Applied Hydrogeology IV

1. Applied Hydrogeology IV Прикладная Гидрогеология Yoram Eckstein, Ph.D. Fulbright Professor 2013/2014 Tomsk Polytechnic University Tomsk, Russian Federation Spring Semester 2014

2. Useful links • http://www.onlineconversion.com/ • http://www.digitaldutch.com/unitconverter/ • http://water.usgs.gov/ogw/basics.html • http://water.usgs.gov/ogw/pubs.html • http://ga.water.usgs.gov/edu/earthgwaquifer.html • http://water.usgs.gov/ogw/techniques.html • http://water.usgs.gov/ogw/CRT/

3. Applied Hydrogeology IV. Physical Properties of water-bearing formations

4. ρs ≈ 2.65 g⋅cm-3

5. Porosity of Sedimentary Rocks Primary Porosity: - porosity between grains - acquired syngenetically with the rock or sediment - sedimentary rocks usually have lower porosity than unconsolidated sediment because of compaction, and infilling of cementing material (e.g. calcite, dolomite, silica), although dissolution can reverse the latter effect

6. Effective porosity is the fraction of the porosity that is available for transporting water (excludes fraction of pores too small to hold water, or those that are not inter-connected • - can be measured in the lab directly by saturating a dried sample of known volume and measuring water uptake in a sealed chamber over time • - for unconsolidated coarse-grained sediments there is no significant difference

7. Uniformity • coefficient • - measure of sorting • On a grain-size • vs %finer plot: • d60 is the grain size diameter that corresponds to 60% finer by weight • d10 is the grain size diameter that corresponds to 10% finer by weight (i.e. d60 is coarser than d10) • Cu < 4 is well sorted • Cu > 6 is poorly sorted

8. Secondary Porosity: - porosity acquired post-genetically • Secondary pores (fractures) can be enlarged through dissolution by the ground water flow • sedimentary rock may have primary porosity from deposition and secondary porosity from fractures along bedding planes • secondary porosity also possible in cohesive sediments through wetting/drying, tectonic activity, etc.

9. limestones, dolomites, gypsum can all have deposition reversed • when in groundwater zone dissolution can occur • flow starts initially through limited pore spaces, fractures, and bedding planes, and porosity enlarges over time

10. Porosity of Plutonic and Metamorphic Rocks • primary porosity extremely low, but often not zero • porosity increased over time by weathering and fracturing • fracturing increases porosity of crystalline rocks 2 to 5%

11. Porosity of Plutonic and Metamorphic Rocks • chemical and physical weathering increases with porosity • highly weathered plutonic and metamorphic rocks can have porosities between 30 to 60% • sheet-like structures of weathering minerals such as micas can have very high porosities

12. Porosity of Volcanic Rocks • lava cools rapidly at surface, traps degassing products • holes in rock (vesicular) may or may not be interconnected • pumice (very high gas content) can have porosity approaching 90% (but effective porosity if not this high)

13. Porosity of Volcanic Rocks • cracks form during cooling • volcanic rocks vary in porosity but can be very high • basalt has lower gas content with porosity between 1 and 12% • weathering of volcanic deposits will also increase porosity

14. Physical Properties Density of Fluid - mass per unit volume (e.g., kg/m3 or g/cm3). Dynamic Viscosity of Fluid - resistance to relative flow of a Newtonian fluid (Pa-s or poise (g/s-cm)) Bulk Modulus - Proportionality constant between density and pressure. Inverse of compressibility (Pa or kg/cm2)

15. Properties of Earth Materials associated with porosity Specific Yield (Sy) = ratio of the volume of water that drains from a saturated rock owing to the attraction of gravity to the total volume of the rock. Specific Retention (Sr) = ratio of the volume of water a rock can retain against gravity drainage to the total volume of the rock.

16. n = Sy + Sr Maximum specific yield occurs in medium to coarse sand size sediments. http://techalive.mtu.edu/meec/module06/Percolation.html

17. Hydraulic Conductivity of saturated media and Darcy’s Law • - ability of the rock to transmit and hold water are the most important hydrologic properties • only effective porosity is important with regards to groundwater flow • vesivcular basalt - lack of interconnectivity • clays and shale – Sr to high in small pores t

18. Darcy’s experiment Reality For educational purposes

19. Darcy’s experiment • Henry Darcy in 1856 was playing around with movement of water through sand filtration columns for the City of Dijon, France. • Darcy found that the flow of water through a bed of “a given nature” is: • - proportional to the difference in the height of the two ends, • - inversely proportional to the length of the flow path • - proportional to the x-sectional area of the pipe • - flow is further related to a coefficient dependent on the nature of the media

23. Hydraulic conductivity • Fluid density and viscosity depend on temperature, salinity and pressure. • Intrinsic Permeability is representative of the porous medium alone. It depends on size of openings, degree of interconnection, and amount of open space. Thus, permeability depends on grain size and sorting. Coarse grained and well-sorted sediments have higher permeabilities.

31. Measuring Hydraulic ConductivityConstant Head Permeameter Constant head test Recommended for coarse-grained soils. Steady total head drop Dh is measured across gauge length L, as water flows through a sample of cross-section area A.

32. Measuring Hydraulic ConductivityFalling Head Permeameter Recommended for fine-grained soils. Total head h in standpipe of area a is allowed to fall; heads h1 and h2 are measured at times t1 and t2. Hydraulic gradient Dh/L varies with time.

33. Range of values of hydraulic conductivity and permeability for various rocks and sediments

34. Storativity (storage coefficient) Water is released from storage via: 1. decrease in fluid pressure 2. increase in pressure from overburden

35. Storativity (storage coefficient) S the volume of water that a permeable unit will absorb or expel from storage under unit surface area per unit change in hydraulic head

36. S > 0.005 • S = 0.02 to 0.3 Storativity (storage coefficient) • S ~ Sy

37. Storativity (storage coefficient) Example Problem: An unconfined aquifer with a storativity of 0.13 has an area of 123 km2. The water table drops 0.9 m during a drought. How much water was lost from storage?

38. Specific Storage (elastic storage coefficient) Ss The volume of water that a unit volume of aquifer releases from storage under a unit decline in hydraulic head. S = Ss× b

39. Compressibility and Effective Stress • Compressibility (general) When pressure is applied to the aquifer, a reduction of volume can occur in three primary ways: • compaction of water • compression of individual sand grains • rearrangement of sand grains into more closely-packed configuration

41. Compressibility and Effective Stress Compressibility (general)

42. Compressibility and Effective Stress Compressibility (general)

43. Compressibility and Effective Stress

44. Compressibility of the Aquifer (α) and Effective Stress Compressibility of Porous Medium 1. “In general”….Terzaghi (1925)

45. Stress Total Fluid Pressure + Effective Stress σt = P + σe dσt = dP + dσe and dP = -dσe

46. Stress Total Fluid Pressure + Effective Stress σt = P + σe dσt = dP + dσe dP = -dσe dP = ρwgdh

47. Compressibility of the Aquifer (α) and Effective Stress Compressibility of Porous Medium α= dVt/Vt dP α = db/b dP

48. Linking the Parameters of α, β, Ss • Water produced by the compaction of the aquifer B. Water produced from expansion of water dVwater = ρgα dVwater = ρgnβ

49. Linking the Parameters of α, β, Ss • Water produced by the compaction of the aquifer • Water produced from expansion of water C. The Link dVwater = ρgα dVwater= ρgnβ dVwater from α+ dVwater from β= Ss ρgα + ρgnβ = Ss and ρg(α + nβ) = Ss

50. Linking the Parameters of α, β, Ss “ a problem to work….” A confined aquifer with initial thickness of 45 m compacts by 0.20 m when hydraulic head is lowered by 25m. a) what is the compressibility of the aquifer? b) If the porosity of the aquifer is 12% after compaction, what is the storativity of the aquifer?