Page 296 - Fundamentals of Gas Shale Reservoirs

276 A REVIEW OF THE CRITICAL ISSUES SURROUNDING

based on the traditional method where pore proximity effects At equilibrium, the chemical potential of the fluid mole­
are ignored may in fact be underestimating the quantity of cules distributed throughout the system should be identical
recoverable fluids. Additionally, because our calculations (McCain, 1990). Because the chemical potential is a function
indicate fewer issues with condensate dropout in the near of the fugacity for real gases, under these conditions of
wellbore region, very small nanopores may in fact result in equilibrium, the fluid distributed throughout the various capil­
very stable production without any drop in productivity for lary tubes should also have identical fugacities. By a process
extended periods of time. Presently though, the influence of of trial and error, the pore pressures in the other pores may be
pore proximity on the acentric factor remains unknown and estimated by finding pressure values in Equation 12.32 that
poorly studied (Cho et al., 1985). result in a fugacity of 937 psia for methane critical pressures
The pore‐proximity correction for fluids in a single‐pore and temperatures appropriately chosen for the respective pore
as described earlier provides different levels of corrections sizes (Zhang et al., 2013a, b). The results obtained for the 2, 4,
in the various size pores of shale. However, there is another 6, 8, and 10 nm pores are as follows:
factor of importance when dealing with a network of
interconnected pores of prescribed size distributions. When 1. The pore pressures are estimated as 935, 943, 950,
different pore throats and pore bodies are involved in a net­ 953, and 957 psia, respectively.
work having a certain connectivity pattern (coordination 2. The real‐gas deviation factors of the confined gases
number) (Civan, 2001, 2002a), the conditions of pressure are 1.0, 0.992, 0.987, 0.985, and 0.981, respectively.
and composition of the fluid in different size pores are also 3. The densities of methane within each pore can then be
likely to be different (Zhang et al., 2013a, b). However, the estimated as 34.0, 34.5, 34.9, 35.1, and 35.4 g/m ,
3
description of effective fluid phase behavior for relatively respectively.
larger reservoir or rock volumes continues to remain chal­ 4. Further, if we assume all cylindrical pores of length
lenging. At this time, existing knowledge of fluid phase 100 nm, then the number of molecules confined in
behavior is largely restricted to single pore sizes. each cylindrical pore are 400, 1626, 3704, 6625, and
One approach to finding appropriate fluid properties in a
connected pore system is to require the chemical potential, 10419, respectively.
and therefore the fugacity of the fluid components are the These results imply that due to pore proximity effects in nano­
same in every pore. The Peng–Robinson EOS relating pores resulting in modified critical properties and gas com­
pressure P, temperature T, and molar volume V as shown in pressibility factors, methane in different pores exist in
m
Equation 12.32 may be used to derive an expression for equilibrium at different densities and at different pore pres­
fugacity for real gases (McCain, 1990).
sures. Although this work presents an exploratory analysis of
a the implications of pore proximity, to our knowledge this con­
P T V b RT (12.32) stitutes the first model‐based approach to quantifying fluid
VV m b b V m b m
m
storage and pore pressure in connected pore systems. The
f A Z 2 . 05 1 B results highlight the complex interplay between pore geometry
ln Z 1 ln(Z ) B ln and fluid properties in nanoporous media and indicate that
p 2 . 15 B Z 2 . 05 1 B under equilibrium even a single‐component fluid is likely to be

(12.33) characterized by different pore pressures in different pore sys­
tems. We are continuing to investigate the full implications of
where this proposed storage model; however, experimental verifica­
tion of the results presented earlier are a necessary next step
aP bP
A T and B prior to extending the results to large‐scale porous media and a
RT 2 RT
discussion of the implications for reservoir performance.
For purposes of demonstrating the challenges associated with
describing fluid storage and pore pressure when pore confine­ 12.6.1 Viscosity Corrections
ment effects become dominant, we examine methane storage for While in the previous section, the focus was largely centered
the simple connected pore system, where methane in bulk at on phase behavior, Beskok and Karniadakis (1999) also dis­
1000 psia and 200F is connected to pores of different sizes of 2, cuss variations of gas viscosity with the Knudsen number Kn
4, 6, 8, and 10 nm size pores (Figure 13 in Zhang et al., 2013a). previously defined. Due to the effects of rarefaction of the
As mentioned earlier, equilibrium conditions may be gas, the viscosity is shown to decrease with increasing
determined by equating the fugacity of methane in these dif­ Knudsen number or decreasing pore size as given by
ferent pores. In the example earlier, the fugacity of methane
in the bulk using bulk properties for methane is 937 psia. 1 (12.34)
The corresponding z‐factor is 0.947. 1 Kn