Contaminant Hydrogeology II

1. Contaminant Hydrogeology II Гидрогеология Загрязнений и их Транспорт в Окружающей Среде Yoram Eckstein, Ph.D. Fulbright Professor 2013/2014 Tomsk Polytechnic University Tomsk, Russian Federation Fall Semester 2013

2. Basic Concepts • Mass Balance and the Control Volume • Physical Transport of Chemicals • Advective Transport • Fickian Transport • Turbulent Diffusion • Dispersion • Molecular Diffusion • The Advection-Dispersion-Reaction Equation

3. Mass Balance and the Control Volume M – mass of a chemical S – storage RS – reaction product S Mout Min • RS = Generation - Consumption Accumulation = ΔS = Min - Mout± RS

4. An open system mass balance in a control volume (контрольныйобъем)

5. Control volume (контрольныйобъем)

6. Control volume

7. Control volume

8. An open system mass balance • 0 = ΔS = Min - Mout± RS

9. An open system mass balance • Question: what is the magnitude of internal sinks of butanol? ΔS = Min - Mout± RS

10. Answer Input + Generation = Output + Accumulation + Consumption • RS = Generation – Consumption = 0 – x = - x • ΔS = Accumulation = 0 • Min= 20kg/d • Mout= Qout 10-4kg/m3= 3 104m3/d 10-4kg/m3 = 3kg/d • RS= Min – Mout = 20kg/d - 3kg/d = 17kg/d . . .

11. Transport phenomena in the natural environment Advection • transport mechanisms of a substance or a conserved property with a moving fluid. The fluid motion in advection is described mathematically as a vector field, and the material transported is typically described as a scalar concentration of substance, which is contained in the fluid.

12. Transport phenomena in the natural environment Advection • An example of advection is the transport of pollutants or silt in a river: the motion of the water carries these impurities downstream.

13. Advection

14. Advective transport velocity where the velocity vector v has components u, ω and w in the x, y and z directions respectively and is the divergence operator.

15. Quantification of advective transport Assuming one-dimensional steady-state transport velocity v we can define flux density (or mass flux): J = C∙v

16. Quantification of advective transport Assuming one-dimensional transient transport velocity v we can define flux density (or mass flux):

17. Another commonly advected property is heat, and here the fluid may be water, air, or any other heat-containing fluid material. Any substance, or conserved property (such as heat) can be advected, in a similar way, in any fluid.

18. Advection is important for the formation of orographic cloud and the precipitation of water from clouds, as part of the hydrological cycle.

19. Advective & convective heat transport in the ocean

20. Tectonic cycle

21. Turbulent diffusion The fluid flow in the natural environment such as the atmosphere, world oceans, lakes and rivers occurs as random complex turbulent movements. Superimposed on a mean flow circulation are eddy-like motions of varying intensities and temporal and spatial scales. These eddy-like motions are three dimensional, but the horizontal eddies are much larger than those of the vertical eddies. A direct consequence of the turbulent diffusion processes is the transport and dispersion of chemical and biological species.

22. Turbulent diffusion of smoke

23. Turbulent diffusion of cloud vapors

24. Vincent Van Gogh

25. Turbidities at the feet of a continental slope

26. Paleoseismic turbidities

27. Molecular diffusion • Turbulent diffusion occurs within fluids/gases moving at certain velocity • Molecular diffusion, driven solely by chemical concentration gradients, occurs within static (or quasi-static) fluids

28. Molecular diffusion

29. Molecular diffusion

30. Molecular diffusion

31. Mass transfer equations: Fick’s Law

32. J– The Mass Flux – the movement of mass from one point to another in a given time. The flux is what we are measuring when studying diffusion (течение, поток) Units: the units of moles/(time ∙ area). Note: area has units of length2. Example: mol/(h ∙ ft2), mol/(s ∙ m2).

33. D– Diffusivity – is the constant that describes how fast or slow an object diffuses. Units: the units of area/time. Example: ft2/h, or cm2/s D is proportional to the velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6∙10-9 to 2∙10-9 m2/s.

34. C – Concentration – is the amount of mass in a given volume. The symbol ΔC refers to the change in concentration from when the object had not diffused at all, to the final concentration when the object was done diffusing. Units: amount of substance/volume. Note: volume is the representation of size in three dimensions. Therefore it has the units of length3. Example: mol/cm3, mol/L

35. Fick’s 1st Law of Diffusion g/cm3/s

36. Fick’s 1st Law: example Think of the last time that you washed the dishes. You placed your first greasy plate into the water, and the dishwater got a thin film of oil on the top of it, didn’t it? Data: the sink is 18 cm deep (Δx = 18 cm) D = 7 ∙ 10-7cm2/s the concentration of oil on the plate Cplate= 0.1 mol/cm3; the concentration of oil on the top of the sink Csurface= 0 mol/cm3; Find the flux, J, of oil droplets through the water to the top surface.

37. The answer: J = -D ∙ΔC/Δ x J = -(7 ∙ 10-7 cm2/s) ∙ (0 - 0.1 mol/cm3)/(18 cm) J = 4 ∙ 10-4mol/(cm2s)

38. Fick’s 2nd Law of Diffusion g/cm3/sec

39. Fick’s 2nd Law of Advection-Diffusion g/cm3/sec

40. Fick’s 2nd Law of Advection-Diffusion with sources or sinks g/cm3/sec

41. Fick’s 2nd Law of Advection- Diffusion with sources or sinks in 3-dimensions g/cm3/sec

42. Diffusion through porous materials where f is the formation factor

43. Diffusion through porous materials f = f(φ,τ) where: φ is the porosity (fraction) τ is the tortuosity (length) (извилистость, кривизна, уклончивость)

44. Tortuosity τ = l/m

45. Fick’s 2nd Law of Diffusion through saturated porous medium and

46. Fick’s 2nd Law for Diffusion and Advection through Saturated Porous Medium

47. Mechanical Dispersion

48. Mechanical Dispersion

49. Mechanical Dispersion

50. Mechanical Dispersion Dl = alv’ and Dt = atv’ where: Dl & Dt are longitudinal and transversal coefficiants of dispersion, respectively al & at are longitudinal and transversal dispersivity, respectively v’ is seepage velocity