Page 297 - Fundamentals of Gas Shale Reservoirs

UPSCALING HETEROGENEOUS SHALE‐GAS RESERVOIRS INTO LARGE HOMOGENIZED SIMULATION GRID BLOCKS 277

where is the unconfined fluid viscosity. The mean‐free mature stimulated organic shale reservoirs tend to have a com­
path in this formulation is taken as the bulk gas value. The plex pore geometry on the micron scale. There exist pores in
gas viscosity representing the resistance to gas transfer under the organic and inorganic matrix, and natural and simulation
various transport regimes as given by this equation that rep­ fractures. These four pore systems have different geometries
resents flow beyond true viscous flow should ideally be and also different wettabilities. However, in order to perform
referred to as the pseudo‐viscosity because the concept of reservoir‐scale modeling, it is necessary to find a set of
viscosity at free molecular and transition flow regimes loses equivalent grid cell properties such as anisotropic permeabil­
its true meaning. The rarefaction coefficient α is correlated ities, porosity, capillary pressure, and relative permeability
by Civan (2010a, b, 2011). curves that accurately represent the flow behavior at the
nanoscale. In order to accomplish this, it is necessary to per­
A
o 1 (12.35) form some form of multiphase upscaling and this continues to
Kn B be a topic of active research. Successful standard approaches
to upscaling assume the reservoir can on a macroscale be
where A, B, and α are the empirical parameters. The rarefac­ divided into flow units, each of which have capillary pressure
o
tion coefficient considers all possible regimes in one equation curves and relative permeability curves of the same shape, and
whose value depends on the Knudsen number. In the limit of permeability values that are distributed in some simple way
low Knudsen number flows or under the viscous flow regime, such as a log‐normal distribution. It is also assumed that labo­
the pseudo‐viscosity essentially reduces to the viscosity ratory measurements on core or bulk fluids can be used to
defined for Darcy law. Gouth et al. (2007) used molecular provide the input to characterize each flow unit. This is clearly
dynamic simulation to investigate the Beskok and Karniadakis not the case for organic shale reservoirs, and consequently
equation. They found for multi‐component gases that vis­ upscaling shale microstructural features may necessitate some
cosity is not correctly treated by Equation 12.34. They were new approaches in order to reproduce flow characteristics of
not able to find a modification to the viscosity that worked for shales at the reservoir scale. For the case of nanometer‐scale
all percentage mixes of two components.
heterogeneity, core measurements are made on samples that
are a combination often unspecified of the multiple pore types
12.6.2 Corrections for Interfacial Tension that exist on the nanoscale. As such to be correctly used they
must be modeled to extract the intrinsic properties of each
Assume that gas is the nonwetting phase and the liquid film pore type. These can then be input into a nanoscale model and
over the pore surface is a wetting phase (Hamada et al., 2007). upscaled. It cannot be assumed that the effective value for a
In a cylindrical pore system containing gas and liquid phases, quantity obtained from core measurement provides the effec­
the diameter of the gas–liquid interface varies with the gas (or tive value at any other scale or geometry.
liquid) saturation. Therefore, the effect of pore confinement The other issue associated with upscaling is that the con­
to the apparent interfacial tension (IFT) γ between the gas nectivity of the different pore systems continues to be poorly
and liquid phases is given by the following equation (Civan understood. Although 3D imaging of shales has revealed
et al., 2012b), modified after Hamada et al. (2007): some organic pore connectivity, the connectivity of the
c (12.36) organics to the inorganic background remains unclear. As
/
DS 12 shale imaging technology evolves, we are likely to be able to
G
p
resolve some other challenges, such as the continuity of the
where is the limit value of the apparent gas–condensate organics and whether the organic matrix feeds directly into
IFT when the pore size D attains the infinity, D is the mean‐ the high conductivity fractures or whether the hydrocarbons
p
p
pore diameter, c is the empirical constant, and S is the gas move serially from the organics to the inorganics and even­
G
saturation. This correlation can be used to predict the effect of tually to the fracture systems. If gas is almost completely
pore proximity on the capillary pressure by using the Leveret stored in the organic pores than the small amount of water
J‐function. In mature organic pores, gas is relative wetting with produced during production would seem to imply that the
respect to water so this approach would need to be modified. inorganic pores contain no free water and/or the organic
pores couple directly into the stimulation fractures.
The accuracy of numerical simulation is better when the
12.7 UPSCALING HETEROGENEOUS SHALE‐ grid block sizes are smaller. However, when dealing with
GAS RESERVOIRS INTO LARGE HOMOGENIZED simulation of large shale reservoirs, sufficiently large grid
SIMULATION GRID BLOCKS blocks need to be used to reduce the number of grid blocks in
order to be able to generate simulation results of practical
As described above, shales are characterized by an organic importance with reasonable computational effort and numerical
matrix embedded in an inorganic background. Additionally, accuracy. This can be accomplished by replacement of
there may be microcracks within the matrix and consequently, intricately detailed models by larger scale models that still