Mathematical Modeling of Pollutant Transport in Groundwater

1. Mathematical Modeling of Pollutant Transport in Groundwater Rajesh Srivastava Department of Civil Engineering IIT Kanpur

2. Outline of the Talk • Sources • Processes • Modelling • Applications

3. Sources of GW Pollution • Irrigation • Landfills • Underground Storage tanks • Industry

5. Advection • Mass transport due to the flow of the water • The direction and rate of transport coincide with that of the groundwater flow. Diffusion • Mixing due to concentration gradients Dispersion • Mechanical mixing due to movement of fluids through the pore space

6. Velocity Position in Pore Dispersion • Spreading of mass due to • Velocity differences within pores • Path differences due to the tortuosity of the pore network.

9. Stagnant or Immobile liquid Pore Spaces Mobile/flowing liquid Intra-particle pores Gas Figure: Courtesy Sylvie Bouffard, Biohydrometallurgy group, Vancouver 12 18

10. Brief Chronology • Unsaturated flow equation by Richards (1931) • Coats and Smith (1964)proposed dead-end pores in oil wells • Equilibrium reactive transport theories proposed • Breakthrough curves with pronounced tailings observed • Non-equilibrium models developed • Goltz and Roberts (1986)physical non-equilibrium model • Brusseau et al. (1989)developedMPNE • Slow and Fast Transport model developed by Kartha (2008)

11. 1 1 C/Co C/Co 0 0 Time Time Start Start A B Experimental Setup INFLOW A OUTFLOW B

13. Conservation of Liquid Mass where Sl is source/sink term. Darcy velocity in unsaturated porous medium Hydraulic head based on elevation head z Hydraulic conductivity Darcy velocity Liquid pressure in unsaturated conditions Intrinsic permeability in unsaturated conditions

14. Brooks-Corey and van Genuchten Relations • Relation between suction pressure, liquid pressure, and liquid saturation • Relation between relative permeability and liquid saturation Effective saturation is given as Gas pressure Pg is considered zero, therefore

15. van Genuchten equations

18. Transport Model • Reactive advective-dispersive equation • Here we use multi-process non-equilibrium equations. • MPNE model • Liquid exists in mobile and immobile phase. • Solid in contact with mobile and immobile liquid. • Instantaneous sorption mechanism between liquids and solids. • Rate-limited sorption mechanism between liquids and solids.

19. MPNE Equations Where, Si - concentration of metal in sorbed phase (i.e. solid), Ki - adsorption coefficient, ki - sorption rate, α - mass transfer rate between mobile and immobile liquid, Fi - fraction for instantaneous sorption, f - fraction of sorption site in contact with mobile liquid.

20. Numerical Solution for Unsaturated Flow • The mass conservation equation is solved for liquid pressure • Implicit finite-difference method is used Residual form of conservation of mass equation for liquid Taylor’s series expansion of residual equation will lead to the following form Pressure values updated at each iteration step

21. Numerical Solution for MPNE Transport • Conservation of mass for metal is solved for concentration in liquid • Implicit finite-difference in time step used for formulations • Residual formulation obtained for concentration in mobile liquid The finite-difference formulation for sorbed concentration is The residual formulation for solute concentration in mobile liquid is: Taylor’s series expansion of the above residual equation Updated Concentration is

22. Inflow qt = 3 cm/d 10 cm Water Table Verification of the Numerical Model FLOW (Compared with VG’s Flow Model and Kuo et al. (1989) Infiltration Model) 150 cm

23. MPNE Transport 30 cm Input Parameters

24. I Immobile Liquid Cim and σim II Slow Liquid Csland σsl III Fast Liquid Cfsand σfs αim αsf Kim Ksl ksl kim V Rate – limited Sorption Site, Sim2 VII Rate-limited Sorption Site, Ssl2 IV Instant Sorption Site, Sim1 VI Instant Sorption Site, Ssl1 Concept of Slow and Fast Transport • Movement of liquids is heterogeneous • Liquid flow is conceptualized as slow and fast zones • Multiple sources of non-equilibrium solute interactions occurs between solids and different liquids 4

25. Conservation of solute mass • Solute mass conservation in fast liquid • In slow liquid

26. Conservation of solute mass…. • Rate of change of instantaneously sorbed solute mass • Rate of change of rate-limited sorbed mass Similar instantaneous and rate-limited sorption exist for immobile liquid • Solute mass conservation in immobile liquid

27. FINITE-DIFFERENCE FORMULATION OF SFT MODEL The implicit finite-difference form of metal mass conservation in fast moving liquid in a FD cell is: The implicit finite-difference form of metal mass conservation in slow moving liquid in a FD cell is: The implicit finite-difference form of metal mass conservation in immobile liquid in a FD cell is:

28. Formulations continued…. Residual equations are formed for the finite-difference equations for conservation of metal mass in fast and slow moving liquids. Residual equations expanded using Taylor’s series approximation. The linear system of equations is solved Update concentration terms:

29. Verification and Evaluation(Brusseau et. al., 1989) Numerical Model Validation….. Brusseau, M.L., Jessup, R.E., Rao, P.S.C.: Modeling the transport of solutes….. Water Resources Research 25 (9), 1971 – 1988 (1989)

30. REMEDIATION OF GROUNDWATER POLLUTION DUE TO CHROMIUM IN NAURIA KHERA AREA OF KANPUR Central Pollution Control Board Lucknow National Geophysical Research Institute Hyderabad Industrial Toxicology Research CentreLucknow Indian Institute of Technology Kanpur

31. ~ 5 km2 Location map of Nauriyakhera IDA, Kanpur, U.P.

32. CGWB Observations in Kanpur 1994-2000 • Cr 6+ found in groundwater generally exceed > 0.11 mg/l (Permissible Limit is 0.05 mg/l) • Cr 6+ observed in Industrial areas in depth range of 15 – 40 m >10 mg/l • Nauriakhera (Panki Thermal Power Plant Area) Cr 6+ 14 m - 8.0 mg/l 15 m – 0.31 mg/l 35 m – 7.0 mg/l 40 m – 0.68 mg/l • Used Chromite ore (Sodium Bichromate) dumped in pits and low lying areas cause of Cr pollution • Persistence in the phreatic zone up to 40 m depth despite presence of thick clay zones

34. Observation Wells in Nauriyakhera IDA, Kanpur, U.P.

35. March 2005 Total Chromium (mg/l) in groundwater - Nauriyakhera IDA, Kanpur

36. Total Chromium (mg/l) in groundwater -Nauriyakhera IDA, Kanpur

37. Fence Diagram – Nauriyakhera IDA, Kanpur

38. Total Chromium Plume from Source after 10 years

39. Total Chromium Plume from Source after 40 years

40. Application to Heap Leaching • Heap leaching is a simple, low-cost method of recovering precious metals from low-grade ores. • Ore is stacked in heaps over an impermeable leaching-pad. • Leach liquid is irrigated at the top • Liquid reacts with metal and dissolves it. • Dissolved metal collected at the bottom in the leaching pad.

42. Why Heap Leaching ? • Traditional methods of gold extraction viz - ore sieving, washing, etc. are obsolete and uneconomical. • Pyro-metallurgy is highly costly and non-viable for low-grade ores. • Leaching is the only process to extract metallic content from the low-grade ores. • Among leaching methods – Heap leaching is most economical

43. Why we are interested in Heap Leaching? • Heaps are generally stacked in unsaturated conditions. • The dissolution reaction occurs in the presence of oxygen. • The flow of liquid and metals inside the heaps are governed by principles of flow and solute transport through porous medium • Solving unsaturated flow equations and reactive transport equations enables us to model heap leaching process.

44. Mine Pit ORE PREPARATION Sprinklers or wobblers Leach pad Recovery Plant Pregnant solution pond Barren Solution Pond Types of leaching • Underground in-situ leaching • Tank leaching • Heap leaching • Pressure leaching Heap • Impermeable leach pad • Liners • Crushed metal ore • Irrigation system • Pregnant solution pond • Barren solution pond Components of a heap

45. MPNE Model Effluent outflow into the leaching pad Average outflow Cumulative outflow • The average outflow gradually attains steady state • Sudden decrease in outflow on stoppage of irrigation • Rate of recovery reduced after stoppage

46. MPNE Model Sensitivity Analyses of MPNE parameters • Sensitivity Analysis conducted to assess influence of model input parameter on output. • Parameters considered are – α, km and kim Influence of α Recovery curves

47. MPNE Model - Sensitivity Analyses.. Higher recovery and higher peaks for cases having higher sorption rates Influence of km & kim Breakthrough Curves Recovery Curves

48. MPNE Model Effect of variation in irrigation Recovery Curves Outflow Curves Higher recovery of metal at slower irrigation rate Breakthrough Curves

49. Two Dimensional Heap Leaching by SFT method 1.5 m SFT Parameters ksl = 4.98×10-6 s-1 (σsl)max = 0.065 αsf = 2.875×10-7 s-1 0.5 m • Grid Spacing • Horizontal Direction = 1.72 cm • Vertical Direction = 1.69 cm 2.5 m Average concentration of metal in the outflow is computed as

50. SFT Model Influence of αsf Sensitivity Analyses of SFT Parameters Breakthrough curves αsf has considerable influence in breakthroughs and recovery of metal after the irrigation is stopped Recovery Curves