Evaluating Diffusivity of Toluene in Heavy Oil Using Nuclear Magnetic

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Evaluating Diffusivity of Toluene in Heavy Oil Using Nuclear Magnetic Resonance Imaging Amir Fayazi, Sergey Kryuchkov, and Apostolos Kantzas Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02464 • Publication Date (Web): 05 Jan 2017 Downloaded from http://pubs.acs.org on January 23, 2017

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Evaluating Diffusivity of Toluene in Heavy Oil Using Nuclear Magnetic Resonance Imaging Amir Fayazi1, Sergey Kryuchkov1,2, Apostolos Kantzas1,2 1: Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, Canada 2: PERM Inc., Calgary, AB, Canada

Abstract Solvent-based processes have shown technical advantages over thermal techniques for recovery of heavy oil and bitumen. The success of these processes relies on accurate computation of molecular diffusion coefficient which determines how fast a solvent penetrates into oil. Concentration profile measurements of solvent in oil are used for the determination of the molecular diffusion coefficient. Although numerous experimental techniques have been proposed, the accurate estimation of this parameter is still a topic of debate in the literature. In this work, 1-D Nuclear Magnetic Resonance Imaging (MRI) is employed to obtain diffusivity data for a toluene-heavy oil system. Diffusion of toluene in heavy oil was monitored for 20 days at a controlled temperature of 35 °C and ambient pressure. Over time, toluene diffusion into oil leads to changes in spatial distribution of T1 and T2 that affect the received signal. This serves as the basis of the solvent and heavy oil concentration estimation. Consequently, concentration profiles were established by converting the MRI signals to concentration values. This conversion was achieved by creating samples with known concentrations of heavy oil-toluene and measuring their response in the same environment and parameter settings. A concentrationdependent diffusion coefficient was obtained from concentration profiles. The results show that

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relaxation based 1D MRI is an accurate and robust tool to obtain diffusivity data in complex fluids such as heavy oil. Keywords: Diffusion Coefficient; 1D MRI; Heavy oil; T1, T2 relaxation times; Toluene; Solvent

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Introduction There are about 1.7 trillion barrels of heavy oil and bitumen in Canada which cannot be recovered efficiently by conventional methods. Several techniques based on oil viscosity reduction have been applied in oil industry to produce from these challenging reservoirs 1. Thermal recovery processes using steam are inefficient and uneconomic particularly in reservoirs with thin pay zones, high water saturation and low porosity due to large heat losses 2. As an alternative, solvent based processes such as Vapour Extraction (VAPEX) and Solvent Aided Process (SAP) had proven to be good recovery candidates for these reservoirs. In these methods, less dense solvent diffuses into highly viscous heavy oil/bitumen, thus reducing its viscosity and allowing for improved flow of oil to the production well. However, the effects of solvents on heavy oil/bitumen must be understood prior to implementing in-situ solvent injection into a reservoir. Obviously, mass transfer is the first and most important mechanism to occur when solvent comes to contact with oil which is governed by diffusion coefficient. Diffusion coefficient calculations in complex fluids require measurements of concentration profiles and it is preferable to measure diffusion experimentally for each system because its value varies considerably with different oil/solvent pairs and it is sensitive to operating and reservoir conditions. Accurate diffusion data are necessary to determine (1) the amount and injection rate of solvent, (2) the extent of heavy oil/bitumen reserves that would undergo the viscosity reduction, (3) the time required by the reserves to become less viscous and more mobile as desired, and (4) the rate of diluted oil production from the reservoir 3. However, measurements of mass transfer characteristics are challenging due to difficulties in measuring point values of concentration and 3


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having a mixture rather than a pure fluid 4. Therefore, there is no universally applicable technique to calculate the diffusion coefficient values in different systems. The mass transfer of various solvents in heavy oil/bitumen have been experimentally determined by several researchers using (1) direct methods

5, 6

and (2) indirect methods. Direct

measurements of solvent mass transfer into oil require compositional analyses as a function of time which are expensive, time-consuming, and prone to large experimental errors. In addition, the need for compositional analysis disturbs the system which adversely affects the accuracy of the measurements. Therefore, mass transfer is usually determined indirectly by measuring other known properties of oil-solvent systems over time. In this case, changes in these properties reflect solvent mass transfer into oil 7. These properties could be solution volume 8, pressure 4, 9, 10

, transparency 11, 12, position of interface 8, 13, mixture density 14, etc.

Funk

15

studied the dissolution behavior of bitumen with low molecular weight parrafins at

ambient temperatures using a spinning disc technique, direct particle-size analysis, and a fluid bed contactor. Their experiments showed that paraffins leach the soluble oil from the bitumen and leave behind a porous network of insoluble asphaltenes. Fu and Phillips

16

determined the

diffusivities of volatile hydrocarbons in semi-solid Athabasca bitumen by a technique which involves diffusion of hydrocarbon from a bitumen-hydrocarbon solution into a flowing stream of nitrogen. They found out that the diffusivities of hydrocarbons in bitumen decrease with increasing molecular weight, branching of molecules, and presence of ring-shaped structures. Oballa and Butler

12

studied the diffusion process in bitumen-toluene system by a free diffusion

method using a vertical cell with closely spaced flat windows. They applied an optical method using infrared light to measure the concentration distributions in vertical direction. Their work 4


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showed that overall diffusion coefficient varies by an order of magnitude over the full concentration range (0 to 100%). In another work, Das and Butler

17

developed empirical

correlations for diffusivity of propane and butane in Peace River bitumen as a function of mixture viscosity using VAPEX experiments in a Hele-Shaw cell. X-ray Computer Assisted Tomography (CAT) has been used by several researchers to obtain concentration profiles

7, 14, 18-22

. CAT distinguishes multicomponent systems based on atomic

density differences. While this enables detection of both the rock matrix and contained fluids, low density difference between the solvent, bitumen, and their mixtures can be a restricting factor in application of X-ray CAT imaging for tracking the diffusion process, in other words, density contrast is low and comparable to the noise level. Salama and Kantzas

22

applied X-ray

Computer Assisted Tomography to monitor mass transfer of solvents in bulk heavy oil and bitumen. They also did a series of experiments to observe the diffusion of hydrocarbon solvents with heavy oils in the presence of sand by placing different solvents on top of oil/sand mixtures. The same technique was used by Luo, Kryuchkov and Kantzas

21

to obtain concentration

profiles. They extended the diffusion model for heavy oil-hydrocarbon solvent systems by combining the concentration profiles with data on volume changes. Zhang, et al.

23

used X-ray

transmission tomography to establish composition profiles within the liquid phase for bitumenpentane system and applied a data analysis method to account for the variation of mutual diffusion coefficient and density with composition. Later, Wen and Kantzas

24

used NMR

Relaxometry to measure changes of oil-solvent properties as a function of time. Since NMR Relaxometry only measures bulk properties without any spatial variability considerations, they had to use CAT scanning in parallel to obtain the spatial information. Sadighian, et al. 5


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measured the mutual diffusion coefficients and forced mass transfer coefficients for Athabasca bitumen-pentane and Athabasca atmospheric residue-pentane mixtures. They measured force mass transfer by placing a high shear impeller in the pentane-rich phase adjacent to pentanefeedstock interface and evaluated the mass transfer coefficients on the basis of interface movement over time and composition changes of well-mixed pentane-rich phase above the interface. In 2013, Fadaei, Shaw and Sinton

11

measured the toluene diffusivity in Athabasca

bitumen using a microfluidics approach. They quantified the one-dimensional diffusion process via through-plane visible light transmission imaging using the semitransparency characteristic of bitumen on the microscale. In this contribution, MRI is used to obtain diffusion data for static mixing of toluene and heavy oil. Then, diffusion equation is solved to back calculate the concentration-dependent diffusion coefficient from concentration profiles.

Diffusion Equation When two miscible fluids, which are not thermodynamically in equilibrium, are brought into close contact, transfer of one or more components may occur between them by molecular diffusion 8. Diffusivity can be measured experimentally by: (1) Steady state or quasi-steady state methods (diffusion flux is constant), (2) Unsteady state methods (diffusion flux changes with time) 12. The unsteady state diffusion process in the absence of chemical reactions is governed by Fick’ second law of diffusion:

∂C A ∂  ∂C  = D A  ∂t ∂x  ∂x 

(1)

6


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where C A is the concentration of diffusing substance A in B; x is the space coordinate; t is time; and D is the binary diffusion coefficient (here, heavy oil is assumed as a pseudocomponent)

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. This equation can be solved with two types of boundary conditions: (1) Infinite

boundary condition which physically is like having a bottomless diffusion cell, and (2) Finite boundary condition which either concentration or flux are assumed to be constant at boundaries. According to Guerrero Aconcha and Kantzas

14

, diffusion coefficient can only be considered

constant when: (1) the molecular diameter and shape of the molecules are similar, (2) the intermolecular forces are negligible, and (3) no reaction occurs between diffusion pair. These assumptions are not valid for solvent-heavy oil system. Therefore, in complex systems, diffusion coefficient in Eq. (1) is a function of concentration.

Solution of Diffusion Equation In most of the available literature, the diffusion coefficient is treated as a constant value at various concentrations of solvent in oil. However, some researchers have shown either experimentally or theoretically that this coefficient is concentration dependent

7, 12, 14, 19, 27-29

.

When diffusivity is a function of concentration, the partial differential equation (Eq. 1) can be converted to an ordinary differential equation by using the variable λ = x / t suggested by Boltzmann 30:

2 ∂  ∂C A  ∂C A =− D  ∂λ λ ∂λ  ∂λ 

(2)

Integrating Eq. (2) with respect to λ and substituting λ with x and t result in:

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DC =C1 = −

1  ∂x    2t  ∂C A C

∫

C1

0

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xdC A

(3)

1

where C1 is any concentration between 0 and initial concentration of substance A, C 0 . Solving Eq. (3) requires the calculation of the above integral and derivative terms. Here, the trapezoidal rule was used for integration and the central difference scheme was used for derivation. At concentration extremes, the integral term approaches zero while the derivative term approaches infinity, hence an accurate estimation of the diffusion coefficient is challenging there. It should be noted that this technique is suitable for infinite systems, and is used here for early concentration profiles before the diffusive front reaches the physical boundaries of the diffusion cell.

NMR Principles The phenomenon of magnetic resonance is most widely known through its applications in physics and chemistry and most recently in its medical application, MRI (Magnetic Resonance Imaging). Nuclear Magnetic Resonance (NMR) has been used frequently since the 1990s to determine porosity, permeability and pore size distribution 31, characterize heavy oil and bitumen 32-34

, determine compositions of oil/brine emulsions

viscosity

38

35-37

, and determine the heavy oil/bitumen

. Low field NMR (operating at magnetic field strengths on the order of 0.01 T) is

usually applied in oil industry, since it is more suitable for analysis of fluids in bulk and in porous media than high field NMR (operating on the order of 1T and higher) and also lower field measurements minimize the possibility of data degradation

39

. It should be noted that Nuclear

Magnetic Resonance is a general term used to describe magnetic resonance technology, however 8


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there are three different techniques which are currently used in petroleum industry: (1) NMR Imaging or MRI is used to determine the spatial distribution of fluids, (2) NMR Relaxometry is used for fluid typing and pore size analysis, and (3) NMR spectroscopy is used to determine the structure of compounds. Diffusion of solvent into oil as a function of time needs spatial information. NMR Relaxometry only provides bulk measurements without any spatial variability considerations. Therefore, NMR Imaging is used in this work to study the diffusion process (NMR Imaging and MRI are used interchangeably in this paper). It has to be noted that the method of this work relies mostly not on the image of the fluid saturation distribution, but on the image of the relaxation times distribution, as described later in the paper. Hydrogen protons have a property known as spin, which causes the protons to act as small bar magnets. In the presence of an external magnetic field B0 , the protons will tend to line up along the magnetic field, this process being counteracted by thermal motion. The protons are then tilted onto a transverse plane (x-y plane) by an oscillating magnetic field pulse B1 (t ) . When the magnetic pulse is removed, the tilted magnetization relaxes back to its longitudinal direction. The time constant, which describes how longitudinal magnetization M z returns to its equilibrium value M 0 , is called the spin-lattice relaxation time, T1 :

(

M z (t ) = M 0 1 − e −t / T1

)

(4)

The time constant, which describes the disappearance of the transverse magnetization M xy , is called the spin-spin relaxation time, T2 :

M xy (t ) = M xy0 e−t / T2

(5) 9


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By observing these two relaxation mechanisms, which is the basis of NMR Relaxometry, an incredible wealth of information can be obtained about the reservoir fluids under investigation. Magnetic Resonance Imaging resolves the NMR signal by spatially altering the magnetic field with magnetic field gradients. In a homogenous magnetic field, all nuclear spins within the sample precess at frequencies that are close to the frequency known as Larmor frequency, f L . When a magnetic gradient is applied during the signal acquisition, spins in different positions in the sample precess at different frequencies. If the frequency variation as a function of position is known, the spatial variation in spin density may be established via Fourier Transform of the time-dependent signal. For instance, under the application of a linear gradient field, the spatiallydependent precession frequency can be represented by:

f ( x) =

γ (B0 + g x x ) = f L + γ g x x 2π 2π

(6)

where γ is the gyromagnetic ratio and g x is frequency-encoding gradient

40

. Therefore, spatial

information can be extracted from the sample’s various precession frequencies. 1D MRI experiments are performed using a Hahn echo experiment and consist of a 90-degree radio frequency pulse, a 180-degree pulse, and two gradient pulses as shown in Figure 1 41. Gradients are characterized by their duration D and strength G. The echo is acquired during the second gradient pulse. In NMR experiments, samples with higher viscosity will relax faster than samples with lower viscosity. Protons in less viscous toluene have the T2 value on the order of seconds, but the T2 value for viscous heavy oil is much smaller (typically, on order of milliseconds). As a result, when solvent comes into contact with heavy oil/bitumen, the mobility of hydrogen bearing 10


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molecules of both solvent and oil changes. These changes are detectable through changes in the NMR characteristics of both solvent and oil and serve as an indication of mass transfer and mixing of the fluids and can be correlated to mass flux and concentration variations 42.

Experimental procedure The experiment was conducted in a sealed glass bottle 10 cm high and 5 cm in diameter. The glass bottle was first filled with heavy oil and then toluene was added to the top of the heavy oil, carefully and slowly, so that no convection currents were set up (Figure 2). Properties of the heavy oil are presented in Table 1. Toluene was chosen as a solvent because asphaltene precipitation does not occur with toluene compared to other solvents such as heptane and hexane. Then, the bottle was properly sealed to prevent solvent losses by evaporation. Initially, there is a sharp, well-defined, interface between the two fluids. The mass transfer process started immediately after the two fluids were placed in contact with each other at t=0. The diffusion measurement was vertical and static without any mechanical stirring or displacement to aid the mixing (delay of mixing due to density contrast is neglected). Therefore, diffusion happened only due to the concentration gradients. All NMR experiments were performed at a controlled temperature of 35 °C and ambient pressure with an “Oxford Instruments” NMR apparatus operating at a resonance frequency of 2.5MHz, which corresponds to hydrogen nuclei spin precession in magnetic field of ~0.06 T. The bottle was positioned in the sweet spot of the NMR machine for optimal results. The sweet spot, which is located approximately 5 cm along the centroid of the magnet, is the most homogeneous magnetic field volume of the magnet. It should be noted that in the presence of gradient in a static magnetic field, molecules move into a region

11


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with different magnetic field strength 42. This self-diffusion caused by magnetic field gradients is negligible. The NMR signal of the mixture is distinctly different from the signal of heavy oil and toluene. Over time, solvent diffusion into oil creates mixtures with the viscosities that are intermediate between the oil and solvent viscosities, and as a result, changes in the received signal. This is the basis of the solvent and heavy oil concentration estimation in this work. In other words, changes in the NMR signal were related to the change of oil and solvent concentration as solvent diffused into oil.

NMR Parameters In order to get a high resolution MRI profile, it is necessary to select proper experimental parameters such as sample size, gradient strength (G) and duration (D), number of acquisition points (SI), etc. Choosing these parameters is not a trivial task since an interdependence of the parameters exists. The amplitude of MRI signal depends on both T1 and T2 which are substantially different in the solvent oil, and their mixtures. At the time of the first echo (around which the signal is acquired for MRI measurement) the amplitude is:

A ∝ (1 − e

−

RD T1

−

)e

2·TAU T2

(7)

RD is the time between successive scans (typically several scans are performed in each measurement to increase the signal to noise ratio, SNR). TAU is the time between 90° and 180° pulses in one scan which should be selected based on T2 value of the sample. If it is longer than 12


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T2 , the acquired signal amplitude during the second gradient pulse in each scan is low and vice versa. In order to get a high contrast of the signal intensity in the mixing zone, it is necessary to suppress both solvent and oil signal amplitudes and increase the mixture signal amplitude to have a distribution of signal amplitude in mixing zone. Solvent, due to lower viscosity, has a long T1 (on the order of seconds) and its signal amplitude can be suppressed by shortening the RD. Heavy oil, due to higher viscosity, has short T2 (on the order of milliseconds) and its signal amplitude can be suppressed by increasing TAU by making it a few times longer than T2 . Within the mixing zone, the two factors in Eq. (7) act in favor of increasing the signal amplitude, since the mixture has a shorter T1 compared to solvent and a longer T2 compared to oil. Based on the above explanations, these two parameter (RD and TAU) were adjusted for the heavy oil-toluene system before starting the experiment. Some of the NMR parameters are listed in Table 2.

Results and discussion Concentration profiles The diffusion experiment was monitored for 20 days and composition changes that occurred in the vicinity of the original interface were detected by recording the NMR signal. The scanning was repeated every hour for the first day, and later on, every 12 hours. At each mixing time, the following data acquisition procedure was performed: 1- The NMR signal in the time domain was acquired during the second gradient pulse in two channels (Figure 3).

13


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2- Fourier Transform was applied to translate the signal from time domain to frequency domain which is linearly related to the position (Figure 4). 3- Magnitude over two channels was calculated (Figure 5a). The width of the signal is related to the length of the sample and the height variations reflect the variation in the amplitude in each cross section. The signal shown in Figure 5a is in the frequency domain which should be converted to space coordinates by comparing the width of signal response corresponding to a known fluid level. For this purpose, the responses of a sample with three different fluid levels were acquired which is shown in Figure 6. Using this figure, a conversion factor was obtained by counting the number of points corresponding to each fluid level and the resulting signal in space coordinate is shown in Figure 5b. The NMR signals for several mixing times after using the above linear point-to-length conversion are shown in Figure 7 (the ordinate is the signal amplitude and the abscissa is the sample length). The original oil-solvent interface was set at x=0. Positive values of x, with lower signal amplitude, correspond to oil phase and the negative values of x correspond to solvent phase. As was mentioned previously, both of the suppressing factors in mixing zone are less effective and the signal amplitude grows substantially which improves the signal resolution. Finally, these MRI signals were converted to concentration profiles through calibration. This was achieved by creating samples with known concentrations of heavy oil-toluene and measuring their responses in the same environment and parameter settings used previously. To this end, well-mixed samples with concentrations varying between 0-100% (weight percent) were prepared. The viscosity and density variation of these samples are plotted in Figure 8 (viscosity 14


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was measured with Brookfield LVDV-III/HBDV-II viscometer and density was measured by Anton Parr DMA 4100 densitometer). As expected, mixture density showed a linear relationship with concentration and Lederer’s equation was successfully fitted to measured viscosity values ( w = 0.3 ):

µ mix = µ s f µ o f s

fo =

(8)

o

wC o , wC o + C s

f s = 1 − fo

(9)

Calibration curve (see Figure 9a) was obtained by measuring the signal amplitude for each concentration. As shown in this figure, a polynomial curve is fitted to the experimental data to have a continuous signal amplitude over the whole oil concentration range. The corresponding error generated while using the fitted curve is shown in Figure 9b (the maximum introduced error is less than 1%). The decline in the amplitude at the high-oil-concentration end is due to the short T2 value in oil. The decline in calibration curve at the high-solvent-concentration end is due to the long T1 value in toluene. One can see that the inclusion of both factors present in Eq. (7) is important and allows obtaining good conversion of amplitude into concentration for the whole range of those, from 0% to 100%. Using this calibration curve, the concentration profiles at each time were calculated based on acquired signals as shown in Figure 10a. The curves were then smoothed using a moving average filter, since calculation of diffusion coefficient from concentration profiles includes numerical differentiation, hence, is very sensitive to experimental data scatter (Figure 10b). These profiles are different from normal S-shaped behavior related to constant diffusivity. This difference is 15


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more pronounced at high oil concentrations indicating concentration dependency of diffusivity. The inflection point for each curve at different times can be considered as a virtual interface separating oil-rich portion and solvent-rich portion. It can be observed that solvent concentration increases within the oil-rich phase and decreases within the solvent-rich phase over time. Before the diffusive front reaches the physical boundaries of the diffusion cell, the solvent concentration in oil gradually decreases along the diffusion direction and reaches zero value at the end. At the same position, solvent concentration in oil increases with time. After about 100 hours, oil reaches the outlet end of solvent-rich portion (x=-3.5 cm) and after about 300 hours, solvent reaches the outlet end of oil-rich portion (x=3.6 cm). This shows that oil propagation within the solvent is faster compared to solvent propagation within the oil which is an expected result.

Diffusion Coefficient In Figure 11, the concentration profiles are expressed as a function of x / t . The measured concentration values at various times almost lie on a single curve which indicates that the diffusion coefficient depends on concentration only and confirms that the measured process is diffusion-dominated (without convective or other effects). However, diffusion curves at longer times fit better compared to diffusion curves at early times and it is more significant on solvent side (for solvent concentration higher than 60%). This amount of deviation is reported by other researchers 11. Based on the concept of Slope and Intercept method, which was first developed by Hall extended later by Sarafianos

44

43

and

, the plot of u (u is defined in Eqs. 10 and 11) against distance

16


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yields a curve with straight line in regions of low and high concentrations with constant values for slope (h) and intercept (k). C 1 = erfc (u ) C0 2

(10)

u = hx + k

(11)

Here, a straight line was fitted to the data of u against x at low and high concentration regions to remove noises present at these regions, especially at high concentration values of toluene. Then, concentration values were calculated again based on corrected curve of u versus x. Finally, the concentration-dependent diffusion coefficient was calculated for diffusion data before breakthrough using Eq. (3) and the results for different mixing times were plotted in Figure 12. It is clear that diffusion coefficient is a strong function of concentration which is consistent with previous literature. In addition, the diffusion coefficient obtained from NMR is in the same order of magnitude as reported in literature 11, 12, 24 as shown in Table 3. This curve rises to a maximum when the oil content is ~40% in a similar manner shown by other researchers 11, 12, 24. Oballa and Butler

12

suggested that the high peak in diffusion coefficient could be related to

depolymerization of asphaltenes and they confirmed the presence of this peak theoretically. As expected, all values of diffusivity are within the range between heavy oil (~10-7cm2/s) and toluene (~3×10-5cm2/s) self-diffusion coefficients. However, the measured diffusion coefficient trend toward the self-diffusion of heavy oil but do not trend toward the toluene self-diffusion. when solute and solvent molar masses are close, self-diffusion and mutual diffusion coefficients are similar

45

. In general, however, mass and size of solute and solvent molecules are different

and the overall rate of transfer may be expressed as the combined effect of bulk-flow and true 17


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diffusion resulting from the random motion of non-uniformly distributed molecules. From the point of view of interpreting diffusion coefficients in terms of molecular motions, the mutual diffusion coefficient thus appears to be unnecessarily complicated by the presence of the bulkflow

46

. Therefore, diffusion experiments in heavy oil-solvent systems can provide useful data

for mutual diffusion coefficients but they are not appropriate for determining the self-diffusion coefficient of a pure solvent 11.

Conclusions In this work, Nuclear Magnetic Resonance Imaging that maps spatial distribution of relaxation times was used to obtain the diffusivity data in a toluene-heavy oil system. Direct measurement of concentration profiles over the whole concentration range provides a sound basis for computation of diffusivity. The diffusion experiment for toluene-heavy oil was monitored for 20 days at a controlled temperature of 35 °C and ambient pressure and concentration profiles were obtained by converting the NMR signals to concentrations. The calculated concentration values versus x/t0.5 lied on a single curve which confirms the diffusion-controlled behavior of the process and accuracy of the technique. The concentration curves were different from ideal Sshaped curves associated with constant diffusivity indicating that diffusion coefficient is a strong function of concentration. Concentration-dependent diffusion coefficient was obtained from concentration profiles with results being consistent with those reported in the literature for similar systems. It was shown that diffusion coefficient is bounded within self-diffusivities of both solvent and heavy oil and exhibits a non-linear behavior as expected. The results show that NMR Imaging is a powerful tool for measurement and evaluation of solvent diffusivity in heavy

18


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oil which would be of value when estimates of mass transfer in solvent-based recovery process are required.

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Acknowledgments The authors wish to acknowledge the financial support of the NSERC/AITF IRC in Fundamentals of Unconventional Resources (FUR) and the industrial sponsors: Athabasca Oil Corp, Brion Energy, Devon Canada, Foundation CMG, Husky Energy, Laricina Energy, Maersk Oil, Suncor. The authors also gratefully acknowledge the contributions of the staff at PERM Inc. and Tomographic Imaging and Porous Media Laboratory, especially Scott Wickens for helping with the experiments.

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Nomenclature A

signal amplitude

B0

external magnetic field, T

C

concentration, wt%

D

diffusion coefficient, cm2/s

fL

Larmor frequency

gx

frequency-encoding gradient, T/cm

Mz

transvers magnetization

M xy

longitudinal magnetization

RD

relaxation delay, µs

T1

spin-lattice relaxation time, ms

T2

spin-spin relaxation time, ms

TAU

time between 90° and 180° pulses, µs

w

weighting factor

Greek Letters

γ

gyromagnetic ratio, MHz/T

λ

transformation variable, cm/s0.5

µo

oil viscosity, mPas

µs

solvent viscosity, mPas

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References 1. Fadaei, H.; Scarff, B.; Sinton, D., Rapid Microfluidics-Based Measurement of CO2 Diffusivity in Bitumen. Energy & Fuels 2011, 25, (10), 4829-4835. 2. Butler, R. M.; Mokrys, I. J., A New Process (VAPEX) For Recovering Heavy Oils Using Hot Water And Hydrocarbon Vapour. Canadian Petroleum Technology 1991. 3. Upreti, S. R.; Lohi, A.; Kapadia, R. A.; El-Haj, R., Vapor Extraction of Heavy Oil and Bitumen: A Review. Energy & Fuels 2007, 21, (3), 1562-1574. 4. Etminan, S. R.; Maini, B. B.; Chen, Z.; Hassanzadeh, H., Constant-Pressure Technique for Gas Diffusivity and Solubility Measurements in Heavy Oil and Bitumen. Energy & Fuels 2010, 24, (1), 533-549. 5. Nguyen, T. A.; Ali, S. M. F., Effect of Nitrogen On the Solubility And Diffusivity of Carbon Dioxide Into Oil And Oil Recovery By the Immiscible WAG Process. Journal of Canadian Petroleum Technology 1998, 37, (02), 24-31. 6. Moulu, J. C., Solution-gas drive: experiments and simulation. Journal of Petroleum Science and Engineering 1989, 2, (4), 379-386. 7. Diedro, F.; Bryan, J.; Kryuchkov, S.; Kantzas, A., Evaluation of Diffusion of Light Hydrocarbon Solvents in Bitumen. In Canada Heavy Oil Technical Conference, Society of Petroleum Engineers: Calgary, Alberta, Canada, 2015. 8. Jamialahmadi, M.; Emadi, M.; Müller-Steinhagen, H., Diffusion Coefficients of Methane in Liquid Hydrocarbons at High Pressure and Temperature. Journal of Petroleum Science and Engineering 2006, 53, (1–2), 47-60. 9. Riazi, M. R., A New Method for Experimental Measurement of Diffusion Coefficients in Reservoir Fluids. Journal of Petroleum Science and Engineering 1996, 14, (3), 235-250. 10. Tharanivasan, A. K.; Yang, C.; Gu, Y., Measurements of Molecular Diffusion Coefficients of Carbon Dioxide, Methane, and Propane in Heavy Oil under Reservoir Conditions. Energy & Fuels 2006, 20, (6), 2509-2517. 11. Fadaei, H.; Shaw, J. M.; Sinton, D., Bitumen–Toluene Mutual Diffusion Coefficients Using Microfluidics. Energy & Fuels 2013, 27, (4), 2042-2048. 12. Oballa, V.; Butler, R. M., An Experimental Study Of Diffusion In The Bitumen-Toluene System. Journal of Canadian Petroleum Technology 1989, 28, (02), 63-69. 13. Do, H. D.; Pinczewski, W. V., Diffusion Controlled Swelling of Reservoir Oil by Direct Contact with Injection Gas. Chemical Engineering Science 1991, 46, (5), 1259-1270. 14. Guerrero Aconcha, U. E.; Kantzas, A., Diffusion of Hydrocarbon Gases in Heavy Oil and Bitumen. In Latin American and Caribbean Petroleum Engineering Conference, Society of Petroleum Engineers: Cartagena de Indias, Colombia, 2009. 15. Funk, E. W., Behavior of Tar Sand Bitumen with Paraffinic Solvents and Its Application to Separations for Athabasca Tar Sands. The Canadian Journal of Chemical Engineering 1979, 57, (3), 333341. 16. Fu, B. C. H.; Phillips, C. R., New Technique for Determination of Diffusivities of Volatile Hydrocarbons in Semi-solid Bitumen. Fuel 1979, 58, (8), 557-560. 17. Das, S. K.; Butler, R. M., Diffusion Coefficients of Propane and Butane in Peace River Bitumen. The Canadian Journal of Chemical Engineering 1996, 74, (6), 985-992. 18. Song, L.; Kantzas, A.; Bryan, J. L., Experimental Measurement of Diffusion Coefficient of CO2 in Heavy Oil Using X-Ray Computed-Assisted Tomography Under Reservoir Conditions. In Canadian

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Unconventional Resources and International Petroleum, Society of Petroleum Engineers: Calgary, Alberta, Canada, 2010. 19. Guerrero-Aconcha, U. E.; Salama, D.; Kantzas, A., Diffusion Coefficient of n Alkanes in Heavy Oil. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers: Denver, Colorado, USA, 2008. 20. Luo, H.; Kantzas, A., Investigation of Diffusion Coefficients of Heavy Oil and Hydrocarbon Solvent Systems in Porous Media. In SPE Symposium on Improved Oil Recovery, Society of Petroleum Engineers: Tulsa, Oklahoma, USA, 2008. 21. Luo, H.; Kryuchkov, S.; Kantzas, A., The Effect of Volume Changes Due to Mixing on Diffusion Coefficient Determination in Heavy Oil and Hydrocarbon Solvent System. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers: naheim, California, USA, 2007. 22. Salama, D.; Kantzas, A., Monitoring Of Diffusion Of Heavy Oils With Hydrocarbon Solvents In The Presence Of Sand. In PE International Thermal Operations and Heavy Oil Symposium, Society of Petroleum Engineers: Calgary, Alberta, Canada, 2005. 23. Zhang, X.; Fulem, M.; Shaw, J. M., Liquid-Phase Mutual Diffusion Coefficients for Athabasca Bitumen + Pentane Mixtures. Journal of Chemical & Engineering Data 2007, 52, (3), 691-694. 24. Wen, Y. W.; Kantzas, A., Monitoring Bitumen−Solvent Interactions with Low-Field Nuclear Magnetic Resonance and X-ray Computer-Assisted Tomography. Energy & Fuels 2005, 19, (4), 13191326. 25. Sadighian, A.; Becerra, M.; Bazyleva, A.; Shaw, J. M., Forced and Diffusive Mass Transfer between Pentane and Athabasca Bitumen Fractions. Energy & Fuels 2011, 25, (2), 782-790. 26. Fayazi, A.; Ghazanfari, M. H., Random Walk Simulation of Miscible Flow through Heterogeneous 2D Porous Media Considering Dispersion Tensor. Chemical Engineering Science 2015, 132, 81-92. 27. Wilke, C. R.; Chang, P., Correlation of Diffusion Coefficients in Dilute Solutions. AIChE Journal 1955, 1, (2), 264-270. 28. Afsahi, B.; Kantzas, A., Advances in Diffusivity Measurement of Solvents in Oil Sands. In Canadian International Petroleum Conference, Petroleum Society of Canada: Calgary, AB, Canada, 2006. 29. Wen, Y.; Kantzas, A.; Wang, G. J., Estimation of Diffusion Coefficients in Bitumen Solvent Mixtures Using X-Ray CAT Scanning and Low Field NMR. In Canadian International Petroleum Conference, Petroleum Society of Canada: Calgary, Alberta, Canada, 2004. 30. Boltzmann, L., Zur Integration der Diffusionsgleichung bei variabeln Diffusionscoefficienten. Annalen der Physik 1894, 289, (13), 959-964. 31. Coates, G. R.; Xiao, L.; Prammer, M. G., NMR logging: principles and applications. Haliburton Energy Services: 1999. 32. Freedman, R.; Lo, S.; Flaum, M.; Hirasaki, G. J.; Matteson, A.; Sezginer, A., A New NMR Method of Fluid Characterization in Reservoir Rocks: Experimental Confirmation and Simulation Results. SPE Journal 2001, 6, (04), 452-464. 33. Mirotchnik, K.; Kantzas, A.; Starosud, A.; Aikman, M., A New Method for Group Analysis of Petroleum Fractions in Unconsolidated Porous Media. Journal of Canadian Petroleum Technology 2001, 40, (07), 38-44. 34. Mirotchnik, K. D.; Allsopp, K.; Kantzas, A.; Curwen, D.; Badry, R., Low-Field NMR Method for Bitumen Sands Characterization: A New Approach. SPE Reservoir Evaluation & Engineering 2001, 4, (02), 88-96. 35. Allsopp, K.; Wright, I.; Lastockin, D.; Mirotchnik, K.; Kantzas, A., Determination of Oil and Water Compositions of Oil/Water Emulsions Using Low Field NMR Relaxometry. Journal of Canadian Petroleum Technology 2001, 40, (07), 58-61.

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36. Peña, A. A.; Hirasaki, G. J., Enhanced Characterization of Oilfield Emulsions via NMR Diffusion and Transverse Relaxation Experiments. Advances in Colloid and Interface Science 2003, 105, (1–3), 103150. 37. Peña, A. A.; Hirasaki, G. J.; Miller, C. A., Chemically Induced Destabilization of Water-in-Crude Oil Emulsions. Industrial & Engineering Chemistry Research 2005, 44, (5), 1139-1149. 38. Bryan, J.; Kantzas, A.; Bellehumeur, C., Oil-Viscosity Predictions From Low-Field NMR Measurements. SPE Reservoir Evaluation & Engineering 2005, 8, (01), 44-52. 39. Morriss, C.; Rossini, D.; Straley, C.; Tutunjian, P.; Vinegar, H., Core Analysis By Low-field NMR. The Log Analyst 1997, 38, (02), 84-95. 40. Bernstein, M. A.; King, K. F.; Zhou, X. J., Handbook of MRI Pulse Sequences. Elsevier Science: 2004. 41. Callaghan, P. T., Principles of Nuclear Magnetic Resonance Microscopy. Clarendon Press: 1993. 42. Wen, Y.; Bryan, J.; Kantzas, A., Estimation of Diffusion Coefficients in Bitumen Solvent Mixtures as Derived From Low Field NMR Spectra. Journal of Canadian Petroleum Technology 2005, 44, (04), 2935. 43. Hall, L. D., An Analytical Method of Calculating Variable Diffusion Coefficients. The Journal of Chemical Physics 1953, 21, (1), 87-89. 44. Sarafianos, N., An Analytical Method of Calculating Variable Diffusion Coefficients. Journal of Materials Science 1986, 21, (7), 2283-2288. 45. Zhang, X.; Shaw, J. M., Liquid-phase Mutual Diffusion Coefficients for Heavy Oil + Light Hydrocarbon Mixtures. Petroleum Science and Technology 2007, 25, (6), 773-790. 46. Crank, J., The mathematics of diffusion. Oxford university press: 1979. 47. Straley, C.; Leu, G., Low-Field NMR Profiles for Verification of Oil and Water Saturations in Cores In International Symposium of the Society of Core Analysts, Trondheim, Norway, 2006.

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Tables Table 1: Properties of the heavy oil used in this work

Property

Value

API gravity

11.5

Density @ 15.56 °C (60 °F), g/cm3

0.9887

Viscosity @ 15.56 °C (60 °F), mPas

46597

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Table 2: NMR parameters for toluene-heavy oil system

Parameter

Description

Value

P90 (µs)

Duration of 90-degree pulse

28.6

P180 (µs)

Duration of 180-degree pulse

57.2

NS

Number of scans (Multiple scans are used to increase signal to noise ratio)

300

SI

Number of acquisition points

1024

TAU

Time between the 90 and 180 degree pulses

5000

DW (µs)

Time between successive points

5

RD (µs)

Time between successive scans

1000000

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Table 3: Comparison of measured bitumen diffusion coefficients in different crude oils

Temperate, °C

Diffusion coefficient, cm2/s

Reference

Athabasca Bitumen 1

20

5×10-7 – 4.8×10-6

12

Athabasca bitumen 2 (2000 Pa.s @ 21 °C)

21

4.3×10-7 – 2×10-6

1

Cold Lake bitumen (130 Pa.s @ 25 °C)

30

9.26×10-6

24

Heavy oil (14.3 Pa.s @ 25 °C)

35

10-7 – 4.8×10-6

This work

Oil type

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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

Figures

Figure 1: Hahn echo experiment which consists of a 90-degree and a 180-degree pulse 47

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Figure 2: Schematic of diffusion cell

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5

×10

4

Channel 1 Channel 2

4

3

Siganl amplitude

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

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2

1

0

-1

-2

-3

0.009

0.0095

0.01 Time (µs)

0.0105

0.011

Figure 3: NMR signal in time domain (this signal is acquired at t=24 hours)

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1

×10

6

Channel 1 Channel 2

0.8 0.6 0.4

Signal amplitude

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

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0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Frequency

Figure 4: NMR signal after applying Fourier Transform (this signal is acquired at t=24 hours)

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10

×10

5

(a)

10

×10

5

(b)

Conversion

8

8

Signal amplitude

Signal amplitude

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

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6

4

2

0 -0.05

6

4

2

0

0

0.05

-10

Frequency

-5

0

5

10

x (cm)

Figure 5: (a) The magnitude of signals over two channels in frequency domain, (b) The final signal after point-to-length conversion (this signal is acquired at t=24 hours)

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9

×10

5

3.2 cm 5.1 cm 6.7 cm

8 7 6

Signal amplitude

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

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5 4 3 2 1

0 -0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Frequency

Figure 6: NMR signals acquired for three different fluid levels

33


0.04

0.05

Energy & Fuels

10 9 8 7

Signal amplitude

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

×10

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5

10 hr 24 hr 48 hr 72 hr 120 hr 240 hr 360 hr 480 hr

6 5 4 3 2 1 0

-3

-2

-1

0

1

2

X (cm)

Figure 7: The NMR signals at different mixing times

34


3

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1 Viscosity Lederer's equation Density

103

102

0.9 101

10

10

0.85

0

-1

0

10

20

30

40

50

60

70

80

90

0.8 100

Oil concentration (wt%)

Figure 8: Variation of density and viscosity values for different concentrations at 35 °C

35


Density (g/cc)

0.95

Viscosity (cp)

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

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Signal amplitude

10

(a)

×10 5

8 6 4 2 0 0

20

40

60

80

100

80

100

Oil concentration (wt%) (b) 1.5

Absolute relative error (%)

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

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1

0.5

0 0

20

40

60


Figure 9: (a) Calibration curve for converting signal amplitude to concentration, (b) the generated errors using the fitted curve

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(a)

(b)

100

100 10 hr 24 hr 48 hr 72 hr 120 hr 240 hr 360 hr 480 hr

60


80


80


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

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40

20

60

40

20

0 -3

-2

-1

0

1

2

0

3

-3

-2

X (cm)

-1

0

1

2

3

X (cm)

Figure 10: Oil concentration profiles at different mixing times before smoothing (a) and after smoothing (b).

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100 90 80


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

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70


60 50 40 30 20 10 0 -0.02

-0.015

-0.01

-0.005

0 0.005 x/ t (cm/ s)

0.01

Figure 11: Concentration profiles as a function of x/t0.5

38


0.015

0.02

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1

×10

-5

10 hr 24 hr 48 hr 72 hr

0.9 0.8

Diffusion coefficient (cm2 /s)

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

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

10

20

30

40

50

60

70

80


Figure 12: Diffusion coefficient dependence on concentration

39


90

Evaluating Diffusivity of Toluene in Heavy Oil Using Nuclear Magnetic

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