Crisman Annual Report 2009 - Harold Vance Department of ...

An Analytical Approach to Model Shale Gas Reservoir Flow Including Desorption
Effects
Objectives
The objective of this work is to develop a semianalytical
model to represent the pressure-time
performance of shale gas reservoirs including
desorption. To achieve this goal, we have developed
a suite of simulation cases to study the effect of
the desorption term, reservoir properties (primarily
permeability), and gas flowrates. We have
formulated a “dimensionless” form of the viscositycompressibility
product as a mechanism to visualize
and characterize the non-linear behavior of this
case.
Approach
The “diffusivity equation” including desorption (as
an effective compressibility, c e
) is given as:
1 p
p gicei
g ce
p
r
r r
r
k
gicei
t
Where
c
m gSC
VL
pL
ce
cg
2
[ p p]
We use numerical simulation to generate a suite
of constant rate pressure-time responses for an
infinite-acting circular reservoir. The behavior of
the nonlinearity (i.e., μ g
c e
) was studied for specific
reservoir properties and flowrate. Using these
results we developed an appropriate dimensionless
time function (t D
) to account for the effects due to
desorption and formation permeability.
In addition to a dimensionless time function, we
also created a dimensionless rate function (q D
),
which accounts for permeability and flowrate. In
Fig. 1 we present the overall “correlation” of the
non-linear term as functions of dimensionless time
and rate.
Significance
» The non-linear desorption term can be expressed
as an effective compressibility term in the gas
diffusivity equation.
» The effects of desorption can be incorporated into
an appropriately defined dimensionless time.
» The effects of reservoir properties and flowrate
can be incorporated in an appropriately defined
dimensionless rate.
g
L
p
Fig. 1. Overall “correlation” of the non-linear term, presented as functions
of dimensionless time and rate.
» For higher values of the flowrate (or dimensionless
flowrate), the non-linear term becomes more
dominant (deviates from liquid flow theory).
Future Work
» Develop an exhaustive sequence of cases to
investigate the non-linear behavior caused by
pressure-dependent gas expansion and gas
desorption.
» Develop a semi-analytical solution for the pressuretime
behavior of this case based on the correlation
of the non-linearity.
Project Information
1.2.9 Modeling Shale Gas Reservoir Performance
Related Publications
Bumb, A.C. and McKee, C.R. Gas-Well Testing in the
Presence of Desorption for Coalbed Methane and Devonian
Shale. SPEFE (March 1988): 179-185.
Contacts
Tom Blasingame
979.845.2292
t-blasingame@tamu.edu
Sonia Jam
CRISMAN INSTITUTE
24
Crisman Annual Report 2009