Page 290 - Fundamentals of Gas Shale Reservoirs

270 A REVIEW OF THE CRITICAL ISSUES SURROUNDING

Following the discussion in Sigal et al. (2013), the volume Since C was small for this sample, the difference is due to the
p
occupied by the adsorbed gas also satisfies a Langmuir pore volume taken up by the adsorbed methane.
pressure relationship given by This example and the general discussion clearly show that
the total methane resource in an organic shale reservoir must
VP() V L (12.8)
a amax be calculated in a way that accounts for the volume occupied
by the adsorbed phase. In implementing a simulation code, it
V amax is the maximum adsorbed gas volume in moles. The must be programmed to properly account for the dependence
maximum molar density of methane in the adsorbed layer is of free gas pore volume on both pore volume compressibility
given by ρ and the density at any pressure by ρ .
amax a and the pore space lost to adsorption. In measuring total gas
S storage, it would be best to measure it on “fresh” core with
r amax amax (12.9)
V amax methane at reservoir temperature and stress, for a series of pore
pressures ranging from abandonment pressure to initial
a amax L (12.10) pressure. Sigal (2013b) has developed an approximate formula
The pore volume available for free methane storage at a given that could be used with a selected set of reservoir condition
confining pressure and zero pore pressure is V . Taking the measurements to correct standard measurements.
p0
pore volume compressibility as C then V (P) the volume
p
p
occupied by free gas is given by
12.4 FLUID TRANSPORT
VP() V C VP VP() (12.11)
p p0 p p0 a
Current and ongoing research efforts have documented the
Using the real gas equation of state, the moles of free gas n need for more appropriate physical formulations to describe
sp
stored in V are given by transport of gas through nanometer‐scale porous media, and it
p
is increasingly recognized that Darcy’s law with a constant
PV
n ( P T) p (12.12) value of permeability may be inadequate in shale nanopores.
,
sp ( zRT) Various approaches to modifying the gas flow equations have
been proposed (Swami et al., 2012). At the time of writing this
where z is the compressibility factor and R is the universal chapter, none of these have been adequately tested using exper­
gas constant (McCain, 1990). In nanometer‐scale pores, the imental data from complex porous media. In contrast to the
compressibility factor z can be a function of pore size transport equations valid for most conventional reservoirs, the
(Michel et al., 2012). The total number of moles of gas flow in very low permeability shale gas reservoirs undergoes a
stored in V at pore pressure P and temperature T n is then transition from a Darcy regime, where viscous coupling bet­
s
given by ween molecules controls the flow condition, to other regimes
where molecular collisions with the pore walls have a
n n S
s sp a (12.13) significant effect on transport. Such effects are well known to
petrophysicists and are generally referred to as “Klinkenberg
Based on Equations 12.6–12.13, Sigal et al. (2013) described effects,” after his 1941 paper. These effects cause an increase in
a methodology for measuring total storage on a core plug. In the apparent permeability to gas flow as the pore pressure
an example from the paper, the five parameters (S amax , P , decreases. Although the rock compressibility effects tend to
L
ρ amax , V , and C ) were determined on a Barnett plug from a modify the permeability as the pore pressure changes, the
p0
p
fit to measurement of total methane storage as a function of phenomenon described in this chapter is purely a result of the
pore pressure as determined from a series of high‐pressure transport of fluids confined in nanopores.
pycnometer measurements. For this fit, the bulk fluid value Beskok and Karniadakis (1999) (also see Karniadakis et al.,
of z in Equation 12.12 was used. Given the five parameters, 2005), based on theoretical arguments and experimental data,
the conventional methane storage curve for this sample can have developed a gas transport equation for a nonadsorbing gas
also be calculated assuming the pore volume is taken for all flowing through straight capillary tubes, which is valid for all
pressures as V and the storage is given by Sigal et al. flow regimes, encompassing no‐slip, transition, slip, and free
p0
(2013). molecular flows. Florence et al. (2007) also considered flow
through a single straight tube. Civan (2010a, b) extended the
n PV /( zRT) S application of their equation to describe transport through a
sconventional p0 a (12.14)
bundle of tortuous flow paths formed in extremely‐low perme­
n sconventional is the total storage calculation used in standard shale ability porous media with a single size (uniform) tube size. The
gas simulators and most reserve calculations. The conven­ equation developed by Beskok and Karniadakis (1999) has
tional calculation overestimates the total methane storage by been used as the starting point in the development of a gas
24% at initial reservoir pressure (Figure 5 in Sigal et al., 2013). transport equation to be used in more general porous media.