Transcript Document
K is a tensor with 9 components 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
q
= -
K
grad
h q x q y q z
= -
K xx K xy K xz K yx K yy K yz K zx K zy K zz
q x
K xx
h
x
K xy
h
y
K xz
h
z
h
x
h
y
h
z
q x
K xx
h
x
K xy
h
y
K xz
h
z q y
K yx
h
x
K yy
h
y
K yz
h
z q z
K zx
h
x
K zy
h
y
K zz
h
z
z global z’ local K xx K yx K zx K xy K yy K zy K xz K yz K zz x [K] = [R] -1 [K’] [R] K’ x 0 0 0 K’ y 0 0 0 K’ z x’
global z
Assume that there is no flow across the bedding planes
local z’ grad h q x’
h
x
0
q z
K zz
h
z q x
K xz
h
z
x
q x
'
K x
' (
h
x
)' K z ’=0
q z
'
K z
' (
h
z
)' 0
q x
K xx
h
x
K xy
h
y
K xz
h
z q y
K yx
h
x
K yy
h
y
K yz
h
z q z
K zx
h
x
K zy
h
y
K zz
h
z
General governing equation for steady-state, heterogeneous, anisotropic conditions, without a source/sink term
x
(
K x
h
x
)
y
(
K y
h
y
)
z
(
K z
h
z
) 0
x
(
K x
h
x
with a source/sink term )
y
(
K y
h y
)
z
(
K z
h
z
)
R
*
x
(
K x
h
x
)
y
(
K y
h
y
)
z
(
K z
h
z
)
R
* 2D horizontal flow; homogeneous and isotropic aquifer with constant aquifer thickness, b, so that T=Kb.
Poisson Eqn .
2
h
x
2 2
h
y
2
R T
C.E. Jacob’s Island Recharge Problem
y L 2
h
x
2 2
h
y
2
R T
ocean R= 0.00305 ft/d T= 10,000 ft
2
/day L = 12,000 ft well 2L ocean ocean x
ocean
C.E. Jacob’s Island Recharge Problem R
h
datum groundwater divide
b ocean x = - L x = 0 x = L We can treat this system as a “confined” aquifer if we assume that T= Kb.