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

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III. Physical Properties of water-bearing formations

Porosity of Earth Materials The porosity of earth materials is defined as the part of rock or soil that is void space, often expressed as a percentage: where n is the porosity V v is the void volume V T is the total volume. Porosity has the units of R.E.V. = representative elementary volume

Representative elementary volume

Types of porosity  Primary porosity – porosity that ocurred syngeneticly with the geologic formation

Types of porosity  Primary porosity – porosity that ocurred syngeneticly with the geologic formation well-sorted sedimentary deposit having high porosity poorly sorted sedimentary deposit having low porosity

Types of porosity  Primary porosity – porosity that ocurred syngeneticly with the geologic formation well-sorted sedimentary deposit consisting of pebbles that are themselves porous, so that the deposit as a whole has a very high porosity well-sorted sedimentary deposit whose porosity has been diminished by the deposition of mineral matter in the interstices

Types of porosity  Secondary porosity – porosity that formed postgeneticly with the geologic formation rock rendered porous by solution, e.g., development of karst solution channels in limestone

Types of porosity  Secondary porosity – porosity that formed postgeneticly with the geologic formation rock rendered porous by fracturing

Determination of porosity in the laboratory Porosity can be determined in a couple of ways in laboratory. One method is to take a known volume of sediment and dry it in an oven at 105 °C until it reaches a constant weight. This removes moisture in the sample, but not water in the mineral structure. The dried sample is then added to a known volume of water, and the resulting increase in volume as determined by the increased water level represents the volume of the solid part of the sample. The bulk volume (solid + voids) are determined by geometric measurements (e.g., of a core sample).

Determination of porosity in the laboratory Alternatively, if one determines the bulk density of the sample, one can calculate its porosity. The bulk density (ρ b ) represents the density of the sample including its voids. Recall that density is mass over volume, and the volume used in bulk density is the volume of solids plus voids, or R.E.V.: while the density of the solid part of the sample (ρ s ) does not include the voids: For most rock and soil, the particle density is 2.65 g ⋅ cm -3

Determination of porosity in the laboratory ρ s ≈ 2.65 g ⋅ cm -3

Porosity ranges in unconsolidated sediments MaterialPorosity (%) Gravel, coarse24-36 Gravel, fine25-38 Sand, coarse31-46 Sand, fine26-53 Silt34-61 Clay34-60

Porosity ranges in consolidated sedimentary rocks RockPorosity (%) Sandstone5-30 Siltstone21-41 Limestone dolomite 0-40 Karst limestone0-40 Shale0-40

Porosity ranges in igneous (crystalline) rocks RockPorosity (%) Dense crystalline rocks 0-5 Fractured crystalline rocks 0-10 Basalt3-35 Weathered granite34-57 Weathered gabbro42-40

Grain-size distribution The grain-size distribution expresses the percent of the sediment mass that is finer than a given grain size

Grain-size distribution The grain-size distribution expresses the percent of the sediment mass that is finer than a given grain size

Grain-size distribution The grain-size distribution expresses the percent of the sediment mass that is finer than a given grain size

Grain-size distribution The grain-size distribution expresses the percent of the sediment mass that is finer than a given grain size Grain-size distribution curve of a silty fine to medium sand.

Grain-size distribution An important parameter used to describe the grain size distribution is the uniformity coefficient, C u, which is the ratio of the grain size for which 60% of the sediment is finer by weight, to the grain size for which 10% of the sediment is finer by weight. Cu =Cu = dddd A sediment with C u less than 4 is well sorted. If C u is more than 6, the sediment is poorly sorted.

Grain-size distribution heterogeneous homogeneous

WELL SORTED Coarse (sand-gravel) POORLY SORTED Coarse - Fine WELL SORTED Fine (silt-clay) Permeability and Hydraulic Conductivity HighLow Sorting of material affects groundwater movement. Poorly sorted (well graded) material is less porous than well-sorted material.

Porosity and Permeability  Porosity - the percentage of rock or sediment that consists of voids or openings  Measurement of a rock’s ability to hold water  Loose sand has ~30-50% porosity  Compacted sandstone may have only 10-20% porosity  Permeability - the capacity of a rock to transmit fluid through pores and fractures  Interconnectedness of pore spaces  Most sandstones and conglomerates are porous and permeable  Granites, schists, unfractured limestones are impermeable

Specific Yield Specific yield (S y ) is the volume of water that drains from a saturated rock or sediment by gravity, relative to the total volume of the rock: The water retained by the rock or sediment is called pendular water, and volume to the total volume of the rock is called the specific retention (S r ). S r = n - S y

Specific Yield

Types of Terrestrial Water Ground water SoilMoisture Surface Water

Unsaturated Zone / Zone of Aeration / Vadose (Soil Water) Pores Full of Combination of Air and Water Zone of Saturation (Ground water) Pores Full Completely with Water

Subsurface Water  Zone of Aeration or Vadose Zone or Unsaturated Zone: Overlies Phreatic Zone. Pore spaces partly filled with water. Contains soil moisture. Saturated Zone  Zone of Saturation or Phreatic Zone: saturated zone overlying impermeable bed rock. Water fills all the available pore spaces  Water Table: top of the zone of saturation where not confined by impermeable rock

Specific Yield Specific yield (S y ) is the volume of water that drains from a saturated rock or sediment by gravity, relative to the total volume of the rock: The water retained by the rock or sediment is called pendular water, and volume to the total volume of the rock is called the specific retention (S r ). S r = n - S y

 Water table follows the topography but more gently  Intersection of water table and ground surface produces lakes, streams, spring, wetlands…  Ground water flows from higher elevation to lower, from areas of lower use to higher use, from wet areas to dry areas.

Permeability and hydraulic conductivity  Permeability is a physical property of material, describing the ability of the material to transmit fluids or gases  In 1856, Darcy investigated the flow of water through sand filters for water purification.  h 1 and h 2 – water levels above a datum level are called hydraulic heads

Permeability and hydraulic conductivity Q ∞ AQ ∞ A – cross-sectional area of the tube hydraulic gradient

Darcy’s observations: Q = - K A dh dl K – hydraulic conductivity v = = - K QAQA dh dl

Hydraulic conductivity Q = - K A dh dl K = - Q A dh dl K units: K = = (L/T) - (L 3 /T) (L 2 )(L/L)

Hydraulic conductivity K = - Q A dh dl In 1956 Hubbert pointed out that Darcy’s coefficient of proportionality K is a function of both the porous medium and the physical properties of the fluid passing through it Q ∞ d 2 γ 1/μ γ = ρ g

Hydraulic conductivity intrinsic permeability k i = C d 2 (L 2 ) k i in hydrogeology: intrinsic permeability in oil industry: permeability 1 darcy = 9.87×10 -9 cm 2

Intrinsic permeabilities and hydraulic conductivities for unconsolidated sediments. MaterialIntrinsic permeability (darcys) Hydraulic conductivity (cm/sec) Clay10 -6 – – Silt, sandy silts, clayey sands, till – – Silty sands, fine sands10 -2 – – Well-sorted sands, glacial outwash 10 0 – – Well-sorted gravel10 1 – – 10 0

Confined (artesian) and unconfined (phreatic) aquifers

Aquifers and Aquitards  Hydrogeologists distinguish between rocks that transmit water easily and rocks that do not easily transmit water.  Aquifer – A rock that easily transmits water  Aquitard – A rock that does not transmit water easily (i.e. retards water motion)  Aquifuge – A rock that does not transmit water at all Unconfined Aquifer – An aquifer that has direct access to the surface of the EarthUnconfined Aquifer – An aquifer that has direct access to the surface of the Earth –Can be quickly recharged by meteoric water Confined Aquifer – An aquifer that is trapped below an aquitard or aquifugeConfined Aquifer – An aquifer that is trapped below an aquitard or aquifuge

Confined and Unconfined Aquifer  Unconfined Aquifer: open to atmosphere e.g., overlain by permeable rocks and soils  Confined aquifer: sandwiched between aquitards  Artesian System: Water rises above the level in aquifer because of hydrostatic pressure  Potentiometric surface: Height to which water pressure would raise the water.

Storativity or the storage coefficient is the volume of water released from storage per unit decline in hydraulic head in the aquifer, per unit area of the aquifer

Storage coefficient  It's the volume of water that a permeable unit will absorb or loss from storage per unit surface area per unit change in head.  S = b S s (Confined aquifer)  S = Sy +h S s (Unconfined aquifer)

Confined (artesian) and unconfined (phreatic) aquifers

artesian aquifer aquifer cone of depression confined aquifer Darcy's Law (all terms) discharge effluent stream flow lines flow net groundwater hydraulic conductivity hydraulic gradient hydraulic head infiltration influent stream overdraft overland flow perched aquifer permeability pores porosity recharge residence time soil water specific retention specific yield spring unconfined aquifer vadose zone water table water table contour lines Groundwater Terms