Slide 2 Final Exam May 10, 5 7:30 pm, ESS 081 Slide 3 Energy
Transformation 1 Caloria of heat = energy necessary to raise the
temperature of one gram of pure water from 14.5 15.5 o C Latent
Heat of vaporization Hv = 597.3 0.564T (Cal./g) Latent Heat of
condensation Slide 4 Energy Transformation, Cont. Latent heat of
fusion Hf 1 g of ice at 0 o C => ~80 cal of heat must be added
to melt ice. Resulting water has same temperature. Sublimation
Water passes directly from a solid state to a vapor state. Energy =
Hf + Hv => 677 cal/g at 0 o C. Hv > 6Hf > 5 x amt. to warm
water from 0 o C -> 100 o C Slide 5 Hydrologic Equation Inflow =
outflow +/- Changes in storage Equation is simple statement of mass
conservation Slide 6 Slide 7 Condensation Condensation occurs when
air mass can no longer hold all of its humidity. Temperature drops
=> saturation humidity drops. If absolute humidity remains
constant => relative humidity rises. Relative humidity reaches
100% => condensation => Dew point temperature. Slide 8 Cool,
moist Warm, dry Limited soil-moisture storage Slide 9 All
infiltrate some water always on the surface Puddles and overland
flow Slide 10 Q0Q0 Slide 11 Determining ground water recharge from
baseflow (1) Meyboom method (Seasonal recession method): utilizes
stream hydrographs from two or more consecutive years. Assumptions:
the catchment area has no dams or other method of streamflow
regulation; snowmelt contributes little to the runoff. Slide 12
Determining ground water recharge from baseflow (2) Rorabaugh
method (Recession curve displacement method): utilizes stream
hydrograph during one season. Slide 13 Aquifer Properties:
Porosity, specific yield, specific retention. Potential:
Transmissivity, storativity. Types: confined, unconfined. Hydraulic
conductivity, Physical Laws controlling water transport. Slide 14
Slide 15 d 60 d 10 Slide 16 Sediment Classification Sediments are
classified on basis of size of individual grains Grain size
distribution curve Uniformity coefficient C u = d 60 /d 10 d 60 =
grain size that is 60% finer by weight. d 10 = grain size that is
10% finer by weight. C u = 4 => well sorted; C u > 6 =>
poorly sorted. Slide 17 Specific Yield and Retention Specific yield
S y : ratio of volume of water that drains from a saturated rock
owing to the attraction of gravity to the total volume of the rock.
Specific retention S r : ratio of the volume of water in a rock can
retain against gravity drainage to the total volume of the rock. n
= S y + S r. S r increases with decreasing grain size. Slide 18
Darcys Law Q = -KA(dh/dl). dh/dl = Hydraulic gradient. dh = change
in head between two points separated by small distance dl. Slide 19
Laminar flow (Small R < 10) Turbulent flow (Large R) Flow lines
Darcys Law: Yes Darcys Law: No Slide 20 Hydraulic conductivity K =
hydraulic conductivity (L/T). K is also referred to as the
coefficient of permeability. K = -Q[A(dh/dl)] [ L 3 /T/[L 2 (L/L)]
= L/T] V = Q/A = -K(dh/dl) = specific discharge or Darcian
velocity. Slide 21 Intrinsic Permeability Intrinsic permeability K
i = Cd 2 (L 2 ). K = K i (/) or K = K i (g/ ) Petroleum industry 1
Darcy = unit of intrinsic permeability K i 1 darcy = 1 cP x 1 cm 3
/s / (1 atm/ 1 cm). cP centipoise - 0.01 dyn s/cm 2 atm atmospheric
pressure 1.0132 x 10 16 dyn/cm 2 1 darcy = 9.87 x 10 -9 cm 2 ~ 10
-8 cm 2 Slide 22 Aquifer Aquifer geologic unit that can store and
transmit water at rates fast enough to supply amounts to wells.
Usually, intrinsic permeability > 10 -2 Darcy. Confining layer
unit with little or no permeability < 10 -2 Darcy. aquifuge
absolutely impermeable unit. aquitard - a unit can store and
transmit water slowly. Also called leaky confining layer. Raritan
formation on Long Island. -- all these definitions are in a
relative sense. Slide 23 Slide 24 Transmissivity The amount of
water that can be transmitted horizontally through a unit width by
the full saturated thickness of the aquifer under a hydraulic
gradient of 1. T = bK T = transmissivity. b = saturated thickness.
K = hydraulic conductivity. Multilayer => T 1 + T 2 + + T n
Slide 25 Specific Storage Specific storage S s = amount of water
per unit volume stored or expelled owing to compressibility of
mineral skeleton and pore water per unit change in head (1/L). S s
= w g(+n) = compressibiliy of aquifer skeleton. n = porosity. =
compressibility of water. Slide 26 Storativity of confined Unit S =
b S s S s = specific storage. b = aquifer thickness. All water
released in confined, saturated aquifer comes from compressibility
of mineral skeleton and pore water. Slide 27 Storativity in
Unconfined Unit Changes in saturation associated with changes in
storage. Storage or release depends on specific yield S y and
specific storage S s. S = S y + b S s Slide 28 Volume of water
drained from aquifer V w = SAdh V w = volume of water drained. S =
storativity (dimensionless). A = area overlying drained aquifer. dh
= average decline in head. Slide 29 Hydraulic head, h Hydraulic
head is energy per unit weight. h = v 2 /2g + z + P/g. [L]. Unit:
(L; ft or m). v ~ 10 -6 m/s or 30 m/y for ground water flows. v 2
/2g ~ 10 -12 m 2 /s 2 / (2 x 9.8 m/s 2 ) ~ 10 -13 m. h = z + P/g.
[L]. Slide 30 Slide 31 Flow lines and flow nets A flow line is an
imaginary line that traces the path that a particle of ground water
would flow as it flows through an aquifer. A flow net is a network
of equipotential lines and associated flow lines. Slide 32 Boundary
conditions No-flow boundary flow line parallel to the boundary.
Equipotential line - intersect at right angle. Constant-head
boundary flow line intersect at right angle. Equipotential line -
parallel to the boundary. Water-table boundary flow line depends.
Equipotential line - depends. Slide 33 Estimate the quantity of
water from flow net q = Kph/f. q total volume discharge per unit
width of aquifer (L 3 /T; ft 3 /d or m 3 /d). K hydraulic
conductivity (L/T; ft/d or m/d). p number of flowtubes bounded by
adjacent pairs of flow lines. h total head loss over the length of
flow lines (L; ft or m). f - number of squares bounded by any two
adjacent flow lines and covering the entire length of flow. Slide
34 Slide 35 Slide 36 Slide 37 Water table Water table = undulating
surface at which pressure in fluid in pores = atmospheric pressure.
Water table Slide 38 Our purpose of well studies Compute the
decline in the water level, or drawdown, around a pumping well
whose hydraulic properties are known. Determine the hydraulic
properties of an aquifer by performing an aquifer test in which a
well is pumped at a constant rate and either the stabilized
drawdown or the change in drawdown over time is measured. Slide 39
Drawdown T = Q/ 4 (h 0 -h)G(u) G(u) = W(u) - completely confined.
W(u,r/B) leaky, confined, no storage. H(u, ) leaky, confined, with
storage. W(u A,u B, ) - unconfined. Slide 40 Slide 41 Aquifer test
Steady-state conditions. Cone of depression stabilizes.
Nonequilibrium flow conditions. Cone of depression changes. Needs a
pumping well and at least one observational well. Slide 42 Aquifer
tests T = Q/ 4 (h 0 -h)G(u) G(u) = W(u) - completely confined.
W(u,r/B) leaky, confined, no storage. H(u, ) leaky, confined, with
storage. W(u A,u B, ) - unconfined. Slide 43 Slide 44 Slide 45
Slide 46 Slug test Overdamped water level recovers to the initial
static level in a smooth manner that is approximately exponential.
Underdamped water level oscillates about the static water level
with the magnitude of oscillation decreasing with time until the
oscillations cease. Slide 47 Cooper-Bredehoeft-Papadopulos Method
(confined aquifer) H/H 0 = F( , ) H head at time t. H 0 head at
time t = 0. = T t/r c 2 = r s 2 S/r c 2 Slide 48 Slide 49
Underdamped Response Slug Test Van der Kamp Method confined aquifer
and well fully penetrating. H(t) = H 0 e - t cos t H(t) - hydraulic
head (L) at time t (T) H 0 - the instantaneous change in head (L) -
damping constant (T -1 ) - an angular frequency (T -1 ) Slide 50 =
ln[H(t 1 )/H(t 2 )]/ (t 2 t 1 ) = 2 /(t 2 -t 1 ) Slide 51
Underdamped Response Slug Test (cont.) T = c + a ln T c = -a
ln[0.79 r s 2 S(g/L) 1/2 ] a = [r c 2 (g/L) 1/2 ] / (8d) d = /(g/L)
1/2 L = g / ( 2 + 2 ) Slide 52 Slide 53 Slide 54 Slide 55 Mass
transport of solutes Diffusion both ionic and molecular species
dissolved in water move from area of higher concentration (chemical
activity) to areas of lower concentration. Advection moving water
carries it dissolved solutes. Slide 56 Diffusion Ficks laws Ficks
first law F = -D dC/dx F = mass flux of solute per unit area per
unit time. D = diffusion coefficient (area/time) C = solute
concentration (mass/volume) dC/dx = concentration gradient
(mass/volume/distance). D ranges from 1 x 10 -9 to 2 x 10 -9 m 2
/s, for the major cations and anions. Slide 57 Diffusion Ficks laws
(cont.) Ficks second law C/ t = D 2 C/ x 2 D = diffusion
coefficient (area/time) C = solute concentration (mass/volume) t =
time Slide 58 Advection Advecting contaminants travel at the same
rate as the average linear velocity of ground water v x = -(K/n e )
dh/dl v x = average linear velocity K = hydraulic conductivity n e
= effective porosity dh/dl = hydraulic gradient Slide 59 Mechanical
Dispersion Longitudinal dispersion: if the mixing occurs along the
pathway of fluid flow - it moves faster through the center of the
pore; - some of the fluid will travel in longer pathways; - fluid
travels faster through larger pore. Transverse or lateral
dispersion: if the mixing occurs normal to the pathway of fluid
flow. - flow paths can split and branch out to the side. Slide 60
Hydrodynamic Dispersion Hydrodynamic dispersion: D L = D* + a L v x
D L = longitudinal coefficient of hydrodynamic dispersion D* =
effective molecular diffusion coefficient a L = dynamic
dispersivity v x = average linear ground-water velocity Slide 61
Advection-dispersion Equation D L 2 C/ x 2 v x C/ x = C/ t D L 2 C/
x 2 dispersion (diffusion + dispersivity). v x C/ x Advection Slide
62 Solute Transport by Advection- Dispersion C = C 0 /2{erfc[(L-v x
t)/2(D L t) 1/2 ] + exp(v x L/D L )erfc[(L-v x t)/2(D L t) 1/2 ] }
C = solute concentration (M/L 3, mg/L) C 0 = initial concentration
(M/L 3, mg/L) L = flow path length (L; ft/m) v x = average ground
velocity (L/T) t = time since release of the solute (T) D L =
longitudinal dispersion coefficient (L 2 /T) Slide 63 Slide 64
Retardation Factor Retardation factor = 1 + ( b / )(K d ) b = dry
bulk mass density of the soil (M/L 3 ; gm/cm 3 ) = volumetric
moisture content of the soil (dimensionless). K d = distribution
coefficient for solute with the soil (L 3 /M; mL/g) Slide 65 Solute
Movement with Retardation v c = v x /[1+ ( b / )(K d )] v c =
velocity of the solute front. In one- dimensional column the solute
concentration is one-half of the original value (L/T; ft/day or
m/day). v x = average linear velocity (L/T; ft/day or m/day). Slide
66 x = -y/tan(2 Kbiy/Q) Q - pumping rate K - conductivity b initial
thickness i initial h gradient x 0 = -Q/(2 Kbi) y max = Q/(2Kbi)
Confined Slide 67 Static fresh and slat water Ghyben-Herzberg
principle Slide 68 Slide 69
