Subscriber access provided by University of Newcastle, Australia
Article
EFFECTS OF MINERAL SURFACE PROPERTIES ON SUPERCRITICAL CO2 WETTABILITY IN A SILICICLASTIC RESERVOIR Julien Botto, Samantha J Fuchs, Bruce W. Fouke, Andres F. Clarens, Jared T Freiburg, Peter M Berger, and Charles J. Werth Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b03336 • Publication Date (Web): 06 Apr 2017 Downloaded from http://pubs.acs.org on April 9, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
EFFECTS OF MINERAL SURFACE PROPERTIES ON SUPERCRITICAL CO2 WETTABILITY IN A SILICICLASTIC RESERVOIR Julien Botto1, Samantha J. Fuchs1, Bruce W. Fouke2, Andres F. Clarens3, Jared T. Freiburg4, Peter M. Berger4, Charles J. Werth1,* 1. Department of Civil and Environmental Engineering, 301 E Dean Keeton, University of Texas at Austin, Austin, Texas 78705 2. Department of Geology, 605 E. Springfield Avenue, University of Illinois at Urbana Champaign, Champaign, Illinois 61820 3. Civil and Environmental Engineering, 351 McCormick Road, University of Virginia, Charlottesville, Virginia 22904 4. Illinois State Geological Survey, 615 E Peabody Dr, Champaign, University of Illinois at Urbana Champaign, Illinois 61820
KEYWORDS Geological Carbon Sequestration, Wettability, Contact angle, surface roughness, mineral heterogeneity, CO2 storage capacity, pore scale transport
ACS Paragon Plus Environment
1
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 45
ABSTRACT
Wettability is a key reservoir characteristic influencing geological carbon sequestration (GCS) processes such as CO2 transport and storage capacity. Wettability is often determined on a limited number of reservoir samples by measuring the contact angle at the CO2/brine/mineral interface, but the ability to predict this value remains a challenge. In this work, minerals comprising a natural reservoir sample were identified, and the influence of their surface roughness and mineralogy on contact angle was quantified to evaluate predictive models and controlling mechanisms. The natural sample was obtained from the Mount Simon formation, a representative siliciclastic reservoir that is the site of a Department of Energy CO2 injection project. A thin section of the Mount Simon sandstone was examined with compound light microscopy, and environmental scanning electron microscopy (ESEM) coupled with energy dispersive X-ray spectroscopy (EDS). Quartz and feldspar were identified as dominant minerals, and were coated with various reddish-black precipitates consistent with illite clay and the iron oxide hematite. Contact angle (θ) measurements were conducted for the four representative minerals and the Mount Simon sample over a range of pressures (2-25 MPa) at 40°C. At supercritical conditions, all samples are strongly water wet, with contact angles between 27° and 45. Several predictive models for contact angle were evaluated for the mineral and Mount Simon samples, including the Wenzel and Cassie-Baxter models, plus newly proposed modifications of these that account for the fraction of different minerals comprising the reservoir sample surface, surface roughness, and the extent that roughness pits are filled with brine. Modeling results suggest the fraction of mineral surfaces containing roughness pits filled with brine is the most important reservoir characteristic that controls wettability in the Mount Simon sandstone,
ACS Paragon Plus Environment
2
Page 3 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
followed by surface mineralogy. To our knowledge, this is one of the few studies to investigate the effects of individual minerals on the wettability of a natural reservoir sample.
ACS Paragon Plus Environment
3
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 45
INTRODUCTION The atmospheric concentration of CO2 due to human activities has increased drastically over the last century, and is the likely driver of climate change [1]. Geological carbon sequestration (GCS) has the potential to greatly reduce anthropogenic carbon emissions by capturing CO2 directly from stationary sources and injecting it into deep subsurface reservoirs [2]. Deep saline formations have the largest carbon sequestration potential in the US [3], with a total storage capacity of almost one thousand times the total national CO2 emissions per year [4]. However, concerns regarding CO2 reservoir capacity and storage safety persist, and represent challenges to implementation of this emerging technology. Key processes that affect these challenges include CO2 migration pathways during injection [5] [6] [7] [8], leakage through fractures in caprock [9] [10] and the capacity for permanent storage via capillary trapping [11, 12, 13]. While significant advancements in understanding these processes have been made over the last decade, considerable uncertainty remains. One factor that affects each of these processes and contributes to this uncertainty is capillary pressure [14, 15, 16], which is a direct function of reservoir wettability [17]. Reservoir wettability has frequently been quantified by measuring the contact angle of CO2 in the pore space [18] or on polished surfaces [19] of brine-saturated reservoir samples. More frequently, contact angles have been measured on relatively pure mineral samples that are present in reservoirs, in some cases before and after exposure to CO2, to understand the controlling mechanisms [19]. Very little work has been done to connect the mechanisms controlling wettability of pure mineral samples to wettability of heterogeneous reservoir samples, where surface roughness, surface charge, and mineral surface coverage likely play key roles.
ACS Paragon Plus Environment
4
Page 5 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
The influence of surface roughness on wettability has received considerable attention [20], especially in the last decade. However, the effects are still poorly understood. Contact angle measurements for the wetting phase (e.g., water drop on a hydrophilic surface in air) have shown both increasing and decreasing trends with increasing surface roughness. For example, the contact angle for water on aluminum and copper substrates in air increased with surface roughness [21], but decreased on a gold substrate [22]. Also, the contact angle for water on a (hydrophilic) titanium surface in octane increased with roughness [23]. More consistent results have been obtained for the non-wetting phase (e.g., water drop on a hydrophobic surface). For example, the contact angle for brine or water on a paraffin surface in air increased or stayed constant, respectively, with increasing roughness [24], and that for mercury on silica glass in air increased [25]. Conventional theory predicts the contact angle for a wetting phase (e.g., water drop on hydrophilic surface) should decrease with increasing surface roughness, and that for the nonwetting phase should increase [26]. Conflicting trends may be due to small differences in sample preparation or treatment, and the entrapment of the nonwetting phase between the wetting phase and rough substrate surface. For example, the aforementioned contact angle trend for titanium was attributed to the entrapment of octane between water and titanium [23]. Several models have been developed to account for the effect of surface roughness on wettability of chemically uniform surfaces. The Wenzel model assumes that the drop (e.g., CO2) invades all roughness pits on the mineral surface [26]. In contrast, the Cassie-Baxter model assumes that the surrounding fluid (e.g., brine) invades these roughness pits [27]. For each of the models, sawtooth, sinusoidal, and square wave geometries of surface roughness have been used [28, 29, 30]. Application of these models to data has been met with varying degrees of success [25, 27, 26] [21, 24, 31, 32]. In general, better agreement is obtained for more uniform surface
ACS Paragon Plus Environment
5
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 45
roughness [33] and when the dimensions of roughness are small compared to the size of the droplet being analyzed [34]. There are many studies of contact angle measurements on pure mineral samples, and in some cases the results were related to surface chemical properties, including surface charge. Contact angle measurements with mineral samples include quartz, feldspar, calcite and mica, all of which were found to be strongly (θ≤50°) to weakly water-wet (50°≤θ≤70°). Interpretation of these measurements, however, is confounded by the large variability in results for similar mineral-fluid systems. For example, contact angle measurements for water on quartz, feldspar, calcite and mica vary from 0°-90°, 15°-40°, 10°-60°, and 15°-75°, respectively [19]. At least some of this variability is due to sample cleaning methods, which can physically alter the mineral surface or leave residual fluids [35, 36], differences in solution chemistry, contact angle hysteresis, and natural surface heterogeneity among different samples of the same mineral [19]. It is well established that the wettability of a mineral is affected by surface charge, which is a function of the pH of the surrounding fluids. Several studies have shown that contact angle values for quartz, microcline (i.e., a common potassium feldspar), calcite and mica are a maximum at the point of zero charge [37, 38], i.e., when the surface is most hydrophobic. There are fewer published studies of contact angle measurements on natural reservoir samples, and even fewer performed with CO2 and brine at reservoir pressure and temperature. Reservoir samples evaluated for CO2 wettability under representative conditions include several limestone samples [18, 39], a sandstone [40] and a carbonate-rich cap rock [41]. Varying contact angles were measured, but they were not related to basic reservoir properties such as surface roughness, surface charge, or surface mineralogy. Instead, they were intended as input for CO2 transport models and for characterizing CO2 trapping capacity and leakage process. One
ACS Paragon Plus Environment
6
Page 7 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
exception is a recent study [42], where oil and brine contact points on a sandstone rock surface were evaluated; brine films covered most quartz surfaces, while oil directly contacted the rock at some asperities and clay aggregates. The Cassie model was developed to predict the wettability of a chemically heterogeneous and smooth surface based on wettability of the individual homogeneous components comprising the composite surface. This model has been applied to control samples with patterned surface variability, often with good agreement. For example, hydrophobic and hydrophilic parallel strips were deposited on a gold film by patterning self-assembled monolayers of hexadecanethiol and mercaptohexadecanoic acid, respectively. Measured contact angle values for water, a buffer solution, ethylene, glycerol, glycol and formamide, all in air, agreed with predicted values, while that for hexadecane in air failed to show good agreement because of its strong affinity for hydrophilic strips [43]. Similarly, trends in contact angle values (but not absolute values) for water drops in air on silicon wafers with hexagonal arrays of square posts treated with different silanization agents agreed with theory [32]. In contrast, poor agreement with theory was obtained for water on silicon wafers with varying numbers of perfluoroalkyl (hydrophobic) spots [31]. This model works best when the scale of surface heterogeneity is small compared to the size of the droplet [44]. No models to date have been used to predict the wettability of a natural reservoir sample comprised of different mineral fractions. While the Cassie model is perhaps the most relevant, it fails to account for surface roughness. The goal of this paper is to quantify the effects of surface roughness, charge, and mineralogy on CO2 wettability of a natural heterogeneous reservoir sample. The Mount Simon formation was selected as a typical siliciclastic storage reservoir, and a core from this formation was obtained at the Illinois Basin-Decatur Site (IBDS). The IBDS is one of several Department
ACS Paragon Plus Environment
7
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 45
of Energy geological carbon sequestration demonstration sites [45]. Mineralogy of the Mt. Simon sandstone was determined using a combination of polarized light microscopy, and scanning electron microscopy (SEM) coupled energy dispersive x-ray spectroscopy (EDS). The wettability of the sandstone sample and its primary mineral components was measured under reservoir conditions. Both rough and polished samples were evaluated. Several theoretical models that account for the effects of surface roughness and mineralogy on contact angle at the CO2/brine/mineral interface were evaluated to interpret how CO2 and brine compete for surface coverage on rough mineral surfaces, and to estimate how this roughness and different mineral fractions affect wettability of the reservoir sample.
EXPERIMENTAL SECTION Materials. Liquid CO2 (99.5% purity, Praxair) was used for all experiments. A synthetic brine was made from DI water and the following salts: sodium chloride, calcium chloride, magnesium chloride, potassium chloride, potassium bromide, lithium chloride, strontium chloride and borax. Total chloride and ionic strength in the synthetic brine are 149 g/L and 5.19 M. Synthetic brine composition is based on Mount Simon formation brine, and is presented in Table S-1 (Supporting Information), along with individual salt purity and supplier information. Experimental setup. All contact angle experiments were carried out in a custom-built high pressure and temperature view cell using the experimental setup shown in Figure S-1 (Supporting Information). The view cell was previously described by Wang et al [37]; it is a stainless steel cylinder with an outer diameter of 3.8 inch, an inner diameter of 1 inch, and two sapphire viewing windows on either end. A glass sample holder 1.5 inches long by 1 inch
ACS Paragon Plus Environment
8
Page 9 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
diameter was placed inside the view cell. It held the rock or mineral sample at a centered and fixed position. The view cell was fixed on an L-shaped stainless steel stage, which was fixed to a Solid Aluminum Optical Breadboard (Newport) by four adjustable screws. The heights of the screws were adjusted to level the mineral sample. A CO2 tank was connected to a Teledyne Isco pump model 100DM. The pump injected CO2 into both a pre-equilibration stainless steel reactor (HIP OC-3 Series) and the view cell. The equilibration cell was first filled with brine. The CO2 was then pumped into the equilibration cell, until the target pressure of an experiment was reached. The brine and CO2 mixture was then allowed to equilibrate overnight (approximately 12 hours). Heating tape (Briskheat BIH051020L) wrapped around the view cell was used to control temperature. Two Omega Ktype thermocouples were used to measure the temperature of the heating tape and of the view cell itself, and were monitored by a National Instrument Data Acquisition (NIDAQ) system and Labview software. A constant temperature of 40°C within the view cell was maintained throughout all experiments. This temperature maintained CO2 in the supercritical state at pressures above 7.38 MPa, and is representative of temperatures in typical reservoirs [15, 46, 47] [48]. Pressure was measured with the internal pressure transducer of the Isco pump. An AVT CCD camera (Guppy F-038C NIR) with a 16mm zoom lens (Fujinon) was used to capture images of CO2 bubbles on the mineral surface; these were analyzed using ImageJ with the axisymmetric drop shape analysis plugin (Dropsnake). Conventionally, contact angle is measured through the densest phase [49], so in the remainder of this paper “contact angle” refers to the angle through brine between the CO2/brine interface and the solid surface. The Dropsnake plugin was used to determine the horizontal line on the solid surface outside the CO2 bubble, the
ACS Paragon Plus Environment
9
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 45
lines tangent to the CO2 / brine interface at each of the two CO2 / brine / solid contact points, and the (contact) angles between these lines through the brine phase. Experimental procedure. Reservoir core and mineral samples were rinsed with DI water, soaked in acetone for 3 hours, then oven dried at 100°C for 2 hours, which is higher than the boiling point of acetone (57°C), and finally sonicated in DI water for one minute. There are alternative cleaning methods, and they can result in different results [35, 19]. This method was chosen because acetone treatment removes residual oils that may accumulate on samples during handling, heating eliminates residual acetone on the sample surface, and sample agitation (e.g., ultrasound) is brief and did not appear to result in sample loss. We note that SEM images taken before and after sample cleaning showed no significant differences in surface features. After sonication, the wet sample was placed into the holder, and inserted into the open view cell. The open ends were sealed with the sapphire viewing windows, and then the view cell was filled with the aforementioned brine pre-equilibrated with CO2 in the pre-equilibration reactor. The system was allowed to equilibrate at 40oC for one hour, and then a small bubble of supercritical CO2 was injected directly from the Isco pump at a constant pressure into the bottom side of the view cell through an 18 gauge needle; it detached from the needle and came to rest on the underside of the mineral sample. Kaveh et al. explored the effect of the bubble size of CO2 on the wettability of the CO2/brine/Bentheimer sandstone system, and found that bubble diameters less than 2.3 mm had no significant effect on the contact angle of CO2 [40]. Therefore, only bubbles below this threshold were considered in this study. Each experiment lasted at least 24 hours, and at least six different bubbles on the mineral surface were examined during this period. Each bubble was always removed before introducing a
ACS Paragon Plus Environment
10
Page 11 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
new one by briefly tilting the view cell. Four different images were taken and analyzed for each bubble. Replicate samples of the same minerals were also tested at 20 MPa; individual results are presented in Figure S-2 (Supporting Information), and were used to calculated average and confidence interval values presented in this paper. Contact angle hysteresis was not the focus of this effort; it can occur, for example, when bubbles move across a surface or change in size [50], or when solution conditions change over time due to mineral dissolution or the build up of impurities [51]. We took care to minimize contact angle hysteresis by pre-equilibrating brine with CO2 to prevent CO2 bubble dissolution, by rinsing all reactor and view cell components between experiments at each unique condition (i.e., at each pressure and temperature condition), and by only measuring contact angles for similarly sized and static CO2 bubbles on flat horizontal surfaces. To confirm contact angle hysteresis was minimized, we measured contact angles for each unique experiment using multiple CO2 bubbles over 24 hours, and for one control experiment over 4 days using the same CO2 bubble. In both cases, contact angle values were not significantly different and showed no trends with time. Reservoir core and mineral sample preparation. The Mount Simon core sample used in this study was taken from the CO2 injection well at the Illinois Basin-Decatur site, under the direction of the Midwest Geological Sequestration Consortium. It is a sidewall core from Verification Well #1, taken from a depth of 6985.72 ft (2.129 km). Between November 2011 and November 2014, nearly one million metric tons of CO2 were injected over the depth interval of 6984-7050 ft (2,135 m), directly into the lower Mount Simon sandstone [52]. The Mount Simon sandstone is a high permeability material [8], representative of the lower Mount Simon reservoir. Contact angles were measured on the Mount Simon core material, and on representative minerals
ACS Paragon Plus Environment
11
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 45
identified in the Mount Simon formation. Representative minerals are quartz, microcline, illite, and hematite; their selection is justified in the results. An additional sample comprised of hematite powder deposited on illite was prepared to represent mixed iron oxide-illite. A 1-inch diameter by 0.3 inch thick sample was cut from the Mount Simon core sample by Wagner Petrographic. This was used for contact angle measurements. A standard 30 micron thin section was also prepared by Wagner Petrographic from the same core. This was used for evaluation of minerals that dominate grain surfaces via optical microscopy, environmental scanning microscopy, and energy dispersive spectroscopy. All representative pure minerals were purchased from Ward’s science (catalog number 493640, 465122, 460315, 463862 for quartz, microcline, illite and hematite, respectively); they were cut with a wet saw into 1 inch x 1 inch x 0.125-0.3 inch samples. A subset of replicate mineral and Mount Simon sandstone samples was polished using crystallite diamond disks, with a fine polishing lap of 6 microns. Another subset was sand blasted using an econoline sandblaster (model RA 36-1) to increase roughness, with the exception of illite and the Mount Simon sandstone because they were too friable. The surface roughness was measured using a Wyko NT 9100 Optical Profilometer, which is capable of measuring surface roughness from nm’s to um’s. To create the iron-illite sample, approximately 100mg of hematite fine powder was uniformly deposited on top of a 1 in2 illite slab in air, cleaned as previously described. It was then soaked for 12 hours in the synthetic brine at ambient pressure and temperature, and briefly rinsed with DI water to remove free powder particles from the surface. Microscopy, spectroscopy, and zeta potential methods. A Leica DM 2500 compound light microscope was used to characterize the mineralogy of the Mount Simon thin section. The 2X and 4X objectives were used to map the location of grains and pores in the thin section. The
ACS Paragon Plus Environment
12
Page 13 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
40X and 60X objectives were used to focus on individual pores for characterization of minerals at the pore-grain boundaries. The eyepiece magnification was 10x, so the maximum magnification used was 600x. Images were taken with and without light polarization. A Philips/FEI XL30 environmental scanning electron microscope (ESEM) was used at high vacuum with an accumulation of 20kV to characterize the morphology of minerals in the aforementioned six pores. As our thin section was non-conductive, it was first coated with 25nm of carbon using a LaddVacuum evaporator. The maximum magnification was approximately 5800x. ESEM was coupled with energy dispersive spectroscopy (EDS) to characterize the elemental composition of the minerals of interest. Spectra were acquired on specific spots as small as 275nm, and on areas as large as 40µm2. The zeta(ζ)-potential was characterized using a ZetaCompact zetameter (Z9000, CAD Instruments, FR) by converting the measured electrophoretic mobility (EPM) into ζ-potential using the Smoluchowski equation built into the instrument software. Wettability models. Several wettability models have been developed to describe the relationship between contact angle, surface roughness and surface mineral area coverage. These are described below in the context of a mineral, CO2, brine system. The Young and Dupré model can be used to describe the ideal contact angle, , of a CO2 drop on a flat homogeneous mineral surface surrounded by brine [17]: cos = ( − )
(1)
The parameters , and are, respectively, the interfacial tension between the brine and
the CO2, the mineral and the CO2, the mineral and the brine. The parameter is assumed to ACS Paragon Plus Environment
13
Energy & Fuels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 45
remain constant for all minerals at a given pressure and temperature; the parameters and are assumed to remain constant for each mineral sample at a give pressure and temperature, but may vary with surface roughness. Therefore, contact angle can depend on surface roughness. It can also depend on the presence of brine that coats a mineral surface and prevents direct mineral contact by CO2. The Wenzel model was developed for a rough but chemically homogeneous surface, and assumes the (CO2) fluid drop invades all roughness pits. It uses a roughness ratio, r, defined as the ratio of the 3D area of the solid surface to its 2D projection, to relate the ideal contact angle in equation 1 to the apparent (or measured) contact angle on a rough surface [26]: cos θ = rcosθ
(2)
The Cassie model was developed for a flat heterogeneous surface. It assumes that the 2D fractional surface area of each homogeneous component on the surface, f , can be used to relate the ideal contact angle of each homogeneous component to the apparent contact angle [27]: cos θ = ∑ f cosθ,
(3)
Like the Wenzel model, the Cassie-Baxter model was developed for a rough but chemically homogeneous surface. However, it assumes the brine surrounding the CO2 drop fully invades all roughness pits. Building on the fractional surface coverage approach used in the Cassie model, and assuming the theoretical contact angle of the surrounding brine is zero, the theoretical contact angle is related to the apparent contact angle as follows: cos θ = f cosθ, + f
(4)
ACS Paragon Plus Environment
14
Page 15 of 45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
The parameters fm and f are the fractional surface area coverage of the mineral and brine, respectively, and θ, is the theoretical contact angle.
A new model was developed to consider the case when both brine and CO2 invade and share the roughness pits of a single mineral surface. It combines both the Wenzel (2) and CassieBaxter equations (4). A modified roughness ratio, r*, is proposed, and represents the 3D solid surface area contacted by CO2, divided by its 2D projection. For square wave, trapezoidal and triangular geometries, r* is, respectively: ∑
%$ ∗ =
" − 1 − & %
,- ∗ =
" − 1 − .
,6 ∗ =
. − 012 35 + 012 3
!
!
!
'(,)*)
++1
/012 3 24 3
(5)
∑
%$5& %
'(,)*)
++1
(6)
(7)
The parameter A2D,tot is the total projected area, ∑8 78 is the total vertical surface area of the walls of brine filled pits, and φ is the angle that the trapezoids or triangles make with the horizontal plane. The parameter r* is used to calculate the surface fraction of CO2 which is in 9∗ ! 5. !: ;
contact with the mineral .9 ∗
This fraction, equation (2) and equation (4) are combined
together to create equation (8), called the Modified Cassie-Wenzel model: 9∗
cos