Final Review
• Exam cumulative: incorporate complete midterm review
Calculus Review
Derivative of a polynomial
• In differential Calculus, we consider the slopes of curves rather than straight lines
• For polynomial y = axn + bxp + cxq + …, derivative with respect to x is:
• dy/dx = a n x(n-1) + b p x(p-1) + c q x(q-1) + …
Example
a 3 n 3 b 5 p 2 c 5 q 0
0
2
4
6
8
10
12
14
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x
y
y = axn + bxp + cxq + …
-5
0
5
10
15
20
25
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x
y
dy/dx = a n x(n-1) + b p x(p-1) + c q x(q-1) + …
Numerical Derivatives
• ‘finite difference’ approximation
• slope between points
• dy/dx ≈ y/x
Derivative of Sine and Cosine
• sin(0) = 0 • period of both sine and cosine is 2• d(sin(x))/dx = cos(x) • d(cos(x))/dx = -sin(x)
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7
Sin(x)
Cos(x)
Partial Derivatives
• Functions of more than one variable• Example: h(x,y) = x4 + y3 + xy
1 4 7
10 13 16 19S1
S7
S13
S19
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
X
Y
2.5-3
2-2.5
1.5-2
1-1.5
0.5-1
0-0.5
-0.5-0
-1--0.5
-1.5--1
Partial Derivatives
• Partial derivative of h with respect to x at a y location y0
• Notation ∂h/∂x|y=y0
• Treat ys as constants• If these constants stand alone, they drop
out of the result• If they are in multiplicative terms involving
x, they are retained as constants
Partial Derivatives
• Example: • h(x,y) = x4 + y3 + x2y+ xy • ∂h/∂x = 4x3 + 2xy + y
• ∂h/∂x|y=y0 = 4x3 + 2xy0+ y0
1 4 7
10 13 16 19
S1
S7
S13
S19
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
X
Y
WHY?
Gradients
• del h (or grad h)
• Darcy’s Law:
y
h
x
hh
ji
hKq
Equipotentials/Velocity Vectors
Capture Zones
Watersheds
http://www.bsatroop257.org/Documents/Summer%20Camp/Topographic%20map%20of%20Bartle.jpg
Watersheds
http://www.bsatroop257.org/Documents/Summer%20Camp/Topographic%20map%20of%20Bartle.jpg
Capture Zones
Water (Mass) Balance
• In – Out = Change in Storage– Totally general– Usually for a particular time interval– Many ways to break up components– Different reservoirs can be considered
Water (Mass) Balance
• Principal components:– Precipitation– Evaporation– Transpiration– Runoff
• P – E – T – Ro = Change in Storage
• Units?
Ground Water (Mass) Balance
• Principal components:– Recharge– Inflow– Transpiration– Outflow
• R + Qin – T – Qout = Change in Storage
Ground Water Basics
• Porosity
• Head
• Hydraulic Conductivity
Porosity Basics
• Porosity n (or )
• Volume of pores is also the total volume – the solids volume
total
pores
V
Vn
total
solidstotal
V
VVn
Porosity Basics
• Can re-write that as:
• Then incorporate:• Solid density: s
= Msolids/Vsolids
• Bulk density: b
= Msolids/Vtotal • bs = Vsolids/Vtotal
total
solidstotal
V
VVn
total
solids
V
Vn 1
s
bn
1
Ground Water Flow
• Pressure and pressure head
• Elevation head
• Total head
• Head gradient
• Discharge
• Darcy’s Law (hydraulic conductivity)
• Kozeny-Carman Equation
Pressure
• Pressure is force per unit area• Newton: F = ma
– Fforce (‘Newtons’ N or kg ms-2)– m mass (kg)– a acceleration (ms-2)
• P = F/Area (Nm-2 or kg ms-2m-2 =
kg s-2m-1 = Pa)
Pressure and Pressure Head
• Pressure relative to atmospheric, so P = 0 at water table
• P = ghp
– density– g gravity
– hp depth
P = 0 (= Patm)
Pre
ssur
e H
ead
(incr
ease
s w
ith d
epth
bel
ow s
urfa
ce)
Pressure Head
Ele
vati
on
Head
Elevation Head
• Water wants to fall
• Potential energy
Ele
vatio
n H
ead
(incr
ease
s w
ith h
eigh
t ab
ove
datu
m)
Eleva
tion
Head
Ele
vati
on
Head
Elevation datum
Total Head
• For our purposes:
• Total head = Pressure head + Elevation head
• Water flows down a total head gradient
P = 0 (= Patm)
Tot
al H
ead
(con
stan
t: h
ydro
stat
ic e
quili
briu
m)
Pressure Head
Eleva
tion
Head
Ele
vati
on
Head
Elevation datum
Head Gradient
• Change in head divided by distance in porous medium over which head change occurs
• A slope
• dh/dx [unitless]
Discharge
• Q (volume per time: L3T-1)
• q (volume per time per area: L3T-1L-2 = LT-1)
Darcy’s Law
• q = -K dh/dx– Darcy ‘velocity’
• Q = K dh/dx A– where K is the hydraulic
conductivity and A is the cross-sectional flow area
• Transmissivity T = Kb– b = aquifer thickness
• Q = T dh/dx L– L = width of flow field
www.ngwa.org/ ngwef/darcy.html
1803 - 1858
Mean Pore Water Velocity
• Darcy ‘velocity’:q = -K ∂h/∂x
• Mean pore water velocity:v = q/ne
Intrinsic Permeability
g
kK w
L T-1 L2
More on gradients1 2 3 4 5 6 7 8 9 10 11
2.445659 2.445659 2.937225 3.61747 4.380528 5.182307 5.999944 6.817582 7.619361 8.382418 9.062663 9.554228 9.5542283.399753 3.399754 3.685772 4.152128 4.722335 5.348756 5.99989 6.651023 7.277444 7.847651 8.314006 8.600023 8.6000234.067833 4.067834 4.253985 4.582937 5.007931 5.490497 5.999838 6.509179 6.991744 7.416737 7.745689 7.931838 7.9318384.549766 4.549768 4.679399 4.917709 5.235958 5.605464 5.999789 6.394115 6.76362 7.081868 7.320177 7.449806 7.4498064.902074 4.902077 4.99614 5.172544 5.412733 5.695616 5.999745 6.303874 6.586756 6.826944 7.003347 7.097408 7.0974085.160327 5.160329 5.230543 5.363601 5.546819 5.764526 5.999705 6.234885 6.452591 6.635808 6.768864 6.839075 6.8390755.348374 5.348377 5.402107 5.504502 5.646422 5.815968 5.999672 6.183375 6.35292 6.494838 6.597232 6.650959 6.6509595.482701 5.482704 5.52501 5.605886 5.718404 5.853259 5.999644 6.146028 6.280883 6.393399 6.474273 6.516576 6.5165765.574732 5.574736 5.609349 5.675635 5.768053 5.879029 5.999623 6.120216 6.231191 6.323607 6.389891 6.424502 6.424502
5.63216 5.632163 5.662024 5.719259 5.799151 5.895187 5.999608 6.10403 6.200064 6.279955 6.337188 6.367045 6.3670455.659738 5.659741 5.68733 5.740232 5.814114 5.902965 5.999601 6.096237 6.185087 6.258968 6.311867 6.339453 6.339453
5.659741 5.68733 5.740232 5.814114 5.902965 5.999601 6.096237 6.185087 6.258968 6.311867 6.339453 6.339453
1 2 3 4 5 6 7 8 9 10 11
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
10.5-11
10-10.5
9.5-10
9-9.5
8.5-9
8-8.5
7.5-8
7-7.5
6.5-7
6-6.5
5.5-6
5-5.5
4.5-5
4-4.5
3.5-4
3-3.5
2.5-3
2-2.5
1.5-2
More on gradients
• Three point problems:
h
h
h
400 m
412 m
100 m
More on gradients
• Three point problems:– (2 equal heads)
h = 10m
h = 10m
h = 9m
400 m
412 m
100 m
CD • Gradient = (10m-9m)/CD
• CD?– Scale from map– Compute
More on gradients
• Three point problems:– (3 unequal heads)
h = 10m
h = 11m
h = 9m
400 m
412 m
100 m
CD • Gradient = (10m-9m)/CD
• CD?– Scale from map– Compute
Best guess for h = 10m
Types of Porous Media
Homogeneous Heterogeneous
Isotropic
Anisotropic
Hydraulic Conductivity Values
Freeze and Cherry, 1979
8.6
0.86
K
(m/d)
Layered media (horizontal conductivity)
M
ii
M
ihii
h
b
KbK
1
1
Q1
Q2
Q3
Q4
Q = Q1 + Q2 + Q3 + Q4
K1
K2
b1
b2
Flow
Layered media(vertical conductivity)
M
ihii
M
ii
v
Kb
bK
1
1
/
Controls flow
Q1
Q2
Q3
Q4
Q ≈ Q1 ≈ Q2 ≈ Q3 ≈ Q4
R1
R2
R3
R4
R = R1 + R2 + R3 + R4
K1
K2
b1
b2
Flow
The overall resistance is controlled by the largest resistance: The hydraulic resistance is b/K
Aquifers
• Lithologic unit or collection of units capable of yielding water to wells
• Confined aquifer bounded by confining beds
• Unconfined or water table aquifer bounded by water table
• Perched aquifers
Transmissivity
• T = Kb
gpd/ft, ft2/d, m2/d
Schematic
i = 1
i = 2
d1
b1
d2
b2 (or h2)
k1
T1
k2
T2 (or K2)
Pumped Aquifer Heads
i = 1
i = 2
d1
b1
d2
b2 (or h2)
k1
T1
k2
T2 (or K2)
Heads
i = 1
i = 2
d1
b1
d2
b2 (or h2)
k1
T1
k2
T2 (or K2)
h1
h2
h2 - h1
Flows
i = 1
i = 2
d1
b1
d2
b2 (or h2)
k1
T1
k2
T2 (or K2)h1
h2 h2 - h1
qv
Terminology
• Derive governing equation:– Mass balance, pass to differential equation
• Take derivative:– dx2/dx = 2x
• PDE = Partial Differential Equation• CDE or ADE = Convection or Advection
Diffusion or Dispersion Equation• Analytical solution:
– exact mathematical solution, usually from integration• Numerical solution:
– Derivatives are approximated by finite differences
Derivation of 1-D Laplace Equation
• Inflows - Outflows = 0
• (qx|x- qx|x+x)yz = 0
x
hKq
x y
qx|x qx|x+xz
0
zyx
hK
x
hK
xxx
0
x
xh
xh
xxx
02
2
x
h
Governing Equation
Boundary Conditions
• Constant head: h = constant
• Constant flux: dh/dx = constant– If dh/dx = 0 then no flow– Otherwise constant flow
General Analytical Solution of 1-D Laplace Equation
Ax
h
xAxx
h
BAxh
02
2
x
h
xxx
h0
2
2
Particular Analytical Solution of 1-D Laplace Equation (BVP)
Ax
h
BAxh
BCs:
- Derivative (constant flux): e.g., dh/dx|0 = 0.01
- Constant head: e.g., h|100 = 10 m
After 1st integration of Laplace Equation we have:
Incorporate derivative, gives A.
After 2nd integration of Laplace Equation we have:
Incorporate constant head, gives B.
Finite Difference Solution of 1-D Laplace Equation
Need finite difference approximation for 2nd order derivative. Start with 1st order.
Look the other direction and estimate at x – x/2:
x
hh
xxx
hh
x
h xxxxxx
xx
2/
x
hh
xxx
hh
x
h xxxxxx
xx
2/
h|x h|x+x
x x +x
h/x|x+x/2
Estimate here
Finite Difference Solution of 1-D
Laplace Equation (ctd)
Combine 1st order derivative approximations to get 2nd order derivative approximation.
h|x h|x+x
x x +x
h|x-x
x -x
h/x|x+x/2
Estimate here
h/x|x-x/2
Estimate here
2h/x2|x
Estimate here
02
22/2/
2
2
x
hhh
xx
hh
x
hh
xxh
xh
x
h xxxxx
xxxxxx
xxxx
Solve for h:
2xxxx
x
hhh
2-D Finite Difference Approximation
h|x,y h|x+x,y
x, y
y +y
h|x-x,y
x -x x +x
h|x,y-y
h|x,y+y
4,,,,
,
yyxyyxyxxyxx
yx
hhhhh
Poisson Equation
• Add/remove water from system so that inflow and outflow are different
• R can be recharge, ET, well pumping, etc.• R can be a function of space• Units of R: L T-1
x y
qx|x qx|x+xb
R
x y
qx|x qx|x+x
x yx yx y
qx|x qx|x+xb
R
Derivation of Poisson Equation
x y
qx|x qx|x+xb
R
x y
qx|x qx|x+x
x yx yx y
qx|x qx|x+xb
R(qx|x- qx|x+x)yb + Rxy =0
x
hKq
yxRybx
hK
x
hK
xxx
T
R
x
xh
xh
xxx
T
R
x
h
2
2
General Analytical Solution of 1-D Poisson Equation
AxT
R
x
h
xAxT
Rx
x
h
BAxxT
Rh 2
2
T
R
x
h
2
2
xT
Rx
x
h2
2
BAxxT
Rh 2
2
Water balance
• Qin + Rxy – Qout = 0• qin by + Rxy – qout by = 0• -K dh/dx|in by + Rxy – -K dh/dx|out by = 0• -T dh/dx|in y + Rxy – -T dh/dx|out y = 0• -T dh/dx|in + Rx +T dh/dx|out = 0
BAxxT
Rh 2
2
x y
qx|x qx|x+xb
R
x y
qx|x qx|x+x
x yx yx y
qx|x qx|x+xb
R
Dupuit Assumption
• Flow is horizontal• Gradient = slope of water table• Equipotentials are vertical
Dupuit Assumption
K
R
x
h 22
22
(qx|x hx|x - qx|x+x h|x+x)y + Rxy = 0
x
hKq
yxRyhx
hKh
x
hK xx
xxx
x
K
R
x
xh
xh
xxx
2
22
x
hh
x
h
22
Transient Problems
• Transient GW flow
• Diffusion
• Convection-Dispersion Equation
• All transient problems require specifying initial conditions (in addition to boundary conditions)
Storage Coefficient/Storativity
• S is storage coefficient or storativity: The amount of water stored or released per unit area of aquifer given unit head change
• Typical values of S (dimensionless) are 10-5 – 10-3
• Measuring storativity: derived from observations of multi-well tests
• GEOS 4310/5310 Lecture Notes, Fall 2002Dr. T. Brikowski, UTD
http://www.utdallas.edu/~brikowi/Teaching/Geohydrology/LectureNotes/Regional_Flow/Storativity.html
1-D Transient GW Flow
1-D Transient GW Flow: Deriving the Governing PDE
• Vw = xy S h
x
bqx|x qx|x+x
(qx|x - qx|x+x)yb = Sxyh/t
t
hyxSyb
dx
dq
t
h
b
S
xxh
K
t
h
T
S
x
h
2
2
x
hKq
)(xKK
Finite Difference Solution
• First order spatial derivative:
h|x h|x+x
x x +x
C/x|x+x/2
Estimate here
x
hh
xxx
hh
x
h xxxxxx
xx
2/
Second order spatial derivative
h|x h|x+x
x x +x
h|x-x
x -x
h/x|x+x/2
Estimate here
h/x|x-x/2
Estimate here
2h/x2|x
Estimate here
2
2/2/2
2
2
x
hhh
xx
hh
x
hh
xxh
xh
x
h
xxxxx
xxxxxx
xxxx
Finite Difference Solution
h|x, t
x
x +x
C/t|t-t/2 Estimate here
t-t
t
x -x
t
hh
t
h
t
h ttxtx
,,
h|x, t-t
• Temporal devivative
All together:
t
hh
T
S
x
hhhttyxtxttxxttxttyxx
,,,
2,,,,
2
2,,,
,,
2
x
hhh
S
tThh ttxxttxttxx
ttxtx
t
h
T
S
x
h
2
2
• Stability criterion (Mesh Ratio): Tt/(S(x)2) < ½.
Diffusion
x + x
y
z
x
jx|x Jx|x+x
zyxt
Czyjj
xxxxx
• Fick’s Law:
x
CDj
zyxt
Czy
x
CD
x
CD
xxx
t
C
x
x
CD
x
CD
xxx
t
C
xx
C
D
t
C
x
CD
2
2
• Heat/Diffusion Equation:
Temporal Derivative
C|x, t
x
x +x
C/t|t-t/2 Estimate here
t-t
t
x -x
t
CC
t
C
t
C ttxtx
,,
C|x, t-t
All together:
ttxxttxttxxttxtx CCC
x
tCC
,,,2,, 2
)(
D
t
C
x
CD
2
2
t
CC
x
CCCD ttxtxttxxttxttxx
,,
2
,,,
)(
2
Boundary conditions
• Specify either– Concentrations at the boundaries, or – Chemical flux at the boundaries (usually zero)
• Fixed concentration boundary concept is simple. • Chemical flux boundary is slightly more difficult. We go
back to Fick’s law:
Notice that if ∂C/∂x = 0, then there is no flux. The finite difference expression we developed for ∂C/∂x is
• Setting this to 0 is equivalent to
x
CDj
x
CC
x
C xxx
xx
2/
xxxCC
Convection-Dispersion Equation
x
CnDjd
qCja
zyxnt
Czy
x
CnDqC
x
CnDqC
xxxx
xx
t
C
x
xC
DvCxC
DvCxx
xxx
x
•Key difference from diffusion here!
• Convective flux
CDE
t
C
x
xC
xC
Dx
CCv xxxxxx
t
C
xxC
Dx
Cv
t
C
x
CD
x
Cv
2
2
Finite Difference: Spatial
C|x C|x+x
x x +x
C|x-x
x -x
C/x|x+x/2
Estimate here
C/x|x-x/2
Estimate here
2C/x2|x
Estimate here
2
2/2/2
2
)(
2
x
CCC
xx
CC
x
CC
x
xC
xC
x
C
xxxxx
xxxxxx
xxxx
Finite Difference: Temporal
C|x, tx
x +x
C/t|t-t/2 Estimate here
t-t
t
x -x
t
CC
t
C
t
C ttxtx
,,
Centered Finite Difference
• For first order spatial derivative:
x
CC
x
C xxxx
x
2
x
CC
x
C xxx
xx
2/
• Worked for estimating second order derivative (estimate ended up at x).
• Need centered derivative approximation
All together:
• prone to numerical instabilities depending on the values of the factors Dt/(x)2 and vt/2x (CFL)
t
CC
x
CCC
x
CCttxtxttxxttxttxxttxxdtxx
,,
2
,,,,,
)(
2D
2v-
ttxxttxxttxxttxttxxttxtx CC
x
tCCC
x
tCC
,,,,,2,, 2
v2
)(
D
t
C
x
CD
x
Cv
2
2
Boundary conditions• Specify either
– Concentrations at the boundaries, or – Chemical flux at the boundaries
• Fixed concentration boundary concept is simple• Chemical flux boundary is slightly more difficult. We go back to the
flux
Notice that if ∂C/∂x = 0, then there is no dispersive flux but there can still be a convective flux. This would apply at the end of a soil column for example; the water carrying the chemical still flows out of the column but there is no more dispersion. One of the finite difference expressions we developed for ∂C/∂x is
• Setting this to 0 is equivalent to
x
CnDqCj
x
CC
x
C xxx
xx
2/
xxxCC
Fitting the CDE
0
0.2
0.4
0.6
0.8
1
1.2
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Time (sec)
Rel
ativ
e C
on
cen
trat
ion
Model
Data
Adsorption Isotherm
• Linear: Cs = Kd C
C
Cs
Koc Values
• Kd = Koc foc
Organic Carbon Partitioning Coefficients for Nonionizable Organic Compounds. Adapted from USEPA, Soil Screening Guidance: Technical Background Document. http://www.epa.gov/superfund/resources/soil/introtbd.htm
Compound mean Koc (L/kg) Compound mean Koc (L/kg) Compound mean Koc (L/kg)
Acenaphthene 5,028 1,4-Dichlorobenzene(p) 687 Methoxychlor 80,000
Aldrin 48,686 1,1-Dichloroethane 54 Methyl bromide 9
Anthracene 24,362 1,2-Dichloroethane 44 Methyl chloride 6
Benz(a)anthracene 459,882 1,1-Dichloroethylene 65 Methylene chloride 10
Benzene 66 trans-1,2-Dichloroethylene 38 Naphthalene 1,231
Benzo(a)pyrene 1,166,733 1,2-Dichloropropane 47 Nitrobenzene 141
Bis(2-chloroethyl)ether 76 1,3-Dichloropropene 27 Pentachlorobenzene 36,114
Bis(2-ethylhexyl)phthalate 114,337 Dieldrin 25,604 Pyrene 70,808
Bromoform 126 Diethylphthalate 84 Styrene 912
Butyl benzyl phthalate 14,055 Di-n-butylphthalate 1,580 1,1,2,2-Tetrachloroethane 79
Carbon tetrachloride 158 Endosulfan 2,040 Tetrachloroethylene 272
Chlordane 51,798 Endrin 11,422 Toluene 145
Chlorobenzene 260 Ethylbenzene 207 Toxaphene 95,816
Chloroform 57 Fluoranthene 49,433 1,2,4-Trichlorobenzene 1,783
DDD 45,800 Fluorene 8,906 1,1,1-Trichloroethane 139
DDE 86,405 Heptachlor 10,070 1,1,2-Trichloroethane 77
DDT 792,158 Hexachlorobenzene 80,000 Trichloroethylene 97
Dibenz(a,h)anthracene 2,029,435 -HCH (-BHC) 1,835 o-Xylene 241
1,2-Dichlorobenzene(o) 390 -HCH (-BHC) 2,241 m-Xylene 204
-HCH (Lindane) 1,477 p-Xylene 313
Retardation
• Incorporate adsorbed solute mass
n
KdR b1
Vs
VR
Sample problem:
A tanker truck collision has resulted in a spill of 5000 L of the insecticide diazinon 2000 m from the City of Miami’s water supply wells. Use a rule of thumb to estimate the dispersivity for the plume that is carrying the contaminant from the spill site to the wells.
Sample problem:
The transmissivity determined from aquifer tests is 100,000 m2 d-1 and the aquifer thickness is 20 m. The head in wells 1000 m apart along the flow path is 3.1 and 3 m. What is the gradient? What is the mean pore water velocity and what is the dispersion coefficient?
Sample problem:
• You look up the Koc value of diazinon (290 ml/g). The aquifer material you tested has an foc of 0.0001. What is the Kd? If the porosity is 50% and the bulk density is 1.5 Kg L-1, what is R?
• Assume retarded piston flow and estimate the arrival time of the insecticide at the well field using the appropriate data from the preceding problems.
Retardation
t
CR
x
CD
x
Cv
2
2
Aquifer Tests
• TheisMatching aquifer test data to the Theis type curve has resulted in the match point coordinates 1/u = 10, W(u) = 1, t = 83.9 minutes, and s =0.217 m. The pumping rate is 1 m3 min-1 and the observation well is 100 m away from the pumping well. Compute the aquifer transmissivity and storativity. Be sure to
specify the units.
Hints:
T = Q/(4s) W(u) S = 4Ttu/r2.
Ghyben-Herzberg
zz
h
Pf = Ps
g(h+z) = sgz
(h+z) = sz
h = (s- z→ h /(s- = z
Ghyben-Herzberg
• Seawater: 1.025 g cm-3
• h /(s- = z
• h /(- = z
• h = z
Major Cations and Anions
• Cations:– Ca2+, Mg2+, Na+, K+
• Anions:– Cl-, SO4
2-, HCO3-
Chemical Concentration Conversions
• Usually given ML-3 (e.g. g L-1 mg L-1)
• Convert to mol L-1:
123
21 105.21040
10
molLmgCa
molCaCamgL
• Convert to mol (+/-) L-1:
122
122 )(105)(2
105.2
LmolmolCa
molLmolCa
Charge Balance
)()(
)()( BalanceCharge
Piper DiagramsMiami Beach GW and 1-7% Miami Beach sea water
Ca2+
Mg2+
Na+ + K
+CO3
2- + HCO3
-
SO42-
Cl-
SO4
2- + C
l- Ca 2+
+ Mg 2+
1000
0100
100 0
1000
0100
100 0
100
100
0 0
EXPLANATION
1378.352602
35800
• Convert to % mol (+/-)
Stiff Diagrams
http://water.usgs.gov/pubs/wri/wri024045/htms/report2.htm
Redox Reactions
• O2 (disappear)
• NO3- (disappear)
• Fe/Mn (appear in solution)
• SO42- (disappear)
• CH4 (appear)