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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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Physical explanation: As we saw above, the higher exposure of the fractured horizontal well,
though its 20 tips initially produces a divergence from the single equivalent fracture. This is
good news until... the fractures start to interfere with each other. Then the rate of pressure
change will progressively return to that of a single fracture for our specific case – but please
keep in mind that more complex behaviours are very possible.
Summary:
Modeling analytically or numerically a fractured horizontal well will take into
account the improvement of productivity due to the higher exposure to the reservoir. After a
transition that may last tens of years, the productivity will reduce again due to the interference
with the fracture. Using a single fractured well model, or a straight line analysis will now
produce errors of up to 100% or more (fractures length or permeability overestimated).
10 – Adding desorption
It is relatively straightforward to take into account desorption effects in the numerical NL
solution – rather than recalling equations we will just show the comparison of two simulations
of the same multi-fractured horizontal well reference solution (§3 with k=1E-4 md) with and
without desorption (again, the desorption parameters are listed in §3). Ignoring desorption
leads to an over-estimation of the reservoir permeability by 50% in our case.
We can include desorption in the material balance equation (SPE 20730, King, 1993) but our
problem in the present case is that we are far from the establishment of boundary dominated
flow... In theory a desorption compressibility c
d
can be derived that take into account the
additional desorbed gas in the diffusivity equation during transient flow (SPE 107705) – in that
case the gas compressibility c
g
is replaced by c
g
*=c
g
+c
d
in all equations, with (in oil field
units):