Page 298 - Fundamentals of Gas Shale Reservoirs

278 A REVIEW OF THE CRITICAL ISSUES SURROUNDING

correctly capture the production behavior of the detailed shale are lumped into four tanks and then the material bal­
models. This process is frequently referred to as upscaling. ances of these tanks are written by considering the connec­
The shale formation quad‐porosity system contains tivity of the various tanks and their internal storage and
essentially the subsystems of organic, inorganic, natural transport mechanisms by appropriate material balance and
fractures, and induced fractures. These subsystems can be transfer‐rate equations. Obviously, this approach requires
connected to each other by six possible paths (Figure 1 in various empirical transfer functions whose storage and trans­
Civan et al., 2012b). However, the nature and degree of con­ port parameters need to be determined to match the results of
nectivity are generally unknown and must be inferred by the finely detailed block simulation. The matching of finely
modeling and history matching. In general, the distribution detailed block simulations may not be unique. The leaky
of these subsystems is also not known a priori but bulk‐ tank model approach has the advantage that it does not
volume fractions can be inferred by measurements with require a detailed microscopic description once transfer
shale core samples or other means. As demonstrated later, an functions are established, but the transfer functions do not
approach of considering the microdescription as a statistical seem to have a straightforward interpretation, or tie to core
description and preserving this in the upscaling to a larger measurements. They though may be obtainable by modeling
scale quad‐porosity system in a manner to preserve the total core measurements with a tank model (Matejka et al., 2002).
porosity of each system can yield satisfactory results. Under Different tank models can be developed for four‐porosity
the initial reservoir conditions, the organic and inorganic systems depending on the nature of connectivity between the
subsystems can contain gas but the natural and hydraulic subsystems of the quad‐porosity shale, such as series,
fractures contain mostly water. Simulation of gas/water sys­ parallel, and parallel with cross flow (Hudson et al., 2012).
tems also requires the relative permeability data for these For example, flow may occur in series through the organic,
subsystems. Adsorption is mostly significant for the organic inorganic, natural fractures, and hydraulic fracture when the
pores, but usually neglected in the inorganic. organic regions are distributed as isolated pockets in the
To use commercial simulators, it is sometimes reasonable inorganic. In another example, flow may occur in parallel
to group the various flow units of shale into two categories to from organic and inorganic into the fracture subsystem. A
construct a dual‐porosity model. For example, the first can be more complicated case may involve parallel flow through
the inorganics and the fracture network including the micro­ the organic and inorganic porosity systems feeding into the
channels and microfractures. The second can be the organics natural fractures as well as having a cross flow between the
distributed throughout the inorganics. In another example, organic and inorganic subsystems. The rate equations
the quad‐porosity shale system can be separated into a group involving the latter example involving the parallel organic
of the organic subsystem combined with the natural fractures and inorganic flows with cross flow given by Hudson (2011,
and a second group of the inorganic porosity subsystem 2013) can be compiled in a matrix equation form as
combined with the induced fractures. It may sometimes be
possible to combine the quad‐porosity system into a homog­ R O ON OI 0 0 0 0 R O
enized single‐porosity system. It is important to recognize R I 0 0 0 R I
that there is no general proof that such simplifications will d R OI IN 0 0 R , t 0
correctly capture production over the life of the reservoir. dt N ON I IN NF N
The hydraulics of fluid in the heterogonous quad‐porosity R F 0 0 NF FW 0 R F
system can be modeled by a finely detailed reservoir simula­ R W 0 0 0 FW 0 R W
tion block and the production with time can be predicted by (12.37)
simulation. This result can then be used for upscaling this
finely detailed description to a coarse model that matches the where λ , λ , λ , λ , and λ denote the transfer‐rate
OI
IN
NF
FW
ON
production trends of the finely detailed model. For this purpose, coefficients for mass transfers occurring between the sub­
two approaches to upscaling are illustrated here. The first is systems of the organic O, inorganic I, natural fractures N,
based on upscaling of the finely detailed continuum model of induced fractures F, and the well W, and R , R , R , R , and
N
I
O
F
shale to a lumped‐parameter leaky tank model of shale, and the R denote the mass contained in these subsystems,
W
second is based on upscaling of the finely detailed continuum respectively.
model of shale to coarse continuum model. The initial conditions are given by
R R o
12.7.1 Upscaling Fine Continuum Model of Shale to R O R OP
o
Lumped‐Parameter Leaky Tank Model of Shale I IP
R 0 t , 0 (12.38)
Extending the approaches by Civan (1993, 1998, 2000), R N 0
Gupta and Civan (1994), Civan and Rasmussen (2001), and F
Matejka et al. (2002), the subsystems of the quad‐porosity R W 0