Fuel 184 (2016) 344–361
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Fuel
journal homepage: www.elsevier.com/locate/fuel
Review article
A review on capillary condensation in nanoporous media: Implications
for hydrocarbon recovery from tight reservoirs
Elizabeth Barsotti a, Sugata P. Tan a, Soheil Saraji a,⇑, Mohammad Piri a, Jin-Hong Chen b
a
b
Department of Petroleum Engineering, University of Wyoming, Laramie, WY 82071, USA
Aramco Services Company: Aramco Research Center – Houston, TX 77084, USA
h i g h l i g h t s
Insight into capillary condensation may improve gas recovery from tight reservoirs.
Insight into capillary condensation is limited by the scarcity of experimental data.
A review on the experimental data available in the literature is presented.
A review on theories for modeling capillary condensation is presented.
The extension of experimentally verified models to the reservoir scale is promoted.
a r t i c l e
i n f o
Article history:
Received 11 May 2016
Received in revised form 24 June 2016
Accepted 27 June 2016
Keywords:
Capillary condensation
Confinement
Hydrocarbon
Nanopores
Tight reservoirs
a b s t r a c t
The key to understanding capillary condensation phenomena and employing that knowledge in a wide
range of engineering applications lies in the synergy of theoretical and experimental studies. Of particular
interest are modeling works for the development of reliable tools with which to predict capillary
condensation in a variety of porous materials. Such predictions could prove invaluable to the petroleum
industry where an understanding of capillary condensation could have significant implications for gas in
place calculations and production estimations for shale and tight reservoirs. On the other hand,
experimental data is required to validate the theories and simulation models as well as to provide possible
insight into new physics that has not been predicted by the existing theories. In this paper, we provide a
brief review of the theoretical and experimental work on capillary condensation with emphasis on the
production and interpretation of adsorption isotherms in hydrocarbon systems. We also discuss the
implications of the available data on production from shale and tight gas reservoirs and provide
recommendations on relevant future work.
Ó 2016 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capillary condensation of hydrocarbon gases in tight formations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capillary condensation: theoretical perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.
Density and phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.
Mechanism of condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.
Ideal case: the Kelvin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.
Advanced models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Capillary condensation: experimental perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.
Nanoporous media: materials and characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.
Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.
Experimental data on hydrocarbon systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
⇑ Corresponding author.
E-mail address: [email protected] (S. Saraji).
http://dx.doi.org/10.1016/j.fuel.2016.06.123
0016-2361/Ó 2016 Elsevier Ltd. All rights reserved.
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E. Barsotti et al. / Fuel 184 (2016) 344–361
5.
Conclusions and final remarks
Funding . . . . . . . . . . . . . . . . . . .
Appendix A.
Supplementary
References . . . . . . . . . . . . . . . .
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1. Introduction
An improved understanding of the physical behavior of
confined fluid is important to a multitude of disciplines and will
allow for the development of better insights into catalysis [1–3],
chemistry [4], geochemistry [5], geophysics [1], nanomaterials [1]
and improved methods of battery design [2], carbon dioxide
sequestration [6,7], drug delivery [2], enhanced coalbed methane
recovery [8], lubrication and adhesion [1], materials characterization [9–13], micro/nano electromechanical system design [14],
pollution control [1,7,15–17], and separation [2], as well as hydrocarbon production from shale and other tight formations [18–35].
In oil production, for example, full advantage of enhanced oil
recovery by carbon dioxide injection into shale formations can only
be taken once a better understanding of confined fluid behavior,
including the phase equilibria, is gained [36,37].
It is well known that the physical behavior of fluids in confined
spaces differs from that in the bulk [1,2,4,5,7,14,15,18,20–22,24,
26–28,38–55]. In nanoporous media with pore diameters less than
100 nm [56] and greater than 2 nm, molecular size and mean free
path cannot be ignored compared to pore size [1,23,57]. At this
scale, due to confinement, distances are decreased among molecules, so intermolecular forces are large, and consequently, phase
behavior becomes not only a function of fluid-fluid interactions,
as it is in the bulk, but also a function of fluid-pore-wall interactions. Capillary and adsorptive forces [1,15,18,23,26,27,57] alter
phase boundaries [1,2,7,15,18,21–24,26,27,42,45,49,50,52,55],
phase compositions [1,27,52,58], interfacial tensions [22], fluid
densities [1,5,23,24,49,51], fluid viscosities [18,22], and saturation
pressures [20,24,42,43,46]. The extent to which the phase behavior
is altered by confinement depends on the interplay of the
fluid-fluid and the fluid-pore-wall interactions. Although pore size,
shape, and interconnectivity; pore wall roughness, composition,
and wettability; and fluid composition and molecular size are
qualitatively known to influence the physical behavior of confined
fluids [1,5,27,45,52], a quantitative understanding of the relative
effects of each characteristic is presently lacking.
2. Capillary condensation of hydrocarbon gases in tight
formations
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358
358
358
358
hydrocarbons in shale and tight formations, impediments to
production from them remain and are manifested in nanoscopic
properties such as fine grain sizes [18,22], nanopores
[18,22–24,27,61], low porosities (2–10%) [19], and nanodarcy
permeabilities [18,19,22,24,33], as well as complex mineral
compositions [62]. These characteristics limit conventional
methods of reservoir evaluation [33], complicating estimations of
original hydrocarbons in place and ultimate recovery [18,20] and
culminating in an inability to accurately predict the profitability
of a reservoir. Case in point, a good history match for oil production
from wells in the middle Bakken formation is obtained only after
considering the fluid phase behavior in small pores [24].
In estimating hydrocarbon recovery, the physicochemical
properties of the reservoir fluids are combined with information
about the petrophysical properties of the matrix in order to
interpret well logs [20,21,61], compute original hydrocarbons in
place [20,24], determine drainage areas, calculate well spacing
[27], evaluate various production scenarios, and predict ultimate
recovery. For shale and tight reservoirs, uncertainties in the
determinations of water saturation [32], capillary pressure, and
absolute and relative permeabilities [31,32] along with
non-Darcy flow [33], delayed capillary equilibrium, and confined
phase behavior necessitate comprehensive theoretical and experimental studies of these nanoscale phenomena and the development of specialized methods for estimating hydrocarbon recovery.
In shale gas reservoirs (i.e., at reservoir conditions), strong
affiliation of reservoir fluids to pore walls is often present. Because
hydrocarbon gases are predominately stored in the organic-matter
nanopores [24] of the shale in which they are the wetting fluid
[20,21], capillary condensation is highly probable, although more
information is needed to understand how and when it occurs.
Typical compositions of petroleum gases can be found in Table 1
for conventional geological formations and shale formations.
Capillary condensation has major implications for estimating
hydrocarbons in place in shale and tight gas reservoirs. This is in
strict contrast to conventional gas reservoirs where nanopores
represent an inconsequential percentage of the total porosity in
Table 1
Typical compositions of conventional and unconventional petroleum gases.
Component
Tight formations and their analogs, shale gas and shale oil
reservoirs, are unconventional resources, which are defined as rock
formations bearing large quantities of hydrocarbons in place that,
as a result of reservoir rock and fluid properties, cannot be
economically produced by conventional methods. Only in the past
decade have the depletion of conventional reservoirs and the
increasing worldwide demand for hydrocarbons generated enough
interest in shale and tight reservoirs to establish technological
innovations that make the production from these resources
profitable.
Shale is ‘‘a laminated, indurated rock with [more than] 67%
clay-sized minerals” [59]. The U.S. Energy Information
Administration estimates that 345 billion barrels of recoverable
oil and 7,299 trillion cubic feet of recoverable gas are stored in shale
formations worldwide, making shale oil accountable for 9% of total
(proven and unproven) oil reserves and shale gas accountable for
32% of total gas reserves [60]. Despite the abundance of
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Methane
Ethane
Propane
n-Butane
Isobutene
n-Pentane
Isopentane
Hexane
Heptane
Octane
Nonane
Decane+
Nitrogen
Carbon Dioxide
Oxygen
Mole fraction
Conventionala
Shaleb
0.9500
0.0320
0.0020
0.0003
0.0003
0.0001
0.0001
0.0000
0.0000
0.0000
0.0000
0.0000
0.0100
0.0050
0.0002
0.6192
0.1408
0.0835
0.0341
0.0097
0.0148
0.0084
0.0179
0.0158
0.0122
0.0094
0.0311
0.0013
0.0018
0.0000
a
Typical composition of conventional natural gas composition taken from
Driscoll and Maclachlan [63].
b
Composition of Eagle Ford Shale gas taken from Deo and Anderson [64].
346
E. Barsotti et al. / Fuel 184 (2016) 344–361
comparison to macropores, and thus, no significant changes to the
overall phase behavior is observed [54]. In spite of the implications
of capillary condensation for unconventional gas reservoirs, current methods of calculating reserves in shale only consider
adsorbed gas on the pore walls and free gas in the pore bodies
[20,21,30,32,33,35,60] with the largely immobile adsorbed phase
accounting for up to half of the total gas in place [19]. In one study,
Chen et al. estimated in principle that accounting for capillary
condensation could increase reserve estimations by up to threeto six-times [20]. Because the densities of phases are different in
nanopores, however, more reliable models are needed in order to
confirm such estimations. On the other hand, the presence of a
condensed phase would reduce the permeability in the reservoir
as it blocks the gas flow near the wellbore. Nevertheless, confinement by nanopores introduces different conditions at which two
phases may coexist. Therefore, the net effect of accounting for
capillary condensation on the estimates of recoverable reserves is
still unknown. Again, as mentioned earlier, reliable models are
needed to obtain more accurate estimates.
Prerequisite to the parameterization of the equations of state
(EOS) used in such models and their validation for applications in
real systems is comprehensive experimental data on capillary
condensation. At present, however, experimental data is hardly
available even for many of the simplest hydrocarbon-adsorbent
pairings. It must be noted that capillary condensation data, not
adsorption data, is the missing prerequisite for EOS parameterization. Adsorption without phase transition is much better understood
than capillary condensation, and since it is associated with surface
forces, i.e., the disjoining pressure, which appears to be negligible
in comparison to capillary condensation forces [65], little can be
gained from adsorption-only experiments, in this respect. For this
reason, we exclude adsorption-only data from Section 3.3 on available experimental results.
The current reviews on capillary condensation in the literature
either are composed for general applications across a wide variety
of industries with no mention of oil or gas [66] or introduce capillary condensation as it pertains to the much broader studies of
phase behavior [1,67], adsorption, materials characterization
[2,51,68], and fluid dynamics [69]. This paper, however, focuses
specifically on the implications of capillary condensation phenomena for the petroleum industry. In this endeavor, an overview of
the relevant theoretical and experimental methods for the study
of the capillary condensation of hydrocarbon gases will be presented to reflect the current state of knowledge and to suggest
the direction for future research. Such future research will provide
a fundamental understanding of capillary condensation, without
which applications of it in shale and tight formations cannot be
reliably effective.
Fig. 1. Confined phases and densities: (a) local densities in a pore, where the adsorbed phase contains molecules layered on the wall, while the capillary condensation occurs
when the low-density phase (vapor-like phase) abruptly changes into a higher-density phase (condensed phase) in the pore space far from the wall. Adapted with permission
from grand-canonical Monte Carlo (GCMC) simulation by Walton and Quirke [70]. Copyright 1989 Taylor & Francis, Ltd. (b) Cartoon showing confined density defined as the
number of moles of a given confined fluid phase filling a pore divided by the total volume of the pore.
E. Barsotti et al. / Fuel 184 (2016) 344–361
3. Capillary condensation: theoretical perspective
The key to understanding the confinement phenomena, from
which shale gas and/or tight gas recovery may benefit, lies in
systematic studies of capillary condensation. The current, albeit
sparse, body of knowledge regarding capillary condensation is
the result of studies from many disciplines, primarily adsorption
experiments and molecular simulation studies.
3.1. Density and phases
Prior to further discussion, there is a need to define a common
ground in using the terms density and phases to describe the behavior of confined fluids. As facilitated by the established theoretical
and experimental approaches for fluids in the bulk, we use our
understanding from the bulk properties for the case of confined
fluids even though we know it may not apply at the nanoscale of
the confinement.
As known from many studies, the fluid molecules are unevenly
distributed inside each pore as is shown in Fig. 1a, which is
adapted from a molecular simulation [70], due to fluid-pore-wall
interactions as manifest in pore wettability [16,71]. Therefore,
the density is localized in the confined space; there are more molecules near the pore wall. To still use density in the usual meaning,
the confined density is taken to be the moles of the fluid in the pore
divided by the total pore volume as shown in Fig. 1b.
As in the bulk, densities may be used to infer states of matter or
phases. Therefore, based on Fig. 1, two different phases may exist
in nanopores and are of primary interest to shale and tight gas
recovery. The first phase is the vapor-like phase in the pore prior
to condensation with an average density of qA, while the second
is the liquid-like condensed phase with an average density of qL
that forms at capillary condensation [1,2,42,49,52,68,69,72]. The
first phase consists of molecules that are mostly adsorbed on the
pore walls, so it has a density, as newly defined, between that of
the bulk vapor phase and that of the condensed phase [49,72,73].
From this point on, we call it the adsorbed phase. The bulk vapor
phase outside the pore and this adsorbed phase are in thermodynamic equilibrium with each other prior to condensation. At
condensation, the equilibrium also involves the condensed phase.
After the phase transition, the condensed phase replaces the
adsorbed phase in the equilibrium.
3.2. Mechanism of condensation
Exposing gas to a clean, outgassed porous material introduces a
phenomenon well known as adsorption, where molecules of the
347
bulk vapor phase (i.e., adsorbate) are physically bound to the
surface of pore-walls (i.e., adsorbent) to form a monomolecular
layer of the adsorbed phase. If the pores are small enough and
the vapor phase sufficiently wets the pore surface,
inter-molecular forces can build multiple molecular layers of the
adsorbed phase until, at some threshold temperature and pressure
below the bulk phase boundary of the fluid, a new condensed
phase nucleates and fills the pore [1,2,49,52,55,68,72–75]. This
phase is separated from the gas or bulk vapor phase at the pore
throat by a curved meniscus [76]. This phenomenon is called capillary condensation, and is generally categorized either as a second
order phase transition for one-dimensional (cylindrical) pores [49]
or as a first order [2,49,68,76] or nearly-first-order phase transition
[69] for two- (slit-like) and three-dimensional pores.
Capillary condensation data is commonly derived from adsorption isotherms that relate the amount of fluid adsorbed on a solid
surface (i.e., in the pore space) to the operating bulk pressure at
constant temperature [76]. In ordered nanoporous materials,
adsorption isotherms displaying a steep vertical or near-vertical
step are indicative of the rapid pore filling associated with capillary
condensation [38]. Of the variety of adsorption isotherms recognized by the International Union of Pure and Applied Chemistry
(IUPAC) [47,56], the Type IVa, IVb, and V isotherms (see Fig. 2)
are most consistent with this observation and, thus, are the most
relevant to the study of capillary condensation in ordered nanoporous materials [17,45–47,56].
Although ordered nanoporous materials – porous materials
containing a regular array of nanopores with the same geometry
– are not representative of real adsorbents such as shale rocks, they
are a mainstay of present research into capillary condensation.
Their well-defined pores allow for studies into even the most basic,
yet still not understood, phenomena related to fluid-pore-wall
interactions that are not observable in adsorbents with highly
irregular arrays of pores and poorly defined surfaces.
Adsorption isotherms exhibiting capillary condensation can
either be reversible, as in Type IVb isotherms, or irreversible (i.e.,
hysteretic), as in Type IVa and Type V isotherms. The hysteresis
loop in the Type IVa isotherm indicates capillary condensation
[76,77] when the temperature of the confined fluid is above the
triple-point of the bulk fluid [1]. The different paths of adsorption
and desorption in hysteretic isotherms are dependent on pore
chemistry, geometry and temperature [47,73] and may arise either
from the formation of metastable states (Type H1 hysteresis)
[1,2,38,56,66,74], or from pore blocking or networking effects
due to heterogeneity of pore geometries, such as is found in
inkbottle shaped pores or interconnected pores (Type H2 hysteresis) [47,56,66,73,74,76].
Fig. 2. IUPAC Type IV(a), IV(b), and V isotherms. The shaded regions in the figure indicate the condensation/evaporation steps. Types IV(a) and IV(b) isotherms are typical of
nanoporous adsorbents in which the adsorbate is the wetting phase. Type IV(a) isotherms may exhibit hysteresis caused either by the formation of metastable states or from
pore blocking or networking. The first is exhibited in the IUPAC H1 hysteresis loop as indicated by the solid line [1,2,38,56,66,74], while the second is exhibited in the IUPAC
H2 hysteresis loop as indicated by the dotted line [47,56,66,73,74,76]. While Type V isotherms are characteristic of adsorbents in which the adsorbates are non-wetting [56].
The wettability of the adsorbent to its adsorbate is demonstrated by the shape of the isotherm prior to condensation. Wetting fluids almost immediately begin to form layers
on the sides of the pores as evidenced by a convex curve, while non-wetting fluids do not share this behavior, as shown by their concave curve. Adapted with permission from
Thommes et al. [56]. Copyright 2015 IUPAC.
348
E. Barsotti et al. / Fuel 184 (2016) 344–361
Fig. 3. Temperature dependence of a hysteresis loop: O2 in 4.4-nm MCM-41. Adapted from with permission from Morishige et al. [73]. Copyright 2004 American Chemical
Society.
no hysteresis occurs; this is denoted as the hysteresis critical
temperature (Th) [55,66,73,78]. Th is less than TCp, while decreases
in temperature from Th result in expansion of the hysteresis loop
[13,38,55,73,77,78], as illustrated in Fig. 3. This is supported by
the work of Morishige and coworkers, who experimentally
observed capillary condensation at a wide range of temperatures
from below Th to TCp, including the disappearance of the differences
between confined fluid phases at TCp, for argon, nitrogen, oxygen,
ethylene, and carbon dioxide in MCM-41 [38,73] and SBA-15 [78].
These results were further corroborated for many fluids in wide
variety of adsorbents by Qiao et al. [40], Russo et al. [15], Yun
et al. [7] and Tanchoux et al., who also noted that Th decreases with
pore size [13].
However, relatively recent studies from Morishige et al. and
Horikawa et al., which detailed the capillary condensation of water
in ordered mesoporous carbons (OMC’s), are in disagreement with
these findings [72,79]. Unlike the capillary condensation of gases in
mesoporous silicas where condensation pressures rose with
Fig. 4. Isotherms for water in OMC (7.0 nm pore diameter) [72]. The positions of the
adsorption and desorption branches of the hysteresis loop are constant regardless
of temperature. Adapted with permission from Morishige et al. [72]. Copyright 2014
American Chemical Society.
In many senses, as previously mentioned, capillary condensation
is the phase transition of the confined fluid into a condensed phase,
similar to the vapor-liquid phase boundary in the bulk. For a pure
fluid in the bulk, this phase transition can occur up to the critical
point (TC), above which only a homogenous supercritical phase
can exist. For a confined fluid in a given adsorbent, the condensed
phase and the lighter adsorbed phase are distinguishable only up
to the so-called pore critical temperature (TCp), which is normally
lower than TC [1,49,73,78]. For fluids that show hysteresis in their
adsorption isotherms, there also exists a temperature above which
Fig. 5. Experimental indication that the adsorption branch of the isotherm (open
circles) is closer to equilibrium than the desorption branch (filled circles). Data is for
O2 in 4.4-nm MCM-41 [73]. Adapted with permission from Morishige et al. [73].
Copyright 2004 American Chemical Society.
E. Barsotti et al. / Fuel 184 (2016) 344–361
increasing temperature [38,78], the condensation pressures of the
water in OMC’s remained constant with increasing temperature
(Fig. 4) [72,79]. Morishige et al. attributed this inconsistency to
differences in the wettabilities of the adsorbents to their respective
fluids [72].
Regardless of the relationships among the confined critical
temperatures and condensation pressures, for all fluids confined
in porous media, TCp and Th depend on the fluid chemistry,
pore-wall chemistry, pore size, and/or pore geometry [1,66]. The
complex dependency of Th on these properties has given rise to
controversy as to which branch of the hysteresis loop represents
the equilibrium phase transition [12,15,55,66,74].
Neimark et al., who matched data from their model to
experimental isotherms and Derjaguin-Broekhoff-de Boer
isotherms for argon and nitrogen in MCM-41 type pores [80],
proposed the desorption branch as the equilibrium branch. This is
supported by the theory, where minimization of the grand potential
energy results in a wider range of available fluid configurations
(i.e., densities) for the adsorption branch than the desorption
branch, thus indicating that more metastable states develop during
adsorption so that desorption, rather than adsorption, occurs at the
true phase equilibrium [42]. This designation is further supported by
Pellenq et al., who have compared isotherms from their mean field
model to those of argon in MCM-41-type materials [81], and
has been adopted by the IUPAC [56]. However, it is in strict contrast
to the experimental work of others [38,72–74,78]. In their
experimental studies, Morishige and coworkers have investigated
the temperature progression of the chemical potential difference
(with respect to that of bulk liquid) of adsorption and desorption
during capillary condensation in hysteretic isotherms [73,78], as
shown in Fig. 5. Based on the continuity of the slope along the
adsorption branch across Th in Fig. 5, Morishige and coworkers present a compelling argument for the existence of thermodynamic
equilibrium only during adsorption. In other words, their work
shows that the adsorption branch is the true phase transition and,
thus, should be used for identifying capillary condensation from
adsorption isotherms [14,69].
Based on observations from the adsorption isotherms, capillary
condensation in nanopores is attributed to strong intermolecular
forces [15,18,23,26,27,46,57,69,76], although the nature of the
pore-fluid interactions and the ways in which pore geometry,
pressure, and temperature quantitatively affect these interactions
is unknown [1]. However, some progress has been made in the analysis of the forces exerted by capillary condensed fluids on the walls
of their confining pores, and vice versa. For example, Gor et al. have
compared capillary condensation adsorption isotherms of
n-pentane in MCM-41 and SBA-15 to both experimental and
theoretical capillary condensation strain isotherms [8]. Strain isotherms, as shown in Fig. 6, are plots of relative pressure versus strain
at constant temperature, typically produced via small angle X-ray
349
scattering (SAXS). Based on discrepancies between theoretical and
experimental isotherms, Gor et al. concluded that capillary condensation changes the elastic properties of SBA-15 but not of MCM-41.
They attributed this difference to the presence of micropores in the
SBA-15, alone, even though their SBA-15 sample (8.1 nm) had more
than twice the pore diameter of their MCM-41 sample (3.4 nm).
Thus, it cannot be known from their work how pore size affects
changes in pore wall elasticity during capillary condensation [8].
In a complimentary work by Günther et al., small angle X-ray diffraction was used to show that increasing adsorption before capillary
condensation causes pores to expand, while capillary condensation
causes the pores to contract [50]. Therefore, changes in pore
diameter due to adsorption, as shown in the work of Gor et al. and
Günther et al., could affect the onset of capillary condensation [8,50].
Because the strain of the adsorbent is directly related to the
pressure of its occupying fluid, the strain isotherms produced by
Gor et al. can also be interpreted as showing the pressures of the
fluid within the pores. Through this interpretation, it is evident
that adsorbed fluid layers before capillary condensation possesses
a positive pressure (i.e., cause positive strain, or expansion, of the
adsorbent), while the condensed phase during capillary condensation has a negative pressure (i.e., causes negative strain, or contraction, of the adsorbent), often referred to as tension or being
stretched. The condition under tension is supported by simulation
observations, such as those by Long et al. [4], who found that for
pores with widths greater than 5 molecular diameters of the
confined fluid, the pressure in the condensed phase was always
negative. Both the work of Gor et al. and Long et al. are consistent
with evidence from capillarities, such as water plugs in nanochannels [82], peculiar behavior of soil water [83], centrifuge capillarypressure experiments [84], and sap transport in trees [85]. Though
liquids under negative pressure are theoretically in a metastable
state [86], they show stable behavior in confinement [84]; and thus
can exist even for geological times [135]. They may also exceed the
stability limit where cavitation should occur to stabilize the system
[87]. This fact may offer an alternative explanation to the delayed
desorption phenomenon if adsorption is considered to be the true
phase equilibrium.
Likewise, evidence as to the fluid-wall interactions during
capillary condensation has been produced by Naumov et al. [46].
Using Pulsed Field Gradient Nuclear Magnetic Resonance (PFG
NMR), they showed that for cyclohexane in Vycor glass and porous
silicon, the hysteresis of the adsorption isotherm is accompanied
by hysteresis of the self-diffusivities [46]. Self-diffusivity is the random, microscopic movement of the fluid molecules due only to
their own thermal energy [46]. Naumov et al. attribute hysteresis
of the self-diffusivities to the differences in the densities of the
fluid filling the pores during adsorption and desorption [46]. The
self-diffusivity was lower during desorption due to the
pore-blocking effects that occur when evaporation proceeds via
Fig. 6. Typical strain isotherms for adsorbents during the capillary condensation of (a) a wetting fluid and (b) a non-wetting fluid [8]. These correspond to the IUPAC Type IV
(b) and Type V adsorption isotherms, respectively [8]. Adapted with permission from Gor et al. [8]. Copyright 2013 American Chemical Society.
350
E. Barsotti et al. / Fuel 184 (2016) 344–361
In capillary condensation, the Young-Laplace equation is used in
the vapor-liquid equilibria (VLE) to account for the effect of the
nanopores. For bigger pores, where the vapor phase may be
considered ideal and the liquid phase is incompressible, the use
of the Young-Laplace equation in the VLE leads to the Kelvin
equation [12,14,44,46,88,90,91]:
ln
Fig. 7. Hysteresis of self-diffusivities of cyclohexane in Vycor glass at 297 K as
compared to that in the corresponding adsorption isotherm. Adapted with
permission from Naumov et al. [46]. Copyright 2008 American Chemical Society.
cavitation, which is at least partially dependent on pore geometry
[46]. A self-diffusivity hysteresis loop is shown in comparison to
hysteresis of an adsorption isotherm in Fig. 7.
3.3. Ideal case: the Kelvin equation
To account for fluid-pore interactions, many theoretical methods take into consideration the pressure difference between the
confined and the bulk phases in the form of the disjoining pressure,
the capillary pressure, or both. Before capillary condensation
occurs, disjoining pressure is the only form of interfacial pressure
and exists as the pressure difference between the adsorbed layers
and the vapor phase filling the pore body [8,12,14]. Once the
adsorbed film reaches its limit of stability, the layers of the
adsorbed phase converge upon each other in the process of capillary condensation [12], and the center of the pore is filled with
the condensed phase which is separated from the bulk vapor at
the pore throat junction by a meniscus. At this point, equilibrium
is reached between the bulk vapor and the condensed phase in
the pore, and the capillary pressure can be defined as the difference
in the pressures on either side of the meniscus [8]. It is important
to note, however, that even after capillary condensation occurs
there are still some layers of fluid adsorbed on the pore wall,
meaning that a disjoining pressure is still present, although it
now represents the pressure difference between the adsorbed
layers and the condensed phase. In some studies, the disjoining
pressure appears to be negligible in comparison with the capillary
pressure [65].
Capillary pressure, P cap , is defined by the Young-Laplace
equation [14,18,22–24,46,88,89]. The equation for the case of a
cylindrical pore is:
Pcap ¼ PNW PW ¼
2c
cos h
rp
PV
1
2c
qL RT rp
Psat
ð2Þ
where PV is the operating pressure of the vapor phase at which
capillary condensation occurs, Psat is the saturated vapor pressure
of the fluid in the bulk, qL is the molar density of the liquid phase
in the bulk, R is the universal gas constant, and T is the absolute
temperature. If both sides of Eq. (2) are multiplied by temperature,
then the expression on the left-hand side is the same as the vertical
axis in Fig. 5, while the right-hand side is a continuous function of
temperature. Therefore, Morishige and coworkers have practically
shown that the adsorption branch behaves according to Eq. (2),
which accounts for the phase equilibrium.
The Kelvin equation is used extensively in both experiments
and models to mathematically describe capillary condensation
[81,90]. It is frequently employed in the prediction of the occurrence of capillary condensation under different conditions
[14,42,46] and the evaluation of the forces that are exerted on
the adsorbent by condensates [14,75], the thickness of adsorbed
layers [75,88], pore size [75], and pore size distribution [44,88,92].
Despite its frequent use, the Kelvin equation is based on many
assumptions that may not be valid for scenarios associated with
capillary condensation. For example, the Kelvin equation assumes
that the liquid is incompressible, the vapor is ideal, and both the
surface tension and the molar density are independent of the pore
radius [55,89,91], all of which are not necessarily true for fluids confined in nanopores. Furthermore, it does not account for adsorbed
phases or the fluid-pore wall forces that cause them [2,46,55].
Likewise, because it is based on macroscopic thermodynamics for
a liquid and vapor in equilibrium, its accuracy when used in
hysteretic isotherms is largely dependent on whether or not the
true equilibrium branch is selected for the calculations [2,46,55].
ð1Þ
where PNW is the pressure of the non-wetting phase, which is
commonly the bulk vapor phase; P W is the pressure of the wetting
phase, which is commonly the liquid-like condensed phase in the
pore; c is the surface tension between these two fluid phases; rp
is the radius of the pore; and h is the contact angle of the meniscus
with the pore wall.
Fig. 8. The difference between capillary condensation pressure for nitrogen in a slit
pore predicted by the Kelvin equation (the dashed line) and GCMC simulation (the
solid line). The experimental data for a similar system is shown by the filled circles.
The figure shows significant deviations between predictions by the Kelvin equation
and experimental data for pore diameters below 7 nm. Taken from Walton and
Quirke [70], in the format adapted by Aukett et al. [95]. Copyright 1992 Elsevier.
E. Barsotti et al. / Fuel 184 (2016) 344–361
Although the Kelvin equation and its variants have been shown
to be valid in pores with radii as small as 4 nm for some confined
systems [43,93,94], the validity of its assumptions decreases with
pore size [91]. A study by Aukett et al. showed that the Kelvin
equation deviates from simulation results and experimental data
in the prediction of capillary condensation for pores smaller than
7 nm (Fig. 8) [95]. Nevertheless, using the gas composition from
a Marcellus well and the pore size distribution of kerogen pores
in a hypothetical shale rock, Chen et al. incorporated the multicomponent version of Kelvin equation [96] into estimations of gas in
place [20]. The resulting theoretical adsorption isotherms
exhibited condensation steps, which, when incorporated into Chen
et al.’s estimations, lead to increased gas in place estimates for the
hypothetical rock of up to six times [20].
Some efforts have been made to extend the accuracy of the
Kelvin equation to nanoscale systems, among which are the inclusion of the effect of the meniscus on the surface tension [97] and
direct adjustments to the pore radius to account for the thickness
of the adsorbed phase [92,98].
Regardless, when the Kelvin equation is applied in the
characterization of porous media, it has been shown to underestimate pore size by approximately 25% in pores with radii below
10 nm [99]. Because many studies involving capillary condensation
include porous materials with radii below 10 nm [8,13,15,72,74]
and below 4 nm [6–8,10,13,15,38–40,48,72,73,78], more accurate
approaches are needed to better describe the fluid phase behavior
in nanopores.
3.4. Advanced models
Efforts to account for large departures from the ideal
assumptions of the Kelvin equation include the utilization of
various versions of density functional theory (DFT), e.g., non-local
density functional theory (NLDFT) and quench solid density
functional theory (QSDFT). DFT relies on the minimization of the
grand potential energy, which accounts for all the thermodynamic
energies of the system at the same chemical potentials throughout
all phases, to achieve the most stable energy state for the fluidpore system [1,2,12,66]. DFT deals with energy functionals [100],
which also account for pore geometry [2] and fluid-pore wall interactions [12], and results in the fluid density profile within the pores
at the most stable energy state (Fig. 1a) [1,2,12,66]. In studies of
capillary condensation, this density can correspond either to the
condensed or the vapor phase in the pore [12]. Using DFT, metastable states can be modeled for the investigation of hysteresis,
although many calculations for identification of the sorption branch
(adsorption or desorption) that corresponds to phase equilibrium
are contradictory to the aforementioned experimental findings of
Morishige et al. [2,12,66]. Indeed, comparisons of DFT isotherms
with experimental isotherms have shown DFT to be incapable of
precise quantitative predictions of hysteresis in even the simplest
cylindrical pores [12,66]. The inaccuracies of DFT have been
attributed to oversimplifications in the functionals that include
the disregard of pore wall surface roughness [2], models of infinite
pores that have little relation to their finite experimental counterparts, and improper treatments of pore-fluid potentials [2,12,100].
Despite its shortcomings, however, NLDFT, in particular, has gained
popularity for its ability to estimate pore size distribution more
accurately than approaches involving the Kelvin equation [2,12].
With the current lack of experimental data and the difficulty in
obtaining them, molecular simulations have been carried out for
adsorbents of varying wettability [52,53] and pore geometry [4]
for theory validation purposes. Similar to DFT, molecular simulations offer microscopic treatments of capillary condensation that
take into account fluid-fluid and fluid-pore wall interactions [2],
most commonly grand canonical Monte Carlo simulation (GCMC)
351
[1,2,4,44,66,68,69,101,102] and Molecular Dynamics (MD)
[1,66,68,69]. Because molecular simulations can account for the
individual interactions of atoms and molecules [69], they allow
for easier description of complicated molecular structures [66]
and provide for more invasive investigation into the underlying
mechanisms of capillary condensation compared to DFT
[2,44,53,66]. Likewise, molecular simulations allow for easy
adjustment of properties that are difficult, if not impossible, to
control in experiments [1,66,69]. However, oversimplifications of
input functions, inadequate algorithms, and the extensive amount
of computational time required to perform realistic simulations
[58], render current molecular simulations as inaccurate as DFT
[2,66]. The uncertainties as to the influence of the various chemical
and physical parameters persist and, along with the present
inability to exactly model both real and synthesized nanoporous
materials, generate inaccuracies that prevent further progress into
the development and evaluation of theories [52]. Even so, simulations are useful for qualitative studies of capillary condensation
and are particularly valuable for their insight into properties that
are experimentally inaccessible. A sample density profile of
confined fluid available through GCMC simulations is shown in
Fig. 1a, which is in excellent agreement with that available through
DFT [103].
Long et al. used GCMC simulations to evaluate the effect of pore
geometry on the pressure of argon [4]. Based on their simulations,
they showed that, for a given temperature, the capillary
condensation of argon occurred first (at the lowest pressure) for
spherical pores, followed by cylindrical pores and then slit pores
[4]. They attributed this to the direct proportionality of the pore
wall curvature to pore-fluid interactions as manifest in a pressure
tensor for the argon that, over the given pressure range, exhibited a
rapidly increasing tangential pressure [4].
Singh et al. used grand-canonical transition-matrix Monte Carlo
(GC-TMMC) simulations to study the critical properties, surface
tensions, phase coexistence, density profiles, and orientation
profiles of methane, ethane, propane, butane, and octane in graphite and mica slit pores with different widths [53]. Though their
findings are in general agreement with experimental data for the
given adsorbate-adsorbent systems, their study suffers from a lack
of comprehensiveness; for their simulations included only a limited selection of fluids in just two pore types [53]. In another work,
Yun et al. were able to use their own experimental isotherms to
validate GCMC simulations and ideal adsorbed solution theory
(IAST) for the prediction of the adsorption of methane, ethane,
and a methane-ethane mixture in MCM-41 [7]. Likewise, He and
Seaton used their own experimental isotherms to validate GCMC
simulations for the prediction of the adsorption of carbon dioxide,
ethane, and a carbon dioxide-ethane mixture in MCM-41 [104].
Although neither Yun et al. nor He and Seaton specifically studied
capillary condensation in their systems, their data showed
condensation at some experimental conditions.
While the above rigorous computational approaches do not
provide accurate descriptions of macroscopic behavior, simpler
methods with equations of state (EOS) have been used to model
the confined phase equilibria. In such modeling, the equilibrium
of the condensed phase in pores (L) and the vapor phase in the bulk
(V) can be generalized in terms of chemical potential, or more
commonly, in terms of fugacity, where the equifugacity equations
for a mixture with N components are expressed as:
^f L ðx; T; PL Þ ¼ ^f V ðy; T; PV Þ i ¼ 1; . . . ; N
i
i
ð3Þ
Note that the pressures of the phases are different. The pressure
difference can be expressed in terms of capillary pressure as in
Eq. (1) where L is the condensed phase, which is wetting; and V is
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E. Barsotti et al. / Fuel 184 (2016) 344–361
Fig. 9. Qualitative shift of a phase envelope when bulk-phase parameters are
applied to a cubic EOS [106]: the critical point (C.P.) does not change; it remains the
same as in the bulk.
the bulk vapor phase, which is non-wetting; x and y are the fluid
composition in phases L and V, respectively.
In addition to Eq. (3), the system has to satisfy the material
balance. Solving these equations is analogous to the vapor-liquid
phase equilibrium calculation in the bulk, but at different pressures across the phase boundary. This approach is free from
assumptions imposed on the Kelvin equation while still dependent
on the validity of the Young-Laplace equation for extremely small
pores.
Though a simple cubic EOS may also be used here, some
difficulties arise in using this class of EOS, as it requires critical
properties for parameterization. In nanopores, where the critical
points of pure substances are shifted from their bulk values, a cubic
EOS must be applied either by using the shifted critical properties
as the new EOS parameters [18] or by ignoring the confinementinduced shift altogether, thus, using the bulk-phase parameters
[57,105] while the Laplace equation, Eq. (1), is added to account
for the effects of confinement [24,106].
For multicomponent fluids in confinement, it is generally
agreed upon that the phase envelope in the P-T phase diagram is
also shifted from that of the bulk, even though the shift of the critical point has not yet been experimentally verified. An analysis of
the envelope shift has been recently made [106] using a theoretical
approach inspired by the multicomponent version of the Kelvin
equation [96,107]. In the analysis, which applied a cubic EOS with
the Laplace equation, the critical point of a multicomponent fluid
was found to be invariant, while the cricondentherm (the
maximum temperature of the envelope) was found to shift to a
higher temperature, as shown in Fig. 9. The bubble points were also
found to be suppressed for temperatures up to the critical point, as
were the dew points up to the bulk cricondentherm. However, the
portion of the envelope between the critical-point temperature
and the bulk cricondentherm was found to shift to higher pressures. These findings, except for the shift of the cricondentherm,
are similar to those of some other studies including that of
Nojabaei et al. [24] and Jin and Firoozabadi [108], where the
cricondentherm was found to be invariant.
On the other hand, when using shifted critical properties as the
new EOS parameters, the resulting phase envelopes dramatically
change, as shown in Fig. 10 [18]. The shifted critical properties
can be numerically derived from theory, as done by
Zarragoicoechea and Kuz with regard to the ratio of molecular
diameter (r) to pore radius (rp) [109]:
Fig. 10. Qualitative shift of a phase envelope when shifted-phase parameters are
applied to a cubic EOS [18]: dew points and bubble points can be higher than those
in the bulk.
DuC
uC
2
r
r
0:2415
¼ 0:9409
rp
rp
ð4Þ
where u can be temperature or pressure, and DuC is the shift of the
critical property in the pores from its value in the bulk.
Zarragoicoechea and Kuz studied the critical temperature and
pressure shift of argon, xenon, carbon dioxide, oxygen, nitrogen,
and ethylene in MCM-41 [109]. In view of their ability to match
experimental data relatively well [109], it would be beneficial to
see further validations of their model with the hydrocarbon
constituents of shale and/or tight reservoirs, as presented in Table 1.
Using another approach, Alharthy et al. correlated shifted
critical pressures and temperatures to results from GCMC
simulations by Singh et al. for n-alkanes in graphite slit pores,
where d is the pore diameter [18,53]:
DP C
¼ 0:4097d þ 1:2142
PC
DT C
¼ 0:093764 0:929d
ln
TC
ð5aÞ
ð5bÞ
The main drawback of the approach with shifted critical
properties, however, is that, as in Eq. (5a), there is no way to reduce
the systems to the bulk phase if the porous medium is removed,
where the new parameters in cubic EOS refer to different chemical
substances in the bulk. Furthermore, as seen in Fig. 10, the bubble
points can be higher or lower than those in the bulk phase, while
the dew points are even higher than their bulk-phase counterparts,
which both contradict the notion introduced by experimental data
[89].
In view of the present lack of experimental data necessary to
validate the above approaches, some studies [26,110] have even
combined the approaches that utilize both the shifted critical
properties as the EOS parameters and the Laplace equation to
account for the effects due to the surface tension.
In an effort to better account for the effects of nanoconfinement, additional terms can be supplied to a cubic EOS.
For example, Travalloni’s term [57], written here as f, can be added
to the Peng-Robinson EOS [111] in the following form:
P¼
RT
v bp
a
ap
v
2
þ 2bp v bp
2
f ðr p ; dp ; ep Þ
ð6Þ
where dp = {dp,i} and ep = {ep,i} are the parameters that represent the
potential width and potential energy between the pore wall (p) and
E. Barsotti et al. / Fuel 184 (2016) 344–361
the fluid molecules (i), respectively, while the pore-modified energy
and size parameters of the EOS are:
XX
bi þ bj
xi xj aij 1 hðrP Þ
i
j
X
bp ¼
xi bi C i ðbi ; r p Þ
ap ¼
ð7Þ
ð8Þ
i
where h and C are functions of the pore radius rp and must reduce to
h ? 1 and C ? 1 in the bulk, i.e., when rp ? 1, so that the modified
parameters also reduce to the bulk parameters.
The original Travalloni’s work [57] also presents the term f
added to van der Waals EOS, which is used to construct isotherms
for methane, ethane, toluene, 1-propanol, nitrogen, and hydrogen
adsorbed on MCM-41, MSC-5A molecular sieve, DAY-13 zeolite,
and JX-101 activated carbon. Though their work closely matched
experimental data, the majority of their experimentally verified
work did not include capillary condensation [57]. Nevertheless,
its good prediction of the condensation of ethane in MCM-41
makes it a promising candidate for future studies [57].
Likewise, contributions from surface forces can be added to the
Laplace equation within the Peng-Robinson EOS environment [65]:
Parp ¼ Pbrp 2c A123
r p 6pz30
ð9Þ
where A123 is the Hamaker constant between the bulk phase b and
the pore material in the presence of condensed phase a, and z0 is
the distance to the pore wall. The Hamaker constant can be derived
as [112]:
A123 ¼
3
ðn ðe1 ; e2 ; e3 ÞkT þ n2 ðn1 ; n2 ; n3 Þhma Þ
4 1
ð10Þ
where ei is the dielectric constant, ni is the refractive index of material i, k is the Boltzmann constant, h is the Planck constant, and ma is
the adsorption frequency. However, because the additional contribution of the surface forces turns out to be small in comparison
to that of the surface tension in the Laplace equation, it can usually
be safely neglected [65].
Recently, a robust EOS based on statistical mechanics, i.e., the
perturbed-chain statistical associating fluid theory (PC-SAFT EOS)
[113], has been used to calculate fugacity coefficients coupled with
the modified Laplace equation [89]. The modified Laplace equation
is written as:
Parp ¼ Pbrp 2c
rp ð1 kÞ
353
discrepancy between the calculated and experimental dew-point
pressures is currently of unknown origin that needs further
investigations.
The main drawback impeding this approach is the scarcity of
experimental phase-equilibrium data in the literature for confined
systems of both pure components and their mixtures from which
to derive the parameter k in Eq. (11). Therefore, the promising
results of this approach warrant experimental measurements on
the phase behavior of confined fluids for its further development.
For unconventional oil and gas recovery applications, those
measurements must be eventually made both with hydrocarbons
and other compounds generally present in the entrapped oil or
gas and with adsorbents representative of reservoir rock.
4. Capillary condensation: experimental perspective
4.1. Nanoporous media: materials and characterization
In order to improve the fundamental understanding of the
physics involved in capillary condensation, reliable experimental
data in nanoporous media with disconnected pores, uniform pore
geometry, and known homogeneous chemistry is required. The
interpretation of experimental data in such porous media is mostly
straightforward. The most commonly used adsorbents are the
ordered nanoporous silicas, MCM-41 [6–8,10–13,15,38,40,50,73,
77,78,115] and SBA-15 [8,9,12,15,74,78,115]. MCM-41 and
SBA-15 both contain hexagonally ordered cylindrical pores constructed of silicon dioxide, which can be easily synthesized in a
variety of pore sizes [116,117]. A comprehensive comparison of
the characteristics of MCM-41 to those of SBA-15 can be found in
the work of Galarneau et al. [117].
The simple geometry of MCM-41 and SBA-15 and their oil-wet
counterparts, i.e., ordered mesoporous carbons (OMC’s) [72], are
ð11Þ
where k is a new parameter that depends on the fluid and the pore
material and is readily derived from capillary condensation experimental data. With the use of experimental data for the derivation of
the parameter k, this particular approach differs from its predecessors in that the actual effects due to the fluid-wall interactions are
well represented. Consequently, the EOS has strong predictability in
modeling confined fluid mixtures when the bulk behavior of the
system is known.
This approach has been applied to study the capillary condensation of non-associating fluids in MCM-41 (nitrogen, argon, oxygen,
carbon dioxide, n-pentane, n-hexane), SBA-15 (nitrogen), and
Vycor (nitrogen, nitrogen-argon mixture, krypton-argon mixture)
[89]; and associating fluids in MCM-41 (water, ethanol), stainless
steel plates (ethanol, acetone, acetone-ethanol mixture, ethanolwater mixture), and porous carbon plates (ethanol, acetone,
acetone-ethanol mixture, ethanol–water mixture) [114]. All results
proved consistent with the available data from experiments and
simulations except in the case of dew-point pressure predictions
for an ethanol-water mixture in stainless steel, i.e., a strongly
associating fluid in a highly polar porous medium [114]. The
Fig. 11. Differences in pore diameter derived from different characterization
methods for two different MCM-41 samples using nitrogen isotherms at 77 K.
Sample 2 was synthesized to have a smaller pore diameter than Sample 1. Adapted
from Kruk et al. [11] (BJH(a) and BJH(d): BJH method applied to the adsorption
branch and desorption branch of a hysteretic isotherm, respectively; NLDFT:
non-local density functional theory; BET: pore sizes derived from the BET specific
surface area and the BET pore volume; and Geometric: pore size calculated by
relating the volume of the pore space to the volume of the solid adsorbent for a
highly uniform array of cylindrical pores [i.e., MCM-41 and SBA-15]) [11].
354
E. Barsotti et al. / Fuel 184 (2016) 344–361
over-simplified compared to naturally-occurring adsorbents and
porous media encountered in industry. More realistic models for
these applications are adsorbents with interconnected pores,
including controlled pore glass (CPG) [46,49], Vycor glass [39,46],
SBA-16 [15], LPC [15], mesocellular foam [15], MCM-48 [16], silica
glass [46], and shale core plugs [21]. Although it is challenging to
interpret data from these more complex adsorbents, they are more
relevant to practical applications of capillary condensation
phenomena. This is particularly true to the petroleum industry
where capillary condensation happens in the random pore
networks, geometries, and chemistries of shale and tight reservoir
rocks. Nevertheless, systematic studies need to start with very
simple cases before dealing with complex ones.
Regardless of the adsorbent, appropriate characterization of the
material is needed, including information about pore wall
wettability [51], pore size, pore volume, pore size distribution, pore
connectivity, and pore surface area [9–13,41,48], in order to help systematize the interpretation of capillary condensation data
[2,9–12,41,51,55,76,88,92,117–121]. Commonly used characterization methods include the Clausius-Clapeyron equation [122,123] for
analysis of pore surface homogeneity [6,7,15,16], the
Barrett-Joyner-Halenda (BJH) method [55,66,92] for determination
of pore size distribution [9,11,16,17,48,72,77], and the
Brunauer-Emmett-Teller (BET) method [2,51,56,76,118,121,124] for
quantitative determination of the specific surface area of the adsorbent and qualitative determination of the fluid-solid interaction
energy [7–9,11,13,16,38,48,72–74,77]. A critical examination of these
methods can be found elsewhere in the literature [11,56,88,92,
118,120]. Scrutiny of them has led to complementary and alternative
characterization methods including X-ray diffraction (XRD) [6,7,9–11,
13,15,16,38,40,41,48,72,77,78,125], transmission electron microscopy (TEM) [48,77,115], scanning electron microscopy (SEM)
[21,45,48,77], geometrical considerations [11], the alpha-plot method
[40,74], and density functional theory [2]. A comparison among pore
sizes determined using different characterization methods can be
found in Fig. 11.
In spite of the obvious differences in the results obtained from
various characterization methods, as shown in Fig. 11, it is difficult
to order the characterization methods hierarchically with respect
to accuracy. Of primary importance are limitations in accuracy
due to the assumptions used in the different mathematical
interpretations of the experimental data. Other factors include
analytical and experimental limitations such as small sample mass,
small sample cell volume, condensation among adsorbent
particles, the appropriate identification of the equilibrium branch
(in hysteretic isotherms), and a proper curve fit between
experimental data points [120].
4.2. Measurement techniques
Measurement techniques used to study capillary condensation
in nanoporous media mostly involve adsorption experiments.
Although various apparatuses have been used, as described later,
the most commonly employed techniques are volumetry [7,9–11,
13,38,46,48,49,72–74,78] and gravimetry [6,8,15–17,21,40,49,72,
77,115] because of their applicability to the broadest range of
conditions pertaining to nanopore size, temperature, and pressure
[2]. Volumetry uses an equation of state to relate the known pressures, temperatures, and volumes of two holding vessels to the
amount of gas adsorbed and/or condensed in the pores of the
adsorbent; while gravimetry utilizes a balance to directly weigh
changes in the mass of the adsorbent, which result from adsorption
[51].
Volumetric apparatuses are most commonly used for the
characterization of porous materials through nitrogen adsorption
at 77 K [2,6,9–11,16,38,48,72,74]. The detailed descriptions of
both commercial [7,10,11,16,46,48,72,74] and homemade
[7,13,38,46,48,49,73,78] apparatuses are available in the literature.
Gravimetric apparatuses also come in a variety of homemade
[8,15,16,126] and commercial [6,9,17,40,72,77,115] designs. One
of the most popular gravimetric apparatuses used in the literature
is the magnetic suspension balance [6,17,51,72,127]. In extending
measurements to multicomponent adsorbates for both volumetry
and gravimetry, a gas chromatograph is required to derive the
concentrations of the individual components that are condensed
in the pore space, as will be later described [7,51].
The popularity of gravimetry and volumetry has led to comparison of the two [127]. While volumetry is known for its economy
and simplicity [127], and gravimetry is known for its comprehensiveness; a comparison of the accuracy of the two is difficult, since
such a comparison is partially dependent upon the applicability of
each specific apparatus. Application limitations include temperature, pressure, chemical resistance, and flow potential. For example,
many of the microbalances (excluding magnetic suspension balances [5]) used in gravimetric measurements cannot withstand
temperatures or pressures far removed from standard conditions
[2,76], while the accuracy of volumetric measurements are highly
dependent on the equations of state used [127]. Furthermore,
volumetry, which is often used for the characterization of adsorbents [2,76], can easily withstand extreme temperatures such as
the boiling point of nitrogen (77 K) [2,76], while gravimetry gives
direct, real-time recordings of the amount adsorbed or desorbed,
providing insight into the kinetics of capillary condensation.
By pairing a volumetric and a gravimetric apparatus with
similar capabilities, Belambkhout et al. carried out a comparison
of the two for high-pressure adsorption measurements [127]. In
their study, Belambkhout et al. used a homemade volumetric
apparatus and a RubothermÒ magnetic suspension balance for high
pressure adsorption measurements [127]. Their results showed
volumetric data to differ from gravimetric data by 3%, with the
gravimetric method considered to be more accurate, especially at
high pressures where extreme deviations between the volumetric
and gravimetric data became predominate [127]. In view of this,
Belambkhout et al. concluded that, in terms of accuracy, the two
measurement techniques can be interchangeably used at low pressures (less than 360 psi) as long as care is taken to accurately
measure the reference volumes of volumetric apparatuses, while
appropriate equations of state are used when necessary, and gas
leaks in the apparatuses are prevented [127].
Like volumetry and gravimetry, some alternative methods
produce adsorption isotherms, such as NMR [46] and optical
interferometry [45], which measure condensation by detecting
the intensity of a nuclear spin echo or of the spectra of reflected
light, respectively. Others are used in systems where a surface tension is defined to infer the growth of condensate from the change
in height of a meniscus (multiple beam interferometry)
[90,93,94,128] or the change in force between a probe and the
adsorbed or capillary condensed fluid (AFM) [128,129]. While
optical interferometry and multiple beam interferometry are both
dependent on changes in the wavelength of light for their
measurements, pulse-echo ultrasonic wave transit measurements
[75], as the name suggests, uses the transit time of ultrasonic
waves to determine pore filling and the longitudinal modulus
and effective shear modulus of the adsorbent [75]. For instance,
in the work of Schappert et al., pulse-echo ultrasonic wave transit
measurements were coupled with capacitative distance sensor
measurements to directly evaluate changes in adsorbent sample
size (i.e., pore diameter) due to strain generated during adsorption
or condensation within the pore space [75]. Some measurement
methods also make use of X-ray diffraction peaks to identify
capillary condensation (SAXD) [50,130] or use X-ray scattering to
determine how the lattice parameter of an adsorbent changes as
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E. Barsotti et al. / Fuel 184 (2016) 344–361
Table 2
Alternative measurement techniques used in the literature for studies of capillary condensation.
Adsorbate
Adsorbent
Method
Reference
Deuterium
Deionized Water
Water
Water
Deuterated Water
Deuterated Methane
Argon
MCM-41
Mica-Cytop Dielectric Stack
SBA-15
Vycor Glass
MCM-41
SBA-15
Vycor Glass
Neutron Diffraction
Electro-wetting on Dielectric Surface Force Apparatus
SAXS
Spectrophotometry
Neutron Spin Echo Measurements
SANS
Positron Annihilation Spectroscopy
Carbon Dioxide
Propane
Isopropanol
Pentane
Benzene
Packed Silica Spheres
Packed Silica Spheres
Nanoporous Alumina
MCM-41
Silicon Wafers
Krypton
Krypton
Cyclohexane
Cyclohexane
n-Hexane
MCM-41
Vycor Glass
Mica
Vycor 7930
Controlled Pore glass, Woodford Shale Core
Plugs, Sandstone Core Plugs
Nanoporous Alumina
Controlled Pore Glass
Controlled Pore Glass
MCM-41
SBA-15
Controlled Pore Glass
Vycor Glass
Vycor Glass
Visual Observation
Visual Observation
Optical Interferometry
SAXD
Fourier-Transform IR Microscope with Focal Plane Array
Detector and a Single Element Detector
Neutron Diffraction
Positron Annihilation Spectroscopy
Surface Force Apparatus
NMR
Weight Gain, NMR
Floquet et al. [134]
Gupta et al. [90]
Erko et al. [131]
Ogwa and Nakamura [135]
Yoshida et al. [136]
Chiang et al. [137]
Alam et al. [39], Jones and
Fretwell [133]
Ally et al. [138]
Ally et al. [138]
Casanova et al. [45]
Günther et al. [50]
Lauerer et al. [139]
Toluene
Octane
Decane
Dodecafluoropentane
Dodecafluoropentane
Octane + Decane
Nitrogen + Argon
Krypton + Argon
Optical Interferometry
DSC
DSC
SAXD
SAXD
DSC
Positron Annihilation Spectroscopy
Positron Annihilation Spectroscopy
a result of capillary condensation (SAXS) [8,131]. Alternatively,
unlike any of the aforementioned methods which all involve the
measurements of various properties at constant temperature,
differential scanning calorimetry (DSC) and positron annihilation
spectroscopy [39,132,133] are employed at constant pressure. In
the latter case, this results in the creation of adsorption isobars.
Similar to isotherms, isobars may exhibit a step or a hysteresis loop
indicative of capillary condensation. A compilation of data
available from alternative experimental methods is presented in
Table 2.
More recently, a preliminary work has emerged on the direct
imaging of the fluid phases during capillary condensation [139].
Using infrared microscopy, Lauerer et al. were able to capture
images of benzene in two different silicon 5–10 nm pore slit
geometries during adsorption and desorption at different
pressures, including the condensation step [139]. Refinement of
this novel approach may allow for direct, visual observation of
the distribution of fluid molecules throughout the pore, including
observations of the mechanisms by which adsorption and
desorption occur [139].
In the case of gas mixtures, the composition of equilibrium
phases at the point of capillary condensation is another required
parameter for characterization of the system. Two primary
methodologies exist for extending measurements to multicomponent systems. The first is the open flow method employed by
Yun et al. [7], in which bulk fluid of a known composition is flowed
through the adsorbent at constant temperature, until steady state
flow is achieved. Therefore, the bulk vapor in a control volume
surrounding the adsorbent is at constant temperature, pressure,
and composition, necessitating constant chemical potential [7].
At each pressure step, the total weight of the adsorbed phase is
plotted against the bulk pressure to get the adsorption isotherm
of the mixture. Likewise, using a chromatograph, the number of
moles for each component of the mixture may be individually
plotted versus the bulk pressure to determine the uptake of each
compound over the course of the isotherm.
Floquet et al. [134]
Jones and Fretwell [133]
Maeda and Israelachvili [128]
Naumov [46]
Chen et al. [21]
Casanova et al. [45]
Luo et al. [140]
Luo et al. [140]
Günther et al. [50]
Zickler et al. [130]
Luo et al. [140]
Alam et al. [39]
Jones and Fretwell [132]
The second is a static method, in which the overall composition
of fluid is kept constant throughout the entire experiment. In this
method, pressure increases result in depletion of the more
selectively adsorbed component from the bulk fluid until the
dew-point curve of the confined fluid is hit. Therefore, the situation
is different from that experienced for the phase behavior of a bulk
fluid, where the composition of the bulk vapor phase is the same as
the overall composition of the unconfined fluid at the dew point.
Because the dew-point pressure of the confined fluid and the
corresponding composition of the bulk vapor are unknown beforehand, it is not straightforward to compare the result from this type
of experiment with that obtained from observations of the phase
behavior of a fluid in the bulk with the same overall composition.
To decide which experiment is more relevant, the circumstances encountered in gas reservoirs and in their recovery must
be considered. The overall composition in the reservoir might not
be known, but that of the bulk vapor phase (i.e., produced hydrocarbon gases from production wells) can be analyzed and, due to
the enormity of its presence, may be assumed constant. Therefore,
the open-flow setup with constant vapor composition would
provide data with more practical use to the petroleum industry.
4.3. Experimental data on hydrocarbon systems
We have collected published experimental adsorption isotherms, from which the data on capillary condensation may be
derived, for components typically found in petroleum gases in
Table 3. It should be noted that this table is not an exhaustive list
of research on this topic due to limited space in this paper.
Likewise, a compilation of fluids not found in petroleum gases is
tabulated in the Supplementary Material. This latter data set could
be useful for general validation purposes.
As seen from Table 3, most of the data was measured at a single
temperature and/or for a single pore size, while model parameters
that represent the interaction between fluid molecules and the pore
walls may vary with temperature and pore size. This introduces a
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E. Barsotti et al. / Fuel 184 (2016) 344–361
Table 3
List of available experimental adsorption isotherms, from which capillary condensation data may be derived, in the literature for petroleum gas components. (V represents
volumetry, and G represents gravimetry.)
Adsorbate
Adsorbent
Pore size (nm)
Temperature (K)
PV/Psat
Method
Reference
Methane
(deuterated)
Ethane
Ethylene
n-Butane
MCM-41
2.5
77.5
0–1
V
Llewellyn et al. [141]
MCM-41
MCM-41
MCM-41
2.7–3.9
1.8
2.1–3.6
264.6–273.55
144.1–148.1
283
0–1
0–1
0–1.2
V
V
V
He and Seaton [104] and Yun et al. [7]
Morishige et al. [38]
Ioneva et al. [48]
n-Pentane
MCM-41d
SBA-15
2.0–4.57
7.31–8.14
258–298
258–298
0–1
0–1
V, G
G
MCM-48
SBA-16
HSB
CMK-3
LPC
MCF
Alumina
membrane
3.78
8.15
3.54
4.90
20.62
13.47–20.47
N/Ac
298
298
298
298
298
298
308
0–1
0–1
0–1
0–1
0–1
0–1
0–1
G
G
G
G
G
G
G
Rathouský et al. [142] and Russo et al. [15,143]
Findenegg et al. [144], Gor et al. [8] and Russo et al.
[15,143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Tzevelekos et al. [145]
Cyclopentane
MCM-41
3.7–4.57
253–293
0–1
V
Rathouský et al. [142]
Neopentane
MCM-41d
1.9–9.9
258–333
0–1
V, G
SBA-15
MCM-48
SBA-16
HSB
CMK-3
LPC
MCF
7.31–7.87
3.78
8.15
3.54
4.90
20.62
13.47–20.47
258–273
273
273
273
298
273
273
0–1
0–1
0–0.95
0–0.9
0–0.9
0–1
0–1
G
G
G
G
G
G
G
Carrott et al. [146], Long et al. [147], Qiao et al. [40],
Russo et al. [15,143] and Tanchoux et al. [13]
Russo et al. [15,143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
Russo et al. [143]
n-Hexane
MCM-41
MCM-48
1.9–4.2
3.2
293–323
303.15
0–1
0–0.8
G
G
Carrott et al. [146], Jänchen et al. [148] and Qiao et al. [40]
Shim et al. [16]
Benzene
MCM-41
1.9–4.4
273–303
0–1
V, G
MCM-48
3.2
303.15
0–0.75
G
Carrott et al. [146], Choma et al. [149], Jänchen, et al.
[148] and Nguyen et al. [150]
Shim et al. [16]
Cyclohexane
MCM-41
Vycor 7930
2.6–3.9
6
298
297
0–0.8
0–0.9
G
V, NMR
Long et al. [147]
Naumov, Sergej [46]
n-Heptane
MCM-41
SBA-15
Porous Silicon
Shale
2.7
6.4–6.6
6.5
3.8
298
293–298
291
298
0–0.97
0–0.95
0–0.95
0–0.95
G
V, G
V
G
Zandavi and Ward [71,115]
Kierys et al. [151] and Zandavi and Ward [115]
Grosman et al. [152]
Zandavi and Ward [153]
Methylcyclohexane
MCM-41d
SBA-15
MCM-48
SBA-16
HSB
CMK-3
LPC
MCF
2.39–4.57
7.31–7.59
3.78
8.15
3.54
4.90
20.62
13.47–30.47
298
298
298
268–298
298
298
268–298
278–298
0–1
0–0.95
0–1
0–0.95
0–0.95
0–0.97
0–1
0–1
G
G
G
G
G
G
G
G
Russo
Russo
Russo
Russo
Russo
Russo
Russo
Russo
n-Octane
MCM-41
CPGh
Shale
2.6
4.3–38.1
3.8
298
N/A
298
0–0.95
N/A
0–1
G
DSC
G
Zandavi and Ward [71]
Luo et al. [140]
Zandavi and Ward [153]
n-Butylbenzeneb
Anodized Aluminaf
Porous Silicon
6.9–12.2
1.7–9.7
273
273
0–0.8
0–0.8
V
V
Nonaka [154]
Nonaka [154]
et
et
et
et
et
et
et
et
al.
al.
al.
al.
al.
al.
al.
al.
[143]
[143]
[143]
[15,143]
[143]
[143]
[15,143]
[15,143]
n-Nonane
MCM-41
2.88
313
0–0.6
G
Berenguer-Murcia et al. [155]
Decaneh
CPG
4.3–38.1
N/A
N/A
DSC
Luo et al. [140]
Water
Mesoporous Silica
MCM-41e
3.8–10.5
2.1–4.0
298
293–323
0–1
0–1
G
G
SBA-15
6.6–8.9
278–298
0–1
G, SAXD
OMC
PSM
RD-silica
6.2–9.2
2.0
2.1
264.8–298
323
323
0–1
0–0.9
0–0.9
V, G
G
G
Hwang et al. [156]
Branton et al. [157,158], Jänchen et al. [148],
Kittaka et al. [159],
Russo et al. [160], Saliba et al. ,[161] and
Zandavi and Ward [115]
Erko et al. [131], Hwang et al. ,[156] and
Zandavi and Ward [115]
Morishige et al. [72] and Horkawa et al. [79]
Saliba et al. [161]
Saliba et al. [161]
Nitrogena
MCM-41
SBA-15
OMC
2.4–4.4
6.0–11
6.2–9.2
63.3–119.2
69–121.8
77
0–1
0–1
0–1
V
V
V
Morishige et al. [38] and Morishige and Ito [78]
Morishige and Ito [78]
Morishige et al. [72]
Oxygen
MCM-41
1.8–4.4
77–139.4
0–1
V, G
Branton et al. [162], Inoue et al. [163], Morishige et al. [38],
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E. Barsotti et al. / Fuel 184 (2016) 344–361
Table 3 (continued)
Adsorbate
Adsorbent
Pore size (nm)
Temperature (K)
PV/Psat
Method
Reference
Morishige and Nakamura [73] and Sonwane et al. [164]
Inoue et al. [163]
Inoue et al. [163]
Inoue et al. [163]
FSM1
FSM2
GB1
2.5
3.4
3.0
77
77
77
0–1
0–1
0–1
G
G
G
Carbon Dioxide
MCM-41
1.8–4.4
185.5–273
0–1
V, G
Carbon Monoxide
MCM-41
2.5
77
0–1
V
Llewellyn et al. [141]
Methane + Ethane
MCM-41
3.9
264.75
0–435g
V
Yun et al. [7]
CO2 + Ethane
MCM-41
2.70
264.6
7.25–
261g
V
He and Seaton [104]
Octane + Decaneh
CPG
4.3–38.1
N/A
N/A
DSC
Luo et al. [140]
Berenguer-Murcia et al. [155], He and Seaton [104],
Sonwane et al. [164], Morishige and Nakamura [73]
and Morishige et al. [38]
a
The capillary condensation of nitrogen has been widely observed for the purpose of materials characterization. As such, only a few sample references are given here
[38,73,78].
b
Although the adsorption isotherms clearly indicate capillary condensation in the form of hysteresis loops, some isotherms are incomplete [154].
c
The adsorbent was a pellet of compacted alumina powder. The powder had an average particle diameter of 20 nm [145].
d
Some MCM-41 samples included the surface group trimethylsilane [165], were grafted with aluminum [160], or had been modified with chloromethyltriethoxysilane
[143].
e
Some MCM-41 samples were grafted with aluminum [160].
f
Experiments were carried out in anodized aluminum pores with and without silicate coatings [154].
g
Pressures are given in psi for mixtures.
h
DSC measurements were carried out at atmospheric pressure for temperatures from 320 K to 540 K. The CPG adsorbent was treated to include the surface group
hexamethyldisilazane [140].
serious barrier to developing robust models that have sound
predictability. Most of the experimental data is also limited to ideal
adsorbents and single component fluids, which are far removed
from the conditions encountered in practical applications. Despite
these limitations, the current body of experimental work on
hydrocarbon systems presents many breakthroughs in the effort
to understand confined phase phenomena. Such breakthroughs
include progress made in evaluating fluid-fluid and fluid-pore
interactions in confined spaces.
For example, to show how fluid properties affect capillary condensation, Ioneva et al. produced separate capillary condensation
isotherms for ethane, propane, and butane in MCM-41 samples
[48]. They found the onset of capillary condensation to occur at a
relative vapor pressure of 0.8 for ethane, 0.62 for propane, and
0.38 for n-butane in 3.6 nm diameter pores at 283.15 K [48]. This
provides evidence that, in single-component isothermal systems,
capillary condensation generally occurs at lower relative pressures
for the fluids with larger molecules. The same hierarchy of
capillary condensation pressure with regard to bulk vapor pressures has been observed by Russo et al. in their study of toluene,
methylcyclohexane, n-pentane, and neopentane [15]; Casanova
et al. in their study of isopropanol and toluene [45]; and Shim
et al. in their study of benzene, toluene, n-hexane, cyclohexane,
acetone, methanol, methyl ethyl ketone, and trichloroethane [16].
These findings are consistent with the Kelvin equation, i.e. Eq.
(2), where the molar density of the liquid, which depends on the
molecular size, is inversely related to the capillary condensation
pressure.
With further regard to fluid-fluid interactions, Shim et al. found
differences among the heats of capillary condensed benzene, cyclohexane, hexane, toluene, trichloroethylene, acetone, and methanol
in MCM-48, despite the fact that all adsorbates wet the adsorbent
[16]. This was taken as a qualitative indication that fluid-fluid
interactions do play a role in capillary condensation. In particular,
Qiao et al. calculated the isosteric heat of capillary condensation
for hexane in MCM-41 and found it to be higher than the heat of
condensation for hexane in the bulk and to increase with decreasing pore size [40]. On the other hand, Morishige et al., have used
small isosteric heats of adsorption to characterize weak
fluid-pore interactions, and vice versa [38].
In the investigation of fluid-pore-wall interactions, as manifest
in wettability, Zandavi et al. have shown the contact angle of the
condensed phase with the pore wall to be zero once capillary condensation has occurred. This was done by calculating pore size
based on isotherms for water, heptane, octane, and toluene in
MCM-41 and SBA-15 while assuming a contact angle of zero and
then comparing the results to pore size values taken from transmission electron microscopy [115]. However, the wettability of
nanopores does differ from one adsorbate to another, as shown
by Shim et al. using thermogravimetric analysis [16]. They found
the wetting order of several fluids in MCM-48, which they
described as ‘‘energetically heterogeneous” based on isosteric heat
calculations, in order of decreasing wettability to be acetone,
methanol, n-hexane, benzene, cyclohexane, and toluene [16].
Furthermore, in their observations of the capillary condensation
of toluene, methylcyclohexane, neopentane, and n-pentane, Russo
et al. used isosteric heats to study the effects of pore geometry and
interconnectivity [15]. Their capillary condensation isotherms for
MCM-41, SBA-15, SBA-16, LPC, and mesocellular foam (MCF), led
to heat calculations, where significantly higher heats of desorption
(rather than heats of adsorption) for fluids in SBA-16 and LPC were
observed, indicating that both adsorbents have narrow pore
mouths and facilitate a desorption mechanism different than that
of MCM-41 or SBA-15, whose fluids exhibit heats of desorption
that are only slightly larger than their heats of adsorption [15].
Similarly, the identical heats of desorption and adsorption for
MCF were attributed to larger pore mouths [15]. The effect of pore
geometry is echoed by a more fundamental study by Ioneva et al.,
who showed that for n-butane at 283 K in pore diameters of
2.1 nm, 2.6 nm, 2.8 nm, and 3.6 nm, capillary condensation
occurred at relative vapor pressures of 0.20, 0.23, 0.34, and 0.38,
respectively [48]. This supports theoretical predictions that
capillary condensation occurs first in the smallest pores and was
confirmed in the works of Tanchoux et al. and Qiao et al., who
both studied the capillary condensation of hexane in MCM-41
[13,40].
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E. Barsotti et al. / Fuel 184 (2016) 344–361
At the cutting edge of the research, studies of capillary
condensation in shale rock also include the work of Chen et al.,
who related the amount of hexane adsorbed in shale core plugs
to the total organic content of the plugs [21]. By estimation, they
determined that the amount of hexane in the pores could not be
due to surface adsorption alone and, thus, was a product of
capillary condensation [21]. Their results show that capillary
condensation may factor greatly into understanding how gas is
stored in and produced from organic nanopores. However, much
more work is yet to be done to include the unknown effects of
other pore and fluid properties, before any correlation can be made
between organic content and propensity for condensation [21].
5. Conclusions and final remarks
In summary, capillary condensation is a confinement-induced
phase transition. Although many efforts have been made to elucidate
it, there are still many unknowns yet to be investigated. While theoretical development is in progress to fully understand the phenomenon, due to immediate needs in industry, semi-empirical
models including equations of state, which have been successfully
established for bulk fluids, have been modified to account for the
strong intermolecular interactions between fluids and pore walls.
Some of these models have shown promise in accurately matching
the limited available experimental data and making sound predictions, but abundant experimental data is required to tune model
parameters. Though extensive parameterization has previously
been carried out for bulk systems, the parameters relevant to the
study of capillary condensation must include new factors, not
encountered in the bulk, to account for confinement. Such factors
must relate to the chemistry and the geometry of the confining porous medium.
Although the experimental means for the investigation of simplified systems (i.e., single component fluids in simple pore geometries such as those found in MCM-41) are readily available, few
studies have been made on capillary condensation. Moreover, technical restrictions may hinder the measurements for multicomponent fluids in more complex pore systems. Such measurements
will require the ability to work at a wide range of temperatures
and pressures in order to produce capillary-condensation data for
a broad range of fluids and adsorbents. Furthermore, in replicating
reservoir conditions, the ability to flow, high-temperature, highpressure reservoir fluids through real shale- and/or tight-rock core
plugs is paramount, as is a mechanism for the replication of net
overburden stress. The development of such a unique technique
relevant to applications in hydrocarbon recovery from tight
formations is the subject of our future work.
Overcoming these restrictions so that experiments and models
can evolve hand in hand will culminate in a comprehensive understanding of capillary condensation that may improve estimations
of both reserves in place and recoverable reserves. Furthermore,
this understanding will inherently provide useful insights into
nano-scale fluid phase behavior beyond phase transition, which
is also of great importance in the search for more efficient methods
of oil and gas recovery from shale and tight formations.
Funding
We gratefully acknowledge the financial support of Saudi
Aramco, Hess Corporation, and the School of Energy Resources at
the University of Wyoming.
Appendix A. Supplementary material
A list of adsorption isotherm data with capillary condensation
available in the literature for fluids not found in natural gases is
included. Supplementary data associated with this article can be
found, in the online version, at http://dx.doi.org/10.1016/j.fuel.
2016.06.123.
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