Thickness Dependence of the Diffusivity and Solubility of Cyclohexane in Nanoscale Bitumen Films.

Diffusivity and solubility of cyclohexane in nanoscale bitumen films coated on hydrophilic substrates at ambient conditions were studied using a gravimetric analyzer. Three substrates were used, and they are as follows: sample A, monodisperse spherical glass beads; sample B, polydisperse spherical glass beads mixed with polydisperse irregular-shape kaolin clay particles; and sample C, irregular-shape residual solids generated from a solvent extraction process of an oil sand ore. All of the above samples had a mean diameter of 150 μm. Diffusion coefficients were determined based upon the initial rates of cyclohexane absorption when bitumen-coated samples at various amounts (thicknesses) were exposed to a carrier gas with cyclohexane vapors at two levels of relative saturations (RSs), and they were found to be in the range of 10-18 to 10-16 m2/s. A double-first-order kinetics model fits well to the absorption data, suggesting that there exists a concentration gradient of polar (or nonpolar) bitumen molecules in the nanoscale films. This is because the hydrophilic substrates attract the relatively polar fraction of bitumen molecules to the region close to the substrates and the nonpolar fraction resides in the region near the free surface. As a result, the measured diffusion coefficients exhibited positive thickness dependence when the thickness of the bitumen films was at the nanoscale. The molecules near the substrates tended to diffuse slower than those in the free surface region. However, diffusivity was insensitive to the cyclohexane RS. On the other hand, the measured solubility of cyclohexane in the nanoscale bitumen films exhibited no thickness dependence but strong cyclohexane RS dependence. These results suggest that solubility is not affected by the inhomogeneous distribution of bitumen molecules in the nanoscale films and that it follows more or less Henry's law.

Introduction

In a variety of industrial and environmental remediation processes, removal of organic solvent is a necessary step. For example, in the polyethylene industry, for safety reasons, residual solvent in the freshly made polyethylene pellets needs to be removed before they are transported to the customer sites. In typical soil remediation processes, the solvent is removed to minimize the negative impact on the environment. Recently, our group has been developing a process where cyclohexane is used to extract bitumen from oil sand ores and this process generates waste materials, hereafter referred to as gangue, that contain mainly solid particles (coarse sand particles and fine clay particles) and a small amount of residual bitumen.[1−3] Cyclohexane, which is also in gangue, needs to be removed for obvious environmental and process economics reasons. The amount of residual bitumen in gangue is generally in the range of 0.5–2 wt %. Despite such a small amount, it was found that the residue bitumen significantly reduces the removal rate of cyclohexane[3] and that one of the rate controlling steps is the diffusion of cyclohexane in the residual bitumen.

Given the amount of bitumen in gangue, it is interesting to note that the thickness of the bitumen film on the solid residue could be at the nanometer scale. Interestingly, there are a number of studies suggesting that thermal, mechanical, transport, and absorption properties including the diffusion coefficient in nanoscale polymer films are thickness-dependent.[4−13] This is because for nanoscale films, there exists a near-substrate layer slowing down the rate of diffusion.[4] For example, the effect of the substrate chemical structure was evaluated and shown to have an impact on the diffusivity of water in poly(vinyl pyrrolidone) nanofilms.[14] The confinement effect was also evaluated for the transport of water in thin Nafion films.[8] This led to the speculation that the diffusivity of solvent in nanoscale bitumen films would also be thickness-dependent. It was also previously reported that the spontaneous formation of water droplets at the oil/substrate interface might occur in the presence of water or in a humid environment.[15−17] This effect was not considered in the current study and requires a separate rigorous experimental study.

Nevertheless, experimental studies of the diffusion of organic solvents in bitumen films are scanty. Using a gravimetric technique, Noorjahan et al.[18] measured the diffusion coefficients of a couple of solvents in asphaltene (the most polar fraction of bitumen) films. However, the effect of thickness was not evaluated. A couple of previously reported studies attempted to determine the diffusion coefficients of volatile solvents in bulk bitumen, and the values for cyclohexane were estimated to be ∼3 × 10–12 m/s2.[19,20] Most of the measurements were done on well-defined geometries, plane sheets in particular. Given that gangue particles have irregular shapes, we are interested in studying whether the shape of gangue particles compared to particles with well-defined geometry (e.g., sphere) but with comparable mean diameter would yield different diffusion coefficients. In this regard, we are interested in three samples. The first one is monodisperse spherical glass beads with a diameter of 150 μm. The second sample contains large spherical glass beads and fine, irregular-shape kaolin clay particles with an overall mean diameter of 150 μm. The final sample is the gangue with a mean particle size of 150 μm. A gravimetric technique will be used to study the diffusivity of cyclohexane in the aforementioned substrates with different amounts of coated bitumen at ambient conditions. Since solubility can be readily obtained from the experiments, we will also report such results.

Theory on the Measurement of Diffusion Coefficient

One of the oldest methods for the experimental determination of diffusion coefficients is based on the rate of uptake of a diffusing component by a plane sheet.[21−23] In these experiments, a plane sheet with thickness l is placed in an environment with a known ratio of carrier gas to solvent vapor at constant temperature and pressure and the mass change of the plane sheet is monitored as a function of time. The solution for the diffusion equation for this configuration is given by[24]where M is the mass of vapor absorbed at time t and M∞ is the equilibrium mass of vapor absorbed. When the value of is equal to 0.5, which occurs at the initial stage in many cases, eq can further be approximated as follows:and the diffusion coefficient can be found using eq It is important to mention that eq is valid under the assumption that, as soon as the plane sheet is in contact with the vapor, the concentration at the free surface is equal to the equilibrium concentration (M∞) and remains unchanged thereafter. This leads to the situation that the mass uptake is linearly proportional to the square root of time at the initial absorption stage.

It has been observed that the initial stage diffusion coefficient can be calculated by plotting the relative mass uptake as a function of the square root of time. At the early stage, the plot has a linear shape and thus the initial stage constant diffusion coefficient can be calculated directly from the slope of the plotted line:[23]Plotting against (t/l2)1/2 yields the curve that is a straight line at the initial part with the slope R. This slope R of a linear part (i.e., the early stage) of the curve can be determined asThen, the early-stage absorption diffusion coefficient at the initial time is calculated asIt is worth saying that eqs −6 are only valid when the plane sheet has a uniform thickness. This can also be applied to the cases that the material is coated on a solid support with well-defined geometries with a uniform thickness.[21,23,25]

However, films, especially in naturally occurring materials such as oil sand ores, are not always coated on a plane sheet geometry and curving of the film surface might occur. This can bring up a question of whether it is reasonable to consider a nanoscale film coated on a micron-scale spherical or irregular-shape particle as a plane sheet. For instance, when a film has a spherical shape with an internal diameter a and external diameter b, it hence has thickness l = b – a. The total uptake of the diffusing substance in the spherical wall is given by Crank[21]For the case of diffusion through the spherical wall, the amount traveling through the spherical surface isHowever, according to Crank,[21] the case when is defined as a plane sheet, and b/a ≥ 4 is a hollow sphere, so it does not seem unreasonable to consider the bitumen nanoscale films used in the present work, which had thicknesses below 1.25 μm, as plane sheets since b/a is approximately 1 due to the fact that the size of the spherical particle used as a solid support is orders of magnitude larger than the film thickness. Regarding the irregular-shape particles, when their size dimensions were converted into an equivalent diameter using the concept of sphericity, such particles also satisfied the above plane sheet requirement.

Results and Discussion

SEM

Scanning electron microscopy images of samples A, B, and C before and after bitumen coating are shown in Figure a–c respectively. Since the thicknesses of the bitumen films and the size of the particles differ by orders of magnitude, it is impossible to see the bitumen films, which are in the nanoscale in these images. However, given the uniform coating achieved on similar particles, it was assumed that the bitumen film was evenly coated on all samples. As can be seen in Figure b, after bitumen coating, some fine clay particles in sample B attach to the surface of large sand particles. Figure c clearly shows that the shape of the particles in sample C is irregular. Although bitumen may not be coated uniformly on the edges of such particles, it is also assumed that the film thickness is uniform in order to calculate the corresponding diffusion coefficients.

Figure 1

SEM images. Left images represent the particles before coating (scale bar = 100 μm); right images show the particles after coating (scale bar = 20 μm): (a) sample A, (b) sample B, and (c) sample C.

CHNS Analysis

The CHNS analysis was used to determine the actual amount of coated bitumen on the samples. The results are shown in Table .

Table 1

Amount of Bitumen Coated on Various Substrates (wt %)

sample A	0.20 ± 0.02
	0.74 ± 0.04
	1.10 ± 0.07
	1.14 ± 0.10
	2.23 ± 0.65
sample B	0.11 ± 0.01
	0.54 ± 0.04
	0.88 ± 0.11
	0.98 ± 0.12
	2.55 ± 0.69
sample C	0.62 ± 0.09a
	0.78 ± 0.00
	1.01 ± 0.19
	1.86 ± 0.10
	2.06 ± 0.12

Soxhlet solids after the Dean–Stark extraction with no bitumen added (the sample still contains a small amount of residual bitumen).

In general, the mass of bitumen actually coated on the particles was approximately half of the bitumen that was initially used for the coating process. This is attributed to the unavoidable loss of bitumen that coated on the walls of glassware. However, the range of the bitumen actually coated (i.e., 0.5–2 wt %) corresponds to that observed in gangue obtained from the solvent extraction process.[26] The “average thickness” of each sample was calculated as the thickness on particles of each mass fraction “weighted” against the total surface area of the sample calculated based upon the surface area of particles in each mass fraction. The details of the average thickness calculations are given below.

To calculate the thickness of sample A, we first estimated the number of glass beads: based on spherical geometry, the volume of one particle was calculated. Then, the mass of one particle was found as a product of volume and borosilicate density. To estimate the total amount of particles in the monodisperse sample, the total sample mass was divided by the mass of one particle. The mass of bitumen on each glass bead was determined based on the assumption that bitumen was evenly distributed among the glass beads. Using the estimated mass of bitumen on each particle (from the bitumen content analysis) and known bitumen density at room temperature, we then calculated the volume of bitumen on each glass bead (spherical shape), thereby the bitumen film thickness.

In the case of sample B, the average thickness was calculated as follows: the sample with known average bitumen content was separated based on the particle sizes using four sieves (500, 212, 150, and 45 μm). Then, the average bitumen content was measured on each size fraction using the CHNS analyzer, each measurement of the size fraction sample was repeated five times, and the average value was calculated. For instance, for the sample with 0.54 wt % average bitumen content, it was found that the average bitumen content on particles with a diameter of 500 μm and larger was 0.39 wt %, that with a diameter of 212 μm was 0.48 wt %, that with a diameter of 150 μm was 0.61 wt %, and that with a diameter of 45 μm and smaller was 0.89 wt %. Then, as mentioned before, the average thickness on each size fraction was calculated by finding the volume of bitumen on each glass bead. Using the estimated number of beads of each size in the sample, the total surface area of all beads and the surface area provided by each size fraction of beads were estimated. For instance, it was found that the surface area of beads with a size of 45 μm and smaller accounted for almost 30% of the total surface area of the sample even though the weight fraction of such fine particles was only around 5%. Then, the average thickness weighted by the area fractions was calculated: “surface average thickness” was found as a summation of the thickness of bitumen on particles of one size multiplied by the fraction of surface area these particles account for in the total sample area. This procedure was then repeated for the remaining four coating ratios, and the average thickness was calculated for each sample.

Similarly, the thickness was estimated for sample C. However, due to the shape of the particles being irregular, the equivalent diameter was calculated using the sphericity, Φs,[27] defined as the surface-volume ratio of a sphere divided by the surface-volume ratio of an irregular particle as given in eq :

Assuming that the volumes of particles with the same apparent size (i.e., passed the same sieve) are approximately the same, we end up with

Here, D is the diameter of the particle. Therefore, as suggested by eq , the ratio of diameter of the sphere and the corresponding diameter of the irregular-shape particle is equal to the square root of sphericity, which was chosen to be 0.65 (tabulated for crushed glass or flint sands),[27] and the diameter of the spherical particle was calculated as a product of the irregular-shape particle diameter and the square root of 0.65. This means that, for the particle with an irregular shape, as in sample C, the equivalent diameter of the spherical particle is smaller. Calculated thickness values for all samples are summarized and plotted in Figure .

Figure 2

Calculated bitumen film thickness based upon the amount of bitumen coated (wt %) on various samples.

Gravimetric Absorption Analysis

To determine the diffusion coefficients and solubility of cyclohexane for all 15 samples, the corresponding absorption curves were obtained. For illustration purposes, only the absorption curves for sample A at the lowest and highest bitumen film thicknesses and two cyclohexane RS (20 and 90%) are shown here (see Figure ). The rest of the absorption curves are shown in the Supporting Information (see Figures S1–S3). As Figure shows, the initial rate of absorption (the initial slope), regardless of the RS, decreases with increasing bitumen film thickness and a higher cyclohexane RS yields a shorter time for reaching equilibrium. The cyclohexane RS dependence is consistent with the concept of Henry’s law where solubility increases with increasing partial pressure of the solvent involved. However, the first observation deserves some explanation.

Figure 3

Cyclohexane absorption curves of sample A at two bitumen film thicknesses and two cyclohexane relative saturations.

To get insight into the above absorption curves, two models were attempted to fit into the mass uptake data: the Weibull relaxation model and double-first-order kinetics model.[1,6,28,29] The Weibull model (eq ) with a relaxation parameter ς related to the relaxation time of viscoelastic materials[29,30] was previously found to be a good fit for data for water absorption in polymers:It appeared that the Weibull model, which assumes only one stage of diffusion, does not fit well to the present experimental data, suggesting that there exists more than one diffusion mechanism involved in the absorption process. On the other hand, the double-first-order (DFO) kinetics model (eq ) shows a much better fit of the experimental data, which suggests that there are two kinetic mechanisms involved in the uptake of cyclohexane by the nanoscale bitumen film:

Here, ϕ is the mass fraction of the bitumen in which diffusion takes place by the first mechanism and k1 and k2 represent the rates of the mass uptake at the initial and final stages of absorption, respectively. The fitting was done to all samples. Fitting of the DFO kinetics model to all samples is shown in Figure S4 in the Supporting Information. For convenience, only the lowest and the highest bitumen film thicknesses for sample A are shown. Figure shows the DFO kinetics model fit into the experimental data. Black lines represent experimental data, while the red lines are those for the DFO kinetics model.

Figure 4

(A) Fitting of the double-first-order kinetics model into the absorption data for sample A with 108 nm film thickness: (a) 90% cyclohexane saturation and (b) 20% cyclohexane saturation. Black curves signify experimental data; red curves signify the fitted DFO kinetics model. (B) Fitting of the double-first-order kinetics model into the absorption data for sample A with 1250 nm film thickness: (a) 90% cyclohexane saturation and (b) 20% cyclohexane.

All k values for fitted absorption curves of samples A, B, and C are summarized in Tables S1–S3, respectively, of the Supporting Information and are plotted in Figure . All k values plotted as a function of thickness in one plot are shown in Figure S5. It is clear from Figure that k1 (initial absorption rate) decreases while k2 (final absorption rate) increases with increasing bitumen film thickness. Since the initial dissolution rate is used to determine the diffusion coefficients, let us explore the thickness dependence of k1. First, it is worth pointing out at the outset that bitumen is a chemically inhomogeneous material. Bitumen consists of four class fractions, namely, saturates, aromatics, resins, and asphaltenes (known as SARA in the petroleum industry).[31] For example, bitumen used in the present work contains by weight ∼10.3% saturates, 5.3% aromatics, 62.3% resin, and 22.2% asphaltenes. Also, such fractions exhibit a range of polarities with the asphaltenes fraction being the most polar. Given that the substrates used in this work are hydrophilic, it is believed that most polar molecules (e.g., asphaltenes) are attracted to the substrate surfaces while the relatively nonpolar molecules (e.g., saturates) tend to reside in regions near the free surface. This naturally generates a concentration gradient of polar (or nonpolar) molecules in the film thickness direction. It should be emphasized that the concentration gradient does not signify a phase separation from a thermodynamics perspective. Since k1 is the largest for the thinnest film and cyclohexane is nonpolar, the thickness dependence of k1 suggests that the concentration of nonpolar molecules near the free surface regions of the thinner bitumen films is higher than those of the thicker bitumen films. On the other hand, the concentration of polar molecules near the substrate surface of thinner bitumen films should be higher than those of the thicker films. This leads to a slightly positive thickness dependence of k2. This is because the dissolution process taking place in the final stage involves the dissolution of cyclohexane into a relatively polar environment in the region near the substrate surface.

Figure 5

Rate constants k1 and k2 as determined by fitting the double-first-order kinetics model to the absorption curves of all samples.

The average diffusion coefficients and the equilibrium solubility of cyclohexane at different bitumen film thicknesses are shown in the Supporting Information section (see Tables S4, S5, and S6). The results are also plotted against bitumen film thickness and are shown in Figures and 7.

Figure 6

Absorption diffusion coefficient of cyclohexane in bitumen: solid symbols indicate a cyclohexane relative saturation of 90% while open symbols indicate a 20% cyclohexane relative saturation: sample A, black; sample B, red; sample C, blue.

Figure 7

Solubility of cyclohexane in bitumen: solid symbols indicate a cyclohexane relative saturation of 90% while open symbols indicate a 20% cyclohexane relative saturation: sample A, black; sample B, red; sample C, blue.

Obviously, the measured diffusion coefficient exhibits thickness dependence but essentially no RS dependence while the solubility data exhibits the opposite behavior. Let us discuss the diffusivity behavior first. Unlike the observed thickness dependence of k1, the diffusion coefficient increases with increasing bitumen film thickness. According to eq , the one we used to determine the diffusion coefficient shows explicit positive thickness dependence. However, there is also an indirect thickness dependence term in the equation and that is the mass uptake term. The mass uptake term (M/M∞), as quantified by k1, exhibits a negative thickness dependence. Such opposite thickness dependence in eq suggests that when a film is very thick (k1 becomes relatively small), and the diffusion coefficient would be thickness-independent as observed experimentally.[5] However, when the bitumen film thickness is at the nanoscale (i.e., k1 becomes relatively large and is in the order of 10–2), the diffusion coefficient shows an overall positive thickness dependence.

The above discussion alludes to the idea that the substrate chemical properties could affect the diffusion in nanoscale bitumen films. This speculation was reported for polymer films.[5,14] Despite both polymers[5] and bitumen exhibited the thickness dependence effect, the underlying molecular mechanisms may be different. First, polymers are chemically homogeneous substances while bitumen is not. Unlike the case of polymers, diffusion of cyclohexane in bitumen is a complex process that takes place in a mixture of chemically different species. Second, the molecular weight of polymers is significantly higher than the molecular weight of bitumen (up to hundreds of thousands of Daltons versus up to only hundreds of Daltons for bitumen).

The measured diffusion coefficient appeared to be dependent on particle size distribution (Figure ). At a given thickness, the measured diffusion coefficient of sample A was higher than those in samples B and C. The effect is more pronounced at high film thickness. This is due to the fact that the average thicknesses of samples A, B, and C were different with sample A having the thickest films.

As the calculations show, the measured diffusion coefficients are of the order of ∼10–16 m2/s, which indicates an extremely slow diffusion process. However, such slow rates of diffusion were previously reported by Kokes and Long[32] in their study of organic vapor diffusion in poly(vinyl acetate). In that study, the diffusion coefficients were estimated to be 0.48 × 10–16 and 1.3 × 10–15 m2/s for benzene and acetone, respectively. Kokes and Long attributed such observation to the strong interactions present in the systems as quantified by the Flory–Huggins interaction parameters. The evaluation of the Flory–Huggins interaction parameters might be also informative for further understanding of the solvent–bitumen interaction of our systems.

Unlike the diffusion coefficient, the solubility did not exhibit thickness dependency but showed a strong cyclohexane RS dependence. The cyclohexane RS dependence seems to be consistent with the concept of Henry’s law where solubility increases with increasing partial pressure of the solvent involved.[33] However, in this work, it is not sure whether such dependence is linear or not as only two RSs were used. While the saturation concentration values seem to be almost the same for all three samples at 20% cyclohexane RS, the results for 90% RS seem a bit more disperse: in particular, sample C exhibits slightly lower values. There is no obvious reason for it; however, we believe that this might be due to the irregular shape geometry of the particles in sample C. The irregularity of the shape might create capillaries impermeable to cyclohexane but still containing some bitumen accounted for in thickness calculations.

Conclusions

In this study, the thickness dependence of the diffusivity and solubility of cyclohexane in a nanoscale bitumen thin film coated on particles with different shapes and size distributions was studied at ambient conditions using a gravimetric technique. A good fitting of the double-first-order-kinetics model to the experimental data suggested that there existed a concentration gradient of polar (or nonpolar) bitumen molecules in the film thickness direction with higher concentration of more hydrophilic molecules near the hydrophilic substrates (slower diffusion) and more hydrophobic molecules near the free surface (faster diffusion). This led to the observation of the thickness dependence of the diffusion coefficient in nanoscale bitumen films. The diffusion coefficient was observed to increase with increasing thickness of the bitumen film. It appeared that relative saturation of cyclohexane in the vapor phase had no effect on the measured diffusion coefficient. Monodisperse particles (sample A) yielded higher diffusivity compared to the polydisperse particles (samples B and C). This is because the mean bitumen film thickness of sample A was higher than those of samples B and C. The measured values of diffusion coefficients at the initial absorption stages were found to be in the range of 10–18 to 10–16 m2/s. Unlike the diffusion coefficient, the saturation concentration of cyclohexane in nanoscale bitumen films appeared to have no thickness dependence; however, a strong relative cyclohexane vapor saturation dependence was observed. The solubility of cyclohexane in bitumen films was not affected by the concentration gradient present in the nanoscale films but only by the partial pressure of cyclohexane in the carrier gas.

Experimental Section

Materials

The gangue was collected after the non-aqueous extraction (Dean–Stark extraction) described elsewhere in the literature[26] using oil sand-rich grade ore that was provided by Imperial Oil. The ore contained 11.5 ± 0.6% bitumen content by weight. ACS-certified cyclohexane was purchased from Fischer Chemical. Spherical borosilicate glass beads (standard sizes: 425–600, 150–212, ≤160 μm) were purchased from Sigma Aldrich. USA. Standard test sieves nos. 35, 70, and 100 were purchased from Fischer Scientific, USA. Standard testing sieve no. 325 was purchased from Advantech Manufacturing. Pure kaolin clay (irregular shape clay particles) with size of <45 μm was purchased from Acros Organics. Nitrogen, the carrier gas, was purchased from Praxair (99.999% purity).

Sample Preparation

As mentioned, three types of particles were of interest in the present work and they were all coated with bitumen at various bitumen particle weight ratios: Sample A contained monodisperse spherical glass beads with a size of 150 μm. Sample B contained polydisperse spherical glass beads (600–45 μm) mixed with fine (<45 μm) glass beads and fine kaolin clay (<45 μm) particles. The fine kaolin clay to fine glass bead weight ratio was 45:55. As in the original gangue, the mean particle size by weight in sample B was 150 μm. Sample C contained reconstituted gangue composed of irregular-shape particles with a mean diameter of 150 μm by weight.

Sample A

The purpose of preparing sample A is to create a reference sample containing monodisperse particles with a spherical geometry that represents the gangue particles. Considering the fact that gangue contains essentially particles with an irregular shape and that the concept of sphericity is used to quantify their size, we decided to use spherical particles as the reference particles.[27]

Given that the weight average diameter of the real gangue sample was approximately 150 μm, spherical borosilicate glass beads with a diameter of 150 μm (monodisperse) and a particle density of 2.26 g/cm3 were used. Figure shows two glass beads with a diameter of 3 mm with and without coated bitumen. The coated glass bead had approximately 0.2 wt % bitumen. The coating was carried out using a rotary evaporator Heidolph Hei-VAP Core. Bitumen was first dissolved into cyclohexane, and the solution with a concentration of 0.05 g bitumen/1 mL of cyclohexane was mixed with glass beads (monodisperse) in a round flask so that the calculated mass of bitumen was 0.5 wt % of the mass of glass beads. The round flask was connected to the aforementioned rotary evaporator so that the cyclohexane was slowly evaporated. The evaporation of solvent was carried out at a speed of 40–60 rpm and 55 °C for approximately 6 h followed by vacuum drying at 60 °C for 4 h. The reason for using a rotary evaporator was that bitumen films with a uniform thickness would be obtained. This was previously achieved in our lab by using the rotary evaporator for coating on glass beads.[34]

Figure 8

Bare spherical glass bead with a diameter of 3 mm (right) and a similar-size glass bead coated with a layer of bitumen (left) using a rotary evaporator. The amount of coating was ∼0.2 wt % or ∼1 μm thick.

The thickness was controlled by varying the amount of bitumen solution added to each sample before rotary evaporation. For a given sample of particles, at the start, we arbitrarily added 1 mL of bitumen solution to it. After the rotary evaporation and vacuum oven conditioning, the amount of bitumen settled on the particles was calculated (mass difference before and after). After the thickness was calculated as described below, we estimated the amount of bitumen solution needed to be added to achieve the desired range of thicknesses.

The CHNS analysis was later done to determine the actual mass of bitumen coated. Nonetheless, it appeared that the bitumen was evenly coated on the entire glass bead (Figure ).

Sample B

This sample was composed of two broad classes of particles. They were spherical borosilicate particles (45–600 μm) and fine particles (<45 μm) made up of fine kaolin clay mixed with fine glass beads.[24,26] To mimic the gangue characteristics, for sample B, we mixed the aforementioned types of particles with a particle size weight distribution and weight average diameter similar to those of real gangue. To do so, we mixed borosilicate glass beads of various sizes, 45 to 600 μm (glass beads were also sieved to separate them by size) using the same weight ratios of different sizes as found in gangue and given in Table . For the fine particles, 55% of the required amount was “modeled” by the glass beads with less than 45 μm diameter and the remaining 45% was “modeled” by using fine kaolin clay particles. The ratio 55:45 was used from the previously reported fine particle composition.[24] Kaolin clay was sieved on a 45 μm sieve, and the clay particles passing the sieve were collected and used as the model of fine particles, which are reported to clays, predominantly kaolin. The coating procedure was the same as that used for sample A. Again, SEM imaging and CHNS analysis were done for the sample characterization.

Table 2

Particle Size Distribution of the Gangue

size	wt %
>500 μm	7.4
500 μm > ... > 212 μm	11.3
212 μm > ... > 150 μm	50.5
150 μm > ... > 45 μm	25.1
<45 μm (fine)	5.7

Sample C

The residual solids after the Dean–Stark procedure was divided into small portions, placed on weighing dishes, and left overnight in a fume hood. After drying in a fume hood, the gangue was placed into a vacuum oven at 60 °C for 4–6 h to remove any traces of solvent that could have potentially been left in the residual solids. The vacuum-dried gangue was then collected and sieved through four standard testing sieves (500, 212, 150, and 45 μm). The approximate size distribution by weight is given in Table and the corresponding weight average diameter was calculated. One noteworthy point is that the Dean–Stark procedure did not remove all bitumen (Table ).

The same coating procedure used for sample A was used. The resultant sample was subjected to SEM and CHNS analysis.

Experimental Methods

Scanning Electron Microscopy

SEM images were obtained on a Zeiss Sigma Field Emission–Scanning Electron Microscope (FE-SEM). The beam voltage was set to 10 kV, and the working distances were in the range of 5–15 mm. An in-lens detector was used.

CHNS Analysis

A Thermo-Scientific Flash 2000 CHNS/0 analyzer was used to determine the bitumen contents of all samples. For each sample (i.e., samples A, B, and C), there were five bitumen samples with different contents prepared. As a result, there were a total of 15 samples. For each sample, the bitumen content measurement was repeated five times and the corresponding average value is reported.

Gravimetric Absorption Analysis

Mass uptake was measured using the Hiden Isochema intelligent gravimetric analyzer (IGA). The experiment setup and operation protocols are described elsewhere.[18]Figure shows a schematic setup for the instrument. The temperature of experiments was set to 25 °C. The temperature was chosen to be as close as possible to the normal ambient temperature and at the same time high enough to avoid condensation of cyclohexane on the sample surface. The pressure was set to the atmospheric pressure 1 atm. Both temperature and pressure were controlled throughout the entire experiment. The temperature was controlled using a water bath temperature controller. First, the sample was subjected to an 8 h conditioning when the sample was retained in a carrier gas (N2) environment at a constant flow rate of 100 mL/min to remove any residual volatile compounds and impurities before the experiment as suggested by previous observations and experiments.[18] Then, in the next step, cyclohexane was introduced into the carrier gas stream at the RS of interest (20 or 90%) one value of RS at a time. This was done to compare if there could be any variations in the diffusion coefficients in low and high RS cases. RSs of 20 and 90% were limited by the instrumentation to avoid condensation. The change of mass of the sample, which was measured by a microbalance with an accuracy of ±0.1 μg was monitored as a function of time. All experiments were repeated at least three times.

Figure 9

Schematic representation of an IGA system.