Introduction. macroscopic geological properties of materials through which ground water flows

Transcription

1 Introduction Hydrogeology is the science of water inside the earth. The name was introduced by J.-B. Lamarck (pictured) in From Greek: υδραινω = hydros = water γεο = geo = earth λογος = logos = science Jean-Baptiste Lamarck ( ) Table 1. Relation of hydrogeology to other disciplines. Geomorphology Stratigraphy Tectonics Topography Soil science Mineralogy and petrology Chemistry Biology Hydrology Climatology Physics Fluid mechanics Mathematics Statistics macroscopic geological properties of materials through which ground water flows physical, chemical and biological properties of the environment and processes outside forcing fluid flow fluid and media properties - p.1/26

2 Water below the land surface Subsurface water is all water beneath the ground surface. Ground water is the water in the zone of saturation (below water table). In agronomy, the term ground water is used to denote the subsurface water below and above the water table. Almost all ground water is meteoric water (i.e., water that is circulating in the water cycle). A small part of ground water may be from other sources, such as magmatic. Isotopic studies of O and H indicate that the magmatic component is less or much less than 1% of total circulating water. Clouds Movement of moist air masses Sublimation Snow and ice Precipitation (on land) Clouds ;; yy ;;;;; yyyyy I SR I Leakage Unsaturated flow N Groundwater table Spring SR I ET SR Groundwater flow (saturated flow) E Lake Evapotranspiration (from vegetation) RF River Transpiration E Return flow from septic tanks Freshwater - salt water interface SR Precipitation (on the ocean) Evaporation ;;; yyy Sea water Ocean Abbreviations: ET = evapotranspiration; E = evaporation; I = infiltration; SR = surface runoff; RF = return flow from irrigation; N = natural replenishment Fig. 1. Schematic representation of water cycle (Bear and Verruijt, 1987, Modeling groundwater flow and pollution, Reidel, 414 p).

3 Infiltration Precipitation: - wetting and infiltration - surface runoff - evaporation Temperate climates: infiltration is ca. 300 mm/yr (good as a first guess). Arid climates: infiltration is close to 0, except along rivers and mountain fronts. Recharge occurs mostly in winter time.

4 Properties of water Chemical form: H 2 O Physical states: gas (vapor) liquid (water) solid (ice, snow) m = 1 Å Molecular structure: One oxygen atom and two hydrogen atoms are arranged as in the figure below. The molecule is polar (it has dipole moment). It has a positive charge on the side of the two hydrogen atoms and negative charge on the opposite side. Water is a good solvent because ot the polarity of water molecule. Physical properties: ρ = density (kg m -3 ) µ = viscosity (Pa s) ß = compressibility (Pa -1 ) Table 2. Physical properties of water. Temperature ( C) Density (kg m -3 ) Viscosity (10-3 Pa s) Compressibility (10-10 Pa -1 ) Range (%) Data from de Marsily, 1986, Quantitative Hydrogeology, Academic Press, 440 p.

5 Isotopic composition: Three stable isotopes of oxygen: 16 O - common (abundance 99.76%) 18 O - rare (0.20%) 17 O - very, very, very rare (0.04%) Two stable isotopes of hydrogen: 1 H - common (99.984%) 2 H = D = deuterium - rare (0.016%) Combination H 2 O may result in: 1 H 16 O - "normal water" Z = 8 16 O 17 O 18 O N = Z = 2 3 He 4 He Z = 1 1 H 2 H 3 H N = HD 16 O - heavy water H 18 2 O - heavy water Radioactive isotope of hydrogen: 3 H = T = tritium half-life of 12.3 y β decay to helium-3: T -> 3 He + β - Beta decay of 3 H to 3 He occurs by emitting β - (or e - ), neutron becomes proton. e pnn e ppn e Decay of tritium is used for dating of young ground water (up to few tens of years). Isotopes - lead to fractionation. Useful in studies of environmental processes, such as: - evaporation, - recharge, - mixing. - p.5/26

6 Types of water on contact with solid Hygroscopic immobile water (adsorbed in figure): High binding energy. 1-3 molecules, attached to surface of grain due to molecular attraction. Can remove by heating to 150 C. Hygroscopic mobile water (adsorbed in figure): Lower binding energy molecules, it is maximum degree of hygroscopicity. Can remove by heating to 90 C. Constitute 15-20% of all water in clays, but less than 5% in coarser materials. Also varies according to mineralogy, e.g.: 0.9% in quartz, 8-17% in feldspars, 36-48% in micas. Pellicular water (or pendular or funicular; adhesive in figure): Low binding energy. It is a film over hygroscopic water. It is mobile. Maintained by molecular forces. Free water in capillaries (small pores) gravitational (moving) Chemically bound water: In minerals as H 2 O (e.g., gypsum, CaSO 4 2H 2 O), HO -, (e.g., gibbsite, Al(OH) 3 ), H + and H 3 O + ; ;; ;;; ; Bond energy (Pa) adsorbed adhesive ;; ;; free water Distance (10-6 m) Fig. 2. Binding energy for water molecules (G. de Marsily, 1986, Quantitative hydrogeology, Academic Press, San Diego).

7 Origin of ground water Juvenile water From the interior of the earth. Has never been in surficial water cycle. It is first water created from O and H. Mantle: largest source, kg Crust: from to kg (from mantle) Example: mineral muscovite (KAl 2 (OH) 2 Si 4 O 10 ) has 8.5% OH and 4.5% H 2 O Connate water (or formation water or fossil water) It was once a part of surficial water cycle and then it was trapped in sediments. Has composition dependent on rock through which it flows (dissolution and precipitation are important factors controlling chemical composition of water). Meteoric water (or precipitation water) Water presently circulating between the atmosphere and the hydrosphere. Enters groundwater systems by infiltration. It has composition similar to rain water, but evolves towards equilibrium with rock formation. Meteoric water is of interest to us because of its occurrence in the shallow subsurface. - p.7/26

8 Darcy s law Introduction Imagine a parcel of water (A) in a column of water (figure); the parcel has the following characteristics: (1) elevation z (2) pressure p (3) velocity v (4) density ρ z A ρ, v, p ψ h datum, z=0, p=p 0 (p 0 = atmospheric) Parcel A has total energy that is the sum of potential, kinetic and elastic energies. Define: hydraulic head (h) - a measure of total energy of water Hydraulic head has two components: pressure head (ψ) - due to pressure of water above A elevation head (z) - due to elevation of A above the datum h = z + ψ

9 Darcy s experiment h 2 z 1, p 1 ; y ;; yy ; ;; ; A = cross-sectional area h 1 dl Q datum: z = 0 = z 2 Henry Darcy ( ) z 2, p 2 Darcy (1856) observed that flow Q is: (1) proportional to head difference dh (2) inversely proportional to column length dl (3) proportional to cross-sectional area A Add a proportionality constant (K), which depends on properties of fluid and properties of soil (porous medium), to get Darcy s law: Q = KA dh dl h = hydraulic head [L] A = column cross-sectional area [L 2 ] L = column length [L] K = hydraulic conductivity [LT -1 ] Q = flow rate [L 3 T -1 ] dh = h 2 -h 1 = change of hydraulic head along the flow line [L] h 2 = is head down the flow line; h 1 is head up the flow line -dh/dl = hydraulic gradient [-] Reference: Darcy, H., 1856, Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. - p.9/26

10 Darcy s law per unit area: q Q = --- = K dh A dl Flow velocities are faster than the specific discharge because flow occurs in pores only. Therefore, we have seepage (linear) velocity, v: v q = -- = n K dh n dl where n is the porosity (fraction of volume of aquifer that is taken by pores). This is average macroscopic velocity of water that is used for calculations of travel time. Travel time calculation: Given the distance (d) and the velocity (v), the travel time (t) is computed as: t = d -- v Example: A factory has been dumping chemical waste into an abandoned well (figure below). Calculate the specific discharge (q) through the system. If the chemical travels with the water velocity, estimate how long it will take to contaminate the lake. Specific discharge: ;y ;yh=124 m ;; yy PLUME 500 m K=8.25 m/d n=0.15 h=122 m ;y;y LAKE q = -K (dh/dl) = ( )/500 = m/d Travel time: t = d/v = d/(q/n) = 500/(0.033/0.15) = 2728 d = 7.47 y

11 Hydraulic conductivity In Darcy s law, the proportionality constant K is called hydraulic conductivity (units: L T -1 ). Graphically, it is the slope of the line in Darcy s law: q q = - K(dh/dL) K -dh/dl What does the hydraulic conductivity depend on? where k is the intrinsic permeability, ρ is water density, g is the acceleration due to gravity, and µ is the viscosity. Dimension of K: Intrinsic permeability (k) is a function of the porous medium alone. In general, it is considered proportional to some characteristic length, e.g., grain size: k = cd 2, where c is a dimensionless proportionality constant that may be found experimentally, and d is median grain size. Dimension of k: L 2 Common unit: darcy = 10-8 cm 2 = m 2 Typical values of hydraulic conductivity (m/s): gravel sand sandstone silt clay karst limestone crystalline rock See also the figure on the next page. K= k ρg µ L 2 ML 3 L 2 T 2 = LT 1 K has units of velocity ML 2 T 2 L 2 T - p.11/26

12 Fig. 3. Range of values of permeability (k) and hydraulic conductivity (K). From R.A. Freeze and J.A. Cherry, 1979, Groundwater, Prentice Hall, Englewood Cliffs.

13 Porosity Definitions: n = V void /V total Primary porosity - between grains Secondary porosity - fracture or solution porosity Fractures - similar definition of porosity: V void /V total Total porosity - defined earlier; total pore space in a porous medium; total water content n = pore volume total volume Effective porosity - interconnected pore space. Some water is in dead-end pores or otherwise captured and excluded from circulation. n e = interconnected pore volume total volume ;; yy yyyy ;;;; ;;;;;; yyyyyy ;;;;;;; yyyyyyy ;;;;; yyyyy ;;; yyy ; y Total porosity and effective porosity are related as in the figure below Porosity Total porosity Effective porosity Mean grain diameter (mm) Fine clay Clay Silt Fime sand Coarse sand Fine gravel Coarse gravel Blocks Fig. 4. Porosity and effective porosity for different grain sizes (G. de Marsily, 1986, Quantitative hydrogeology, Academic Press, San Diego). - p.13/26

14 Aquifers and aquitards Aquifer - geological formation which contains and yields water. - saturated, permeable geologic unit which can transmit significant quantities of water. Aquitard - saturated, permeable geologic unit which cannot transmit significant quantities of water (but can transmit small quantities). Also called a semi-pervious formation or leaky formation. Types of aquifers (1) Unconfined aquifer is one whose upper boundary is the water table, i.e., where pressure is zero (p=0). Look ate the total head h: h = z + p/γ At the top of the aquifer, h top = z top + p top /γ but because p top = 0, we have: h top = z top which means that if the head (h) increases, groundwater table rises.

15 There are four types of unconfined aquifers: (a) valley aquifer VALLEY AQUIFER water table vadose zone phreatic aquifer divide bedrock Sources of water: infiltration of rain water; surface water bodies; lateral influx. Sink of water: rivers. Water table reflects topography. Saturated zone - below water table. Unsaturated (vadose) zone - above water table. Examples: High Plains aquifer (Ogallala Formation), Coastal Plains aquifer (Atlantic, Gulf). - p.15/26

16 (b) valley aquifer in arid zones Surface recharge is negligible because of high evapotranspiration rates. Only in valleys, rivers may carry water from mountains and recharge the aquifer. VALLEY AQUIFER (IN ARID ZONES) ;; yy flooded wadi water table divide Here, contrary to valley aquifers (in humid, temperate climatic zones), water table is highest beneath rivers. Examples: North African aquifers (Nubian Aquifer), aquifers in the American Southwest (Arizona, New Mexico).

17 (c) alluvial aquifer Along streams. Usually in equilibrium with the stream, i.e., alternately drains and recharges streams along their length and at different times. Example: Rhine River ;yrhine River Stream may be either gaining water from the aquifer or losing water to the aquifer. Stream losing part (upstream) gaining part (downstream) red = equipotentials green = flow directions (d) perched aquifer Located on impermeable lenses or discontinuous layers. ;;;; yyyy ;;;; yyyy yyy perched water table sand clay lens water table - p.17/26

18 (2) Confined aquifer is one in which the top of the saturated zone is confined (bounded) by an aquitard, i.e., at the top of the aquifer, pressure is not zero (p top 0). h top = z top + p top /γ thus, h top z top which means that if the head (h) increases, the pressure (p) also increases. In a confined aquifer, the piezometric head (or water level in an observation well, or a piezometer) is higher than the upper boundary of the aquifer. If the head is higher than the surface elevation, the aquifer is artesian. Piezometric surface - a conceptual, imaginary (!) surface joining the water levels in all piezometers in the aquifer. In a phreatic aquifer, it was the water table and it had a physical meaning. ;; yy ;y ;;;;; yyyyy ;ywell discharge area piezometric surface artesian well recharge area Examples of artesian aquifers: the Great Artesian Basin in Australia, Milk River aquifer in Alberta (Canada).

19 Storage of water We will use the usual mass balance in a reservoir: Qin - Qout = storage Look at a pumping well in a confined aquifer (Figure below). If the aquifer is unbounded on the sides (that is, if it is confined on top and bottom, but not on the sides), water comes from the sides. But in a system that is totally isolated on all sides, pumped water comes from storage ( storage < 0). Q Q clay sand clay ;; yy ;;; yyy ;;; yyy ;;; yyy ;; yy isolated laterally isolated only on top and bottom isolated on top and bottom, and on the sides Where does the water come from? (1) water expands (water is compressible); (2) matrix consolidates (e.g., grains rearrange). Define specific storage coefficient, S s, as the volume of water released per unit volume of aquifer per unit decline of hydraulic head: S S = dv w ( dh) V T It is computed using compressibility (α and β) and porosity (n) values as follows: S s = ( α + nβ) ρg = ( α + nβ) γ - p.19/26

20 Some values: water: β = 4.4E-10 m 2 /N clay: α = 10-6 to 10-8 m 2 /N sand: α = 10-7 to 10-9 m 2 /N jointed rock: α = 10-9 to m 2 /N solid rock: α = to m 2 /N Typical values of S s : 3x10-6 m -1 Related (derivative) storage parameter: Storativity = S = Ss b where b is the thickness of the aquifer. Water-table aquifer: More water released by unit volume per unit decline of water table. Why? Pores are drained. In clean sand it may be 30-40% of the total volume that is drainable. Define specific yield = S y = volume of water drained per unit area of phreatic aquifer per unit decline of water table. S y < n S y = n - specific retention Specific retention = S R = amount of water that remains in porous medium after gravity draining, i.e., due to chemistry etc. Specific retention is high in clays, low in sands. Examples: n (%) S y (%) S R (%) Clay Sand Gravel

21 Transport of miscible substances Advection - transport with groundwater velocity (v) Flux density = J = C v [M L -2 T -1 ] (mass per unit area per unit time) C = concentration [M L -3 ] v = velocity [L T -1 ] Dispersion - mixing due to water flowing around grains in porous medium Mechanisms of dispersion J = -D (dc/dx) [M L -2 T -1 ] (mass per unit area per unit time) where D is the mechanical dispersion coefficient (what are the units of D?) Diffusion - molecular (Brownian motion) Pore-scale mixing ;; yy ;y ;y ;y ;y ;y B A C average water flow direction 1-D: J = -D * (dc/dx) Adsorption and retardation If solute reacts with the medium, the molecules can be sorbed (attached) to the medium, and the transport of these molecules is slowed (retarded). In that case the retardation factor R>1. Otherwise, if solutes do not react with the medium, R=1. Parabolic distribution of velocities in pores Velocity differences between pores ;; yy v 2 v 1 v 2 < v 1 - p.21/26

22 Solution to advection-dispersion equation for non-reactive solutes (R=1) Pulse input, 1-D: Cxt (, ) = M exp n 4πDt ( x vt) Dt where M is the total mass of chemical introduced into the system. Continuous, 1-D: Cxt (, ) = C erfc x vt Dt where C 0 is the initial (or input) concentration, erfc() is the complementary error function (it is tabulated, and the tables are googleable). Examples of transport - pulse input Q ;; ;; ;; ;; ;; yy yy yy yy yy ; y ; y ; y ; y ; y ;; ;; yy ;; yy yy ;; yy Concentration t 0 t 1 t2 Distance No retardation Concentration With retardation (R=3) With retardation and tailing Time

23 Aquifer pumping tests Aquifer tests are performed to obtain aquifer hydraulic properties: hydraulic conductivity, K (throught its derivative, transmissivity, T), and specific storage coefficient (throught its derivative, storativity, S). If aquifer is infinite and confined, supply of water is from storage transient flow. Q h = h 0 at r = infinity for all t For long pumping test (at least an hour), the solution for drawdown (s) is: s Q 2.25Tt = ln Jacob solution 4πT r 2 S where: Q = pumping rate [L 3 T -1 ] T = transmissivity (=K b) [L 2 T -1 ] t = time [T] r = distance from pumping well [L] S = storativity (=Ss b) [-] In terms of decimal log the solution is: 2.3Q s = log Tt 4πT r 2 S - p.23/26

24 Computing T and S from pumping-test data using the Jacob method: We measure drawdown (s) as a function of time (t). Plot these on semi-log graph. Late-time data (long t) should form a straight line. t 0 log t Change to decimal log t 2 t 1 2.3Q s = log --- 4πT s s = Q ln Tt 4πT r 2 S For one log t cycle, we have log(t 2 /t 1 ) = log 10 = 1, and the solution for T is T = Q 4π s Because we know the intercept (at s = 0), we can also calculate the storativity S: S = 2.25Tt r 2

25 Groundwater fluctuations water level long-term trend (due to mining of aquifer) plus short-term fluctuations (due to variable pumping) 0 5 time (years) heavy pumping 0 1 time (months) winter recharge J F M A M J J A S O N D 0 ET = A(dh)S y A = area dh = decline in water table S y = specific yield 1 yr summer ET time Main causes of groundwater fluctuations are: pumping and seasonal changes in inputs (e.g., snowmelt) and outputs (e.g., evapotranspiration). Some other causes of groundwater fluctuations: barometric pressure changes, tides, earth tides, earthquakes, explosions, passing trains. - p.25/26

26 Radioisotope dating of ground water Assume that at time t=0 we have N atoms of a radioactive isotope. The isotope decays at a constant rate λ (=ln2/t ½ ). N changes with time according to: dn = λn linear, first order ODE dt or dn = λdt N Integrate to get: lnn = λt + C From the initial condition N = N t = 0, integration constant C = lnn 0, and the solution is: N = N 0 e λt N N 0 This can be solved for time: 1 t = ln----- N λ N 0 ½ N 0 After one half-life (t ½ ) one half of the original N 0 remains, after two half-lives (2 t ½ ) one-fourth remains, etc. We date ground water by measuring N and computing t. This is the time since recharge. Note that in this method we need to know the initial concentration N 0 at time t=0, which may or may not be possible. However, methods exist to bypass this requirement. Radioisotopes commonly used for groundwater dating: - tritium, 3 H, t ½ =12.3 y - radiocarbon, 14 C, t ½ =5730 y - chlorine-36, 36 Cl, t ½ = y 0 0 t 1/2 Can also use 3 He- 3 H system, where 3 He is from radioactive decay of 3 H (this method does not require the knowledge of N 0 ). ¼ N 0 2 t 1/2 t