1. Mathematical Model governing equation & initial conditions boundary conditions

2. Initial conditions Zheng & Bennett

3. Boundary Conditions specified concentration no mass flux Specified mass flux Zheng & Bennett

4. Simplest form of the ADE Uniform 1D flow; longitudinal dispersion; No sink/source term; no chemical reactions There is a famous analytical solution to this form of the ADE with a continuous line source boundary condition. The solution is called the Ogata & Banks solution.

5. CoCo Aquifer is infinitely extensive

6. Zheng & Bennett

7. Ogata and Banks solution in a spreadsheet Spreadsheet can be accessed from the course homepage. Short Form: valid only for small values of D when x = v t; C/C o = ½

8. ADE with 1D flow: longitudinal dispersion & retardation With instantaneous pulse input source at the boundary….

9. University of Illinois codes on the web Find the link on the Geology 727 course homepage

10. ADE with 1D flow & 3D dispersion, retardation & 1 st order reaction term Uniform 1D flow; 3D dispersion; no sink/source term; retardation; 1 st order irreversible reaction ( is the same for the dissolved phase and the sorbed phase) Patch source solutions: 1.In an infinitely extensive aquifer: Illinois codes 2.In a confined (vertically bounded) aquifer: ATRANS

12. ATRANS

13. Zheng & Bennett

14. ATRANS Boundary Conditions

15. ATRANS Example in Zheng & Bennett Zheng & Bennett 3D dispersion: Source is 0.5 m thick (occupies 5% of the aquifer thickness) and 2 m wide (in the y direction). = 10 m 2D dispersion: Source is 10 m thick (occupies 100% of the aquifer thickness) and 2 m wide (in the y direction). 1D dispersion: Source is 10 m thick and infinitely wide in the y direction.

16. X = 10 Z = 5 centerline Z Z = 0 Z = 10 Source configuration for 3D dispersion problem in Z&B

17. 20 m 5 m wide Homework Problem Aquifer is 100 m thick. Source occupies 20% of the aquifer. Observation point is at x = 30 m. 3D dispersion: Source is 0.5 m thick (occupies 5% of the aquifer thickness) and 2 m wide (in the y direction). 2D dispersion: Source is 10 m thick (occupies 100% of the aquifer thickness) and 2 m wide (in the y direction). 1D dispersion: Source is 10 m thick and infinitely wide in the y direction. Observation point is on the centerline at x= 10 m Breakthrough curves 3D 1D 2D

18. 1D 3D

19. ADE with 1D flow & 3D dispersion, retardation & 1 st order reaction term Uniform 1D flow; 3D dispersion; no sink/source term; retardation; 1 st order irreversible reaction ( is the same for the dissolved phase and the sorbed phase) Patch source solutions: 1.In an infinitely extensive aquifer: Illinois codes 2.In a confined (vertically bounded) aquifer: ATRANS

20. X = 30 Z = 50 centerline Z Homework Problem Z = 0 Z = 100

21. 20 m 5m wide Aquifer is 100 m thick. Source occupies 20% of the aquifer. y z Problem Set #1

22. 20 m 5 m wide Homework Problem Aquifer is 100 m thick. Source occupies 20% of the aquifer. Zheng & Bennett Fig. 5.6 Aquifer is 10 m thick. Source is 0.5 m thick. Source occupies 5% of the aquifer. Observation point is at x = 30 m. Observation point is at x= 10 m 2 m wide 0.5 m

23. X = 30 Z = 50 centerline Z Homework Problem

24. X = 10 Z = 5 centerline Z Z = 0 Z = 10 Source configuration for 3D dispersion problem in Z&B