(Z&B)

1. Calibration step (calibrate flow & transport model) Design conceptual model Assess uncertainty Steps in Transport Modeling Adjust parameter values (Z&B)

2. Designing a Transport Model Conceptual model of the flow system Governing equation 1D, 2D, or 3D steady-state or transient flows steady-state or transient transport Boundary conditions Initial conditions Design the grid Time step Input parameters

3. TMR (telescopic mesh refinement) TMR is used to cut out and define boundary conditions around a local area within a regional flow model. From Zheng and Bennett

4. GWV option for Telescopic Mesh Refinement (TMR)

7. Input Parameters for Transport Simulation Flow hydraulic conductivity (Kx, Ky, Kz) storage coefficient (Ss, S, Sy) recharge rate pumping rates All of these parameters potentially could be estimated during calibration. That is, they are potentially calibration parameters. Transport porosity () dispersivity (L, TH, TV) retardation factor or distribution coefficient 1st order decay coefficient or half life source term (mass flux)

8. Input Parameters for Transport Simulation Flow hydraulic conductivity (Kx, Ky, Kz) storage coefficient (Ss, S, Sy) recharge rate pumping rates v = K I /  D = vL + Dd Transport porosity () dispersivity (L, TH, TV) retardation factor or distribution coefficient 1st order decay coefficient or half life source term (mass flux)

9. We need to introduce a “law” to describe dispersion, to account for the deviation of velocities from the average linear velocity calculated by Darcy’s law. True velocities Average linear velocity

10. Microscopic or local scale dispersion Figure from Freeze & Cherry (1979)

11. Macroscopic Dispersion (caused by the presence of heterogeneities) Homogeneous aquifer Heterogeneous aquifers Figure from Freeze & Cherry (1979)

12. Dispersivity () is a measure of the heterogeneity present in the aquifer. A very heterogeneous porous medium has a higher dispersivity than a slightly heterogeneous porous medium.

13. Option 1: Assume an average uniform K value and simulate dispersion by using large values of dispersivity. Z&B Fig. 3.24

14. Field (Macro) Dispersivities Gelhar et al. 1992 WRR 28(7) Also see Appendix D In book by Spitz and Moreno (1996) A scale effect is observed.

15. Schulze-Makuch, 2005 Ground Water 43(3) Unconsolidated material

16. Theoretical “ideal” plume Tompson and Gelhar (1990) WRR 26(10)

17. Option 2: Simulate the variablity in hydraulic conductivity and use small (micro) dispersivity values. Hydraulic conductivity field created using a random field generator Tompson and Gelhar (1990), WRR 26(10)

18. Model Application: The MADE-2 Tracer Test Injection occurs halfway between the water table and the bottom of the aquifer. See Section 14.4.2 (p. 429) in Z&B

19. Theoretical “ideal” plume MADE-2 Tracer Test Injection Site

20. Generating the hydraulic conductivity field Kriging Random field generator

23. Incorporating the geology Anderson et al. (1999), Sedimentary Geology

24. Synthetic deposit of glacial outwash Anderson et al. (1999) Sedimentary Geology

25. Weissmann et al. (2002), WRR 38 (10)

26. 4 Facies Weissmann et al. (1999), WRR 36(6)

27. LLNL Site (LaBolle and Fogg, 2001) Instantaneous source Note the complex shape of the plume.

28. Summary Option 1: Assume an average uniform K value and simulate dispersion by using large values of dispersivity. Option 2: Simulate the variablity in hydraulic conductivity and use small (micro) dispersivity values. Option 2 requires detailed geological characterization that may not be feasible except for research problems.

29. Input Parameters for Transport Simulation Flow hydraulic conductivity (Kx, Ky, Kz) storage coefficient (Ss, S, Sy) recharge rate pumping rates v = K I /  D = vL + Dd Transport porosity () dispersivity (L, TH, TV) retardation factor or distribution coefficient 1st order decay coefficient or half life source term (mass flux)

30. “…the longitudinal macrodispersivity of a reactive solute can be enhanced relative to that of a nonreactive one.” Burr et al., 1994, WRR 30(3) At the Borden Site, Burr et al. found that the value of L needed to calibrate a transport model was 2-3 times larger when simulating a chemically reactive plume. They speculated that this additional dispersion is caused by additional spatial variability in the distribution coefficient. Research by Allen-King (NGWA Distinguished Lecturer) shows similar effects.

31. Input Parameters for Transport Simulation Flow hydraulic conductivity (Kx, Ky, Kz) storage coefficient (Ss, S, Sy) recharge rate pumping rates v = K I /  D = vL + Dd Transport porosity () dispersivity (L, TH, TV) retardation factor or distribution coefficient 1st order decay coefficient or half life source term (mass flux)

32. Simulated: smooth source concentration (best calibration) Simulated: double-peaked source concentration (best calibration) Borden Plume Z&B, Ch. 14

33. from Z&B Goode and Konikow (1990), WRR 26(10) Transient flow field affects calibrated (apparent) dispersivity value

34. Calibrated values of dispersivity are dependent on: • Heterogeneity in hydraulic conductivity (K) • Heterogeneity in chemical reaction parameters (Kd and ) • Temporal variability in the source term • Transience in the flow field

35. Input Parameters for Transport Simulation Flow hydraulic conductivity (Kx, Ky, Kz) storage coefficient (Ss, S, Sy) recharge rate pumping rates v = K I /  D = vL + Dd Transport porosity () dispersivity (L, TH, TV) retardation factor or distribution coefficient 1st order decay coefficient or half life source term (mass flux)

36. Common organic contaminants Source: EPA circular

37. fraction of organic carbon Spitz and Moreno (1996)

38. Spitz and Moreno ( 1996)