Diffusion and Adsorption Coefficients of Aromatic Hydrocarbons in Gas Chromatography Capillary

134 Pages·2017·10.88 MB·English

WWeesstteerrnn UUnniivveerrssiittyy
SScchhoollaarrsshhiipp@@WWeesstteerrnn
Electronic Thesis and Dissertation Repository
11-14-2014 12:00 AM
DDiiffffuussiioonn aanndd AAddssoorrppttiioonn CCooeeffifficciieennttss ooff AArroommaattiicc HHyyddrrooccaarrbboonnss
iinn GGaass CChhrroommaattooggrraapphhyy CCaappiillllaarryy CCoolluummnnss
Gabriela Navarro Tovar, The University of Western Ontario
Supervisor: Dr. Hugo de Lasa, The University of Western Ontario
A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree
in Chemical and Biochemical Engineering
© Gabriela Navarro Tovar 2014
Follow this and additional works at: https://ir.lib.uwo.ca/etd
Part of the Analytical Chemistry Commons, Partial Differential Equations Commons, and the Transport
Phenomena Commons
RReeccoommmmeennddeedd CCiittaattiioonn
Navarro Tovar, Gabriela, "Diffusion and Adsorption Coefficients of Aromatic Hydrocarbons in Gas
Chromatography Capillary Columns" (2014). Electronic Thesis and Dissertation Repository. 2524.
https://ir.lib.uwo.ca/etd/2524
This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted
for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of
Scholarship@Western. For more information, please contact [email protected].
DIFFUSION AND ADSORPTION COEFFICIENTS OF AROMATIC
HYDROCARBONS IN GAS CHROMATOGRAPHY CAPILLARY COLUMNS

(Thesis format: Monograph)

by

Gabriela Navarro Tovar

Graduate Program in Chemical and Biochemical Engineering

A thesis submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy

The School of Graduate and Postdoctoral Studies
The University of Western Ontario
London, Ontario, Canada

© Gabriela Navarro Tovar 2014.
Abstract
This study focuses on a mathematical description of aromatic species elution peaks from a
gas chromatographic (GC) 30m x 0.25mm x 0.25µm BPX5 capillary column. Using the
recorded chromatographic peaks, statistical moments of different order are calculated for
toluene, naphthalene, phenol and 2-naphthol. This thesis reports two modelling approaches
involving laminar gas flow, distribution coefficients (K ) and diffusion coefficients in the
s
stationary phase (D ).
s
Firstly, a linear isotherm model with adsorption at equilibrium is considered in order to
describe symmetric peaks for toluene and naphthalene. Moreover, a linear isotherm model
with non-equilibrium adsorption is also proposed in order to describe asymmetric
chromatographic peaks generated by phenol and 2-napthol. In addition to the K and D
s s
parameters, this model involves adsorption kinetic constants (k ).
ads
Validation of both mathematical models is developed by performing experiments at different
carrier gas velocities and GC column temperatures (T ). The model with adsorption at
c
equilibrium, reports that the carrier gas velocity does not affect the first statistical moment
(M ) or the second statistical moment (M ). Thus, the equilibrium coefficients, K , and the
1 2 s
diffusion coefficients (D ), solely depend on the solute and stationary phase properties.
s
Furthermore, the model under non-equilibrium adsorption conditions provides k
ads
parameters for phenol and 2-naphthol. However, and in order for the second moments,
M to fit the second moment, M , a revised model for the BPX5 capillary column
2,model 2,exp
involving two classes of sites for solute adsorption is considered: one site with adsorption at
equilibrium and the other site with adsorption at non-equilibrium.
Thus, this PhD thesis establishes two chromatographic models that provide both adsorption
and diffusion parameters for aromatic hydrocarbon species peaks eluted from a BPX5
capillary column. Both mathematical models represent an important contribution to the
knowledge of solute interactions in capillary columns for GC. These models may potentially
have a significant impact on the future of GC analysis of complex mixtures such as tars from
biomass gasification.

ii
Keywords

Gas Chromatography; Capillary Columns; Elution Chromatography; Chromatographic
Modelling; Distribution Coefficient; Diffusion Coefficient; Adsorption Coefficient; Finite
Volume Method.

iii
Acknowledgments
The completion of my PhD dissertation has been a long journey. I am delighted to say that I
did not only obtain a graduated degree, I also earned professional and personal experiences. I
have met extraordinary people who have influenced and changed me in many ways and for
those reasons I will always have The University of Western Ontario and Canada in my heart.
These lines are meant to thank to people who have been part of this journey.
I would like to express my sincere gratitude to Dr. Hugo de Lasa for being an excellent
advisor and professor. His patience, flexibility, genuine caring and concern during these
years, enabled me to complete my PhD. studies. He has been an important part of my
professional and personal growth.
I also want to thank all the teachers and professors who have contributed to my professional
development at The University of Western Ontario. I would especially like to thank to Dr.
Dimitre Karamanev, Dr. Shahzad Barghi, Dr, Ronald Martin and Dr, Ying Zheng
(University of New Brunswick) for taking part in my PhD thesis as examination committee
members. I appreciate every comment and suggestion they have made with respect to my
work.
I am grateful to The National Council of Science and Technology in Mexico (CONACyT-
Mexico) for the scholarship awarded. My graduated studies could not have been possible
without the financial support of CONACyT). I also appreciate the financial support of
Mandel Scientific Co. and NSERC to this PhD project.
My sincere thanks also go to Pastor Solano and Jose Muñoz for their technical support. They
provided insights on gas chromatography and valuable suggestions to perform experiments in
the laboratory.
My recognition also goes to Patricio Valadés Pelayo and Jesus Moreira for their
collaboration in this PhD thesis. They gave invaluable help in the mathematical modelling of
this PhD dissertation.
iv
I would also like to express my gratitude to Florencia de Lasa for the contributions made to
this work. She always had excellent comments to improve this dissertation.
I would especially like to thank my good friends: Ana María Aguirre, Cristina Salomé Lugo,
Salvador Escobedo, Fanny Leveau, Monserrat de Santiago and Francisco Flores for their
friendship, sincere help and kind words when I was in difficult moments. All the laughter,
tears, coffee breaks and special moments with them meant a lot to me.
My gratitude is also extended to my friends: Sonia Gutierrez, Natalia Lesmes, Juan Manuel
Restrepo, Luis Luque, Diego Cufiño, Heather Ferris, Jose García, Rafael Alarcón, Yira
Aponte, Angel Lanza, Isabela Reiniati, Reyna Gómez, Maritza Gómez, Claudia Arana, Jorge
González, Shruti Srivastava and T.K. Dwarkanath for being an important part of my time in
Canada.
I would like to thank to Teresa Torres, José Jorge García, Mitzi, Iván and Deyanira García,
Jafet and Matías Duran for their support. I feel very lucky to have them in my life.
Most important, I would like to thank my family. Firstly, I give my profound gratitude to my
parents, Gregorio Navarro and Silvia Tovar. Words are not enough to express how thankful I
am for their love, hard work and the sacrifices they have made for our family. They inspired
me and encouraged me to find my own path. I also would like to thank to my sister, Mariana,
my brother, Omar and my nephew, Balam Rafael. No matter the distance, or different paths
we have had in life, they are always in my heart. Every day I thank for being part of this
family and I dedicate this thesis to them.
My entire gratitude is for my lovely husband, Jorge A. García Torres. I could not have
finished my studies without him. He moved to Canada to share this dream with me. He has
been a wonderful support, an incredible friend, an amazing father and the person who I want
to spend the rest of my life with. I also dedicate this thesis to him because his love is in every
written word of this thesis.
To end these acknowledgments, my heartfelt gratitude goes to my beautiful daughter, Emma
Victoria García Navarro. She has changed my view of the world and her love kept me strong
to finish this thesis. She is the most precious thing I have and all my efforts, goals and my
entire life are dedicated to her.
v
Table of Contents
Acknowledgments .............................................................................................................. iv

Table of Contents ............................................................................................................... vi

List of Tables ..................................................................................................................... ix

List of Figures ..................................................................................................................... x

List of Appendices ........................................................................................................... xiii

Nomenclature ................................................................................................................... xiv

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

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

Chapter 2 ............................................................................................................................. 4

2
  Introduction .................................................................................................................... 4

2.1
  General Features of Gas Chromatography .............................................................. 4

2.1.1
  Separation of Chemical Species in Gas Chromatography .......................... 6

2.1.2
  Types of Gas Chromatography Columns .................................................... 9

2.1.3
  Solute Interaction Parameters in Gas Chromatography ............................ 12

2.2
  Solute-Polymer Phase Physical Forces and Interactions ...................................... 14

2.2.1
  Adsorption Isotherms in Chromatography ................................................ 17

2.2.2
  Mathematical Chromatographic Models ................................................... 19
2.2.2.1 Linear Chromatography at the Equilibrium……………………... 20
2.2.2.2 Linear Chromatography at Non-Equilibrium …………………… 21
2.2.2.3 Non Linear Chromatography at the Equilibrium ……………….. 21
2.2.2.4 Non Linear Chromatography at Non-Equilibrium ………………22
2.2.2.5 Non Linear Reaction Chromatography ………………………….22
2.2.2.6 General Strategy for GC Capillary Column Studies …………….23
2.3
  Statistical Moments of Different Order: M , M and M ...................................... 26

1 2 3
vi
2.3.1
  Calculation of Statistical Moments of Different Order ............................. 28

2.4
  Conclusions and Goals for the Present Ph.D Study .............................................. 30

Chapter 3 ........................................................................................................................... 31

3
  Scope of the Research .................................................................................................. 31

Chapter 4 ........................................................................................................................... 33

4
  Introduction .................................................................................................................. 33

4.1
  Model Compound Solution Preparation and Elution in a BPX5 Capillary Column
33

4.2
  Experimental Set-Up ............................................................................................. 34

4.3
  SEM Images of a Radial Cut of the Narrow Bore BPX5 Capillary Column ........ 37

4.4
  Conclusions ........................................................................................................... 37

Chapter 5 ........................................................................................................................... 38

5
  Introduction .................................................................................................................. 38

5.1
  Adsorption at Equilibrium Model in Capillary Column ....................................... 38

5.2
  Statistical Moment Descriptors for an Adsorption at Equilibrium Model in GC
Capillary Column .................................................................................................. 44

5.3
  General Description of Elution of Aromatic Species in BPX5 capillary Column 45

5.4
  Validation of an Adsorption at Equilibrium Model for a BPX5 Capillary Colum 47

5.4.1
  Evaluation of the Adsorption Parameters in BPX5 Capillary Colum Using
First Order Statistical Moment (M ) ......................................................... 47

1
5.4.2
  Evaluation of the Axial Mixing and Diffusivity in a Capillary Column
Using Second Order Statistical Moment (M *) ......................................... 50

2
5.5
  Conclusions ........................................................................................................... 54

Chapter 6 ........................................................................................................................... 55

6
  Introduction .................................................................................................................. 55

6.1
  Mathematical Model Equations for a Non-Equilibrium Adsorption Model ......... 56

6.2
  Evaluation of the Numerical Solution ................................................................... 59

vii
6.2.1
  Response to a Tracer Impulse Using the Non-Equilibrium Adsorption
Model ........................................................................................................ 61

6.2.2
  Influence of the Diffusion Coefficient in the Mobile Phase (D ) in a Non-
G
Equilibrium Adsorption Model ................................................................. 62

6.2.3
  Influence of Diffusion Coefficient in the Stationary Phase (D ) in the Non-
s
equilibrium Adsorption Model ................................................................. 63

6.2.4
  Mesh Independency Test Using the Non-Equilibrium Adsorption Model 66

6.2.5
  Evaluation of the Implemented Numerical Method for Non-Equilibrium
Adsorption Model ..................................................................................... 69

6.3
  Determination of the Distribution Coefficient (K ) with Non-Equilibrium
s
Adsorption Model ................................................................................................. 70

6.4
  Determination of the Adsorption Constant (k ) with a Non-Equilibrium
ads
Adsorption Model ................................................................................................. 73

6.5
  Determination of the Diffusion Coefficient in the Stationary Phase (D ) Using an
s
Adsorption Non-Equilibrium Model ..................................................................... 76

6.6
  A Revised Model with Allowance for Equilibrium and Non-equilibrium
Adsorption Sites .................................................................................................... 77

6.7
  Conclusions ........................................................................................................... 81

Chapter 7 ........................................................................................................................... 82

7
  Conclusions and Recommendations ............................................................................ 82

7.1
  Conclusions ........................................................................................................... 82

7.2
  Recommendations for Future Work ...................................................................... 83

References ......................................................................................................................... 85

Appendices ........................................................................................................................ 93

Curriculum Vitae ............................................................................................................ 113

viii
List of Tables
Table 1 Comparison Between Packed and Capillary Column for GC .................................... 11

Table 2 Mathematical Model Equations to Describe Elution Chromatography by Adsorption
and Diffusion Parameters ........................................................................................................ 22

Table 3 Statistical Moments to Describe Chromatography Peaks ......................................... 27

Table 4 Gas Chromatograph and Mass Detector Parameters ................................................. 34

Table 5 Isotherm Conditions for Aromatic Species Tested .................................................... 36

Table 6 Adsorption Parameters Obtained from the Model as per Eq (5.13) for Both Toluene
and Naphthalene in a BPX5 Capillary Column ...................................................................... 50

Table 7 Values of Constants “a” and “b” in Eq (5.16) when n=2 and n=0 for Toluene and
Naphthalene ............................................................................................................................ 52

Table 8 Evaluation of a Tracer in the non-equilibrium Adsorption Model ............................ 61

Table 9 Influence of Axial Dispersion Coefficient (D ) in the Non-equilibrium Adsorption
G
Model* .................................................................................................................................... 63

Table 10 Influence of Diffusion Coefficient in the Stationary Phase (D ) Using the Non-
s
equilibrium Adsorption Model. .............................................................................................. 64

Table 11 Adsorption Parameters Obtained from the Model as per Eq (5.13) for both Toluene
and Naphthalene in a BPX5 Capillary Column. ..................................................................... 73

Table A. 1 Average Distribution Constant (K ) and Diffusion Coefficient in the Stationary
s
Phase (D ) ................................................................................................................................ 94

s
Table A. 2 Skewness (S) Values of Chromatographic Peaks of Toluene, Phenol, Naphthalene
and 2-naphthol in GC/MS Analysis with BPX5 Capillary Column ....................................... 97

ix