Article pubs.acs.org/Langmuir
Condensation in Nanoporous Packed Beds Javed Ally, Shahnawaz Molla, and Farshid Mostowfi* Schlumberger DBR Technology Center, 9450 17 Avenue, T6N 1M9 Edmonton, Canada ABSTRACT: In materials with tiny, nanometer-scale pores, liquid condensation is shifted from the bulk saturation pressure observed at larger scales. This effect is called capillary condensation and can block pores, which has major consequences in hydrocarbon production, as well as in fuel cells, catalysis, and powder adhesion. In this study, high pressure nanofluidic condensation studies are performed using propane and carbon dioxide in a colloidal crystal packed bed. Direct visualization allows the extent of condensation to be observed, as well as inference of the pore geometry from Bragg diffraction. We show experimentally that capillary condensation depends on pore geometry and wettability because these factors determine the shape of the menisci that coalesce when pore filling occurs, contrary to the typical assumption that all pore structures can be modeled as cylindrical and perfectly wetting. We also observe capillary condensation at higher pressures than has been done previously, which is important because many applications involving this phenomenon occur well above atmospheric pressure, and there is little, if any, experimental validation of capillary condensation at such pressures, particularly with direct visualization.
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INTRODUCTION Fluid behavior in nanoporous structures is important in a wide variety of applications, including hydrocarbon production from shale. Although shale has become an important hydrocarbon source,1−3 the mechanisms of fluid production and transport through nanometer-scale pores remain poorly understood4 and cannot be described by the porous media and phase behavior models used in conventional reservoir modeling.4−7 Fundamental, pore-scale understanding of nanofluidic phase and transport behavior is necessary for accurate resource estimation, optimizing well stimulation, and reducing environmental impact,8,9 especially in light of growing economic and regulatory constraints on shale production and hydraulic fracturing.10 Understanding condensation in such reservoirs is particularly important, as condensation within the shale matrix can dramatically reduce fracture permeability.9 There have been various models of shale well performance proposed in the literature.1,11,12 These models generally make assumptions about the rate of diffusion of fluid through the shale matrix into fractures and require tuning with historical production data. They also neglect phase change and related issues such as condensate banking, which cause formation damage.9 What is missing from the current picture is an understanding of nanoscale fluid behavior in the shale matrix. Early works focused on diffusion through macroscopic shale samples in order to study hydrocarbon expulsion from source rock.13 More recently, nanofluidic phase behavior in porous materials has been studied in the context of shale as well as a wide variety of other applications such as nanofluidics, catalysis, fuel cells, and powder adhesion. However, experimental investigations of phase change in nanoconfinement at pressures above atmospheric are rare, though deviations from bulk behavior are clearly suggested by numerical studies.4,6,7 Most © 2016 American Chemical Society
previous nanopore condensation studies have also used wellcharacterized materials such as porous glasses or silica, but extrapolated fluid phase behavior indirectly from permeability changes or mass balance.14,15 There have also been studies of fluid transport and phase behavior using etched nanochannels;16−18 however, nanoconfinement is typically limited to sizes > 30 nm in one dimension, and there are practical difficulties with characterization, e.g., due to channel deformation.18 In confined geometries, interfacial energy in the pores or capillaries of solid material drives fluid condensation, in addition to the intermolecular interactions between the fluid molecules. As fluid molecules adsorb onto the solid, they form tiny menisci in the corners and pores of the material. Stable liquid in these highly curved menisci can exist due to the interfacial tension between the liquid and the vapor phases; i.e., the cohesive forces between the fluid molecules are able to overcome the repulsive forces between them more easily than in bulk geometry. This effect is called capillary condensation and is typically described by the Kelvin equation for a spherical interface of an ideal fluid that is incompressible in its liquid phase:19 ⎛ PV ⎞ −2v Lγ LV cos θ + v L(PV − P∞) RT ln⎜ ⎟ = rcap ⎝ P∞ ⎠
(1)
The Kelvin equation relates the pressure PV of the vapor phase to the equilibrium radius of curvature rcap of the liquid meniscus given fluid temperature T, molar volume vL, liquid−vapor Received: March 17, 2016 Revised: April 15, 2016 Published: April 26, 2016 4494
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interfacial tension γLV, and liquid contact angle θ with the solid phase. Molar volume, interfacial tension and contact angle values are based on bulk values at T, as they are independent of pressure due to the incompressibility of the liquid. P∞ is the bulk fluid saturation pressure; R is the universal gas constant. The Kelvin equation has been experimentally validated for certain pure, single-component fluids to predict meniscus curvatures as small as 10 nm.14,20 It also serves as the basis of pore size measurements using gas adsorption,21 including pore size measurements of shale.22 Such measurements are usually made with the assumption of cylindrical pores and spherical menisci.21 A multicomponent version derived by Shapiro and Stenby23 showed that similar behavior occurs in the cases of nonideal fluids and retrograde condensation as well, although to the authors’ knowledge there has been no experimental validation, as in the case of high pressure and hydrocarbon fluids. To study hydrocarbon and carbon dioxide condensation in nanopores at room temperature, we use a microfluidic device with an ordered packed bed of 150 nm diameter silica particles in a channel (Figure 1), allowing direct visual observation of
Article
METHODS
Packed beds of silica particles were formed in 80 × 10 mm2 microfluidic chips (McGill University) composed of a straight 50 × 50 μm2 channel, 60 mm long with 150 μm holes at each end (Figure 1a). The channel had two circular pillars, 30 mm from one of the holes, to hold the bed in place due to particles jamming in the reduced cross-section. The microfluidic channels and holes were etched in silicon anodically bonded to glass. Silica particles, 150 nm diameter with a 10% coefficient of variation, were supplied suspended in distilled, deionized water at 10% (w/v) solids concentration (Polysciences, Warrington, PA, USA), and further diluted by a factor of 100. To produce a packed bed, a 100 μm long plug made of ∼6 μm diameter iron oxide particles (Sigma-Aldrich, St. Louis, MO, USA) was first formed to block the silica particles by flowing them through the channel with water. The silica particle suspension was then flowed through to form a ∼8 mm long packed bed upstream of the pillars, followed by toluene at ∼0.05 mL/min to pick up residual particles and aid in ordering. Liquid was removed by blowing nitrogen through the bed at 13.8 MPa, followed by holding under vacuum for 1 h. The packed chip is placed in a holder connected to pressure sensors on either end (PX409-USBH, OMEGA Engineering Inc., Stamford, CT, USA; ±0.08% accuracy). Fluid is supplied to both ends of the chip simultaneously to minimize filling time (Figure 1b). The pressure drop in the lines supplying the downstream side of the chip is greater than on the other side, such that the packed bed is pressed against the pillars during filling. The apparatus is connected to a floating piston sample cylinder via a micrometering valve, with constant fluid pressure maintained with a syringe pump (ISCO, Lincoln, NE, USA). On both sides of the chip, 0.5 μm filters are used to block solid contaminants. The entire apparatus was held under vacuum for 2 h before each experiment. Pressure in the system was increased in steps by slowly bleeding fluid over ∼5 min from the sample cylinder into the chip using the micrometering valve until the desired pressure was reached and then allowing the system to equilibrate for 1 min before observation. The 1 min equilibration time was established based on the fact that, in all cases, it took less than 45 s for the appearance of the packed bed to stabilize; therefore 1 min was considered excess time. All experiments were carried out at an ambient temperature of 21.5 °C. A 400 × 50 μm2 region of the packed channel was observed using a microscope (Zeiss BX-51) with incident lighting and an eyepiecemounted camera. Reflection spectrometry measurements of the central 50 μm part of the observed region were performed to confirm ordering of the packed bed using a spectrometer and tungsten− halogen lamp (Ocean Optics, Dunedin FL, USA), which were connected with a split fiber to a collimator at the microscope camera port.
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RESULTS As propane was introduced into the evacuated packed bed and the pressure increased, no change was observed until 448 kPa, where the packed bed became slightly darker, corresponding to a 9% decrease in intensity in the region shown in Figure 2a. When the pressure was increased to 655 kPa, the packed bed turned substantially darker (Figure 2a). As the pressure was increased further, clear regions began to appear, until the entire packed bed appeared clear (Figure 2a) at 724 kPa. The fluid in the microchannel became liquid at the expected propane bulk saturation pressure of 870 kPa.25,26 Initial darkening of the packed bed observed at 448 kPa with propane may be due to an adsorbed layer, presumably of propane, forming on the surface of the particles, modifying the refractive index of the particles, reducing the intensity, and slightly changing the scattering angles of the observed light wavelengths. We hypothesize that the mechanism of this initial change is different from the subsequent darkening of the interface because the change occurs suddenly, within one
Figure 1. Schematic of the experimental apparatus: (a) packed bed microchannel; (b) fluid supply system.
fluid phase behavior due to light scattering. This effect has been used elsewhere to create sensitive gas adsorption sensors.24 The small volume of porous medium in the microchannel (∼20 nL) allows complete flushing and filling with fluid, facilitating lower permeabilities than other methods (e.g., core flooding) because of the reduced pressure drop, and allowing operation at high pressures. The packed bed is formed by flowing a suspension of silica particles through the 50 × 50 μm2 channel with a porous obstruction (Figure 1) followed by drying of the apparatus under vacuum. The packed bed is then observed with a microscope under hydrostatic conditions, with fluid introduced in gradual steps between observations. 4495
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in the filled appearance of the packed bed for propane and carbon dioxide are due to the difference in refractive index of the two liquids, 1.34 and 1.20, respectively; the refractive index of silica is 1.5. The packed bed apparatus used allows the bed structure to be inferred from light scattering. Under vacuum, a well-ordered packed bed has an orange-pink hue, due to preferential reflection of red light from the packed bed to the microscope objective (Figure 3a) due to different wavelengths of light to be
Figure 2. Images of packed beds filled with propane and carbon dioxide at increasing pressures. The dark regions at the top and bottom of the images are shadows from the microchannel walls. (a) Packed bed appearance at various filling pressures with propane. The 448 kPa image shows 9% decrease in intensity from the 102 kPa image. (b) Packed bed appearance at various filling pressures with carbon dioxide. The 791 kPa image shows 4% decrease in intensity from the 448 kPa image. The dark band in the center of the image is due to a ∼1 μm deep dimple of the microchannel bottom profile that results from the fabrication process. Figure 3. Reflection spectrum of an ordered packed bed and a disordered packed bed, both under vacuum. Insets show the appearance of the packed beds.
pressure step, in contrast to the gradual change in reflected light intensity observed afterward. Composition of any adsorbed layer could also be strongly affected if the adsorbed water initially present on the silica particles of the packed bed was not completely removed by holding the apparatus under vacuum. If this is the case, the amount of water adsorbed in the pores of the packed bed could be significant relative to the pore size, and the adsorbed layer may be a complex of propane and water. Darkening of the packed bed observed at 655 kPa with propane is due to liquid formation in the pores. As liquid forms in the crevices between particles, it creates many small vapor− liquid interfaces within the packed bed. These interfaces disperse the incident light in many different directions, reducing the light reflected from the pack back to the microscope objective lens, thus causing the dark appearance observed. When the pores are completely filled, the packed bed appears clear because of the similar refractive indices of the liquid and silica particles. Similar results were observed with carbon dioxide (Figure 2b). At 791 kPa, a slight darkening of the bed was observed, corresponding to a 4% decrease in intensity; this change may also be due to adsorption and could be affected by residual water in the same manner as with propane.27 At 5436 kPa, the packed bed became slightly darker, indicating liquid formation. At 5606 kPa, the bed appearance changed significantly as more liquid appeared to condense. The packed bed turned clear at 5816 kPa, followed by liquid forming in the microchannel part of the chip at the expected bulk saturation pressure of 5934 kPa.25,28 The results shown in Figure 2 are for different packed beds for the propane and carbon dioxide. Results for the same fluid in a packed bed were repeatable within one pressure step, i.e., 14 kPa for propane and 70 kPa for carbon dioxide. Differences
reflected back toward the objective at different angles. The scattering angle of a particular wavelength is related to the geometry of the packed bed by Bragg’s law. For a face-centered cubic (fcc) or hexagonal close packed (hcp) bed of particles with diameter D and refractive index np in contact with one another and viewed in their slip planes, the scattered wavelength λb and scattering angle ψ can be approximately related as29,30 λb =
2 D[(n pϕp + n f ϕf )2 − sin 2 ψ ]1/2 3
(2)
ψ is measured from the axis of the microscope objective. nf and ϕf are respectively the refractive index and volume fraction of the fluid. The intensity of the light scattered depends on the difference in refractive indices of the particles and surrounding medium in the packed bed.29−31 Based on eq 2, any change to the refractive index of the particles or the surrounding fluid will lead to a change in the scattering angles of the various wavelengths and the apparent color of the packed bed, leading to a visually apparent change. The orange-pink hue and reflectance spectrum Figure 3 indicate that the well-ordered packed bed contains a sufficient proportion of ordered regions to preferentially scatter light due to Bragg diffraction. Although the packed bed consists of fcc, hcp, and randomly packed domains in various orientations, the observed Bragg diffraction indicates that a sufficient proportion of ordered, close-packed domains exist to allow measurement of fluid properties optically. No diffraction is observed from an evacuated, poorly ordered packed bed that was produced by rapid flow of the silica particle suspension (Figure 3). The poorly ordered bed 4496
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constant curvature to have constant pressure in the fluid, as described by the Young−Laplace equation33 for an axisymmetric interface:
was formed by omitting the toluene step in the procedure described above. Assuming the packed bed particles are in contact and form ordered, close-packed regions, the average pore throat size can be determined from the packing geometry. For an fcc or hcp packing, there are two types of structural cells, tetrahedral and octahedral (Figure 4), with average interstitial pore radii of 17
ΔP = 2γ LVH
2H =
(4a) d2z dr 2
⎡ ⎢⎣1 +
3/2 dz 2 ⎤ dr ⎥ ⎦
+
( )
dz dr
⎡ r ⎢1 + ⎣
1/2 dz 2 ⎤ dr ⎥ ⎦
( )
(4b)
where ΔP is the pressure difference across the interface and
H=
1 2
(
1 r1
+
1 r2
) is the mean curvature of the interface with
principal radii of curvature r1 and r2; r and z are the radial and axial position coordinates of the interface, respectively. To quantitatively describe the images in Figure 2 in terms of the capillary meniscus geometry, a more general curvature radius term in the Kelvin equation is required: Figure 4. Ordered, close-packed region is comprised of tetrahedral and octahedral cells with interstitial volumes illustrated with red spheres. Both types of cell are bounded by pore throats between three particles (red region). The same types of cell exist for both fcc and hcp structures.
⎛ PV ⎞ −2v Lγ LV cos θ + v L(PV − P∞) RT ln⎜ ⎟ = r* ⎝ P∞ ⎠
where the curvature term
and 33 nm, respectively, for 150 nm diameter particles. Both types of cell are bounded by pore throats between three particles (Figure 4). The average hydraulic diameter Dh of the pore throats can be related to the particle diameter D based on the geometry shown in Figure 4: Dh =
2 3 −π D ≈ 0.103D π
curvature
1 rcap
1 r*
=
1 r1
+
1 r2
(5)
replaces the spherical
. The contact angle θ for both fluids with the silica
particles is assumed to be 0°. Since the contact angles considered here involve nonpolar liquids with their own vapors and a baked-out silica surface (i.e., high surface energy), the assumption of complete wetting is reasonable. Surface tension and molar volume values were calculated using the NIST REFPROP software25 for both fluids.26,28 The shape of the pendular rings can be determined by solving eq 4 as an initial value problem,33,34 starting at the contact line on one particle to the midpoint of the interface. Using eq 4b, the filling angle, i.e., the position of the contact line on a particle (Figure 6), can be calculated as a function of the curvature of the interface, which in turn can be determined from the pressure using the Kelvin equation, as shown in Figure
(3)
For 150 nm particles, the average hydraulic pore throat diameter is 15 nm.
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DISCUSSION Knowing the geometry of a packed bed, its appearance can be related to the geometry of the liquid menisci formed between the particles. In capillary condensation measurements to determine pore size, a spherical interface shape is typically assumed. Such a shape is not possible for a packed bed of spheres with a constant contact angle, however. In a sphere packing (fcc, hcp, or random), the narrowest regions are found around the contact points between the spheres. These crevices will support the smallest menisci in the geometry;32 therefore, capillary condensation will initially occur around the contact points in the form of pendular rings (Figure 5). For the pendular ring menisci to be stable, there cannot be any fluid flow; therefore, the shape of the menisci must have a
Figure 6. Filling angle of the pendular rings as a function of r*. The red dot indicates the experimental value at which filling was observed with propane; the black dot indicates the experimental value for carbon dioxide. The gray lines indicate the corresponding values of r* and filling angles.
Figure 5. Pendular ring liquid menisci (red) in (a) a tetrahedral cell of spheres in contact, (b) an octahedral cell, and (c) a pore throat. 4497
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liquid−vapor interface. In practice, this means that differences in geometry and wettability must be considered when comparing capillary condensation behavior in different materials, e.g., between porous glass and materials such as shale, tight sandstone, or spherical packs which may have very different pore shapes, though similar in scale.
6. This was done using a solver written in Python using the SciPy ODEINT implementation of the lsoda routine. For propane, the appearance of the packed bed began to change significantly at 655 kPa, corresponding to an absolute meniscus radius of curvature of 5.2 nm. For carbon dioxide, the first significant change in appearance occurred at 5606 kPa, corresponding to a meniscus radius of 3.6 nm. The packed bed appeared clear, i.e., filled with liquid, at 724 and 5816 kPa for propane and carbon dioxide, corresponding to curvature radii of 7.8 and 8.9 nm, respectively. The meniscus radii of curvature predicted with the Kelvin equation at the pressures where complete filling is first observed are much smaller than the interstitial radii of the packed bed cells. This means there must be some other mechanism for filling in addition to condensation. Before the condensate volume becomes large enough to fill the space between the spheres, the pendular rings make contact (Figure 5c). At this point, imbibition would occur; contact between pendular rings creates a high curvature region at the point of contact, creating a pressure gradient in the liquid phase and causing liquid to be sucked into the pore from neighboring pores. These pores would be refilled in turn by additional capillary condensation replacing the drained liquid, since the vapor pressure in the system remains constant. This chain of imbibition and refilling would cause the entire packed bed to become filled with liquid, as observed, once the radius of the pendular rings is large enough for them to make contact; i.e., the filling angle ψ = π/6 (Figure 6). This type of filling would only occur for a packed bed of sub-micrometer particles, i.e., is restricted to nanoscale geometries. For larger particles, the curvature of the pendular rings would not be large enough to create an appreciable pressure shift for pore filling from the bulk saturation pressure. The dependence on the meniscus geometry also means that filling would depend on the contact angle between the condensed liquid and particle surface. Contact between the pendular ring menisci between spheres occurs, assuming a contact angle < 90°, when the contact lines on the sphere surfaces meet. For 150 nm diameter spheres with a contact angle of 0°, contact between the pendular rings occurs when the radius of curvature of the meniscus is 8.9 nm. The experimental radii of curvature for propane and carbon dioxide at filling were 7.8 and 8.9 nm, corresponding well with the predicted value based on the proposed pore-filling mechanism. Possible sources of error include experimental error in the particles’ sizes and pressure sensor; pressure-induced deformation of the particles; adsorbed layers reducing effective meniscus curvature; and wetting instabilities. Although use of bulk fluid properties for thermodynamic analysis at the scales considered here has some support in the literature,14 surface tension and molar volume may deviate from their bulk values in nanoconfinement, and thus also contribute to error in the analysis. Filling during capillary condensation due to contact between pendular rings is similar to pore filling during pure imbibition35,36 and has been previously proposed36−38 although there has been no previous experimental validation. The results of this study support this mechanism, showing that imbibition due to meniscus contact plays a key role in pore filling during capillary condensation, as complete pore filling occurs at a meniscus radius well below the interstitial pore radii of the packed bed. Pore filling thus depends not only on the hydraulic diameter of the pores but also on the specific pore geometry and surface properties which determine the shape of the
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AUTHOR INFORMATION
Corresponding Author
*E-mail: FMostowfi@slb.com. Tel.: +1 (617) 768-2152. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Thanks to Dr. Cedric Floquet for assistance with the spectrometry measurements and Dr. Vincent Sieben for valuable comments. F.M. acknowledges Dr. Neda Nazemifard for fruitful discussions.
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