Diffusivity of CO2 in Bitumen: PressureâDecay Measurements

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Diffusivity of CO2 in Bitumen: Pressure−Decay Measurements Coupled with Rheometry Ehsan Behzadfar and Savvas G. Hatzikiriakos* Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, V6T 1Z3, Canada ABSTRACT: The combined pressure-decay technique with rheometry is developed to measure the diffusivity of carbon dioxide (CO2) in bitumen at temperatures of 30, 50, and 70 °C and pressures of 2 and 4 MPa. Mixing due to shear imposed by a rheometer allows rapid direct measurement of the equilibrium pressure in CO2−bitumen systems accurately. The comparison of the measured equilibrium pressures with the values obtained from the data regression demonstrates significant discrepancies, which can lead to a great deviation in the diffusivity, up to 5-fold different than the true values. The measured values for the diffusivity of CO2 into the bitumen increase with temperature, following the Arrhenius equation. By changing the temperature from 30 °C to 70 °C, the diffusivity increases by 88% at 2 MPa and 54% at 4 MPa. The diffusivity also increases with the pressure, suggesting the ease of diffusion at the presence of the CO2 molecules in the liquid phase. The effect of pressure is more dominant at lower temperatures while the diffusivity increase is 53% at 30 °C, compared to 25% at 70 °C. Furthermore, the findings demonstrate that the CO2−bitumen system does not follow any constant pattern in the diffusivity−viscosity− temperature relationships, which is due to the ongoing phase change at the studied temperature range.

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INTRODUCTION Diffusion takes place as a result of the random and thermal motion of molecules and originates from a gradient in the chemical potential (usually concentration) of a component in a multicomponent system. Diffusivity (diffusion coefficient) is a physical parameter, which is used to describe the diffusion process quantitatively. In general, the diffusivity measurement techniques are classified as direct and indirect techniques. Direct techniques include the compositional analysis of the mixture,1,2 while indirect techniques encompass measurement of the physical properties, which are correlated to the diffusivity.3−14 The indirect measurements in gas−liquid systems may include measurement of the pressure of the diffusing gas,3−6 the gas−liquid interface level,7−9 the density of the liquid phase,10−12 the refraction of electromagnetic radiation,13 and the swelling of a pendant droplet.14 One of the most popular techniques to measure the diffusivity of the gas−liquid systems is the pressure−decay technique, which was introduced by Riazi3 for reservoir fluids. Unlike other conventional techniques, the pressure−decay technique is convenient, simple, and accurate for engineering applications.4,6 In the oil and gas industry, this technique is widely used to measure the diffusivity of gases into different oils. Carbon dioxide (CO2)−heavy oil/bitumen systems have recently drawn a great deal of attention, because of the growing tendency to use CO2 in the enhanced oil recovery, while attempting to store it in depleted reservoirs. Table 1 lists several studies that have employed the pressure−decay technique to determine the diffusivity of CO2 in heavy oils and bitumens.4−6,15−17 In the pressure−decay technique, the pressure of the gas phase is monitored over time, while the molecules diffuse into the liquid. The diffusion equations in the gas and liquid phases, along with the mass conservation equations on the interface, then are solved to calculate the diffusivity. To solve the diffusion equations, a sufficient number of boundary conditions © 2014 American Chemical Society

should be imposed. An assumption for the concentration of the gas at the interface is an influential factor for which three different assumptions are commonly used. The first assumption, termed as the equilibrium boundary condition, considers the gas concentration at the interface as the saturated concentration of the gas at the equilibrium pressure, which remains the same during the diffusion process.3,4 The second assumption is to consider the interface concentration as the saturated concentration that corresponds to the overhead pressure, which continuously varies with time,5,6 termed as the quasi-equilibrium boundary condition. Finally, the last assumption is to consider the nonequilibrium boundary condition, where the interface concentration is calculated from a linear equation between the diffusant mass flux and the difference of the saturation concentration at the equilibrium pressure and the present concentration at the interface.18,19 Numerous studies have investigated the effect of the three different boundary conditions on the diffusivity of the CO2−heavy oil/bitumen systems.15,20 Sheikha et al.15 showed that these assumptions did not influence the calculated value of diffusivity more than 14.1%, while Tharanivasan et al.20 reported a significant influence at small diffusion times. Besides choosing proper boundary conditions, selecting appropriate values for the initial and equilibrium pressures is notably important for the diffusivity calculations in the pressure−decay technique.21 Yang and Gu14 ignored the early interface filling and thermal instability phenomena in their measurements and selected the pressure at the isothermal point as the initial pressure. Sheikha et al.21 discussed the uncertainties in selecting the initial pressure and demonstrated that the values of diffusivity are strongly influenced by the initial Received: November 27, 2013 Revised: January 21, 2014 Published: January 21, 2014 1304

dx.doi.org/10.1021/ef402392r | Energy Fuels 2014, 28, 1304−1311

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Table 1. Selected Studies Using the Pressure−Decay Method To Measure the CO2−Oil Diffusivity authors 4

Zhang et al. Upreti and Mehrotra5 Upreti and Mehrotra6 Sheikha et al.15 Tharanivasan et al.16 Unatrakarn et al.17

liquid phase

T (°C)

p0 (MPa)

peq (MPa)

D (× 109 m2/s)

remarks (B.C. and assumptions)

heavy oil Athabasca bitumen Athabasca bitumen bitumen heavy oil heavy oil

21 25−90 50−90 75, 90 23.9 30−55

3.4 4 8 4 4.2 3.1

∼2.85 ∼3.1−3.5 N/A ∼3.1−3.2 ∼3.5 ∼2.6

4.76 0.16−0.47 0.40−0.93 0.51−0.79 0.46−0.57 0.34−0.36

equilibrium quasi-equilibrium quasi-equilibrium quasi-equilibrium equilibrium, quasi-equilibrium, nonequilibrium nonequilibrium

value of pressure. Zhang et al.4 reported that the diffusivity is highly sensitive to the estimated value of the equilibrium pressure, while it varies up to 6.38% by altering the equilibrium pressure value only by 0.2%. For gas−liquid mixtures comprised of highly viscous liquids such as heavy oils and bitumen, the equilibrium state of the mixture is unreachable in the absence of any mixing. This is indicative of the difficulties in determining the equilibrium pressure with certainty. Several techniques have been employed to predict the equilibrium pressure in such systems.4,17−20 Most studies have used the extrapolation method (or asymptotic line) to predict the equilibrium pressure,4,17,20 while a few have examined other methods such as model-assisted analysis,18 solubility data analysis,16 and optimization method.19 However, the reported values are only predictions to the realistic equilibrium pressure. In this paper, the pressure−decay technique is combined with rheological experiments not only to measure the equilibrium pressure precisely, but also to determine the diffusivity based on the final equilibrium state. Mixing due to shear imposed by rheometry allows rapid direct measurement of the equilibrium pressure with a high degree of accuracy. This is achieved by monitoring both the viscosity and pressure of the system at the shearing step to ensure that the system reaches equilibrium. This is based on our previous studies, which indicate the sensitivity of the viscosity to small amounts of the dissolved gas in bitumen.22,23 The advantage of the proposed technique is that the diffusivity is calculated directly from the measured equilibrium pressure with no assumptions. In addition, it is easy to apply and it eliminates the errors from the uncertainty of estimating the equilibrium pressure.

can be considered an isothermal one-dimensional diffusion process occurring along the z-axis, which leads to: ∂c ∂ 2c ∂c =D 2 −ν ∂t ∂z ∂z

(1)

where c is the concentration of the diffusant in the liquid phase, t the time, D the diffusivity of the diffusant in the liquid phase, z the axis of diffusion, and ν the velocity in the liquid phase. Given the high viscosity of the liquid phase, the effect of the bulk flow is eliminated and, thus, the diffusion equation reduces to:

∂c ∂ 2c =D 2 ∂t ∂z

(2)

Assuming the equilibrium boundary condition for the concentration at the interface, the initial and boundary conditions are as follows: I.C.: for all z

t=0 c=0

(3a)

B.C.1: z = L c = csat (peq )

for t > 0

(3b)

B.C.2: z=0

∂c ∂z

=0

for t > 0 (3c)

z=0

The diffusivity is a physical parameter that is dependent on the diffusant concentration. However, since the variation of the diffusivity during a diffusion experiment is relatively small,5,6 it can safely be considered constant.4,16,17,21 The analytical solution of eq 2 for the concentration profile subject to the initial and boundary conditions described by eqs 3a−3c, is:

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THEORETICAL BACKGROUND The first step in the calculation of the diffusivity is to define the appropriate mass-transfer equations. As illustrated in Figure 1, for a nonvolatile liquid phase, the pressure−decay experiment

∞

c(t , z) = csat +

∑ (−1)n n=1

4csat (2n − 1)π

⎛ π2 ⎞ ⎛ π ⎞ exp⎜ −(2n − 1)2 2 Dt ⎟ cos⎜(2n − 1) z⎟ 2L ⎠ ⎝ 4L ⎠ ⎝ (4)

From the mass transport point of view, the mass flow rate of the gas through the interface is described as follows: dmg dt

= −DA

∂c ∂z

z=L

(5)

where mg is the mass of the gas phase and A is the crosssectional area of the interface. Assuming nonvolatile liquid, negligible swelling of the liquid phase (here, bitu-

Figure 1. Typical cylindrical geometry for the pressure−decay experiment. 1305


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men)4,15,17,20,24 and constant compressibility for the gas phase,4,15,25 the consumption rate of the diffusant molecules is: dmg dt

=

Table 2. Compositional and Elemental Analysis of the Bitumen

Vg

dp ZgRT dt

Compositional Analysis

(6)

where Vg is the volume of the gas phase, R the universal gas constant, T the temperature, Zg the compressibility factor of the gas, and p the pressure of the gas phase. In an isolated system, the consumption rate of the gas molecules is equal to the mass flow rate of the gas through the interface, which yields the following differential equation: ⎛

∞

Vg

2DAcsat dp =− ZgRT dt L

∑ exp⎜−(2n − 1)2 ⎝

n=1

π2 ⎞ Dt ⎟ 4L2 ⎠

8csatZgRTVl π 2Vg

∞

∑

(7)

n=1

1 (2n − 1)2

⎛ π2 ⎞ exp⎜ −(2n − 1)2 2 Dt ⎟ ⎝ 4L ⎠

2c*ART Vg

D πt

element

mass fraction

C H N S Oa atomic H/C ratio metal Fe V Mn Ni

83.42 10.10 0.52 4.77 0.79 1.45 ppm 1.99 126 0.15 34.4

Calculated from the difference of mass fractions of other elements from 1.

(8)

n-pentane completely. Both retentates and permeates were weighted to obtain the weight percentage of the asphaltenes and maltenes. Elemental analysis of the sample was performed using the 2400 Perkin−Elmer CHNS/O Analyzer by combustion at 1000 °C. The oxygen content was calculated from subtraction based on the weight contents of the other elements. Metal analysis data were provided from the supplier based on ASTM−D5600. The bitumen was stored at ambient temperature before testing and neither phase dissociation nor evaporation occurred. Carbon dioxide, with purity of 99.99%, was purchased from Praxair Co., Canada. Pressure Cell Setup. The pressure cell setup was consisted of various parts, including the gas cylinder, regulator, sample cylinder, pressure supply unit, pressure transducer, liquid cup, measuring geometry, thermocouples, and tubing between the parts. A schematic of the setup is depicted in Figure 2. The measuring geometry and cup of the pressure cell setup was mounted on a stress/strain controlled rotational rheometer (Model MCR501, Anton Paar, Austria). A fourblade vane geometry was used. The thickness of the blades was 1 mm, which was negligible compared to the cup diameter of 27 mm. The inner walls of the cup were separated from the spinning four-blade vane by 1.2 mm gap (vane diameter was 24.6 mm). The geometry in the pressure cell was driven by a magnetic coupling, which was attached directly to the torque measuring system of the rheometer. The special design of the cell makes the calibration and motor adjustment steps important. These were performed carefully using standard oils prior to each set of experiments. The advantages of using the vane−cup geometry are to minimize any potential of wall slip and increase the mixing efficiency, which is of great importance in reaching saturation. A certain amount of the oil was placed in the cup (∼18 mL), and the cup was sealed from the environment by means of tightening several screws and nuts. During this procedure, enough care was taken not to disturb the oil. Enough time was allowed for the oil temperature to reach equilibrium at the desired set temperature. Simultaneously, carbon dioxide was allowed to enter the sample cylinder (see Figure 2) and then the valve was closed. A preheat time of 60 min was applied in order to ensure stability of the gas temperature. The temperatures of the other parts of the setup were adjusted by means of rope heaters, thermocouples, and a temperature controller. Consecutively, CO2 was allowed to enter the cup by opening the valve between the sample cylinder and the pressure supply unit for a few seconds. As discussed above, CO2 started to saturate the interface (incubation stage), which caused the pressure to drop significantly.

(9)

where p0 is the initial pressure and c* is the instantaneous saturation concentration at the interface. Therefore, it is more accurate to obtain the diffusivity from the regression of eq 8 on the pressure profile excluding the initial pressure and the early stage pressure drop due to interface-filling phenomenon.

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18.32 81.68

a

where Vl is the volume of the liquid phase. In eq 8, it is assumed that, at infinity, the system reaches equilibrium where peq is the equilibrium pressure. The series in eq 8 is estimated by the first few terms in the right-hand side that yield the diffusivity if the function is fitted to the pressure profile in the pressure−decay experiment. Apart from the diffusion process occurring continuously in the pressure−decay experiment, an interface-filling (or incubation) phenomenon takes place by the gas molecules at the early stages of the experiment. During the interface-filling phenomenon, the pressure drops significantly and the pressure profile tends to deviate from eq 8. To describe this phenomenon, Danckwerts26 used the following model for the pressure decay of the gas: p = p0 −

mass fraction

C5 asphaltenes maltenes Elemental Analysis

Integration of eq 7 from an arbitrary t to infinity leads to: p = peq +

fraction

EXPERIMENTAL SECTION

Materials. The investigated gas−liquid system in this study includes bitumen as the liquid phase and carbon dioxide as the gas phase. The specific gravity of the bitumen sample was 0.97 at 22 °C. The compositional and elemental analysis of the bitumen sample are listed in Table 2. The asphaltenes and maltenes (saturates, aromatics, resins) contents of the bitumen were determined based on their solubility in n-pentane (see Table 2). The bitumen was mixed with n-pentane on a weight ratio of 1:40 and stirred overnight. The mixture was filtered twice using paper filters of different pore sizes, namely 1−5 and 0.2 μm, respectively. Filtration was accompanied with continuous vacuuming and extra solvent was used to make the filter paper colorless. The retentates were dried in an oven at 60 °C for 30 min and left in a vacuum oven at room temperature for 48 h. The permeates were placed in a rotary evaporator at 60 °C to remove the 1306


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Figure 2. Schematic diagram of the pressure cell setup. The experiment was conducted in three steps. No shearing was applied in the first step to capture the static diffusion process thoroughly. The second step was commenced after allowing the measuring geometry (vane) to spin gently at shear rates of 10−30 s−1. In the third step, saturation takes place by diffusion, which is facilitated by shear. Higher shear rates of 30−50 s−1 were applied to ensure the equilibrium state of the system. During testing, the viscosity and pressure are monitored simultaneously in order to ensure that the mixture has reached its saturated and final equilibrium state. The shear rates were imposed to the sample in a manner to avoid any potential disturbance or bubbling in the system. The nominal maximum pressure and temperature allowed by the specifications of the system were 15 MPa and 200 °C, respectively. The experiments were performed at three different temperatures, namely, 30, 50, and 70 °C (±0.01 °C). Two pressure levels were used for each temperature in order to investigate the effect of the pressure on diffusivity. The low-pressure measurements were conducted at ∼2 MPa, and the high-pressure experiments were run at ∼4 MPa. At 30 °C, the applied shear rates were lower since at these temperatures bitumen is solid-like and subject to fracture.22,23 The saturation of the bitumen with CO2 was monitored by observing the pressure and viscosity the experiment was considered as complete when no further reduction in pressure and viscosity were observed.

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RESULTS AND DISCUSSION The pressure profiles obtained from the pressure−decay experiments at 30, 50, and 70 °C are presented in Figures 3−5, respectively. The three steps of the experiment discussed above are separated by vertical dashed lines. As it is inferred from Figures 3−5, the pressure starts decaying once carbon dioxide is allowed to come into contact with the bitumen. This is the case for a period of ∼28 h (first step). This allows the pressure−decay analysis to be performed in order to calculate the diffusivity as described above. Once shear is applied, the pressure drops dramatically due to the shear-induced diffusion (second step). The second step continues for ∼35 h. To ensure the saturation of the system, a higher level of shear is applied in order to enhance the mixing until saturation occurs and, therefore, no further decrease in pressure and viscosity are observed (third stage). As shown in Figures 3−5, the high shear rate did not change the pressure level significantly, indicating that the equilibrium pressure was essentially reached during the shearing period at a moderate level. The level of shear has been selected carefully in order to avoid fluid instabilities that would cause bubbling or perturbation in the system, leading to wrong viscosity measurements. The Kelvin−Helmholtz instability is one of

Figure 3. Pressure−decay experiments at 30 °C: (a) initial pressure of p0 = 2.423 MPa and (b) initial pressure of p0 = 4.034 MPa. The experiment starts with diffusion under no shear and is followed by the application of shear (10 and 30 s−1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gasfree bitumen at the same temperature. The dashed line shows the fitted eq 8 using the measured value of the equilibrium pressure (peq), while the solid line is the fitted eq 8 with peq as an adjustable variable.

the common instabilities in the gas−liquid systems, which is prevented by satisfying the Richardson number (Ri) criterion,27 Ri ≡ 1307

g N2 1 =− ρ ≫ Ricr = 2 2 4 U ρ0 U dx.doi.org/10.1021/ef402392r | Energy Fuels 2014, 28, 1304−1311

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where N is the Brunt−Väisälä frequency, U the representative velocity of the geometry, g the gravitational acceleration, ρ0 the liquid density, and ρ̅ the density difference between liquid and gas in the interface. Bubbling might also happen due to cavitation if the shear rate exceeds a certain value. This phenomenon does not occur by choosing relatively low shear rates, which are 10−30 s−1 at 30 °C, and 30−50 s−1 at 50 and 70 °C. Another concern is with respect to the accuracy of the measurements, where a high shear rate should be selected to generate enough torque and, at the same time, be low enough to avoid the above instabilities. This concern is also eliminated by choosing the above-mentioned shear rates, which produce sufficient torques for accurate measurements. To determine the diffusivity values from the pressure-decay experiments, eq 8 was fitted to the first part of the pressure profile, shown in Figures 3−5. In order to examine the impact of the measured equilibrium pressure on the calculation, two scenarios are considered. In the first scenario, the parameters in eq 8 are calculated by presetting peq from the measured equilibrium pressures. In the other scenario, eq 8 is fitted to the experimental data by allowing the equilibrium pressure to be an adjustable parameter. Table 3 lists the calculated diffusivities from both scenarios. It also presents the measured peq along with the values obtained for peq as an adjustable parameter.

Table 3. Calculated Parameters from the Analysis of the Pressure-Decay Experiments T (°C)

p0 (MPa)

30

2.423 4.034

50

2.311 5.008

70

2.244 4.794

peq (MPa)

R2

D (× 109 m2/s)

adjustable measured adjustable measured

2.251 1.997 3.566 3.311

0.990 0.985 0.992 0.990

2.632 0.493 1.871 0.755


2.122 1.932 3.796 4.280

0.997 0.994 0.998 0.998

2.660 0.731 5.586 1.080


1.115 1.896 4.506 4.173

0.996 0.992 0.994 0.993

0.110 0.928 4.419 1.162

The values of peq determined from the data regression underestimate or overestimate the experimental values of the equilibrium pressure by 8% in the best case to 41% in the worst case. This can also be observed in Figures 3−5, where the two fitted lines diverge with time. This discrepancy influence the 1308


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equilibrium pressures: ∼2 MPa and ∼4 MPa. The diffusivity increases significantly with temperature, because of the increase of the molecular mobility with temperature increase, e.g., altering the temperature from 30 °C to 50 °C and 70 °C leads to increases of 88% and 54% in the diffusivity, respectively. This increase can be described by the Arrhenius equation effectively (dashed lines in Figure 6). These equations are listed in Table 4

diffusivities determined from the pressure-decay experiments. The calculated diffusivities show that the adjusted peq causes significant overprediction of the diffusivity values in most cases, except in one case that the diffusivity is underestimated. The diffusivities found by using the measured peq are in the range of the diffusivity values reported in the literature5,6,8 (see Table 1). The values are well below the self-diffusivity values of CO228−30 and lower than the diffusivities for CO2−heavy oil systems,4 yet slightly above the reported values for the CO2− Athabasca bitumen system.5,6 This is due to the difference in the oil composition which directly influences the physical properties including the diffusivity. This finding also emphasizes the usefulness of using the measured peq in the accurate determination of the diffusivity values using the pressure−decay experiments. Thus, an accurate measurement of peq is essential in the pressure−decay experiments, which is achieved practically by employing the combined pressure− decay technique with rheometry. Figures 3−5 also plot the reduced viscosity of bitumen with shear, as a function of time. The viscosity values are normalized to the viscosity of the pure bitumen, which is 490, 30.55, and 4.1 Pa.s at 30, 50, and 70 °C, respectively. The viscosity of the CO2−bitumen mixture decreases significantly with time, and this is due to the continuous CO2 diffusion into the oil. This decrease is neither due to thixotrophy nor due to shear thinning, since bitumen does not show any significant thixotropic or shear thinning behavior at temperatures above 30 °C.23 The decrease in viscosity is more dominant at lower temperatures and higher pressures, which leads to the dissolution of higher amounts of CO2 into the oil. This is in agreement with the findings reported previously in the literature.23,31 It can also be observed from Figures 3−5 that the viscosity values reach their steady-state values before pressure. This is because the height of the rotating geometry (here, a four-blade vane) is 19 mm, which is shorter than the total height of the liquid sample in the cup (28−31 mm). Thus, once the height of liquid phase in contact with the geometry is saturated with CO2, the viscosity measurements do not show any further reduction. However, the diffusion process continues to saturate the remaining liquid below the four-blade vane. Figure 6 depicts the calculated diffusivities from the above analysis, based on using the measured values of peq. These are presented as a function of temperature at two different levels of

Table 4. Arrhenius Equations for the Diffusivity and Viscosity of the CO2−Bitumen System activation energy (kJ)

fitted equation

p (MPa)

parameter

ambient

diffusivity viscosity

N/A

diffusivity

D = 1.17 × 10−7 exp −

2

viscosity

4

diffusivity viscosity

μ = 6.32 × 10−16 exp

(

103634 RT

)

N/A 103.6

( 13743 RT ) 70276 −11 μ = 3.54 × 10 exp( RT )

13.7

( 9436 RT ) 61401 −10 μ = 4.59 × 10 exp( RT )

9.4

D = 3.33 × 10−8 exp −

70.3

61.4

for different equilibrium pressures. The calculated activation energies, as presented in Table 4, suggest that the diffusivities are slightly more sensitive to temperature at lower pressures. Moreover, the diffusivity values show an increase with pressure, which indicates the effect of the dissolved gas in facilitating the diffusion process. At higher pressures, the solubility of CO2 in the bitumen increases as more gas is dissolved. This finding is in agreement with the trend reported for the CO2−heavy oil systems in the literature.6 The diffusivity increase with pressure is more significant at 30 °C (increase by 53%), compared to an increase of 25% at 70 °C. This is due to the higher solubility of the bitumen at lower temperatures.31 The measured viscosities are also plotted in Figure 6. The viscosity-temperature relationship is adequately described by the Arrhenius equations, listed in Table 4. The temperature causes the viscosity to decrease, while this decrease is more evident for the gas-free bitumen. This can be also inferred from the activation energies where a drop of 32% in the activation energy occurs by addition of CO2 when the pressure increases from ambient to 2 MPa. The role of temperature in decreasing the viscosity is slightly different at the two different equilibrium pressures, which is a difference within experimental error. Numerous studies have proposed models to account for the relationship of the diffusivity with temperature and viscosity.32,33 The most well-known model is Einstein’s model, which is D=

kT 6πRAμ

(10)

where k is the Boltzmann constant, RA the radius of the diffusing particle, and μ the viscosity of the liquid mixture. Other models have also been proposed based on Einstein’s model attempting to relate the diffusivity to temperature, viscosity, and molecular characteristics. These models suggest that the quantity of Dμ/T is constant for a given system and does not vary with temperature. In order to examine the accuracy of these models for the CO2−bitumen system, several

Figure 6. Measured diffusivities and viscosities against inverse of temperature at equilibrium pressures of ∼2 MPa and ∼4 MPa. The dashed lines show the Arrhenius equations fitted to every dataset. 1309


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while the diffusivity increase is 53% at 30 °C, compared to 25% at 70 °C.

groups of the parameters including diffusivity, temperature, and viscosity are plotted as functions of temperature in Figure 7.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Wen, Y.; Kantzas, A.; Wang, G. Presented at Canadian International Petroleum Conference, Paper 064, Calgary, AB, Canada, 2004. (2) Schmidt, T.; Leshchyshyn, T.; Puttagunta, V. Annual Technical Meeting of the Petroleum Society of CIM, Paper 82, Calgary, AB, Canada, 1982. (3) Riazi, M. R. J. Pet. Sci. Eng. 1996, 14, 235−250. (4) Zhang, Y. P.; Hyndman, C. L.; Maini, B. B. J. Pet. Sci. Eng. 2000, 25, 37−47. (5) Upreti, S. R.; Mehrotra, A. K. Ind. Eng. Chem. Res. 2000, 39, 1080−1087. (6) Upreti, S. R.; Mehrotra, A. K. Can. J. Chem. Eng. 2002, 80, 116− 125. (7) Das, S. K.; Butler, R. M. D. Can. J. Chem. Eng. 1996, 74, 985− 992. (8) Fadaei, H.; Scarff, B.; Sinton, D. Energy Fuels 2011, 25, 4829− 4835. (9) Jamialahmadi, M.; Emadi, M.; Müller-Steinhagen, H. J. Pet. Sci. Eng. 2006, 53, 47−60. (10) Zhang, X.; Shaw, J. M. Pet. Sci. Technol. 2007, 25, 773−790. (11) Song, L.; Kantzas, A.; Bryan, J. SPE Int. Conf., SPE 137545, New Orleans, LA, 2010. (12) Zhang, X.; Fulem, M.; Shaw, J. M. J. Chem. Eng. Data 2007, 52, 691−694. (13) Yu, C-S. L. The Time-dependent Diffusion of Carbon Dioxide in Normal-hexadecane at Elevated Pressures, M.Sc. Thesis; University of Calgary; Calgary, AB, Canada, 1984. (14) Yang, C.; Gu, Y. Ind. Eng. Chem. Res. 2006, 45, 2430−2436. (15) Sheikha, H.; Pooladi-Darvish, M.; Mehrotra, A. K. Energy Fuels 2005, 19, 2041−2049. (16) Tharanivasan, A. K.; Yang, C.; Gu, Y. Energy Fuels 2006, 20, 2509−2517. (17) Unatrakarn, D.; Asghari, K.; Condor, J. Energy Procedia 2011, 4, 2170−2177. (18) Civan, F.; Rasmussen, M. SPE J. 2006, 11, 71−79. (19) Civan, F.; Rasmussen, M. L. Chem. Eng. Sci. 2009, 64, 5084− 5092. (20) Tharanivasan, A. K.; Yang, C.; Gu, Y. J. Pet. Sci. Eng. 2004, 44, 269−282. (21) Sheikha, H.; Mehrotra, A. K.; Pooladi-Darvish, M. J. Pet. Sci. Eng. 2006, 53, 189−202. (22) Behzadfar, E.; Hatzikiriakos, S. G. Fuel 2013, 108, 391−399. (23) Behzadfar, E.; Hatzikiriakos, S. G. Fuel 2014, 116, 578−587. (24) Svrcek, W. Y.; Mehrotra, A. K. J. Can. Pet. Technol. 1982, 21 (4), 31−38. (25) Ghaderi, S. M.; Tabatabaie, S. H.; Hassanzadeh, H.; PooladiDarvish, M. Fluid Phase Equilib. 2011, 305, 132−144. (26) Danckwerts, P. V. Textbook of Gas−Liquid Reactions; McGraw− Hill Book Co.: New York, 1970. (27) Miles, J. Phys. Fluids 1986, 29, 3470−3471. (28) Groß, T.; Buchhauser, J.; Lüdemann, H.-D. J. Chem. Phys. 1998, 109, 4518−4522. (29) Winn, E. B. Phys. Rev. 1950, 80, 1024−1027. (30) Higashi, H.; Iwai, Y.; Arai, Y. Ind. Eng. Chem. Res. 2000, 39, 4567−4570. (31) Mehrotra, A.; Svrcek, W. J. Can. Pet. Technol. 1982, 21, 95−104. (32) Einstein, A. Textbook of Investigations on the Theory of the Brownian Movement; BN Publishing: Thousand Oaks, CA, 2011.

Figure 7. Various groups of parameters plotted as a function of temperature. The dashed lines are fitted lines to the experimental data. The viscosity symbols μbit and μ denote the viscosities of the pure bitumen and CO2−bitumen mixtures, respectively.

As Figure 7 shows, the quantity Dμ/T strongly depends on T for the CO2−bitumen system from 30 °C to 70 °C. The significant deviation from eq 10 shows that the CO2−bitumen should not be considered as a simple liquid phase, since elements of maltenes yet undergo the melting process as the temperature changes from 30 °C to 70 °C.34 The diffusivity itself, D, is also shown to be strongly dependent on T (doubles over a span of 40 °C).

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CONCLUSIONS The diffusivities of CO2 into bitumen are measured by employing a new technique that is the combined pressure− decay technique coupled with rheometry. This technique enhances mixing due to imposed shear and thus enables rapid direct measurement of the equilibrium pressure, which is essential in the calculation of diffusivity in gas−liquid systems as shown in this work. This technique benefits from the enhanced diffusion, induced by shear, after the initial diffusion process, which takes place in the absence of any shear. Thus, ensuring that no instability occurs in the system, the equilibrium state is reached efficiently even for highly viscous liquids. The comparison of the measured equilibrium pressure with the predicted equilibrium pressure, obtained from assuming it as an adjustable parameter, demonstrates the significant deviation of the true value, which leads to a great discrepancy in the calculated diffusivity, e.g., ∼5-fold for the CO2−bitumen system. The combined pressure−decay technique with rheometry eliminates the errors associated with the prediction of the equilibrium pressure by using various regression methods. The diffusivity for the CO2−bitumen system can be described by the Arrhenius equation (effect of temperature). The diffusivity increases with temperature (30−70 °C) by 88% at the equilibrium pressure of 2 MPa and 54% at the equilibrium pressure of 4 MPa, respectively. The calculated diffusivity increases with pressure suggesting the ease of diffusion in the presence of more CO2 molecules in the liquid phase. This increase is more dominant at lower temperatures, 1310


Energy & Fuels

Article

(33) Umesi, N. O.; Danner, R. P. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 662−665. (34) Bazyleva, A.; Fulem, M.; Becerra, M.; Zhao, B.; Shaw, J. M. J. Chem. Eng. Data 2011, 56 (7), 3242−3253.

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Diffusivity of CO2 in Bitumen: PressureâDecay Measurements

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Diffusivity of CO2 in Bitumen: PressureâDecay Measurements