Faculty of Bioscience Engineering
Academic year 2014-2015
Effect of mass transfer limitations on enzymatic
reactions in microreactors: a model-based
analysis
David Fernandes del Pozo
Promotor: Prof. dr. ir. Ingmar Nopens
Tutors: ir. Timothy Van Daele, ir. Daan Van Hauwermeiren
Master’s dissertation submitted at Ghent University in partial fulfillment of the requirements
for the degree in Chemical Engineering at the University of Santiago de Compostela.
De auteur en promotor geven de toelating deze scriptie voor consultatie beschikbaar te stellen en
delen ervan te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen
van het auteursrecht, in het bijzonder met betrekking tot de verplichting uitdrukkelijk de bron te
vermelden bij het aanhalen van resultaten uit deze scriptie.
The author and the promoter give their permission to use this dissertation for consultation and
to copy parts of it for personal use. Every other use is subject to copyright laws, in particular,
that the source be extensively specified when using results from this thesis.
Ghent, January 2015
The promoter,
Tutor,
Prof. dr. ir.
Ingmar Nopens
ir. Timothy
Van Daele
Tutor,
ir. Daan
Van Hauwermeiren
The author,
David Fernandes
del Pozo
Acknowledgements
In this dissertation were spent a lot of hours and David resources, and it would be much more
complicated or impossible if I did not have some kind of help and support. I would like to thank
the following people for their contribution in this dissertation.
First, I would like to express my deepest appreciation to one of my tutors, ir. Timothy Van
Daele. He continually and persuasively delivered the reviewed documents with a lot of corrections,
progressively from green to red ink (suspicious...). Without his supervision and suggestions, this
dissertation would not have been possible. Sorry for continuously going into your desk to ask you
endless questions. Thanks!
Second, I would like to thank Prof. dr. ir. Ingmar Nopens, which has been a wise promotor
with his endless PDF corrections and definitely establishing the Santiago-Ghent connection. I
want to apologise for my very bad English grammar. In this line, I would like to thank my
Spanish promoter Marta Carballa because she solved all my administrative doubts and made real
the possibility to make this dissertation abroad. Thanks are also due to the Technical School
of Chemical Engineering, University of Santiago de Compostela and the Bioscience Engineering,
University of Ghent for choosing me as an Erasmus student.
Thirdly, but not less important, I would like to thank my other tutor ir. Daan Van Hauwermeiren
(aka jos) for his good American-to-English corrections and generating the OpenFOAM meshes.
It is worth mentioning the contribution of the BIOMATH community to generate a relaxed and
hard-work environment. Although I had no idea of Dutch, it was really funny to hear you laughing
and talking in a really weird language. Especial mention to Jose Arias because he provided me with
nice statistics conversations (pinche copulas) while having the horrible coffee from the department.
I also cannot forget the Uppsala community for having nice conversations and dinners at the home
residency. Sven Snow (the Albert Heijn country guy), you are INDEED a good friend!
My family was also an important part and I would like to thank them all for their emotional
support. Especially, Leslie Fernandes for correcting my English and help me with the TOEFL
$#!*. Maribel, Doris and future chemical engineering Monica were essential to keep me always
with a smile.
Furthermore, I would like to thank the group of friends from Santiago (Nati, Iaguito, Zas and
Pili) and the COLEGHAS group (Eloy, Lukitas, Frodo, and the last on purpose Hadri). For all
of you: +1.
Finally, I would like to express my sincere appreciation to Paula (the Skype caller), which has
been these last years a source of inspiration, advice, and of course, of maxerı́a.
i
ii
Abstract
Industrial biotechnology is promoted as an alternative solution with the potential to transform
the chemical, petrochemical and pharmaceutical industries. Biocatalytic processes are addressed
as part of an environmentally friendly technology, which regardless of their scope and location,
can provide green solutions to eliminate toxic substances, reduce greenhouse gas emissions and
be safer. Nowadays, low productivity and low process intensity of biotechnological processes
hamper the widespread use of these technologies. To overcome these shortcomings, microreactor
biotechnology is an attractive alternative because it enhances productivity, process controllability
and reduces scale-up reactor problems. In this dissertation, the performance of two microreactor
configurations (immobilised enzyme and two split-inlet) is assessed. The main aims of this study
are divided in two sections: First, to analyse the impact of different microreactor degrees of
freedom (diffusion coefficient, maximum reaction rate, residence time, microreactor width and
microreactor configuration) on conversion and mass transfer limitation by using Computational
Fluid Dynamics (CFD); Second, to determine whether dimensionless numbers can be used to
predict mass transfer limitations. The microreactor hydrodynamics were modelled using the
opensource CFD library OpenFOAM to obtain velocity and pressure profiles. The substrate
and product profiles were obtained by solving the advection-diffusion-reaction equation for each
species in OpenFOAM. The different scenarios were performed using Python scripts, wrapped
around OpenFOAM C++ libraries to automate the simulations. The CFD results were compared
with theoretical plug flow profiles in order to extract information about mass transfer limitations.
These comparisons were used to assess the strengths and weaknesses of dimensionless numbers.
iii
iv
Contents
Acknowledgements
i
Abstract
iii
Contents
vii
List of Symbols
ix
List of Abbreviations
xiii
List of Figures
xiii
List of Tables
xvi
1 Problem statement
1.1 Introduction . . . . . . . . . . . . . . . . . . . .
1.2 Problem Statement . . . . . . . . . . . . . . . .
1.3 Objectives of this research . . . . . . . . . . . .
1.4 Outline: The roadmap used in this dissertation
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2 Literature Review
2.1 Production of chiral amines using transaminases . . . . . . . . . . .
2.1.1 Biocatalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Advantages and disadvantages of biocatalysts . . . . . . . . .
Advantages of biocatalysts . . . . . . . . . . . . . . . . . . .
Disadvantages of biocatalysts . . . . . . . . . . . . . . . . . .
2.1.3 ω-Transaminase reaction and biochemical features . . . . . .
2.1.4 Process challenges . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamic limitations of the reaction system . . . . . .
Limitations of biocatalysts . . . . . . . . . . . . . . . . . . .
2.1.5 Kinetic model of ω-Transaminase reactions . . . . . . . . . .
2.2 Overview of mass transfer limitation . . . . . . . . . . . . . . . . . .
2.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Performance of microreactors under mass transfer limitation
2.2.3 Mass transfer limitation in microreactors . . . . . . . . . . .
2.2.4 Methods to determine mass transfer limitation . . . . . . . .
2.3 Microreactor technology . . . . . . . . . . . . . . . . . . . . . . . . .
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1
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2.3.1
2.3.2
2.4
2.3.3
2.3.4
Fluid
2.4.1
2.4.2
History and fabrication techniques . . . . . . . . .
Advantages and disadvantages of microreactors . .
Advantages of microreactors . . . . . . . . . . . . .
Disadvantages of microreactors . . . . . . . . . . .
Control of reaction and process intensification . . .
Process techniques for enzyme microreactors . . .
dynamics . . . . . . . . . . . . . . . . . . . . . . . .
Navier-Stokes equations . . . . . . . . . . . . . . .
Important dimensionless numbers in microreactors
3 Materials and Methods
3.1 Introduction . . . . . . . . . . . . . . . . .
3.2 Software . . . . . . . . . . . . . . . . . . .
3.2.1 Python . . . . . . . . . . . . . . .
3.2.2 OpenFOAM . . . . . . . . . . . . .
3.3 Discretisation of Navier-Stokes equations .
3.4 Advection-diffusion-reaction equation . . .
3.5 Methodology . . . . . . . . . . . . . . . .
3.6 Microreactor configurations . . . . . . . .
3.7 Dimensionless numbers derivation . . . . .
3.7.1 Immobilised enzyme configuration
3.7.2 Two split-inlet configuration . . .
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4 Results
4.1 Immobilised enzyme microreactor . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Individual impact of the degrees of freedom . . . . . . . . . . . . . . . . . .
Effect of the diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . . .
Effect of maximum reaction rate . . . . . . . . . . . . . . . . . . . . . . . .
Effect of residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Effect of microreactor width . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Impact of the combination of the degrees of freedom . . . . . . . . . . . . .
Influence of the diffusion coefficient and maximum reaction rate on conversion
Influence of the diffusion coefficient and maximum reaction rate on mass
transfer limitation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Influence of residence time on conversion and mass transfer limitation . . .
Influence of residence time and microreactor width on conversion and mass
transfer limitation . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Prediction of mass transfer limitation . . . . . . . . . . . . . . . . . . . . .
Damköhler number analysis for diffusion coefficient and maximum reaction
rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Damköhler number analysis for residence time and microreactor width . . .
Prediction of mass transfer limitation using Damköhler number . . . . . . .
4.2 Two split-inlet enzyme microreactor . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Individual impact of the degrees of freedom . . . . . . . . . . . . . . . . . .
Effect of the diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . . .
vi
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35
4.3
Maximum reaction rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Residence time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Microreactor width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Impact of the combination of the degrees of freedom . . . . . . . . . . . . .
Influence of the diffusion coefficient and maximum reaction rate on conversion
Influence of the diffusion coefficient and maximum reaction rate on mass
transfer limitation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Influence of residence time and microreactor width on conversion and mass
transfer limitation . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Prediction of mass transfer limitation . . . . . . . . . . . . . . . . . . . . .
Dimensionless number analysis for diffusion coefficient and maximum reaction rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Dimensionless number analysis for residence time and microreactor width .
Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
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42
5 Conclusion and future perspectives
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Future perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
45
46
Bibliography
47
vii
viii
List of Symbols
β
D
T
U
µ
ρ
f
parameter dependent from channel geometry in the Taylor dispersion coefficient equation
Taylor diffusion coefficient
deviatoric of the total stress tensor
velocity vector
kinematic viscosity
density of the fluid
other body forces: gravitational and/or centrifugal
[A]
[A0 ]
[A]bulk
[A]CF D
[A]CM
aP
[A]surf ace
concentration of substrate A
initial concentration of substrate A
concentration of substrate at bulk
final concentration substrate calculated from CFD
final concentration substrate calculated from the plug flow chemical model
diagonal coefficients of the sparse matrix representing properties of the cell considered
concentration of substrate at surface
Bo
Bodenstein number
D
dH
Da
DaI
DaII
Dcritical
δ
∆G
molecular diffusion coefficient
hydraulic diameter
Damköhler number
first Damköhler number
second Damköhler number
critical diffusion coefficient
diffusion layer
change in Gibbs free energy
F
FA
flux of the cell
flow of substrate A
ΓA
moles per unit of area of reactive sites occupied by substrate molecules
ix
H(U)
transport and source parts derived from the integral form of the momentum equation
K
k
k0
f
Kcat
r
Kcat
KEQ
KiA
KiQ
KM
A
KM
B
KM
P
KM
Q
KM
A
KSi
B
KSi
P
KSi
Q
KSi
Kn
thermodynamic equilibrium constant
first order kinetic constant
intrinsic reaction rate constant
catalytic turnover coefficient of the forward reaction
catalytic turnover coefficient of the reverse reaction
chemical equilibrium constant
inhibition parameter for solute A
inhibition parameter for solute Q
Michaelis-Menten constant
Michaelis-Menten parameter for solute A
Michaelis-Menten parameter for solute B
Michaelis-Menten parameter for solute P
Michaelis-Menten parameter for solute Q
substrate A inhibition constant for the forward reaction
substrate B inhibition constant for the forward reaction
product P inhibition constant for the reverse reaction
product Q inhibition constant for the reverse reaction
Knudsen number
L
λ
length of the microreactor
molecular free path
nenzyme
total amount of enzyme
p
Pe
P e2D
pressure
Peclet number
two dimension Peclet number
Re
% rel.dif.
Reynolds number
percentage of relative difference
S
outward-pointing face area vector perpendicular to the surface cell
t
τ
τmod
time
time residence
modified time residence
u
velocity of the fluid
x
Vmax
Vmax, critical
maximum reaction rate
critical maximum reaction rate
W
width of the microreactor
x
average displacement of a Brownian particle
xi
xii
List of Abbreviations
ACE
APH
Acetone
Acetophenone
CFD
CLEA
Computational Fluid Dynamics
Cross-Linked Enzyme Aggregate
FVM
Finite Volume Method
GNU
GRAS
GUI
General Public License
Generally Regarded As Safe
Graphical User Interface
IPA
ISPR
2-Propylamine
In Situ Product Removal
MBA
Methylbenzylamine
OpenFOAM
Open-source Field Operation And Manipulation toolbox
PDE
PEA
PLP
PSF
Partial Differential Equations
1-Phenylethylamine
Pyridoxal 5’-phosphate
The Python Software Foundation
SIMPLE
Semi-Implicit Method for Pressure Linked Equations
xiii
xiv
List of Figures
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Schematic representation of a Ping-Pong Bi-Bi reaction scheme . . . . . . . . . . .
5
ω-transaminase reaction pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Transamination catalysed by ω-transaminase illustrating the synthesis of 1-phenylethylamine
(PEA) and a co-product acetone (ACE) from the substrates acetophenone (APH)
and 2-propylamine (IPA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
Example of a two split-inlet Y-shape microreactor. . . . . . . . . . . . . . . . . . . 13
Schematic illustration of an enzyme immobilised microreactor. . . . . . . . . . . . 16
Flow chart representation of the solution procedure followed to obtain data for the
analysis of mass transfer limitation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic representation of an immobilised enzyme microreactor with a laminar
flow profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic representation of a two split-inlet microreactor configuration. Substrate
and enzyme are fed into the microreactor in different parallel streams. . . . . . . .
Influence of the diffusion coefficient and maximum reaction rate on conversion in
an immobilised enzyme microreactor at constant values of τ = 10 min and W =
200 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Influence of the diffusion coefficient and maximum reaction rate on mass transfer
limitation represented as percentage relative difference in a immobilised enzyme
microreactor at constant values of τ = 10 min and W = 200 µm. . . . . . . . . . .
Influence of residence time on conversion and mass transfer limitation. Representation of conversion and percentage relative difference with sets of diffusion coefficient
and maximum reaction rate, from top to bottom, for τ = 1 min, τ = 10 min and τ
= 30 min with a constant value of W = 200 µm. Dashed lines are constant values
of conversion and the greyrmap shows values of percentage relative difference. . . .
Influence of residence time and microreactor width on conversion and mass transfer
limitation in an immobilised microreactor. . . . . . . . . . . . . . . . . . . . . . . .
Damköhler number analysis with changes in sets of diffusion coefficient and maximum reaction rates at constant values of τ = 10 min and W = 200 µm. . . . . . .
Representation of Damköhler number for sets of diffusion coefficient and maximum
reaction rate for τ = 1, 10, 30 min and W = 200, 400, 1000 µm. . . . . . . . . . .
Figure presenting predictions of mass transfer limitation in an immobilised enzyme
microreactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
21
23
23
28
29
30
31
32
34
35
4.8
4.9
4.10
4.11
4.12
4.13
Influence of the diffusion coefficient and maximum reaction rate on conversion in a
two split-inlet microreactor with constant values of τ = 10 min and W = 200 µm.
Influence of the diffusion coefficient and maximum reaction rate on mass transfer
limitation represented as percentage relative difference in a two split-inlet microreactor at constant values of τ = 10 min and W = 200 µm. . . . . . . . . . . . . . .
Influence of residence time and microreactor width on conversion and mass transfer limitation in a two split-inlet microreactor configuration with sets of diffusion
coefficient and maximum reaction rate at τ = 1, 10, 30 min and W = 200, 400,
1000 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dimensionless number analysis with changes in sets of diffusion coefficient and
maximum reaction rates with constant values of τ = 10 min and W = 200 µm. . .
Dimensionless number analysis with D and Vmax with τ = 1, 10, 30 min and W =
200, 400, 1000 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General representation of mass transfer limitation as a function of the microreactor
configuration. Dashed lines represent percentage relative difference values between
the ideal model and the Computational Fluid Dynamics (CFD), for the sets of
diffusion coefficients and maximum reaction rates. . . . . . . . . . . . . . . . . . .
xvi
38
38
40
41
42
43
List of Tables
4.1
Degrees of freedom and the constants used for analysing mass transfer limitation
in both microreactor configurations. D, k and Vmax also have intermediate points
(5 · 10−x , where x is the current order of magnitude). . . . . . . . . . . . . . . . . .
4.2 Values from a test case to obtain the impact of diffusion in conversion and percentage relative difference in an enzyme immobilised microreactor at τ = 10 min,
W =200 µm, Vmax =2.271 mM s−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Values from a test case to obtain the impact of the maximum reaction rate on conversion and percentage relative difference in an enzyme immobilised microreactor
at τ = 10 min, W =200 µm, D=10−11 m2 s−1 . . . . . . . . . . . . . . . . . . . . . . .
4.4 Values from a test case to obtain the impact of the residence time on conversion and percentage relative difference in an enzyme immobilised microreactor at
W =200 µm, Vmax =2.271 mM s−1 , D=10−11 m2 s−1 . . . . . . . . . . . . . . . . . . .
4.5 Values from a test case to obtain the impact of the enzyme immobilised microreactor
width on conversion and percentage relative difference at τ = 10 min, Vmax =2.271
mM s−1 , D=10−11 m2 s−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Values of Damköhler numbers and percentage relative difference with sets of diffusion coefficient and maximum reaction rate for constant values of τ = 10 min and
W = 200 µm, extracted from Figure 4.5. . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Values from a test case to obtain the impact of the diffusion coefficient on conversion and mass transfer limitation in a two split-inlet microreactor at τ = 10 min,
W =200 µm, and Vmax =2.271 mM s−1 . Mass transfer limitation data from the
immobilised enzyme microreactor is added to allow comparison. . . . . . . . . . . .
4.8 Values from a test case to obtain the impact of the maximum reaction rate on conversion and mass transfer limitation in a two split-inlet microreactor at τ = 10 min,
W =200 µm, D=10−11 m2 s−1 . Mass transfer limitation data from the immobilised
enzyme microreactor is added to allow comparison. . . . . . . . . . . . . . . . . . .
4.9 Values extracted to obtain the impact of residence time on conversion and mass
transfer limitation for a two split-inlet microreactor at W =200 µm, Vmax =2.271
mM s−1 , D=10−11 m2 s−1 . Mass transfer limitation data from the immobilised enzyme microreactor is added to allow comparison. . . . . . . . . . . . . . . . . . . .
4.10 Values from a test case to obtain the impact in a two split-inlet microreactor width
on conversion and percentage relative difference at τ = 10 min, Vmax =2.271 mM s−1 ,
D=10−11 m2 s−1 . Mass transfer limitation data from the immobilised enzyme microreactor is added to allow comparison. . . . . . . . . . . . . . . . . . . . . . . . .
xvii
25
26
27
27
28
33
35
36
36
37
4.11 Criterion to determine mass transfer limitation with dimensionless numbers for
a two split-inlet microreactor. The two dimension Peclet number is used when
Vmax <Vmax, critical . The Damköhler number is used (calculated at a constant Vmax, critical )
when Vmax >Vmax, critical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
xviii
CHAPTER 1
Problem statement, research objectives
and outline
1.1
Introduction
Industrial biotechnology has been promoted as an alternative solution with the potential to transform the chemical, petrochemical and pharmaceutical industries. Biocatalytic processes are addressed as part of an environmentally friendly technology that, which regardless of their scope and
location, can provide green solutions to eliminate toxic substances, reduce greenhouse gas emissions and be safer. This technology reduces the use of organic solvents through aqueous chemistry,
removes metal catalysts and fosters mild operational conditions. Biocatalysts are the preferred
choice when high selectivity is required, but they still suffer from low productivity, low process
intensity, and a higher cost compared to the widely used chemical processes. These drawbacks
hamper the widespread use of these bioprocesses in the industry. The Biointense project aims to
investigate how the overall bioprocess efficiency can be improved for the specific case of the enzyme
omega-transaminase. It is EC-funded through the 7th Framework Cooperation Programme that
supports research activities in key scientific and technology areas that are in agreement with EU
policies. Within the BioIntense project microfluidics platforms are used because it enhances reaction performance and permits rapid data collection. Miniaturised platforms use smaller amounts
of reagents and work in an efficient way with the biocatalyst. Modelling can speed up this investigation, by reducing the number of lab experiments drastically performing experiments much
faster in silico than in real life. However one should make sure that the models researched are
adequately defined and well calibrated. The first aim is to perform a thorough analysis of microreactor performance in terms of the extent of the reaction and mass transfer limitation. The
second aim is to test whether dimensionaless numbers can be used as a mass transfer limitation
prediction approach.
1.2
Problem Statement
Chemical reaction systems which suffer from mass transfer limitations have a lower productivity
and show an overall decrease in microreactor performance. Reduction of production cost is essential to lower the total cost of a biocatalytic process. In order to include mass transfer limitation,
2
1.3 OBJECTIVES OF THIS RESEARCH
this study expanded a transport equation that combines convection and diffusion with a kinetic
model.
1.3
Objectives of this research
The aim of this thesis is to analyse the effects of mass transfer limitation in microreactors with free
and immobilised enzymes by changing critical degrees of freedom (diffusion coefficient, maximum
reaction rate, residence time, and microreactor width). CFD is used to model the hydrodynamics
of the microreactor. The CFD solves the hydrodynamic equations coupled with the advectiondiffusion-reaction equation for the different substrates and products, in order to obtain the velocity,
substrate, product and mass profiles for the microreactor. Literature consulted mentions the use of
different dimensionaless numbers to predict the presence of mass transfer limitations in enzymatic
reactors. The aim is to verify whether the proposed dimensionless numbers are generally applicable
in enzymatic microreactors.
1.4
Outline: The roadmap used in this dissertation
Section 2 provides an overview of the literature and the essential information needed for understanding contexts such as enzyme kinetics, microreactor technology and fluid dynamics. This is
followed by a brief explanation in Section 3 about the materials and procedures followed to obtain
the results. It contains information on the software, and the computer methodology used, the fundamental equations and the derivation of dimensionless numbers. The results are presented and
discussed in Section 4. And finally, Section 5, provides the conclusions and future perspectives.
CHAPTER 2
Literature Review
2.1
Production of chiral amines using transaminases
Biocatalysis technology offers a new approach to produce chiral amines. Enantiomerically pure
chiral amines have increased their commercial value in view of their application as resolving agents,
chiral auxiliaries/bases, and catalysts for asymmetric synthesis. Moreover, chiral amines are often
interesting as intermediates because of their pronounced biological activity (Turner et al., 2005).
These compounds are therefore important in the pharmaceutical and agrochemical industry and
can be produced both by chemical and biocatalytic synthesis (Breuer et al., 2004). Traditionally,
the production of optically pure amines is based upon the resolution of racemates by recrystallisation of diastereomeric salts. Targeted synthesis of the active enantiomer can improve process economics though reduction of employed substrates and process costs. Hence, traditional techniques
are being replaced by biocatalytic based processes because they offer a more environmentally
friendly solution and better efficiencies. Transaminases are suitable biocatalyst enzymes used in
these processes due to their high stereoselectivity and ability to operate under environmentally
mild conditions (most of the time operating at ambient temperature and pressure).
2.1.1
Biocatalysis
A classical organic chemistry exponent might probably hesitate to consider a biochemical solution
for one synthetic problem. Hesitation is probably justified due to the poor understanding of
biochemical reaction mechanisms and the “black box” empirical approach to deal with this kind
of reactions. This technology has been proven to be useful in recent years and so the lack of
understanding of the underlying mechanisms is not so important. As a result, biocatalysis has
matured to become a standard technology in the chemical industry, which is reflected by the
number of bioindustrial processes running on a commercial scale (Straathof et al., 2002). There is
still a lot of research being conducted nowadays in organic synthesis by using enzymes and whole
cells as biocatalyst. Industrial biocatalysis is foreseen to grow rapidly as individual industries
develop relevant experience.
Every biocatalytic process is developed taking into account its economic feasibility. The development of such a process requires the input of a lot of iterative expertises and work, also referred
to as the biocatalyst cycle (Schmid et al., 2001). The physical state of biocatalysts can be very
diverse. The use of isolated enzymes or whole microorganisms, either in a free or immobilised
4
2.1 PRODUCTION OF CHIRAL AMINES USING TRANSAMINASES
form, depends on many factors. The main points are the type of reaction, need for recycling
cofactors, and scale in which the biotransformation has to be performed. At the enzyme level,
better activities, substrate range and enzyme stability have to be mainly considered. Whole cell
systems need to account for solvent resistance, substrate import, product export, elimination of
side-reactions, and process control. Production of chiral amines is not an exception and must also
balance these factors.
2.1.2
Advantages and disadvantages of biocatalysts
The use of biocatalyst in a process involves the analysis of the following advantages and disadvantages (Faber, 2011).
Advantages of biocatalysts
ˆ Enzymes are efficient catalysts. Typically the rates of enzyme processes are faster by a
factor of 108 − 1010 than those of the corresponding non-catalysed reactions. This enables
most enzymatic reactions to perform reasonable well at mole percentages of 10−3 − 10−4
of catalyst, which are far less than the chemical catalyst concentrations around 0.1-1%.
Although this is true, some enzymatic systems show very slow reaction rates despite the
increase of efficiency.
ˆ Enzymes act under mild conditions. They act at about pH 5-8 (typically around 7) and at
temperatures of 20-40◦ C (preferably around 30◦ C).
ˆ Biocatalyst are environmentally benign reagents since they are completely biodegradable.
Traditional catalysts use heavy metals and energy requirements that usually lead to a less
environmentally friendly process.
ˆ Some enzymes are compatible with each other. Since enzymes generally function under the
same or similar conditions, several biocatalytic reactions can be carried out in a reaction
cascade. Sequential reactions permits simplification of processes and can even shift an
unfavourable equilibrium towards the desired product.
ˆ Enzymes can catalyse a broad spectrum of reactions. They accelerate reactions but have
no impact on the thermodynamic equilibrium. Sometimes they catalyse reactions that are
not possible otherwise. Since enzymes are present in biological mediums, they exhibit high
selectivity. Chemoselectivity allows enzymes to recognise single types of functional groups.
Regioselectivity allows enzymes to distinguish functional groups depending on their position,
due to their complex three-dimensional structure. Finally, enantioselectivity allows kinetic
resolution, which means separation of both enantiomers of a racemic substrate. Enzyme
selectivity can provide an enantiomer, that is important in chiral synthesis.
Disadvantages of biocatalysts
There are, however, also some drawbacks in the use of biocatalysts:
ˆ Enzymes are prone to inhibition phenomena. Many enzymatic reactions are prone to substrate and/or product inhibition. Product inhibition is complicated because it requires
CHAPTER 2 LITERATURE REVIEW
5
gradual removal of product by physical means in order to recover the initial enzyme activity.
ˆ Enzymes require narrow operation parameters. There is only a narrow operational window
for optimal performance. Elevated temperatures as well as extreme pH lead to deactivation
of the protein, as do high salt concentrations. On this subject, enzymes are known to have
a low stability and tend to be fragile.
ˆ Enzymes display their highest catalytic activity in water. The majority of organic compounds are, however, poorly soluble in aqueous media. Hence, working in other solvents
reduces the catalytic activity of the enzyme.
ˆ Enzymes are bound to their natural cofactors. These cofactors are relatively unstable
molecules and prohibitively expensive to be used in stoichiometric amounts. Recycling
cofactors is still not a trivial task.
ˆ Enzymes are provided in only one enantiomeric form.
2.1.3
ω-Transaminase reaction and biochemical features
Transaminases are a type of enzymes which transfer an amino group from an amino acid to an
α-keto acid, requiring Pyridoxal 5’-phosphate (PLP) as a prosthetic group for the catalytic action.
Transaminases are divided into subgroups, and ω-TA designates all transaminases in subgroup
II. They catalyse the transfer of an amine group from an amine donor, usually an amino acid or
a simple amine, to a pro-chiral acceptor ketone, yielding a chiral amine as well as a co-product
ketone (Malik et al., 2012).
Transaminases are known as a typical enzyme obeying a Ping-Pong Bi-Bi mechanism (Shin, JongShik and Kim, 1998). A stringent feature of this mechanism is the formation of an intermediary
enzyme form in the reaction with the first substrate, usually by transferring a reactive group
(Bisswanger, 2008).
Figure 2.1: Schematic representation of a Ping-Pong Bi-Bi reaction scheme. Enzyme (E), amino substrate (A), keto product (P), keto substrate (B) and amino
product (Q). This mechanism involves 4 steps: An amino donor binds the enzyme
(1), the keto-product releases from the enzyme (2), an amino acceptor binds the
modified enzyme (3) and final release of the amino product (4). The reaction rate
constants are denoted with the letter k, followed by the index number of the reaction. A positive number stands for the forward reaction and a negative number
for the reverse reaction (Van Hauwermeiren, 2014).
6
2.1 PRODUCTION OF CHIRAL AMINES USING TRANSAMINASES
In the ω-transaminase reaction, the reaction is divided in two half reactions: oxidative deamination
of an amino donor and reductive amination of an amino acceptor. This is illustrated in Figure
2.2:
Figure 2.2: ω-transaminase reaction pathway consisting of a) oxidative deamination of an amino donor (box) which converts E-PLP to E-PMP and b) reductive
amination of an amino acceptor (triangle) which accompanies regeneration of EPLP (Malik et al., 2012).
The production of optically pure amines can be achieved by three methods: kinetic resolution,
deracemization and asymmetric synthesis. The first method is the commonly used option in
industry although it is hampered by a maximum theoretical yield of 50%, unless a racemization
step is included. The deracemization process converts a racemic mixture into a single enantiomer.
The asymmetric synthesis technique transfers the amino group to prochiral ketones yielding a
theoretical yield of 100%, but has difficulties with reaction equilibrium and stereoselectivity. When
comparing both strategies, this thesis will focus on asymmetric synthesis since it is the preferred
reaction configuration for the future and, because shifting the equilibrium will provide higher yields
and better enantioselectivities (Koszelewski et al., 2010b), even though it is more challenging than
the resolution strategy (Tufvesson et al., 2011).
2.1.4
Process challenges
The biocatalytic transaminase catalysed production scheme consists of four major steps: fermentation, biocatalyst formulation, reaction and product recovery. This section will focus on
the challenges of the last three. Tufvesson et al. (2011) has summarised published studies to
compare how the state-of-the art of the transaminase technology relates to process metrics industrial requirements. Most studies are far from meeting the required industrial process so process
improvements are needed. In order to overcome these problems, a thorough knowledge of the
reaction system is required. Reaction thermodynamics, physical characteristics of the reaction
components, and limitations of the biocatalyst are the main challenges.
Thermodynamic limitations of the reaction system
Thermodynamical equilibrium of the reaction system will determine which process solutions are
feasible on an industrial scale. The transamination reaction is reversible and, hence, the maximum achievable conversion is determined by the initial concentrations and the thermodynamical
equilibrium constant (K) of the reaction. K is determined by the change in Gibbs free energy
CHAPTER 2 LITERATURE REVIEW
7
∆G. For most systems, K is around unity or below. It is clear that the availability of a strong
amine donor could be beneficial for shifting K to higher values. By knowing the reaction ∆G,
the process strategy needs can be determined to meet process requirements in terms of yield and
product concentration. In order to overcome these hurdles, the most common strategies are listed
below.
ˆ Addition of excess amine donor : It is the easiest option for shifting the equilibrium towards
a high yield. This method is limited to those cases where the equilibrium is only slightly
unfavourable. To illustrate this, if a 90% yield is desired and the K value is 10−1 , an excess
of 100-fold of amine donor is required. However, if the K value is 10−3 , an unrealistic excess
of 10000-fold is required.
ˆ Removal of product or co-product: An alternative to the previous method is that of shifting
the equilibrium in favour of the desired product by removing the product or co-product
from the reaction media. This method is called In Situ Product Removal (ISPR). The
concentration of product or co-product is again a function of the desired yield and the
equilibrium constant. The best strategy for ISPRs will depend on the properties of the amine
product the other components in the reaction mixture. A large driving force is required and
the most common physico-chemical properties exploited are volatility, solubility, charge,
hydrophobicity and molecular size. There are limitations with all separation strategies.
Common limiting factors are selectivity of the separation and relative concentrations of the
reaction components, including the solvent. If a new phase is added, enzyme stability has
to be encountered. In situ recovery techniques applied to biocatalytic transamination are
liquid-liquid extraction, adsorbing resins for extracting product and evaporation of a volatile
product.
ˆ Auto-degradation of co-product: This is a very convenient option but is not a widely applicable approach. Self-degrading products or co-products are for example cycled, thereby
shifting the equilibrium.
ˆ Enzymatic cascade reactions: The idea of this concept is to couple the transamination
reaction with other enzymatic steps in order to convert co-product into a non-reactive species
or back to the original substrate. It is a strategy which has gained a lot of interest over
the past few years. The multi-enzyme process approach is not limited to the transaminase
process, so it can also be applied to a broad spectrum of enzymes (Santacoloma et al., 2011).
A broad range of possibilities can be defined depending on the pathway (i.e. cascade, parallel
or series), inside or outside a cell (in-vivo and ex-vivo) and the configuration of the reactors
(i.e. continuous or discontinuous). Regardless of the cascade system, the interactions and
compatibility of each of the enzymes and their associated reagents need to be considered.
Nevertheless several challenges remain for multienzyme processes including complexity and
interaction between enzymes.
ˆ Whole-cell biocatalysis: A similar approach is used to overcome the challenges of the enzymatic cascade reaction techniques by using a whole-cell as a biocatalyst. It is a very
promising field especially for biotransformations that require a cofactor addition or regeneration. Slow reaction rates, uncontrolled side reactions and adequate expression level of each
protein remain as hard challenges.
8
2.1 PRODUCTION OF CHIRAL AMINES USING TRANSAMINASES
Limitations of biocatalysts
Even if an enzyme with the desired specificity and selectivity is found, activity and stability
must be high enough to achieve the desired biocatalyst productivity at feasible biocatalyst cost.
Improvement of biocatalyst is often necessary in industrial processes and transamination is not
an exception (Tufvesson et al., 2011). The cost of a biocatalyst depends on expression level,
efficiency of the fermentation stage, enzyme specific activity and form of the biocatalyst. The
biocatalyst can be in the form of a whole-cell, cell-free extract (also known as crude enzyme),
purified or immobilised enzyme. Common problems are substrate and product inhibition of the
enzyme. As an example, in the transamination of Methylbenzylamine (MBA) from acetophenone,
severe substrate and product inhibition takes place even at millimolar concentrations (Truppo
et al., 2009).
ˆ Improvement of the biocatalyst: Although large improvements can be achieved, this technique comes at a high cost because it requires simultaneous development and screening for
the desired properties. The methodology of protein engineering is usually based on random
changes to the protein, understanding of the relationship between protein structure, and its
properties and selective pressure to find the improved protein mutants. A biomass requires
inactivation of the genetically engineered cells when a process is based on recombination.
ˆ Separation and recycling of biocatalyst: This is the main issue with downstream separation
processes. When the reaction is finished, enzymes need to be eliminated or removed to ensure
purity and enzymatic resolution. There is also a need to avoid problems with emulsions and
foams. This is especially important when using whole cells and high concentrations of organic
matter. The majority of enzymes can be removed by denaturalisation through acidification
and subsequent filtration. This method is economically feasible when the product has a high
added value, but if not, recycling of the biocatalyst should be considered.
ˆ Immobilisation: This technique provides several advantages compared to free-flow enzymes
and includes easy recovery, reuse, improved operational and storage stability, the possibility of continuous operation and minimisation of protein contamination. The drawbacks
are decrease in enzymatic activity and the possibility of mass transfer limitation. When
scaling-up a reaction, consideration should be given to the resistance of the particles and
microorganism stress to mechanical forces. This limits the maximum flow speed and amount
of mixing. Conventional whole-cell ω-transaminase immobilisation is carried out in calcium
alginate beads, covalently linked to different support materials and entrapment in sol-gel
matrices. Koszelewski et al. (2010a) demonstrated that in sol-gel matrix, immobilisation of
ω-transaminase retained its activity over a broad range of temperatures and pH compared
to the native enzyme.
ˆ Solubility problems and use of organic solvents: In nature, enzymes work in aqueous environments. In aqueous biocatalytic processes, low solubility of many substrates lead to low
volumetric productivity and high cost of downstream processing. In non-aqueous solvents,
the catalytic activity of enzymes is low and they can experience mass-transfer limitations
due to the insolubility of enzymes in organic solvents. Two approaches are taken: increase
of solubility and use of organic solvents. If the substrate is added beyond its solubility, a
second phase is formed. This can cause toxicity and stability problems to the microorganism
CHAPTER 2 LITERATURE REVIEW
9
and the enzyme. To increase productivity, a co-solvent miscible in water can be used like
iso-propanol or dimethyl sulfoxide. In the second approach, many different solvents can be
used for this purpose but it is really important that solvents are Generally Regarded As
Safe (GRAS), which limits the availability of usable solvents. The phases are separated
after the biocatalytic step, followed by subsequent product adsorption, liquid extraction or
distillation, generally from the apolar phase (Schmid et al., 2001). As a transamination
reaction example, Shin et al. (2001) used a packed-bed reactor in the resolution of MBA
with cyclohexanone. The aqueous/inorganic phases were separated by a membrane and a
ninefold increase of the reaction rate was observed.
2.1.5
Kinetic model of ω-Transaminase reactions
An accurate understanding of enzyme kinetics is a prerequisite to model the ω-transaminase reaction. Most of the enzyme systems can be modelled by a simple Michaelis-Menten kinetic model,
meaning that the order is generally between zero and one. The problem with the ω-transaminase
system is that there is no consensus in the literature about the exact kinetic expression. Figure
2.3 shows an example of an ω-TA reaction:
Figure 2.3: Transamination catalysed by ω-transaminase illustrating the synthesis
of 1-phenylethylamine (PEA) and a co-product acetone (ACE) from the substrates
acetophenone (APH) and 2-propylamine (IPA) (Al-Haque et al., 2012).
Al-Haque et al. (2012) proposed a kinetic expression based on the fact that the reaction is heavily
influenced by inhibition of the substrate and product in the asymmetric synthesis, besides having
unfavourable reaction equilibrium. The general rate equation proposed is shown in equation (2.1).
This equation consists of several parameters including catalytic turnover numbers of the reaction
f
r ), the Michaelis-Menten parameters (K A , K B , K P , K Q ), inhibition parameters for
(Kcat
, Kcat
M
M
M
M
the substrate and the product (KiA ,KiQ ), the intermediate complex inhibition constants for the
A , K B ) and the products (K P , K Q ),and the equilibrium constant K
substrates (KSi
EQ . Al-Haque
Si
Si
Si
et al. (2012) recommend simplifying the equation (2.1) for calibration purposes in order to obtain
these parameters in a fast and reliable manner. The simplification is done by splitting the full
model into submodels. For example, when we consider only the initial period of the reaction, the
product concentration is close to zero, and it can be assumed that product inhibition does not occur
as well as non-existing the reverse reaction. Submodels have the advantage that less parameters
need to be estimated simultaneously and thus will lead to an estimation of the parameter values
with potentially lower uncertainty. The following equation models the reaction shown in Figure
2.3 with Acetophenone (APH) as A, 2-Propylamine (IPA) as B, 1-Phenylethylamine (PEA) as P
and Acetone (ACE) as Q:
10
2.2 OVERVIEW OF MASS TRANSFER LIMITATION
r[P P ]
]
f
r
[E0 ] Kcat
Kcat
[B] [A] − [Q][P
KEQ
= −r[SA] = [B]
[P ]
[A]
[Q]
r
A
r
B
Kcat KM [B] 1 + K B + K P + Kcat KM [A] 1 + K A + Q
KSi
Si
Si
Si
!
Q
P
[A]
[B]
[Q]
[P ]
f KM [P ]
f KM [Q]
+Kcat
1 + A + Q + Kcat
1+ B + P
KEQ
KEQ
KSi KSi
KSi KSi
P
B
f KM [B] [Q]
f [Q] [P ]
r
r KM [A] [P ]
+Kcat [B] [A] + Kcat
+ Kcat
+Kcat
KEQ
KEQ KiB
KiP
(2.1)
The constitutive equation of the chemical equilibrium is formulated using the Haldane relationship
and is given by equation (2.2):
KEQ =
f
Kcat
r
Kcat
!
P KQ
KM
M
A KB
KM
M
(2.2)
Other kinetic models for the same process are available in the literature. One example is in the
kinetic resolution with ω-transaminases in Shin, Jong-Shik and Kim (1998), where only product
inhibition was considered in the reverse reaction.
2.2
Overview of mass transfer limitation
2.2.1
Definition
Mass transfer limitation is related to the mass gradient existing between the enzyme and the
substrate. When the enzyme is immobilised in the microreactor, it is redefined by considering it
as the mass gradient existing between the enzymatic surface and the most distant point in the
reactor (half of the width of the microreactor). Mass transfer limitation negatively impacts the
overall reaction rate, which in microreactors is mainly governed by diffusion.
2.2.2
Performance of microreactors under mass transfer limitation
Diffusion is a spontaneous movement and mixing of atoms or molecules in a medium by random
thermal motion. The rate of diffusion is a function of temperature, viscosity, and particle size and
mass. There are two types of diffusion: self-diffusion and chemical diffusion. Self-diffusion is an
equilibrium state where particles are self-propelled by thermal energy. It is also called Brownian
motion. Chemical diffusion is a non-equilibrium state where a net transport of mass is produced
when there is a concentration gradient in the system. In immobilised enzyme microreactors, the
concentration gradient will be a consequence of the depletion of substrate by an enzymatic reaction
on the microreactor walls. Mass transfer limitation takes place when the rate of mass transport
by diffusion is lower than the rate of consumption by the enzymes. Fluid flow is insufficient in this
case to resupply substrate to active enzyme sites causing a difference of substrate concentration
between the surface and the bulk. The diffusive flux of substrate will be equal to the rate of
reaction on the surface where enzymes are attached (Kerby et al., 2006):
D · ([Abulk ] − [Asurf ace ])
k 0 ΓA =
δ
(2.3)
CHAPTER 2 LITERATURE REVIEW
11
Where: k 0 is the intrinsic reaction rate, ΓA is the moles per unit area of reactive sites occupied by
substrate molecules, D is the molecular diffusivity, [A]bulk and [A]surf ace are the substrate bulk
and surface concentration, and δ is the diffusion layer thickness.
The performance of the microreactor can be improved if the system is not controlled by mass
transfer. Knowing the boundaries of this region are fundamental to properly identify mass transfer
limitations.
2.2.3
Mass transfer limitation in microreactors
Microreactors offer the potential to screen hundreds or thousands of different combinations of
enzymes, substrates and solution conditions. Enzyme microfluidics systems are increasingly being
used to determine enzyme kinetics (Lee et al., 2003; Kerby et al., 2006; Ristenpart et al., 2008).
The reason is that they can reduce the distance between the substrate to the active site because of
their small dimensions. In this way, one expects to obtain intrinsic kinetic constants of a proposed
model without any mass transfer limitation. Effect of diffusion on general catalysed microreactors
is discussed in Walter et al. (2005), Adeosun and Lawal (2005) and Nagy et al. (2012) wherein they
emphasise on reaction conditions, reorientation of fluid interfaces and pre-mixing requirements in
small-scale flow systems, respectively. Effects of enzyme diffusion were discussed by Ristenpart
et al. (2008) and studied by Swarts et al. (2010).
In immobilised enzyme microreactors, the conventional enzyme assays require adjustment in the
microfluidic format. Changes in enzyme, substrate, and especially buffer composition to avoid
adsorption to the surface of the chip channel, have to be adjusted to avoid hampering of results.
A large surface-volume ratio modifies the adsorption-desorption characteristics of reactants and
products, which alter the kinetics of the reaction and affects the reproducibility of the results.
A decrease in enzymatic efficiency was observed when immobilisation of enzymes is used (Kerby
et al., 2006). However, when a microreactor is operated with a continuous flow solution-phase,
that is, the enzyme and substrate are fed into the microreactor, an increase in enzymatic efficiency
as compared to conventional batch experiments was observed (Galvanin, 2014; Yamashita et al.,
2009).
In the immobilised form, Kerby et al. (2006) collected data from other articles and showed a
surprising variability in data interpretation when computing kinetic constants. There arises a
difficulty in explaining such data variability when we compare the same to solution-phase assays
with immobilised enzyme microreactors. Mass transfer limitation, imperfect immobilisation chemistry, altered conformation of the enzyme, steric hindrance, deactivation of the active sites and
erroneous kinetic models are the main explanations to try to answer this question. At present,
an overall analysis of the exact contribution of each argument has not been studied yet in an
immobilised enzyme microreactor, so the debate is still open. In the Michaelis-Menten kinetic
model, prediction of kinetic constants fails at high substrate conversions. Experimental results
reveal a flow dependence of the Michaelis-Menten constant in some enzyme systems. Kerby et al.
(2006) argue that the Michaelis-Menten mechanism is incorrect because it does not take into account adsorption effects and does not capture the complex behaviour of some enzyme systems.
Galvanin (2014) studied the effect of adsorption on ω-transaminase enzymes. They state that the
surface-volume ratio affects the kinetic parameter values compared to the solution-phase reaction,
but they assume the validity of the simple Michaelis-Menten mechanism.
12
2.2.4
2.3 MICROREACTOR TECHNOLOGY
Methods to determine mass transfer limitation
The simplest method to check for mass transfer limitation is that of performing laboratory experiments under mass transfer and kinetic limitation conditions. However, the amount of experiments,
resources and time spent can be a serious drawback. Computational Fluid dynamics (CFD) is a
powerful alternative to check for mass transfer limitation. A broad range of experimental conditions can be researched in less time. The main bottleneck is the need to model the enzymatic
behaviour inside the microreactor that accounts for the exact kinetic model, flow behaviour and
channel entrance effects. It can also be computationally very expensive, especially in transient
calculations, with difficulties to achieve convergence. Mass transfer limitation can be quantified by
three methods: calculating the Damköhler number of the system, the radial concentration profiles
or the critical time (Kerby et al., 2006; Hayes and Kolaczkowski, 1994; Swarts et al., 2010).
In Swarts et al. (2010), critical time is used as an indicator of the effect of diffusion on reactor
efficiency. It needs product concentration exiting the microreactor with diffusion (from numerical
models) and the concentration without diffusion limitation (from analytical equation). Critical
time is defined as the residence time required to achieve 90% of the analytical concentration value.
Swarts et al. (2010) used criteria from Hayes and Kolaczkowski (1994) to determine mass transfer
limitation in microreactors. This method requires radial concentration profiles to be calculated.
Mass transfer limitation will likely occur if the difference between average radial and surface
concentration at the wall is above 97%. Both methods require the use of CFD model solutions.
An alternative is to use the Damköhler dimensionless number. The Damköhler number (Da) is a
useful ratio to determine whether diffusion rates or reaction rates have a big impact for defining a
steady-state chemical distribution over the length and time scales of interest. Hence the definition:
Da =
Diffusion time
Reaction rate
=
Diffusion rate
Reaction time
For Da >> 1 the reaction rate is much greater than the diffusion rate distribution and therefore
the system is diffusion limited (diffusion is slower than reaction so reaction is assumed to be instantaneously in equilibrium). For Da << 1 the diffusion takes place much faster than reaction
and therefore the system is said to be reaction limited. Hence, estimating the Damköhler number allows one to have an intuitive idea about which process dominates a chemical distribution,
but this is not a trivial task. The Damköhler number depends on the kinetic expression of the
reaction rate and the extent of the reaction. Moreover, it depends on the geometry of the system
because of the diffusion term. There are multiple ways to calculate a Damköhler number for each
system, so comparison between Damköhler numbers found in the scientific literature is often not
straightforward. However, calculating Damköhler numbers can provide a quick estimation of mass
transfer limitation whenever there is a correlation between Damköhler values and mass transfer
limitation values. Kerby et al. (2006) calculated a Damköhler number for multiple literature data
to investigate mass transfer limitation but did not determine the extent of it.
2.3
Microreactor technology
Advances in precision engineering lead to the manufacturing of new equipment that can be used
in chemical processing with better or newer characteristics to perform chemical transformations
(Gavriilidis et al., 2002). Even though chemistry is scale-independent, transport phenomena
CHAPTER 2 LITERATURE REVIEW
13
are not. This is the starting point of miniaturisation. Microreactors are defined as continuous
miniaturised reaction systems fabricated by using (at least partially), methods of microtechnology
and precision engineering. At least one of the geometric dimensions is operating in the micron to
hundreds or thousands of microns range. Figure 2.4 shows an example of the configuration of a
microreactor:
Figure 2.4: Example of a two split-inlet Y-shape microreactor (Micronit, 2014).
2.3.1
History and fabrication techniques
The first stages of this discipline can be found in the late 1960s with the first attempts to adapt
microfabrication techniques to create silicon sensors. The field of MEMS (micro-electromechanical
systems) gradually emerged with the addition of microactuators and interface circuitry. Almost
in parallel, miniaturisation of chemical analytical devices started with a microfabricated gas chromatograph in the late 1970s. In 1989, micro total analysis systems (µTAS) were proposed as an
alternative to chemical sensors. A µTAS is a subset of labs-on-chips in which all information is extracted at once by integrating sequences of processes. The concepts of µTAS along with precision
engineering and microfabrication permeated in chemical engineering gave rise to microreaction
technology. Creating new processes or improving existing ones rather than generate information,
were the main objectives of working at the microscale (Gavriilidis et al., 2002). Microreactor
fabrication techniques were initially developed in the microelectronics industry for silicon-based
microprocessors. They allow the manufacture of micro-engineering structures mainly from metals,
ceramics, silicon, polymers, quartz, glass, and plastics. The use of these materials is conditioned
by chemical, thermal, and pressure compatibility. Ease of fabrication and cost will also influence
the choice of the microreactor material.
2.3.2
Advantages and disadvantages of microreactors
This technology has its pros and cons so it is important to balance these features to obtain a
process scheme which is always better than conventional ones.
Advantages of microreactors
ˆ High surface-area-to-volume: The main feature of microreactors is the high surface-volume
values. Specific surface area values lie between 10000 and 50000 m2 m−3 , compared to the
traditional reactor values which have about 100 m2 m−3 . Heat-transfer coefficients are in
14
2.3 MICROREACTOR TECHNOLOGY
the order of 10 kWm−2 K −1 and specific phase interface values for liquid-liquid mixtures lie
between 5000 and 50000 m2 m−3 (Jähnisch et al., 2004). This feature enables rapid heat and
mass exchange and suppression of spots of accumulated temperature or matter.
ˆ Mass transport enhancement: On the micro-scale, due to high viscous forces, turbulence
is not induced and mixing is dominated by molecular diffusion. Mixing can further be
improved by lamination. One way is to split two reagent streams into thin streams and
subsequently bringing them back together to allow a larger degree of diffusive mixing at the
point of confluence (micromixing can reduce mixing times to milliseconds). In enzymatic
reactions, a high aspect ratio reaction channel increases the interfacial surface. Substrates
need to diffuse over shorter distances to the enzymes and, hence, higher reaction rates can
be achieved.
ˆ Laminar flow : The hydrodynamic flow in the microchannel is mostly laminar. This feature
allows the possibility to simulate and model systems to develop microreactors by a rational
design and to achieve the optimal reactor design (Bodla et al., 2013). In many cases, basic
physical mechanisms and intrinsic kinetics parameters can be directly applied without the
problematic interference of other phenomena (i.e. turbulence).
ˆ Numbering-up: This was among the major predictions on microreaction technology benefits.
Depending on demand, more microreactors can be connected in parallel so that the required
intermediate products and end-products can be produced in their required amounts. Dimensionalisation and capacity utilisation, problems faced in traditional scale-up, would be
eliminated.
Disadvantages of microreactors
It is obvious that there are many areas of application that cannot be implemented by microreaction technologies, despite their advantages. The main disadvantages are high fabrication cost,
low capacity, immaturity of the technology, incompatibility with solids and initial poor industrial
acceptance (reluctance to change proven conventional technology). Other challenges are associated with obtaining low dead volumes, solving the problem of fouling, continuous flow, leak-free
connections between the pump and device and flow equipartition when running parallel microreactors.
2.3.3
Control of reaction and process intensification
Process parameters such as temperature, pressure, flow rate, and residence time are more easily
controlled in reactions that take place in small volumes. Higher safety is achieved in reactions
with toxic substances, strongly exothermic, explosive reactions and higher operating pressures
(Jähnisch et al., 2004). Acquiring information for on-line monitoring is achieved in shorter times
compared to conventional reactors, leading to broader operational ranges and better safety conditions. Microreactor technology also gives opportunity for a new production concept. Process
intensification can be achieved when using microreactors, by matching fluidics inside the reactor
to the physico-chemical requirements of a reaction. Process intensification is intended to reduce
the size of reactors while achieving production objectives, higher yields, and higher selectivity.
The potential to integrate sensors and control components along the microreactor can speed-up
CHAPTER 2 LITERATURE REVIEW
15
analysis time, enable on-line monitoring and reduce waste flows and operating cost. It is important to bear in mind that process intensification is ideal when chemical reactions are fast and,
consequently, the process is controlled by mass transfer or heat transfer. Biotransformations are
often slow (enzyme catalytic reaction constants are around 10−2 −102 s−1 ) and produce little heat.
This implies that only in selected cases of enzyme catalysed reactions, those involving transport issues, miniaturisation to microscale potentially results in substantial improvements (Bolivar et al.,
2011).
2.3.4
Process techniques for enzyme microreactors
An important stage in the development of a biocatalytic process is to choose the catalyst formulation inside the microreactor. Enzymes can be inside a host cell (whole-cell catalyst), or it
can be present in isolated forms. In the latter case, one has to decide the way the enzyme needs
to be purified because enzyme purification has a great impact on the production cost. The way
the catalyst is formulated also affects the stability of the enzyme, the possibility for recycling
co-factors, the selectivity, mass-transfer, and operational conditions. In Straathof et al. (2002),
current industrial biocatalytic reactions are mostly performed in the whole-cell catalysis form,
but more processes are shifting to isolated enzyme forms because they are not restricted by living
cell conditions. Chemical production processes need a high catalyst productivity (kg of product
per kg of catalyst) while keeping the reactor volume as low as possible. This leads to the idea of
reusing the enzyme. This can be achieved in two ways: separation of enzymes from the product
stream or by immobilising the enzymes on the wall or on beads. An advantage of immobilising
is that it allows enzymes to operate in non-aqueous environments. The main drawbacks are the
decrease of enzyme activity and stability (compared to the soluble form). The most relevant
process techniques used nowadays are (Miyazaki and Maeda, 2006):
ˆ Continuous-flow solution-phase reactions: Substrate and enzyme are loaded into the microreactor by separate inlets. Such reactions mainly rely on rapid mass transfer of the
reactants, and especially the substrate because it has a much lower molecular weight than
the enzyme.
ˆ Stopped-flow reaction: Reagents are mobilised by an applied force that could be chemical or
physical for a designated time. The flow is paused by the removal of the applied field before
reapplication of the field. By applying this method, higher residence times can be achieved.
Reaction rate can be increased by photothermal stimulation during the pause.
ˆ Enzyme immobilisation within microchannels: This technique is based on beads or monoliths
in which enzymes are trapped. Polystyrene and agarose derivates are the preferred materials
in beads. Monolithic immobilisation is often performed by means of a porous polymer or
silica derivates. Entrapment of the enzyme in the beads or monoliths is achieved by covalent
or non-covalent bonds to these materials. The preparation of the immobilised enzyme with
powdered material or a monolith is significantly easier; however, it is unfavourable in largescale processing because pressure loss can be high in beads and monoliths.
ˆ Enzyme immobilisation on membranes: Enzymes can be immobilised on a membrane embedded within the microchannel. The membrane is often a polymer and it suffers from
instability and it is technically difficult to immobilise enzymes. The Cross-Linked Enzyme
16
2.4 FLUID DYNAMICS
Aggregate (CLEA) technique offers an alternative solution because it can improve the stability with respect to organic solvents and for prolonged periods by creating a membrane
attached to the microreactor surfaces.
ˆ Enzyme immobilisation on microchannel surfaces: This process technique takes advantage of
the high surface-to-volume ratio. This advantage is being used for immobilisation on surfaces
but without the effect of increasing pressure observed in beads or monoliths. Immobilisation
can be done by adsorption-affinity or covalent bonding depending on the nature of the bond.
Physical adsorption and covalent cross-linking are the preferred options. In order to obtain
an even larger surface area, nanostructures, sol-gel, and polymer coating can be used to
cover the microchannel surface. Physical stability, clogging of microchannels, selectivity
in protein bonding, and reversible immobilisation are the main challenges that have to be
addressed. Figure 2.5 shows a schematic representation of this process technique.
Figure 2.5: Schematic illustration of an enzyme immobilised microreactor. a)
The enzyme has been immobilised on one of the surfaces. A sharp enzyme front
is to provide a uniform starting point. Flow over the surface is essentially uniform
across the width of the channel due to the high aspect ratio. b) Difference in rates
of reaction and transport give rise to a concentration boundary layer (Gleason
and Carbeck, 2004).
2.4
Fluid dynamics
From previous sections, it is clear that implementing microreaction technology offers a new approach to understand the underlying processes of enzymatic reactions. Microreactors can be
modelled to obtain a deeper understanding of the process (enzyme, substrate and product properties) for screening different biocatalysts and process alternatives much faster and with fewer
experiments compared to reality (Bodla et al., 2013). In this sense, CFD offers the possibility to
model the microreactor with a degree of accuracy dependent from the computational time spent
performing the simulations. Fluid dynamics aims at approximating the real world with mathematical equations that follow the foundational axioms of conservation laws. These axioms are
conservation of mass, conservation of linear momentum and conservation of energy. In addition
to these axioms, a thermodynamical equation of state giving pressure is required to completely
specify the problem. Fluid dynamics can also incorporate other associated phenomena such as
chemical reactions by defining additional equations and coupling and solve them simultaneously.
CHAPTER 2 LITERATURE REVIEW
17
The behaviour of the fluid is described in terms of macroscopic properties and includes their space
and time derivatives. These should be interpreted as averages over a large number of molecules.
As mentioned previously, fluids are assumed to obey the continuum assumption, so the fact that
the fluid is made of discrete molecules is ignored for practical purposes. This assumption permits
properties such as density, pressure, temperature and velocity to be constant in well-defined points,
and are assumed to vary continuously to other points. The Knudsen number (Kn) in a particular
flow determines the degree of validity of the continuum model (Gad-el Hak, 1999). The continuum
model is valid when the characteristic length of the microreactor (λ, molecular free path) is much
smaller than the characteristic flow dimension (dH , hydraulic diameter). In order to apply the
no-slip boundary condition for the simulations, it is necessary to have a Kn < 10−3 . In water,
for λ=3 · 10−10 m, the no-slip boundary condition can still be applied in microreactors with dH =
3 · 10−7 m.
λ
(2.4)
Kn =
dH
2.4.1
Navier-Stokes equations
These equations are a non-linear set of partial differential equations that describe the movement
of a fluid. At present, an analytical solution to these equations is not available yet and it is only
available for certain types of flow and simple situations. In 2000, the Clay Mathematics Institute
called the Navier-Stokes equations one of the seven most important puzzles in modern mathematics, and pledged 1 million $ to anyone who could solve one of these. It states that there is a need
of a proof that demonstrates the smoothness and uniqueness of a solution given a set of initial
conditions in three space dimensions and time. Instead of solving them analytically, numerical
solutions can be an alternative to solve these equations. Computational Fluid Dynamics(CFD) is
the branch of fluid mechanics that obtains a numerical solution using numerical methods. In an
inertial frame of reference, the general form of the equation is:
∂ρU
+ U · ∇ρU = −∇p + ∇ · T + f
(2.5)
∂t
Where: U represents the velocity vector, ρ represents the volumetric density, p represents pressure,
T represents the deviatoric of the total stress tensor, f represents body forces per unit of volume
acting (i.e. gravity) and ∇ represent the gradient operator.
Equation (2.5) can be simplified by considering the fluid a Newtonian and incompressible fluid in
laminar flow. This requires the assumption of considering the material density constant within a
fluid parcel.
ρ
∂U
+ U · ∇U = −∇p
∂t
(2.6)
The left side of equation (2.6) represents all the inertial forces applied to the portion of fluid. The
first term is associated with unsteady acceleration and the second is the convective acceleration.
In steady-state systems, the unsteady acceleration is zero. The convective acceleration can be
seen as the effect of time-independent acceleration of a fluid with respect to space and is a nonlinear effect. The right hand side of equation (2.6) only contains the pressure gradient. It is
important to know that only the gradient of pressure matters and not the value of pressure itself,
so that the fluid accelerates from the high pressure to low pressure direction. Viscosity and other
forces were neglected from the left side of Equation 2.5. It is worth noting that the solution of
18
2.4 FLUID DYNAMICS
the Navier-Stokes equation yields a velocity and pressure field. An alternative approach to these
computational fluid dynamics simulations is the lattice Boltzmann equation. It is based on an
integral-differential equation which characterises the dynamics and kinetics of the distribution of
micro-scale particles. The lattice Boltzmann equation has some important advantages over the
Navier-Stokes equation: mesh-free, intrinsic linear scalability in parallel computing and efficient
inter-phase interaction (i.e. multiphase and multicomponent flow). However, it has not been
used widely mainly because it is still computationally very expensive, it encounters problems with
turbulence modelling, and, at the moment, it only provides unsteady simulations. Therefore, it
is too early to say that the Lattice Boltzmann will change the landscape of the CFD market
(Shengwei, 2011).
2.4.2
Important dimensionless numbers in microreactors
In microreactors, different properties can be characterised using dimensionless numbers. A dimensionless number is a quantity without an associated physical dimension, and they are often defined
as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out
when grouped together. Flow regime is characterised by the Reynolds number (Re) which relates
inertial force to viscous force:
ρ · u · dH
(2.7)
Re =
µ
Where: ρ is the density of the fluid, u is the velocity of the fluid, dH is the hydraulic diameter of
the microchannel and µ is the kinematic viscosity of the fluid. In microreactors, due to the low
flow velocities and hydraulic diameter in the micrometer range, Re is often less than 1 meaning
that viscous forces are dominant over inertial force. Systems with laminar flow (Re < 2000)
exhibit a parabolic flow profile, so the Reynolds number is valid to check the laminar flow profile
inside the microreactor. The Bodenstein number (Bo) can also be useful to check the parabolic
flow profile. It is defined as the ratio of convection to dispersion:
Bo =
u·L
D
(2.8)
Where: L is the length of the microreactor and D is the Taylor dispersion coefficient. If Bo is
high, convection is more important than axial diffusion and the parabolic profile is maintained. If
Bo is low, axial diffusion is rapid enough to create a plug-flow behaviour inside the microreactor.
In small-scale flow systems, convection dominates axial diffusion so the diffusion term can be neglected (Nagy et al., 2012), for systems with small deviation from plug-flow, Bo > 100 (Levenspiel,
1999). The Taylor dispersion coefficient incorporates the effect of both diffusion and convection
in the axial direction. It is also a function of channel geometry with β = 30 in square channels.
D=D+
u2 · dH 2
4·β·D
(2.9)
The axial Peclet number (P e) is defined when molecular diffusion is substituted in the Bodenstein
number. Microreactors are recommended to have a residence time below 30 min to avoid a high
Peclet number (Matthias Junkers, 2014). Enzyme inactivation has been reported due to instability
effects because of the high convective forces (Karande et al., 2010).
Pe =
u·L
D
(2.10)
CHAPTER 3
Materials and Methods
3.1
Introduction
This Section first offers a brief description of all the software, before discussing the methods
used to numerically solve the Navier-Stokes equations. Next, the kinetic model and transport
equation used, to obtain the solutes profiles are introduced, and this is followed by a description
of the solution procedure used to obtain data from simulations. Finally, the derivation of the
dimensionless numbers for an immobilised enzyme and the two split-inlet microreactor is provided.
3.2
Software
3.2.1
Python
Python is a high-level and open source programming language. It supports multiple programming
paradigms including object-oriented, imperative and functional programming. Python has some
attractive features such as: clean syntax, nested-programming for treating heterogeneous data,
object-oriented programming, efficient numerical computing and possibility of integration with
other languages such as C++ or Java (Langtangen, 2008). Intellectual property rights behind
Python and its libraries are held by The Python Software Foundation (PSF), under the General
Public License (GNU) (Python-Software-Foundation, 2014).
In this dissertation, Python is used as a scripting language (creating scenarios and their analysis)
hereby creating a bridge to high-performance languages. A self-made scientific computing environment, executed from the interactive environment Spyder, is created to speed-up tasks such as
converting data types, administering numerical indexes, extracting numerical data and visualisation. For this purpose, standard packages like pandas (data structures and analysis), NumPy
(scientific computing data package) and matplotlib (2-D plotting library) have been used. The
Bio-intense ODE package was used to solve the chemical model, which is an ideal plug flow reactor.
The chemical model from Equation 3.1 provides reference values without mass transfer limitation
for comparison with the CFD results.
Z [A]0
d [A]
(3.1)
τ=
−rA
[A]
Where: τ is the residence time, [A] is the concentration of substrate A, and −rA is the substrate
reaction rate.
20
3.2.2
3.3 DISCRETISATION OF NAVIER-STOKES EQUATIONS
OpenFOAM
Open-source Field Operation And Manipulation toolbox (OpenFOAM) is an open-source collection of C++ class libraries developed for simulating continuum mechanics. As OpenFOAM does
not have a Graphical User Interface (GUI) all files and executables are called by the command line.
One feature of OpenFOAM is that it mimics standard vector and tensor notation with high-level
code, thus allowing complicated mathematical and physical models to be represented by high-level
mathematical expressions (Kimbrell, 2012). OpenFOAM is used in this dissertation to discretisise
Partial Differential Equations (PDE) and solve them numerically. It is freely distributed by the
OpenFOAM Foundation, under the GNU license (OpenFOAM, 2014).
3.3
Discretisation of Navier-Stokes equations
Equation 2.6 must be discretised and solved in order to obtain the velocity and pressure profile.
OpenFOAM uses the Finite Volume Method (FVM) as a discretisation approach, where the solution domain is subdivided into control volumes with the solution points defined at the centroids.
Values from the centroids are interpolated to the surface (faces) of the control volumes.
In OpenFOAM notation, equations are solved iteratively until convergence with a fixed tolerance:

P
n


aP Up = H(U) − S(p)f
f
P 1
P 1


S
·
(∇p)
=
S · (H(U))f

f
aP
aP
f
f
#
"
1
H(U)
−
(∇p)f
F = S · Uf = S ·
aP
aP f
(3.2)
(3.3)
Where aP denotes the central coefficients on the diagonal of the linear sparse matrix of the system,
Unp is the velocity of the cell centroid at time level n, H(U) is a term which holds the off-diagonal
contributions as well as additional source terms, S(p)f is an outward-pointing face (f) area vector
dependent of pressure (p), and F is the flux in the considered cell. For steady-state calculations,
the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is adopted. More
details about the general solution procedure can be found in Jasak (1996).
3.4
Advection-diffusion-reaction equation
Solutes do not influence the flow of the fluid in the microreactor, so they can be solved separately
from the Navier-Stokes equations. This simplification leads to huge savings in computational
resources because the velocity and pressure field only have to be calculated once. The solution
of the Navier-Stokes equation produces a velocity and pressure field in steady-state, which is
then used in the advection-diffusion-equation. This equation models contributions of convection,
diffusional effects and enzymatic reaction at any point of the microreactor from a mass conservation
perspective.
∂[A]
| ∂t
{z }
unsteady state term
= ∇ · (DA ∇[A]) − ∇ · (U[A]) +
|
{z
}
| {z }
diffusional term
convection term
rA
|{z}
source or sink term
(3.4)
CHAPTER 3 MATERIALS AND METHODS
21
In Equation 3.4, signs will depend on whether the solute is leaving or entering the microreactor.
The sink term has a negative sign and corresponds to a second order reaction kinetic model. The
reaction term will only appear at each cell depending on the chosen microreactor configuration.
Vmax
rA = −k [E] [A] = −
[A]
(3.5)
[A]0
The system can be solved by much faster and easier linear system solver than the kinetic model
from Equation 2.1. Vmax is defined as the multiplication of k, [E] and [A0 ]. This assumption is
valid for a Michaelis-Menten mechanism when [A] << KM because the kinetic model turns into
a first order kinetic model when [E] is kept constant.
3.5
Methodology
In Figure 3.1, a general overview of the solution procedure is represented in a flow chart. Firstly,
all parameters concerning mesh, boundaries, solver and constant parameters have to be set. The
Navier-Stokes equations are then solved for the desired initial parameters to generate a pressure
and velocity field.
Figure 3.1: Flow chart representation of the solution procedure followed to obtain
data for the analysis of mass transfer limitation.
Python is used to generate the scripts that contain the information of the scenarios. Enzyme
concentration is set up and is followed by fixing D and Vmax values for the scenarios. These
steps are done by running the python scripts of OpenFOAM in Python, which is followed by
22
3.6 MICROREACTOR CONFIGURATIONS
the performance of the simulations and recording of the simulation results. A mass balance
check is performed to ensure convergence and conservation of mass balance. In case of violations,
simulations are repeated with the failed set of degrees of freedom. Simulation data is loaded into
the PC from the cluster server for further analysis.
Python is initialised to obtain values from the chemical model from Equation 3.1 to provide the
reference values. Finally, data from CFD are compared with values from the chemical model and
the corresponding plots are generated for further analysis. A new set of degrees of freedom is
determined and the previous procedure is repeated.
The performance of the microreactor is evaluated with two variables: conversion and percentage
relative difference. Conversion is a measure of the extent of the reaction. Percentage relative difference is the relative difference, expressed in percentage, upon comparing the CFD solution with
that of the chemical model. This latter variable expresses the extent of mass transfer limitation
in the microreactor.
conversion =
[A]0 − [A]
[A]0
relative dif f erence (%) =
([A]CM − [A]CF D ) · 100
[A]CM
(3.6)
Where: [A]CM is the final concentration of substrate calculated from the chemical model and
[A]CF D is the final concentration of substrate calculated from the simulation using CFD.
3.6
Microreactor configurations
This study analysed two types of microreactor configurations. The first is the immobilised enzyme
and the second is the two split-inlet configuration. In order to take this into account, OpenFOAM
needs a generated mesh to apply the solution procedure by solving the collection of PDEs. Meshes
can be different depending on the chosen microreactor configuration. In order to generate these
meshes, a few assumptions have to be made. It is important to emphasise that simulations are
done in 2D, but meshes are generated in 3D.
ˆ Immobilised enzyme configuration: Enzymes are attached to the wall and a single inlet
stream containing substrate is fed to the microreactor. Due to the laminar flow profile, the
microreactor can be considered symmetric, with a symmetry plane around the centre. In
order to reduce computational load, the final mesh only contains one side of the symmetry
plane. Length and width of the microreactor are the only dimensions considered for simulation purposes. Effects in height are not considered because it is assumed that the flow profile
does not change significantly in this dimension. For immobilised enzyme and two split-inlet
configuration, the calculated fluxes and concentrations ratios of the 3D and the 2D model
were below a relative difference of 1% in Van Hauwermeiren (2014). W is defined as half
the width of the microreactor only for the immobilised enzyme microreactor configuration.
A schematic representation of this configuration is represented in Figure 3.2.
ˆ Two split-inlet configuration: Enzyme and substrate are fed into the microreactor by separate parallel inlet streams. Length and width are the only dimensions considered for simulation purposes and height is assumed to be not relevant. W is defined in this case as the total
width of the microreactor. A schematic representation of this configuration is represented
in Figure 3.3.
CHAPTER 3 MATERIALS AND METHODS
23
Figure 3.2: Schematic representation of an immobilised enzyme microreactor
with a laminar flow profile represented as velocity vector arrows and a parabolic
profile. The upper and bottom part of the microreactor are fixed with enzyme.
The simulation will only consider the bottom part and the width W is redefined
as half of the total width of the microreator. x-axis represents flow direction by
convection. y-axis represents the diffusion dimension.
Figure 3.3: Schematic representation of a two split-inlet microreactor configuration. Substrate and enzyme are fed into the microreactor in different parallel
streams. Substrate and enzyme profiles are shown by means of diffusion. LD
indicates the position in x-direction where diffusion of substrate is complete. xaxis represents flow direction by convection. y-axis represents diffusion dimension.
Modified from: Swarts et al. (2010).
3.7
Dimensionless numbers derivation
From the previous chapter, Damköhler numbers are known to have different expressions depending
on the characteristics of the system. Therefore the dimensionless numbers need to be derived for
each case. For this purpose, derivation is done for both, the two split-inlet and the immobilised
enzyme configurations.
3.7.1
Immobilised enzyme configuration
The enzymatic reaction only occurs on the microchannel wall, Equation 2.3 is used to consider
the substrate balance at y = W :
∂ [A]w
= −vA,surf ace = k 0 · ΓA
D·
∂ y(W )
D · ([A]0 − [A]w )
= k · ΓA
W
mmol
m2 · s
(3.7)
24
3.7 DIMENSIONLESS NUMBERS DERIVATION
Defining reaction rate per unit of volume, instead of per unit of area, with length and height
constant:
area −vA,volume = −vA,surf ace ·
= k 0 · ΓA · W
volume
Vmax W [A]w
k 0 · ΓA = k · [E] · [A]w · W =
[A]0
Substituting and rearranging in Equation 3.7 gives the final Damköhler number:
[A]0 − [A]w =
[A]w
1−
=
[A]0
3.7.2
Vmax W · W
· [A]w
D · [A]0
Vmax W 2
D[A]0
[A]w
[A]w
= Da ·
[A]0
[A]0
(3.8)
Two split-inlet configuration
Enzyme and substrate are fed into the microreactor in parallel streams. The reaction takes place
along the microreactor length, but substrate needs to diffuse into the enzyme stream first. At
steady-state, the conservation equation in the bulk is given by the advection-diffusion-equation
from Equation 3.4. The y-direction is the direction where diffusion takes place and the x-direction
is the direction where convection takes place. Moreover, it is assumed that convective transport
by means of a mean fluid velocity u dominates over axial diffusive transport in the downstream
x-direction. This assumption can be made in most microfluidics conditions because the Peclet
number is large enough (Ristenpart et al., 2008). The equation for the substrate at steady-state
involving the enzymatic reaction is given by:
D
∂ 2 [A]
∂[A] Vmax
=u
+
[A]
2
∂y
∂x
[A]0
(3.9)
Recasting Equation 3.9 in dimensionless terms gives:
X=
D
x
;
L
Y =
y
;
W
A=
[A]
[A]0
∂ ([A]0 A) Vmax
∂ 2 ([A]0 S)
=u
+
([A]0 A)
∂ y 2 (W Y )
∂ (LX)
[A]0
∂2A
=
∂Y2
P e2D =
uW 2
DL
uW 2
;
DL
∂A
+
∂X
Vmax W 2
D[A]0
Da =
A
Vmax W 2
D[A]0
(3.10)
(3.11)
Equation 3.10 yields two dimensionless numbers. The first number resembles the Peclet number
but modified to include the width of the microreactor. It will be called henceforth as the two
dimension Peclet number (P e2D ), and is defined by the ratio between diffusion time along the
y-axis and the residence time along the x-axis. The second number is the Damköhler number,
which exactly matches Da from Equation 3.8 for the immobilised microreactor. This dimensionless
number is often referred to as the second Damköhler number (DaII ). Other authors have derived
the Damköhler number in different ways but they will not be used here because they are not
derived from the fundamental equations.
CHAPTER 4
Results
“No thief, however skillful, can rob one of
knowledge, and that is why knowledge is the
best and safest treasure to acquire”.
L. Frank Baum, The Lost Princess of Oz
In this chapter, results are presented and interpretation of data is performed based on the microreactors introduced in Chapter 3.6. A degree of freedom is changed in the system and its
impact is determined by comparison with other figures and with the ideal model. Due to the
broad range of values evaluated, figures are plotted on a logarithmic scale along both axis for better visualisation. The chapter is divided into the following two subsections: Immobilised enzyme
microreactor and two split-inlet microreactor. In both subsections, an individual analysis of the
effect of the degrees of freedom in the microreactor performance is first performed. This is then
followed by a combined analysis. Finally, to predict mass transfer limitation, an analysis based
on dimensionless numbers is provided. Table 4.1 contains information on the degrees of freedom
and constants used in all simulations unless explicitly stated otherwise. These degrees of freedom
and constants are typical values found for numerical calculations involving enzymatic reactions
(Bodla et al., 2013; Ristenpart et al., 2008):
Table 4.1: Degrees of freedom and the constants used for analysing mass transfer
limitation in both microreactor configurations. D, k and Vmax also have intermediate points (5 · 10−x , where x is the current order of magnitude).
Symbol
D
k
Vmax
τ
[E]0
[A]0
4.1
Degree of freedom
Diffusion coefficient
Kinetic constant
Maximum reaction rate
Residence time
Enzyme concentration
Initial substrate concentration
Dimensions
Range
m2 s−1
s−1
mM s−1
min
mM
mM
[10−13 − 10−9 ]
[10−4 − 103 ]
[2.27 · 10−4 - 2.27 · 103 ]
1, 10, 30
0.0454
50
Immobilised enzyme microreactor
For the microreactor configuration in Figure 3.2, on needs to understand the influence of the
degrees of freedom on the performance of the microreactor. The degrees of freedom studied are:
diffusion coefficient (D), maximum reaction rate (Vmax ), residence time (τ ) and width (W ).
26
4.1.1
4.1 IMMOBILISED ENZYME MICROREACTOR
Individual impact of the degrees of freedom
An individual analysis is performed to understand the effect of changing a degree of freedom on the
immobilised microreactor configuration, in terms of conversion and percentage relative difference.
Effect of the diffusion coefficient
Table 4.2 shows that increases in the diffusion coefficient lead to increases in conversion and
decreases in percentage relative difference. A big increase in conversion and a big decrease in
percentage relative difference (% rel.dif.) is observed for certain values of diffusion coefficient.
This indicates a strong influence of the diffusion coefficient within a small range of values [10−12 −
10−11 ] m2 s−1 .
Table 4.2: Values from a test case to obtain the impact of diffusion in conversion
and percentage relative difference in an enzyme immobilised microreactor at τ =
10 min, W =200 µm, Vmax =2.271 mM s−1 .
Diffusion coefficient
[m2 s−1 ]
conversion
relative difference
(%)
1 × 10−13
5 × 10−13
1 × 10−12
5 × 10−12
1 × 10−11
5 × 10−11
1 × 10−10
5 × 10−10
1 × 10−9
0.044
0.118
0.183
0.492
0.707
0.993
0.999
1
1
99.54
88.15
81.72
50.82
29.27
0.069
0.019
0
0
Effect of maximum reaction rate
From Table 4.3, increases in maximum reaction rate lead to increases in conversion and percentage
relative difference. This means that increases in maximum reaction rate has a positive influence
on conversion but a negative one in mass transfer. The percentage relative difference appears to
decrease at high maximum reaction rates. This can be explained because conversion, calculated
with the ideal chemical model, has a constant value at high maximum reaction rates. The substrate reaches the enzyme at a constant mass transport rate and then reacts immediately, thereby
depleting the surroundings of the enzymes. Therefore, little additional conversion is achieved even
when maximum reaction rate is increasing in orders of magnitude.
Effect of residence time
The effect of residence time is studied in the immobilised microreactor. In order to be able to
change residence time (τ ) without changing the microreactor dimensions, on needs to change the
inlet flow, to provide a different velocity of the fluid inside the microreactor.
Table 4.4 shows that an increase in residence time leads to an increases in conversion and a decrease
in percentage relative difference. This means that an increase in residence time positively affects
the extent of the reaction and mass transfer. This is because the substrate spends more time in the
CHAPTER 4 RESULTS
27
Table 4.3: Values from a test case to obtain the impact of the maximum reaction
rate on conversion and percentage relative difference in an enzyme immobilised
microreactor at τ = 10 min, W =200 µm, D=10−11 m2 s−1 .
Maximum reaction rate
[mM s−1 ]
conversion
relative difference
(%)
2.27 × 10−4
2.27 × 10−3
2.27 × 10−2
2.27 × 10−1
2.27
2.27 × 101
2.27 × 102
2.27 × 103
0.002
0.026
0.203
0.589
0.707
0.721
0.723
0.724
0.15
1.84
14.63
36.97
29.27
27.86
27.63
27.59
microreactor, so more substrate is converted to product and any diffusional effects are lowered. At
high residence time, substrate molecules have more time to diffuse from the stream to the enzyme
surface.
Table 4.4: Values from a test case to obtain the impact of the residence time on
conversion and percentage relative difference in an enzyme immobilised microreactor at W =200 µm, Vmax =2.271 mM s−1 , D=10−11 m2 s−1 .
Residence time
[min]
conversion
relative difference
(%)
1
10
30
0.173
0.707
0.969
81.46
29.27
3.07
Effect of microreactor width
The effect of changing the microreactor width is studied. In order to be able to compare data
from different microreactor widths, kinetic conditions must remain constant. This is achieved by
maintaining the modified residence time (τmod ) constant, which is defined by Walter et al. (2005)
as:
nenzyme
Enzyme mass
τmod =
=
(4.1)
Reactant f low
FA
Where nenzyme is the total amount of enzyme and FA is the substrate flux at the inlet.
Enzyme and substrate volumetric concentration need to remain constant. As an example, when
W is doubled, nenzyme needs to be doubled. This is important when defining the total amount
of enzyme in OpenFOAM at the surface of the microchannel. It is assumed that there are no
restrictions to fix enzymes to the microchannel walls, even though in reality this assumption is
not valid.
From Table 4.5, an increase in microreactor width leads to lower conversion and higher percentage
relative difference values. This means that increases in microreactor width negatively affect the
extent of the reaction and the mass transfer. Substrate molecules need to diffuse further to reach
28
4.1 IMMOBILISED ENZYME MICROREACTOR
Table 4.5: Values from a test case to obtain the impact of the enzyme immobilised
microreactor width on conversion and percentage relative difference at τ = 10 min,
Vmax =2.271 mM s−1 , D=10−11 m2 s−1 .
Width
[µm]
conversion
relative difference
(%)
200
400
1000
0.707
0.323
0.133
29.27
67.74
86.73
the enzyme fixed on the wall from the centre of the microreactor, so some of them leave the
microreactor without reaching the enzymes.
4.1.2
Impact of the combination of the degrees of freedom
Previously, the effect of the individual degrees of freedom was studied. The next section looks
at the influence of simultaneously changing the degrees of freedom in terms of conversion and
percentage relative difference. The following analysis is performed to evaluate this impact but
by maintaining the kinetic conditions constant (constraint to compare results). The individual
figures are first presented separately to evaluate the effect on conversion and percentage relative
difference. The effect on the performance, at different residence times, is then studied. Finally, a
global analysis is performed by representing the combined impact of the four degrees of freedom
(diffusion coefficient, maximum reaction rate, residence time and microreactor width).
Influence of the diffusion coefficient and maximum reaction rate on conversion
Figure 4.1 shows 160 conversion values for the different degrees of freedom sets for diffusion
coefficient and maximum reaction rate. The dashed lines represent sets of degrees of freedom
with a constant conversion value. A linear interpolation is performed between adjacent simulation
values to generate continuous dashed lines.
9
10
log10(D)
11
13
0.05
12
3
2
0.15
0.10
1
0.90
0.75
0.60
0.45
0.30
0
1
log10(Vmax)
2
3
4
Figure 4.1: Influence of the diffusion coefficient and maximum reaction rate on
conversion in an immobilised enzyme microreactor at constant values of τ = 10
min and W = 200 µm. Dashed lines represent sets of degrees of freedom with
constant conversion values.
CHAPTER 4 RESULTS
29
A representation of the combined effect of diffusion coefficient and maximum reaction rate provides
a better understanding of the performance of the microreactor at specific degrees of freedom.
Figure 4.1 shows that conversion is dependent on both degrees of freedom. At high maximum
reaction rates, conversion decreases from full to low conversion when the diffusion coefficient
decreases. The reaction proceeds so fast that mass transport rates govern the system because
they are much slower. Since the conversion only depends on the diffusion coefficient, the system is
said to be mass transfer controlled. However, at low maximum reaction rates, conversion is only
dependent on maximum reaction rates at high diffusion coefficients, meaning that the system is
kinetically controlled. Mass transport rates are so fast that the reaction rates are the limiting
factor. It is worth mentioning here that conversion values match the ones calculated from the
chemical model. At low diffusion coefficients, conversion seems to be dependent on both degrees
of freedom as represented in the transition “curve”. In this region, there is not a mechanism
that fully controls the microreactor system because reaction and mass transfer rates lie in similar
orders of magnitude.
Influence of the diffusion coefficient and maximum reaction rate on mass transfer limitation
Mass transfer limitation can be represented explicitly by plotting the difference between the ideal
model and the simulation values, using the percentage relative difference. Figure 4.2 clearly shows
the degrees of freedom in which mass transfer limitations occur.
9
1
3
5
10
10
log10(D)
15
30
45
60
75
11
12
90
13
3
2
1
0
1
log10(Vmax)
2
3
4
Figure 4.2: Influence of the diffusion coefficient and maximum reaction rate on
mass transfer limitation represented as percentage relative difference in a immobilised enzyme microreactor at constant values of τ = 10 min and W = 200 µm.
Dashed lines represent sets of degrees of freedom with constant values of percentage relative difference.
A representation of the percentage relative difference throws more light on mass transfer limitation
and provides a quantitative way to measure it. Figure 4.2 shows that at low maximum reaction
rates, there is a “linear” behaviour in percentage relative difference for almost every diffusion coefficient. This behaviour is seen when the enzyme system reacts slowly for each mass transfer rate.
At constant diffusion coefficient in this region, mass transfer limitation decreases while decreasing
the maximum reaction rate. Full conversion is achieved at high maximum reaction rates. When
a substrate molecule entirely diffuses towards the enzyme (attached to the microchannel wall),
it reacts with it immediately. No information can be retrieved from the Figure in terms of mass
30
4.1 IMMOBILISED ENZYME MICROREACTOR
transfer limitation because the reaction is complete. However, a decrease in the diffusion coefficient leads to an increases in mass transfer limitation, independent of the maximum reaction rate.
When a substrate molecule diffuses to the enzymes, it reacts immediately creating a depletion in
the immediate surroundings of the microchannel wall, thereby generating a substrate gradient.
These sets of degrees of freedom are considered to be fully mass transfer limited.
50
log10(D) -11
25
-12
3
2
1
0
1
log10(Vmax)
2
3
4
-9
100
50
log10(D) -11
25
-12
-13
3
2
1
0
1
log10(Vmax)
2
3
4
-9
10
5
1
0
100
0.90
0.75
0.50
0.25
0.10
0.05
75
-10
50
log10(D) -11
25
-12
-13
% relative diference
75
0.90
0.75
0.50
0.25
0.10
0.05
-10
10
5
1
0
3
2
1
0
1
log10(Vmax)
2
3
4
% relative diference
-13
% relative diference
75
-10
0.01
The influence is checked by representing
sets of degrees of freedom of the diffusion
coefficient and the maximum reaction rate
with constant residence times. This procedure permits the simultaneous analysis of
the impact of these three degrees of freedom on microreactor performance. The
analysis is done for three residence times
of 1, 10 and 30 minutes.
Conversion and mass transfer limitation is
improved for almost every set of degrees
of freedom by increasing residence time.
This is reflected in Figure 4.3 by expansion of the set of degrees of freedom where
full conversion is achieved. Worth noticing
is that the transition to the mass transfer controlled area, for every set of degrees of freedoms occurs at the same maximum reaction rate. This value of maximum reaction is called critical maximum
reaction rate (Vmax, critical ). The critical
maximum reaction rate is not constant
for the residence times studied and decreases with lower residence times, ranging between 10−2 and 100 (mM s−1 ). Mass
transfer limitation is positively affected by
an increase in residence time, this effect
being more important at lower residence
times.
100
0
0.9
0.75
0.50
0.25
0.10
Influence of residence time on conversion and mass transfer limitation
0.01
-9
10
5
1
0
Figure 4.3: Influence of residence time on conversion and mass transfer limitation. Representation of conversion and percentage relative
difference with sets of diffusion coefficient and
maximum reaction rate, from top to bottom,
for τ = 1 min, τ = 10 min and τ = 30 min
with a constant value of W = 200 µm. Dashed
lines are constant values of conversion and the
greyrmap shows values of percentage relative
difference.
Influence of residence time and microreactor width on conversion and mass transfer
limitation
The influence is shown by representing conversion and percentage relative difference values for
different sets of degrees of freedom of the diffusion coefficient and maximum reaction rate for τ
CHAPTER 4 RESULTS
31
= 1, 10, 30 minutes and for W = 200, 400, 1000 µm for an immobilised enzyme microreactor
configuration.
1000 µm
-10
-11
0.8
-12
-13
-9
0.6
-10
-11
-12
0.4
-13
-9
-10
0.2
-11
-12
1 min
0.90
0.60
0.30
0.10
0.90
0.60
0.30
0.10
10 min
0.90
0.60
0.30
0.10
0.90
0.60
0.30
0.10
0.30
0.10
0.90
0.60
0.30
0.10
30 min
0.90
0.60
0.30
0.10
0.90
0.60
0.30
0.10
100
75
50
% relative diference
log10(D)
400 µm
200 µm
1.0
-9
25
0.90
0.60
0.30
0.10
-13
0.0
0.0 3 2 1 0 0.2
1 2 3 4 30.42 1 0 1 20.63 4 3 2 0.8
1 0 1 2 3 1.0
4
log10(Vmax)
10
5
1
0
Figure 4.4: Influence of residence time and microreactor width on conversion and
mass transfer limitation in an immobilised microreactor, with sets of diffusion
coefficient and maximum reaction rate at τ = 1, 10, 30 min and W = 200, 400,
1000 µm. Each subfigure represents percentage relative differences as a greymap,
where conversion is shown as dashed lines.
The combined effect of the four degrees of freedom is visualised in Figure 4.4. Microreactor width
has a negative impact on the overall conversion and percentage relative difference at any residence
time. In terms of conversion when comparing the top-left Figure with the right-bottom Figure, it
is preferable to operate the microreactor with high residence time and microreactor width rather
than low residence time and microreactor width. This implies that there are more sets of degrees of
freedom in which conversion is higher. In terms of mass transfer limitation, when the maximum
reaction rate is over the critical maximum reaction rate (Vmax > Vmax, critical ), the percentage
relative difference values are observed to be lower at τ = 30 min and W = 1000 µm than at τ =
1 min and W =200 µm. When the maximum reaction rate is lower than the critical maximum
reaction rate (Vmax < Vmax, critical ), the opposite behaviour takes place.
32
4.1.3
4.1 IMMOBILISED ENZYME MICROREACTOR
Prediction of mass transfer limitation
The influence of the degrees of freedom on mass transfer limitation was discussed in the previous
section, wherein some trends at specific sets of degrees of freedom were revelead. The objective
is to set a criterion to determine whether a system, with the considered degrees of freedom (D,
Vmax , τ and W ), is able to predict the type of mechanism that will control the system. The
Damköhler number (Da) is proposed as a possible method to meet this objective. Firstly, an
analysis based on the Damköhler numbers is performed for a system consisting of a diffusion
coefficient and a maximum reaction rate with constant residence time and width. Secondly, the
analysis is extended to different residence times and microreactor widths to examine its validation
for other sets. And finally, a figure is proposed to determine mass transfer limitation in enzymatic
immobilised microreactors.
Damköhler number analysis for diffusion coefficient and maximum reaction rate
The Damköhler numbers in Equation 3.8 are plotted at constant values shown in dashed lines,
superimposed with values of percentage relative difference in Figure 4.5.
-9
75
50
log10(D) -11
25
-12
-13
3
2
1
0
1
log10(Vmax)
2
3
4
% relative diference
-10
100
.00
00
10.
0
1.0
0.1
0
0.0
1
100
10
5
1
0
Figure 4.5: Damköhler number analysis with changes in sets of diffusion coefficient
and maximum reaction rates at constant values of τ = 10 min and W = 200
µm. Dashed lines correspond to Damköhler numbers, the vertical solid line is the
critical maximum reaction rate (Vmax, critical ) and the horizontal solid line is the
critical diffusion coefficient (Dcritical ).
The representation of Damköhler numbers in Figure 4.5 approximately matches percentage relative
values when the maximum reaction rate is lower than the critical maximum reaction rate (Vmax
< Vmax, critical ). When the maximum reaction rate is above the critical maximum reaction rate
(Vmax > Vmax, critical ), the Damköhler number cannot predict values of mass transfer limitation.
This is because the system becomes mass transfer limited. In this region, a critical diffusion
coefficient (Dcritical ) can be determined to know when mass transfer limitation is going to occur
and it is represented in Figure 4.5. Dcritical represents the lowest diffusion coefficient that permits
substrate molecules to reach the enzyme wall within a given residence time. This is done by
calculating Dcritical using the Einstein equation for the Brownian motion of a suspended particle:
p
p
x2 = λ = 2 · Dcritical · t
(4.2)
CHAPTER 4 RESULTS
33
Where: x2 is the square of the mean Brownian displacements of a substrate molecule in the
considered axis, λ is the displacement in the considered axis which a particle experiences on
average and t is the time spent to complete the displacement.
For Figure 4.5, the critical diffusion coefficient is the result of substituting the longest distance
that a substrate has to travel to reach the enzymes attached to the microchannel wall (W ) and the
residence time of the system considered (τ ). Above this value, substrate molecules have almost
completely reacted. The critical diffusion coefficient does not predict full conversion because some
molecules at the centre have left the microreactor within a shorter time than the mean residence
time, due to the laminar profile. This is why the critical diffusion coefficient predicts a conversion
around of 95 % in Figure 4.5.
Below the critical diffusion coefficient, the Damköhler number can predict mass transfer limitation
if the maximum reaction rate in Equation 3.8 is substituted with the critical maximum reaction
rate. Matching Damköhler numbers with percentage relative values provide a criterion to predict
mass transfer limitation in immobilised microreactors, and is represented in Table 4.6.
Table 4.6: Values of Damköhler numbers and percentage relative difference with
sets of diffusion coefficient and maximum reaction rate for constant values of τ =
10 min and W = 200 µm, extracted from Figure 4.5.
Da
relative difference (%)
0.01
0.1
1
10
>100
< 0.5
1
5-10
30-45
>75
Damköhler number analysis for residence time and microreactor width
Representing Damköhler numbers for sets of diffusion coefficient and maximum reaction rate for
τ = 1, 10, 30 min and for W = 200, 400, 1000 µm in an immobilised microreactor, yields Figure
4.6.
From Figure 4.6, the Damköhler number analysis can be extended to residence time and microreactor width. It is observed that at low values of residence time, criterion from Table 4.6 suffer
small deviations, especially when the Damköhler number is larger than unity (Da > 1). However,
the criterion from Table 4.6 can still be used to determine mass transfer limitation when the maximum reaction rate is lower than the critical maximum reaction rate (Vmax < Vmax, critical ). Above
this value, the critical diffusion coefficient needs to be calculated to a certain upper boundary of
the diffusion coefficient. In this way, the Damköhler number can predict mass transfer limitation,
below the critical diffusion coefficient, by substituting the maximum reaction rate with the critical
maximum reaction rate. Calculation of the critical diffusion coefficient was observed to be a useful
method for determining the lowest diffusion coefficient to obtain an empirical 95 % conversion.
Prediction of mass transfer limitation using Damköhler number
Mass transfer limitation was previously predicted by calculating the Damköhler number for an
immobilised microreactor configuration. Figure 4.7 presents a useful method to determine mass
34
4.2 TWO SPLIT-INLET ENZYME MICROREACTOR
1000 µm
-10
1 min
0 0
0.01 0.10 1.0010.0100.0
10 min
0 0
0.01 0.10 1.0010.0100.0
30 min
0 0
0.01 0.10 1.0010.0100.0
-11
0.8
-12
-13
-9
0.6
-10
75
0 0
0.01 0.10 1.0010.0100.0
0 0
0.01 0.10 1.0010.0100.0
0 0
0.01 0.10 1.0010.0100.0
50
-11
-12
0.4
-13
-9
-10
0.2
-11
100
.0
100
0.1 1.0 10.0100.0
.0
100
0.1 1.0 10.0100.0
.0
100
0.1 1.0 10.0100.0
-12
-13
0.0
0.0 3 2 1 0 0.2
1 2 3 4 30.42 1 0 1 20.63 4 3 2 0.8
1 0 1 2 3 1.0
4
log10(Vmax)
% relative diference
log10(D)
400 µm
200 µm
1.0
-9
25
10
5
1
0
Figure 4.6: Representation of the Damköhler number for sets of diffusion coefficient and maximum reaction rate for τ = 1, 10, 30 min and W = 200, 400, 1000
µm. Dashed lines correspond to Damköhler numbers, the vertical solid line is the
critical maximum reaction rate (Vmax, critical ) and the horizontal solid line is the
critical diffusion coefficient (Dcritical ).
transfer limitation by representing microreactor width on the x-axis (geometry of the system) and
the Damköhler terms from the reaction (diffusion coefficient, maximum reaction rate and initial
substrate concentration) on the y-axis,.
4.2
Two split-inlet enzyme microreactor
One needs to have knowledge of the influence of the degrees of freedom on the performance of
the microreactor in Figure 3.3. The degrees of freedom evaluated in this analysis are diffusion
coefficient (D), maximum reaction rate (Vmax ), residence time (τ ) and width of microreactor
(W ). The parameters from Table 4.1 have to remain constant when performing this analysis. The
exceptions are the initial concentration values of enzyme and substrate. For comparison purposes
these concentrations must be adjusted in order to have the same total amount of enzyme and
substrate, as in the case of the immobilised enzyme microreactor configuration. Concentration
CHAPTER 4 RESULTS
35
109
MASS TRANSFER LIMITED
Da = 10
108
Vmax
−2
(D ·[A]0 ) (m
)
TRANSIENT ZONE
107
Da = 0.1
106
KINETICALLY LIMITED
105
102
103
L (µm)
Figure 4.7: Figure presenting predictions of mass transfer limitation under
Vmax, critical in an immobilised enzyme microreactor. Dashed lines represent constant Damköhler numbers. The percentage relative difference can be derived using
the criterion presented in Table 4.6
adjustments must also be taken into account for the different volumes of both inlet streams when
a new microreactor width is set.
4.2.1
Individual impact of the degrees of freedom
Effect of the diffusion coefficient
The diffusion coefficient has a negative impact on conversion and mass transfer limitation, from
Table 4.7. A slight improvement in performance with the same sets of degrees of freedom in
conversion and percentage relative difference can be noticed, upon comparison with data from
Table 4.7 for the immobilised microreactor.
Table 4.7: Values from a test case to obtain the impact of the diffusion coefficient
on conversion and mass transfer limitation in a two split-inlet microreactor at τ =
10 min, W =200µm, and Vmax =2.271 mM s−1 . Mass transfer limitation data from
the immobilised enzyme microreactor is added to allow comparison.
Diffusion coefficient
[m2 s−1 ]
conversion
relative difference
(%)
immobilised relative
difference (%)
1 × 10−13
5 × 10−13
1 × 10−12
5 × 10−12
1 × 10−11
5 × 10−11
1 × 10−10
5 × 10−10
1 × 10−9
0.030
0.125
0.211
0.572
0.779
0.996
0.999
1
1
96.97
87.48
78.86
42.80
22.13
0.39
0.01
0
0
99.54
88.15
81.72
50.82
29.27
0.069
0.019
0
0
36
4.2 TWO SPLIT-INLET ENZYME MICROREACTOR
Maximum reaction rate
The maximum reaction rate has a positive influence on the conversion and mass transfer limitation
as compared to data from Table 4.8. Microreactor performance increases when the reaction proceeds faster. Upon comparing data with that in Table 4.8, the system reaches a higher conversion
at the same residence time when Vmax reaches high values. The comparison also reveals that mass
transfer limitation is reduced in the two split-inlet microreactor but increased in the immobilised
configuration with an increase in maximum reaction rate.
Table 4.8: Values from a test case to obtain the impact of the maximum reaction
rate on conversion and mass transfer limitation in a two split-inlet microreactor
at τ = 10 min, W =200 µm, D=10−11 m2 s−1 . Mass transfer limitation data from
the immobilised enzyme microreactor is added to allow comparison.
Maximum reaction rate
[mM s−1 ]
conversion
relative difference
(%)
immobilised relative
difference (%)
2.27 × 10−4
2.27 × 10−3
2.27 × 10−2
2.27 × 10−1
2.27
2.27 × 101
2.27 × 102
2.27 × 103
0.002
0.016
0.138
0.551
0.779
0.820
0.825
0.825
40.53
40.73
42.33
41.01
22.13
17.99
17.50
17.44
0.15
1.84
14.63
36.97
29.27
27.86
27.63
27.59
Residence time
Conversion and mass transfer limitation are positively affected by an increase in residence time,
as can be seen in Table 4.9. The system performance is more sensitive at lower values of residence
time. Comparing with the immobilised enzyme microreactor values, it can be seen that at higher
residence time, conversion and percentage relative difference are slightly improved.
Table 4.9: Values extracted to obtain the impact of residence time on conversion
and mass transfer limitation for a two split-inlet microreactor at W =200 µm,
Vmax =2.271 mM s−1 , D=10−11 m2 s−1 . Mass transfer limitation data from the
immobilised enzyme microreactor is added to allow comparison.
Residence time
[min]
conversion
relative difference
(%)
immobilised relative
difference (%)
1
10
30
0.033
0.779
0.988
86.25
22.13
1.22
81.46
29.27
3.07
Microreactor width
As described in the introduction of Section 4.2, the initial concentrations of enzyme and substrate
need adjusting in order to be able to compare data for the different microreactor widths. The
CHAPTER 4 RESULTS
37
adjustment of the microreactor width keeps the ratio of the volumes of the two streams inside the
microreactor constant, and therefore the change is proportional in both streams.
Table 4.10: Values from a test case to obtain the impact in a two split-inlet
microreactor width on conversion and percentage relative difference at τ = 10
min, Vmax =2.271 mM s−1 , D=10−11 m2 s−1 . Mass transfer limitation data from
the immobilised enzyme microreactor is added to allow comparison.
Width
(µm)
conversion
relative difference
(%)
immobilised relative
difference (%)
200
400
1000
0.779
0.426
0.170
22.13
57.37
83
29.27
67.74
86.73
An increase in microreactor width leads to a decrease in conversion and an increase in percentage
relative difference as evident in Table 4.10. This means that an increases in microreactor width
negatively affects the performance of the two split-inlet microreactor. Comparing the percentage
relative difference values of Table 4.10, it seems that the effect of changing the microreactor
width is similar for both microreactor configurations, but sensitivity is higher at low values of
microreactor width.
4.2.2
Impact of the combination of the degrees of freedom
Section 4.1.1 describes that an individual analysis to study the effect of the degrees of freedom
may obscure information about the behaviour of the system performance. First, individual figures
are presented separately to evaluate the effect on conversion and percentage relative difference,
with changes in diffusion coefficient and maximum reaction rate. Finally, a global analysis is
performed with simultaneous changes in diffusion coefficient, maximum reaction rate, residence
time and microreactor width.
Influence of the diffusion coefficient and maximum reaction rate on conversion
The influence of the diffusion coefficient and maximum reaction rate is checked by representing 160
value sets of these degrees of freedom in Figure 4.8. It is observed that specific sets of degrees of
freedom achieve full conversion at high values of diffusion coefficient and maximum reaction rate.
Conversion is only dependent on maximum reaction rate at high values of diffusion coefficient.
Likewise, conversion is only dependent on diffusion coefficients at low values of maximum reaction
rate. Upon comparing data with Figure 4.1, it seems that the two split-inlet microreactor achieves
lower conversion values as compared to the immobilised enzyme microreactor at low values of
diffusion coefficient and maximum reaction rate.
Influence of the diffusion coefficient and maximum reaction rate on mass transfer limitation
The representation of mass transfer limitation in Figure 4.9 reveals that there are two areas of constant percentage relative difference. The linear relationship of the percentage relative difference is
not seen at low maximum reaction rates like in the immobilised configuration. This indicates that,
in these two areas, the diffusion coefficient is primarily limiting the performance of the system.
38
4.2 TWO SPLIT-INLET ENZYME MICROREACTOR
9
10
log10(D)
11
0.1
0.105
0.0
5
12
13
3
2
1
0.90
0.75
0.60
0.45
0.30
0
1
log10(Vmax)
2
3
4
Figure 4.8: Influence of the diffusion coefficient and maximum reaction rate on
conversion in a two split-inlet microreactor with constant values of τ = 10 min
and W = 200 µm. Dashed lines represent sets of degrees of freedom with constant
values of conversion.
9
1
3
5
10
10
log10(D)
15
30
45
60
75
11
12
90
13
3
2
1
0
1
log10(Vmax)
2
3
4
Figure 4.9: Influence of the diffusion coefficient and maximum reaction rate on
mass transfer limitation represented as percentage relative difference in a two splitinlet microreactor at constant values of τ = 10 min and W = 200 µm. Dashed lines
represent sets of degrees of freedom with constant values of percentage relative
difference. The vertical solid line correspond to Vmax, critical . The horizontal solid
line corresponds to Dcritical .
This can be explained because the reaction area is increasing along the microreactor proportional
to the diffusion coefficient but independent of the reaction rate. It is interesting to notice that
the transition always takes place at a single value of Vmax for every diffusion coefficient. This
Vmax value corresponds to Vmax, critical , which was defined previously for the immobilised enzyme
microreactor configuration in Section 4.1.2. This behaviour could be explained by Equation 3.10:
∂2A
=
∂Y 2
uW 2
DL
∂A
+
∂X
Vmax W 2
D[A]0
A
(4.3)
It is possible that these two areas, with constant percentage relative difference, are influenced by
the value of the dimensionless numbers (the two dimension Peclet and Damköhler). The transition
is observed to occur at a specific value of maximum reaction rate (Vmax, critical ), where reaction
rate overcomes convection forces. Dividing both dimensionless numbers yields a new dimensionless
CHAPTER 4 RESULTS
39
number, which is often referred to as the first Damköhler number (DaI ) and gauges the reaction
rate and convection:
DaI =
Vmax W 2
D[A]0
uW 2
DL
=
Vmax L
u[A]0
(4.4)
Ristenpart and Stone (2012) state that neglecting the concentration term is argued to be correct
if the inequality (DaI << 1) is satisfied. This simplification implies that the two dimension
Peclet number (P e2D ) has a large impact on the solution of the equation, thus leading to different
mass transfer limitation. Similarly, when the first Damköhler number is near or above unity,
the Damköhler number (Da) is the most important term in Equation 4.3. The transition takes
place when the inequality is not satisfied and both terms contribute significantly to the solution.
Therefore, it would be natural to calculate the critical maximum reaction rate from the first
Damköhler number. This is summarised in Equation 4.5:

uW 2



if
Da
≤
1.2
mass
transfer
limitation
is
governed
by
P
e
=
I
2D


DL


if 1.2 > DaI > 12 mass transfer limitation is governed by both dimensionless numbers.




Vmax,critical W 2


 if DaI ≥ 12 mass transfer limitation is governed by Da =
D[A]0
(4.5)
The first boundary value for the first Damköhler number has been calculated from the critical
maximum reaction rate observed (10−1 ) in Figure 4.9. The second boundary value for the first
Damköhler number has been calculated from the maximum reaction rate values where percentage
relative difference was constant at the right (100 ). The calculation of Dcritical from Equation 4.2
shows that it is still a valid method to obtain the lowest diffusion coefficient for a conversion of
around 95%.
Influence of residence time and microreactor width on conversion and mass transfer
limitation
The influence is shown by representing conversion and percentage relative difference values for
different sets of degrees of freedom of diffusion coefficient and maximum reaction rate for τ = 1,
10, 30 min and for W = 200, 400, 1000 µm, for a two split-inlet microreactor configuration.
Figure 4.10 shows that mass transfer limitation is negatively affected by an increase in microreactor
width and a decrease in residence time. It seems that, for a better microreactor performance, it is
preferable to operate at high τ and W rather than at low τ and W . The transition is observed at
the same critical maximum reaction rate Vmax, critical as in Section 4.1.2 with changes in residence
time. This is now reinforced by Equation 4.4, which states that the critical maximum reaction
rate is dependent on velocity (residence time) but not on microreactor width. The same argument
can be used in the immobilised enzyme microreactor because the critical maximum reaction rate
showed the same behaviour with these degrees of freedom.
4.2 TWO SPLIT-INLET ENZYME MICROREACTOR
1000 µm
log10(D)
400 µm
200 µm
1.0
-9
-10
-11
0.8
-12
-13
-9
0.6
-10
-11
-12
0.4
-13
-9
-10
0.2
-11
1 min
10 min
0.90
0.60
0
0.1 .30
0
0.90
0.60
0.30
0.10
0.60
0.30
0.10
0.90
0.60
0.30
0.1
0
0.90
0.60
0.30
0.10
0.90
0.60
0.30
0.1
0
-12
30 min
0.90
0.60
0.30
0.1
0
0.90
0.60
0.3
0
0.10
100
75
50
% relative diference
40
25
0.90
0.60
0.30
0.10
-13
0.0
0.0 3 2 1 0 0.2
1 2 3 4 30.42 1 0 1 20.63 4 3 2 0.8
1 0 1 2 3 1.0
4
log10(Vmax)
10
5
1
0
Figure 4.10: Influence of residence time and microreactor width on conversion
and mass transfer limitation in a two split-inlet microreactor configuration with
sets of diffusion coefficient and maximum reaction rate at τ = 1, 10, 30 min and
W = 200, 400, 1000 µm. Each subfigure represents percentage relative difference
as a greymap, and conversion in dashed lines.
4.2.3
Prediction of mass transfer limitation
The objective is to check whether the dimensionless numbers Damköhler (Da) and the two dimension Peclet number (P e2D ) are suitable for predicting mass transfer limitation, and if so, ascertain
if there is some correlation with percentage relative difference values.
Dimensionless number analysis for diffusion coefficient and maximum reaction rate
The dimensionless numbers are calculated and represented from Equation 4.5 in Figure 4.11.
Representation of the dimensionless numbers on Figure 4.11 yield different criterion for correlating
the dimensionless number values to percentage relative difference values. It seems that percentage
relative difference could be predicted as a function of two dimensionless numbers. These correlation
values are listed in Table 4.11. To calculate Damköhler numbers, it is necessary to substitute the
maximum reaction rate with the critical maximum reaction rate. In this way, the system is
CHAPTER 4 RESULTS
41
-10
log10(D) -11
-12
-13
100
0.1
5.0
5
10
25
10.0
40.0
3
75
1
1.0
50
25
75
2
1
0
1
log10(Vmax)
2
3
4
% relative diference
-9
10
5
1
0
Figure 4.11: Dimensionless number analysis with changes in sets of diffusion
coefficient and maximum reaction rates with constant values of τ = 10 min and
W = 200 µm. The greymap correspond to percentage relative difference values.
The two dimension Peclet numbers (P e2D ) are represented at the left with dotted
lines. The Damköhler numbers (Da) are represented at the right with dashed
lines.
assumed to be no longer dependent on the reaction rate, and that only the diffusion coefficient
will be able to modify the mass transfer limitation.
Table 4.11: Criterion to determine mass transfer limitation with dimensionless
numbers for a two split-inlet microreactor. The two dimension Peclet number is
used when Vmax <Vmax, critical . The Damköhler number is used (calculated at a
constant Vmax, critical ) when Vmax >Vmax, critical .
4.2.4
P e2D
% rel.dif.
Da
% rel.dif.
0.1
1
5
10
40
1
5-10
25
50
75
1
5
10
25
75
10
15
50
75
Dimensionless number analysis for residence time and microreactor width
The dimensionless number analysis is extended for different residence times (τ = 1, 10, 30 min) and
different microreactor widths (W = 200, 400, 1000 µm) in Figure 4.12. The dimensional analysis
is able to predict mass transfer limitation, with small deviations from the criterion presented in
Table 4.11. These deviations are observed to increase when the microreactor width is increased.
The transition of the constant percentage relative difference values is well predicted by the two
dimensionless numbers and it begins at the critical maximum reaction rate. It is also observed
that the critical maximum reaction rates, calculated by the criterion of Equation 4.5, are the
same when compared with the critical maximum reaction rate observed in the analysis of the
immobilised enzyme microreactor for different residence times.
42
4.3 DISCUSSION OF RESULTS
1000 µm
1
5
-10 10
-11 40
0.8
-12
-13
-9
5
0.6 10
-10 40
1 min
1
5
10
25
75
5
10
25
75
-11
-12
0.4
-13
-9
-10
0.2
-11
40
25
75
0.1
10 min
30 min
1.0
5.0
10.0
40.0
1
5
10
25
75
1
5
10
40
1
5
10
25
75
5
10
40
5
10
25
75
100
0.1
1.0
5.0
10.0
40.0
1
5
10
25
75
75
0
1
5
10
40
1
5
10
25
75
1
5
10
40
1
5
10
25
75
-12
-13
0.0
0.0 3 2 1 0 0.2
1 2 3 4 30.42 1 0 1 20.63 4 3 2 0.8
1 0 1 2 3 1.0
4
log10(Vmax)
50
% relative diference
log10(D)
400 µm
200 µm
1.0
-9
25
10
5
1
0
Figure 4.12: Dimensionless number analysis with D and Vmax with τ = 1, 10, 30
min and W = 200, 400, 1000 µm. Two dimension Peclet numbers are represented
with dotted lines at the left and Damköhler numbers with dashed lines at the
right. Vmax, critical is represented with a vertical solid line. Dcritical is represented
with a horizontal solid line.
4.3
Discussion of results
In the abovementioned analyses, the impact of the four degrees of freedom (the diffusion coefficient
(D), the maximum reaction rate (Vmax ), the residence time (τ ) and the microreactor width (W ))
was checked on the performance (conversion and mass transfer limitation) of the two different
microreactor configurations (immobilised enzyme and two split-inlet). The results of these analyses
agree with other microreactor studies on conversion and mass transfer limitation (Bodla et al.,
2013; Swarts et al., 2010). However, some important observations not mentioned in other articles
were only observed in this study when the degrees of freedom were changed simultaneously, thus
the microreactor configuration is observed to be another important degree of freedom that change
the behaviour of the system.
For the immobilised enzyme microreactor, mass transfer limitation was only dependent on the
diffusion coefficient upon reaching a certain maximum reaction rate value. This value is called
CHAPTER 4 RESULTS
43
the critical maximum reaction rate (Vmax, critical ) and indicates the transition between the linear
and constant relation of the percentage relative difference between the diffusion coefficient and the
maximum reaction rate. This value can be calculated by Equation 4.4 from the first Damköhler
number (DaI ), which indicates the transition between convection forces and the reaction rate.
Prediction of mass transfer limitation is possible using the Damköhler number (Da) with the
criterion developed in Table 4.6. The Damköhler number (Da) used in this dissertation is often referred as the second Damköhler number (DaII ), in order to be able to distinguish both
Damköhler numbers. Prediction beyond the critical maximum reaction is possible if Vmax, critical
is replaced in the Damköhler number. A quick analysis of mass transfer limitation, by including
all degrees of freedom, can be performed in Figure 4.7. The CFD results indicate that residence
time is not needed to calculate the Damköhler number and hence, there is no need to calculate
the conversion first.
The simulations show that the two split-inlet microreactor leads to different mass transfer behaviour. A simultaneous analysis of the degrees of freedom revealed that mass transfer limitation
is primarily dependent on the diffusion coefficient. A transition between constant percentage relative difference values is observed when the maximum reaction rate exceeds the critical maximum
reaction rate (Vmax >Vmax, critical ). This transition visible in Figure 4.13b , at the critical maximum reaction rate, is dependent on the residence time, again predictable by Equation 4.4. Mass
transfer limitation can be predicted by using two dimensionless numbers (P e2D and Da) with
criterion developed in Table 4.11. The prediction method is mathematically supported because
the dimensionless numbers were derived from the fundamental equations.
log10(D)
log10(D)
log10(Vmax)
(a) Immobilised enzyme microreactor configuration.
log10(Vmax)
(b) Two split-inlet microreactor configuration.
Figure 4.13: General representation of mass transfer limitation as a function of the
microreactor configuration. Dashed lines represent percentage relative difference
values between the ideal model and the CFD, for the sets of diffusion coefficients
and maximum reaction rates.
A comparison of both microreactor configurations in Figure 4.13 shows that, when the diffusion
coefficient is constant, mass transfer limitation is negatively affected by an increase in maximum
reaction rate in immobilised enzymes microreactor, but positively is affected in the two splitinlet microreactor. Another observation was that, when the maximum reaction rate is below
the critical maximum reaction rate (Vmax <Vmax, critical ), mass transfer limitation is always lower
in the immobilised enzyme microreactor than in the two split-inlet microreactor. This can be
44
4.3 DISCUSSION OF RESULTS
useful to decide the type of microreactor to extract kinetic data for calibration purposes at low
conversions. The explanation for this phenomenon seems unclear at the moment. In the case of
the immobilised configuration, an increase in Vmax leads to higher mass transfer limitation values
because the enzyme surface surroundings are increasingly being depleted of substrate. In the two
split-inlet microreactor, diffusion limits the amount of substrate reaching the enzyme inside the
reaction zone. An increase in Vmax may not increase mass transfer limitation because Vmax does
not contribute mathematically to solve Equation 4.3 when DaI is below 1.2. A slight improvement
can be seen in terms of mass transfer limitation in the two split-inlet configuration when the
maximum reaction rate is higher than the critical maximum reaction rate (Vmax >Vmax, critical ).
In this region, substrate is consumed in the reaction zone and mass transfer limitation does not
increase with increases in maximum reaction rate. A physical explanation could not be found to
explain why there are two constant values of mass transfer limitation in the whole range of the
maximum reaction rate values.
Instead of percentage relative difference, other variables could be used to verify mass transfer
limitation conditions. The variable used expresses a comparison ratio between the CFD value and
the theoretical no mass transfer limited plug flow value. Although it allows comparison between
different values with different sizes, it does not contain information about the absolute change,
which may obscure important information when interpreting the results. Representing the critical
time for each scenario is also another possibility. It could give an idea of how much residence time
is necessary to achieve a certain percentage value with respect to the theoretical no mass transfer
limitation value.
CHAPTER 5
Conclusions and future perspectives
“Sell your cleverness and buy bewilderment.”
Rumi, Afghanistan poet
5.1
Conclusions
In this dissertation the performance of two types of microreactor configurations (immobilised
enzyme and two split-inlet) was studied using CFD for the ω-transaminase enzyme system.
Four degrees of freedom (diffusion coefficient (D), maximum reaction rate (Vmax ), residence time
(τ ), and microreactor width (W )) were varied to obtain the impact on the microreactor performance.
A total of 2880 CFD scenarios were simulated in OpenFOAM, which had a high computational cost
especially for high diffusion coefficient and maximum reaction rate (10 cores in parallel running for
several hours for each scenario). Savings in computational resources were obtained by decoupling
the calculation of the compound profiles and the hydrodynamic equations.
The kinetic model is a second-order reaction (Vmax [E][A]), which is a simplification to replace the
complex kinetic model of the ω-transaminase enzymes. As a consequence, the CFD does not fully
model the complex enzyme behaviour of the system.
The CFD simulation results were compared with theoretical plug flow profiles to determine to
which extent mass transfer limitation occurs. Dimensionless numbers were derived from the
fundamental equations for each microreactor to test a mass transfer limitation prediction approach,
based on these numbers. The use of dimensionless numbers also allows to scientists with no access
to CFD to quickly verify whether the current conditions lead to mass transfer limitations in
enzymatic microreactors.
For the immobilised enzyme configuration, a criterion for quantifying mass transfer limitation was
based on the second Damköhler number DaII . For the two split-inlet configuration, a criterion for
quantifying mass transfer limitation was developed based on the two-dimensional Peclet (P e2D )
and the second Damköhler (DaII ) numbers. Mass transfer behaviour was observed to change in
both microreactor configurations at the critical maximum reaction rate (Vmax, critical ). This value
was predicted with a first Damköhler number (DaI ) around unity.
Open source programs and scientific libraries were used and seen as an advantage as opposed to
other closed source software simulation programs. Researchers have more degrees of freedom during the setup of the simulation case, and it allowed better comprehension of the simulation results.
Despite these advantages, high programming skills and a good knowledge and understanding of
46
5.2 FUTURE PERSPECTIVES
transport phenomena and enzyme kinetics were required, especially when programming using
OpenFOAM.
5.2
Future perspectives
This dissertation looked at mass transfer limitation in a theoretical framework. An experimental
validation needs to be performed in order to determine whether the CFD modelling and the
dimensionless number based prediction approach are valid and to what extent.
The scope can be extended further by taking into account more factors. The prediction approach
based on dimensionless numbers can be improved by performing a study of other critical degrees
of freedom in enzymatic microreactors (e.g. enzyme and substrate initial concentrations, pH,
multiple substrates, inlet velocity, etc.). The analysis can also be extended by studying other
types of microreactor configurations (e.g. multiple split-inlet). It is also necessary to take into
account some considerations that can alter the CFD results. For example, 3D microreactor effects,
such as the entrance effect, were not included in the hydrodynamics and it was assumed that the
maximum amount of enzyme that can be fixed to the microchannel wall is unlimited. In addition,
loss of enzyme activity and adsorption effects on the microchannel walls can also be introduced
in further analyses.
A second-order reaction kinetic model was used to perform the mass transfer limitation analyses.
An important issue is to investigate whether the dimensionless number prediction approach can
be applied to other types of kinetics (e.g. Michaelis-Menten or ω-transaminase kinetic model).
Dimensionless numbers can be used in practice by scientists to check mass transfer limitations
for microreactor scale-up, design of new microreactors, improvement and optimisation of existing microreactors, and furthermore for the design of calibration experiments, among other uses.
However, more research should be carried out in order to help improve mass transfer limitation
strategies such as the multiple split-inlet to reduce the substrate and product diffusion distances.
Reactions that are slow and hampered by substrate and/or product inhibition (ω-transaminase
reaction) can be improved by identifying the best split-inlet microreactor configuration with dimensionless numbers. An optimal configuration should aim for a ratio of species transport times
to reaction time of approximately one (Bodla et al., 2013).
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