#### Transcript Document

```General governing equation for transient,
heterogeneous, and anisotropic conditions

h

h

h
h
( Kx ) 
( Ky ) 
( K z )  Ss
 R*
x
x
y
y
z
z
t
Specific Storage
Ss = V / (x y z h)
OUT – IN =
qx
qy qz
(


 R*) x y z
x
y
z
= change in storage
= - V/ t
Ss = V / (x y z h)
V = Ss h (x y z)
t
t
OUT – IN =
qx
qy qz
(


 R*)
x
y
z
= - V
t
h
 Ss
t

h

h

h
h
( Kx ) 
( Ky ) 
( K z )  Ss
 R*
x
x
y
y
z
z
t
Law of Mass Balance + Darcy’s Law =
Governing Equation for Groundwater Flow
--------------------------------------------------------------div
q = - Ss (h t) +R* (Law of Mass Balance)
q = - K grad h
(Darcy’s Law)
div (K grad h) = Ss (h t) –R*

h

h

h
h
( Kx ) 
( Ky ) 
( K z )  Ss
 R*
x
x
y
y
z
z
t
2D confined:
2D unconfined:

h

h
h
(Tx ) 
(Ty )  S
R
x
x
y
y
t

h

h
h
( hKx ) 
( hKy )  S
R
x
x
y
y
t
Storage coefficient (S) is either storativity or specific yield.
S = Ss b & T = K b
 2h
x 2
S h

T t
1D, transient, homogeneous, isotropic,
confined, no sink/source term
• Explicit solution (with stability criterion)
• Implicit solution
Reservoir Problem
Confined Aquifer
1D, transient
t=0
t>0
 2h
x 2
t=0
t>0
S h

T t
datum
x
0
L = 100 m
BC:
h (0, t) = 16 m; t > 0
h (L, t) = 11 m; t > 0
IC: h (x, 0) = 16 m; 0 < x < L
Modeling “rule”: Initial conditions should represent a
 2h
h1
x
datum
0
2
 0
h2
x
L = 100 m
At t = tss the system reaches
h(x) = ((h2 –h1)/ L) x + h1
(Eqn. 4.12
W&A)
Explicit Solution
Water Balance
IN
OUT
t>0
Storage
IN + change in storage = OUT
+
Flow in
Storage
Flow out
Convention: Water coming out of storage
goes into the aquifer (+ column).
Water going into storage comes out
of the aquifer (- column).
```