Pete 324 L14 1

1
Superposition

• First Superposition in space

2
Multiple Wells
A
Observation point
B
3
Using the line source (E1) solution
dimensionless form
Where qch can be
selected as one of the rates or the sum
4
How will we use superposition in space?

• The concept of "image" well

No-flow boundary
q
q
q
5
Second Superposition in TimeOther name
variable rate convolution

• Modeling variable rate history
• The simple most frequent variable rate case is
  constant rate followed by shut-in
• But the variable-rate "convolution" can be
  applied for any rate history

6
Constant rate followed by shut-in
q
q rate before the shut-in tp Production
time Dt Shut-in time pws Shut-in pressure
Dt
t
7
Build-up
p1
p2

t
t
Dp
p
Dt
tp
8
Build-upE1 solution
p2
p1

t
t
pw
Dpw
Dt
t
9
Build-upE1 solution
Horner form
Build-upln approximation
Build-uplog approximation Field units t gt tp
mHorner
the skin does not appear in it!