time required for C/Co to equal 0.1 at the base of the liner. Plot the results and assume a precision of 2 decimal places in the analytical solution. Vx Dp a Dh [L/T] [L'IT] [L] [L²/T] Со [mg/L³] 1.00E-03 1 1.00E+00 50 Spatial Interval = 1❘m Ogata-Banks Terms x-Vt 1st term 2nd term C/Co 0 -800 2.00E+00 6.73E-89 1.0000 1 -799 2.00E+00 1.11E-88 1.0000 2 -798 2.00E+00 1.82E-88 1.0000 3 -797 2.00E+00 2.99E-88 1.0000 4 -796 2.00E+00 4.91E-88 1.0000 5 -795 2.00E+00 8.06E-88 1.0000 6 -794 2.00E+00 1.32E-87 1.0000 7 -793 2.00E+00 2.17E-87 1.0000 8 -792 2.00E+00 3.55E-87 1.0000 9 -791 2.00E+00 5.81E-87 1.0000 10 -790 2.00E+00 9.51E-87 1.0000 11 -789 2.00E+00 1.56E-86 1.0000 12 -788 2.00E+00 2.54E-86 1.0000 13 -787 2.00E+00 4.15E-86 1.0000 14 -786 2.00E+00 6.77E-86 1.0000 15 -785 2.00E+00 1.10E-85 1.0000 16 -784 2.00E+00 1.80E-85 1.0000 17 -783 2.00E+00 2.93E-85 1.0000 18 -782 2.00E+00 4.78E-85 1.0000 19 -781 2.00E+00 7.77E-85 1.0000 20 -780 2.00E+00 1.26E-84 1.0000 Time Interval = 150 days Breakthrough Curve Position = 100 m [L] 800 Dn't 2*sqrt(D₁*t) t [L] [T] 800.8 56.60 800 Ogata-Banks Terms Concentration 1.2 1 0.8 0.6 0.4 0.2 Note that L and T units must be consistent for all parameters Here L is in metres and T is in days Required input parameters are in blue 0 0 5 10 Distance 55 15 20 25 vx*t Dh*t 2*sqrt(D₁*t) x- Vt 1st term 2nd term C/Co 1 1 150 150 1.001 150.150 2.001 99 0.00E+00 0.00E+00 0.00E+00 Breakthrough Curve 1.2 24.507 -50 2.00E+00 8.57E-04 9.98E-01 300 300 300.300 34.658 -200 2.00E+00 1.68E-16 1.00E+00 1 450 450 450.450 42.448 -350 2.00E+00 1.29E-31 1.00E+00 600 600 600.600 49.014 -500 2.00E+00 2.52E-47 1.00E+00 750 750 750.750 54.800 -650 2.00E+00 2.87E-63 1.00E+00 900 900 900.900 60.030 -800 2.00E+00 2.50E-79 1.00E+00 1050 1050 1051.050 64.840 -950 2.00E+00 1.88E-95 1.00E+00 1200 1200 1201.200 69.317 -1100 2.00E+00 1.28E-111 1.00E+00 Concentration 0.8 0.6 1350 1350 1351.350 73.521 -1250 2.00E+00 8.27E-128 1.00E+00 0.4 1500 1500 1501.500 77.498 -1400 2.00E+00 5.11E-144 1.00E+00 1650 1650 1651.650 81.281 -1550 2.00E+00 3.06E-160 1.00E+00 02 1800 1800 1801.800 84.895 -1700 2.00E+00 1.80E-176 1.00E+00 1950 1950 1951.950 88.362 -1850 2.00E+00 1.04E-192 1.00E+00 0 2100 2100 2102.100 91.697 -2000 2.00E+00 5.90E-209 1.00E+00 0 500 1000 1500 2000 2500 3000 3500 2250 2250 2252.250 94.916 -2150 2.00E+00 3.32E-225 1.00E+00 2400 2400 2402.400 98.029 -2300 2.00E+00 1.86E-241 1.00E+00 Time 2550 2550 2552.550 101.046 2700 2700 2702.700 103.975 2850 2850 2852.850 106.824 3000 3000 3003.000 109.599 -2450 2.00E+00 1.03E-257 -2600 2.00E+00 0.00E+00 -2750 2.00E+00 0.00E+00 -2900 2.00E+00 0.00E+00 1.00E+00 1.00E+00 1.00E+00 1.00E+00