Visualization of Fluid Dynamics in Nanoporous Media for Unconventional Hydrocarbon Recovery

by

Arnav Jatukaran

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Arnav Jatukaran 2018

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Visualization of Fluid Dynamics in Nanoporous Media for

Unconventional Hydrocarbon Recovery

Arnav Jatukaran

Master of Applied Science

Department of Mechanical and Industrial Engineering

University of Toronto

2018

Abstract

Evaporation at the nanoscale is critical to hydrocarbon production from nanoporous shale, a

process that has reshaped global energy supply. However, there is a lack of understanding

pertaining to phase change of hydrocarbons trapped in nanopores. This thesis develops and applies

nanofluidics for the direct study of evaporation as relevant to shale oil and gas. Onset and dynamics

of propane evaporation are studied in two-dimensional nanomodel. With sub-10 nm confinement,

evaporation is vapor transport dominated with the Knudsen flow effect twice the viscous flow

effect. A nanomodel is also developed that couples the inherent heterogeneity in shale pore sizes

(100 nm pores gated by 5 nm-pores) to study vaporization of ternary hydrocarbons. Distinct spatio-

temporal dynamics of vaporization are observed as a function of superheat. Results are compared

to a vapor transport model. The differences highlight the inherent complexity of multi-component

fluids in multi-scale geometries at the heart of unconventional resources.

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Acknowledgments

I would like to express my deep gratitude to my advisor Professor David Sinton for his invaluable

guidance and encouragement over the past two years. Thank you for always challenging me to

improve as a researcher.

I am also grateful to have worked with some great people in the lab who were always willing to

help troubleshoot issues encountered in the cleanroom or during experiments. Special thank you

to Junjie Zhong, and post-docs Dr. Aaron Persad and Dr. Ali Abedini.

I would also like to acknowledge the staff at Toronto Nanofabrication Centre and the Centre for

Microfluidic Systems facilities for help with fabrication. Additionally, I would like to thank the

NanoMechanics and Materials Laboratory and Centre for Nanostructure Imaging for help with

AFM and SEM characterization, respectively.

Finally, I would like to thank my family and friends for always supporting me.

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Table of Contents

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

Table of Contents ........................................................................................................................... iv

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

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

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

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

1.1 Motivation ............................................................................................................................1

1.2 Introduction to Nanofluidics ................................................................................................3

1.3 Application of Nanofluidics in Phase Change .....................................................................4

1.4 Thesis Overview ..................................................................................................................6

Chapter 2 ..........................................................................................................................................8

Direct Visualization of Evaporation in a Two-Dimensional Nanoporous Model for

Unconventional Natural Gas .......................................................................................................8

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

2.2 Experimental Section ...........................................................................................................9

2.3 Results and Discussion ......................................................................................................11

2.4 Conclusion .........................................................................................................................19

2.5 Additional Comments Not Included in the Paper ..............................................................20

2.6 Supporting Information ......................................................................................................21

Chapter 3 ........................................................................................................................................32

Shale Nanomodel: Large Pores Gated by a 5-nm Pore Network ..............................................32

3.1 Introduction ........................................................................................................................32

3.2 Results & Discussion .........................................................................................................35

3.3 Conclusion .........................................................................................................................43

3.4 Additional Comments Not Included in the Paper ..............................................................44

v

3.5 Supporting Information ......................................................................................................46

Chapter 4 ........................................................................................................................................52

Conclusions ...............................................................................................................................52

4.1 Summary ............................................................................................................................52

4.2 Outlook and Future Work ..................................................................................................53

References ......................................................................................................................................55

Appendices .....................................................................................................................................65

MATLAB Model for Evaporation Dynamics for Chapter 3 Analysis ......................................65

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List of Tables

Table 2-1: Temperature settings for 𝑇ℎ and 𝑇𝐻 and the corresponding 𝑇 measurement........... 23

Table 2-2: Summary of onset of evaporation results. Error bars in the columns for 𝑃0 and

𝑃𝑒𝑣𝑎𝑝 represent standard deviation measured for at least three separate replicates. ................... 26

Table 2-3: Evaporation rates predicted from resistance model compared to experimental results

....................................................................................................................................................... 30

Table 3-1: Estimate of cleanroom usage cost for one fabrication cycle resulting in 16 usable

chips (as used in Chapter 2 and Chapter 3 work) ......................................................................... 45

Table 3-2: Summary of fluid parameters used in the modelling of evaporation dynamics. ........ 51

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List of Figures

Figure 1-1. Production of tight oil (left) and natural gas (right) from shale reserves. Data is

obtained from the U.S. Energy Information Administration [5]. ................................................... 1

Figure 1-2. Pore sizes in shale. (A) SEM image of a shale sample showing nanoscale porosity.

Scale bar represents 50 nm. Reprinted (adapted) with permission from ref. [9]. Copyright © 2015

American Chemical Society. (B) Typical shale pore size distribution of Western Canadian Horn

River Shale sample showing small pores contributing overwhelmingly on a number basis while

larger pores dominate on a volume basis. Figure 1-2B is obtained from reference [7]. AAPG ©

2012. Reprinted by permission of the AAPG whose permission is required for further use. ........ 2

Figure 2-1. 2D sub-10 nm porous media for hydrocarbon evaporation (a) Optical microscopy

image of evaporation in the 2D nanoporous media with clear distinction between the vapor (light

red) and the liquid phase (dark red). The nanoporous media is 500 μm long and 80 μm wide. In

this example, evaporation proceeds from left (nanopore inlet) to right (dead-end). Panel below

shows a sketch of the pore scale evaporation mechanism indicating the imaging technique taking

advantage of a Fabry Perot optical resonant cavity due to the presence silicon nitride film below

the nanoporous media. (b) Scanning electron microscopy (SEM) images of the nanoporous

media showing the top view (top panel) and cross-sectional view (bottom panel). (c) Atomic

force microscopy (AFM) image of the porous media topography (top panel) and a cross sectional

profile of the pattern (bottom panel). Each pore is 225 nm wide and 9 nm deep. ........................ 10

Figure 2-2. Onset of evaporation in the 2D nanoporous media compared to the bulk saturation

pressure [47], capillary pressure as determined through the Kelvin equation for the 2D

nanoporous media geometry and capillary pressure determined using the Kelvin equation

assuming one immobile propane layer on all surfaces. Error bars reflect the dominant source of

error, the fluctuation of pump (±0.005 MPa), and contain the results for all three replicates for

each point shown........................................................................................................................... 13

Figure 2-3. Evaporation dynamics and model at 287.2 K (𝑃𝑠𝑎𝑡 = 0.716 MPa) (a) Time-lapse

sequence of evaporation at 0.56 𝑃𝑠𝑎𝑡 (0.402 MPa) and (b) 0.83 𝑃𝑠𝑎𝑡 (0.594 MPa). The images

have been converted to grayscale and processed by subtracting the background and enhancing

the contrast. Here, the vapor phase appears bright and the liquid phase appears dark. Only chosen

viii

frames are displayed for clarity. A zoom-in in (a) and (b) are shown adjacent to respective panels

highlighting the vapor phase percolation mechanism. (c) Total vapor fraction (𝜒𝑣) for six

different target pressures plotted as a function of square root time (all experiments performed at

287.2 K). (d) Total vapor fraction growth rate as a function of time during the early stages of

evaporation for the 0.56 𝑃𝑠𝑎𝑡 and 0.83 𝑃𝑠𝑎𝑡 run. (e) Resistance model considering vapor mass

transport and evaporation at the liquid-vapor interface. Total vapor fraction is determined by

taking the ratio of the calculated evaporation front length (𝐿𝑉𝐿), and the nanoporous media

length (L). Scale bar represents 50 μm (f) Example of model predictions compared to

experimental results at 0.56 𝑃𝑠𝑎𝑡 (g) Comparison of evaporation rates calculated from model to

experimental data. Error bars in (c), (f) and (g) represent standard deviation from three repeated

experiments performed on two different nanoporous media each (six replicates). Only

representative standard deviation errors bars are shown in (c). .................................................... 16

Figure 2-4. Evaporation mechanisms induced by initial loading pressures in the capillary

condensation regime. (a) Time-lapse sequence of continuous evaporation at filling pressures of

0.99 𝑃𝑠𝑎𝑡. (b) Time-lapse sequence of discontinuous evaporation at filling pressures of 0.93

𝑃𝑠𝑎𝑡. In both (a) and (b), the final pressure was reduced to 0.75 𝑃𝑠𝑎𝑡 to observe evaporation. (c)

Comparison of evaporation rates at different loading pressures. Error bars represent standard

deviation over three replicate experiments. Yellow bars indicate conditions that triggered

discontinuous evaporation and red bars indicates conditions that led to continuous evaporation.

The horizontal black line shows the evaporation rate predicted by the resistance model for

reference. ....................................................................................................................................... 19

Figure 2-5: Nanoporous media fabrication. (a) Schematic of the fabrication protocol used. (b)

Final fabricated device following bonding with glass and dicing. Each device has four isolated

chips with individual inlet ports. Each chip has eleven isolated nanoporous media. The zoom-in

image in (b) shows an example of a porous media (rotated clockwise 90°) during an evaporation

experiment..................................................................................................................................... 22

Figure 2-6: Schematic of the experimental set-up. For clarity, only a singe nanofluidic chip is

shown. ........................................................................................................................................... 24

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Figure 2-7: Magnitude of resistance terms as a function evaporation front length for (a) early

stages of evaporation (b) and over the entire length of the porous media as calculated from the

resistance model. ........................................................................................................................... 28

Figure 2-8: Time-lapse sequence of discontinuous evaporation with initial liquid saturation 0.95

𝑃𝑠𝑎𝑡 and final target pressure of 0.75 𝑃𝑠𝑎𝑡 ................................................................................. 30

Figure 2-9: Total vapor fraction (χv) for three different initial saturation conditions plotted as a

function of square root time (all experiments performed at 287.2 K with final target pressure of

0.75 𝑃𝑠𝑎𝑡). .................................................................................................................................... 31

Figure 3-1. Oil/gas production from shale reservoirs (A) SEM image illustrates an example of

nanoporous matrix in shale reservoirs containing nanoporosity that leads to the dual-mixture

problem inherent to shale oil/gas (B) Schematic of the shale nanomodel fabrication showing key

steps: (i) etching of 5-nm pore network, (ii) etching of large nanopores and (iii) anodic bonding

to a glass slide. (C) Final fabricated device completely saturated with liquid (liquid filled pores

are dark and isolated pores are bright) The nanomodel is connected to the inlet at the bottom and

is dead-ended at the top. Scale bar represents 1 mm. (D) Characterization of shale nanomodel

with SEM (top panel) and AFM (bottom panel) (E) Comparison of the shale nanomodel

cumulative pore volume distribution to major North American shale formations (shale data

obtained from Zhao et al.[78]) ...................................................................................................... 34

Figure 3-2. Observation of desorption in the shale nanomodel using a ternary hydrocarbon

mixture. (A) Bulk pressure-temperature plot for the C1-C3-C5 mixture (0.1/0.4/0.5 mol. fraction)

(B) Initial filling of the nanomodel with the mixture sample at 4 MPa. Dark circles represent

liquid-filled pores while bright circles represent empty or isolated pores. The solid white arrow

represents the liquid-filling direction. Processed image shows liquid-filled pores colored blue and

all isolated pores colored grey. (C) Images taken during the vaporization process at high

superheat. The dashed white line represents the direction of vapor transport. Processed image

shows all connected vapor-filled pores colored red, and all isolated pores colored grey. ............ 38

Figure 3-3. Liquid filling dynamics in the nanomodel. (A) Spatio-temporal progression of chip

filling at 4 MPa. Color represents relative time at which pore fills with liquid (B) Pore-scale

visualization of filling in a 3 x 2 set of pores at ~69 minutes. Each image is taken after an interval

x

of two minutes. (C) Global filling dynamics in the nanomodel shows a linear dependence on time

in contrast to the Hagen- Poiseuille equation for filling experiments at 4 MPa. .......................... 39

Figure 3-4. Spatio-temporal progression of vaporization events in the nanomodel. Each panel is

2 mm in width and 1.5 mm in length and contains ~ 5500 connected pores. All isolated pores

have been subtracted from the image. Grey pores represent pores that remained saturated with

liquid and did not vaporize in the time period (A-C) Map showing dynamics in the high-

superheat run ~ 0.76 MPa, medium-superheat run ~0.44 MPa, and low-superheat run ~0.25 MPa.

(D-F) Comparison of vaporization progression determined through experiment and vapor

transport governed evaporation model as a function of time corresponding to high superheat,

medium superheat and low superheat. Each data experiment was repeated twice (see Figure 3-8

for the result of the duplicate experiment) .................................................................................... 41

Figure 3-5. Simplified geometry used to calculate the evaporation dynamics (top-view). The

time taken for vapor flow through the small pore network, tsmall, is calculated by determining the

volumetric flow rate through small pores using a resistance model containing both Knudsen flow

resistance and viscous flow resistance contributions. The time taken to transport vapor volume

held in a large pore, tlarge, is calculated by using the small pore network volumetric flow rate and

the volume of a large pore ............................................................................................................ 43

Figure 3-6: Schematic of the experimental set-up. For clarity, only a nanomodel is shown. ..... 48

Figure 3-7. Pore-scale observation of vaporization. The relative intensity in the middle pore in

the snapshots is plotted as a function of time for the high superheat test (Figure 3-4A). The pore

gradually becomes brighter as vaporization progresses in the pore. ............................................ 49

Figure 3-8. Vaporization data from replicate experiments shows good agreement. (A) Data for

0.76 MPa superheat and (B) 0.25 MPa superheat. Solid lines are same as in Figure 3-4A and 3-

4C, respectively. Dashed lines represent repeat experiment. ........................................................ 49

Figure 3-9. Vaporization data for 0.25 MPa vaporization case compared to evaporation model

assuming mixture parameters (same as for Figure 3-4F) and for pure pentane. The pure pentane

evaporation model trends towards the experimental result potentially implying enrichment of

liquid in the nanomodel with heavier pentane due to early desorption of lighter fractions.......... 50

1

Chapter 1

Introduction

1.1 Motivation

Technological advancements in horizontal drilling and hydraulic fracturing have brought with

them unprecedented production from shale and tight oil reservoirs that were previously considered

inaccessible due to their ultra-low permeability and nanoscopic porosity. This boom in production

is expected to continue well into the future as shown by the projections from the United States

Energy Information Administration (Figure 1-1) bringing with it significant economic and geo-

political disruption. This growth has the potential of ushering in a period of long-term North

American energy security. Among the many changes associated with the growth of these

unconventional resources, is a shift away from coal to natural gas for electricity production which

has resulted in a significant reduction in US emissions [1], [2]. While the technology is generally

associated with the United States, shale geological formations are ubiquitous around the globe [3].

Canada is currently the second largest shale oil producer with current output of 335,000 bpd and

this rate is expected to grow to 420,000 bpd within the decade [4].

Figure 1-1. Production of tight oil (left) and natural gas (right) from shale reserves. Data is

obtained from the U.S. Energy Information Administration [5].

Despite this rapid growth, the extraction process is highly inefficient and is hampered by ultra-low

recovery factors (70-80% of hydrocarbons in place are not recovered), sharp declines in production

rates following a couple of years of operation and, highly intensive water usage [6]. These

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operational challenges are in part due to a lack of knowledge of the underlying pore-scale

mechanisms governing hydrocarbon recovery [6]. In contrast to conventional oil and gas

reservoirs, hydrocarbons in shale are confined to nanoscopic pores where bulk theories on phase

change dynamics and transport are expected to break down. Figure 1-2a shows an SEM image of

a shale sample showing nanoscopic pores. Figure 1-2b illustrates the pore size distribution of

Canadian Horn River formation shale sample on both a number basis and volume basis. Pores less

than 10 nm in diameter represent 90% of the pores, while their volume contribution is less than

2%. On the other hand, pores larger than 100 nm in diameter represent less than 1% of the total

number of pores while they contribute to approximately 50% of the total pore volume [7], [8].

During production pressure drawdown, early desorption is favored in larger pores, while the

subsequent transport of fluids through the porous matrix is expected to be limited by the smaller

pores where factors such as molecule-wall interactions become important. Understanding the

thermodynamics and fluid transport of fluids in such extreme confinement is important for

maximizing and sustaining long-term production.

Figure 1-2. Pore sizes in shale. (A) SEM image of a shale sample showing nanoscale porosity.

Scale bar represents 50 nm. Reprinted (adapted) with permission from ref. [9]. Copyright © 2015

American Chemical Society. (B) Typical shale pore size distribution of Western Canadian Horn

River Shale sample showing small pores contributing overwhelmingly on a number basis while

larger pores dominate on a volume basis. Figure 1-2B is obtained from reference [7]. AAPG ©

2012. Reprinted by permission of the AAPG whose permission is required for further use.

Although computer modeling is often employed to predict fluid behavior at the nanoscale,

conclusions are often contradictory as models are often based on different assumptions [10]. The

requirement for experimental results is highlighted by a recent review paper that concludes that

there is a “lack of data at the challenging range of pore scales, less than 10 nm, for simulation

3

validation purposes” [11]. Accordingly, in the following thesis, liquid-to-vapor transitions are

studied using nanofluidic devices that simulate porous media with sub-10 nm features. Evaporation

onset and dynamics are studied in idealized geometries using single-component fluids (Chapter 2)

and in complex geometries using hydrocarbon mixtures (Chapter 3).

1.2 Introduction to Nanofluidics

Microfluidics have become a valuable tool for operators in informing pore-sale phenomenon in oil

sands and conventional oil/gas applications. However, their nanoscale counterparts (nanofluidic

devices with at least one dimension at the nanometer scale) have only recently started gaining

prominence. Interest in the field is primarily driven by the need for fundamental data on fluid

properties under nano-confinement [10]. Broadly, current nanofluidic devices for oil/gas

applications include consolidated and random nanoporous media and silicon-glass (Si-glass) based

discrete nanochannels.

Consolidated porous media can be formed by packing spherical particles such as SiO2

nanoparticles and Vycor glass spheres into a macro-scale channel and the voids between adjoining

particles act as the nanopore space [12], [13]. Micron-thick media with nanoporous voids have

also been formed by anodizing silicon substrates with pores as small as ~ 3 nm in diameter [14].

Such platforms are attractive due to their quasi-3D geometry that closely mimics the randomness

of nanoporous media found in geology and biology. While pore-scale resolution through optical

means is difficult, these platforms do allow for the ability to study of fluid dynamics globally.

Nanopores etched into silicon substrates are another type of nanofluidic devices that are popular

choice due to their (1) ability to withstand high pressure and temperatures, (2) ability to optically

differentiate between fluid phases and (3) relatively well-established fabrication protocols that

allow precise control over pore sizes.

Borrowing techniques from the semi-conductor industry, silicon-glass (Si-glass) nanofluidic chips

are fabricated by first spin coating resist onto a silicon substrate. The desired pattern is then

transferred using lithography techniques. Photolithoraphy allows for 1-D nanoscopic features with

channel widths down to 1 μm, while electron-beam lithography can be used to achieve 2-D

nanoscopic features with channel widths potentially down to 20 nm. Following development to

remove the exposed pattern, the silicon substrate is etched to nanoscale dimensions using wet or

dry etching techniques. Wet-etching is generally fast and provides good selectivity, however, the

4

process results in isotropic, tapered channel profiles and requires working with hazardous

chemicals. Dry-etching can be used to achieve relatively anisotropic etching profiles with vertical

channel walls. The remaining resist is removed in a bath of Piranha solution (H2SO4 and H2O2 in

a 3:1 solution) and the spin-coating, lithography, etching, and Piranha cleaning steps are repeated

to create the micron-scale channels that connect the nanopores to the inlet of the device.

Characterization tools such as atomic force microscopy (AFM), scanning electron microscopy

(SEM) and profilometers can be used at this stage to verify the etch depth and roughness of the

nanochannels. Finally, after drilling inlet holes to allow access to the external experimental set-up,

the silicon substrate is anodically bonded to a glass slide to complete the fabrication. While this

recipe is adequate for fabricating and visualizing fluid dynamics in ~100 nm channels, optically

resolving liquid-vapor phases in channels shallower than 10 nm is extremely difficult. Recently Li

et al., developed a novel method to enhance the contrast between liquid and vapor phases in 8-nm

channels by fabricating the 8-nm pores above a silicon nitride layer [15].

1.3 Application of Nanofluidics in Phase Change

As pressure changes during shale oil/gas production, hydrocarbons confined to nanoscopic pores

may undergo phase change at conditions different than those in bulk. Relevant phase change

phenomenon include condensation and vaporization. Increasing the pressure (or reducing

temperature) above a certain threshold results in the condensation of the vapor phase into liquid

phase. On the other hand, reducing pressure (or increasing temperature) below the threshold can

result in the liquid phase vaporizing via evaporation or cavitation. Evaporation is a surface process

that describes vaporization of liquid at the liquid-vapor interface. Cavitation describes the

nucleation of vapor bubbles that can occur at or below the liquid surface. With the ability to

optically distinguish liquid-vapor phases, nanofluidics lends itself well towards measuring the

onset and dynamics of phase change. The following section provides a brief overview of literature

pertaining to these two concepts.

Nanofluidics have been used to study the onset of capillary condensation down to a few

nanometers with the condensation of water shown to well described the classical Kelvin equation

in 4 nm conduits [16] and in 8-nm channels for propane [17]. Capillary evaporation has also been

shown to be in good agreement with the Kelvin equation at the ~100 nm scale for water [18] and

down to 30 nm for propane [19]. The bubble point of hexane, heptane and octane were also

5

measured in 50-nm deep channels and found to be well described by a Peng-Robinson Equation

of State model [20]. While the bubble point temperature binary and ternary hydrocarbon mixtures

were comparable to bulk values in 50-nm and 100-nm deep channels, higher temperatures were

required to observe phase change in 10-nm channels [21]. Heterogeneous nucleation of vapor

bubbles were investigated using cavities and posts with diameters ranging from 50 nm to 5 microns

and it was found that a higher degree of superheat was required to nucleate a vapor bubble for

smaller cavity sizes [22]. Homogeneous nucleation of propane vapor bubbles in 88-nm deep

channels required significant superheat. Here, cavitation was observed at pressures closer to the

spinodal limit than the classical nucleation theory [23]. Generally, the literature shows that smaller

pores promote condensation at lower pressures as opposed to larger pores and vaporization through

evaporation and cavitation can be significantly delayed as the degree of confinement increases.

From a transport perspective, nanofluidic devices have been used to study the growth of propane

condensate in 70-nm deep channels operating in the transitional flow regime. Here, condensate

growth was mainly limited by the vapor transport through the nanochannel. The vapor transport

resistance, comprising of Knudsen diffusion and viscous flow components, contributed

approximately 70% to the overall resistance with the remainder attributed to the interfacial

resistance across the liquid-vapor interface [24]. Capillary condensation dynamics of propane and

CO2 were also studied in nanoporous packed beds (pore size ~17 nm) and pore-filling dynamics

were attributed to an interplay between condensation and imbibition [25]. Such effects have been

further explored in 8-nm nanochannels where condensate growth was modelled accurately by

including condensation at the nanochannel inlet described by the Hertz-Knudsen equation and the

subsequent liquid flow though the nanochannel described by the Poiseuille equation [17].

Vaporization kinetics of water have also been explored in 72-nm deep channels [26] and in

channels with depths ranging from 29 nm to 122 nm [27]. In both these studies, the extremely

sharp corners of the nanochannels resulted in corner flow and liquid film flow playing a dominant

role in addition to vapor diffusion describing the evaporation kinetics. Additionally, in 56 nm and

shallower channels, a phenomenon termed as “discontinuous evaporation” was observed where a

liquid bridge formed ahead of the receding meniscus. This observation was attributed to possible

defects on the nanochannel surface [27]. Gradients in channel height also led to an interesting

observation in 58-nm channel wherein a vapor bubble appeared at the entrance of the nanochannel

during evaporation and migrated towards the center of the nanochannel. The formation of the vapor

6

bubble was attributed to a slightly deeper profile of the nanochannels at the entrance [28].

Desorption via heterogeneous cavitation of water was also studied in an extreme ink-bottle

geometry by coupling random 5 nm pores to 625 large pores with depths of 27 μm. In this

experimental system, the small pores remain saturated with liquid while bubbles were allowed to

nucleate in the larger pores as pressure was reduced. Pore emptying was observed to follow a cycle

of sudden bursts of cavitation followed by periods without any activity. The mechanism was

attributed to an increase in local pressure following a cavitation event that suppressed further

cavitation events around the region. Drying dynamics were described by a combination of mass

transport and stochastic nucleation kinetics [29].

Use of nanofluidics for phase change studies is a growing research topic and there are still several

areas that have yet to be explored. The sub-10 nm scale is relatively uncharted territory for

researchers. At this scale, the pore size can be comparable to the molecular size of the experimental

fluid and confinement effects are expected to be even more pronounced [10], [11]. Additionally,

while most experimental data focus on single components such as water and propane, the targeted

applications (such as shale oil/gas) are often characterized by a diverse mixture of fluid

components. Currently, there are only a handful of experimental studies published in literature that

study mixtures and more experimental data is required to verify phase change onset and dynamics

for mixtures. Similarly, experimental studies using nanofluidics are mainly performed at discrete

length scales, however, pores in shale formations typically encompass a wide distribution of

lengths ranging from microns to several hundred nanometers and down to a few nanometers. In

these complex systems, vaporization should occur first in larger pores, however the smaller pores

can limit the transport of fluids. Studying the interaction of these length scales is critical to

capturing the heterogeneity inherent to the reservoir. Another interesting area for future work is

studying the effect of surface chemistry on phase change in nanoconfinement.

1.4 Thesis Overview

The main objective of the thesis is to visualize liquid-vapor phase change dynamics in nanoscopic

pores as relevant to unconventional oil and gas.

In Chapter 2, evaporation dynamics in the sub-10 nm pore size range – the largest in terms of their

abundance – is studied. Onset and kinetics of propane evaporation is visualized under isothermal

conditions in a two-dimensional nanoporous model comprised of a network of channels with ~200

7

nm width and 9 nm depth. The main outcomes from this work include (1) the observation that

evaporation onset is delayed as compared to saturation conditions predicted by the Kelvin

equation, (2) that evaporation dynamics at these scales is mainly governed by vapor transport and

that (3) lower initial saturation conditions can trigger cavitation events ahead of the evaporation

front resulting in faster evaporation rates.

Chapter 3 expands upon the work in Chapter 2 by physically simulating the dual-mixture challenge

inherent to shale oil/gas reservoirs – namely mixture fluid components confined in a mixture of

radically different pore sizes. A shale nanomodel with ~ 30,000 total pores is fabricated that

couples the dominant pore size range (<10 nm and ~100 nm pores) and vaporization dynamics of

a ternary hydrocarbon mixture are visualized. The main outcomes from this work include (1)

design and fabrication of a dual-nanoscale shale nanomodel (2) visualization of filling dynamics

of liquid in the nanomodel and (3) visualization of vaporization dynamics under different degrees

of superheat in the nanomodel.

8

Chapter 2

Direct Visualization of Evaporation in a Two-Dimensional Nanoporous Model for Unconventional Natural Gas

This chapter was published in ACS Applied Nano Materials – Reprinted with permission from ref.

[30]. Copyright © 2018 American Chemical Society. The applicant was the primary author for this

work and played the primary role in experimental design, fabrication, data collection and analysis,

and write-up. The efforts of Junjie Zhong, Dr. Aaron H. Persad, Yi Xu, Dr. Farshid Mostowfi and

Professor David Sinton are gratefully recognized.

2.1 Introduction

Evaporation and vapor transport in two-dimensional (2D) nanoporous media plays an important

role in many natural processes and synthetic systems such as in biological membranes [31], plant

hydrodynamics [32][33], electronic cooling devices [34], steam generation [35]–[39], water

desalination strategies [40] and the recovery of hydrocarbons from unconventional oil and gas

reservoirs [3], [10], [24], [41]. There is particular urgency regarding the latter as hydraulic

fracturing has reshaped the global energy supply, while there is a lack of understanding of the

processes taking place in the nano-sized pores. These reservoirs are typically characterized by

pores that can be smaller than 10 nm [9]. The dynamics of phase change in such nanoporous media

are complex, largely unexplored, and critical to quantifying potential recovery and ultimately

assessing energy security associated with these resources [3], [42]. Experimental techniques to

study the onset and dynamics of evaporation in porous media at such length scales are urgently

required to validate the applicability of classical theories, improve the efficiency of production,

and inform policy makers and the public.

Recent advances in nanofluidic device fabrication has enabled the study of thermodynamics at the

nanoscale. Liquid to vapor transitions such as evaporation [14], [26], [27], [43]–[45] and cavitation

[23], [28], [29], [46], in particular, have garnered significant attention. The majority of studies

employ pore or channel dimensions in the range of 100 nm. Experimental techniques to study

evaporation at smaller scales are hindered by both the challenge of fabricating precise 2D

9

nanoscopic conduits and the difficulty in directly visualizing vapor and liquid phases in extreme

nanoconfinement (<10 nm). As such, literature on the direct visualization of liquid to vapor

transitions is limited to a single idealized one-dimensional nanochannels with dimensions from

120 nm down to 20 nm [28]. Even this simple nanoconfined geometry showed rich physics

including evaporation-induced-cavitation not accessible at larger scales [28].

Herein, liquid evaporation is directly visualized in a well-controlled 2D sub-10 nm nanoporous

media (composing of a network of nanopores fabricated on nanofluidic device with a height of

9 nm and a width of ~200 nm) using propane as a working fluid. A silicon nitride layer below the

nanopores forms a Fabry-Perot optical resonance cavity to enhance the contrast between liquid

and vapor phases [15]. The onset of evaporation in the 2D nanoporous media is measured at a wide

range of temperature and pressure conditions, and occurs at significant lower pressures compared

to the classical Kelvin equation predictions. Evaporation dynamics are visually detected at sub-10

nm scale for the first time, and found to be chiefly governed by the vapor transport resistance in

the nanopores. Initial liquid-phase saturation conditions can also lead to different types of

evaporation mechanisms (continuous evaporation and discontinuous evaporation with isolated

cavitation). In providing a clear picture of evaporation in the sub-10 nm nanoporous media, this

work demonstrates the breakdown of classical theories for evaporation at sub-10 nm confinement

to inform natural and industrial processes where phase change occurs at the nanoscale.

2.2 Experimental Section

Figure 2-1 shows the experimental schematic of the set-up and characterization of the nanoporous

media. The nanopores were patterned using electron beam lithography on a silicon wafer coated

with 200-nm thick silicon nitride film and a 9-nm thick silicon dioxide film. The silicon dioxide

film was then etched using a buffered oxide etchant to form the nanopores as shown in SEM and

AFM images in Figure 2-1b and 2-1c, respectively. Porosity of the porous media was determined

using SEM images to be ~77%. AFM was used to determine nanopore depth and width of 8.86 ±

0.16 nm and 224.9 ± 2.5 nm, respectively. Following etching of the microchannels and drilling of

the inlet holes, the nanopores were sealed via an anodically bonded glass layer to complete the

chip fabrication (see Section 2.5.1). During the experiments, the pressure of vapor propane and

temperature in the nanopores was closely controlled and measured (see Section 2.5.2). A typical

snapshot of evaporation in the nanoporous media under the bright field of an optical microscope

10

is shown in Figure 2-1a. The Figure 2-1a image is raw, as-observed using brightfield microscopy

in combination with the Si3N4 base layer, with the vapor phase appearing light red, differentiated

from the dark red liquid phase.

Figure 2-1. 2D sub-10 nm porous media for hydrocarbon evaporation (a) Optical microscopy

image of evaporation in the 2D nanoporous media with clear distinction between the vapor (light

red) and the liquid phase (dark red). The nanoporous media is 500 μm long and 80 μm wide. In

this example, evaporation proceeds from left (nanopore inlet) to right (dead-end). Panel below

shows a sketch of the pore scale evaporation mechanism indicating the imaging technique taking

advantage of a Fabry Perot optical resonant cavity due to the presence silicon nitride film below

the nanoporous media. (b) Scanning electron microscopy (SEM) images of the nanoporous media

showing the top view (top panel) and cross-sectional view (bottom panel). (c) Atomic force

microscopy (AFM) image of the porous media topography (top panel) and a cross sectional profile

of the pattern (bottom panel). Each pore is 225 nm wide and 9 nm deep.

Prior to running experiments, entire system was vacuumed for three hours while allowing the

system to achieve thermal equilibrium at an experimental temperature (𝑇). Afterwards, liquid-

phase propane was injected at pressures above the saturation pressure (𝑃𝑠𝑎𝑡), corresponding to 𝑇.

11

This initiation procedure was repeated a minimum 10x prior to running experiments reported here.

The pressure was lowered to a target below the saturation pressure to observe evaporation. Once

the pressure was lowered below saturation, the liquid in the bulk reservoir evaporated almost

instantaneously. At each target pressure, the waiting time to observe possible evaporation in the

nanopores was five minutes. In the event where evaporation in the nanopores was not observed,

the set-up was vacuumed and the experiment was repeated at a lower target pressure (see Section

2.5.2).

2.3 Results and Discussion

2.3.1 Evaporation in Nanoporous Media

The onset of evaporation was measured under isothermal conditions with 𝑇 ranging from 287.2 K

to 317.5 K and results are shown in Figure 2-2. For reference, Figure 2-2 also shows both the

saturation pressure for bulk (𝑃𝑠𝑎𝑡) [47] and the Kelvin equation predictions (𝑃𝐾𝑒𝑙𝑣𝑖𝑛) for the

experimental nanopore geometry. 𝑃𝐾𝑒𝑙𝑣𝑖𝑛 for the nanoconfinement is calculated by menisci radii

of height (ℎ) and width (𝑤):

ln (𝑃𝐾𝑒𝑙𝑣𝑖𝑛

𝑃𝑠𝑎𝑡) =

2𝛾𝑉𝐿𝑐𝑜𝑠𝛳

𝑅𝑇(

1

ℎ+

1

𝑤) (2.1)

Where 𝛾 and 𝑉𝐿 are the surface tension and molar volume of propane liquid at 𝑇, 𝑅 is the gas

constant, and 𝛳 is the contact angle of propane on the nanopore surface (0° on the silica/silicon

nitride). As shown in Figure 2-2, the experimental pressures at which evaporation was observed

(∆𝑃𝑒𝑣𝑎𝑝), was significantly lower than 𝑃𝐾𝑒𝑙𝑣𝑖𝑛. The deviation from the pressure predicted by the

Kelvin equation ranged from 3.3% to 11.1% (see Section 2.5.3). Note that in Figure 2-2, the largest

experimental error was no more than ± 0.01%

There is debate in literature on whether the Kelvin equation is applicable in predicting the onset of

capillary evaporation or capillary condensation at the sub-10 nm scale [48], [49]. The Kelvin

equation has been used to predict capillary condensation in porous media and nanochannels down

to a few nanometers [16], [24], [50]. Nevertheless, in typical adsorption-desorption isotherms for

nanopores on the order studied here, a hysteresis in the saturation condition is observed between

the pressures at which pores fill (condensation) and the pressures at which the pores empty

(evaporation) [51]. Factors that influence the degree of hysteresis include pore size, temperature

12

and the type of adsorbate [52]. Previous research shows that the Kelvin equation can accurately

predict capillary evaporation of both water and propane confined to tens of nanometers [18], [19],

indicating negligible hysteresis effects in those cases. However, in ~6 nm cylindrical pores, the

Kelvin equation predicted capillary condensation pressures reasonable well, but failed to predict

capillary evaporation [53], [54]. In the experiments, evaporation onset for propane is also delayed

as compared to the Kelvin equation (up to 11%). Immobile liquid films often observed in

nanopores can also contribute to this deviation by lowering the effective pore size [15], [55].

Assuming immobile propane (diameter ~0.43 nm) films on all surfaces, Kelvin equation would

predict the trend shown in Figure 2-2. While considering this effectively smaller channel size

trends towards the experimental results, the prediction is well off. Hence, one or even two

immobile liquid films of propane cannot entirely explain the deviation observed here.

The hysteresis between capillary condensation and evaporation is speculated to increase with

nanoconfinement, as shown in previous studies in adsorption/desorption experiments at similar

length scales [56]. Researchers have suggested that pore-blocking during desorption, wherein

liquid in interior pores not directly connected to the exterior vapor reservoir cannot evaporate, can

lead to hysteresis [57]. This hysteresis effect is significant at ~10 nm scale, causing significant

deviation of capillary evaporation to capillary condensation and the Kelvin equation.

280 290 300 310 3200.5

0.7

0.9

1.1

1.3

1.5

Pre

ssu

re (

MP

a)

Temperature (K)

Bulk Saturation Pressure

Kelvin Equation Prediction with AFM Measured Pore Size

Kelvin Equation Prediction with One Immobile Propane Layer

Experimental Results

13

Figure 2-2. Onset of evaporation in the 2D nanoporous media compared to the bulk saturation

pressure [47], capillary pressure as determined through the Kelvin equation for the 2D nanoporous

media geometry and capillary pressure determined using the Kelvin equation assuming one

immobile propane layer on all surfaces. Error bars reflect the dominant source of error, the

fluctuation of pump (±0.005 MPa), and contain the results for all three replicates for each point

shown.

2.3.2 Effect of Superheat on Evaporation Dynamics

To study the evaporation dynamics, experiments were conducted for different superheat conditions

at a constant 𝑇 of 287.2 K. Figure 2-3a and Figure 2-3b show time-lapse sequence of evaporation

images obtained with high superheat (0.402 MPa/0.56 Psat) and low superheat (0.593 MPa/0.83

Psat). As shown in the corresponding timestamps (Figure 2-3a and 2-3b), high superheat resulted

in faster evaporation. In both cases, upon lowering the pressure to the target value, evaporation

began at the nanopore inlet with a sudden burst of liquid expulsion into vapor phase followed by

reduction in evaporation growth rate over time. As the vapor-liquid interface receded deeper into

the porous media, evaporation was punctuated by the invasion of a vapor column that grew a short

distance into the porous media ahead of the lagging vapor-liquid front. The vapor column then

expanded laterally and downwards eventually converging with the lagging vapor-liquid front. This

vapor percolation typically occurred at later stages in the process (>1 second) and was especially

pronounced for cases with low superheat. Low superheat conditions (Figure 2-3b) resulted in the

evaporation front becoming rough with more vapor percolation. With high superheat, the greater

pressure differential allowed the lagging vapor-liquid front to proceed quickly with minimal vapor

column percolation, resulting in a relatively uniform evaporation front (shown in zoom-in inset

images in Figure 2-3a and 2-3b).

The vapor percolation observed here is in general not possible in 1D nanochannels and rather

requires, at minimum, a 2D nanoporous geometry. Additionally, the planar nature of the

nanoporous media allows for accurate optical resolution of the entire advancing evaporation front,

something not possible in nanoporous media platforms such as anodized porous silicon layers [14]

and nanoporous Vycor glass [12] where much of the two-phase interface is obscured by the media.

Additionally, for a given nanoporous media, vapor percolation pathways were relatively similar

for all repeated experiments. This affect may be attributed to artefacts of fabrication, namely local

14

heterogeneities in the nanoporous media surface (such as small variations in height or surface

heterogeneities).

Figure 2-3c shows the total vapor fraction (𝜒𝑣) at 287.2 K at different target pressures of 0.56 𝑃𝑠𝑎𝑡 ,

0.62 𝑃𝑠𝑎𝑡, 0.73 𝑃𝑠𝑎𝑡, 0.76 𝑃𝑠𝑎𝑡, 0.80 𝑃𝑠𝑎𝑡 and 0.83 𝑃𝑠𝑎𝑡, with greater superheats resulting in faster

evaporation. Despite the difference in the degree of vapor percolation for different applied

superheats, the total vapor fraction for all runs exhibit a square-root-of-time dependence. In real

time (s) the total vapor fraction grows rapidly during the first 1 s and then stabilizes, as shown for

the highest superheat and lowest superheat cases in Figure 2-3d. Similar behavior was also

observed through molecular dynamic simulations on methane extraction from nanoporous kerogen

and has been proposed to be a mechanism for the steep decline in the productivity of shale gas

wells [58].

To model the observed evaporation dynamics, the evaporation front (𝐿𝑉𝐿) is assumed to be uniform

as shown in Figure 2-3e, and assumed to recede smoothly from the inlet. The model includes both

evaporation across the vapor-liquid interface and vapor transport from the interface to the nanopore

inlet. As the Knudsen number for the vapor transport in the sub-10 nm system is expected to be

~1 here (see Section 2.5.4), resistance for vapor transport can be described by the combination of

viscous flow resistance (𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠) and Knudsen flow resistance (𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛) [59] acting in parallel

as shown in Figure 2-3e. In addition, the effect of molecular exchange at the vapor-liquid interface

is described using the Hertz-Knudsen equation (interfacial resistance, 𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒) [24]. Combining

the three terms that contribute to the resistance, and taking into account the degree of superheat

(∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡), the liquid phase receding rate can be calculated as (see Section 2.5.4):

𝜕𝐿𝑉𝐿

𝜕𝑡=

∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡

𝜌𝐿𝜌𝑔

(𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛𝑅𝑉𝑖𝑠𝑐𝑜𝑢𝑠

𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛+𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠+𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒)

(2.2)

Where 𝜌𝐿 and 𝜌𝑔 are the density of the liquid and gas phase, respectively. Integrating the above

equation leads to an expression for 𝐿𝑉𝐿 as a function of time. There is no corresponding flow

resistance in the liquid phase as there is a no-flow condition in the dead-end system. Considering

the simplification of a uniform evaporation front, the total vapor fraction can then be defined as

the ratio of 𝐿𝑉𝐿 to the length of the nanoporous media (𝐿=500 μm) over the duration of the

experiment.

15

Figure 2-3f compares the experimental result obtained for total vapor fraction at 0.56 𝑃𝑠𝑎𝑡 with

that predicted by the resistance model, showing a similar trend and reasonable agreement. Figure

2-3g further shows a comparison of the evaporation growth rate determined using experimental

data and the modelling results for all six tested target pressures, with the predictions closely

matching the measured values (see Section 2.5.4). The vapor mass transport resistance

significantly dominates the interfacial resistance, especially after 𝐿𝑉𝐿 exceeds ~8 nm. With

nanoconfinement, both the Knudsen flow resistance and viscous flow resistance are significant.

Here, Knudsen flow resistance magnitude in the overall vapor transport is approximately twice

that of the viscous flow resistance (see Section 2.5.4).

These results deviate from previous work in macro-porous media [60], [61] and in one-

dimensional nanochannels [26], [27] that include a significant contribution from liquid corner flow

and thin film flow in addition to vapor transport. Recent experiments in nanochannels with depths

of 29 nm and greater show enhanced evaporation due to corner flow [27]. The geometry of long

single nanochannels allows corner flow to be particularly strong - so much so that the water

evaporation rates can be insensitive to known drivers such as relative humidity [26]. In contrast to

single nanochannel systems, however, results here show reasonable agreement with vapor

transport model predications including superheat, and without specific correction for corner flow.

16

Figure 2-3. Evaporation dynamics and model at 287.2 K (𝑃𝑠𝑎𝑡 = 0.716 MPa) (a) Time-lapse

sequence of evaporation at 0.56 𝑃𝑠𝑎𝑡 (0.402 MPa) and (b) 0.83 𝑃𝑠𝑎𝑡 (0.594 MPa). The images have

been converted to grayscale and processed by subtracting the background and enhancing the

contrast. Here, the vapor phase appears bright and the liquid phase appears dark. Only chosen

frames are displayed for clarity. A zoom-in in (a) and (b) are shown adjacent to respective panels

highlighting the vapor phase percolation mechanism. (c) Total vapor fraction (𝜒𝑣) for six different

target pressures plotted as a function of square root time (all experiments performed at 287.2 K).

(d) Total vapor fraction growth rate as a function of time during the early stages of evaporation for

the 0.56 𝑃𝑠𝑎𝑡 and 0.83 𝑃𝑠𝑎𝑡 run. (e) Resistance model considering vapor mass transport and

evaporation at the liquid-vapor interface. Total vapor fraction is determined by taking the ratio of

the calculated evaporation front length (𝐿𝑉𝐿), and the nanoporous media length (L). Scale bar

represents 50 μm (f) Example of model predictions compared to experimental results at 0.56 𝑃𝑠𝑎𝑡

(g) Comparison of evaporation rates calculated from model to experimental data. Error bars in (c),

(f) and (g) represent standard deviation from three repeated experiments performed on two

different nanoporous media each (six replicates). Only representative standard deviation errors

bars are shown in (c).

17

2.3.3 Discontinuous Evaporation Induced by Initial Liquid Saturation

A distinct form of liquid-to-vapor transition is also observed when the initial liquid pressure was

between 𝑃𝐾𝑒𝑙𝑣𝑖𝑛 and 𝑃𝑠𝑎𝑡. In the case where the initial liquid pressure was at or above the bulk

saturation pressure, smooth evaporation from the nanopore inlet was observed (herein referred to

as “continuous evaporation”). Although the evaporation front took on various profiles in the results

of Figure 2-3, all cases were continuous in that liquid-to-vapor transition occurred only at the

evaporation front. However, when the initial liquid loading pressure was below bulk saturation

pressure, nucleation of vapor bubbles in the porous media was observed in addition to the

evaporation from front – a hybrid herein referred to as “discontinuous evaporation”. To study this

phenomenon, experiments were performed at 291.6 K for initial saturation conditions ranging from

0.93 𝑃𝑠𝑎𝑡 to 0.99 𝑃𝑠𝑎𝑡 (𝑃𝐾𝑒𝑙𝑣𝑖𝑛 = 0.93 𝑃𝑠𝑎𝑡). Time-lapse sequences of evaporation from media

loaded at 0.99 𝑃𝑠𝑎𝑡 and 0.93 𝑃𝑠𝑎𝑡 are plotted for comparison in Figure 2-4a and 2-4b, respectively.

For an initial liquid pressure of 0.99 𝑃𝑠𝑎𝑡, continuous evaporation was exclusively observed

(Figure 2-4a). However, when the chip was loaded at 0.93 𝑃𝑠𝑎𝑡, both evaporation from the inlet of

the nanopores and isolated cavitation within the porous media was observed (Figure 2-4b). In this

case, evaporation and the appearance of the isolated vapor bubbles were effectively instantaneous

upon the reduction in pressure to the target value. The vapor bubbles that cavitated within the

nanoporous media grew and eventually converged with the growing evaporation front. In general,

this effect was observed consistently, with a higher number of cavitation events corresponding to

lower initial liquid pressures (see Section 2.5.5).

Evaporation rates for the discontinuous cases were higher than for continuous evaporation under

comparable superheats. Figure 2-4c shows a comparison between the evaporation rates for three

different initial liquid saturation pressures once pressure was reduced to a constant target value of

0.75 𝑃𝑠𝑎𝑡. The evaporation rate for the discontinuous evaporation was determined by the total area

evaporated, including via both evaporation from the nanopore inlet and the growth of the cavitated

vapor bubbles. Similar to continuous evaporation, a square-root-time dependence was observed

for this total vapor fraction measure (see Section 2.5.5). The horizontal black line in Figure 2-4c

shows the evaporation rate as predicted by the model. The model shows a relatively good match

to the case where the initial liquid pressure was at 0.99 𝑃𝑠𝑎𝑡. However, with discontinuous

18

evaporation, evaporation can be as much as 10% faster as compared to the continuous evaporation

experimental result.

Two possible mechanisms are suggested to explain the origins for continuous vs discontinuous

evaporation. Firstly, the density and order of molecules packed within the nanopores at a given

pressure in the adsorption regime is expected to be strongly influenced by the height of the channel

and the saturation condition as shown via molecular dynamic simulations [62]–[65]. At relatively

high initial liquid saturation conditions (≥ 𝑃𝑠𝑎𝑡), the order in propane molecule structuring is

expected to be the strongest and continuous evaporation is exclusively observe. With lower initial

liquid saturation pressures (< 𝑃𝑠𝑎𝑡), the liquid phase can a lower density of molecules and weaker

structuring of propane molecules especially in regions of the porous media with local expansions

in size and/or fabrication defects. Upon reduction in the pressure, these regions are more

susceptible to cavitation. Secondly, at lower initial saturation conditions, propane vapor pockets

may be trapped in surface heterogeneities. A reduction in pressure can result in these pre-existing

vapor pockets growing and eventually appearing as cavities. Such vapor pockets have been long

reported to influence initiation of cavitation in macroscale systems [66]. Pre-pressurization can

thus suppress these cavitation sites resulting only in evaporation from the inlet of the nanopores.

Similar pre-pressurization effects have also been reported in bulk systems with water as the test

fluid [67]–[69]. Previous experimental studies at the nanoscale have shown that deviations from

the traditional picture of continuous evaporation from the front can be induced by fabrication

artefacts [27],[28] and different evaporation rates [70], [71]. Nevertheless, through the experiments

show that discontinuous evaporation observed here takes place only under specific experimental

conditions.

19

Figure 2-4. Evaporation mechanisms induced by initial loading pressures in the capillary

condensation regime. (a) Time-lapse sequence of continuous evaporation at filling pressures of

0.99 𝑃𝑠𝑎𝑡. (b) Time-lapse sequence of discontinuous evaporation at filling pressures of 0.93 𝑃𝑠𝑎𝑡.

In both (a) and (b), the final pressure was reduced to 0.75 𝑃𝑠𝑎𝑡 to observe evaporation. (c)

Comparison of evaporation rates at different loading pressures. Error bars represent standard

deviation over three replicate experiments. Yellow bars indicate conditions that triggered

discontinuous evaporation and red bars indicates conditions that led to continuous evaporation.

The horizontal black line shows the evaporation rate predicted by the resistance model for

reference.

2.4 Conclusion

In summary, evaporation was imaged in 2D sub-10 nm porous media using isothermal conditions

with propane as a working fluid. In doing so, deviations from bulk conditions with regards to

evaporation onset and dynamics were demonstrated. The onset of evaporation is significantly

delayed as compared to the Kelvin equation predicted pressures. Evaporation dynamics, in contrast

to recent literature, is found to be well predicted by vapor transport alone. With regards to the

vapor transport term, the magnitude of the Knudsen flow resistance term is twice as much as the

viscous flow resistance term. Additionally, a phenomenon wherein lower initial liquid saturation

pressures trigger discontinuous evaporation including both vapor bubble nucleation in the porous

media and evaporation from the front was observed. The results of this study have implications

towards understanding and optimizing a number of processes where evaporation occurs in

nanoporous media. Perhaps more imminently, delayed onset of evaporation and the subsequent

20

decline in evaporation rates observed here could help forecast production from shale gas reservoirs

and inform decline curve analysis to model productivity of shale gas wells.

2.5 Additional Comments Not Included in the Paper

The following section includes additional commentary on difficulties, failures and challenges that

may be useful for future experimentalist working in this field.

From a fabrication perspective, work presented here was the first step towards creating a

nanomodel with 2D nanoscopic features by patterning the design using electron-beam lithography.

In the design, the channel widths were less than 50 nm, however, due to the use of wet-etching,

isotropic etching was observed resulting in the channels becoming significantly larger (~200 nm).

While wet-etching was very successful for sub-10 nm 1D nanochannels (where control of the

vertical depth dimensions were more critical than the width dimensions) [15], [17], dry-etching

may be more suitable for future nanomodels where extremely low-aspect ratio channels may be

desired (albeit by sacrificing some control over channel depth). Anodic bonding was a stage at

which numerous fabrication cycles failed. Due to the silicon nitride film and the ultra-shallow

depths, the channels were observed to collapse under high voltages (600 V) that are used in typical

anodic bonding recipes. Lower voltages were used to avoid channel collapse, however, this led to

regions on the chip that were poorly bonded with air gaps that rendered the chip unusable. This

could be a result of incomplete cleaning during the Piranha cleaning stage. Extreme care should

be taken to ensure the chip is clean after Piranha by closely examining both the substrate and the

glass slide. Anodic bonding parameters that worked well include: temperature of 673 K, pressure

of 10-3 Pa, force of 100 N, voltage of 100 V. The anodic bonding process was stopped once the

charge reached 100 mC (after ~ 5 minutes). The overall chip manufacturing process is expensive

and time-consuming. Breakdown of costs and analysis is presented in Section 3.4 for Chapter 3

and the discussion is also applicable to the work in Chapter 2.

During experiments, care should be taken to mitigate leaks in the tubing and pipe-systems. Leaks

can result in impurities in the system that can affect results. Leak tests should be performed at each

connection by using soapy water. Additionally, during experiments, it was noted that the first few

runs were not repeatable, while results became consistent after ~10 runs. This observation

potentially indicates that as the channels aged, the surface chemistry became more uniform. Data

21

presented in this thesis were all obtained following this initial channel surface aging (see Section

2.6.2) and future studies could investigate this process further.

2.6 Supporting Information

2.6.1 Nanoporous Media Fabrication

Each fabricated chip contained eleven nanoporous media (500 μm long and 80 μm wide) placed

perpendicular to the 20 μm deep service microchannel that had a drilled inlet hole for the propane

injection. The fabrication process is shown in schematic form in Figure 2-5a and final fabricated

device is shown in Figure 2-5b. To fabricate the device, 1) a 200-nm thick film of silicon nitride

was first deposited onto the bare silicon wafer (4-inch diameter, 1-mm thick silicon wafer) using

low pressure chemical vapor deposition (Expertech CTR-200 LPCVD). 2) A 9-nm thick silicon

dioxide layer was then deposited onto the wafer using plasma enhanced chemical vapor deposition

(Oxford Instruments PlasmaLab System 100 PECVD). 3) Following this, ZEP-520A e-beam resist

was spin-coated onto the wafer and the nanoporous media was patterned using electron-beam

lithography (Vistec EBPG 5000+ Electron Beam Lithography System). 4) A buffered oxide etch

solution (BOE, 20:1) was used to etch the nanoporous pattern resulting in the 9-nm deep and ~225-

wide network of channels. 5) Following this, the service microchannel pattern was written on a

photo mask (Heidelberg μPG 501) and transferred onto the wafer coated with AZ9260 photoresist

using UV lithography (Suss MicroTec MA6 Mask Aligner). The service microchannels were then

etched using Reactive Ion Etching (Oxford PlasmaPro 100 Cobra ICP-RIE). Five 400 μm deep

channels were also etched 1 mm above the location of the nanoporous media into which

thermocouples were inserted to determine experimental temperature following experiment. Inlet

holes were then drilled through the silicon wafer. 6) After cleaning the wafer and a 2-mm thick

Borosilicate glass slide in Piranha solution (H2SO4:H2O2 = 3:1) for 1 hour, the two were anodically

bonded at 673 K, 10-3 Pa and 100 V for approximately 5 minutes (AML AWB-04 Aligner Wafer

Bonder). 7) The bonded device was then diced into the desired shape to fit the experimental set-

up (Disco DAD3220 Automatic Dicing Saw).

22

Figure 2-5: Nanoporous media fabrication. (a) Schematic of the fabrication protocol used. (b)

Final fabricated device following bonding with glass and dicing. Each device has four isolated

chips with individual inlet ports. Each chip has eleven isolated nanoporous media. The zoom-in

image in (b) shows an example of a porous media (rotated clockwise 90°) during an evaporation

experiment.

2.6.2 Experimental Procedure and Temperature Measurements

The nanofluidic device was mounted on a custom-built high-pressure manifold and connected to

the experimental set-up shown in Figure 2-6. All components of the set-up (tubing, piston cylinder,

valves and manifold) were thoroughly cleaned using DI water and dried using an air gun. The

nanofluidic chip was placed under an optical microscope (Leica DM 2700M) with a 10X objective

lens, allowing the visualization of evaporation in two different nanoporous media simultaneously.

Evaporation was recorded using a camera (Leica DMC 2900) with a frame rate of approximately

21 frames-per-second.

Temperature was controlled by applying a temperature gradient over the chip. A copper block

connected to an electric heater (accuracy ± 0.1 K) was placed close to the entrance of the nanopores

and set to a temperature (𝑇𝐻) that was above the saturation temperature corresponding to the

23

experimental pressure conditions. That is, a vapor state was ensured at the inlet of the nanochannels

in all cases. A second copper block connected to a circulating water bath was set to a relatively

lower temperature (𝑇ℎ) (accuracy ± 0.01 K) and placed directly underneath the nanoporous media.

The two blocks were separated by a ~1 mm thick insulation layer. A relatively hotter temperature,

𝑇𝐻, over the inlet microchannel ensures a vapor condition at the inlet of the nanopores at all test

conditions here. The experimental temperature (𝑇) was determined by measuring the temperature

close to the nanopores by inserting a thermocouple in a 400 μm deep channel etched 1-mm above

the location of the nanopores and with the same 𝑇𝐻 and 𝑇ℎ settings (measurement accuracy of ±

0.1 K). The temperature settings for 𝑇𝐻 and 𝑇ℎ and the corresponding 𝑇 measured values are shown

in Table 2-1.

Table 2-1: Temperature settings for 𝑇ℎ and 𝑇𝐻 and the corresponding 𝑇 measurement

𝑇ℎ (K) 𝑇𝐻 (K) 𝑇(K)

283.0 299.0 287.2

289.0 299.0 291.6

291.0 353.0 305.8

297.0 353.0 309.8

303.0 353.0 314.0

308.0 353.0 317.5

The propane sample was transferred into the piston cylinder from a propane gas tank (research

grade, Praxair 99.99% purity). Two separate experimental configurations were employed

depending on the pressure range under investigation. For the high-pressure experimental

conditions (greater than 0.9 MPa), the piston cylinder was filled with liquid-phase propane at room

temperature and at pressures above saturation. Pressure in the chip was controlled using an Isco

pump and measured using a pressure transducer (accuracy ± 0.001 MPa). The fluctuation in the

Isco pump pressure during the course of a typical experiment was ± 0.005 MPa. In the low-pressure

range (below 0.9 MPa), the piston cylinder was filled with gas-phase propane at room temperature

and at pressures below saturation. In this regime, pressure in the chip was controlled using ideal

gas law based on the constant-volume piston cylinder. The initial pressure was controlled by

24

adjusting the relative opening of the gas cylinder valve and the drawdown pressure was achieved

by opening the vacuum valve until the target value was achieved.

Figure 2-6: Schematic of the experimental set-up. For clarity, only a singe nanofluidic chip is

shown.

Prior to running experiments, the system was allowed to reach thermal equilibrium and the system

was vacuumed for three hours at 2 × 10-7 MPa (PFPE RV8) to remove residual air from the system.

For every new chip, the first ten runs were discarded to ensure uniform surface chemistry. To

determine onset of evaporation, the chip was initially filled with liquid phase propane at pressures

above saturation for the corresponding 𝑇. After waiting 2 minutes, the pressure was systematically

lowered to a target pressure below the saturation pressure to observe evaporation. Once the

pressure was lowered below the saturation pressure, the liquid in the microchannel evaporated

almost instantaneously. At each target pressure, there was a five minute wait time for observing

evaporation in the nanopores. Evaporation generally took place within a few seconds (~10

seconds) following a reduction in pressure, therefore, a 5-minute window was deemed to be long

25

enough to observe evaporation. In the event where evaporation in the nanopores was not observed,

the set-up was vacuumed and the experiment was repeated at a lower target pressure.

The dynamics of evaporation were determined under isothermal conditions (291.6 K). The

nanoporous media was loaded with liquid propane pressures above saturation. Following a 2-

minute waiting period, the pressure was lowered to a target value below the pressure at which

evaporation was first observed at 287.2 K. The range of final target pressure conditions tested

included: 0.56 𝑃𝑠𝑎𝑡 (0.402 MPa), 0.62 𝑃𝑠𝑎𝑡 (0.446 MPa), 0.73 𝑃𝑠𝑎𝑡 (0.525 MPa), 0.76 𝑃𝑠𝑎𝑡 (0.546

MPa), 0.80 𝑃𝑠𝑎𝑡 (0.574 MPa) and 0.83 𝑃𝑠𝑎𝑡 (0.593 MPa).

To study the appearance of discontinuous evaporation in the nanoporous media, the initial liquid

saturation conditions were varied at a constant temperature of 291.6 K. The initial liquid saturation

conditions include: 0.93 𝑃𝑠𝑎𝑡 (0.746 MPa), 0.95 𝑃𝑠𝑎𝑡 (0.766 MPa) and 0.99 𝑃𝑠𝑎𝑡 (0.796 MPa).

Following a 2-minute waiting period the pressure was lowered to 0.75 𝑃𝑠𝑎𝑡 (0.603 MPa) to observe

evaporation for all three initial liquid saturation conditions.

2.6.3 Onset of Evaporation Measurements

To study the appearance of discontinuous evaporation in the nanoporous media, the initial liquid

saturation conditions were varied at a constant temperature of 291.6 K. The initial liquid saturation

conditions include: 0.93 𝑃𝑠𝑎𝑡 (0.746 MPa), 0.95 𝑃𝑠𝑎𝑡 (0.766 MPa) and 0.99 𝑃𝑠𝑎𝑡 (0.796 MPa).

Following a 2-minute waiting period the pressure was lowered to 0.75 𝑃𝑠𝑎𝑡 (0.603 MPa) to observe

evaporation for all three initial liquid saturation conditions.

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = |𝑃𝐾𝑒𝑙𝑣𝑖𝑛−𝑃𝑒𝑣𝑎𝑝

𝑃𝐾𝑒𝑙𝑣𝑖𝑛| × 100% (2.3)

For all data points, evaporation was observed at pressures below that predicted by the Kelvin

equation. Additionally, compared to the difference between 𝑃0 and 𝑃𝑒𝑣𝑎𝑝, and the standard

deviation for each 𝑃𝑒𝑣𝑎𝑝 measurement, the pressure fluctuations in the Isco pump was generally

higher (± 0.005). Hence, in Figure 2-2, data points are plotted with error bars that include this

larger error range.

26

Table 2-2: Summary of onset of evaporation results. Error bars in the columns for 𝑃0 and 𝑃𝑒𝑣𝑎𝑝

represent standard deviation measured for at least three separate replicates.

𝑇 (K) 𝑃𝑠𝑎𝑡 (MPa) 𝑃𝐾𝑒𝑙𝑣𝑖𝑛

(MPa)

𝑃0 (MPa) 𝑃𝑒𝑣𝑎𝑝 (MPa) Deviation

from Kelvin

Eq. (%)

287.2 0.716 0.662 0.644 ± 0.002 0.640 ± 0.004 3.32

291.6 0.806 0.750 0.694 ± 0.001 0.690 ± 0.000 7.96

305.8 1.157 1.093 0.975 ± 0.002 0.972 ± 0.001 11.11

309.8 1.271 1.207 1.085 ± 0.002 1.081 ± 0.001 10.42

314.0 1.402 1.336 1.258 ± 0.008 1.249 ± 0.001 6.54

317.5 1.519 1.454 1.366 ± 0.002 1.364 ± 0.000 6.18

2.6.4 Resistance Model

To model the observed evaporation dynamics, it is assumed that the evaporation front is uniform

as shown in Figure 2-3e. This vapor growth is expected to be described by an interplay between

evaporation across the vapor-liquid interface and vapor mass transport from the vapor-liquid

interface to the inlet of the nanopores. The Hertz-Knudsen relationship is used to describe the

interfacial resistance (𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒) [24]:

𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 = 𝜌𝑔

𝛼√

2𝜋𝑅𝑇

𝑀 (2.4)

Here, 𝜌𝑔 is the density of the gas phase, 𝛼 is the evaporation coefficient equal to one,[72] 𝑅 is the

gas constant, 𝑇 is temperature and 𝑀 is the molar mass.

Considering the hydraulic diameter of the nanopores (𝑑ℎ) and the mean free path of propane (𝜆),

the Knudsen number is calculated as:

𝐾𝑛 =𝜆

ℎ=

𝑘𝐵𝑇

√2𝜋𝑑2𝑃

ℎ (2.5)

27

Where 𝑘𝐵 is the Boltzmann constant, 𝑑 is the size of the molecule (0.43 nm for propane), 𝑃 is the

experimental pressure condition at which evaporation was observed and h is the pore height. At

the lowest superheat condition tested (0.83 𝑃𝑠𝑎𝑡/0.594 MPa), 𝐾𝑛 is calculated to be 0.90 and at the

highest superheat condition tested (0.56 𝑃𝑠𝑎𝑡/0.402 MPa), 𝐾𝑛 is calculated to be 1.33. Therefore,

the system is assumed to be within the transitional region, requiring that the vapor mass transport

is described by both the viscous flow resistance (𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠) and Knudsen flow resistance (𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛)

[59] acting in parallel as shown in Figure 2-3e. Here, 𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛 is calculated as:

𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛 =3𝜌𝑔

𝑚𝑜𝑙𝜏𝐿𝑉𝐿

4ℎ𝜑√1

2𝜋𝑅𝑇𝑀

(2.6)

where 𝜌𝑔 𝑚𝑜𝑙 is molar density, 𝜏 is the tortuosity of the porous media, 𝐿𝑉𝐿 is the average evaporation

front length as indicated in Figure 2-3e, ℎ is the height of the pores and 𝜑 is the porosity of the

pores. Porosity is calculated to be ~0.77 using the SEM images shown in Figure 2-1b. Using the

Bruggeman correlation (𝜏 = 𝜑−0.5) tortuosity is calculated to be 1.14.

Likewise, 𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠 is calculated to be:

𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠 =𝐿𝑉𝐿𝜂𝑣𝑎𝑝𝑜𝑢𝑟

𝑘 (2.7)

where 𝜂𝑣𝑎𝑝𝑜𝑢𝑟 is the vapor viscosity and 𝑘 is the permeability of the nanoporous media. To

determine permeability, a series of filling experiments were performed and Darcy equation was

used to calculate permeability:

𝑑𝐿

𝑑𝑡=

𝑘∆𝑃

𝜂𝑙𝑖𝑞𝑢𝑖𝑑𝐿(𝑡) (2.8)

where 𝑘 is permeability, 𝜂𝑙𝑖𝑞𝑢𝑖𝑑 is liquid viscosity, 𝐿 is the length of the porous medium and ∆𝑃

is the pressure difference between the nanopore inlet and the nanopore dead-end. Integrating the

equation results in an expression for permeability that is a function of the time required to fill the

length of the porous media:

𝑘 =𝐿2𝜂𝑙𝑖𝑞𝑢𝑖𝑑

∆𝑃𝑡 (2.9)

28

In these experiments, the chip was initially held under vacuum and liquid propane was injected at

0.8 MPa at 291.6 K. The filling process was recorded through 13 separate runs and the time taken

for the liquid to completely fill the 500 μm long nanoporous media was determined to be 1.18 s

(standard deviation of 0.14 s). The permeability was then calculated to be (1.39 ± 0.14) × 10-17 m2.

This value is in the range of permeabilities expected for shale oil/gas formations [73].

The magnitude of the three resistance terms as a function of the evaporation front length (𝐿𝑉𝐿) is

plotted in Figure 2-7. The interface resistance term dominates the vapor transport terms up to an

evaporation front length of ~8 nm. As shown in Figure 2-7, at an evaporation front length of 500

μm, the Knudsen flow resistance is calculated to be 1.83 × 1010 𝑃𝑎∗ 𝑠

𝑚 whereas the viscous flow

resistance is 9.36 × 109 𝑃𝑎∗ 𝑠

𝑚. The magnitude of the Knudsen flow resistance term is thus

approximately twice that of the viscous flow resistance.

Figure 2-7: Magnitude of resistance terms as a function evaporation front length for (a) early

stages of evaporation (b) and over the entire length of the porous media as calculated from the

resistance model.

Combining the three terms that contribute to the resistance (equations 2.4, 2.6 and 2.7), and taking

into account the degree of superheat (∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡) the vapor flow rate (𝑉𝑔) can be calculated to be:

𝑉𝑔 =∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡

(𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛𝑅𝑉𝑖𝑠𝑐𝑜𝑢𝑠

𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛+𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠+𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒)

(2.10)

29

Where ∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡 is the difference between the pressure at which evaporation initiation was

observed (𝑃𝑒𝑣𝑎𝑝) and the final target pressure.

To calculate the receding liquid rate (𝑉𝐿), the continuity equation is applied at the liquid-vapor

interface:

𝜌𝑔𝑉𝑔 = 𝜌𝐿𝑉𝐿 (2.11)

Here, 𝜌𝑔 and 𝜌𝐿 are the density of the gas and liquid, respectively. Combining equation S8 and S9

gives:

𝑉𝐿 =𝜕𝐿𝑉𝐿

𝜕𝑡=

∆𝑃𝑠𝑢𝑝𝑒𝑟ℎ𝑒𝑎𝑡

𝜌𝐿𝜌𝑔

(𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛𝑅𝑉𝑖𝑠𝑐𝑜𝑢𝑠

𝑅𝐾𝑛𝑢𝑑𝑠𝑒𝑛+𝑅𝑣𝑖𝑠𝑐𝑜𝑢𝑠+𝑅𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒)

(2.12)

Integrating the above equation leads to an expression for the length of the evaporation front (𝐿𝑉𝐿)

as a function of time. Experimentally, the total vapor fraction (𝜒𝑣) can then be calculated as the

ratio of 𝐿𝑉𝐿 to the length of the nanoporous media (𝐿) over the duration of the experiment:

𝜒𝑣(𝑡) =𝐿𝑉𝐿(𝑡)

𝐿 (2.13)

The evaporation rate was determined by plotting 𝜒𝑣 as a function of √𝑡 and calculating the slope

of the linear relationship. The calculated evaporation rates from the model and the corresponding

evaporation rates from the experiment at 287.2 K are shown in Table 2-3 and plotted in Figure 2-

3g. The model matched the evaporation trends observed experimentally and generally performed

well in predicting the rates. The deviation between the model and experiment are also included in

Table 2-3 showing a maximum deviation of ~25% at lower superheat. The error between the

experimentally determined evaporation rate (𝑅𝑎𝑡𝑒𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡) and that predicted by the model

(𝑅𝑎𝑡𝑒𝑚𝑜𝑑𝑒𝑙) is calculated as follows:

𝐸𝑟𝑟𝑜𝑟 =𝑅𝑎𝑡𝑒𝑚𝑜𝑑𝑒𝑙−𝑅𝑎𝑡𝑒𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡

𝑅𝑎𝑡𝑒𝑚𝑜𝑑𝑒𝑙× 100% (2.14)

30

Table 2-3: Evaporation rates predicted from resistance model compared to experimental results

Superheat

(𝑃/𝑃𝑠𝑎𝑡)

𝑅𝑎𝑡𝑒𝑚𝑜𝑑𝑒𝑙 (1/√𝑠) 𝑅𝑎𝑡𝑒𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡 (1/√𝑠)

(± s.d. over 6 runs)

Error (%)

0.56 0.392 0.404 ± 0.003 -2.9

0.62 0.354 0.375 ± 0.004 -5.9

0.73 0.273 0.305 ± 0.002 -12.0

0.76 0.246 0.283 ± 0.002 -15.0

0.80 0.206 0.249 ± 0.003 -20.4

0.83 0.174 0.219 ± 0.001 -25.5

2.6.5 Evaporation Mechanisms

Discontinuous evaporation was also observed when the initial liquid saturation was 0.95 𝑃𝑠𝑎𝑡 as

shown in in the time-lapse sequence of evaporation in Figure 2-8. Compared to the 0.93 𝑃𝑠𝑎𝑡 initial

liquid saturation case, fewer cavitation events are noted when the initial liquid saturation was

relatively higher at 0.95 𝑃𝑠𝑎𝑡. With 0.93 𝑃𝑠𝑎𝑡 5 cavitation events are observed (Figure 2-4b)

compared to 3 cavitation events observed with 0.95 𝑃𝑠𝑎𝑡.

Figure 2-8: Time-lapse sequence of discontinuous evaporation with initial liquid saturation 0.95

𝑃𝑠𝑎𝑡 and final target pressure of 0.75 𝑃𝑠𝑎𝑡

The total vapor fraction for the discontinuous evaporation also showed a square-root-of-time

dependence as shown in Figure 2-9:

31

Figure 2-9: Total vapor fraction (χv) for three different initial saturation conditions plotted as a

function of square root time (all experiments performed at 287.2 K with final target pressure of

0.75 𝑃𝑠𝑎𝑡).

32

Chapter 3

Shale Nanomodel: Large Pores Gated by a 5-nm Pore Network

The work presented in this chapter is a based on a manuscript currently in preparation. The

applicant was the primary author for this work and played the primary role in experimental design,

fabrication, data collection and analysis, and write-up. The efforts of Junjie Zhong, Dr. Ali

Abedini, Atena Sherbatian, Professor Zhehui Jin and Professor David Sinton are gratefully

recognized.

3.1 Introduction

Transport and thermodynamics of fluid mixtures in nanoporous media with a complex distribution

of length scales is critical to a number of fields including biology [29], [74] and geology [3], [6].

In particular, the importance of the latter is highlighted by the rapid emergence of unconventional

shale oil/gas that underscores long-term North American energy security [75]. Here, horizontal

wells (> 1 km in length) are drilled deep into the reservoir and the natively ultra-low permeable

shale is fractured by pumping highly-pressurized fracturing fluids. This process effectively opens

the source rock for production, and particles within the fracture fluid (proppants) keep the fractures

open as pressure is reduced. While the well productivity is initially high due to rapid depletion of

reservoir pressure and production from larger pores and fractures (10 – 100 m), it significantly

declines over time as the production mechanism ultimately transitions towards nanoscale

phenomenon such as desorption and diffusion from natural fractures and nanoporous matrix [6].

The effectiveness of this process has had profound impacts in global energy and the environment.

Examples include a transition away from coal to less carbon-intensive natural gas in electricity

production [2], establishing US as a major global oil producer [1], [76], depressed oil and gas

prices, as well as the environmental impacts from both the development of these resources (water

use, energy use, CO2 emissions, seismic activity) and the ultimate use of the fossil fuel [1], [76],

[77]. While the broad implications of hydraulic fracturing technology are becoming clearer, and

industry continues to develop these processes, there is lag in fundamental understanding of this

complex, yet important, process. Understanding the fluid transport and thermodynamics central

33

to this process is both challenging and crucial for predicting oil/gas production, environmental

impacts and ultimately energy security.

The fundamental complexity at the heart of this process is a “dual-mixture” problem, i.e., the

thermodynamics associated with the nature of multi-component fluid mixtures and the radically

multi-scale systems (numerous nanopores at different scales connected to macro fractures). Pore

size distributions of shale reservoirs present an interesting dichotomy wherein small pores

(particularly ≤10 nm in diameter) dominate in terms of their number and larger pores (≥ 100 nm

in diameter) dominate in terms of volume [7], [8] and store most of the accessible hydrocarbons

[78]. During pressure drawdown, desorption via bubble nucleation and evaporation is favored in

the larger pores [74], however, the subsequent transport of fluids in the nanoporous matrix is

limited by smaller conduits where nanoconfinement effects such as Knudsen diffusion become

significant [24], [30]. Further complexity is added by the fact that composition of fluids in these

pores is heterogeneous and evolves as production proceeds. Lighter, volatile components desorb

first enriching the nanopores with heavier fractions that are potentially difficult to extract.

Experimental tools are urgently needed to probe the interaction of these two variables –

heterogeneous length-scales and fluid compositions – in the reservoir.

While micromodels have become an integral tool for visualizing pore scale mechanisms associated

with the oil sands and conventional reservoirs [79]–[81], micromodels with nanoscopic features

representing shale oil/gas (herein referred to as ‘nanomodels’) are still in their infancy [42], [82].

Recent advances in nanofabrication enable the direct study nanoconfinement effects at a single

length scale in discrete nanochannels, differentiating fluid phases in sub-10 nm deep channels

using simple working fluids such as propane and water [17], [28]. While these contributions have

provided insight into the fundamentals of fluid behavior in nanoconfinement, idealized pore-

geometries and pure fluid systems do not capture the dual-mixture complexity inherent to shale

reservoirs.

Here, a shale nanomodel that encompasses dominant length scales in the nanoporous matrix with

~100 nm large pores gated by a ~5 nm small pore network is developed. Using this platform,

vaporization dynamics of a ternary hydrocarbon mixture is studied in order to simulate the primary

production phase of liquid-rich natural gas. Significant superheat is required to desorb the

hydrocarbon mixture from the nanopores. Depending on the applied superheat, markedly different

34

spatio-temporal dynamics are observed. Higher superheats result in faster and more uniform

vaporization fronts where desorption initiates at the nanomodel inlet and the liquid front recedes

into the large pores. Low superheat results in more random and isolated vaporization events

throughout the porous media. A relatively simple model accounting for vapor mass transport

adequately describes the vaporization dynamics at high superheat. However, the model

overpredicts vaporization dynamics at low superheat. While the focus here is on fluid transport

during primary production here, the nanomodel device may potentially be used for informing

several pore-scale mechanisms associated with shale oil/gas recovery.

Figure 3-1. Oil/gas production from shale reservoirs (A) SEM image illustrates an example of

nanoporous matrix in shale reservoirs containing nanoporosity that leads to the dual-mixture

problem inherent to shale oil/gas (B) Schematic of the shale nanomodel fabrication showing key

steps: (i) etching of 5-nm pore network, (ii) etching of large nanopores and (iii) anodic bonding to

a glass slide. (C) Final fabricated device completely saturated with liquid (liquid filled pores are

dark and isolated pores are bright) The nanomodel is connected to the inlet at the bottom and is

dead-ended at the top. Scale bar represents 1 mm. (D) Characterization of shale nanomodel with

SEM (top panel) and AFM (bottom panel) (E) Comparison of the shale nanomodel cumulative

pore volume distribution to major North American shale formations (shale data obtained from

Zhao et al.[78])

35

3.2 Results & Discussion

3.2.1 Shale Nanomodel Fabrication and Characterization

The 2 mm x 1.5 mm shale nanomodel was designed to match shale nanoporous matrix properties

(dominant length scales, porosity, permeability etc.) closely, highlighting the dynamics of large

internal pores connected by a smaller nanoporous matrix. Figure 3-1B shows the nanomodel

fabrication procedure with a detailed description included in Section 3.4.1. Briefly, the small pore

network mask was created using a modified Voronoi pattern generated on AutoCad with channel

widths of ranging from 40 nm to 200 nm. The pattern was transferred onto a silicon substrate

(previously coated with a 200-nm thick silicon nitride film) using electron beam lithography and

etched to a depth of 5.54 ± 0.25 nm using deep reactive ion etching (DRIE) resulting in two-

dimensional (2-D) nanoscopic features. Voronoi patterns have been widely used to introduce

geometric heterogeneity in micromodels to study flow and transport [83]–[85]. An array circular

one-dimensional (1-D) large pores (~ 5.8 μm in diameter and center-to-center spacing of 17 μm

following etching) were then transferred onto the substrate using UV lithography and etched to a

depth of 82.2 ± 2.9 nm using DRIE. The large pores were created with microscale diameters to

allow for visualization under an optical microscope during the experiment. Since accurate

alignment of the 1-D large pores to the 2-D 5-nm pore network is not possible, an excess of large

pores were fabricated to ensure relatively good connectivity. Therefore, approximately 40% of the

large pores remained isolated from the 5-nm pore network and did not play a role in the

experiments. A third cycle of lithography and DRIE was then performed to create the 20 μm deep

inlet microchannel. To complete the fabrication, the substrate was anodically bonded to a glass

slide to seal off the nanomodel from the atmosphere. The fabricated nanomodel was mounted onto

a high-pressure manifold and connected to the external experimental system including the transfer

cylinder containing the test fluid (see Section 3.5.2 for experimental set-up).

Figure 3-1C shows a snapshot of the fabricated shale nanomodel imaged via an optical microscope

during an experiment. Dark circles represent liquid-saturated large pores while bright circles

represent isolated large pores that are not connected to the small pore network. Approximately

5,500 large pores are connected here to the small pore network (~30,000 pore nodes). The shale

nanomodel was characterized using scanning electron microscopy (SEM) and atomic force

microscopy (AFM) prior to anodic bonding and results are presented in Figure 3-1D. The SEM

36

image shows an example of both large pore connected to the small pore network and an isolated

large pore. Here, the average width of the small pore network channels are ~100 nm. The AFM

cross-section profile illustrates the ~15-fold difference in height between the large pore and the

small pore network. The areal porosity of the small pore network and the large pores were 5% and

10% respectively giving a dual-depth porosity of ~10.5% [86]. The relative volume capacity in the

nanomodel was on the order of picolitres with the volume capacity of the large pores dominating

that of the small pore network by 30:1. Figure 3-1E compares the cumulative pore volume

distribution of the shale nanomodel to major North American shale formations (adapted from

literature data of N2 adsorption measurements [78]) showing relatively good match. Here, both the

N2 adsorption data and the calculations here include the volume contribution of the isolated pores.

Since fluid transmissivity in the nanomodel is expected to be governed primarily by the small

nanopore network, permeability can be estimated by the Kozeny equation using small nanopore

size to be 44 nd. Both the calculated shale nanomodel permeability and porosity, key parameters

that govern fluid transport in porous media, are within the range of real shale reservoirs.

3.2.2 Filling Dynamics in Shale Nanomodel

The hydrocarbon mixture components were chosen to simulate shale light oil and gas condensate

and comprised of 0.1 methane, 0.4 propane and 0.5 pentane (mol. fraction). The phase diagram of

the prepared mixture sample is presented in Figure 3-2A. After vacuuming the nanomodel for three

hours, the hydrocarbon mixture was injected into the chip above the bulk bubble point pressure at

room temperature as indicated by the purple line in Figure 3-2A. Figure 3-2B shows the nanomodel

during and after the filling process. Additionally, an image following processing shows the liquid

saturated pores in blue and isolated pores in grey at the end of the filling process (see Section 3.5.3

for image processing method). Once injected, liquid instantly filled the microchannel and slowly

started flowing into the nanomodel from the inlet. At a filling pressure of 4 MPa, the total filling

time was approximately 3 hours. During this process, time-lapse images were recorded every 2

minutes. The spatio-temporal map illustrating the filling dynamics at 4 MPa is shown in Figure 3-

3A. The global filling dynamics illustrate generally uniform behavior from inlet of the

microchannel towards the dead-ended region of the nanomodel. Figure 3-3B show pore-scale

observations of the filling process in a 3 x 2 set of pores midway in the filling process. Initially the

pores are empty. As filling progresses, grey liquid films first coat the large nanopore boundaries

before completely filling the large nanopore. The filling dynamics observed here can be attributed

37

to possible corner-flow effects previously observed in micropores [81]. While not the focus of this

work, interestingly, the overall filling dynamics in the nanomodel showed a linear dependence on

time as opposed to a square-root-of-time dependence typically predicted for pressure-driven flows.

Figure 3-3C shows the percentage of filled pores as a function of time during an experiment at 4

MPa filling pressure. Additionally, Figure 3-3C also plots the Hagen-Poiseuille predicted

dynamics in a simplified linear arrangement of large nanopores connected to a 5-nm pore network.

In the calculation, it is assumed that liquid transport is limited in the 5-nm pore network and the

transport time, 𝑡𝑠𝑚𝑎𝑙𝑙 is:

𝑡𝑠𝑚𝑎𝑙𝑙 =𝐿𝑠𝑚𝑎𝑙𝑙

2 𝐴𝑠𝑚𝑎𝑙𝑙𝜇𝑙

𝑃𝑓𝑖𝑙𝑙ℎ𝑠𝑚𝑎𝑙𝑙3 𝑤𝑠𝑚𝑎𝑙𝑙

(3.1)

Here, 𝐿𝑠𝑚𝑎𝑙𝑙, 𝐴𝑠𝑚𝑎𝑙𝑙 , ℎ𝑠𝑚𝑎𝑙𝑙 and 𝑤𝑠𝑚𝑎𝑙𝑙 are the length, cross-sectional area, height and width of

the 5-nm pore network, respectively, and 𝜇𝑙 is the liquid viscosity. 𝑃𝑓𝑖𝑙𝑙 is the filling pressure

(difference between the liquid pressure and the capillary pressure in a large nanopore). The time

required to fill a large nanopore through a 5-nm pore is then determine by relating the volume of

a large nanopore to the volumetric velocity in the 5-nm pore network. The calculation results in a

step-function with a square-root-of-time dependence on the time. Here, the horizontal steps

represent the time necessary to fill a large nanopore with liquid and the vertical jumps represent

the relatively fast filling the 5-nm pore network. The total filling time determined through

experiment is approximately four times slower than that predicted by the model. Additionally, the

model does not have the same linear profile as seen in the experiment.

38

Figure 3-2. Observation of desorption in the shale nanomodel using a ternary hydrocarbon

mixture. (A) Bulk pressure-temperature plot for the C1-C3-C5 mixture (0.1/0.4/0.5 mol. fraction)

(B) Initial filling of the nanomodel with the mixture sample at 4 MPa. Dark circles represent liquid-

filled pores while bright circles represent empty or isolated pores. The solid white arrow represents

the liquid-filling direction. Processed image shows liquid-filled pores colored blue and all isolated

pores colored grey. (C) Images taken during the vaporization process at high superheat. The dashed

white line represents the direction of vapor transport. Processed image shows all connected vapor-

filled pores colored red, and all isolated pores colored grey.

39

Figure 3-3. Liquid filling dynamics in the nanomodel. (A) Spatio-temporal progression of chip

filling at 4 MPa. Color represents relative time at which pore fills with liquid (B) Pore-scale

visualization of filling in a 3 x 2 set of pores at ~69 minutes. Each image is taken after an interval

of two minutes. (C) Global filling dynamics in the nanomodel shows a linear dependence on time

in contrast to the Hagen- Poiseuille equation for filling experiments at 4 MPa.

3.2.3 Vaporization Dynamics in Shale Nanomodel

Once the entire chip was saturated with liquid, it was left for ~12 hours to allow for the

hydrocarbon composition in the nanomodel to achieve equilibrium prior to initiating pressure

drawdown. Pressure drawdown was performed under different isothermal conditions (42.5°C,

62.5°C and 82.5°C). Temperature was increased to the target value using an electric heater. After

40

the temperature stabilized, the pressure was lowered stepwise as shown in Figure 3-2A. The time-

lapse images of the process were recorded at a frequency of 10 seconds. At each solid circle in

Figure 3-2A, a waiting time of 15 minutes was set to observe potential phase change. As the

pressure was lowered below the bulk dew point, vapor bubbles started to appear in the

microchannel with no detectable change in the nanomodel. This result is similar to that observed

in recently experiments in single 1-D nanochannels and through density functional theory

modelling where a two-phase envelope was not observed for hydrocarbon binary mixtures and

significantly low pressures below the bulk dew point were required for vaporization [87].

To study phase change dynamics at the nanoscale, the pressure was lowered to below the bulk dew

point by exposing the nanomodel to vacuum condition. Vaporization was observed in the large

pores almost instantaneously in all cases. For the three temperature conditions, the superheat

(defined here as the difference between the bulk dew point pressure and vacuum conditions) were

0.76 MPa (at 82.5°C), 0.44 MPa (at 62.5°C), and 0.25 MPa (at 42.5°C). Figure 3-2C shows images

of nanomodel during the phase change process at 0.76 MPa superheat. Additionally, the final

image shows a post-processed image after 30 minutes with the color grey representing isolated

pores and the color red indicating vaporized pores. At the pore scale, vaporization resulted in the

pore gradually becoming brighter over a period of ~1 second as the pore emptied (relative intensity

over time for a single pore is plotted in Figure 3-7).

Figure 3-4A, 3-4B and 3-4C display the spatio-temporal dynamics of vaporization for the three

conditions (from high superheat to low superheat) showing markedly slower and less spatially

uniform vaporization fronts at reduced superheats. High superheats (i.e. 0.76 MPa and 0.44 MPa)

resulted in vaporization fronts that initiated from the inlet of the nanomodel and progressed

uniformly into the nanomodel. In addition, vaporization events were observed ahead of the

vaporization front – a phenomenon more pronounced at 0.44 MPa superheat compared to 0.76

MPa superheat. Vaporization ahead of the front have previously been reported in nanoporous

media as a result of pre-pressurization conditions [30], and for slow drying rates [71] in single-

component systems. Here, these events may be attributed to lighter components preferentially

vaporizing ahead of the front.

In contrast in the low superheat case of 0.25 MPa, spatio-temporal dynamics of vaporization were

dramatically different with vaporization events dispersed throughout the nanomodel. After 480

41

minutes of vaporization, approximately 760 pores (~14% of total pores), remained saturated with

liquid. These pores were mainly grouped near the entrance of the nanomodel and are colored grey

in Figure 4C.

Figure 3-4. Spatio-temporal progression of vaporization events in the nanomodel. Each panel is 2

mm in width and 1.5 mm in length and contains ~ 5500 connected pores. All isolated pores have

been subtracted from the image. Grey pores represent pores that remained saturated with liquid

and did not vaporize in the time period (A-C) Map showing dynamics in the high-superheat run ~

0.76 MPa, medium-superheat run ~0.44 MPa, and low-superheat run ~0.25 MPa. (D-F)

Comparison of vaporization progression determined through experiment and vapor transport

governed evaporation model as a function of time corresponding to high superheat, medium

superheat and low superheat. Each data experiment was repeated twice (see Figure 3-8 for the

result of the duplicate experiment)

Figure 3-4D, 3-4E and 3-4F plot the experimental data for the percentage of vaporized pores as a

function of time for all three superheat conditions (from high superheat to low superheat).

Replicate experimental data is included in Figure 3-7. Data for all cases illustrates a square root of

time dependence. Figure 3-4D to 3-4F also display the results of a vapor transport resistance model

developed assuming pure evaporation for all three tested cases. In the model, it is assumed that

42

evaporation is limited by vapor transport resistance in the 5-nm pores and is comprised of both

Knudsen flow and viscous flow components acting in parallel. The vapor resistance factor, 𝑅𝑉,

can be calculated to be:

𝑅𝑉 =𝜌𝑙/𝜌𝑔

ℎ𝑠𝑚𝑎𝑙𝑙2

12𝑢𝑔+

2√2ℎ𝑠𝑚𝑎𝑙𝑙3𝜌𝑔

√ �̅̅̅�

𝜋𝑅𝑇

(3.2)

where 𝜌𝑔 and 𝜌𝑙 are the gas and liquid density, ℎ𝑠𝑚𝑎𝑙𝑙 is the height of channel in the small nanopore

network, 𝑢𝑔 is the gas viscosity, 𝑀 is the molar mass, 𝑅 is the gas constant and 𝑇 is the temperature

(see Section 3.4.5 for discussion on mixture parameters). Using a simplified geometry of a linear

arrangement of large pores connected by the 5-nm pore network (as shown in Figure 3-5), the

transport time through the 5-nm pore network, 𝑡𝑠𝑚𝑎𝑙𝑙 , is first calculated:

𝑡𝑠𝑚𝑎𝑙𝑙 =𝑅𝑉𝐿𝑠𝑚𝑎𝑙𝑙

2

2𝛥𝑃 (3.3)

Here, 𝐿𝑠𝑚𝑎𝑙𝑙 is the length of the small nanopore network and 𝛥𝑃 is the superheat. At each large

nanopore location, the time required to empty the volume held in a large pore through the 5-nm

pore network, 𝑡𝑙𝑎𝑟𝑔𝑒, is also determined by relating the large pore volume, 𝑉𝑙𝑎𝑟𝑔𝑒, and the

volumetric vapor flow rate in the 5-nm pore network, 𝑄𝑠𝑚𝑎𝑙𝑙 :

𝑡𝑙𝑎𝑟𝑔𝑒 =𝑉𝑙𝑎𝑟𝑔𝑒

𝑄𝑠𝑚𝑎𝑙𝑙 (3.4)

The cumulative evaporation dynamics show a square root of time dependence with a step-wise

growth. The horizontal steps indicate the emptying time for the volume in the large pores while

the jumps indicate the relatively fast transport of vapor held in the 5-nm pores. Longer times are

required to empty each successive large pore as the transport resistance through the 5-nm pore

network progressively becomes greater.

The simplified evaporation model adequately describes the experimental results for the high

superheat cases at 0.76 MPa and 0.44 MPa. With relatively high driving force, both light and heavy

components readily vaporize from the nanopore inlet as shown through the spatio-temporal plots

in Figure 3-4A. The dynamics is thus mainly governed by liquid evaporation at the liquid-vapor

interface rightly captured in the model. However, in the low superheat case (0.25 MPa),

experimental results indicate the vaporization of mixture in the nanomodel is strongly affected by

43

bubble nucleation in addition to evaporation. The model largely overpredicts the vaporization

dynamics especially at later times. At this condition, lighter components are expected to

preferentially cavitate throughout the nanomodel enriching the liquid system with heavier pentane

that is slower to vaporize. In fact, evaporation model predictions for pure pentane trends towards

the experimental data obtained for the 0.25 MPa with relatively similar magnitude of vaporization

time (see Section 3.5.4).

Figure 3-5. Simplified geometry used to calculate the evaporation dynamics (top-view). The time

taken for vapor flow through the small pore network, tsmall, is calculated by determining the

volumetric flow rate through small pores using a resistance model containing both Knudsen flow

resistance and viscous flow resistance contributions. The time taken to transport vapor volume

held in a large pore, tlarge, is calculated by using the small pore network volumetric flow rate and

the volume of a large pore

3.3 Conclusion

In summary, a nanomodel is developed and fabricated that replicates the dominant length scales

typically found in the shale nanoporous matrix. The nanomodel consists of large nanopores (~100

nm in depth) gated by a 5-nm pore network. The nanomodel was used to quantify the porescale

vaporization of a ternary hydrocarbon mixture, reflective of a shale gas condensate/light oil

system. The evaporation data showed that a large pressure drawdown was required to vaporize

hydrocarbons in the nanomodel. Depending on the applied superheat, different vaporization

dynamics were observed. High superheats resulted in a faster and uniform vaporization initiating

from the model entrance. In contrast, lower superheats resulted in slow vaporization with less

uniform vaporization front. A vapor transport model, considering both Knudsen flow and viscous

44

flow effects, was also developed to model the vaporization dynamics. While the model well

predicts the observed results at high superheats, it fails to describe vaporization dynamics at low

superheat, possibly due to preferential desorption of lighter components that enriches the

nanomodel with heavier fractions.

3.4 Additional Comments Not Included in the Paper

The following section includes additional commentary on difficulties, failures and challenges that

may be useful for future experimentalist working in this field.

The experimental system and associated theory developed in this chapter provide unprecedented

insight into fluid mechanics and thermodynamics of complex multi-component fluids in complex

multi-scale volumes. Analysis of the data collected is still on-going. Specifically, the spatio-

temporal correlations of vaporization large nanopores is something that is currently being further

explored and compared to previous literature. Additionally, the anomalous liquid filling dynamics

observed here (Figure 3-3) are unique and require extended theoretical analysis to understand.

Nanofluidic studies are currently motivated by the need for fundamental understanding, and as

these tools gain commercial interest, cheaper methods will be required. While unprecedented in

terms of scale, the 30,000+ pore/throat model was difficult and expensive to fabricate. Table 3-1

tabulates the current cost of once cycle of Si-Glass manufacturing at the Toronto Nanofabrication

Centre (TNFC) and the Centre for Microfluidic Systems (CMS) at the University of Toronto (U

of T). All steps are performed at TNFC with the exception of Mask writing which is done at CMS.

The table includes the hourly rate for a U of T affiliated user and an external industry user. Since

fabrication can often fail at the critical anodic bonding step (see Section 2.5), 2 nanofluidic devices

were fabricated simultaneously in each cycle. Additionally, each nanofluidic device was designed

to contain 16 chips resulting in a total of 32 chips per cycle. However, at the end of the fabrication

cycle, typically 16 chips survived.

45

Table 3-1: Estimate of cleanroom usage cost for one fabrication cycle resulting in 16 usable chips

(as used in Chapter 2 and Chapter 3 work)

Equipment Hours Cost for U of T ($/hr) Cost for Industry ($/hr)

Low Pressure Chemical Vapor

Deposition (LPCVD)

5.5 68 198

Plasma Enhanced Chemical Vapor

Depsosition (PECVD)

7 68 198

Mask writing 4.5 25 35

Photolithography 5 68 198

Electron beam lithography 5 138 413

Deep reactive ion etching (DRIE) 6 68 198

Inlet hole drilling 2 N/A N/A

Anodic bonding 3 68 198

Dicing 2 46 132

Miscellaneous wetbench work

(spin-coater, piranha cleaning,

development, microscopes, hot

plates, profilometer, chemicals)

10 ~40 ~120

Total 50 3096.50 8933.50

Typically, the total time required to fabricate the Si-Glass nanofluidic device would be 50 hours

with a U of T cost of $3100 and an external industry cost of $9000. Considering the 16 chips

successfully fabricated, the cost per chip is estimated to be $200 for a U of T user and $560 for an

industry user. Note that the cost analysis here does not include labor cost, material cost (~$50 for

wafers, photomasks etc.), facility training costs and additional characterization costs (SEM and

AFM). Additionally, in general, the chips in this work were single-use, which in a commercial

context is expensive. An approach to drive down the fabrication cost is to put many chips on a

single wafer – an approach being developed by a colleague in the Sinton Lab, who has achieved

46

88 chips on a standard 4” wafer. The dimension of each chip is 5 mm by 10 mm. In principle, these

chips could house a nanomodel at a cost of $35/nanomodel for U of T users and $100/nanomodel

for industry users.

It is also likely that once the physics has been established using large models such as this, smaller

nanomodels with less pores, would be more applicable to industrial application, testing for

instance, the role of chemical injections on oil/gas flow back. This would also reduce the cost of

expensive and time-consuming steps such as electron beam lithography.

3.5 Supporting Information

3.5.1 Nanomodel fabrication

Each fabricated chip contained two nanomodels (2 mm × 1.5 mm) placed perpendicular to the 20

μm deep service microchannel that had a drilled inlet hole for the fluid sample injection. A

schematic of key fabrication steps is shown in Figure 3-1B. To fabricate the device, 1) a 200-nm

thick film of silicon nitride was first deposited onto the bare silicon wafer (4-inch diameter, 1-mm

thick silicon wafer) using low pressure chemical vapor deposition (Expertech CTR-200 LPCVD).

2) Following this, ZEP-520A e-beam resist was spin-coated onto the wafer and the 5-nm pore

network was patterned using electron-beam lithography (Vistec EBPG 5000+ Electron Beam

Lithography System). 3) Deep-reactive-ion-etching (DRIE, Oxford Instruments PlasmaPro

Estrelas100 DRIE System) was used to etch the 5-nm pore network pattern resulting in the 5-nm

deep and ~100 nm-wide network of channels. 4) The substrate was then cleaned in a Piranha

solution (H2SO4:H2O2 = 3:1) for 1 hour to remove the photoresist. 5) Following this, the large

nanopore pattern was written on a photo mask (Heidelberg μPG 501) and transferred onto the

wafer coated with S1818 photoresist using UV lithography (Suss MicroTec MA6 Mask Aligner).

The pattern was then etched using DRIE resulting in the ~82 nm deep large nanopore features. 6)

The substrate was then cleaned in Piranha solution for 1 hour. 7) Following this, the service

microchannel pattern was written on a photo mask and transferred onto the wafer coated with

AZ9260 photoresist using UV lithography. The service microchannels were then etched using

DRIE. A 400 μm deep channel was also etched 1 mm above the location of the nanomodel into

which thermocouples were inserted to determine experimental temperature following experiment.

Inlet holes were then drilled through the silicon wafer. 8) After cleaning the wafer and a 2-mm

thick Borosilicate glass slide in Piranha solution for 1 hour, the two were anodically bonded at 673

47

K, 10-3 Pa and 100 V for approximately 5 minutes (AML AWB-04 Aligner Wafer Bonder). 9) The

bonded device was then diced into the desired shape to fit the experimental set-up (Disco

DAD3220 Automatic Dicing Saw).

3.5.2 Experimental set-up

The nanofluidic device was mounted on a custom-built high-pressure, high-temperature manifold

and connected to the experimental set-up shown in Figure 3-6. All components of the set-up

(tubing, piston cylinder, valves and manifold) were thoroughly cleaned using DI water and dried

using an air gun. The nanofluidic chip was placed under an optical microscope (Leica DM 2700M)

with a 10X objective lens, allowing the visualization of evaporation in two different nanoporous

media simultaneously. Evaporation was recorded using a camera (Leica DMC 2900).

Temperature was controlled by placing a copper block connected to an electric heater (accuracy ±

0.1 ºC) below the location of the nanomodel. The experimental temperature (𝑇) was determined

by measuring the temperature close to the nanomodel by inserting a thermocouple in a 400 μm

deep channel etched 1-mm above the location of the nanomodel. Over the course of the

experiment, the temperature variation was approximately ± 0.5 ºC. The hydrocarbon mixture was

produced in-lab by combining a mixture of 80% propane and 20% methane (mol. fraction, Praxair

Canada) and pentane (Sigma Aldrich) in a piston cylinder in liquid-phase. The final liquid

composition was 10% methane, 40% propane and 50% pentane (mol. fractions). Pressure in the

chip was controlled using an ISCO pump and measured using a pressure transducer (accuracy ± 1

kPa).

48

Figure 3-6: Schematic of the experimental set-up. For clarity, only a nanomodel is shown.

Prior to running the experiments, the entire system was vacuumed for three hours at 2 × 10-4 kPa

(PFPE RV8) to remove residual air from the system. The nanomodel was initially filled with liquid

sample at pressures above the bubble point pressure at room temperature (4.0 MPa). After waiting

~12 hours to reach the compositional equilibrium condition, temperature was increased to the

experimental temperature, 𝑇, using the electric heater. Experimental temperatures here included

42.5°C, 62.5°C and 82.5°C. After waiting one hour to allow the system to reach thermal

equilibrium, pressure was lowered to a target pressure below the bubble point pressure to observe

evaporation. At each temperature, pressure was lowered to 2 MPa and 1 MPa and finally to

vacuum. At each increment, the waiting time of 15 minutes was set to observe vaporization.

3.5.3 Image Processing

Images were batch processed by first smoothening the images by applying a Gaussian filter

operation, followed by thresholding to create a binary image to isolate empty circles (both isolated

and vaporized pores). A MATLAB algorithm was then used to count the number of vaporized

pores as a function of time. Isolated pores were removed by subtracting each image by a reference

image taken with the nanomodel fully saturated with liquid.

49

3.5.4 Supplementary figures

Figure 3-7. Pore-scale observation of vaporization. The relative intensity in the middle pore in the

snapshots is plotted as a function of time for the high superheat test (Figure 3-4A). The pore

gradually becomes brighter as vaporization progresses in the pore.

Figure 3-8. Vaporization data from replicate experiments shows good agreement. (A) Data for

0.76 MPa superheat and (B) 0.25 MPa superheat. Solid lines are same as in Figure 3-4A and 3-4C,

respectively. Dashed lines represent repeat experiment.

50

Figure 3-9. Vaporization data for 0.25 MPa vaporization case compared to evaporation model

assuming mixture parameters (same as for Figure 3-4F) and for pure pentane. The pure pentane

evaporation model trends towards the experimental result potentially implying enrichment of

liquid in the nanomodel with heavier pentane due to early desorption of lighter fractions.

3.5.5 Evaporation model

Fluid parameter values used in the modelling of different cases are presented in Table 3-1. Vapor

composition was determined using Equation of State (EOS) calculations at the dew point of the

initial liquid composition used (0.1/0.4/0.5 mol. fraction of C1/C3/C5). Vapor phase composition

was used to determine the average molar mass using mol. fraction of each component, 𝑥𝑖, and

molar mass of each component, 𝑀𝑖,:

�̅� = ∑ 𝑥𝑖𝑀𝑖 = 𝑥𝐶1𝑀𝐶1 + 𝑥𝐶3𝑀𝐶3 + 𝑥𝐶5𝑀𝐶5

Liquid density was obtained using EOS at the bubble point of the initial liquid composition. Vapor

density was calculated by taking the average of the vapor density at the dew point of the initial

liquid composition and vapor density close to the inlet (~ 0 kg/m3 due to vacuum condition). Vapor

viscosity was approximated at the dew point the vapor composition and estimated using

REFPROP. With regards to pentane, the superheat was determined as the difference between

Kelvin equation predicted saturation pressure in the 5-nm pore network and vacuum condition.

51

Liquid density, vapor density and vapor viscosity were obtained using REFPROP at bulk

saturation conditions.

Table 3-2: Summary of fluid parameters used in the modelling of evaporation dynamics.

Model Case Superheat, 𝛥𝑃

(MPa)

Vapor

composition

C1/C3/C5 (mol.

fraction)

Liquid

density, 𝜌𝑙

(kg/m3)

Vapor density,

𝜌𝑔 (kg/m3)

Vapor

viscosity, 𝑢𝑔

(Pa.s)

High

Superheat

0.76 0.24/0.50/0.26 465.97 12.92 1.01E-05

Medium

Superheat

0.44 0.33/0.48/0.19 501.19 8.67 9.94E-06

Low

Superheat

0.24 0.43/0.44/0.13 531.55 6.46 9.69E-06

Pure

Pentane

0.10 0/0/1 603.28 1.81 7.37e-06

MATLAB code for studying the vaporization dynamics is presented below for the high superheat

case is also included in the Appendix.

52

Chapter 4

Conclusions

4.1 Summary

The work presented in this thesis demonstrates the use of nanofluidics for optically studying

evaporation under extreme nanoconfinement – a phenomenon key to understanding hydrocarbon

production from nanoporous shale reservoirs. The thesis first provides a short overview of the

literature pertaining to phase change at the nanoscale with a focus on onset and dynamics of phase

change. The thesis then describes my two contributions to this field:

Firstly, the onset and dynamics of evaporation of propane in two-dimensional nanomodels with

sub-10 nm features. Under pressure drawdown conditions, the onset of evaporation is delayed as

compared to Kelvin equation predicted pressures for a wide range of temperature. Additionally, a

evaporation rates are found to be in good agreement with a model considering vapor transport

resistance. In the transitional flow regime, vapor transport resistance consists of both Knudsen

flow effects and viscous flow effects. The Knudsen flow effect here is approximately twice that of

the viscous flow effect. Additionally, two types of evaporation dynamics are observed depending

on initial liquid saturation pressure. Lower initial liquid saturation triggers discontinuous

evaporation which consists of vapor bubble nucleation in the porous media and evaporation from

the front.

Secondly, the vaporization dynamics of ternary hydrocarbon mixture in a shale nanomodel with

large nanopores (~100 nm) gated by 5-nm pore network is studied. Through this work, a

nanomodel is designed and fabricated that couples two nanoscopic length scales separated by an

order of magnitude. Vaporization dynamics are studied under three different superheats. With

higher superheats, faster and more spatially uniform vaporization fronts are observed.

Additionally, a vapor transport model is in good agreement with vaporization dynamics for high

superheats but overestimates the dynamics in the case of low superheat. The poor match at low

superheat potentially indicates the preferentially desorption of light fractions that enriches the

nanomodel with heavy, slow to vaporize, fractions.

53

4.2 Outlook and Future Work

The experimental system and associated theory developed in Chapter 3 provide unprecedented

insight into fluid mechanics and thermodynamics of complex multi-component fluids in complex

multi-scale volumes. The resulting data was not fully exploited in the course of this work and is

an ongoing focus. Specifically, the spatio-temporal correlations of vaporization large nanopores

is something that is going to be further investigated. Additionally, the anomalous liquid filling

dynamics observed here (Figure 3-3) are unique and require extended theoretical analysis to

understand.

The next logical application of the designed nanomodel could to be to rapidly screen various

chemicals solutions used in fracturing operations by analyzing oil/gas flow back. This study would

require fluorescence microscopy in addition to bright field imaging to differentiate between the oil

and fracturing fluid phases in order to quantify the fracturing fluid infiltration and oil production

during drawdown. Past work has included the study of fracturing fluid dynamics in a nanofluidic

device with a network of 1D 200-nm deep channels [8]. Additionally, enhanced oil recovery

(EOR) strategies have been proposed to help reverse the production rate decline commonly

observed for shale wells. Currently, colleagues at the Sinton Lab are investing the potential of N2

and CO2 flooding along with CO2 huff-n-puff for producing tight oil in relatively simpler 2D

nanomodels with discrete dimensions. Such work can be expanded by analyzing dynamics in

complex multi-scale volumes using the nanomodel designed in this thesis. For such commercial

applications, reducing the costs associated with chip fabrication is also imperative. The estimated

cost for per chip is approximately $200 for U of T users and $560 for industry users. Potential

strategies to minimize the costs associated with fabrication are discussed in Section 3.4 and include

using methodology developed at Sinton Lab to fabricate 88 chips/wafer. Incorporating this

methodology can potentially drive the fabrication cost down to $35/nanomodel.

The nanomodel presented in this thesis generally matches a number of key parameters associated

with nanoporous shale: porosity, permeability and pore sizes with representative volume

contributions. One limitation of the nanomodel is that surface chemistry is extremely uniform.

Heterogeneous surface chemistry can be introduced by coating the substrate with photocurable

polymers that can be made hydrophilic under high-energy UV radiation as demonstrated in

polymer micromodels [81]. While incorporating such a step into the pre-existing fabrication

54

workflow would require considerable work, including heterogeneous surface chemistry would be

the next logical phase for nanomodels. Once this method is developed, parameters can be tuned to

map a particular geological formation onto a chip.

55

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64

Submitted, 2018.

65

Appendices

MATLAB Model for Evaporation Dynamics for Chapter 3 Analysis

Following is the MATLAB code for calculating evaporation dynamics under different

pressure/temperature conditions as relevant to the analysis in Chapter 3 of this thesis. The fluid

mixture parameters presented in the code are for the high superheat case. For other cases, mixture

parameters need to be updated with those presented in Table 3-1. In the code, a linear array of

large nanopores is created that are separated by the 5-nm pore network. First, the vapor transport

time in the 5-nm pore network is determined by including Knudsen flow resistance and viscous

flow resistance components as a function of length. This value is then used to calculate the

volumetric velocity in the 5-nm pore network as a function of length. At each large pore location,

the time required to empty the large nanopore is determined by dividing the large nanopore volume

by the volumetric velocity in the 5-nm pore network. The cumulative vaporization time (comining

5-nm pore network transport time and large pore emptying time) is then determined. The final

output of the model is the Final matrix. The first column of the matrix is the length of the

nanomodel in microns. The second column is the transport time in the 5-nm pore network in

seconds. The third column is the emptying time for each large nanopore in seconds. The fourth

column is the cumative vaporization time. The Final matrix is then exported to EXCEL where

the percentage of vaporized nanomodel (column 1 values divided by 1500 microns) is plotted as a

function of cumulative time (column 4 values)

% Chip geometry

H = 82.15e-9; % large pore height

r = (6/2)*1e-6; % large pore radius

V = pi*r*r*H; % large pore volume

n = 50; % number of large pores after removing isolated pores

h = 5.5e-9; % small pore network height

w = 100e-9; % small pore network width

a = h * w; % small pore network cross section

l = 24e-6; % length of a single small pore network channel

l1= 0.001250; % approximate length of entire nanochannel

assuming no large pore in m

% Components are for ternary mixture

66

ug = 1.01406E-05; % gas viscosity (Pa*s) REFPROP - viscosity at

dew point of composition used

pl = 465.9652733; % liquid density (kg/m3) EOS

pg = 25.833/2;%183.8289408; % average gas density (kg/m3) EOS -

density at dew point of composition

M = 0.242386079*0.01604 + 0.498943051*0.0441 +

0.25867087*0.07215; % molar mass (kg/mol)

R = 8.314; % gas constant (kg*m2)/(s2*K*mol)

T = 82.5 + 273; % temperature (K)

dP = 757240; % superheat (Pa)

% Resistance factor term

R_f =

1/(((h^2)/(12*ug))+(((2*sqrt(2)*h)/(3*pg))*sqrt(M/(pi*R*T)))); %

resistance factor for small pores

L = [0.000001:0.000001:l1]; % Length of the porous media in 1

micron increments

Results=zeros(numel(L),3);

tt=[];

for k=1:1:numel(L)

Results(k,1)=L(k)*1e6; % length in microns

Results(k,2)=((L(k)*L(k))/(2*dP))*R_f*(pl/pg); % time in

seconds

Results(k,3)= L(k)./Results(k,2); % velocity in m/s

Results(k,4)=a*Results(k,3); % volumetric velocity m3/s -

cross section area (m) * velocity (m/s)

Results(25:25:k,5)=1; %location of a large pore - 1 large

pore after every 24 um

Results(k,6)=(V.*Results(k,5))./Results(k,4); %time to

evaporate that large pore - volume of pore/vol. velocity

end

% adding 5 zero cells below each large pore location to increase

the width of the large pore from 1 um to 6 um (Done to small

pore time and large pore time)

time_sm = reshape(Results(:,2)',25,[]);

time_sm(30,50)=0;

time_sm=reshape(time_sm,[],1);

time_lg = reshape(Results(:,6)',25,[]);

time_lg(30,50)=0;

time_lg=reshape(time_lg,[],1);

for i = 1:1:numel(time_sm)

67

if time_sm(i) == 0

time_lg(i)=time_lg(i-1);

end

end

% calculating cumulative evaporation time by combining small

pore evaporation and large pore mass transport from large pore

through small pores. Data for the first small pore segment is

copied first into the new cumulative array "C"

C = [time_sm(1:24)];

C = [time_sm(1:24); zeros(numel(time_sm)-numel(C),1)];

for i = 25:1:numel(C)

if time_lg(i) == 0

C(i) = time_sm(i)-time_sm(i-1)+C(i-1);

else

if time_lg(i) == time_lg(i-1)

C(i) = C(i-1);

else

C(i) = time_lg(i)+C(i-1);

end

end

end

% output data

Length = 1:1:numel(time_sm(:,1)); % Length in 1 um increments

Final = [Length' time_sm time_lg C];

plot(C./60,Length)

xlabel('Time (min)')

ylabel('Length (microns)')