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OH – ET – VA - LL: Analysis of Dynamic Data in Shale Gas Reservoirs – Part 1 – Version 2 (December 2010)
p 18/24
Where p
Avg
is the reservoir average pressure. It is then required to introduce a pseudo-time to
solve the transient flow equation accounting for gas desorption, pseudo-time that is computed
as a function of the average reservoir pressure – hence, with no spatial variability of the
parameters. But having recourse to the average reservoir pressure is in contradiction with our
need for transient flow correction: in all numerical simulations p
Avg
is almost constant (and
equal to the initial pressure), hence introducing c
g
* leads to a negligible correction.
So, desorption does have a significant impact in the early time determination of the flow
parameters; we know how to take desorption into account in the numerical non-linear solution,
we know how to include it in the material balance calculations when boundary dominated flow
occurs, but we do not know how to incorporate it in both early time straight line analysis and
transient flow analytical modelling...
Reference case with and without desorption
The correction of the classical analysis using a “z*” or “c
g
*” does not address the nonlinearity
of the problem but makes a global correction of the material balance of the same magnitude.
What remain, however, are the errors linked to the nonlinearity and geometry issues detailed
in §9 and §10.
Before to conclude, we must concede that the effect is so spectacular here because p
wf
is low
(500 psia) and constant right from the start of production. This situation is unlikely to be
encountered in practical situations where flowing pressure is lowered step by step until a
reasonable plateau is reached. Besides, adsorption parameters may significantly vary from one
shale to another. Desorption will always play a role, but it may not be as important as shown
on the above loglog plot.
Summary:
Desorption cannot be neglected in the analysis, even at early times. It can be
handled numerically and by classical methods once pseudo-steady state flow has been
reached, but there is no practical way to incorporate it in transient analytical solutions for the
time being.