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OH – ET – VA - LL: Analysis of Dynamic Data in Shale Gas Reservoirs – Part 1 – Version 2 (December 2010)
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3 – Early / intermediate time straight line analysis of linear flow
The early time analysis relies on the assumption that fractured horizontal wells exhibit a linear
flow regime at early and intermediate times. This gives us an estimate of k.X
f
2
similar to what
we do in the analysis of the early time behaviour of a single fracture. The classical relationship
defining linear flow between dimensionless times and pressures can be used:
With in our case:
The quantity “X
mf
” is the sum of all individual fractures half-lengths:
A plot of
m/q
sc
as a function of √t should exhibit a straight line of slope
with:
If we introduce A as the surface contact between the fracture and the matrix (A = 4.X
mf
.h):
The underlying assumption is that the fractured horizontal well intersecting n vertical fractures
of ½ length X
f
behaves like a unique, large vertical fracture of half-length n.X
f
. We try to
evaluate in which circumstances this assumption is correct, for how long it is correct, and the
error we make when “pure” linear flow is no longer visible.