Transcript Lecture 15 & 16 Transient well hydraulics

Lecture 15 & 16
Transient well hydraulics
Transient well hydraulics
For homogeneous isotropic aquifer with constant thickness the GPDE is
 h  h
x y
2
2
2

2
S h
T t
Or for axisymmetric problems with appropriate BC & IC
 h 1  h
r r r
2
h
2

2

S h
T t
Assumptions
•
•
•
•
•
•
Homogeneous , isotropic, infinite, confined
Initially horizontal P.S.
Constant Q
Fully penetrating well
Well diameter small
Instantaneous storage release
h(r,0) = h0
h(infinity, t) = 0
Bc at well
Using Boltzman transformation
2
S
r
u
4T t

Thies solution is obtained
Q
W (u)
s
4 T
W (u)  

u
W (u)
1
y
y
e
dy
  0.5772...  ln( u)  u 
u
2

u
3
2 x2! 3x3!
 ......
If u is small then W(u) can be approximated as
W (u)
  0.5772...  ln( u )
Or
s = (Q/4πT) ln(2.25Tt/r2S)
Topics to touch on
• Variable pumping rates
• Pumping near hydrologic boundaries
• Pumping tests
– Aquifer tests, Slug tests, Well tests
• Influence of well storage
• Partial penetration
• Unconfined and leaky aquifers