Microfluidics for Measuring Solubility and Diffusion Coefficient of Solvent in Bitumen

by

SOHEIL TALEBI

A thesis submitted in conformity with the requirements for the degree of Master of Science Graduate Department of Mechanical and Industrial

Engineering, in the University of Toronto

© Copyright by Soheil Talebi 2017

ii

Microfluidics for Measuring Solubility and Diffusion Coefficient of Solvent in Bitumen

Soheil Talebi

Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

2017

Abstract

In this thesis, a microfluidic approach is developed to determine both the solubility and diffusivity

of propane in the Athabasca bitumen at a range of reservoir-relevant pressures and temperatures.

The presented microfluidic approach offers advantages over the conventional methods including

fast quantification, small volume requirement, and ease of operation at high temperatures and

pressures. The fabricated glass-silicon microfluidic chip contains a Pressure – Volume –

Temperature (PVT) microchannel with full temperature and pressure control, connected to both

solvent and bitumen supply. The cross-sectional area of the bitumen supply channel was only 2.5%

that of the cell, approximating a closed PVT system. One-dimensional oil swelling due to solvent

diffusion was captured consecutively using fluorescence microscopy and the solvent solubility and

diffusion coefficient were then determined through image analysis and established mathematical

models. The final results are in strong agreement with the available published data obtained by

conventional methods.

iii

Acknowledgments

I would like to appreciate the great support and encouragement of my supervisor Dr. David Sinton

during my MASc program. His guidance from first day of project was a huge help and I have

learned many research skills from him. I would also like to thank Dr. Ali Abedini and carbon sub-

group team for their great contributions and help in my master project. Also, none of these

achievements become possible without funding from Natural Sciences and Engineering Research

Council of Canada (NSERC) CRD program in partnership with Suncor Energy Inc.

iv

Table of Contents

Abstract ........................................................................................................................................... ii

Acknowledgments.......................................................................................................................... iii

List of Tables ................................................................................................................................. vi

List of Figures ............................................................................................................................... vii

List of Appendices ......................................................................................................................... ix

Chapter 1 ......................................................................................................................................... 1

Introduction ..................................................................................................................................... 1

Chapter 2 ......................................................................................................................................... 7

Microfluidics-based Measurement of Solubility and Diffusion Coefficient of Propane in Bitumen

......................................................................................................................................................... 7

2.1 Introduction ...................................................................................................................... 8

2.2 Experimental .................................................................................................................. 11

2.2.1 Microfluidic apparatus ............................................................................................ 11

2.2.2 Fluids....................................................................................................................... 12

2.2.3 Experimental procedure .......................................................................................... 13

2.3 Results and Discussion ................................................................................................... 15

2.3.1 Bitumen swelling factor .......................................................................................... 15

2.3.2 Propane solubility in bitumen ................................................................................. 17

2.3.3 Propane diffusivity in bitumen................................................................................ 19

v

2.4 Conclusion ...................................................................................................................... 27

Chapter 3 ....................................................................................................................................... 28

Conclusion .................................................................................................................................... 28

3.1 Fabrication cost .............................................................................................................. 28

3.2 Future Work ................................................................................................................... 29

References ..................................................................................................................................... 30

Appendices .................................................................................................................................... 36

1. Silicon Chip Fabrication .................................................................................................... 36

2. Swelling Images ................................................................................................................. 41

3. Mathematical approach ...................................................................................................... 42

vi

List of Tables

Table 1. Experimental conditions of propane solubility tests……………………………………15

Table 2. Comparison of the measured propane diffusion coefficient in different heavy oils and

bitumens obtained by conventional methods with the measured data using the

microfluidic technique developed in this study. ……………………………………...…23

vii

List of Figures

Fig. 1. Schematic of microfluidic apparatus used for measuring the solvent solubility and diffusion

coefficient, with measurement concept shown expanded at right. The red shading indicates

temperature controlled components……………………………………………………....12

Fig. 2. Fluid properties of the bitumen sample. (a) compositional analysis of the original Athabasca

bitumen sample, ρb = 1020 kg/m3 and MWb = 588.8 gr/mole – with C1–C6s = 0, C7s–

C9s = 0.03 wt%, C10s–C19s = 9.72 wt%, C20s–C29s = 21.29 wt%, C30+= 68.96 wt%;

(b) measured bitumen viscosity at different temperatures-viscosity at 20 ºC is expected to

be over 106 mPa.s. The n-C5 asphaltene content of the sample was also determined to be

43.3 wt% using the standard ASTM D2007 [59]……………………………………..…..13

Fig. 3. Bitumen swelling data analysis. (a) fluorescence images of a typical time-lapse 1-D bitumen

swelling inside the micro-PVT cell; (b) time-lapse bitumen swelling factor as a result of

propane dissolution for P/Psat = 0.70; (c) time-lapse bitumen swelling factor as a result of

propane dissolution for P/Psat = 0.86; (d) final bitumen swelling factor at different

temperatures for P/Psat = 0.70 and 0.86……………………………………………….…..17

Fig. 4. Propane solubility analysis. (a) time-lapse average concentration of propane in the bitumen

for P/Psat = 0.70 and 0.86; (b) measured solubility of propane in the bitumen at different

temperatures for P/Psat = 0.70 and 0.86…………………………………………...………19

Fig. 5. Infinite length analysis case. (a) linear least-squares fit of average concentration data vs.

the parameter “m” in Eq. 3 for P/Psat = 0.70; (b) linear least-squares fit of average

concentration data vs. the parameter “m” in Eq. 3 for P/Psat = 0.86; (c) infinite length

diffusion coefficient of propane in the bitumen at different temperatures for P/Psat = 0.70

and 0.86. The slope of the fitted lines is equal to the square root of the propane diffusion

coefficient at each condition; (d) comparison of measured diffusion coefficients with

correlated ones obtained by Walden’s rule (Eq. 4)………………………………………..22

viii

Fig. 6. Finite length case analysis. (a) Left-hand side of Eq. 6 versus time for different values of

parameter “a” for the test conducted at 9.5 bar and 40 ºC. The value of a = 0.30 provides

the same value for the diffusion coefficient as the infinite model; (b) linear least-squares fit

of LHS of Eq. 6 vs. time for P/Psat = 0.70; (c) linear least-squares fit of LHS of Eq. 6 vs.

time for P/Psat = 0.86. The slope of the fitted lines is equal to the propane diffusion

coefficient at each condition; (d) comparison of propane diffusion coefficients obtained by

infinite length and finite length diffusion models…………………………………….…..25

Fig. A1. Solubility chip AutoCAD design. Total number of 9 chips fitted in one single 4ʺ silicon

wafer………………………………………………………………………………….…..36

Fig. A2. Equipment needed for microfabrication. (a) Mask Writer – Heidelberg uPG 501; (b)

Mask Aligner/ Exposure; (c) DRIE – Deep Reactive Ion Etching; (d) Drilling MicroLux

Variable Speed Miniature Drill Press; (e) Bonding; (f) Dicing……………………….…39

Fig. A3. Solubility chip along with channel dimensions…………………..……………………40

Fig. A4. Microfluidic chip with its stainless-steel manifold. (a) Exploded view; (b) assembled

view……………………………………………………………………………………..40

Fig. A5. 1-D bitumen swelling inside the micro-PVT cell at 7.1 bar, 20 ºC………………………41

ix

List of Appendices

1. Silicon Chip Fabrication……………………………………………...………………….36

2. Swelling Images………………………………………….………………………………41

3. Mathematical approach……………………………………………..……………………42

1

Chapter 1

Introduction

More than 170 billion barrels (~10 % estimated worldwide deposits of oil) of the world total oil

reserves are in the form of oil sands, also known as tar sands or more technically bitumen. These

unconventional petroleum deposits are either loose or consolidated sandstones consisting of

naturally occurring mixture of water, sand, and clay saturated with viscous bitumen (dense and

highly viscous type of petroleum). Geographically, oil sands reserves are majorly deposited in

Canada, Kazakhstan, Russia and Venezuela. In Canada, specifically, Alberta’s oil sands including

Athabasca Oil Sand, Cold Lake, and Peace River formations ranked the third largest oil reserves

around the world [1–3]. In 2014, the Albert’s oil sands proven reserves reported to be 166 billion

Barrels (bbl). Approximately 200 billion dollars was invested in the oil sands industry between

1999 and 2013. Due to high demand for energy, particularly in 2012, the investment in oil sands

industry was about 27.2 billion dollars which is the highest investment to date in oil sands history

[1-2]. According to statistics Canada, the oil sands investment would pass the new record of 33

billion dollars by 2020. In terms of employment, in 2014, Alberta’s upstream energy sector

employed approximately 133,000 people in various sections such as oil sands, conventional oil,

gas and mining. According to Alberta Historical Royalty Data (AHRD), in the fiscal year 2013-

2014, synthetic crude oil and bituminous sands royalty accounted for about 5.3 billion dollars out

of 9.6 billion dollars of Albert’s non-renewable resource revenue [4].

Although bitumen resources are abundant, their production techniques differ from those of

conventional oil reservoirs, mainly due to various factors such as large viscosity of the bitumen

(i.e., over 106 mPa.s), low reservoir pressure, and shallow formation depth [5–7]. Conventional

2

crude oil extraction process normally includes drilling a production well into a pay zone, letting

oil flow into the surface using natural reservoir pressure. Primary production techniques mostly

used for conventional oil reservoirs in which the reservoir temperature is at least 50 ºC with a

typical recovery rate of 8-12%. Canadian oil sand reserves are far more dense and viscous and

implementing primary extraction technique barely provide 6% recovery rate [4]

Thus, except for a very small fraction of oil sands which could be extracted using conventional oil

well technology, oil sands reservoirs require special methods of extractions either via mining or in

situ recovery techniques. The major bitumen extraction techniques are surface mining, Cold Heavy

Oil Production with San (CHOPS), Cyclic Steam Stimulation (CSS), Steam Assisted Gravity

Drainage (SAGD), Vapor Extraction (VAPEX), Toe to Heel Air Injection (THAI), and

Combustion Overhead Gravity Drainage (COGD). Except for surface mining, all the

aforementioned methods extract bitumen by reducing the viscosity of the bitumen. It is notable

that approximately 90% of Canadian oil sands are too far below the surface of the ground to use

surface mining [1]. In Canada only the Athabasca oil sands are shallow enough for surface mining.

The oil sands with the thickness of 40 to 60 meters are usually covered by clay and barren sands

on top. So, this type of reservoir could be reached easily by using surface mining method.

Cyclic Steam Stimulation (CSS) or called as “huff-and-puff” method is a production method which

takes advantage of using steam to extract bitumen. The use of steam to recover heavy oil goes back

to 1950s in California. The CSS method consists of three cycles; steam injection, soak, and oil

production. In this method, the steam is initially injected into the well at high temperature (300 –

450 ºC) for a period of weeks to months. Next the wellbore allowed to rest for couple of weeks to

let the heat penetrate into the formation. Finally, the hot oil is pumped out of the well for a period

of weeks or months. This cyclic production continues till the production rate declines and the

3

process is no longer economic. CSS method can potentially improve the recovery rate from 10 to

40 percent, however it is relatively low compared to the other steam process called SAGD [8]

Steam Assisted Gravity Drainage (SAGD) initially introduced and developed by Butler in 1980s

and combined by directional drilling technology in mid 1990s. This method consists of drilling

two horizontal wells into the oil sands, one at the bottom of the formation and another about 5

meters above it. The length of the wells could extend couple of miles in all directions. Steam

assisted-gravity drainage (SAGD) is the main in situ bitumen recovery process in which saturated

steam is injected into the bitumen zone using the upper well. The resulting heat transfer reduces

the viscosity of bitumen allowing bitumen to flow into the lower well [9–13]. SAGD improves the

recovery factor up to 60% and it is relatively cheaper than CSS method. Most major Canadian oil

companies use SAGD for production operations. However, SAGD has economic and

environmental issues and cannot be applied for all types of bitumen formations (especially thin

formations) [7]. Hydrocarbon solvent injection such as Vapor Extraction (VAPEX) has been

proposed and incorporated into the bitumen extraction as an alternative to SAGD to improve its

economic and environmental performances. Solvent may be injected through various scenarios

including non-condensing solvent injection [14–16], condensing solvent injection [17], and cyclic

solvent injection [18–22]. In all cases, a main recovery mechanism is viscosity reduction via

solvent diffusivity into the bitumen, and thus diffusivity and solubility are the key physical

parameters for this process [23–25].

A variety of methods have been employed to determine the solvent solubility and diffusion

coefficient in different oils, from light crude to heavy oil and bitumen. In the common pressure

decay method, the pressure of gas in a PVT cell containing the gas-liquid system is recorded until

the pressure remains uniform and unchanged [26–30]. The volume and temperature of the cell is

4

kept constant during the experiment. The concentration-time equation is then applied to the

pressure measurements to determine the gas concentration in the liquid phase and gas diffusion

coefficient. The solvent solubility and diffusivity have also been determined through isobaric-

isothermal oil volume expansion measurement [31].

Other researchers have used the pendant drop apparatus to determine the solvent solubility and

diffusion coefficient in a high-pressure high-temperature IFT cell [32,33]. The volume of the oil

drop is imaged over time and the solvent diffusion coefficient is determined through a

mathematical model for a pendant drop geometry. This technique is also employed to determine

the solvent extraction pressure and oil-solvent minimum miscibility pressure [34]. Alternatively,

the solvent concentration in the liquid can be determined through sampling the liquid phase at

different times and performing compositional analysis [35]. Nuclear magnetic resonance (NMR)

spectrometry and magnetic suspension balance have also been applied to measure gas solubility

and diffusion coefficients in various fluids [36–38]. X-ray transmission tomography was employed

to determine the mutual diffusion of liquid hydrocarbon solvent and bitumen at ~22 ºC [39,40]. In

a micro glass cell apparatus, a micro syringe is used as a constant volume cell for gas–liquid

equilibrium (GLE) to study gas-nonvolatile liquid phase behavior. In this method, the solubility

calculation is based on the pressure decay method. The apparatus is used for CO2 solubility

measurements in a liquid with low viscosity (water) and also in a liquid with high viscosity

(bitumen). [41]. The wide variety of past approaches points to both the challenge and importance

of these measurements. Although all conventional methods provide details of diffusion process,

they are generally costly in terms of facility and technician time, and have high capital costs. A

significant source of the experiment duration and associated cost shortcomings of conventional

methods stem from the large volume of fluids employed.

5

Microfluidic platforms recently have been used in the oil and gas sector and have been widely

applied to study the displacement processes and phase behavior phenomena [17,42–45].

Microfluidics can provide unprecedented control over composition, pressure, temperature, and

phase saturation conditions, together with optical access and associated fluorescence microscopy

tools. Importantly, the small test volumes enable relatively rapid transport, providing rapid

quantification and reduced operating and capital costs. Microfluidics has been applied to

determine: the bubble/dew points of hydrocarbon mixtures [46]; phase diagram of pure

components [47]; minimum miscibility pressure [48]; onset of asphaltene precipitation [49,50];

and wax appearance temperature [51].

There is precedent for microfluidics-based measurements of diffusivity and solubility. A

microfluidic chip was used to measure temperature-dependent diffusion coefficient of toluene-

cyclohexane system using Raman microscopy [52]. Dissolution and diffusion of carbon dioxide in

liquid solvents and water were quantified in a segmented gas-liquid flow at low pressures [53–55].

This segmented flow approach is most effective for low-viscosity liquids such as water. A hybrid

approach was developed for CO2 diffusivity in water and brine over the range of pressure ~0.5–

5.0 MPa for carbon sequestration applications [56]. For heavy oil and bitumen systems, there is

some precedent. A T-junction microchip was designed to calculate the mutual diffusion of

bitumen-toluene mixture using the bright-field microscopy [57]. A microfluidic cross chip was

applied to study the diffusion of CO2 into a discrete slug of bitumen [58]. With this approach, pre-

loading of the bitumen slug leaves a thick film on the channel surfaces which influences transport

and affect the bitumen-solvent interface under test. The method also requires very precise

balancing of pressures on the slug to avoid flow, and is not applicable to multiplexing.

6

In this thesis, a microfluidics-based approach is developed to measure the bitumen swelling in

response to solvent exposure, and in turn determine the solubility and diffusion coefficient.

Imaging is enabled by fluorescence microscopy, using the inherent fluorescence property of the

oil. This method is applied to the propane-bitumen system at a wide range of temperatures and

pressure characteristic of operations. Established mathematical models are applied to determine

the solvent solubility and diffusion coefficient at each test condition, with results compared to

relevant published data obtained by conventional methods, where possible.

7

Chapter 2

The content of this chapter was published in the journal Fuel, earlier this year, reference below.

Permission to reprint has been requested from the publisher, and a delay in publication of thesis

has been requested.

Soheil Talebi, Ali Abedini, Pushan Lele, Adriana Guerrero, David Sinton. Microfluidics-

based Measurement of Solubility and Diffusion Coefficient of Propane in Bitumen. Fuel.

DOI information: 10.1016/j.fuel.2017.08.049. Reproduced with permission from Elsevier.

Link to publication online: https://authors.elsevier.com/a/1VZQE3iH40Jjp

Microfluidics-based Measurement of Solubility and Diffusion

Coefficient of Propane in Bitumen

Solubility and diffusivity are essential to the design, implementation, and ultimate success of

solvent extraction processes. In this thesis, we demonstrate a microfluidic approach to determine

both the solubility and diffusivity of propane in the Athabasca bitumen at a range of reservoir-

relevant pressures and temperatures (P = 6.0–14.7 bar and T = 20–50 ºC). The glass-silicon

microfluidic chip contains a micro-PVT cell with full temperature and pressure control, connected

to both solvent and bitumen supply. The cross-sectional area of the bitumen supply channel was

only 2.5% that of the cell, approximating a closed PVT system. One-dimensional oil swelling as a

result of solvent diffusion was imaged by fluorescence microscopy and the solvent solubility and

diffusion coefficient were then determined through image analysis and established mathematical

models. The results achieved are in an agreement with the available published data obtained by

https://authors.elsevier.com/a/1VZQE3iH40Jjp

8

conventional methods (i.e., in a range of 2.5–5.1 kg/m3 for solubility and 10–10–10–8 m2/s for

diffusion coefficient for the range of conditions tested). This microfluidic approach offers

advantages over the conventional methods including fast quantification, small volume

requirement, and ease of operation at high temperatures and pressures. With a 1 nL fluid sample,

the microfluidic method presented here requires less than 1 hr., which is 150-fold faster than ~7

days required for a typical pressure decay test in a 500 mL PVT cell with bitumen.

2.1 Introduction

Over 170 billion barrels of the world total oil reserves are in the form of oil sands, also known as

bitumen, which is majorly deposited in Canada including Athabasca Oil Sand, Cold Lake, and

Peace River formations [1–3]. While bitumen resources are abundant, their production techniques

differ from those of conventional oil reservoirs, mainly due to very large viscosity of the bitumen

(i.e., over 106 mPa.s), low reservoir pressure, and shallow formation depth [5–7]. Steam assisted-

gravity drainage (SAGD) is the main in situ bitumen recovery process in which saturated steam is

injected into the bitumen zone [9–13]. However, SAGD has economic and environmental issues

and cannot be applied for all types of bitumen formations (especially thin formations) [7].

Hydrocarbon solvent injection has been proposed and incorporated into the bitumen extraction as

an alternative to SAGD to improve its economic and environmental performance. Solvent may be

injected through various scenarios including non-condensing solvent injection [14–16],

condensing solvent injection [17], and cyclic solvent injection [18–22]. In all cases, a main

recovery mechanism is viscosity reduction via solvent diffusivity into the bitumen, and thus

diffusivity and solubility are the key physical parameters for this process [23–25].

A variety of methods have been employed to determine the solvent solubility and diffusion

coefficient in different oils, from light crude to heavy oil and bitumen. In the common pressure

9

decay method, the pressure of gas in a PVT cell containing the gas-liquid system is recorded until

the pressure remains uniform and unchanged [26–30]. The volume and temperature of the cell is

kept constant during the experiment. The concentration-time equation is then applied to the

pressure measurements to determine the gas concentration in the liquid phase and gas diffusion

coefficient. The solvent solubility and diffusivity have also been determined through isobaric-

isothermal oil volume expansion measurement [31]. Other researchers have used the pendant drop

apparatus to determine the solvent solubility and diffusion coefficient in a high-pressure high-

temperature IFT cell [32,33]. The volume of the oil drop is imaged over time and the solvent

diffusion coefficient is determined through a mathematical model for a pendant drop geometry.

This technique is also employed to determine the solvent extraction pressure and oil-solvent

minimum miscibility pressure [34]. Alternatively, the solvent concentration in the liquid can be

determined through sampling the liquid phase at different times and performing compositional

analysis [35]. Nuclear magnetic resonance (NMR) spectrometry and magnetic suspension balance

have also been applied to measure gas solubility and diffusion coefficients in various fluids [36–

38]. X-ray transmission tomography was employed to determine the mutual diffusion of liquid

hydrocarbon solvent and bitumen at ~22 ºC [39,40]. The wide variety of past approaches points to

both the challenge and importance of these measurements. Although all conventional methods

provide details of diffusion process, they are generally costly in terms of facility and technician

time, and have high capital costs. A significant source of the experiment duration and associated

cost shortcomings of conventional methods stem from the large volume of fluids employed.

Microfluidic platforms have garnered recent interest in oil and gas sector and have been widely

applied to study the displacement processes and phase behavior phenomena [17,42–45].

Microfluidics can provide unprecedented control over composition, pressure, temperature, and

10

phase saturation conditions, together with optical access and associated fluorescence microscopy

tools. Importantly, the small test volumes enable relatively rapid transport, providing rapid

quantification and reduced operating and capital costs. Microfluidics has been applied to

determine: the bubble/dew points of hydrocarbon mixtures [46]; phase diagram of pure

components [47]; minimum miscibility pressure [48]; onset of asphaltene precipitation [49,50];

and wax appearance temperature [51].

There is precedent for microfluidics-based measurements of diffusivity and solubility. A

microfluidic chip was used to measure temperature-dependent diffusion coefficient of toluene-

cyclohexane system using Raman microscopy [41,52]. Dissolution and diffusion of carbon dioxide

in liquid solvents and water were quantified in a segmented gas-liquid flow at low pressures [53–

55]. This segmented flow approach is most effective for low-viscosity liquids such as water. A

hybrid approach was developed for CO2 diffusivity in water and brine over the range of pressure

~0.5–5.0 MPa for carbon sequestration applications [56]. For heavy oil and bitumen systems, there

is some precedent. A T-junction microchip was designed to calculate the mutual diffusion of

bitumen-toluene mixture using the bright-field microscopy [57]. A microfluidic cross chip was

applied to study the diffusion of CO2 into a discrete slug of bitumen [58]. With this approach, pre-

loading of the bitumen slug leaves a thick film on the channel surfaces which influences transport

and obfuscates the bitumen-solvent interface under test. The method also requires very precise

balancing of pressures on the slug to avoid flow, and is not amenable to multiplexing.

In this paper, we present a microfluidics-based approach to measure the bitumen swelling in

response to solvent exposure, and in turn determine the solubility and diffusion coefficient.

Imaging is enabled by fluorescence microscopy, using the inherent fluorescence property of the

oil. We apply this method to the propane-bitumen system at a wide range of temperatures and

11

pressure characteristic of operations. Established mathematical models are applied to determine

the solvent solubility and diffusion coefficient at each test condition, with results compared to

relevant published data obtained by conventional methods, where possible.

2.2 Experimental

2.2.1 Microfluidic apparatus

The schematic diagram of the microfluidic apparatus is shown in Fig. 1. A silicon-glass

microfluidic chip was designed and fabricated using deep reactive ion etching (DRIE) and a

shadow mask process. The chip had three distinct segments including a solvent channel with 50

µm (width) and 20 µm (depth), a bitumen-solvent PVT cell with 50 µm (width) and 20 µm (depth),

and a bitumen channel with 5 µm (width) and 5 µm (depth). The cross-sectional area of the bitumen

channel was very small, only 2.5% that of the cell, approximating a closed PVT system. The total

volume of PVT cell is 2.5 × 10-3 mm3 (2.5 nL), which is significantly less than a typical PVT cell

volume. The volume of bitumen slug involved in the experiment is less than 1.0 × 10-3 mm3 (~1

nL). The microfluidic chip was mounted in a stainless-steel manifold and solvent and bitumen

lines were connected to the manifold inlets. An Olympus BXFM microscope with X-CITE 120

LED light source connected to the Leica MC 170 HD camera was used for imaging process, and

the images were stored in a computer for data analysis. The solvent was initially stored inside a

syringe pump (Teledyne-Isco 260D) that was, in turn, connected to the chip. The Isco pump was

set under constant pressure mode to provide the desired experimental pressure. An ultra-thin heat

sheet (1” × 3”, 115 VAC, McMaster-Carr, 35475K334) – connected to a temperature controller –

was also placed under the chip (i.e., between the chip and manifold) to uniformly control the chip

temperature during the experiments.

12

Fig. 1. Schematic of microfluidic apparatus used for measuring the solvent solubility and diffusion

coefficient, with measurement concept shown expanded at right. The red shading indicates

temperature controlled components.

2.2.2 Fluids

Athabasca bitumen sample Alberta, Canada) was used for solubility experiments which its

compositional analysis and viscosity-temperature data are shown in Fig. 2a and 2b, respectively.

The weight percentage of components ranging C1–C10s is less than 0.1 wt% while weight

percentage of C30+ fraction is ~69 wt%. The bitumen viscosity at 20 ºC is expected to be over 106

mPa.s due to the presence of very large amount of heavy fractions. The measured density and

molecular weight of the bitumen sample were ρb = 1020 kg/m3 and MWb = 588.8 gr/mole,

respectively (all the measurements were carried out at atmospheric pressure). Pure propane (99.5

mol%), purchased from Praxair Canada, was also used as a hydrocarbon solvent during

experiments.

13

Fig. 2. Fluid properties of the bitumen sample. (a) compositional analysis of the original Athabasca

bitumen sample, ρb = 1020 kg/m3 and MWb = 588.8 gr/mole – with C1–C6s = 0, C7s–C9s = 0.03

wt%, C10s–C19s = 9.72 wt%, C20s–C29s = 21.29 wt%, C30+= 68.96 wt%; (b) measured bitumen

viscosity at different temperatures-viscosity at 20 ºC is expected to be over 106 mPa.s. The n-C5

asphaltene content of the sample was also determined to be 43.3 wt% using the standard ASTM

D2007 [59].

2.2.3 Experimental procedure

To eliminate film flow of the bitumen in the channel, the channel interior of the chip was initially

silanized with Trichloro (1H, 1H, 2H, 2H-perfluoro-octyl) silane provided by Sigma Aldrich [60].

The silanization reduced the surface wettability respect to the bitumen; preventing the film flow

of bitumen on the channel sides. During silanization process, the hydrogen peroxide was first

injected into the chip for 10 min to activate the channel surfaces for making strong bonding with

silanized solution. Thereafter, deionized water was injected for about 10 min to completely

displace the hydrogen peroxide inside the channels. Next the chip was placed in a vacuumed oven

and heated up to 150 ºC to evaporate all liquids inside the channel. Afterwards, the Silane solution

was injected into the chip for 10 min followed by toluene injection to remove the solution.

Isopropyl alcohol (IPA) was then injected into the chip for 10 min to displace the toluene and after

that the chip was sonicated inside IPA for 30 min. After sonication, IPA was injected again to

14

completely clean the surface of the channel. Finally, the chip was vacuumed and dried at 150 ºC

for 1 hr.

Prior to the bitumen injection, the chip was mounted in a custom stainless-steel manifold. The chip

and manifold were placed under the microscope with required fluid lines, heating elements and

controllers connected. The fluid lines were 1/16” smooth-bore seamless 316 stainless steel with

internal diameter of 0.022” (maximum pressure of ~44 MPa at ~22 ºC and temperature range of ~

-200–800 ºC), purchased from McMaster-Carr. The bitumen transfer cell was initially heated to

85 ºC to sufficiently reduce its viscosity and make the flow easier. A heating rope (McMaster-

Carr, 3641K24) controlled by a temperature controller (Omega CNi3222) was also used to heat

the lines and facilitate injecting the bitumen into the chip. Once the PVT cell of the chip was loaded

with proper volume of bitumen (a length of ~1000 µm), the bitumen line was disconnected from

the system via a two-way valve and the heating system was turned off. The heat sheet which was

initially mounted on the manifold (i.e., underneath the chip) was then set to the desired

experimental temperature. Once the system reached thermal equilibrium condition, the propane

was introduced into the PVT cell through the solvent line. The time-lapse swelling of bitumen as

a result of solvent diffusion was imaged with the Leica MC 170 HD camera connected on top of

the Olympus BXFM microscope. The images were imported to an image processing software

(ImageJ) to calculate the change in the bitumen length over time. Several tests were performed at

various pressures and temperatures, followed by the aforementioned procedure. Table 1 presents

the experimental conditions (i.e., pressure, temperature, and P/Psat) of all tests.

15

Table 1. Experimental conditions of propane solubility tests.

Run No. PVT cell temperature (ºC) Pressure (bar) P/Psat

1 20 6.0 0.70

2 20 7.1 0.86

3 25 6.8 0.70

4 25 8.2 0.86

5 30 7.5 0.70

6 30 9.3 0.86

7 40 9.5 0.70

8 40 11.7 0.86

9 50 11.9 0.70

10 50 14.7 0.86

2.3 Results and Discussion

2.3.1 Bitumen swelling factor

Bitumen swelling experiments were carried out at pressures and temperatures ranging from 6.0–

14.7 bar and 20–50 ºC, respectively. The pressures of propane at each temperature were selected

so that two distinct values were obtained for the ratio of P/Psat, which were 0.70 and 0.86.

Fig. 3a shows the typical time-lapse 1-D bitumen swelling inside the micro-PVT cell observed

through the fluorescence microscopy. Figs. 3b and 3c plot the bitumen swelling factor – defined

as bitumen length divided by its initial length (SF = l/lo) – vs. time, which illustrate the similar

behavior reported in previous studies [31,33]. For all runs, the bitumen expanded inside the PVT

16

cell and eventually reached a maximum. The clear termination of the swelling process indicates

that any further diffusion up the very small bitumen supply channel did not influence the results.

In short, the cell was effectively closed. In addition, at both P/Psat ratios, the time required for

bitumen to reach the maximum bitumen swelling reduced with increased temperature. While

bitumen expands faster at elevated temperatures, the extent of bitumen swelling was larger at lower

temperatures. Fig. 3d shows the final bitumen swelling factor versus temperature at P/Psat = 0.86

and 0.70, showing that the final bitumen swelling factor uniformly reduced with temperature.

While higher pressures resulted in higher bitumen swelling factors at a given temperature, the

swelling factor increase was more pronounced at lower temperatures. The system here is a gas-

liquid system and thus no asphaltene precipitation was observed during the experiment.

17

Fig. 3. Bitumen swelling data analysis. (a) fluorescence images of a typical time-lapse 1-D bitumen

swelling inside the micro-PVT cell; (b) time-lapse bitumen swelling factor as a result of

propane dissolution for P/Psat = 0.70; (c) time-lapse bitumen swelling factor as a result of

propane dissolution for P/Psat = 0.86; (d) final bitumen swelling factor at different

temperatures for P/Psat = 0.70 and 0.86.

2.3.2 Propane solubility in bitumen

In 1-D bitumen swelling, the change in the bitumen length with time is equivalent to the rate of

variation of bitumen volume [31]:

𝑑𝑉

𝑉 = 𝑑(𝑣𝑠𝐶𝑠,𝑎𝑣) (1)

18

where V is the volume of bitumen, vs is the solvent specific volume under the test pressure and

temperature, and Cs,av is the average concentration of the solvent in the bitumen sample. Since the

bitumen slug in the micro-PVT cell is full depth with uniform cross-sectional area (i.e., the volume

ratio is equal to the length ratio), the average concentration can be defined as given in Eq. 2:

𝐶𝑠,𝑎𝑣 =1

𝑣𝑠𝑙𝑛 (

𝑙

𝑙𝑜) =

1

𝑣𝑠𝑙𝑛(𝑆𝐹) (2)

in which l is the bitumen length, lo is the initial bitumen length, and SF is the bitumen swelling

factor. Fig. 4a shows the time-lapse average propane concentration in the bitumen for both P/Psat

of 0.7 and 0.86, calculated by Eq. 2. The propane concentration in the bitumen increased with time

and reached a maximum value – with the same trend in swelling factor data. This maximum

average propane concentration is the propane solubility in the bitumen. Fig. 4b shows the propane

solubility in the bitumen versus temperature at two different P/Psat ratios. It was observed that

under a constant P/Psat ratio, the propane solubility is identical for different experimental

temperatures, within experimental error (in agreement with previous observations [25,61]). The

average propane solubility in the bitumen was measured to be 2.53 and 5.07 kg/m3 at P/Psat of 0.70

and 0.86, respectively, independent of the test temperature. In addition, the propane solubility

significantly increased with increased pressure (or P/Psat) at constant temperatures.

19

Fig. 4. Propane solubility analysis. (a) time-lapse average concentration of propane in the bitumen

for P/Psat = 0.70 and 0.86; (b) measured solubility of propane in the bitumen at different

temperatures for P/Psat = 0.70 and 0.86.

2.3.3 Propane diffusivity in bitumen

To determine the diffusion coefficient from the swelling data, we applied the mathematical

modeling developed by Jamialahmadi et al. [31]. The model includes 1-D gas-liquid diffusion

equations developed for both infinite and finite length cases, with the assumptions of diffusivity

and liquid density being constant. Both the infinite length and the finite length models were applied

in the analysis of the experimental data. For the infinite length model, the cell was considered

20

infinite – an assumption which is only valid at early times in the diffusion process (here less than

600 seconds, t < 600 s for all tests). For the finite length model, the length considered was that of

the bitumen slug in the micro-PVT cell – invoking the assumption that any diffusion into the

bitumen supply channel was vanishingly small (channel was 2.5% of the PVT cell cross-sectional

area).

For the infinite case analysis, Eq. 3 below provides the relationship between the average propane

concentration, the solvent diffusion coefficient, D, and the initial solvent concentration at the

solvent-bitumen interface, Csi [31]. The initial solvent concentration at the interface is the solvent

solubility under the test condition.

𝐶𝑠,𝑎𝑣 =2 𝐶𝑠𝑖

𝑙𝑜 𝑒𝑥𝑝 (𝑣𝑠 𝐶𝑠,𝑎𝑣)√

𝐷𝑡

𝜋= (

2 𝐶𝑠𝑖𝑙𝑜 𝑒𝑥𝑝 (𝑣𝑠 𝐶𝑠,𝑎𝑣)

√𝑡

𝜋) √𝐷 = 𝑚√𝐷 (3)

Figs. 5a and 5b plot typical results of Eq. 3 with the linear fit using least-squares method. In

general, for a constant P/Psat, the slope of the fitted lines increased with the temperature. Fig. 5c

shows the resulting diffusion coefficients of propane as a function of temperature for both P/Psat

= 0.70 and 0.86. As depicted, the solvent diffusion coefficient increased with temperature.

Likewise, higher pressure (P/Psat) also resulted in higher diffusion coefficient.

Fig. 5d compares the measured diffusion coefficient with correlated ones obtained by Walden’s

rule as given below [62]:

𝐷1 𝜇1𝑇1

=𝐷2 𝜇2

𝑇2 (4)

21

where T is the temperature and µ is the bitumen viscosity at the test temperature. Subscripts “1”

and “2” refer to the two distinct test conditions. In this comparison, we considered the diffusion

coefficient and bitumen viscosity at 20 ºC as a base case for each P/Psat, and then calculated the

diffusion coefficient at higher temperatures by Eq. 4. The viscosity of bitumen was estimated by

the viscosity-temperature data shown in Fig. 2b. While Walden’s rule reflects the general trend in

the data (Fig. 5d) and represents the lower temperature cases well, results deviate at higher

temperatures (> 30 ºC) with over predicted values. This trend is supported by previous

observations [62,63].

22

Fig. 5. Infinite length analysis case. (a) linear least-squares fit of average concentration data vs.

the parameter “m” in Eq. 3 for P/Psat = 0.70; (b) linear least-squares fit of average

concentration data vs. the parameter “m” in Eq. 3 for P/Psat = 0.86; (c) infinite length

diffusion coefficient of propane in the bitumen at different temperatures for P/Psat = 0.70

and 0.86. The slope of the fitted lines is equal to the square root of the propane diffusion

coefficient at each condition; (d) comparison of measured diffusion coefficients with

correlated ones obtained by Walden’s rule (Eq. 4).

23

Table 2 shows published measured values of propane diffusion in extra heavy oil and bitumen

using the conventional laboratory methods as compared to those obtained in this study. The

conventional methods include pressure decay, oil volume expansion measurement, and pendant

drop. Although no case provides an exact match of oil type and temperature/pressure condition,

the results of the present work are in a good agreement with these conventional approaches.

Table 2. Comparison of the measured propane diffusion coefficient in different heavy oils and

bitumens obtained by conventional methods with the measured data using the

microfluidic technique developed in this study.

Solvent Oil viscosity

(mPa.s)

Temperature

(ºC)

Pressure

(bar)

Diffusion coefficient

(m2/s)

Reference

Propane ~20,267 at 23.9 ºC 23.9 4–8 4.9–7.9 × 10–10 [32]

Propane ~23,000 at 23.9 ºC 23.9 4–9 0.9–6.8 × 10–10 [33]

Propane ~24,137 at 23.9 ºC 23.9 2–8 0.53–4.9 × 10–10 [64]

Propane ~127,868 at 23.9 ºC 24.8 4.1 and 8.3 0.26 × 10–10 and 4.17 × 10–10 [65]

Propane ~80,000 at 23.9 ºC 21–35 8.2–10.2 1 × 10–10–5.0 × 10–8 [25]

Propane ~473,000 at 23.9 ºC* 20 6.0 and 7.1 1.9 × 10–10 and 3.8 × 10–10 This study

Propane ~473,000 at 23.9 ºC 25 6.8 and 8.2 5.8 × 10–10 and 7.9 × 10–10 This study

Propane ~473,000 at 23.9 ºC 30 7.5 and 9.3 1.9 × 10–9 and 3.2 × 10–9 This study

Propane ~473,000 at 23.9 ºC 40 9.5 and 11.7 2.9 × 10–9 and 7.4 × 10–9 This study

Propane ~473,000 at 23.9 ºC 50 11.9 and 14.7 9.2 × 10–9 and 3.1 × 10–8 This study

* To be comparable with other oil samples, the bitumen viscosity is estimated at 23.9 ºC using the viscosity-temperature

data shown in Fig. 2b.

For the finite case analysis, Eq. 5 below is applied to model the variation of the average solvent

concentration over time, with mathematical details provided elsewhere [58]. The underlying

assumption in applying this method is that the diffusion from the micro-PVT cell into the bitumen

24

supply stem is negligible, and thus the cell resembles a closed cell. To support this assumption,

the supply channel was fabricated to be very small, 5 μm × 5 μm (2.5% of the cross-sectional area

of the cell). The observed swelling behavior within the cell also supports this assumption,

indicating a clear maximum and negligible residual swelling.

𝑑𝐶𝑠,𝑎𝑣𝑑𝑡

= 𝐷(𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 + 𝐶𝑠,𝑎𝑣)(1 − 𝑣𝑠 𝐶𝑠,𝑎𝑣)

2

𝑙𝑜𝐶𝑠,𝑎𝑣 (1 − 𝑣𝑠 (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)) (5)

Rearranging and integrating both sides of Eq. 5 gives the final equation to calculate the diffusion

coefficient as given in Eq. 6:

∫𝑙𝑜𝐶𝑠,𝑎𝑣 (1 − 𝑣𝑠 (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣))

(𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 + 𝐶𝑠,𝑎𝑣)(1 − 𝑣𝑠 𝐶𝑠,𝑎𝑣)2 𝑑𝐶𝑠,𝑎𝑣

𝐶𝑠𝑖

0

= 𝐷𝑡 (6)

The slope of the line generated by the numerical integration of the left-hand side (LHS) of Eq. 5

versus time produces the diffusion coefficient under the finite length diffusion model. The

integration for initial times (t < 600 s) of the finite length diffusion model (i.e., Eq. 6) gives a

diffusion coefficient which is expected to be the same as that calculated by the infinite length

diffusion model (i.e., Eq. 3) [31]. Thus, the parameter “a” in Eq. 6 is regressed to match the

diffusion coefficients obtained from finite length diffusion model over the early time data with

those calculated by infinite length diffusion model. Based on the pressure, temperature, solvent

type and oil type, the value of “a” varies from zero to one [31,58].

25

Fig. 6a shows results of early time numerical integration of the LHS of Eq. 6 versus time for

different values of parameter “a” for the test conducted at 9.5 bar and 30 ºC (P/Psat = 0.70). With

the same procedure, a single optimum “a” value for each P-T condition was determined. On the

basis of the optimum values of parameter “a”, the numerical integration of the LHS of Eq. 6 was

extended to long periods, with the results of all cases plotted in Figs. 6b and 6c for P/Psat = 0.70

and 0.86, respectively. The slope of the produced lines gave the propane diffusion coefficient at

different conditions. Fig. 6d compares the diffusion coefficients calculated from both the infinite

and finite length diffusion models, showing that there is strong agreement between the calculated

results (a max deviation of ~6%).

26

Fig. 6. Finite length case analysis. (a) Left-hand side of Eq. 6 versus time for different values of

parameter “a” for the test conducted at 9.5 bar and 40 ºC. The value of a = 0.30 provides

the same value for the diffusion coefficient as the infinite model; (b) linear least-squares fit

of LHS of Eq. 6 vs. time for P/Psat = 0.70; (c) linear least-squares fit of LHS of Eq. 6 vs.

time for P/Psat = 0.86. The slope of the fitted lines is equal to the propane diffusion

coefficient at each condition; (d) comparison of propane diffusion coefficients obtained by

infinite length and finite length diffusion models.

In all cases, the duration of the swelling test was under 1 hour, typically 45 min. Once implemented

with image processing software, the analysis method is effectively immediate. The result is

combined solubility and diffusivity test results in less than one hour per condition. This increase

in speed is a product of the low sample volume, 1 nL vs. 500 mL in conventional PVT cells. The

small volume offers a particularly welcome speed advantage in the context of extreme-viscous

fluids like bitumen, which require ~ a week for a conventional pressure decay test in a large cell.

In terms of limitations of this method, a few aspects are noteworthy. We assume the diffusivity

value is a constant throughout the entire diffusion process. In practice, the diffusion coefficient

can vary, locally, within a diffusion process as a function of local oil and solvent concentrations.

For solvent-bitumen systems, this function is weak, for instance, a variation of 10% between

extremes which mostly occurs at very low solvent concentrations [66,67]. Reducing the size of a

PVT cell can, in general, increase the role capillary effects. Here, a mean curvature radius of ~15

µm with the propane-bitumen interfacial tension of ~30 mN/m [68], gives a capillary pressure

differential across the interface of 4 kPa. This pressure difference is well under 1% of the minimum

experimental pressure in our study (i.e., P = 600–1500 kPa), and was neglected here. In future, if

smaller cells or higher interfacial tension systems were employed, this capillary-induced pressure

27

reduction could be taken into account in the analysis. A secondary role of the curved interface is

geometric, that is, a local deviation from 1-D planar geometry assumed in the analysis. Fortunately,

the surface becomes saturated effectively immediately [58] after which diffusion of propane into

the bitumen slug proceeds in the 1-D manner modelled in the analysis. The resulting method

provides a rapid, accurate, combined measurement of solubility and diffusivity to inform emerging

recovery and processing strategies for extra heavy oil and bitumen.

2.4 Conclusion

A microfluidics-based method was developed and applied to measure the solubility and diffusion

coefficient of propane in Athabasca bitumen over a wide range of reservoir-relevant pressures and

temperatures. The one-dimensional swelling of bitumen in response to propane diffusion was

monitored and imaged using fluorescent microscopy, and analyzed in determine the time-varying

average solvent concentration and the resulting solubility. Comparing two sets of tests at a variety

of pressures and temperatures in terms of P/Psat, showed tight correlation (

28

Chapter 3

Conclusion

Throughout this study, a new microfluidics-based method was developed and applied to measure

the solubility and diffusion coefficient of propane in Athabasca bitumen over a wide range of

reservoir-relevant pressures and temperatures. This method uniquely enables high resolution

property data acquisition over the full range of reservoir-relevant conditions required to fully

inform process designers and reservoir engineers. The application of this method is not limited to

only oil and gas applications, but can be applied to a wide variety of liquid -gas samples. The small

volume requirement, fast quantification, and ease of operation are key advantages of this method

over the conventional methods which require large volume of fluid sample and days to weeks for

running the experiments.

3.1 Fabrication cost

Our design involves nine distinct solubility chip pattern on a single 4ʺ silicon wafer, which can be

fabricated simultaneously. The fabrication cost for each silicon wafer is ~$600; making the average

cost per each chip to be ~$67. There is a potential to reduce the cost for each solubility chip by

fitting more chip design on a single silicon wafer. In our latest design, we were able to fit 18

solubility chips in a single wafer which makes each chip cost around 35$. In addition to the cost,

the cleaning procedure for microchips is cumbersome. Specifically, in case of bitumen, the

cleaning and preparation time extend to one day. Recently, in SintonLab, a new concept of silicon

glass chip so-called “disposable chip” has been developed and is currently under testing. With this

new concept, 88 small chips are fitted on a 4ʺ silicon wafer. With this new approach, the cost per

each chip significantly reduced to $5.

29

3.2 Future Work

Optical microscopy provides details of fluid dynamics at small scales with high resolution. In this

study, the one-dimensional visualization using fluorescent microscopy applied microchannel,

leveraging the inherent fluorescence property of crude oil. However, contrast between fluid phases

becomes obscure for nanoscale channels and vanishes at ∼10 nm lengthscales, due to limiting

direct optical interrogation to larger systems. In a recent work by our (Li et al., Nanoscale 2017),

a new method was developed for direct, high-contrast and label-free visualization of fluid

dynamics in sub-10 nanochannels. [69] The direct visualization is achieved with a conventional

bright-field optical microscope by inserting a layer of a high-refractive-index material, silicon

nitride (Si3N4) with 200 nm thickness, between the substrate and the nanochannel. This method is

applicable for bright field optical microscope, and challenges still exist for fluorescent microscopy

visualization in sub-10 nm confinements. There is an ongoing project in SintonLab focusing on

visualizing the fluids in sub-10 nm confinements using fluorescence microscopy.

30

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36

Appendices

1. Silicon Chip Fabrication

A silicon-glass microfluidic chip was designed and fabricated using deep reactive ion etching

(DRIE) and a shadow mask process. The following procedure was followed to fabricate a

glass/silicon chip:

1- The layout of the solubility chip was designed using AutoCAD as shown in Fig. A1. A

total number of nine chip fitted on each 4ʺ wafer due to optimized dimension of the

solubility chip.

Fig. A1. Solubility chip AutoCAD design. Total number of 9 chips fitted in one single

4ʺ silicon wafer.

2- Mask Writer – Heidelberg uPG 501 Fig. A2. (a)

37

a. The final AutoCAD file saved in DXF format since the Mask writer interface

program only read DXF file.

b. The design was selected by the software and converted into machine language.

c. The 5ʺ clean chrome mask loaded into the machine according to its instruction and

the machine started exposing the design onto the surface of the mask.

d. After the exposure, the mask developed in AZ 400K Developer (dilute 1:5 DI water)

solution for 30 S, rinsed with DI water, and then dried with N2 for 1 minute.

e. Next the mask immersed in Cr etchant (CEP 200) for 30 S, rinsed with DI water,

and then dried with N2 for 1 minute.

f. Finally, the mask immersed in photoresist stripper (PRS 100) for 1 min to remove

the residual photoresist.

3- Photolithography using photoresist S1818

a. Si wafer preheated at 100℃ for 1-2 min.

b. The sample holder cleaned in the spin coater using acetone.

c. The surface of the Si wafer coated with HMDS at 2000 RPM for 90 S.

d. On top of HMDS layer, the Si wafer coated with S1818 photoresist at 2000 RPM

for 90 S.

e. The Si wafer soft baked at 100℃ for 5-8 min to drive the solvent from the

photoresist.

4- Mask Aligner/Exposure Fig. A2. (b)

a. Printed mask including the layout of the solubility chip inserted into the machine

and the exposure dosage set to 200 𝑚𝐽

𝑐𝑚2.

b. After exposure, the Si wafer developed in wet-bench using MF312: DI water = 1:1

for 60 S.

c. The Si wafer rinsed with DI water for 60 S.

d. The Si wafer dried with Nitrogen for 60 S.

5- DRIE – Deep Reactive Ion Etching Fig. A2. (c)

a. The solubility pattern etched on Si wafer using DRIE machine. The desired depth

for channels reached by tuning the number of etching cycle.

b. Piranha (𝐻2𝑆𝑂4: 𝐻2𝑂2 = 2.5: 1) solution used to clean the Si wafer for at least 3

hours.

38

c. The residual photoresist on the Si wafers stripped off by using acetone or stripper.

d. After cleaning, the Si wafer rinsed with DI water for 60 S.

e. The Si wafer dried with nitrogen for 60 S.

6- Profilometer and drilling the wholes Fig. A2. (d)

a. The pattern’s dimension measured using profilometer.

b. The inlet and outlet holes on Si wafers drilled using MicroLux Variable Speed

Miniature Drill Press.

7- The residual photoresist on the Si wafer stripped off using acetone.

8- The Si wafer cleaned using ultrasonic DI water for 5 min.

9- Piranha (H2SO4: H2O2 = 2.5: 1) solution used for cleaning of the Si wafers and

borosilicate glass for at least 3 hours.

10- After cleaning, the Si wafer rinsed with DI water for 60 S.

11- The Si wafer dried with nitrogen.

12- Bonding Fig. A2. (e)

a. Initially Si wafer and glass were dry bonded.

b. Si wafer and glass were permanently bonded using anodic bonding machine.

c. The dry bonded chip placed into the bonding chamber.

d. The chamber was vacuumed and the force set to 100N.

e. The lower platen and upper platen temperature set to 400℃.

f. The voltage set to 600V and current set to 4mA. Then “HV supply” enabled and

keeps on till the current is < 0.1 mA.

g. Finally, the temperature of lower platen and upper platen set to 3℃.

13- Dicing Fig. A2. (f)

a. The inlet and outlet holes on the chip sealed with the tape to avoid water imbibition

into the chip.

b. Cut first started from the glass side of the chip, so the cutting line could be seen

clearly on Si wafer.

c. Dicing speed set to 0.3𝑚𝑚

𝑠 .

39

Fig. A2. Equipment needed for microfabrication. (a) Mask Writer – Heidelberg uPG

501; (b) Mask Aligner/ Exposure; (c) DRIE – Deep Reactive Ion Etching;

(d) Drilling MicroLux Variable Speed Miniature Drill Press; (e) Bonding;

(f) Dicing

Solubility chip (microfluidic chip) had three distinct segments including a solvent channel with

50 µm (width) and 20 µm (depth), a bitumen-solvent PVT cell with 50 µm (width) and 20 µm

(depth), and a bitumen channel with 5 µm (width) and 5 µm (depth) Fig A3. The cross-sectional

area of the bitumen channel was very small, only 2.5% that of the cell, approximating a closed

PVT system. The total volume of PVT cell is 2.5 × 10-3 mm3 (2.5 nL), which is significantly less

than a typical PVT cell volume. The volume of bitumen slug involved in the experiment is less

than 1.0 × 10-3 mm3 (~1 nL). The microfluidic chip was mounted in a stainless-steel manifold

and solvent and bitumen lines were connected to the manifold inlets through 10-32 UNF

compression fitting.

(a) (b) (c)

(d) (e) (f)

40

Fig. A3. Solubility chip along with channel dimensions

Fig. A4. (a) and A4. (b) show both exploded and assembled microfluidic chip with its stainless-

steel manifold. The solubility chip sandwiched between two stainless steel slabs while the inlet

and outlet were sealed using 1/16 x-Profile oil resistant Buna-N O-rings. Figure 2 represent both

assembled and exploded view of the chip within manifold.

Fig. A4. Microfluidic chip with its stainless-steel manifold. (a) Exploded view; (b) assembled

view

(a) (b)

41

2. Swelling Images

The swelling images at 20 ºC for P/Psat = 0.86 shown in Fig A5.

Fig. A5. 1-D bitumen swelling inside the micro-PVT cell at 7.1 bar, 20 ºC

t = 0

t = 1

t = 2

t = 3

t = 4

t = 5

t = 6

t = 7

t = 8

t = 9

t = 10

t = 11

t = 12

t = 13

t = 14

t = 15

t = 16

t = 17

t = 18

t = 19

t = 20

t = 21

t = 22

t = 23

t = 24

t = 25

t = 26

t = 27

t = 28

t = 29

t = 30

t = 31

t = 32

t = 33

t = 34

t = 35

t = 36

t = 37

t = 38

t = 39

t = 40

t = 41

t = 42

t = 43

t = 44

t = 45

t = 46

t = 47

t = 48

t = 49

t = 50

t = 51

t = 52

t = 53

t = 54

t = 55

t = 56

t = 57

t = 58

t = 59

t = 60

42

3. Mathematical approach

As mentioned earlier, the mathematical approach used in this work is based on a model presented

by Jamialahmadi et al. to determine diffusion coefficients from swelling data. The variation on bitumen

length with time is equal to the rate of variation of the liquid phase volume:

𝑑𝑉

𝑉= 𝑑(𝑣𝑠𝐶𝑠,𝑎𝑣) (1)

in which 𝐶𝑠,𝑎𝑣 is the average concentration of the solvent in the bitumen sample (𝑘𝑔

𝑚3) and 𝑣𝑠 is the

specific volume (𝑚3

𝑘𝑔) of the solute (C3H8).

𝐶𝑠,𝑎𝑣 = ∫ 𝐶𝑠𝑑𝑉

𝑉

0

𝑉=

1

𝜈𝑠𝑙𝑛

𝑙𝑡𝑙0

(2)

Where 𝑙0and 𝑙𝑡 are the initial bitumen length and bitumen length at time equal to t respectively. This

equation is used to calculate the average concentration.

The one-dimensional diffusion process, was described using the following form of Fick’s law. It

assumed that no chemical reaction is happened in this process. Also, the diffusion coefficient and

density considered to be constant and no chemical reaction is happened.

𝜕𝐶𝑠𝜕𝑡

= 𝐷𝜕2𝐶𝑠𝜕𝑙2

(3)

The initial and boundary condition for infinite system is:

For 0 < 𝑙 < 𝑙𝑡 and 𝑡 < 0, 𝐶𝑠,𝑎𝑣 = 0 s

For 𝑙 = 𝑙𝑡 and 𝑡 ≥ 0, 𝐶𝑠 = 𝐶𝑠𝑖, (𝐶𝑠𝑖 is the concentration at the propane-bitumen interface)

For 𝑥 = 0 and 𝑡 ≥ 0 𝐶𝑠 = 0

43

Considering the associated initial and boundary condition the solution is given by Crank:

𝐶𝑠(𝑙, 𝑡) = 𝐶𝑠𝑖𝑒𝑟𝑓𝑐(𝑙

2√𝐷𝑡) (4)

Total mass of propane diffused in bitumen phase calculated by integrating Eq. 4 over the volume of

the bitumen plug:

𝑚𝐴 = ∫ 𝐶𝑠(𝑙, 𝑡)𝑑𝑉 = 𝑆 ∫ 𝐶𝑠(𝑙, 𝑡)𝑑𝑥 = 2𝑆𝐶𝑠𝑡√𝐷𝑡

𝜋

𝑙

0

𝑉

0

(5)

S is the cross section of the bitumen plug. Then, Eq. 1 Combined with Eq. 5 to relate the average

concentration to time, diffusivity and interfacial concentration:

𝐶𝑠,𝑎𝑣 =2 𝐶𝑠𝑖

𝑙𝑜 𝑒𝑥𝑝 (𝑣𝑠 𝐶𝑠,𝑎𝑣)√

𝐷𝑡

𝜋= (

2 𝐶𝑠𝑖𝑙𝑜 𝑒𝑥𝑝 (𝑣𝑠 𝐶𝑠,𝑎𝑣)

√𝑡

𝜋) √𝐷 = 𝑚√𝐷 (6)

Therefore, by plotting the average concentration versus the m (term in the parenthesis), the slope

will be equal to the square root of the diffusion coefficient.

So for the infinite case analysis, Eq. 6 above provides the relationship between the average

propane concentration, the solvent diffusion coefficient, D, and the initial solvent concentration at

the solvent-bitumen interface, Csi [31]. The initial solvent concentration at the interface is the

solvent solubility under the test condition.

44

For the finite case analysis, the boundary condition is:

For 𝑙 = 0 and 𝑡 ≥ 0 → 𝜕𝐶𝑠,𝑎𝑣

𝜕𝑙= 0,

Integration of 𝜕𝐶𝑠

𝜕𝑡= 𝐷

𝜕2𝐶𝑠

𝜕𝑙2 with respect to l gives:

∫𝜕𝐶𝑠,𝑎𝑣

𝜕𝑡𝑑𝑙 = 𝐷 ∫

𝜕2𝐶𝑠,𝑎𝑣𝜕𝑙2

= 𝐷𝜕𝐶𝑠,𝑎𝑣

𝜕𝑙|𝑙

𝑙

0

𝑙

0

(7)

Using Leibnitz’s integration rule to expand the first term of Equation:

𝑑

𝑑𝑡∫ 𝐶𝑠,𝑎𝑣 𝑑𝑙

𝑙

0

= 𝐷𝜕𝐶𝑠,𝑎𝑣

𝜕𝑙|

𝑙𝑡+ 𝐶𝑠𝑖

𝑑𝑙𝑡

𝑑𝑡 (8)

Differentiation of 𝜕𝐶𝑠

𝜕𝑡= 𝐷

𝜕2𝐶𝑠

𝜕𝑙2 with respect to time gives:

𝑑𝐶𝑠,𝑎𝑣𝑑𝑡

= 1

𝑙𝑡

𝑑

𝑑𝑡∫ 𝐶𝑠,𝑎𝑣 𝑑𝑙

𝑙

0

− 𝐶𝑠,𝑎𝑣

𝑙𝑡

𝑑𝑙𝑡

𝑑𝑡 (9)

Substituting the second term in the right-hand side by Equation 6 leads to:

𝑥𝑡𝑑𝐶𝑠,𝑎𝑣

𝑑𝑡= (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)

𝑑𝑙𝑡

𝑑𝑡+ 𝐷

𝜕𝐶𝑠,𝑎𝑣

𝜕𝑙|

𝑙𝑡 (10)

Now if we divide both sides to 𝑙𝑡 and substitute for 𝑙𝑡 from Equation 1:

𝑑𝐶𝑠,𝑎𝑣𝑑𝑡

= (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)𝜐𝐴𝑑𝐶𝑠,𝑎𝑣

𝑑𝑡+

𝐷

𝑙0 exp(𝜈𝑎𝐶𝑠,𝑎𝑣)

𝜕𝐶𝑠,𝑎𝑣𝜕𝑙

|𝑙𝑡 (11)

To calculate the last term in the right-hand side of the Equation 11, the development presented by

Jamialahmadi was followed. It was assumed that for a moving boundary system, the concentration

profile of the diffusing substance can be described as:

45

𝐶𝑠𝑖 = 𝑏0 + 𝑏1𝑙𝑛 (12)

in which 𝑏0 and 𝑏1are constants and n is defined as:

𝑛 = 𝑎𝜔, 𝜔 =𝐶𝑠𝑖

𝐶𝑠,𝑎𝑣 (13)

The parameter a is positive and independent of time and should be evaluated from the experimental

data. After some mathematical manipulations, the following expression could be reached for the last

term in the right-hand side of the Eq. 7:

𝜕𝐶𝑠,𝑎𝑣𝜕𝑙

|𝑙𝑡 = (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(1 − 𝜈𝑠𝐶𝑠,𝑎𝑣)

𝑥0𝐶𝑠,𝑎𝑣 (14)

we could rewrite the Equation 12, by replacing the Equation 15 in the last term of Equation 8 and

rearranging it:

𝑑𝐶𝑠,𝑎𝑣𝑑𝑡

= 𝐷(𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 + 𝐶𝑠,𝑎𝑣)(1 − 𝑣𝑠 𝐶𝑠,𝑎𝑣)

2

𝑙𝑜𝐶𝑠,𝑎𝑣 (1 − 𝑣𝑠 (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)) (15)

Again, this equation is different from the Equation 29 in Jamialahmadi which defines the relation

between average concentration and the diffusion coefficient. Instead of using analytical solution

proposed by Jamialahmadi, we performed a numerical integration of Equation 15. After rearranging

Equation 15:

𝑙𝑜𝐶𝑠,𝑎𝑣 (1 − 𝑣𝑠 (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣))

(𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 + 𝐶𝑠,𝑎𝑣)(1 − 𝑣𝑠 𝐶𝑠,𝑎𝑣)2 𝑑𝐶𝑠,𝑎𝑣 = 𝐷𝑑𝑡 (16)

Integrating both sides of this equation:

46

∫𝑙𝑜𝐶𝑠,𝑎𝑣 (1 − 𝑣𝑠 (𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣))

(𝐶𝑠𝑖 − 𝐶𝑠,𝑎𝑣)(𝑎𝐶𝑠𝑖 + 𝐶𝑠,𝑎𝑣)(1 − 𝑣𝑠 𝐶𝑠,𝑎𝑣)2 𝑑𝐶𝑠,𝑎𝑣

𝐶𝑠𝑖

0

= 𝐷𝑡 (17)