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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 6 – W ell models -p178/743
6.D.2
Behavior
At early time only the part of the reservoir in front of the fracture will significantly contribute
to the well production, orthogonal to the fracture plane. This is what we call the
linear flow
,
and this is a characteristic feature (see figure below).
Fig. 6.D.2 – Early time linear flow
This linear flow is a particular case of a flow through a section of constant area A. Other
examples of such flow are late time linear flow between two parallel faults. When such flow
occurs there is a linear relation between the pressure change and the square root of the
elapsed time, given by the following relation:
t
ck
t
Area
qB
p
12.8
Where ‘
Area’
is the flowing section in ft². In the case of a fracture, the flowing section is the
area of the fracture rectangle, so
Area =
2X
f
h
. We then get:
2
2
2 2
52.16
06.4
f
t
t
f
kX
t
ch
Bq
ck
t
hX
qB
p
The flow will then progressively deviate from the early linear flow while the rest of the
formation starts impacting the well production, and the area of investigation becomes elliptical.
When the production continues the ellipse grows into a large circle and we reach Infinite Acting
Radial Flow. At this stage the fracture behaves like a standard well with a
negative skin
.