Concentration Dependence of Mutual Diffusivity of Liquid

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Concentration Dependence of Mutual Diffusivity of Liquid Hydrocarbons and Bitumen Franklin Grimaldos, Florian F. Schoeggl, Brij B. Maini, and Harvey William Yarranton Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b01891 • Publication Date (Web): 09 Aug 2019 Downloaded from pubs.acs.org on August 12, 2019

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Concentration Dependence of Mutual Diffusivity of Liquid Hydrocarbons and Bitumen F. Grimaldos, F.F. Schoeggl, B. Maini, H.W. Yarranton* Chemical and Petroleum Engineering, University of Calgary * corresponding author

Abstract The mutual diffusivity of solvent and bitumen is an important parameter in the design of solvent based bitumen recovery processes. It is determined from measured concentration profiles in bitumen. These measurements are difficult because bitumen is opaque and current approaches such as X-ray or magnetic resonance tomography are expensive. A new apparatus was designed and commissioned as a lower cost alternative. It measures the mass transfer in liquid solvent/heavy oil systems based on the density profiles established over time in a column of solvent over bitumen. A one dimensional numerical model based on molecular diffusion was developed to determine the mutual diffusivity from the concentration profiles. The model accounted for the dependence of diffusivity on viscosity through a correlation based on the infinite dilution diffusivities of the solvent and the oil. Mutual diffusivities were determined for Athabasca bitumen with toluene, and for maltenes from the same oil with toluene, n-heptane, and n-pentane at ambient conditions and diffusion times from 3 to 15 days. The measured diffusivities were found to increase monotonically with decreasing viscosity (and solvent content) of the mixture but remained below the selfdiffusion coefficient of the solvent.

Keywords: diffusivity, concentration dependent diffusivity, diffusivity measurement, liquid hydrocarbon, n-pentane, n-heptane, bitumen and heavy oil,

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Introduction In situ recovery processes with solvents involve a combination mass transfer and drainage. Sufficient mass transfer rates are required to obtain economical oil rates. Mass transfer also affects the residence time of the solvent in the reservoir and the amount of solvent that is recovered at the end of the process. Therefore, an understanding of the mass transfer and drainage mechanisms is required to design commercially successful processes. A key parameter for the mass transfer is the dispersion of the gas or liquid solvent into the heavy oil or bitumen. In heavy oil formations, diffusivity is a significant contribution to the dispersion of solvent 1.

Diffusivities from the gas phase into bitumen (or heavy oil) have been measured for hydrocarbons such as methane, ethane, propane, and butane over a range of pressures and temperatures. A summary of these studies can be found elsewhere 1. The mutual diffusivities of liquid hydrocarbons and heavy oil have also been measured with the methods and conditions summarized in Table 1. The majority of the data were collected at atmospheric pressure and temperatures between 20 and 35°C.

Most liquid-liquid mass transfer experiments performed on bitumen and solvent systems involve the measurement of concentration profiles over time. Since mixtures of bitumen and solvent tend to be opaque to normal light, transmitted light methods are limited to high solvent concentrations and narrow gaps. NMR and x-ray transmission can be used at higher concentrations but require specialized equipment and are more costly. All of these concentration profile methods require a calibrated conversion from the measured intensity to solvent concentration.

Other approaches include the Taylor dispersion method, the spinning disk method, and the transpiration method. The Taylor dispersion method involves the measurement of the shape of a bitumen front diffusing through a solvent and has similar limitations as the concentration profile methods. In the spinning disk method, a disk uniformly coated with bitumen is submerged into a receptacle containing a known volume of liquid solvent. The disk is rotated at a constant speed and the average concentration of the bitumen in the solvent are measured versus time. A constant diffusivity can be calculated from the analysis of the bitumen concentration. In the transpiration technique, a homogenous solution of bitumen and a volatile hydrocarbon (with known initial 2 ACS Paragon Plus Environment

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concentration) is placed into a diffusion cell, where the hydrocarbon can escape from the solution to a continuously flowing nitrogen stream or water stream. The mass diffused is determined from the concentration of the hydrocarbon in the nitrogen and a constant diffusivity is calculated from the analysis of the mass transferred over time.

Table 1. Literature data for liquid hydrocarbon diffusivity in bitumen (DME = dimethylether, MN = 1-methylnaphthalene). Oil Type and Viscosity

T (oC)

Measurement Method

Data Analysis Approach

Conc. Dependent

bitumen

25

spinning disk

analytical solution

no

Fu and Phillips3

n-pentane n-hexane n-heptane isohexane dimethylbutane cyclohexane benzene toluene octane

bitumen 56.5 Pa·s @ 25°C

23±1.5

transpiration

analytical solution

no

Oballa and Butler4

toluene


20±0.5

conc. profile light transmission

Boltzmann transformation

yes

Nortz et al.5

MN

vacuum residues

50, 70

Taylor dispersion

Taylor dispersion

no

Tang and Zhang6

phenol


22

transpiration

analytical solution

no

n-hexane isohexane cyclohexane toluene


23±1.5

transpiration

analytical solution

no

22

conc. profile NMR

analytical solution

no

Author

Solvent

Funk2

n-pentane n-heptane n-decane

Tang7

Wen et al.8,9

n-heptane n-hexane n-pentane toluene

bitumen 130 Pa·s @ 25°C heavy oil 6 Pa·s @ 25°C


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naphtha kerosen

bitumen 671 Pa·s @ 25°C

Wen et al.10 Wen and Kantzas11

n-heptane


22

Salama and Kantzas12

n-octane n-heptane n-hexane n-pentane

heavy oil 21.4 Pa·s @ 20°C

22±2

Afsahi and Kantzas13

n-heptane n-hexane n-pentane toluene naphtha kerosene

Zhang and Shaw14 Zhang et al.15

n-heptane n-pentane

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conc. profile NMR+x-ray


conc. profile NMR+x-ray


22

conc. profile NMR

analytical solution

no

22

conc. profile x-ray

semi-analytical solution, variable density

yes

22

conc. profile x-ray

Boltzmann transformation excess volume of mixing

yes

24

conc. profile x-ray

slope and intercept

yes

heavy oil 6 Pa·s @ 25°C

24

conc. profile x-ray

semi-analytical solution, variable density

yes

21

conc. profile microfluidic light

semi-analytical solution, variable density.

yes

bitumen 671 Pa·s @ 25°C bitumen 130 Pa·s @ 25°C bitumen 18 Pa·s @ 25°C

Luo and Kantzas17

n-heptane

heavy oil 21.4 Pa·s @ 20°C

GuerreroAconcha et al.18

n-octane n-heptane n-hexane

heavy oil 6 Pa·s @ 25°C

n-heptane n-heptane

Fadaei et al.20

toluene

yes


Luo et al.16

Sadighian et al.19

yes

bitumen 18 Pa·s @ 25°C atm. residue 2600 Pa·s @ 25°C atm. residue 2000 Pa·s @ 21°C


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transmission Ghanavati et al.21

n-hexane

Diedro et al.22

n-pentane n-propane toluene DME

Fayazi et al.23

toluene

atm. residue 20 Pa·s @ 42°C

30

Taylor dispersion

Taylor dispersion

yes

22

conc. profile x-ray

slope and intercept

yes

25

conc. profile NMR

slope and intercept

yes

bitumen 55 Pa·s @ 22°C heavy oil 12000 Pa·s @ 25°C heavy oil 47 Pa·s @ 15.6°C

Diffusivities are determined from an analytical or numerical model of the mass transfer data. Diffusion of liquid hydrocarbons into bitumen has often been modeled assuming a constant diffusivity

2,3,6-13.

However, the constant diffusivity assumption is only valid for liquid-liquid

diffusion when the solute concentrations are low; that is, approaching the infinite dilution condition. This assumption is usually justified based on the narrow distance, small concentration range, and short diffusion times used in the experiments.

In fact, the mutual diffusivity of liquids varies significantly with the solute concentration

24.

Therefore, at non-dilute conditions, the mutual diffusivity of liquids hydrocarbons and heavy oil cannot be treated as a constant. The choice of model and simplifying assumptions can have a significant effect on the calculated diffusivity. In this review, only the methods applied to calculate diffusivity from concentration profile measurements are considered.

The most commonly used method for interpreting the concentration profiles in mixtures of bitumen or heavy oil and a solvent is the Boltzmann-Transformation approach, an analytical solution to for linear mass transfer 4,10-12,20. These authors all reported a maximum in the diffusivity at a solvent concentration of approximately 50 vol%. Zhang and Shaw

15

noted that the Boltzmann-

Transformation approach considers spatial density gradients to be negligible or zero. To account for these gradients, they solved the continuity equation with a variable density to obtain the diffusivity. Their calculated diffusivity still showed counterintuitive trends versus concentration; however, based on the narrow range of diffusivities observed (1 to 2·10-6 cm²/s), they attributed 5 ACS Paragon Plus Environment

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the apparent maximum to measurement errors. They also concluded that the apparent dependence of the diffusivity on experimental time was caused by ignoring the density gradients. Finally, they established that the diffusivities at ambient conditions were nearly constant. However, Sadighian et al. 19 used the same approach and found that the diffusivity followed a quadratic function of the solvent concentration. Luo et al. 17 evaluated the effect of the volume change of mixing on the diffusivity for n-heptane in heavy oil. They measured a negative volume change upon mixing and then determined the diffusivity as a function of the concentration using a modified Boltzmann-Transformation which included the volume change of mixing. They compared the diffusivity values obtained with the new technique with those obtained from the usual Boltzmann-Transformation approach and concluded that including volume change of mixing into the concentration profiled analyses improved the trend for concentration dependence and eliminated the time dependence of the diffusivity.

The slope and intercept method is another analytical solution to the mass transfer equations that is valid when the component concentration plots linearly versus concentrations. Guerrero-Aconcha et al.

18

; that is, at high or low

used the slope and intercept technique to determine

concentration dependent diffusivities from measured concentration profiles. They found that the diffusivity monotonically decreased as the concentration of bitumen increased. However, at high solvent concentration, their calculated diffusivity was higher than the self-diffusion coefficient of the solvent. Diedro et al.

22

also used the slope and intercept method and reported a monotonic

change of the diffusivity with concentration. They found that for solvent concentrations below 50 vol%, the diffusivity could be taken as a constant. On the other hand, Fayazi et al.

23

obtained

abnormal trends in the concentration dependence for toluene diffusion into bitumen system using the slope and intercept technique. The inconsistences in the results from this slope and intercept method may occur because one of the main conditions to apply this technique cannot be fulfilled. To use the slope and intercept technique, the plot of concentration against distance on a semiprobability paper must lead to a curve with straight-line in the regions of low and high concentrations 25. However, in hydrocarbon solvent-bitumen the plot is curved in these regions.


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In summary, the determination of the mutual diffusivity of liquid hydrocarbons and heavy oil or bitumen is challenging because the mutual diffusivity in these systems is strongly dependent on the concentration of the solvent. No clear relationship has been established between concentration and diffusivity 26 and the reported data are scattered partly because this relationship has not been correctly accounted for. In addition, the available measurement methods are expensive and involve complex data analysis 24. Some the methods are applicable under very specific assumptions and can lead to unexpected values of the diffusivity when the assumptions are violated. Finally, the analysis of any mass transfer experiment with heavy oil and a liquid n-alkane solvent is questionable because asphaltene precipitation is likely. Precipitated asphaltenes may settle and cause convection or they could form a barrier to mass transfer. In either case, the assumptions of the mass transfer model would be violated.

The objectives of this study were to: 1) develop a straightforward method to determine the mutual diffusivities of liquid hydrocarbons (toluene, n-pentane, and n-heptane) and a Western Canadian bitumen; 2) establish a consistent relationship between diffusivity and the mixture viscosity (and therefore indirectly to the solvent concentration). An apparatus was designed and commissioned to measure mass transfer in hydrocarbon/bitumen systems based on the density profile of a column of liquid solvent over bitumen or maltenes after diffusion has occurred for a specified time. The proposed method is suitable for opaque mixtures and therefore for the full range of solvent concentrations. It provides a direct measurement of the mixture density which can be easily and accurately transformed into solvent concentration as long as the solvent and bitumen densities are known. The mass transfer is one-dimensional and therefore its analysis is relatively straightforward. A numerical model of the mass transfer experiments was constructed to determine the diffusivity. Liquid-liquid mass transfer data were collected on the new apparatus for the following pseudo-binary systems: toluene/bitumen, toluene/maltenes, n-heptane/maltenes, and npentane/maltenes at ambient conditions. Maltenes were used to avoid asphaltene precipitation.

Experimental Methods Materials The Western Canadian bitumen sample (WC-B-A3) used in this study was provided by CNOOCNexen and was obtained from a Jacos SAGD process where it had been treated to remove water. 7 ACS Paragon Plus Environment

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The residual water content was less than 1 wt%. The molecular mass, density, viscosity, and SARA assay of the WC-B-A3 bitumen are listed in Table 2. The bitumen was de-asphalted using npentane to obtain maltenes following the procedure described elsewhere 27. The residual pentane content in the maltenes is expected to be less than 3.5%. The maltenes made up 79.8 ±0.5 wt% of the original bitumen.

The following hydrocarbons were purchased from VWR International LLC and used for diffusivity experiments: toluene (99.5% purity) and n-pentane (>98% purity) from Fisher Chemical and n-heptane (technical, mixture of isomers) from Anachemia. The n-pentane and nheptane were also used to obtain the asphaltene yield curves. Additionally, deionized boiled water and toluene were used to calibrate the density meter.

Table 2. Selected properties of WC-B-A3 bitumen and maltenes. Property Density, g/cm³ at 20°C Viscosity at 20°C and 1 atm, mPa.s Molecular weight, g/mol Saturates, wt% Aromatics, wt% Resins, wt% C5-asphaltenes, wt% Asphaltene Onset, wt% n-heptane Asphaltene Onset, wt% n-pentane

WC-B-A3 Bitumen 1.009 358,000 572 19.2 41.0 18.2 20.2 54.6 42.6

WC-B-A3 Maltenes 0.982 12,700 -

Bitumen Characterization and Property Measurements Asphaltene Onset The onset of precipitation is defined as the precipitant content at which asphaltenes first precipitate. The onsets are required to help interpret the liquid-liquid diffusion data with bitumen and nheptane or n-pentane. The onsets were determined by extrapolating asphaltene yield measurements to zero yield. The yield is defined as the mass of precipitated asphaltenes divided by the mass of bitumen. Asphaltene yields were measured gravimetrically following the procedure described 8 ACS Paragon Plus Environment

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elsewhere 28. The asphaltene yields were repeatable to ±0.37 wt% for n-pentane and ±0.45 wt% for n-heptane, based on a 95% confidence interval. The extrapolated onset is precise to ±1 wt% in both cases.

SARA Fractionation The ASTM D4124 method was used to determine the saturate, aromatic, resin, and asphaltene content of the bitumen. Briefly, asphaltenes and solids were precipitated with n-pentane and removed from the bitumen. Then, the maltenes (de-asphalted oil) were fractionated into saturates, aromatics and resins using liquid chromatography. A detailed procedure was provided elsewhere 29.

The SARA composition of the WC-B-A3 bitumen is reported in Table 2. The SARA

composition is repeatable to 0.9 wt%.

Physical Property Measurements The molecular weight of the bitumen was measured with a Jupiter Model 833 Vapor Pressure Osmometer and is reported in Table 2. The equipment and procedure are described elsewhere 30. The molecular weight was repeatable to ±52 g/mol based on a 95% confidence interval.

The density and viscosity of the bitumen were measured from 50 to 175 °C and 0.1 to 10 MPA using an in-house capillary viscometer equipped with an Anton Paar DMA-HPM density meter as described elsewhere 31. The capillary viscometer measurements are reported in Appendix A. The density data were fitted with an empirical correlation from Saryazdi et al. 32 and the viscosity data were fitted with the Expanded Fluid viscosity correlation

33

presented later (Eq. 25). Values at

20°C and 0.1 MPa were determined from the fitted correlations and are reported in Table 2.

The density and viscosity of the maltenes were measured from 15 to 80°C at atmospheric pressure and the properties at 20°C are reported in Table 2. The densities were measured with an Anton Paar DMA 4500M density meter and the viscosities were measured with an Anton Paar MCR-52 Cone and Plate Rheometer, as described elsewhere 34. The precision and repeatability of all density measurements were ±0.01 kg/m³ and ± 0.05 kg/m³ respectively. The repeatabilities of the oil and maltene viscosities were ±5% and ±4%, respectively.


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Liquid-Liquid Diffusivity Measurement A new apparatus was designed to measure the mutual diffusivity of liquid hydrocarbons (toluene, n-pentane and n-heptane) and bitumen or maltenes. In this approach, a column of solvent is placed above a column of bitumen and left to diffuse for a specified time. The combined liquid column is then displaced through a density meter and the density is measured over a series of height intervals. At each height, the solvent content is determined from the measured density and the known density of the components. Hence, the output from the experiment is a concentration profile at a given diffusion time. The diffusivity is determined from a numerical model tuned to match the measured solvent concentration profile. The apparatus, procedure, data processing, and validation are described below while the design checks for the apparatus are provided in the Supporting Information.

Apparatus The apparatus is shown in Figure 1. The main components are a cylindrical vertically aligned diffusion cell equipped with a piston, a pump, a density meter, a data logging computer, and a sample collector. Other components include a hydraulic fluid supply cylinder, and a transfer cylinder for injecting cleaning fluid (usually toluene). The pump is connected to the bottom of the diffusion cell and moves the piston with hydraulic fluid. The density meter is connected to the top of the diffusion cell. The sampling vessel is connected to the outlet of the density meter. The specifications of the main components are as follows: The diffusion cell has an internal diameter of 3.8 cm and a height of 11.7 cm with a maximum fluid capacity of 135 cm³. The Quizix SP-5200 pump delivers metered flow rates in the range of 0.01 to 15 cm³/min, accurate to 0.005 cm³/min. The pump discharge pressure is measured with a built-in sensor with an accuracy of ±0.005 MPa. The Anton Paar DMA-HPM oscillating tube density meter is rated for fluids with densities up to 3 g/cm³, temperatures from 20 up to 200°C, and pressures up to 140 MPa. The temperature of the sample is measured with a built-in sensor, accurate to ± 0.1°C. The density measurements are repeatable to ±1·10-4 g/cm³ at static conditions and ±6·10-4 g/cm³ at flowing conditions. The sample collector is a 100 cm³ glass vial. 10 ACS Paragon Plus Environment

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The pumping pressure, sample temperature, and oscillating period are recorded directly on a computer with a maximum recording rate of 1 measurement per second.

nitrogen density meter sample collector cleaning fluid vessel

toluene

liquid solvent

diffusion cell

heavy oil piston hyd. oil

hydraulic oil reservoir

piston hyd. oil

pump

Figure 1. Schematic of the liquid-liquid diffusivity apparatus.

Procedure To perform an experiment, the piston was set in a cleaned and dried diffusion cell at the predetermined total height (measured from the top of the cell to the top of the piston). To determine the required height, the height of the bitumen and solvent layers were calculated from the specified mass and known density of each fluid. The total height is simply the sum of the component heights.

The lower section of the cell (underneath the piston) was filled with hydraulic oil and closed. The specified mass of bitumen was placed on the top of the piston. To expel any air bubbles from the bitumen, the cell was wrapped with an electrical heating tape and the cell was heated to 40°C for 24 hours. Then, the heating tape was removed and the bitumen was left to cool for 24 hours. After cooling, the cell was weighed. Solvent was poured down the inside wall until the cell was filled. The cell was reweighed and the final mass of solvent was calculated from the change in the cell mass. 11 ACS Paragon Plus Environment

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The cell was closed and left in a vertical position at ambient conditions for the desired diffusion time. Then, the cell was connected to the pump and density meter and the fluid displaced through the density meter at a rate of 1 or 2 cm³/min. The pumping pressure, sample temperature, and oscillating period were recorded at a rate of 1 measurement every second until all of the sample was displaced.

Accuracy and Resolution The proposed liquid-liquid diffusivity apparatus measures density profiles for flowing system (< 2 cm³/min) with a maximum deviation of 6.9·10-4 g/cm³ and a repeatability of ±1.4·10-2 g/cm³ based on a 95% confidence interval. To determine the repeatability, two diffusion cells with the same amounts of bitumen and solvent were left for the same experimental time. Then, the cells were displaced at 1 cm³/min and the density profile were obtained. The deviation between each point (density at each volume displacement) of the two profiles and the average absolute deviation was calculated to obtain the repeatability.

The spatial resolution of the measurement (height represented with each density measurement) is also important when modeling the data to match the concentration profile. The less the height, the better the resolution. The spatial resolution depends on the cross-sectional area of the diffusion cell, the displacement rate, and the data sampling rate. For a displacement rate of 1 cm³/min, a cell diameter of 3.8 cm, and a data sampling rate of 1 measurement per second, the spatial resolution is 1 density measurement per 0.0015 cm. For a 2 cm³/min displacement rate, the spatial resolution is 1 density measurement per 0.003 cm. The resolution is sharper than the range of 0.015 to 0.05 cm reported for other methods 4,14,18,20,22,23.

Converting from Density to Solvent Concentration Mass transfer is more naturally and conveniently examined in terms of a concentration profile versus height rather than a density profile versus displaced volume. Therefore, the displaced volumes were converted to their relative position with respect to the initial interface. In addition, all of the measured densities were converted to solvent mass concentrations expressed in grams of solvent per volume of solution (g/cm³).


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The cumulative volume was converted to the relative position with respect to the initial interface as follows: ()

( )=

(1)

where X(t) is the relative position with respect to the initial interface in cm, Vcum(t) is the cumulative volume at time t in cm³,

is the cross-sectional area in cm², and hsol is the distance from the top

of the cell to the initial top of the bitumen layer in cm. X(t) is negative above the initial interface (solvent side) and positive below the interface (bitumen side).

The mass concentration of the solvent in the mixture, Cs is given by: = where ws is the mass fraction of the solvent and

(2) meas

is the measured density of the mixture in

g/cm³. The solvent mass fraction was calculated from the measured density using the excess volume mixing rule presented later (Eq. 22). A plot of mass fraction versus density is provided in the supporting information. Finally, it is common to normalize the concentration by the initial concentration of solvent, Co. In pure solvent, the initial concentration is equivalent to the solvent density.

Liquid Solvent/Bitumen Mass Transfer Model The solvent/bitumen diffusion model is intended to determine the mutual diffusivities of toluene, n-pentane, and n-heptane with bitumen and maltenes based on measured concentration profiles. Figure 2 is a side view of the diffusion cell in a liquid solvent-bitumen diffusion experiment at two different diffusion times. Initially, the bitumen and solvent are in distinct layers (t = 0 in Figure 2). In the liquid solvent/bitumen system, the solvent diffuses downwards into the bitumen and the bitumen diffuses upwards into the solvent over time (t >> 0 in Figure 2), and the initially distinct interface disappears.


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t >> 0

t=0 ws = 1 Liquid Solvent

Bitumen/Solvent Mixture Bitumen ws = 0

Figure 2. Side view of the diffusion cell at initial condition (t = 0) and after some time (t >> 0).

In this mass transfer process, the density of the fluid at any given location changes with time and therefore a numerical solution was required. This mass transfer process can be considered as a series of isothermal, non-reactive, one-dimensional fluxes through layers under the assumptions outlined in Appendix B. In this case, the mass flow of solvent and bitumen through a fixed plane (such as X = 0 in Figure 2) are given by: (3)

=

(4)

= where

is the mass flow in g/s and Axo is the cross-sectional area in cm² ,

is the density of the

mixture in g/cm³, D is the diffusivity in cm²/s, w is the mass fraction, X is the distance from the interface, and subscripts s and b indicate solvent and bitumen, respectively.

An initial condition is required for each of the two phases. The initial solvent phase condition is given by: ( < where

= 0) =

(5)

is the initial solvent mass fraction in the solvent phase. If the solvent is pure, wso = 1.

Similarly, the initial condition for the bitumen phase is given by: (

Concentration Dependence of Mutual Diffusivity of Liquid

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