Page 347 - Fundamentals of Gas Shale Reservoirs

MS OF GAS ADSORPTION ON MINERALS 327
at each pressure step in the experiment, the gas adsorbed MS in the grand canonical ensemble can be successfully
reduces the void volume. As a result, the initially deter­ applied to shale gas research with a number of simulation
mined void volume must be corrected at the beginning and examples in the following sections.
the end of each pressure step (Ambrose et al., 2012;
Menon, 1968). 15.1.4 Methodology and Workflow
Measurement of the adsorbed phase density or its of Molecular Simulation
volume is not a trivial matter. The local density for the
adsorbed phase is expected to vary across the pore, differ­ Molecular simulation of gas adsorption in shale was carried
ent from its average bulk density due to the added interac­ out by combining MC and MD simulations. The objectives
tions between the adsorbed phase and the solid matrix. were to determine the absolute and excess adsorption iso­
Further, in gas shale where pressure and temperature may therms, adsorbed phase density, RDFs between the minerals
be significantly greater than the supercritical thresholds of and gases such as CH , C H , C H , and CO and their diffu­
6
2
4
2
8
3
some gases, it makes experimental measurements extremely sion coefficients. The workflow consists of setting‐up
difficult. There are several estimates of the adsorbed phase molecular structures and their force fields based on experi­
density such as densities at the critical point (Tsai et al., mental and empirical data.
1985) or densities calculated from the “b” term in the cubic
equation of state (Dubinin, 1960; Haydel and Kobayash, 15.1.5 Simulation Algorithms and Software
1967), and liquid densities at their boiling points at one The molecular simulation procedure consists of MD simula­
atmosphere (Menon, 1968). Ozawa et al. (1976) considered tions in the constant pressure and temperature ensemble and
the adsorbed phase as a superheated liquid with a density MC simulations performed in the GCMC (Zhang et al.,
dependent upon the thermal expansion of the liquid. 2014a). The former is performed using the Gromacs software
However, the density calculated from the “b” term in the (Bae and Bhatia, 2006; Busch et al., 2003; Fitzgerald et al.,
cubic equation of state does not take into account of the 2005), and the latter is performed using an open‐source
temperature and pressure effects. Thus the liquid densities package, RASPA 1.0, developed by Dubbeldam et al. (2008).
at their boiling points at one atmosphere cannot always be The MD and MC methods were previously applied to study
used since gas often would not become liquid state at one hydrate formation (Zhang et al., 2008), gas adsorption in
atmosphere. Li et al. (2003) compared all of the above‐ porous material (Zhang et al., 2012), and coal (Zhang et al.,
mentioned methods to a Langmuir–Freundlich adsorption 2014a). In our simulations, the temperature was fixed by using
model, and found that the adsorbed phase density is tem­ the Berendsen thermostat (Berendsen et al., 1984). As with the
perature dependent. temperature coupling, the system can also be connected to
To circumvent the problems facing these estimates, a pressure bath. We use the Berendsen pressure coupling
Ambrose et al. (2012) used equilibrium MS involving scheme to reach the target pressure, and then switch to the
methane in small carbon slit‐pores of varying sizes and tem­ Parrinello–Rahman coupling (Parrinello and Rahman, 1981)
peratures to address the fundamental issues related to the to keep the pressure constant once the system is in equilibrium
adsorbed phase density and phase transition. They performed as the Berendsen pressure coupling allows the system to
MD simulations with constant numbers of molecules, reach equilibrium quickly, whereas the Parrinello–Rahman
constant volume, and constant temperature (NVT ensemble) coupling can adjust the pressure finely and avoid unex­
with the total number of methane molecules being the pected deformation and fluctuation of the simulation box.
same for two different channel widths, but by changing the Adsorption isotherms are obtained from the GCMC simula­
dimension in one direction to obtain the same volume for tions (Siepmann and Frenkel, 1992). The GCMC simulation
the two slit pores. They used the density profiles to analyze can be switched to the MD simulation to allow the volume to
the adsorbate density and further determine the adsorbed swell or shrink when simulate CH adsorption in coal (Zhang
4
phase and bulk phase. et al., 2014a). The GCMC algorithm allows the system density
For adsorption studies, a more suitable ensemble to use is to fluctuate with insertion and deletion of adsorbate mole­
the grand‐canonical ensemble. In this ensemble, the temper­ cules. Equilibrium is attained when the numbers of successful
ature, volume, and chemical potential are fixed. It simulates insertion and deletion attempts balance each other. The
the experimental setup allowing the adsorbed gas to equili­ GCMC method is detailed in Dubbeldam et al. (2004a, b).
brate with the gas reservoir. Heat exchange is allowed bet­
ween the system studied and a heat bath, and heat transfer
takes place until a thermal equilibrium is reached. The gas in 15.2 MS OF GAS ADSORPTION ON MINERALS
the system and a gas reservoir can be exchanged to allow
equilibrium of chemical potential. This makes the grand Most of the gas shales comprise silty fractions of detrital
canonical simulations different from other ensembles, where quartz and feldspar minerals, biogenic silica, carbonate, clays,
the numbers of molecules are fixed. We describe how the and organics (kerogen). The mineralogical compositions,