Recent Developments on Groundwater Modelling

1. Recent Developments on Groundwater Modelling Felix qui potuit rerum cognoscere causas. (Virgilio) Jesus Carrera Institute Jaume Almera (IJA) for Earth Sciences Higher Council for Scientific Research (CSIC) Barcelona, Spain Recent Developments GW Modelling. Bucuresti, May, 2007

2. Contents • GW Modelling • Where are we now? • Where are we heading? • Reactive transport • Needed? Feasible?: 2 examples • Algorithmic simplifications • What about applications? • One example • The real barriers As seen from Barcelona !!! Recent Developments GW Modelling. Bucuresti, May, 2007

3. GW modeling Traditional use of models • Understanding the past • Evaluating the present • Assessing the future state of aquifers Semi-quantitative modelling is sufficient Recent Developments GW Modelling. Bucuresti, May, 2007

4. Pumping, Qi Recharge, ri Storage var. DSi Lateral exchange, fij Cell j Cell l Cell n Cell m fin Cell i fim fil GW modeling Modeling = Accounting Recent Developments GW Modelling. Bucuresti, May, 2007

5. Modelling: future needs Why important? • A model is the (water or solute mass) accounting system for water bodies • A well managed company needs a reliable accounting system. What about aquifers? • If not, technical hidrogeology will continue to be a minor economic activity, despite of the importance of true hydrogeology. But models need to be realistic, i.e., quantitatively accurate and reliable Recent Developments GW Modelling. Bucuresti, May, 2007

6. Dispersivity porosity Transport • Solute mass conservation • Advection • Difussion/Dispersion • Eq. Constants • Kinetic rates Reactive Transport • Chemical recations • Equilibrium • Kinetics Basic equations Flow • Momentum Conservation • Fluid mass conservation • K, T, S, recarga • B.C’s, geometría Recent Developments GW Modelling. Bucuresti, May, 2007

7. Stan N. Davis Vs Shlomo P. Neuman (Synthesis versus analysis) Question at PhD preliminary exam: You have T estimates from a large number of wells and you have to estimate drainage to a quarry What is the value of T you should use (Teq)? Equal to TG (geometric average of ponit T’s), larger than TG, smaller? Shlomo’d say TG (Matheron) But, if Stan asks, sure T>TG Recent Developments GW Modelling. Bucuresti, May, 2007

8. Flow is mathematically easy, but… K (or T) often grows with spatial scale Martinez-Landa, 2005 Recent Developments GW Modelling. Bucuresti, May, 2007

9. Spatial variability Poorly connected field (Matheron’s implicit assumption) Teff=TG Well connected field More realistic? Teff>>TG (Sanchez-Vila, 1996) Recent Developments GW Modelling. Bucuresti, May, 2007

10. Numerical Simulations • Generate random fields T (constant S) • Simulate pumping test • Analyze simulated drawdowns using Jacob’s method • Compare with Teq derived from parallel flow (Meier et al, 1998) Recent Developments GW Modelling. Bucuresti, May, 2007

11. Fast response = High T connection (= Small Jacob S) Slow response Low T connection (= Large Jacob S) COMPUTED DRAWDOWNS Display constant slope Recent Developments GW Modelling. Bucuresti, May, 2007

12. Jacob’s T is the effective T!!! Poorly connected field (Matheron’s implicit assumption) Teff=TG=TJac Well connected field More realistic? Teff=Tjac>>TG (Sanchez-Vila, 1996) Recent Developments GW Modelling. Bucuresti, May, 2007

13. Conclusions regarding flow • Flow simulation is easy, but Beware of heterogeneity !! • Often, transmissivity increases with scale due to connectivity of high K zones • Conventional Jacob interpretation of pumping test yields effective T Recent Developments GW Modelling. Bucuresti, May, 2007

14. Solute transport • Advection: v = q/f(q proportional to K) • Dispersion: Proportional to: aq • Reactions • Mass Conservation Water flux Porosity Dispersion coeff. Reactions Recent Developments GW Modelling. Bucuresti, May, 2007

15. Solution of ADE Initial Pulse At early times, little displacement, significant dilution and spreading Later on, dilution and spreading continue, but displacement becomes apparent Recent Developments GW Modelling. Bucuresti, May, 2007

16. Scale dependence of dispersivity Data from tracer tests and pollution plumes worldwide Dispersivity grows with test scale (Lallemand-Barres y Peandecerf, 1978) Recent Developments GW Modelling. Bucuresti, May, 2007

17. Kinematic porosity function of residence time Efective porosity in fractured rocks appears to increase with residence time (Guimera, 1998) Recent Developments GW Modelling. Bucuresti, May, 2007

18. Good calibration Good calibration Transport predictions are awful !!! El Cabril (UPC, 1999) Recent Developments GW Modelling. Bucuresti, May, 2007

19. Claassen & White (1973) Paces (1983) 2.0 Delany (1985) Bruton (1986) Velbel (1985) White (1986) 0.0 Physical surface area (log m2/kg water) Liu (1987) Gislason & Eugster (1987) Hurd (1973) -2.0 Herman & Lorah (1987) -4.0 -4.0 -2.0 0.0 2.0 Reactive surface area (log m2/kg water) Reaction rates Observed reaction rates are 2-3 orders of magnitude slower than expected from measurements (White & Peterson,1990) Recent Developments GW Modelling. Bucuresti, May, 2007

20. Simulate transport time Recent Developments GW Modelling. Bucuresti, May, 2007

21. Conclusions regarding transport • Transport simulation is mathematically more complex than flow, but practically easier But heterogeneity makes it impossible !! • Scale dependence of dispersivity and porosity • Tailing Recent Developments GW Modelling. Bucuresti, May, 2007

22. Reactive transport: It involves: 1) Solving the flow equation 2) Solving Ns transport equations 3) Simultaneously with NR chemicalreactions Is it needed? Can it be solved efficiently and be understood? Recent Developments GW Modelling. Bucuresti, May, 2007

23. C Solubility Water 2 Mixture Water 1 Salinity Calcite dissolution in coastal aqf. Mixture of two calcite saturated waters may be under or oversaturated with respect to calcite To simulate this effect, consider 1D diffusion experiment (Rezaei et al, 2005) freshwater calcite saltwater Recent Developments GW Modelling. Bucuresti, May, 2007

24. Reaction Rate Dissolution rate (controlled by diffusion) SI & r Simple mixing (no transport) Mixing leads to maximum undersaturation for 20% salt water and max. dissolution for 50% mixing Saturation Index (SI) Dissolution rate proportional to Diff coeff. and maximum at the fresh water end Recent Developments GW Modelling. Bucuresti, May, 2007

25. Speciation Dissolution causes diffusion of CO2 (acidity) at the freshwater end, which drives further dissolution Recent Developments GW Modelling. Bucuresti, May, 2007

26. Reducing concentration of CO2 at the freshwater end, causes an increase in subsaturation. Therefore, one would expect an increase in dissolution rate However, dissolution rate is dramatically reduced Sensitivity to CO2 Recent Developments GW Modelling. Bucuresti, May, 2007

27. Simulating reactive transport • Define chemical system and components • Solve transport equations for components (and/or primary species) • Speciation: Compute species concentrtns from components (and/or primary species) • Substitute species back into transport equations to obtain reaction rates Procedure Recent Developments GW Modelling. Bucuresti, May, 2007

28. Step 2: Solve transport of u Transport equations where (1) (2) (1)-(2) yields: Analytical solution for 2 species Assume 2 species (e.g. SO42- and Ca2+) in eq. with gypsum Step 1: Chemical system Reaction Components: is conservative! Recent Developments GW Modelling. Bucuresti, May, 2007

29. Step 3: Speciation Solve Together with Step 4: Compute r Plugging C2 into We obtain Transport Chemistry Analytical solution for 2 species Recent Developments GW Modelling. Bucuresti, May, 2007

30. (a) Dimensionless [SO42-] Dimensionless [Ca2+] c1 (e.g., SO42-) water1 mixture  (b) water2  reaction rate c2 (e.g., Ca2+) distance, Solution of binary system for pulse input Recent Developments GW Modelling. Bucuresti, May, 2007

31. u Distancefrom peak of u Spatial distribution of reaction rate reaction rate, r/f u r/f Spatial distribution of reaction rate is more controlled by mixing, than chemistry Distancefrom the peak of u Recent Developments GW Modelling. Bucuresti, May, 2007

32. Dimensionless reaction rate Dimensionless y-distance x-distancefrom the plume centre Solution in 2D total precipitate Recent Developments GW Modelling. Bucuresti, May, 2007

33. Conclusions regarding reactive transport The interplay between transport and reactions is non-trivial. Saturation index calculations are needed but they fail to indicate neither the rate of reactions, nor where or under which conditions they are maxima Therefore Reactive transport modelling is needed to understand the fate of pollutants In many cases • Reactive Transport modelling is not so hard! • Only need to solve for independent components • Dissequlibrium within the medium often controlled by mixing Recent Developments GW Modelling. Bucuresti, May, 2007

34. Can models be accurate? • Unknown parameters, extent and B.C.’s • Unknown actions. Pumping history is (one of) the best guarded secrets of any country! • But, long records of heads, and concentrations, and environmental isotopes, and well logs, and geophisics, and geology, and,.... • Need to test nm combinations to ensure consistency Recent Developments GW Modelling. Bucuresti, May, 2007

35. Modelling the Llobregat Delta Recent Developments GW Modelling. Bucuresti, May, 2007

36. Modelling the Llobregat Delta Recent Developments GW Modelling. Bucuresti, May, 2007

37. Geology CDS-c CDS-c UPC, 2003 Recent Developments GW Modelling. Bucuresti, May, 2007

38. Nice fits, but Spent most time chasing data Vazquez-Sune, 2007 Recent Developments GW Modelling. Bucuresti, May, 2007

39. Spent most time chasing data • Need for communication protocols and standardized data bases, for • Geology • Test data • Hydrographs • Concentration data, etc Recent Developments GW Modelling. Bucuresti, May, 2007

40. Conclusions • Flow simulation is easy, but Beware of heterogeneity !! • Often, transmissivity increases with scale due to connectivity of high K zones • Conventional Jacob interpretation of pumping test yields effective T • Transport simulation is conceptually and mathematically more complex than flow (it is current frontier!), but practically easier • Reactive transport modelling is needed to understand the fate of pollutants, but conceptually not so difficult (for hydrologist!). Chemistry can be complex. • In practice, need for communication, mapping, data handling standards. Recent Developments GW Modelling. Bucuresti, May, 2007

41. Conclusions regarding transport • Flow simulation is mathematically more complex than flow, but practically easier But heterogeneity makes it impossible !! • Scale dependence of dispersivity and porosity • Tailing Recent Developments GW Modelling. Bucuresti, May, 2007

42. Conclusions regarding reactive transport The interplay between transport and reactions is non-trivial. Saturation index calculations are needed but they fail to indicate neither the rate of reactions, nor where or under which conditions they are maxima Therefore Reactive transport modelling is needed to understand the fate of pollutants In many cases • Reactive Transport modelling is not so hard! • Only need to solve for independent components • Dissequlibrium within the medium often controlled by mixing Recent Developments GW Modelling. Bucuresti, May, 2007

43. Langerak Recent Developments GW Modelling. Bucuresti, May, 2007

44. Experimento • Reducing (CH4) sandy aquifer with a bit of ptrite and OM. • Recharge oxic water (O2and NO3-) add Cl- as tracer • Measure • Sediment (CEC, pyrite, OM, ...) • Conc’s (t) Recent Developments GW Modelling. Bucuresti, May, 2007

45. Vertical cross section Recent Developments GW Modelling. Bucuresti, May, 2007

46. Model • Code: RETRASO • Tres modelos para las tres capas • Análisis de sensibilidad • Calibration: • Transport • dispersivity • Geochemistry • CEC • Mineral conc. • Kinetics parameters Recent Developments GW Modelling. Bucuresti, May, 2007

47. Sensitivity to pyrite kandσ • Oxidation byO2 • reactive surface (σ) evolves Recent Developments GW Modelling. Bucuresti, May, 2007

48. CH4 oxidation? Recent Developments GW Modelling. Bucuresti, May, 2007

49. Final model • Aqueous species • e-, H+, Ca2+, Cl-, Fe2+, HCO3-, K+, Mg2+, Mn2+, Na+, NH4+, NO3-, SO42-, CH4 • CaCO3(aq), CaHCO3+, CaSO4(aq), CO2(aq), CO32-, Fe3+, FeCO3(aq), FeHCO3+, Fe(OH)2+, Fe(OH)3(aq), Fe(OH)4, MgHCO3+, MgSO4(aq), H2S(aq), HS-, OH-, O2(aq), MnCO3(aq), MnHCO3+, MnO4-, MnSO4(aq) • Cation exchange • X2-Ca, X2-Fe, X-K, X2-Mg, X2-Mn, X-Na, X-NH4 • Eq. minerals • Fe(OH)3 • Other solid phases (cinéticas) • Pirita (FeS2), materia orgánica (CH2O), calcita (CaCO3), siderita (FeCO3), rodocrosita (MnCO3) • FeS2y CH2O y oxidadospor O2y NO3- Recent Developments GW Modelling. Bucuresti, May, 2007

50. Some results Recent Developments GW Modelling. Bucuresti, May, 2007