10
K = K xx K xy K xz K yx K yy K yz K zx K zy K zz K xx ,K yy, K zz are the principal components of K K is a tensor with 9 components

K =

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K is a tensor with 9 components. K xx K xy K xz K yx K yy K yz K zx K zy K zz. K =. K xx , K yy, K zz are the principal components of K. q = - K grad h. K xx K xy K xz K yx K yy K yz K zx K zy K zz. q x q y q z. = -. global. local. z. z’. x’. - PowerPoint PPT Presentation

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Page 1: K =

K =

Kxx Kxy Kxz

Kyx Kyy Kyz

Kzx Kzy Kzz

Kxx ,Kyy, Kzz are the principal components of K

K is a tensor with 9 components

Page 2: K =

Kxx Kxy Kxz

Kyx Kyy Kyz

Kzx Kzy Kzz

qx

qy

qz

= -

z

h

y

hx

h

q = - K grad h

z

hK

y

hK

x

hKq xzxyxxx

Page 3: K =

z

hK

y

hK

x

hKq

z

hK

y

hK

x

hKq

z

hK

y

hK

x

hKq

zzzyzxz

yzyyyxy

xzxyxxx

Page 4: K =

x

z

x’

z’

global local

Kxx Kxy Kxz

Kyx Kyy Kyz

Kzx Kzy Kzz

K’x 0 0

0 K’y 0

0 0 K’z

[K] = [R]-1 [K’] [R]

Page 5: K =

x

z

x’

z’global local

0x

h

z

hKq xzx

grad h q

z

hKq zzz

)'' ('x

hKq xx

0)'(''

z

hKq zz

Kz’=0

Assume that there is no flow across the bedding planes

Page 6: K =

z

hK

y

hK

x

hKq

z

hK

y

hK

x

hKq

z

hK

y

hK

x

hKq

zzzyzxz

yzyyyxy

xzxyxxx

Page 7: K =

0)()()(

z

hK

zy

hK

yx

hK

xzyx

General governing equationfor steady-state, heterogeneous, anisotropic

conditions, without a source/sink term

*)()()( Rz

hK

zy

hK

yx

hK

xzyx

with a source/sink term

Page 8: K =

*)()()( Rz

hK

zy

hK

yx

hK

xzyx

T

R

y

h

x

h

2

2

2

2

2D horizontal flow; homogeneous and isotropic aquiferwith constant aquifer thickness, b, so that T=Kb.

Poisson Eqn.

Page 9: K =

x

y

ocean

ocean

R= 0.00305 ft/dT= 10,000 ft2/dayL = 12,000 ft

2L

L

T

R

y

h

x

h

2

2

2

2

C.E. Jacob’s Island Recharge Problem

oceanwell

Page 10: K =

b

h

ocean ocean

groundwater divide

C.E. Jacob’s Island Recharge Problem

R

x = 0 x = Lx = - L

We can treat this system as a “confined” aquifer if we assume that T= Kb.

datum


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