Analysis of the In Situ Combustion process in a kinetic ... · Analysis of the In Situ Combustion process in a kinetic cell with optical access using computational uid dynamics (CFD)

Universidad Nacional de Colombia - SedeMedellın

Master’s Thesis

Analysis of the In Situ Combustionprocess in a kinetic cell with optical

access using computational fluiddynamics (CFD).

Author:

Sebastian Lopez Gomez

Supervisor:

Alejandro Molina

Thesis presented as a partial requirement to obtain the degree of:

M.Sc. in Chemical Engineering

Research Group: Bioprocesos y Flujos reactivos

Facultad de Minas, Departamento de Procesos y Energıa

Medellın, Colombia

2014

http://www.medellin.unal.edu.co/


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http://scienti1.colciencias.gov.co:8080/gruplac/jsp/visualiza/visualizagr.jsp?nro=00000000004569

http://www.minas.medellin.unal.edu.co/index.php/es/departamentos/departamento-de-procesos-y-energia

Universidad Nacional de Colombia - SedeMedellın

Master’s Thesis

Analisis de la combustion in situ en unacelda cinetica con acceso opticomediante dinamica de fluidos

computacional (CFD).

Author:

Sebastian Lopez Gomez

Supervisor:

Alejandro Molina

Thesis presented as a partial requirement to obtain the degree of:


Research Group: Bioprocesos y Flujos reactivos


Medellın, Colombia

2014





http://scienti1.colciencias.gov.co:8080/gruplac/jsp/visualiza/visualizagr.jsp?nro=00000000004569


UNIVERSIDAD NACIONAL DE COLOMBIA - SEDE MEDELLIN

AbstractFacultad de Minas



Analysis of the In Situ Combustion process in a kinetic cell with optical

access using computational fluid dynamics (CFD).

by Sebastian Lopez Gomez

A model for the study of the in situ combustion (ISC) process in experimental setups us-

ing computational fluid dynamics (CFD) in the commercial software ANSYS FLUENT

was developed. The model, involving the main phenomena presented in the process

such as chemical reactions, phase equilibria, multiphase flow in a porous media and

correlations for the variation of physicochemical properties with temperature, allows to

simulate different experimental setups commonly used in the study of ISC. The model

was validated against different experimental tests reported in the literature.

The validated model was firstly used to study ramped temperature oxidation tests in a

kinetic cell through the dimensionless Damkohler number, traditionally used as param-

eter to evaluate the homogeneity in reactors. The study determined values for process

conditions that help to approximate the behavior in kinetic cell to that of a perfectly

mixed reactor.

Finally, the model was used to predict the behavior of the different phases during ISC in

a prototype cell that will allow the measurement of gaseous species using laser diagnostic

techniques. Based on the experience obtained with the analysis of the Damkohler on

the homogeneity of the cell, the process conditions for the optical cell were selected so

that the behavior was homogeneous in the core. The simulations in this prototype had

as main objectives to determine the effect of the optical access in the fluid-dynamics

of the different phases involved in the ISC process and to predict the different gaseous

species that could be measured.

The CFD simulations suggested that the core should be partially saturated and in this

way to prevent interference with the measurements of gaseous species with laser diag-

nostic techniques.


http://www.minas.medellin.unal.edu.co/index.php/es/


ii

UNIVERSIDAD NACIONAL DE COLOMBIA - SEDE MEDELLIN

ResumenFacultad de Minas



Analisis de la combustion in situ en una celda cinetica con acceso optico

mediante dinamica de fluidos computacional (CFD).

by Sebastian Lopez Gomez

Se construyo un modelo para el estudio del proceso de combustion in situ (CIS) en

montajes experimentales usando dinamica de fluidos computacional (CFD) en el pro-

grama comercial ANSYS FLUENT. El modelo que involucra los principales fenomenos

que intervienen en el proceso como las reacciones quımicas, el equilibrio de fases, el

flujo multifase en un medio poroso y correlaciones que tienen en cuenta la variacion

de diferentes propiedades fısico-quımicas con la temperatura, permite simular diferentes

montajes experimentales usados comunmente en el estudio de la CIS.

El modelo fue validado con diferentes pruebas experimentales reportadas en la liter-

atura.

El modelo validado se uso en primer lugar para estudiar las pruebas de oxidacion en

rampa de temperatura en una celda cinetica a traves del numero adimensional de

Damkohler, tradicionalmente utilizado como parametro para evaluar la homogeneidad

de los reactores. Con el estudio se determino valores para condiciones del proceso que

ayudan a aproximar el comportamiento en la celda cinetica a la de un reactor de mezcla

perfecta.

Finalmente, se uso el modelo para predecir el comportamiento de las diferentes fases du-

rante el proceso CIS en una celda prototipo que permite la medicion de especies gaseosas

por medio de tecnicas de diagnostico laser. Basado en la experiencia obtenida con el

analisis del numero de Damkohler en la homogeneidad de la celda, se seleccionaron las

condiciones de proceso para la celda optica de manera que el comportamiento fuera

homogeneo en el nucleo. Las simulaciones realizadas en este prototipo tenıan como ob-

jetivos principales determinar el efecto de los accesos opticos en la fluido-dinamica de

las diferentes fases involucradas en el proceso de CIS y predecir las diferentes especies

gaseosas que se podrıan medir.

Las simulaciones CFD sugirieron que la saturacion de aceite en el nucleo debe ser parcial

y de esta manera evitar interferencias en las mediciones de especies gaseosas con tecnicas

de diagnostico laser.


http://www.minas.medellin.unal.edu.co/index.php/es/


Acknowledgements

I want to thank my supervisor, Professor Alejandro Molina. His guidance helped me in

all the time of research and writing of this thesis. His tireless dedication to his students

make him a model to follow.

No words can express my gratitude to my family and friends for their constant and

unconditional support. Without them this thesis would not have been possible

Major financial support for this research was provided by the Colombian Administrative

Department of Science, Technology and Innovation (Departamento Administrativo de

Ciencia, Tecnologa e Innovacion Colciencias) under program “Jovenes investigadores e

innovadores 2011” and ECOPETROL under contract RC. No. 0264 − 2013 for partially

funding this work.

iii

Contents

Abstract i

Resumen i

Acknowledgements iii

List of Figures vii

List of Tables ix

Abbreviations x

Physical Constants xi

Symbols xii

Introduction xv

Research objetives xvii

1 State of the art 1

1.1 Enhanced oil recovery methods . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Thermal recovery methods . . . . . . . . . . . . . . . . . . . . . . 2

1.2 In-situ combustion (ISC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Operational modes of in situ combustion . . . . . . . . . . . . . . . 3

1.2.2 Models of the in situ combustion . . . . . . . . . . . . . . . . . . . 4

1.2.3 Considerations for the implementation of an ISC project . . . . . . 5

1.2.4 Laboratory studies of in situ combustion . . . . . . . . . . . . . . . 6

1.2.5 Simulations of the in situ combustion . . . . . . . . . . . . . . . . 7

1.3 Optical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Physical models and numerical simulation 9

2.1 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.1.1 General mass conservation equation . . . . . . . . . . . . 10

2.1.1.2 General energy conservation equation . . . . . . . . . . . 11

iv

Contents v

2.1.1.3 General volume conservation equation . . . . . . . . . . . 12

2.2 Chemical reaction mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Representation of phase equilibrium . . . . . . . . . . . . . . . . . . . . . 14

2.4 Auxiliary models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.1 Relative permeability . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.2 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5 Physical properties of the components . . . . . . . . . . . . . . . . . . . . 18

2.6 Models and assumitions used in ANSYS FLUENT . . . . . . . . . . . . . 19

2.6.1 ANSYS FLUENT models and UDFs . . . . . . . . . . . . . . . . . 20

2.6.1.1 Multiphase and species models . . . . . . . . . . . . . . . 20

2.6.1.2 Energy model . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6.1.3 Viscous model . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6.1.4 Properties of the flow and the porous medium . . . . . . 22

2.6.1.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 22

2.6.1.6 Physical properties . . . . . . . . . . . . . . . . . . . . . . 22

2.6.2 Solution methods used in ANSYS FLUENT . . . . . . . . . . . . . 22

3 Validation of the CFD model with experimental data 24

3.1 Low temperature oxidation (LTO) . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Pyrolysis and thermal cracking . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 High temperature oxidation (HTO) . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Numerical simulation of a kinetic cell 31

4.1 System dimension and initial settings . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Mesh size independency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.1 Comparison with the simulation by Belgrave et al. . . . . . . . . . 35

4.3.2 Validity of the supposition of complete mixing . . . . . . . . . . . 38

5 CFD simulation of a reactor with optical access 44

5.1 System dimension and initial settings . . . . . . . . . . . . . . . . . . . . . 44

5.2 Evaluation of the multiphase flow in the slits . . . . . . . . . . . . . . . . 46

5.2.1 Time dependent simulation of the core . . . . . . . . . . . . . . . . 46

5.2.2 Steady state simulations in the optical access wiht variable bound-ary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2.3 Time-dependent simulations in the region affected by the slits . . . 50

5.2.4 Partial saturation of the core . . . . . . . . . . . . . . . . . . . . . 51

5.2.5 Simulation of the reactor at 5 atm . . . . . . . . . . . . . . . . . . 55

6 Conclusion 57

7 Future work 58

A User defined functions (UDFs) 59

A.1 Reaction rate of maltenes oxidation (R1) . . . . . . . . . . . . . . . . . . . 59

Contents vi

A.2 Reaction rate of asphaltenes oxidation (R2) . . . . . . . . . . . . . . . . . 61

A.3 Reaction rate of maltenes pyrolysis (R3) . . . . . . . . . . . . . . . . . . . 63

A.4 Reaction rate of asphaltenes pyrolysis to produce coke(R4) . . . . . . . . 64

A.5 Reaction rate of asphaltenes pyrolysis to produce gases(R5) . . . . . . . . 66

A.6 Reaction rate of coke oxidation (R6) . . . . . . . . . . . . . . . . . . . . . 67

A.7 Evaporation of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.8 Condensation of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A.9 Evaporation of maltenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.10 Condensation of maltenes . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.11 Permeability of the gas phase . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.12 Permeability of the oil phase . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.13 Permeability of the water phase . . . . . . . . . . . . . . . . . . . . . . . . 80

A.14 Temperature ramped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.15 Viscosity of the maltenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.16 Viscosity of the asphaltenes . . . . . . . . . . . . . . . . . . . . . . . . . . 83

A.17 Mixing law for the viscosity of the oil phase . . . . . . . . . . . . . . . . . 83

A.18 Mixing law for the density of the oil phase . . . . . . . . . . . . . . . . . . 84

A.19 Pressure profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B 0-D model 86

B.1 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

B.2 Main code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

B.3 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

B.4 Inlet flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

B.5 Equilibrium water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B.6 Equilibrium maltenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B.7 Mechanism Belgrave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B.8 Properties of the pseudo-components . . . . . . . . . . . . . . . . . . . . . 93

C Simulation of the reactor at 5 atm and simulation of the airflow in aprototype for the study of the ISC 95

C.1 Simulation of the reactor at 5 atm . . . . . . . . . . . . . . . . . . . . . . 95

C.2 Simulation of the airflow in the prototype camera . . . . . . . . . . . . . . 96

Bibliography 99

List of Figures

1.1 a) Scheme of the forward ISC process. b) Regions formed in the processand relative temperature. Adapted from [1] . . . . . . . . . . . . . . . . . 4

3.1 Reactor simulated in the study of LTO rections. a) Mesh and boundaryconditions. b) Initial oil saturation. . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Comparison of the experimental data [2] and the prediction of the simu-lation of the LTO reactions (Line = CFD, Points = Experimental data).a) Pseudo-component in the oil phase. b) Coke . . . . . . . . . . . . . . . 25

3.3 Reactor simulated in the study of pyrolysis and thermal cracking rections.a) Mesh and boundary conditions. b) Initial oil saturation. . . . . . . . . 27

3.4 Comparison of the experimental data [3] and the prediction of the sim-ulation of the cracking reactions at 360 K. a) Pseudo-components in theoil phase. b) Coke and gas pseudo-components . . . . . . . . . . . . . . . 27

3.5 Comparison of the experimental data [3] and the prediction of the sim-ulation of the cracking reactions at 397 K. a) Pseudo-components in theoil phase. b) Coke and gas pseudo-components . . . . . . . . . . . . . . . 28

3.6 Packed reactor simulated in the study of HTO rections. a) Mesh andboundary conditions. b) Initial oil saturation. . . . . . . . . . . . . . . . . 28

3.7 Comparison of the experimental data [4] and the prediction of the simu-lation of the HTO reactions. a) O2. b) CO2. c) CO . . . . . . . . . . . . 29

4.1 Kinetic cell simulated. a) Mesh and boundary conditions. b) Initial oilsaturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Mesh size independency in the cell. a) Oxygen molar fraction. b) Cokevolumetric fraction. c) Reaction rate of asphaltene oxidation R2. d)Reaction rate of coke oxidation R6 . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Criteria used for the selection of the time step. a) Time step study. b)Distribution of the Courant number along the cell . . . . . . . . . . . . . 35

4.4 Comparison of the results of the CFD simulation with the results reportedby Belgrave et al. [5]. a)Molar fraction of asphaltenes and oil saturation.b)Coke concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.5 Contours of the CFD simulation for the times 7000 s (495 K), 15000 s(720 K) and 28000 s (1050 K). a)Coke volumtric fraction. b)Oxygen molarfraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 Distribution of different species and reaction rates along the cell. a) 7000s. b) 14000 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.7 Comparison of the CFD and the 0-D model results for different Damkohlernumbers, in the basis case. a) Oil saturation. b) Coke concentration . . . 39

4.8 Deviation of the CFD simulation with the 0-D, for different Damkohlernumbers, in the basis case. a) Oil saturation. b) Coke concentration . . . 40

vii

List of Figures viii

4.9 Comparison of the CFD and the 0-D model results for differentDamkohlernumbers, in the case 2. a) Oil saturation. b) Coke concentration . . . . . 41




5.1 Dimensions of the prototype cell with optical access . . . . . . . . . . . . 45

5.2 Prototypt cell simulated. a) Mesh. b) Distribution of the initial oil satu-ration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3 Velocity field of the oil in the core after 1 h. a) Velocity field in all thecore. b) Region where the velocity field is affected by the slits. . . . . . . 46

5.4 Velocity field of the oil in the region of the core affected by the slits . . . 47

5.5 Mesh used to simulated the behavior of the phases in the optical accessin steady stete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.6 Laser trajectories that could be used for the measurement of gaseousspecies. a) TDLAS. b) PLIF . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.7 a) Mesh used in the transient state simulation of the section affected bythe slits. b) Initial oil saturation . . . . . . . . . . . . . . . . . . . . . . . 51

5.8 Oil saturation in the slits after 10 minutes of operation at 500 K. a)Averageoil saturation. b) Maximum oil saturation . . . . . . . . . . . . . . . . . . 51

5.9 Initial oil saturation proposed to achieve the complete realization of aRTO test avoiding the oil flow in the slits. . . . . . . . . . . . . . . . . . . 52

5.10 Oil saturation in the prototype cell. a) 0.1 h. b) 2.1 h. . . . . . . . . . . . 53

5.11 Oil velocity in the prototype cell. a) 0.1 h. b) 2.1 h. . . . . . . . . . . . . 53

5.12 Coke volumetric fraction in the prototype cell. a) 0.1 h. b) 2.1 h. . . . . . 54

5.13 Vectors velocity of the gas phase in the region of the slits . . . . . . . . . 54

5.14 Vectors velocity in the prototype cell. a) 0.1 h. b) 2.1 h. . . . . . . . . . . 55

5.15 Prediction of the mole fraction of the species that can be measured in thecore at 41 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

C.1 Prediction of the mole fraction of the species that can be measured in thecore at 5 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

C.2 Chamber prototype geometry . . . . . . . . . . . . . . . . . . . . . . . . . 97

C.3 Mesh used in the simulation of the flow air in the chamber prototype . . . 97

C.4 Time of streamlines in the chamber. . . . . . . . . . . . . . . . . . . . . . 98

List of Tables

2.1 Kinetic parameters of the mechanism of Belgrave et al. [5] . . . . . . . . . 14

2.2 Reaction rate expressions of the Belgrave et al. [5] mechanism . . . . . . . 14

2.3 Equilibrium parameters used for the pseudo-components [5] . . . . . . . . 15

2.4 Relative permeability data reported by Belgrave et al.[5] . . . . . . . . . . 17

2.5 Viscosity parameters for the pseudo-component in the oil phase and forthe water phase [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Physico-chemical properties of the pseudo-components used in the model[6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.7 Heat capacity parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1 System properties of the kinetic cell simulated . . . . . . . . . . . . . . . . 32

4.2 Cases used in the analysis of homogeneity in the cell . . . . . . . . . . . . 40

5.1 Cases selected to study the behavior of the oil in the optical access . . . . 49

5.2 Oil volumetric fraction in the slits for different conditions at steady state 50

ix

Abbreviations

CIS Combustion In Situ

DSC Differential Scanning Calorimetry

EOR Enhenced Oil Recovery

HTO High Temperature Oxidation

ISC In Situ Combustion

LTO Low Temperature Oxidation

PLIF Planar Laser Induced Fluorescence

RTO Ramped Temperature Oxidation

TDLAS Tunable Diode Laser Absorption Spectroscopy

TGA Thermal Gravimetric Analysis

SARA Saturate Aromatic Resins Asphaltenes

x

Physical Constants

Gravity g = 9.81 m s−2

Gas constant R = 8.314 m3 Pa K−1 mol−1

xi

Symbols

a Superficial area m2 m−3

A Pre exponential

C Concentration mol m−3

E Activation energy J kmol−1

k Rate constant

D Diffusion m2 s−1

Da Damkohler number

Dp Particle diameter m

h Enthalpy J mol−1

ke Effective permeability Darcy

kr Relative permeability

K Partition constant

P Pressure Pa

S Saturation

Sh Sherwood number

T Temperature K

u Flow velocity m s−1

v Molar volume m3 mol−1

V Volume m3

x Mole fraction

κ Mass transfer coefficient m s−1

ρ Molar density kmol m−3

Ω Control volume

δ Solubility parameter

xii

Symbols xiii

µ Viscosity Pa s

τ Residence time s

φ Porosity

A mis padres y hermanos por el constante apoyo

xiv

Introduction

In situ combustion (ISC) is a heavy-oil thermal recovery technique which presents at-

tractive characteristics, but has not been widely implemented due to the complexity

and the lack of knowledge of the process. While some of the models found in the litera-

ture can properly correlate some experimental data, these models are quite general and

have little details mainly in the reaction mechanisms. The lack of detail in the kinetic

mechanisms is not surprising, when it is considered that experimental characterization

methodologies allow only a general description of the process. It is well known that

to achieve an accurate description of the kinetics of a process the use of non-intrusive

methods that do not affect the performance of the process, have been extensively used

in the study of process as the combustion. An experimental setup which allows mea-

surements of the ISC process “in situ” with non-intrusive techniques it is not reported

in the literature. An experimental setup with these features would be important in the

study of the ISC process, because it could be improved the knowledge of the reactions

that take place in this process.

Based on the above, the research problem points out absence of experimental systems

for the study of the ISC “in situ” and the need of new models to evaluate experimental

designs.

This study is part of a project that contemplates the construction of an experimental

equipment with the characteristics previously mentioned. The research is focused on the

simulation of prototypes that could be used for the study of the ISC process and that

allow the measurement of gas species using laser diagnostic techniques. Having clear the

objective of the research, the following sections show the aspects required to fulfill with

the objectives proposed.

In Chapter 1 a review of the state of the art in the techniques used for the recovery of

heavy oil is shown. We focus the discussion in the ISC process considering the models

proposed by different researchers, the experimental setups used in the study of the oil

reactivity and the advance of the combustion front and the simulations developed at

laboratory and field scales. Finally, we introduce an overview of the optical techniques

that can be implemented in the study of the gas species produced in the process.

Chapter 2 shows the models used to simulate the phenomena involved in the ISC pro-

cess. Models to simulate the chemical reactions, the phase equilibrium, the relative

permeability of the phases and the behavior of the properties with the temperature, are

listed. Additionally, the properties used for the pseudo-components selected are shown

in this chapter. Finally, the models selected and the convergence criteria used in AN-

SYS FLUENT are shown, with an emphasis on the submodels developed to adequately

represent the phenomena involved in the ISC process.

In chapter 3, we carry out a comparison of the results of the CFD simulations using the

kinetic mechanism selected in the research with experimental data. The experimental

data obtained in three different experimental setups were reproduced using in the sim-

ulations the same conditions reported by the researchers. The experiments simulated

were focused in the study of the reactions of oxidation at low temperature, the cracking

and pyrolysis and the oxidation at high temperature.

Chapter 4 shows the results of the simulation of a kinetic cell in which a ramped temper-

ature oxidation (RTO) test is carried out. The study include an evaluation of the mesh

size independency that was used in all the simulations that involve ANSYS FLUENT.

Once the mesh size and the time step were selected, it was carried out a simulation

of a kinetic cell that involves a complete network of models to simulate the different

phenomena presented in the ISC process. In this case a comparison with the results of

a simulation of Belgrave et al. [5] was made, making clear that some differences were

found in both simulations.

Finally, the model was used to evaluate the operational conditions necessary to guar-

antee that the cell behaves as a perfectly mixed reactor. The dimensionless Damkohler

number was used to quantify the extent of the mixing in the cell.

In Chapter 5 the models to simulate the different phenomena presented in the ISC pro-

cess were used in a kinetic cell that have slits in the middle that allow the interrogation

of gas species using laser diagnostic techniques. We focused the study first in the eval-

uation of the fluid-dynamic of the phases in the core, with emphasis in the effect of the

slits in the flow. Once the experimental conditions necessary to avoid the flow of oil

by the slits were defined, the study focused in predict the concentration of the species

that would be measured using laser diagnostic techniques in a RTO test at different

pressures.

Chapter 6 shows the conclusions and the future work proposed in this area of investiga-

tion.

Finally, Appendix A and Appendix B shown the codes written to simulate the phenom-

ena involved in the ISC process and Appendix C shows the simulation of the flow of air

in the prototype that it is want to construct in the research group.

Research objetives

Overall objetive

To evaluate the effect of the implementation of optical access in a kinetic cell for the

study of the in situ combustion process.

Specific objetives

To formulate the equations that describe the phenomena involved in the in situ combus-

tion process.

To construct CFD submodels that predict the behavior of ISC in lab-scale equipment.

To adapt the CFD submodels to an experimental design that allows non-intrusive mea-

surements of the in situ combustion process.

Chapter 1

State of the art

This chapter summarizes some relevant aspects of the In Situ Combustion (ISC) process,

focusing in the researches at lab-scale. A general description of the setups used in the

study of the phenomena involved in the ISC process and an overview of the models and

simulations developed for different researchers around the world, are included. Finally

a brief description of some optical techniques that could be implemented in the study

of ISC process, are incorporated in the chapter.

1.1 Enhanced oil recovery methods

Enhanced Oil Recovery (EOR) methods are technologies used with the aim to extract

the oil that can not be produced with conventional techniques. It is believed that EOR

technologies will play an important role in the coming years mainly because of the few

findings of reservoirs and the high reserves of heavy oils [7]. It is estimated that 60%

of the oil in place cannot be extracted by conventional techniques. The increase in the

oil price makes profitable the implementation of EOR techniques in these reservoirs [8].

This has motivated the study, in all the world, of non-conventional techniques of oil

production and the conditions necessary for a successfull implementation [9–11].

The EOR techniques can be grouped in three categories: Thermal Methods, Chemical

Methods and Fluid Flooding Methods [12].

The basis of the thermal methods is to increase the oil temperature with the aim to

reduce the oil viscosity. This decrease in the oil viscosity enhances the mobility of the

fluid in the porous media making easy the extraction.

In the chemical methods different agents are injected into the reservoir with the aim to

enhance characteristics of the porous media or to change the interaction of the fluids in

the reservoir with the aim to enhance displacement of the oil by another fluid.

1

Chapter 1. State of the art 2

Finally, the fluid flooding methods have as basis the injection of a fluid to displace the oil

in the reservoir [8]. The implementation of an EOR method depends on many economics

and operational factors [13, 14].

1.1.1 Thermal recovery methods

The thermal recovery methods relate to techniques in which a fluid is injected with

the aim to supply thermal energy to the reservoir [15]. The different thermal recovery

methods can be grouped in two categories: methods in which the heat is produced in

the surface and the methods in which the heat is produced in the formation. Although,

the methods in which the heat is produced in the surface present larger heat losses and

some environmental challenges [16], steam injection is the most common and imple-

mented method of thermal recovery [17].

The most common method in which the heat is produced in the formation is In Situ

Combustion (ISC) and despite it is an energy-efficient technique, its implementation is

limited mainly because of the complexity of the phenomena involved and the lack of

knowledge of it [18].

As stated before, the basis of the thermal recovery methods is to increase the oil tem-

perature to enhance the mobility of the oil in the porous media. This makes that some

data are required in the study of the thermal methods being the chemical changes and

the hydrodynamic properties the most important. The chemical and physical trans-

formations, the viscosity, the relative permeability, the thermal expansion, the thermal

capacity, the thermal conductivity and the heat of vaporization are some properties that

have a dependency with the temperature and are necessary in the study of the thermal

methods [15].

1.2 In-situ combustion (ISC)

The ISC or fireflood process is a thermal enhanced oil recovery technique with attractive

energetic and economic characteristics. ISC is a gas-injection, oil recovery method where

heat is used to improve the displacement of the oil. The heat used is generated by the

burning of a portion of the oil in place. The burning is sustained by a continuous

injection of air or oxygen-enriched air, that creates a mobile combustion front. The oil

is driven to the producer wells by a combination of the drive by combustion gases and

water [19].

In the process a small fraction of the oil in the reservoir, generally the heavy fractions

of the oil, are burned. This cause an upgrading of the oil where the lighter components


are extracted in a higher proportion [20, 21]. Additionally, the high temperatures in

the reservoir cause a cracking of molecules of high molecular weight, which produces

molecules with lower molecular weight causing an upgrading of the oil “in situ” [22].

Another attractive characteristic of the ISC process is the low cost of delivering thermal

energy in comparison with the other thermal recovery methods.

Despite the advantages of this technique in the recovery of oil, its implementation is

limited by some operational limitations of the process and the little knowledge of the

phenomena involved in the process [23].

1.2.1 Operational modes of in situ combustion

Based in the combustion front propagation in relation to the direction of the air injec-

tion the ISC process can be classified in forward combustion and reverse combustion.

In forward combustion the air flows in the direction of the combustion front, mean-

while in reverse combustion the air flows in the direction opposite to the combustion

front. Additionally, depending on the injecting fluids the process can be classified in

dry combustion and wet combustion. In dry combustion only air or oxygen-enriched air

is injected, meanwhile in wet combustion additionally water is injected to enhance the

heat transport in the formation [19].

Regardless of the operation mode, several regions are formed in the process that are

common to all the operational modes, which are shown schematically in Figure 1.1a) for

a dry forward combustion process, where the ignition step already occurred. The air is

supplied to the reservoir by a well injector, the oxygen in the air reacts with the coke

formed in the process in a exothermic reaction that generates the energy necessary to

increase the temperature in the formation. This region is known as the combustion zone

and presents the highest temperature of the formation and heats the nearby zones by a

conductive and advective transport of energy. Figure 1.1b) represents the temperature

profiles observed in the process [24].

The region upstream of the combustion zone is known as the burned zone. In this zone,

in which the combustion front previously moved, only air is present and the phenomena

involved in the zone are related to heat transport. Meanwhile, in the region downstream

of the combustion zone different phenomena take place. This zone is known as the

cracking and evaporation region. The high temperatures and the lack of oxygen in the

gases causes the evaporation of the lighter species of the oil, meanwhile the heavy species

of the oil crack and pyrolyze into lighter species and the organic residue known as coke.

The regions between the cracking zone and the producer wells, are zones of condensation

of water and lighter-oil species. Ahead of the condensation zone, temperature drops

gradually to initial reservoir temperature. Normally, a water and light oil bank can be


a) b)

Combustion front

Cracking zone

Condensation zone

Injection

Production well

Bur

ned

zone

Com

bust

ion

zone

Cra

ckin

g, e

vapo

ratio

n an

d vi

sbre

akin

g re

gion

Con

dens

atio

n

Wat

er b

ank

Oil

bank

Distance

Tem

pera

ture

Initi

al z

one

Figure 1.1: a) Scheme of the forward ISC process. b) Regions formed in the processand relative temperature. Adapted from [1]

identified downstream at the condensation zone. Finally the initial zone or the native

region is the zone where the only modification that has suffered the oil it is the flow of

gases produced in the combustion of the coke [21, 25].

The most important and complex aspects in the overall success of the ISC process are

coke formation and combustion. Coke formation determines the amount of fuel available

for combustion. If the quantity is too high, the advance of the combustion front is

retarded. On the other hand, when the amount of coke is insufficient the heat generated

is not enough and the process is not self-sustained. The combustion process determines

the velocity of the combustion front. If the velocity is too high, a larger portion of the

oil are burned, causing a decreasing in the oil recovery. [26].

This leads the necessity of understand the aspects and chemical reactions involved in

the coke formation and combustion.

1.2.2 Models of the in situ combustion

Most of the models developed for the ISC process have as heart the chemical reaction

mechanisms. This reason makes that many investigations only focus in the chemical

transformations of the oil under different conditions. It is widely believed that coke

formation is mainly by the reaction of cracked products and by the carbon residue de-

posited during the pyrolysis of hydrocarbons. Additionally, some researchers support

the idea that a significant amount of coke formation is caused by the flow of oxygen that

does not react with the coke in the combustion front and reacts with oil at lower tem-

peratures. This reactions known as low temperature oxidation (LTO) reactions produce

more viscous oxygenated hydrocarbons [27] that are believed precursors of asphaltenes

that react to produce coke [26, 28].


Coke combustion is a heterogeneous reaction where liquid, solid and gas phases are

involved. The series of transport phenomena involved in this case generates diverse

opinions in the researchers of which it is the controlling step [29], being the reaction

rate [30] and the diffusion of oxygen, the steps involved in the discussion. Although

this discussion has not been resolved, most mechanisms proposed give an overall rate of

reaction and do not specified which is the limitant step [31].

Based on this theoretical basis, many kinetic mechanisms have been proposed. The use

of pseudo-components to represent hydrocarbons with similar characteristics is common

in most models. Grouping according to the solubility in solvents with different polarity

is widely accepted in the study of ISC [32], but some researchers use the common method

in which the association of the pseudo-component is according to the boiling point [33].

Reaction mechanisms based grouping following solubility, such as the one by Belgrave et

al. [5], have been widely accepted and capture the most important crude transformations

produced in the ISC process. This acceptance caused that some researchers took as a

starting point this mechanism and include others reactions to improve the predictions

of some species [34–37].

Using the criteria of solubility in solvents to group the pseudo-components, other mech-

anisms have been proposed but, more pseudo-components have been employed to group

the hydrocarbons. A popular method to group the hydrocarbons, known as SARA (satu-

rates, aromatics, resins, asphaltenes), has been used in the last years for the construction

of kinetical mechanisms in the ISC process [38–41]

Finally, in another kind of models the reactivity of the oil is not the main phenomena

studied and the interest is centred in understanding the different waves generated in the

process [42–45].

1.2.3 Considerations for the implementation of an ISC project

Because the complexity and the amount of phenomena involved in the ISC process, the

implementation of a project in a reservoir needs a series of steps to diminish the posibil-

ities of failure. A brief description of some relevant aspects required when implementing

an ISC project is shown in this section.

The key of a successful ISC project includes various stages in which different actions

need to be taken [20].

The selection of a right reservoir is fundamental. Factors such as porosity, permeability,

mineralogy and catalityc effect of some clays in the reactivity of the oil are important

parameters in this step [46–50].


When the appropriate reservoir has been selected, it is important to design the right

process. In this step, the operational mode of the ISC is defined. Particulary, the nec-

essary air fluxes to operate in the right mode and avoid failures in the process are set

[51–53].

Other important stage is ignition. An appropriate ignition ensures a starts of the pro-

cess in the region of high temperature and a self-sustained operation. For the ignition

different methods can be implemented, being the burner, the electrical resistance and

the injection of hot fluids the most popular [19].

Finally one important stage is the adjustment to correct some problems. Monitoring

the oil production rate and the composition of the gas are measurements that help to

detect troubles in the operation of the process and that can help in the decisionmaking

process required to solve the trouble [54, 55].

1.2.4 Laboratory studies of in situ combustion

The evaluation of the stages mentioned in section 1.2.3 are normally made in lab-scale

equipment. The correct use and the adequate interpretation of the results in the differ-

ent equipment used in the ISC study, give the tools to design a successful project [56].

The equipment can be divided in two categories according to the aim to which they are

used.

On one hand, a series of lab-scale equipment has been used with the aim to determine the

reactivity of the oil in different conditions and to determine the self-sustained temper-

ature. These equipment, mostly of small size, have been important in the construction

of kinetic mechanisms.

On the other hand, different experimental setups have been designed with the aim to

study different operational conditions. These devices seek to emulate a reservoir with

the aim to evaluate parameters changing in space, fluids production and operational

factors.

In the first group, the tests commonly used by different researchers are thermal gravimet-

ric analysis (TGA), differential scanning calorimetry (DSC) [38] and ramped-temperature

oxidation (RTO) [25]. These tests are carried out using a small amount of oil, and in

some case, a combination of sand rock, water and oil.

In the second group the tests have been carried out in equipments such as combustion

tubes and experimental designs that allow the monitoring of parameters such as the

percentage of oil recovery, the velocity of the combustion front [57], heat losses [58] and

the air fluxes required to sustain the process [53].


These tests provide the data required to develop models that, incorporated in a simula-

tor, allow to predict the behavior of the process under different conditions [59, 60].

1.2.5 Simulations of the in situ combustion

The use of simulators in the design of an ISC project is fundamental and allow to draw

conclusion of the possibility to implement this technique in a reservoir or not. Different

simulators have been developed which allow to simulate from lab-scale equipments to

reservoirs. In this section a review of the different simulations developed in this topic is

shown.

The first type of simulations are those in which the interest is to reproduce the changes

produced in the oil by the chemical reactions. Normally these simulations considered a

0-D model and test such as TGA and RTO [60–62].

The second type of simulations are those in which a complete network of phenomena are

involved. The test evaluated at lab-scale are combustion tubes and experimental setups

in which monitoring in different zones is necessary [63–65].

Finally, the third type of simulations, aims to predict the performance of the ISC process

in reservoirs [66–69].

In the first two types of simulations, the main objective is to adjust parameters used

in the models employed in the simulator to represent the phenomena involved in the

ISC process. Meanwhile in the simulations of reservoirs, the models adjusted previously

are used to predict the behavior of the process in the field. Normally, it is necessary

to incorporate some strategies to scale the models used in a laboratory equipment to

a reservoir [18, 32, 70], where some researchers have given more attention to the space

discretization [71–73].

It is interesting to analyze the objectives of different simulations of the ISC process.

Most simulations have been focused in the chemical reaction scheme [5, 34, 74, 75].

Others researchers studied the success of the simulator in phenomenas such as multiphase

equilibrium [76], multiphase flow [14] and the interaction of thermal and reaction waves

[77].

1.3 Optical techniques

Optical diagnostic techniques have been used in many studies with the aim to improve

the measurements without intrusive tools. Although in the reviewed literature, i did

not find any research that use laser diagnostic techniques in the area of ISC, lasers have


been deployed in processes that have similarities with ISC. In the combustion analysis

various aspects such as flow field, flow velocity, droplet size, species concentration, soot

distribution and temperature have been studied. Each case demands a different laser

technique to get the desired results [78].

This thesis is part of a project that focuses in techniques in which the measurements of

species concentration is possible. In this area, techniques such as planar laser induced

fluorescence (PLIF) and tunable diode laser absorption spectroscopy (TDLAS) have

been applied in many researches. In PLIF, a laser sheet is used to excite atoms or

molecules that, once they reach a higher level of energy, spontaneously emit light [79].

PLIF is a well-established technique for detecting the population densities of molecular

or atomic species in specific quantum states. In combustion this technique has been

used to determine important quantities such as mole fraction, temperature and velocity

[79, 80]. In TDLAS, the absorption of the energy of a laser beam by a species is used to

determine its concentration [81]. This technique has been used in the study of species

such as CO, CO2 and H2O presented in the combustion processes [82].

Chapter 2

Physical models and numerical

simulation

This section present a description of the models used to simulate the ISC process. The

equations described for the conservation of material, energy, momentum and volume

are common at the most of models used in the ISC process, meanwhile, the equations

used to describe different phenomena as the chemical reactions, equilibrium of phases,

the resistance of the phases to flow and the correlations used for some properties of

species are particular of this study and were used in all the simulations developed in the

research.

Two types of equations are explained in this section. The first deals with the general

equations used in the ISC process to represent the conservation of mass, energy and

volume. Likewise, the equations used to model the different phenomena that take place

in the ISC process are discussed. These equations are general for the ISC process and

were taken from the literature review.

The second type of equations deals with those used by ANSYS FLUENT to represent

the conservation of mass, energy, volume and momentum. The objective in this case

is to illustrate the methods and models used to adjust the equations used by ANSYS

FLUENT to the ISC process.

2.1 Mathematical model

In the ISC process different phenomena are present, each having its own characteristic

scale. Knowledge of the phenomenon involved and its mathematical description, allows

the prediction of the performance of an ISC process in a reservoir. Most of the existing

models of the ISC process include transport of mass and heat by convection and diffusion,

9

Chapter 2. Physical models and numerical simulation 10

kinetically-controlled chemical reactions and the thermodynamic equilibrium of phases

[1, 43, 63, 83].

The following sections deal with the phenomena involved in the ISC process and their

mathematical representation.

2.1.1 Governing equations

While dealing with multiple phases, it is common practice in the petroleum literature to

distinguish between “general” and “phase” conservation equations. The first one deals

with a balance of the whole volume and does not distinguish phases, the second one

exlusively considers a specie in a specific phase.

The primary equations selected were the mass, energy and volume balances. Two choices

are common in the selection of the primary variables for the ISC process: natural vari-

ables and overall quantity variables. Natural variables are based on saturations and mole

fractions, whereas overall quantity variables are based on total component moles and

total energy/enthalpy. The most common selection by different researchers is to choose

the overall quantity variables as primary variables [1, 84] that include: Nc overall com-

ponent concentrations Ci, total energy U and pressure P [84]. The following equations

illustrate the general balances.

2.1.1.1 General mass conservation equation

Equation 2.1 represents the conservation of the i-th species as derived in [1, 6] for the

ISC process.

d

dt

∫ΩCidΩ +

∫S∇ · ~qmi ndS +

∫S∇ · ~qdi ndS =

∫ΩQm,rea

i dΩ (2.1)

where Ω represent the volume of the porous medium with boundary S and outward

pointing normal vector n, Ci is the overall molar concentration of species i, ~qmi is the

advective molar flux of species i, ~qdi is the diffusive molar flux of species i, and Qm,reai

is the rate of production of the species i by reaction. Equations 2.2, 2.3 and 2.4 express

the overall molar concentration, advective flux and diffusive molar flux for species i,

respectively.

Ci =

Np∑j=1

φρjSjxij (2.2)


~qmi =

Np∑j=1

ρjxij~uj (2.3)

~qdi =

Np∑j=1

Sjαj~uj∇ (xijρj) (2.4)

where xij is the mole fraction of component i in phase j, Sj the saturation of phase j,

ρj the molar density of phase j, φ is the porosity, ~uj is the Darcy velocity of phase j,

and αj is the dispersivity of phase j.

The expression for the rate of production by chemical reactions of species i, Qm,reai , is

explained in section 2.2 ”Chemical reaction model”.

2.1.1.2 General energy conservation equation

Equation 2.5 represent the conservation of energy.

d

dt

∫ΩUdΩ +

∫S∇ ·(~qh,adv + ~qh,cond

)dS =

∫Ω

(Qh,rea

i −Qh,loss)dΩ (2.5)

where U is the total internal energy of the system, ~qh,adv and ~qh,cond are the heat fluxes

by advection and conduction respectively and Qh,reai is the heat source due to chemical

reactions and Qh,loss is the heat loss to the surroundings. Equations 2.6, 2.7 and 2.8

express the total internal energy of the system, the advective heat transport of each of

the mobile phases and the Fourier‘s law to express the heat transport due to conduction,

respectively.

U = φ

Np∑j=1

UjρjSj + (1− φ)Ur (2.6)

~qh,adv =

Np∑j=1

hjρj~uj (2.7)

~qh,cond = −κe∇T (2.8)

where Uj is the specific internal energy of phase j and Ur is the volumetric internal

energy of the porous medium, hj is the molar enthalpy of phase j and κe is the effective


thermal conductivity of the saturated medium.

2.1.1.3 General volume conservation equation

Finally, the principle of volume conservation expresses that fluids and solid phases must

fill all the pore space.

Vp =

Np∑j=1

V j (2.9)

where Vp represents the pore space and V j is the volume occupied by each phase. This

equation leads to the pressure equation. Finally, the multi-phase extension of the Darcy’s

law gives (Eq: 2.10) the velocity of each phase.

~uj =kjeµj

(∇P − ρi~g∇D) (2.10)

where uj is the phase flow velocity, kje is the effective permeability of phase j, µj is the

viscosity of phase j, ρi is the mass density, g is the gravity and D is the depth of the

reservoir.

Equation 2.11 expresses the effective permeability in a multi-phase system [85].

kje = kabskrj (2.11)

where kabs is the total permeability of the medium and krj is the relative permeability,

which ranges from zero to one, and is normally provided by experimental tests.

2.2 Chemical reaction mechanism

Different mechanisms to represent the chemical reactions that take place in the ISC

process have been developed. The existing mechanisms are empirical and use the pseudo-

components concept to associate different petroleum compounds [5, 34, 41, 86, 87]. The

traditional approach to characterize the oil and select the pseudo-components is based on

distillation cuts or boiling points ranges. In the case of the ISC process this approach is

not the best choice and the selection of pseudo-components should capture the different

oxidation behaviours associated to different oil fractions [32].


Grouping hydrocarbons according to their polarity is one of the methods used to charac-

terize the oil. This usually results in the characterization of oil in terms of maltenes and

asphaltenes or the most popular method known as SARA fractions. In this grouping

the fractionation is based on the solubility of the oil components in various solvents.

Maltenes are normally defined as the oil soluble in pentane whereas asphaltenes are the

insoluble fraction in this solvent. Maltenes are separated into saturates, aromatics and

resins fractions in the SARA grouping.

From the kinetic mechanisms available in the literature to represent the chemical reac-

tions that happen in the ISC, it was selected the mechanism proposed by Belgrave et

al. [5]. One of the attractive features of this mechanism is the use of few reactions to

represent the reactivity of the oil under different conditions of temperature and partial

pressure of oxygen, achieving to capture adequately the changes that occur in the pro-

cess. The mechanism of Belgrave et al. [5] consider crude oil as a mixture of maltenes

and asphaltenes. The mechanism considers three reactions of pyrolysis, two reactions

of oxidation at low temperature (LTO) and one reaction of oxidation at high tempera-

ture (HTO). This mechanism listed in reactions R1 to R6 has been extensively used by

different researchers with acceptable results [6, 35, 64].

LTO: Maltenes+ 3.431O2 −→ 0.4726Asphaltenes R1

Asphaltenes+ 7.513O2 −→ 101.539Coke R2

Pyrolisys: Maltenes −→ 0.372Asphaltenes R3

Asphaltenes −→ 83.223Coke R4

Asphaltenes −→ 37.683Gas R5

HTO: Coke+ 1.232O2 −→ COx + 0.565H2O R6

The kinetic parameters reported in the research of Belgrave et al. [5] are listed in Table

2.1, in which the activation energy and entalphy of reaction are reported in J/mol, and

the pre-exponential has different units. Table 2.2 listed the reaction rate expressions

involved in the process.

where the rate constants are Arrhenius-type, as expressed in equation 2.12.

ki = Aiexp

(−Ei

RT

)(2.12)


Table 2.1: Kinetic parameters of the mechanism of Belgrave et al. [5]

Reaction Pre-exponencial (Ai) Activation energy (Ei) Enthalpy

Value Units (J/mol) J/mol

R1 6.819 × 10+3 sec−1Pa−0.4246 86730 1300000

R2 2.133 × 10−10 sec−1Pa−4.7627 185600 2860000

R3 9.092 × 10+12 sec−1 234700 0

R4 4.064 × 10+9 sec−1 177200 0

R5 1.362 × 10+9 sec−1 176300 0

R6 6.2 × 10−8 sec−1Pa 34763 428000

Table 2.2: Reaction rate expressions of the Belgrave et al. [5] mechanism

Reaction Reaction rate

R1 k1φρoSoxmalP0.4246O2

R2 k2φρoSoxaspP4.7627O2

R3 k3φρoSoxmal

R4 k4φρoSoxasp

R5 k5φρoSoxasp

R6 k6φCsPO2

2.3 Representation of phase equilibrium

In the ISC process three phases are involved and some species are present in more than

one phase. For that reason it is necessary to consider how to represent the partition of

the species in each different phase. An approach frequently used is to consider that the

process is in thermodynamic equilibrium. In the ISC process two different equilibriums

exist. Liquid-gas equilibrium of light hydrocarbons and water in the reservoir, and the

solid-liquid equilibrium mainly due to asphaltene precipitation [88, 89]. In this study

only the liquid-gas equilibrium was considered. Although, the solid equilibrium is take

into account implicit in the reaction rates. The K-values frecuently are used to represent

the partition of the species in equilibrium. Belgrave et al. [5] reported expression 2.13

to represent the K-values of the compounds present in the liquid and gaseous phases [5].

Ki =0.133Fi

(exp

(Gi

T+Hi

))P

(2.13)


where T and P are the temperature and the pressure, respectively, and F, G and H are

parameters for the compounds that are present in the two phases which are listed in

Table 2.3.

Table 2.3: Equilibrium parameters used for the pseudo-components [5]

Constant Water Maltenes Asphaltenes

Fi 8.89513 × 107 1.4196 × 108 0

Gi 3.81644 × 103 6.5623 × 103 0

Hi -4.613 × 101 -1.9302 × 102 0

To simulate the phase equilibrium condition the model considers evaporation and con-

densation through mass transfer processes. The idea behind this approach is that this

two processes compete until equilibrium is reached.

The rate of mass transfer for both phenomena was represented by equation 2.14, which

is a relation adapted from adsorption in a chromatography column [90].

∂C

∂t= κcac(C − Ceq) (2.14)

where κc is the mass transfer coefficient, ac is the superficial area and (C−Ceq) represents

the difference between the concentration of a species in one phase and the equilibrium

concentration of the species in the same phase under the conditions of temperature and

pressure of the system. Using the concept of the constant of partition for a system at

equilibrium the ratio of the equation 2.15, involves the concentration of a species in the

phases i and j.

Ceqj = K Ceq

i (2.15)

Using this concept in the equation 2.14 the relation of the equation 2.16 is obtained,

which is the mass transfer of a non-equilibrium system.

∂Cj

∂t= κcac(Ci −

Cj

K) (2.16)

The equation 2.17 was used to calculate the mass transfer coefficient [90].

κc =ShDAB

Dp(2.17)


where the Sherwood number has a value of 2, the diffusivity of water in air is 2.5× 10−6

m2/s at 300 K, the diffusivity of maltenes in air was assumed as the diffusivity of benzene

in air with a value of 1× 10−7 m2/s [91].

Because the equation 2.17 need a diameter of particle, the equation 2.18 was used to

determine a value through properties of the porous media known.

Dp =

√150(1− φ)2k

φ3(2.18)

where φ is the porosity and k is the permeability.

Finally, the equation 2.19 it is the correlation of Blake-Kozeny [92] used to calcule of

specific area.

ac =

√6φ

25 k(2.19)

2.4 Auxiliary models

To achieve a successful simulation of the ISC process, different models to represent

the behavior of the different phases in the porous media and the correlations for the

properties dependent of the temperature are needed. In this section these models are

described.

2.4.1 Relative permeability

Simultaneous flow of oil, water and gas is an important phenomenon that takes place in

the ISC process. Ahead of the reaction front, flue gas displaces oil and water at nearly

reservoir temperature, while in the high temperature zone, oil and water evaporate to

later condense. In both situations three-phase flow takes place [93]. Relative perme-

ability is a quantity that describes the amount of impairment to flow of one phase on

another [85]. The relative permeability of water, oil and gas phases are, respectively,

denoted by krw, kro and krg.

The evaluation of relative permeabilities for three-phase flow is rather difficult and nor-

mally is carried out experimentally. These measurements have indicated that relative

permeabilities for wetting and nonwetting phases in a three phase system are function

of their respective saturations as they are in a two phase system [94], while the interme-

diate wetting phase is function of the three phases.


Stone‘s II model [95] is frequently used to describe the three-phase relative permeabili-

ties. This model, formulated for a system in which water is the wetting phase, can be

used for an oil-wet system by considering that water acts as intermediate wetting phase.

The relative permeabilities of the wetting and nonwetting phases (krw, krg), the relative

permeability to oil in the oil-water system (krow) and the relative permeability to oil

in the oil-gas system (krog) are obtained experimentally. The relative permeability of

intermediate wetting phase was determined according to 2.20 [95].

kro = (krow + krw)(krog + krg)− (krw + krg) (2.20)

The relative permeabilities data provided by Belgrave et al. [5], are reported in Table 2.4.

This table presents the water-oil relative permability and liquid-gas relative permeability.

Using these data and the Stone‘s II model, the relative permeabilities of the three phases

in the system were calculated.

Table 2.4: Relative permeability data reported by Belgrave et al.[5]

Water-oil relative permeability Gases-oil relative permeability

Sw krw krow So krg krog

0.05 0 1 0.07 0.1 0

0.1 0.00039 0.88581 0.16 0.08615 0.00316

0.15 0.00156 0.77855 0.21 0.06632 0.01262

0.25 0.00625 0.58478 0.31 0.03711 0.0505

0.35 0.01406 0.41869 0.41 0.01881 0.11362

0.45 0.025 0.28028 0.51 0.00829 0.20199

0.65 0.03906 0.08651 0.61 0.00296 0.31562

0.75 0.05625 0.03114 0.71 0.00073 0.45449

0.85 0.07656 0.00346 0.80 0.00011 0.6

0.95 0.1 0 0.95 0 0.8908

1 0.12656 0 1 0 1

2.4.2 Viscosity

The viscosity describes a fluid innate resistance to flow. Equation 2.21 is the temperature

dependency correlation proposed by Belgrave et al. [5] for component i in the oil and


water phases. Because, as discuseed below, this thesis reproduced results from Belgrave

et al. [5], this correlation was used in the following simulations.

µi = Aexp

(B

T

)(2.21)

The correlation considers a dependency with temperature (T) and two parameters (A

and B) listed in Table 2.5, determinated experimentally for every component.

Table 2.5: Viscosity parameters for the pseudo-component in the oil phase and forthe water phase [5]

Compound A (cp) B (oC)

Asphaltene 4.89 × 10−25 33147

Maltene 1.936 × 10−05 5369.2

Water 0.00752 1384.86

Equation 2.22 shows the linear logarithmic mixing rule used.

ln(µoil) =Nc∑i

xiln(µi) (2.22)

2.5 Physical properties of the components

Because in the model different pseudo-components were used to represent the oil, gas

mixture and solid organic compound, it is necessary to determine the physical properties

of these compounds. Table 2.6 shows the properties of the compounds used in the

simulations.

The heat capacity of the pseudo-components was determined by the equation 2.23, where

the units are calmol−1K−1.

Cp = Cpa + CpbT + CpcT2 + CpdT

3 (2.23)

Table 2.7 shows the parameters of the heat capacity for the pseudo-components.

The thermal conductivity of the oil, water and gas phases were choosen as 0.155Wm−1K−1,

0.673 Wm−1K−1 y 0.050 Wm−1K−1, respectively.


Table 2.6: Physico-chemical properties of the pseudo-components used in the model[6].

Compound Critical Critical Molecular Mass DensityPressure Temperature weigth

kPa K kg/kmol (kg/m3)

H2O 22107 647 18 1000

Asphaltenes 792 1177 1092.8 1158

Maltene 1478 892 406.7 983.2

Gas 7376 304.2 43 IG

O2 5046 154.6 32 IG

N2 3394 126.2 28 IG

Coke 13.13 1280

Table 2.7: Heat capacity parameters

Compuesto Cpa Cpb Cpc Cpd

Asphaltenes 601 0 0 0

Maltenes 237.6 0 0 0

Gases 4.728 1.754 × 10−2 -1.338 × 10−5 4.097 × 10−9

Coke 0.795 1.287 × 10−2 -1.042 × 10−5 3.503 × 10−9

2.6 Models and assumitions used in ANSYS FLUENT

ANSYS FLUENT is a specialized computer software for modeling fluid flow, heat trans-

fer and chemical reactions in complex geometries. ANSYS FLUENT allows modeling in

two or three dimensions, using structured or unstructured meshes and in a single or in

multiple phases. In ANSYS FLUENT it is possible to include User Defined Functions

(UDFs) to enhance the model’s capabilities. An UDF is a function that it is programmed

by the user and that can be dynamically loaded within the ANSYS FLUENT solver to

enhance the features of the code [96].

While ANSYS FLUENT has various internal sub-models that are available to every

user (e.g. turbulence, multiphase, etc.), the UDFs are particularly designed for the ISC

application and are, therefore, unique of this thesis. The remainder of this section deals

with the selection of the ANSYS FLUENT models and describes the UDFs developed to


simulate the ISC process. It finally explains the strategies followed to solve the problem

in ANSYS FLUENT.

2.6.1 ANSYS FLUENT models and UDFs

2.6.1.1 Multiphase and species models

The Eulerian - Eulerian multiphase model was selected to represent the phases involved

in the ISC process. Four phases were considered in the simulation: coke (treated as a

solid phase), gas, oil and water.

Additionally, the species model was activated in the simulation to represent the multiple

species present in each phase. When these models are used in ANSYS FLUENT the

equations of mass balance that the simulator solves are expressed by equation 2.24.

∂

∂t(ρjSjxij)+∇·(ρjSj~ujxij)+∇·Sj ~Jij = SjRij+SjSourceij+

n∑q=1

(miqj−mi

jq)+R (2.24)

where ~Jij is the diffusion of the species i in the phase j, Rij is the net rate of production

of homogeneous species i by chemical reaction for phase j, miqj is the mass transfer of

species i from phase q to phase j, R is the heterogeneous reaction rate and Sourceij is

the rate of creation by addition from the dispersed phase plus any user-defined sources.

Unlike the models proposed in the literature of ISC process, ANSYS FLUENT choose

the natural variables as primary variables and the ”phase” equations are solved. The

interaction between phases was carried out through heterogeneous reactions. The UDFs

Reac LTO Mal , Reac LTO Asp, Reac Pyr Asp Coke , Reac Pyr Asp Gas and

Reac HTO Coke were used to simulated the reaction rate of the reactions of oxidation

of maltenes (R1), oxidation of asphaltenes (R2), pyrolysis of asphaltenes to produce coke

(R4), pyrolysis of asphaltenes to produce gases (R5)and oxidation of coke (R6), respec-

tively. The pyrolysis of maltenes (R3) was not considered in the interaction of phases

because this is a homogeneous reaction. The UDF Reac Pyr Mal represents the reac-

tion of pyrolysis of maltenes to produce asphaltenes (R3).

Additionally the UDFs Evaporation Water , Condensation Water , Evaporation Maltenes

and Condensation Maltenes were used to simulated the evaporation and condensa-

tion of water and the evaporation and condensation of maltenes, respectively.

Appendix A shows the codes used for all UDFs described in this section.

ANSYS FLUENT solves nc−1 equations in each phase and in this way the composition


of every phase is defined. To define the saturation of each phase, ANSYS solves the

total mass balance 2.25 for every secondary phase.

∂

∂t(ρjSj) +∇ · (ρjSj~uj) =

n∑q=1

(mqj − mjq + Sq) (2.25)

where all the terms were previously defined.

2.6.1.2 Energy model

To describe the conservation of energy in Eulerian multiphase applications, a separate

enthalpy equation can be written for each phase, the equation 2.26 shows the energy

balance.

∂

∂t(ρjSjhj)+∇·(ρjSj~ujhj)+∇·~qj = Sourcej +

n∑q=1

(Qqj +mqjhqj−mjqhjq)+R (2.26)

where Qqj is the intensity of heat exchange between the j and q phases.

2.6.1.3 Viscous model

The laminar viscous model was selected to simulate the fluid flow because the mobile

phases flow in a porous media and the turbulence can be neglected. ANSYS FLUENT

solves the momentum balance for every phase and the pressure drop by the porous media

is through a source term. Equation 2.27 describes the momentum balance for the phase

j.

∂

∂t(Sjρj~uj) +∇ · (Sjρj~uj~uj) = Sj∇P +∇τj + Sjρj~g + Sourcej (2.27)

where Sj is the volumetric fraction of phase j, ~uj is the velocity of phase j, ∇P is the

pressure drop, τj is the phase stress-strain tensor and Sourcej In laminar flows through

porous media, the source term is higher in comparison with the others terms, reducing

the momentum balance to the Darcy law which is expressed in equation 2.28.

∇P =µj

kjeuj (2.28)


2.6.1.4 Properties of the flow and the porous medium

The porosity of the medium, the properties of the porous media and the resistance to flow

of the phases in the porous media were defined in the UDFs Effective Permeability Gas,

Effective Permeability Oil and Effective Permeability Water . All these proper-

ties were considered function of their saturation according to the tables reported by

Belgrave et al. [5] and the Stone‘s II model [95].

2.6.1.5 Boundary conditions

Because in this thesis different simulations were developed, the boundary conditions used

are specified below for each simulation. In general the boundary conditions used were

a mass flow-inlet, a pressure-outlet, a wall condition and an axisymmetric condition.

The UDF Temperature Profile was used to specified the temperature profile used to

simulate the ramped temperature in a RTO test.

2.6.1.6 Physical properties

As described in Section 2.4, some properties were a function of temperature. In these

cases, the UDFs Viscosity Maltenes, Viscosity Asphaltenes and Mixing law oil

were used to simulate the viscosity dependence of the maltenes and asphaltenes (2.21)

with the temperature and the viscosity mixing rule (2.22) used in the oil phase.

2.6.2 Solution methods used in ANSYS FLUENT

In multiphase problems ANSYS FLUENT offers three options to solve the coupled sys-

tems of equations: The Phase coupled SIMPLE, the multiphase coupled and the Full

multiphase coupled method. The phase coupled SIMPLE method was used for the

time-dependent simulations and the Full multiphase coupled method was used for the

steady state simulations. The last method is most robust and demands more CPU time,

but it was necessary in these simulations, because the multiphase simulations in steady

state are difficult to solve and presents instabilities in the convergence. The discretiza-

tion scheme for the volume fraction was explicit for the time-dependent simulations and

implicit for the steady state simulations.

The spatial discretization schemes used were first order upwind for density, volumen frac-

tion, energy and species and second order upwind for momentum, these schemes were

required at the start of the simulation, when the changes in the system were stronger.


Once the simulation advanced over time, the spatial discretization schemes could be

changed without this representing a change in the results of the simulation and a chal-

lenge to convergence.

The under-relaxation factors used by default for the software were chosen in the simu-

lations which for the pressure was 0.3, 0.7 for momentum and 1 for the other equations

and variables. The convergence absolute criteria used were residual values lower than

1× 10−12.

Chapter 3

Validation of the CFD model

with experimental data

Implementation of experiments to validate the CFD model described above is beyond

the objective of this research. As validation is always required in CFD simulations,

the experiments that lead to the well-known Belgrave mechanism [5] were simulated.

All these experiments, by different researchers from Belgrave’s group, for the same oil

(Athabasca bitumen), were carried out in lab-scale equipment. In this chapter the

simulations of these lab-scale experiments and the comparison with the experimental

data are shown with the aim to validate the submodels used in ANSYS FLUENT and,

in general, the results of the CFD simulations.

3.1 Low temperature oxidation (LTO)

The data generated in the research by Adegbesan et al. [2] were used to evaluate the

performance of the CFD simulation in the LTO regime. Adegbesan et al. [2] studied

the reactivity of Athabasca bitumen free of water and minerals in a laboratory-stirred

semiflow batch reactor (internal diameter of 3.49 cm [1.4 in.] and a length of 19.0 cm

[7.5 in.]). They studied the kinetics of the oil at conditions of temperature and partial

pressure of oxygen, in the ranges of 333 to 423 K and 50 to 2233 kPa, respectively. We

used the data recorded at 408 K and 4400 kPa and a molar fraction of oxygen of 0.20

to compare with the CFD simulation.

A two-dimensional structurated mesh of 400 nodes and a time step of 0.1 s were used in

the simulation. The criteria used to select the mesh size and the time step are discussed

in Chapter 4. The reference frames model was used to simulate stirring in the reactor,

a velocity of 3000 rpm was used according to Adegbesan et al. [2].

24

Chapter 3. Validation of the CFD model with experimental data 25

Velocity inlet.0.125 m/s

Pressure outlet.4400 kPa

WallT = 408 K

Oil zone.0.06 kg of bitumen

Reference frame3000 rpm

a) b)1.00

0.80

0.60

0.40

0.20

0.00

Oil volumetric fraction

Figure 3.1: Reactor simulated in the study of LTO rections. a) Mesh and boundaryconditions. b) Initial oil saturation.

a) b)

Figure 3.2: Comparison of the experimental data [2] and the prediction of the sim-ulation of the LTO reactions (Line = CFD, Points = Experimental data). a) Pseudo-

component in the oil phase. b) Coke

Figure 3.1a) shows the mesh and the boundary conditions used in the CFD simulation

and Figure 3.1b) shows the initial oil saturation in the reactor. All the conditions were

taken exactly the same as those used in the research of Adegbesan et al. [2].

Figure 3.2a) shows the result of the CFD simulation and the experimental data for

the pseudo-components in the oil phase. It was observed that the submodel repro-

duced the changes in the mass percentage of asphaltenes and maltenes over time. The

mass percentage of maltenes decrease because of the reaction of oxygenation that pro-

duces components with higher molecular weight, until it grows up to form an asphaltene

molecule. Once the asphaltene concentration is high, asphaltenes react with oxygen and

after a serie of transformations, portion of the asphaltenes produces coke.

Figure 3.2b) compares the result of the CFD simulation and the experimental data

for the coke mass percentage. Unlike the prediction of the oil components, for coke


the model reproduces the tendency, but the predicted amount of coke is less than the

experimental data. The differences in this case can be attributed to many reasons:

- The kinetical parameters used in the reaction to simulate the oxidation of asphaltenes

it is not accurately in all the range of temperature: Because the oil is a mixture of

many compounds and these compounds react in different ranges of temperature and

taking into account that the mechanism used only consider one reaction to represent the

oxidation of the compounds with high molecular weight, it is possible that the kinetic

constants used in the mechanism are the most suitable considering all the ranges of

temperature, but inherently present some differences in each temperature.

- Oxidation of the coke produced: Because in the simulation the coke produced are near

to the injection point, it is possible that coke produced was consumed by the oxygen.

- The kinetic mechanism proposed for the production of coke is very simple and it is

necessary the use of another step as the proposed by Sequera et al. [62], to enhance the

prediction of the coke production by oxidation reactions.

3.2 Pyrolysis and thermal cracking

The research of Hayashitani et al. [3] was used to evaluate the submodels of thermal

cracking reactions. In this research, Athabasca bitumen in a quartz glass tube (Internal

diameter 8 mm and a length of 11.8 cm), was thermally cracked at constant temperature

in a closed system under an inert atmosphere. The gas and oil products were monitored

at different times. Three series of experiments were carried out at different temperatures,

the data reported at 360 C and 397, C were compared with the CFD predictions.

A two-dimensional structured mesh of 120 nodes and a time step of 0.5 s were used in

these cases. Figure 3.3a) shows the mesh and the boundary conditions used in the CFD

simulations and Figure 3.3b) shows the initial oil saturation used in the simulations.

Figure 3.4 and Figure 3.5 show the results of the CFD simulations and the experimental

data for 360 C and 397 C, respectively. It was observed that in both cases (Figure

3.4a) and Figure 3.5b))the mass percentage of the pseudo-components in the oil phase

were captured adequately in the CFD simulation. On the other hand, the prediction

of the gas and coke mass percentage in the CFD simulation present some differences

with the experimental data. In Figure 3.4b) the predictions for coke and gas are higher

than the experimental results. However, the tendency was adequately reproduced. The

comparison, in Figure 3.5b) shows better agreement between experimental data and

simulation. In conclusion, the CFD simulation of the pyrolysis reactions represent ad-

equately the behavior of the pseudo-components involved in the experiment, but it is


Wall

Oil and porous zone

Wall

a) b)

0.00

0.16

0.32

0.48

0.64

0.80

Oil volumetric fraction

Figure 3.3: Reactor simulated in the study of pyrolysis and thermal cracking rections.a) Mesh and boundary conditions. b) Initial oil saturation.

Coke- - Gas

Figure 3.4: Comparison of the experimental data [3] and the prediction of the sim-ulation of the cracking reactions at 360 K. a) Pseudo-components in the oil phase. b)

Coke and gas pseudo-components

clear that some differences were present that could be attributed to inaccuracies in the

kinetic mechanism.

3.3 High temperature oxidation (HTO)

The experimental design developed by Thomas et al. [4] was simulated to validate the

high temperature oxidation submodel used in ANSYS FLUENT. The experimental setup

used by these researchers it was a reactor with a diameter of 2.13 cm and 14.7 cm long.

The experiments were conduced packing the reactor with silica, where only a fraction

of the reactor was saturated with oil that was cracked to produce coke. Once the coke


Figure 3.5: Comparison of the experimental data [3] and the prediction of the sim-ulation of the cracking reactions at 397 K. a) Pseudo-components in the oil phase. b)

Coke and gas pseudo-components

Inlet 1200 cm / h

Pressure outlet4.14 MPa

Wall

Coke zone

Porous zone

3

a) b)

0.0580

0.0464

0.0348

0.0232

0.0116

0.0000

Coke volumetric fraction

Inlet

1200 std‐m3/h

Figure 3.6: Packed reactor simulated in the study of HTO rections. a) Mesh andboundary conditions. b) Initial oil saturation.

was produced and quantified, this coke was combusted by the injection of oxygen at the

reactor. The data recorded at 351 oC and 4.14 MPa and a molar fraction of oxygen

of 0.202 were selected to validate the CFD submodel. A two-dimensional structurated

mesh of 200 nodes and a time step of 0.1 s were used in the simulation. Figure 3.6a)

shows the mesh used in the CFD simulation and the boundary conditions and Figure

3.6b) shows the initial coke volumetric fraction used in the simulation.

The researchers in this case, did not quantify the amount of coke formed at different

times. The only measurement was the monitoring of the gas species concentration. The

percentage of oxygen, carbon dioxide and carbon monoxide were monitored and reported

for different times.

Figure 3.7 shows the comparison of the prediction of the CFD simulation with the

experimental data. It was observed in the oxygen mass percentage an increase with


a)

b)

c)

Figure 3.7: Comparison of the experimental data [4] and the prediction of the simu-lation of the HTO reactions. a) O2. b) CO2. c) CO

.

time advance. On the other hand, carbon dioxide and carbon monoxide had a similar

behavior. The production of both species increased at first, but quickly decreased when

coke was consumed.

Comparing the experimental data and the CFD simulation it was observed that the

tendency was reproduced in the simulation, but the maximum values were reached at

different times. Furthemore some differences in the absolute values at each time were

observed.


3.4 Final remarks

Validation of an ISC model with experimental data available in the literature is a very

difficult task. Particularly given the difficulties of represent the oil in few pseudo-

components such as the reaction mechanism of Belgrave et al. [5] was developed. How-

ever, the simulation in this chapter shows that the CFD code reproduces the behavior of

the main species during ISC, although some differences in the predictions of the absolute

values are evident.

Chapter 4

Numerical simulation of a kinetic

cell

Once determined that the CFD model was able to capture the general trends in ISC,

the kinetic cell reported by Belgrave et al. [5] was simulated. These authors used a

complete reaction network for ISC including pyrolysis, HTO and LTO reactions. In ad-

dition, in this research the authors reported models to represent the species equilibrium,

correlation for some properties of the compounds with the temperature and curves of

relative permeability to represent the multiphase flow in a porous media. It is important

to point out that, while in section 3 the comparison was against experimental data, in

this section the comparison is against predictions by a simulation developed by Belgrave

et al. [5], given this conditions one would expected better agreement between the CFD

simulation and the literature data than that obtained in the previous section.

4.1 System dimension and initial settings

The kinetic cell was simulated with the commercial software ANSYS FLUENT 13.0, via

a two-dimensional (axisymmetric) discretization of the domain. In the CFD simulation

four phases were considered: coke (treated as a solid phase), gas, oil and water, in a

multicomponent system based on an Eulerian - Eulerian approach and include 672 cells

in a structured mesh. In the unsteady state simulation a ∆t of 0.5 s was selected to

complete a normal 9-h simulation of the ISC process. The selection of the mesh size and

the time step is justified later. All properties and conditions required for the simulation

are summarized in Table 4.1.

31

Chapter 4. Numerical simulation of a kinetic cell 32

Table 4.1: System properties of the kinetic cell simulated

Variable Value Units

Length 0.25 m

Diameter 0.0508 m

Porosity 0.412

Initial water saturation 0.05

Initial oil saturation 0.25

Initial gas saturation 0.7

Pressure 4100 kPa

Initial mole frac. Maltene 0.9151

Initial mole frac. Asphaltene 0.0849

Permeability 12000 mD

Figure 4.1a) shows the mesh and the boundary conditions used and Figure 4.1b) shows

the initial oil saturation in the cell. As seen in the figure, the cell was divided into

five regions in which different conditions were specified. Zone 1 was used to simulate

the porous medium used to obtain a good distribution of the injected air into the cell.

This region is free of oil and water and it was used to guarantee that air reaches the set

temperature before reacting with the oil and coke. Zones 2, 3 and 4 were saturated with

oil and water. The division of the cell in these regions is justified because Belgrave et al.

[5] performed a discretization of the cell into three regions, and only reported the results

for each node separately. In order to compare the CFD results with those of Belgrave

et al. [5], these divisions were made. Finally zone 5 was a region free of oil and water.

This zone was used in the simulation to prevent that the oil leaves the cell and to ensure

that all the oil is completely consumed.

4.1.1 Boundary conditions

The following boundary conditions were used in the CFD simulation of the kinetic cell :

Inlet boundary condition: Air was injected (21% O2) at a rate of 0.081 std m3/hr

(1 atm, 298 K), the temperature of the injected fluid was kept constant at 300 K.

Wall boundary conditions: The model was programmed to raise the temperature of

the wall of the kinetic cell at 100 C/hr.

Outlet boundary conditions: The pressure was kept constant at 4100 kPa in the

outlet.


Figure 4.1: Kinetic cell simulated. a) Mesh and boundary conditions. b) Initial oilsaturation.

Axis boundary conditions: The symmetry of the kinetic cell was used to reduce the

nodes number. The use of axisymmetric boundary condition allows to represent the

kinetic cell in a 2D mesh.

4.2 Mesh size independency

In the CFD simulation a discretization of the space was necessary. To determine the

amount of partitions in the space, a study of mesh size independency was made using

the geometry of the kinetic cell. Because the process is inherently time dependent, the

mesh independency was evaluated in a intermediate condition, in which it was possible

to determine the effect of the mesh size in the more important variables. It is well know

that coke combustion is the main source of energy in ISC and this reaction takes place

in a narrow zone. This motivated the evaluation of mesh independence in a intermediate

condition, in which coke was presented in the kinetic cell and the temperature was enough

to burn it. Mesh independency was evaluated when the simulation was running for 5

minutes using as initial conditions a constant temperature of 500 K, an oil saturation of

0.25, a coke volumetric fraction of 0.05, an air injection (21% O2) of 0.081 std m3/hr,

pressure at the outlet of 4100 kPa and the others properties were the same as those in

Table 4.1. A time step of 0.1 s was selected to ensure global courant numbers lower than

0.01. According at the literature reviewed, the variables selected for the study of mesh

size independence were variables having major changes in space. The variables studied

were the volumetric fraction of coke, the molar fraction of oxygen and the reaction rates

of asphaltene and coke oxidation. Because the simple geometry of this case, structured

meshes with 100, 556, 672, 2000 and 4000 nodes were evaluated.


a) b)

c) d)

Figure 4.2: Mesh size independency in the cell. a) Oxygen molar fraction. b) Cokevolumetric fraction. c) Reaction rate of asphaltene oxidation R2. d) Reaction rate of

coke oxidation R6

In Figure 4.2 the four variables were plotted for the different meshes evaluated. The x

axis begins at a length of 0.05 m, this is because of the discretization used in the mesh,

where until at 0.05 m long, only the porous media and air were presented. The variables

most affected for the mesh size were the coke volumetric fraction 4.2b) and the reaction

rate of coke oxidation 4.2d). Under the conditions in which the mesh size was evaluated,

it was observed a high consumption of oxygen along the cell 4.2a). This oxygen react

with the oil and the coke in the cell, and it was observed that close to the injection

point, the production of coke is higher than the consumption of this component. This

explains the increase in coke concentration above the initial condition of 0.05. Meanwhile

in the zones close to the outlet of the cell the volumetric fraction of coke was similar

to the initial value (Figure 4.2b)). Figure 4.2c) and Figure 4.2d) show the reaction

rate of asphaltenes and coke oxidation, respectively. It was observed that close to the

injection point, the rate of reaction was high in both cases and diminish according to

the decreasing molar fraction of oxygen in the cell. The conclusion of this study was

that using a mesh with 672 nodes is enough to guarantee mesh size independency.

Additionally to the study of mesh size independency a time step study was carried out.

Figure 4.3a) shows the results of the simulation developed in the mesh with 672 nodes

with the same conditions of the case of mesh size independence, using time steps of


a)a) a) b)

Figure 4.3: Criteria used for the selection of the time step. a) Time step study. b)Distribution of the Courant number along the cell

0.1, 1 and 10 seconds. The reaction rate of coke oxidation, that was the variable most

sensitive to the mesh size, was selected for this study. It should be noted that the coke

volumetric fraction had a similar behavior as that encountered for the reaction rate of

coke in Figure 4.2b). Because these variables are dependent on each other, only the

reaction rate of coke oxidation was selected in the study of time step independence.

In Figure 4.3a) the predictions for all time steps are basically the same. Although the

selection of a time step of 10 s will expedite the calculation without increasing the error,

a time step of 0.5 s was selected to guarantee stability in the solution. Figure 4.3b),

shows that the cell Courant number for a time step of 0.5 s does not exceed 0.5. This low

value guarantees stability in the solution as the recomended value of the cell Courant

number is less than 1 [96].

4.3 Results

4.3.1 Comparison with the simulation by Belgrave et al.

In the publication of Belgrave et al. [5], the authors only report results for the first node.

As discussed before, the CFD simulation considered five zones, each with multiple nodes.

The second zone node agrees with the first node of the simulation by Belgrave et al.

[5], and it is for this zone that the CFD data were averaged in the figures below. The

transient behavior of the averaged oil saturation, the average asphaltene mass fraction

and the average coke concentration were plotted in Figure 4.4. It was observed that

the behavior of the averaged oil saturation and the average asphaltene mass fraction in

Figure 4.4a) was similar to those found by Belgrave et al. [5], although, some differences

were evident in both variables, particularly in the time necessary to convert all the oil in

the pseudo-component asphaltene, which makes that the behavior in the oil saturation


Asphaltenes mole fraction

Oil saturation

a) b)CFD CFD

Figure 4.4: Comparison of the results of the CFD simulation with the results reportedby Belgrave et al. [5]. a)Molar fraction of asphaltenes and oil saturation. b)Coke

concentration

in the cell had some differences for the last times.

The behavior of the average coke concentration, in figure 4.4b) presented evident dif-

ferences in comparison with the results reported by Belgrave et al. [5]. Even though

the tendency was similar in both models, the beginning in coke production was faster

in the CFD simulation than in the model by Belgrave et al. [5]. A similar behavior

was observed in the maximum concentration of coke, for which a maximum was reached

early in CFD than in the model by Belgrave et al. [5]. The simulation by Belgrave et al.

[5] predicts that all the coke is consumed before six hours contrary the CFD simulation

reports that a significant fraction of the coke remains in the cell even at six hours.

To explain the differences in both simulations, the result of the simulations were ex-

amined in detail. When the CFD simulation was examined, it was found that the

distribution of the different species in the cell was not uniform. In Figure 4.5a) the

coke volumetric fraction is shown for different times. Early in the experiment (7000 s),

coke was formed by the reactions of asphaltenes oxidation. It was observed that the

concentration of coke close to the point where air is injected was high and decreased

according to the consumption of oxygen in the gas phase. At intermediate time (t =

15000 s) a portion of the coke was consumed by oxygen and the coke generation was

mainly by pyrolysis of the remaining asphaltenes in the oil. Closer to the end of the

experiment (t = 28000 s) all the asphaltenes were consumed coke generation stopped

and only coke oxidation took place in the cell.

Figure 4.5b) shows the oxygen molar fraction in the cell for different times. At early

times, the temperature was low and consequently the reaction rates were low too. This

caused a wide zone of reaction, where the main reactions that took place were the oxida-

tion of maltenes and asphaltenes. It was observed that from the middle to the end of the

cell the molar fraction of oxygen was too low, which explains the formation of coke only

close to air injection as was evident in Figure 4.5a). As the experiment advances, the


Figure 4.5: Contours of the CFD simulation for the times 7000 s (495 K), 15000 s(720 K) and 28000 s (1050 K). a)Coke volumtric fraction. b)Oxygen molar fraction

a) b)

Rate of maltenes oxidationRate of asphaltenes oxidationRate of coke oxidation

Rate of maltenes oxidationRate of asphaltenes oxidationRate of coke oxidation

Figure 4.6: Distribution of different species and reaction rates along the cell. a) 7000s. b) 14000 s

oxidation reaction zone changed overalong the cell and due to the higher temperature

the zone of oxidation becaome narrower, causing a decay of the molar fraction of oxygen

in a small region.

In Figure 4.6a and 4.6b the main variables involved in the process were plotted along

the cell for 14000 s and 28000 s, respectively. The molar fraction of gas, the volumetric

fraction of oil, the volumetric fraction of coke, the rate of maltenes oxidation, the rate

of asphaltenes oxidation and the rate of coke oxidation show a behavior similar to that

described above for the molar fraction of oxygen. The non-uniform distribution of these

variables in the cell was stronger towards the end of the experiment. This behavior can

be attribuited to the narrowing in the reaction zone, which was also observed in the

molar fraction of oxygen contours in Figure 4.5b, that caused a significant change in a

small zone of the cell. The results in figures 4.5 and 4.6 suggested that a discretization

with only three nodes is not enough to guarantee a homogeneous behavior in each node

for the species studied.


The differences between CFD results and Belgrave et al. [5] results can be attributed

at the discretization made in these cases. In the Belgrave simulation only three nodes

were used, and the results of the CFD simulation suggest that this discretization is not

enough.

A conclusion of this study is the fact that the behavior in the kinetic cell was distant

from the behavior of a perfect mixed reactor. The implication of this conclusion is very

significant when determining the kinetics for the ISC process. The use of a perfectly

stirred reactor model to process the experimental data obtained in a kinetic cell can

cause significant errors.

4.3.2 Validity of the supposition of complete mixing

Because the assumption of 0-D model simplifies the evaluation of kinetic data from

experiments, it is desirable establish parameters that help in the design of experimen-

tal equipment that satisfy the 0-D assumption. A common analysis used in chemical

reactors to address dispersion makes use of the dimensionless number of Damkohler.

The Damkohler number correlate the rate of consumption of a reactive with the rate

of transport of the reactive by convection [97]. To determine the conditions in which

the behavior of the kinetic cell has a performance similar to a complete mixing reactor,

different conditions were modified so that the Damkohler varied and its effect on the

species distribution in the cell could be determined.

The definition of the Damkohler number used was a combination of the coke Damkohler

number and the oil Damkohler number that were defined in [77]. Using the molar bal-

ance of oxygen, we obtained equation 4.1 that defines the Damkohler number used in

this study.

Da =τφSoρoxO2ρg

(3.431xmalP

0.4246O2

km + 7.513xaspP4.7627O2

ka + 1.232PO2kc)

(4.1)

where τ is the residence time for oxygen in the cell, φ is the porosity, So is the initial oil

saturation, ρ is the molar density, PO2 is the partial pressure of oxygen, xi is the molar

fraction and ki are the kinetic parameters of the oxidation reaction i.

Varying properties and conditions in Table 4.1, different Damkohler numbers were ob-

tained so that the necessary conditions to achieve a behavior similar at a complete

mixing were determined.

Figures 4.7a) and 4.7b) present the average oil saturation and the coke concentration in

the kinetic cell, respectively, when the residence time was modified varying the lengths of


a) b)

Figure 4.7: Comparison of the CFD and the 0-D model results for different Damkohlernumbers, in the basis case. a) Oil saturation. b) Coke concentration

the cell from 25 cm to 2.1 cm, being the shortest length the low value in the Damkohler

number and vice versa. This case, hereinafter is defined as base case. As standard for

0-D behavior, the CFD simulations were compared with the analysis when the system

was modeled as a semibatch reactor and solved in the Matlab lenguaje described in

Appendix B. For the oil saturation the effect of Damkohler was minor and the prediction

for different Damkohler numbers were not far off from those predicted by the complete

mixing model as is evident in Figure 4.7a). Only for the highest Damkohler numbers an

appreciable difference between the CFD prediction and the 0-D prediction was observed.

Unlike the average oil saturation, the average coke concentration was more sensitive to

variations in Damkohler (see Figure 4.7b)). For Damkohler < 10, CFD and 0-D model

predictions agree.

Equation 4.2 quantifies the deviation of the CFD model and the 0-D model for the oil

saturation along the cell. A similar expression was used for coke concentration. Figures

4.8a) and 4.8b) show the deviation for oil saturation and coke concentration for different

times in the base case. Around 2 hours when the rate of consumption of oil was high

and the coke concentration was high it was observed a maximum in deviation of oil

saturation and coke concentration.

Deviation% =

∫ x0

∣∣∣SOCFD−SO0−D

∣∣∣SOmax

× 100%

L(4.2)

Additionally, in the deviation of the coke concentration, another maximum was observed

around 4 hours. In this case the consumption of coke was greater (see figure 4.6b)

where the time is 3.89 h which is close at the maximum mentioned) causing in the

CFD simulation a narrowing in the reaction region (see figure 4.5b) where the time is

4.11 h which is close at the maximum mentioned) which cause a strong non-uniform

distribution of the species in the cell.


a) b)

Figure 4.8: Deviation of the CFD simulation with the 0-D, for different Damkohlernumbers, in the basis case. a) Oil saturation. b) Coke concentration

In Figures 4.8a) and 4.8b), for low Damkohler numbers the deviation of the CFD simula-

tion in comparison with the 0-D model decreased. This suggests that the approximation

of complete mixing is reasonable and the use of a 0-D model is valid for low (< 10)

Damkohler numbers.

To confirm this hypothesis different test were carried out. Table 4.2 shows the different

cases studied and the conditions modified in each case. These conditions involved the

Damkohler number modified were the inlet flow, initial oil saturation, oxygen molar

fraction and pressure. Where increases in initial oil saturation, oxygen molar fraction

and pressure means increases in the Damkohler number, conversely, increases in inlet

flow produces a decreasing in the Damkohler number.

Table 4.2: Cases used in the analysis of homogeneity in the cell

Case So xO2 Inlet flow m3/h Pressure (kPa)

Basis case 0.25 0.21 0.081 4100

Case 2 0.25 0.21 0.198 4100

Case 3 0.15 0.21 0.081 4100

Case 4 0.25 0.30 0.081 4100

Case 5 0.25 0.21 0.081 500

In Figures 4.9, 4.10, 4.11 and 4.12 the average oil saturation and the average coke

concentration for different Damkohler numbers (the residence time was varying using

lengths of the cell from 25 cm to 2.1 cm) for cases 2, 3, 4 and 5 are presented, respectively.

The behavior in all cases was similar to that found for the base case, as the times for

the start of coke formation and maximum concentration of coke were similar. Only in

Case 5 a delay in the maximum concentration of coke was observed mainly bacause of

the higher dependency of the reaction rates of oxidation with the pressure. A similar

behavior was observed in the values of the maximum coke concentration. Only in Case


a) b)

c) d)

Figure 4.9: Comparison of the CFD and the 0-D model results for differentDamkohler numbers, in the case 2. a) Oil saturation. b) Coke concentration

. c) Oil deviation. d) Coke deviation

3, the maximum value of coke concentration was lower, which is product of the lower

availability of oil.

As it was the case in Figure 4.7 lower values of Damkohler approximated the CFD

predictions to those of the perfectly mixed reactor. However the value of Damkohler

where conditions were similar, was lower than those in the base case. It seem that Da

< 7 would guarantee that the CFD and 0-D models agree.

Figures 4.9c,d), 4.10c,d), 4.11c,d) and 4.12c,d) the deviation of the CFD simulations in

comparison with the 0-D model are plotted for the different cases. The maximum devi-

ations in oil saturation and the coke concentration, as case base, were reached at times

when the rate of consumption of oil and coke were high. As expected, the tendency

respect at the Damkohler number it was similar at those found in the base case, where

a lower value represent an approaching at the homogeneous behavior.

According to the analysis above when Damkohler is lower than 7 a 0-D approximation

of the combustion cell should be enough to model the ISC process. The only exception

was Case 5, that demands even lower values of Damkohler to guarantee good mixing.

However, Case 5 was for very low pressures for which the kinetic may be inaccurate.


a) b)

c) d)



a) b)

c) d)




a) b)

c) d)



In conclusion the Damkohler number is a good parameter to indicate mixing in a com-

bustion cell used to study the ISC process. For reference [5], a value of Da less than 7

guarantees that the 0-D model can predict they combustion process correctly.

Chapter 5

CFD simulation of a reactor with

optical access

Once, it was proven that CFD was capable of capturing the phenomena associated to

ISC, the CFD simulation was used to predict the behavior of the process in a prototype

cell with characteristcs similar to that of a kinetic cell. Unlike the kinetic cell the core

used in this prototype has slits used to measure with laser techniques the concentration

of some species present in the process. Understanding the effect of the slits in the ISC

process is of paramount importance. The oil flow in this zone represents a challenge in

the measurement with laser techniques as complete coverage of oil renders impossible

the implementation of these techniques. This importance of the movement of the oil

phase inside the prototype cell justifies the use of CFD to simulate this process.

5.1 System dimension and initial settings

The simulated prototype has in the center an optical access, that can be used to measure

the concentration of different species present in the gas phase with laser techniques such

as TDLAS and PLIF. The geometry and the dimensions of the core proposed in this

prototype are shown in Figure 5.1 and the properties of the crude and core are the same

at those listed in Table 4.1. The geometry and cell characteristics were taking from the

Ph. D. thesis of Copete [98]

The core was represented a structured mesh of 92000 nodes using the commercial soft-

ware ANSYS ICEM CFD. A refinement in the optical access was necessary to capture

the behavior of the different fluids in this slits. The mesh used in the simulation is shown

in Figure 5.2a. An o grid methodology was used to represent the cylindrical shape of

44

Chapter 5. CFD simulation of a reactor with optical access 45

25.4 mm

38.1 mm

1 mm

1 mm

100 mm

Figure 5.1: Dimensions of the prototype cell with optical access

the prototype.

The operational parameters chosen were those in which the Damkohler number had a

low value (lower than 7) in this way assure a correct interpretation of the data obtained

with a perfect mixing model.

The simulation was similar to those conduced for the kinetic cell in the previous sec-

tion. The crude oil was heated at 100 oC/h while air was injected at a rate of 4.17 ×10−05 std m3/s. The initial oil saturation in the core was 0.2, except in the optical

access which it was free of oil and only the gas phase was present.

Figure 5.2b shows the initial oil saturation in the core. The porous zone near the inlet

that it is oil free was used to guarantee that the air injected reached the temperature of

the system before reacting with the oil.

The boundary conditions used in the simulation of the prototype cell were similar to

those used in the simulation of the kinetic cell. A volumetric flow of air of 4.17 ×10−05 std m3/s in the inlet, a pressure of 4100 kPa in the outlet, a ramped temperature

in the wall of 100 oC/h. Two different zones were used in the simulation. One zone to

represent the porous media with a porosity of 0.41 and a permeability of 12000 mD. The

other zone was used to represent the optical access to the core.


Outlet

Inlet

Optical access

Wall

a) b)

Figure 5.2: Prototypt cell simulated. a) Mesh. b) Distribution of the initial oilsaturation

a) b)Oil velocity (m s‐1)

2.656 × 10‐7

2.124 × 10‐7

1.593 × 10‐7

1.062 × 10‐7

5.311 × 10‐8

0.000

Figure 5.3: Velocity field of the oil in the core after 1 h. a) Velocity field in all thecore. b) Region where the velocity field is affected by the slits.

5.2 Evaluation of the multiphase flow in the slits

5.2.1 Time dependent simulation of the core

The main objective in this simulation was to evaluate the effect of the slits in the flow

of the different phases and to evaluate the possibility of the implementation of laser

diagnostic techniques to measure species in the gas phase.

The simulation run until a time at which the temperature was high enough (400 K) so

that oil was able to easily flow, 1 h after the start of the experiment.

Figure 5.3a) shows the velocity vectors of the oil in all the core. It is apparent that the

flow near the region of the slits was affected by this optical access where the resistance


Figure 5.4: Velocity field of the oil in the region of the core affected by the slits

to flow is lower than in the porous media. In Figure 5.3b) the region affected by the slits

is highlighted, this region was used later in other simulation to determine the amount

of oil that flows throug the slits.

Figure 5.4 shows the velocity vectors of the oil phase in the region of the slits. The

vectors indicate flow towards the slits on the first sections and a direction moving away

from the slits in the last sections of the slits.

The small size of the cells in the slits makes necessary the reduction of the time step

to values of the order of 1.0× 10−04 s to guarantee a global courant number smaller to

250 (when the simulation reached this value, ANSYS FLUENT stopped automatically

the simulation) and avoid innestabilities in the calculation. This short time step makes

the simulation too long for the computational capabilities of the research group and,

therefore, makes impractical the complete realization of this simulation. For that reason

the simulation had to be suspended after 1.2 hours. However, that simulation time was

enough to get evidence that the oil flow is affected by the slits.


Pressure inlet

Pressure outlet

Wall

Pressure profile

Figure 5.5: Mesh used to simulated the behavior of the phases in the optical accessin steady stete

5.2.2 Steady state simulations in the optical access wiht variable bound-

ary conditions

To determine if the oil flows through the slits and if the laser measurement could be

affected by this oil, different situations presented in the simulation of the kinetic cell

were selected and simulated in a mesh that represented only the optical access. The

interaction of the slits with the porous media was established through the boundary

conditions, which in turn were obtained from the CFD simulation in transient state of

the kinetic cell, which was described in Section 4.3

In this case a structured mesh of 1600 nodes was constructed. In Figure 5.5 the mesh

and the boundary conditions used in the simulation are shown.

As illustrated in Figure 5.5 the boundary conditions used were an inlet pressure, an

outlet pressure and a profile of pressure along the slits. In the boundary conditions the

volumetric fraction of oil, the volumetric fraction of coke and the mole fraction of the

species in those phases were specified. In addition, in the boundary conditions were

specified only different pressures along the slits according to the results found in the

simulation of the kinetic cell in transient state. To capture the 500 Pa pressure drop

that was estimated in the transient simulation a pressure profile was used along the slits

adjusted to set a pressure drop going from 500 Pa at the bottom to 0 Pa at the top.

Table 5.1 lists the saturation of the different phases in the boundary and the compositions

of these phases for the different cases. The selected conditions were those in which

there were appreciable quantities of oil in the core and in which the temperature were


Line 1

Line 2

Line 3

Plane 1

Plane 2

a) b)

Figure 5.6: Laser trajectories that could be used for the measurement of gaseousspecies. a) TDLAS. b) PLIF

different in each case. In the selected conditions according the temperature increased the

mole fraction of asphaltenes increased too, and the mole fraction of maltenes decreased.

According to the temperature and the mole fractions, different viscosity was expected

in the oil (a decrease in oil viscosity with the rising in temperature).

Table 5.1: Cases selected to study the behavior of the oil in the optical access

Temperature So Sc xmal xasp xO2 xH2O xgas

300 0.250 0 0.800 0.200 0.210 0 0

400 0.251 0 0.794 0.206 0.208 0 0

500 0.090 0.160 0.434 0.566 0.043 0.019 0.033

Figure 5.6a) shows different lines that could be a path used for the implementation

of a technique such as TDLAS. Similarly, Figure 5.6b) show two planes in the optical

access, that can be used for the interrogation of gas species using a technique such as

PLIF. These lines and planes were used to evaluate the possibility to implement optical

techniques in the study of the ISC. The objective of the simulation was to determine the

amount of oil in the region were lines and planes cross the core through the slits and if

the oil blocks the laser light.

The simulations were developed in steady state and the fraction of oil in different regions

(Figure 5.6) of the slits and the average after the simulations are listed in Table 5.2.

In the results of the simulations it was observed that at 300 K the oil was not present

in the slits, which agrees with the results in section 5.2.1. At 400 K the presence of oil

in the slits increases and a technique such as PLIF could be hindered by the presence


Table 5.2: Oil volumetric fraction in the slits for different conditions at steady state

T (K) Average Line 1 Line 2 Line 3 Plane 1 Plane 2

300 0 0 0 0 0 0

400 5.17× 10−3 1.50× 10−7 6.46× 10−8 1.61× 10−5 2.73× 10−5 2.58× 10−2

500 1.74× 10−1 1.76× 10−1 1.64× 10−1 1.84× 10−1 1.74× 10−1 1.71× 10−1

of oil. Contrary, the trajectories traveled by the lines present low almost negligible oil

concentration.

Finally, at 500 K oil saturation was high and may deter the laser measurements. Be-

cause these simulations were developed in steady state, it was desirable to conduct a

simulation that accounts for the time-dependent behavior of the oil saturation in the

slits. According to Table 5.2 500 K is a critical temperature when measurng species in

the gas phase with laser techniques. Therefore, 500 K was selected as the temperaturefor

the analysis of the transient behavior of the oil in the slits.

5.2.3 Time-dependent simulations in the region affected by the slits

As stated previously, a time-dependent simulation was desirable to determine if oil fills

the slits in a scale of time similar to that of the ISC process. According to the results

found previously, the conditions at 500 K listed in Table 5.2 present the higher oil

saturation in the slits and for that reason these conditions were used in the transient

simulation. According to the results of Figure 5.4, the region is a region where the flow is

more affected by the slits. This region of the core, basically the porous space sorrounding

the slits was considered and used in the simulation to reduce the computational time.

Figure 5.7 shows the mesh used in this case and the initial oil saturation distribution in

the core, where the region of the optical access is free of oil and coke.

The results of the simulation are shown in Figure 5.8 where the average oil saturation

and the maximum oil saturation are plotted vs. time, for the different regions stated

previously. The results shows a fast increase in the oil saturation for line 3 and line

2, which suggest that these trajectories are not a good choice in the measurement of

species in the gas phase using TDLAS. In the line 1 the increase in the oil saturation

was low. This position may allow laser measurements.

Additionally a technique such as PLIF could not be implemented under these conditions

because of the high amount of oil that may block the planes of light.

In conclusion, using the conditions of the Table 4.1 in the core with optical access

makes impractical the implementation of a technique such as PLIF because only the


Figure 5.7: a) Mesh used in the transient state simulation of the section affected bythe slits. b) Initial oil saturation

a) b)

Figure 5.8: Oil saturation in the slits after 10 minutes of operation at 500 K.a)Average oil saturation. b) Maximum oil saturation

measurement of species can be performed in a short range of temperatures, before the oil

floods the slits. The implementation of a technique such as TDLAS under the conditions

in Table 4.1 is difficult because most of the optical domain is covered with oil.

5.2.4 Partial saturation of the core

Because the results of the simulations in the slits suggest that laser measurement could

have interference by oil, an alternative design seems mandatory. The alternative was

to saturate only a portion of the core, below the optical slits. To determine the length

of the 8 mm distance between the saturated area and the slits it was considered that

oil was consumed in just over two hours, in which the temperature reached was 520 K.

Considering this temperature, the oil viscosity was calculated and using the equation of

Darcy, the velocity of the oil was determined under these conditions, assuming a pressure

drop of 500 Pa in the region saturated by oil. With this value the length of the core

that would be saturated with oil to avoid the flow of oil in the slits was calculated. The


Figure 5.9: Initial oil saturation proposed to achieve the complete realization of aRTO test avoiding the oil flow in the slits.

maximum advance of the oil in the core was 4.5× 10−03 m, knowing this value we made

the simulation considering only a region of 2.5× 10−02 m saturated with oil in the core.

Figure 5.9 shows the initial contour of the oil saturation in the core. The region close

to the slits is free of oil.

The results of this simulation confirm that only the gas phase flows through the slits,

which suggests as possible the use of laser techniques. Figures 5.10 and 5.11 shown

the oil saturation and the oil phase velocity for different times. The oil stayed in the

porous zone despite the increase in the velocity in the oil caused by an increase in the

temperature of the core. Furthermore the model predicts that coke is only formed in

the porous zone as seen in Figure 5.12.

Once verified that only the gas phase flows through the optical access, the interest was

focused in determining the effect of the slits in the flow and the behavior of species that

could be measured with laser techniques. Figure 5.13 shows vectors of gas velocity in

the core. The higher velocity of the gases through the slits suggests the tendency to

travel through the slits which is logic due to less resistence to flow in comparison with

the porous zone. Figure 5.13 shows that the maximum magnitude in the velocity of the

gases was in the center of the slits and decrease at away of the center.

Figure 5.14 shows the gas velocity vectors in the core for different times. The velocity

is higher for the longer times, as higher temperatures decrease the viscosity, plus the

generation of gases by reaction increase the overall flow.


t = 2.1 hSo = 0.026

t = 0.1 hSo = 0.2

Oil volumetric fraction Oil volumetric fraction 0.20 0.20

0.15 0.15

0.10 0.10

0.05 0.05

0.00 0.00

Figure 5.10: Oil saturation in the prototype cell. a) 0.1 h. b) 2.1 h.

Figure 5.11: Oil velocity in the prototype cell. a) 0.1 h. b) 2.1 h.


Figure 5.12: Coke volumetric fraction in the prototype cell. a) 0.1 h. b) 2.1 h.

Gas velocity (m s‐1) 6.210 × 10‐3

4.658 × 10‐3

3.105 × 10‐3

1.553 × 10‐3

0.000

Figure 5.13: Vectors velocity of the gas phase in the region of the slits

Finally the interest of this simulation was to predict the species in the core, specially in

the gas phase that could be measured with optical techniques and the concentration of

these species at different times.

According to the mechanism used in the simulation the only species that could be

predicted were the CO, CO2 and H2O. The concentration of these species in the regions

showed in Figure 5.6 were the same in all the cases. For that reason the time-dependent

concentration of the different species are shown as the average for the optical access

region. Figure 5.15 shows the molar fraction of CO, CO2, H2O and the molar fraction

of O2 uptake in the simulation of the RTO test. It was observed a behavior in the O2

uptake molar fraction characteristic of the RTO test, where two peaks in the uptake of

oxygen were easily distinguished. Until 1 hour the uptake of O2 was not appreciable


t = 0.1 h t = 2.1 h

Gas velocity (m s‐1) Gas velocity (m s‐1) 9.966 × 10‐3 9.966 × 10‐3

7.475 × 10‐3 7.475 × 10‐3

4.983 × 10‐3 4.983 × 10‐3

2.492 × 10‐3 2.492 × 10‐3

0.000 0.000

Figure 5.14: Vectors velocity in the prototype cell. a) 0.1 h. b) 2.1 h.

because the temperature in the system was low and the oxidation reactions rate were

low too. At 1 hour the uptake of O2 began to increase reaching a maximum near 2

hours where the uptake of O2 declined. In this section the production of gases was not

appreciable and the LTO reactions presented the higher reaction rates.

The decline in the O2 uptake, known as the negative temperature gradient region, repre-

sents a transition between the LTO reactions and the HTO reactions. In this region the

amount of species in the oil phase decreases until disappeareance, while coke production

starts through different reactions. After around 2.5 hours the O2 uptake increases again,

but in this case the production of gaseous species was significant. Around 5 hours the

maximum production of gaseous species and O2 uptake was reached. From then on there

si a decline in the production of CO, CO2 and H2O due to depletion of the residual

coke in the core.

5.2.5 Simulation of the reactor at 5 atm

Because in the research group “Bio-procesos y Flujos reactivos” the objective is the

construction and the implementation of a prototype that allows the study of the species

in the gas phase in a core with characteristics similar to those in Figure 5.1. That design

suggested two more questions. What would be the effect a lower operating pressure, 5

atm, in the experiment?. And, would there be any outflow from the slits into the

windows that would hold the core?.


Figure 5.15: Prediction of the mole fraction of the species that can be measured inthe core at 41 atm.

To reply to these questions,two additional simulations were conducted.

The first simulation was similar to that in section 5.2.4, but in this case a pressure of 5

atm was as that it is the pressure defined in the research group for initial studies.

The second simulation tried to determine the amount of gases that leave the core by the

slits and to evaluate if this amount is significative and could affect the measurement of

the concentration of the gases. Both simulations are the described in the Appendix C,

as, although very relevant to this thesis, were not considered in the initial objetives.

Chapter 6

Conclusion

After the development of multiple user defined functions that address aspects such as

two-phase equilibrium, saturation properties, temperature dependency of physicochem-

ical properties, and, of course, kinetic expresion, it is possible to model the phenomena

present in the ISC process using a commercial software with similar results to those

reported in the state-of-the-art simulations of ISC experiments.

The current kinetic cells used to characterize the ISC process have issues regarding the

homogeneity of the reactants in the porous media. Their behavior is far from that of a

perfectly mixed reactor. However, the analysis of experimental systems to characterize

ISC with dimensionless numbers, such as Damkohler number, can significantly help

in the design of experimental systems so that the analysis of the experimental results

through perfectly mixed models is possible.

When designing a prototype cell for the characterization of the ISC process through

laser techniques, it is impractical to saturate the porous material surrounding the slits

created to give access to the laser beam. The reason for this is that the oil penetrates

into the slits and may block the laser light.

To avoid the possible interference of oil in the measurements using laser diagnosis tech-

niques, this study proposes the partial saturation with oil of the core in the region below

the slits, guaranteeing that the distance between the unsaturated region and the slits

long enough to prevent flow of oil into the optical access.

Using the CFD model we achieved to predict the behavior of the main gaseous species

such as O2, CO, CO2 and H2O that can be detected with laser diagnostic techniques.

The information of the gas species is useful in the experimentation and helps in forecast

of results.

57

Chapter 7

Future work

In a future work is recommended to use a chemical mechanism that incorporates more

pseudo-components in the oil phase to group the hydrocarbons and that take into ac-

count more species in the gas phase. Additionally, taking into account that the kinetic

mechanism used in the simulations was developed for Athabasca bitumen, the kinetic

parameters for different oils can change. For that reason is important to develop exper-

iments with the aim to determine this kinetic parameters for Colombian oils.

It is necessary the developed of simulations of combustion tube tests that give informa-

tion important as the recovery of oil, the advance of the combustion front and in this

way improve the prediction of the performance of the ISC process.

Even though the CFD simulations were especially important in the prototype cell with

optical access in the determination of the operational conditions in which is avoided

the oil flow through the slits, the computational time was high in these simulations.

Because the CFD simulators use models complex that are not necessary in the ISC

process when is considered only the flow through porous zones, this high computational

time can be avoided. For that reason is important the construction of an own simulator

in which the interaction between the porous media and zones, free of rock, used for

laser measurement, do not be strong. And in this way accelerate the calculations in

simulations of the ISC process.

58

Appendix A

User defined functions (UDFs)

A.1 Reaction rate of maltenes oxidation (R1)

#include ”udf.h”

#include <stdio.h>

DEFINE HET RXN RATE(reac het malt,c,t,r,mw,yi,rr,rr t)

#define A 6.819e+3 /*Factor de frecuencia 1/Pa-0.4246 s */

#define E activacion 86730000 /*Energia de activacion J/kmol*/

#define Porosidad 0.412 /*Porosidad del medio poroso*/

#define minimo 1e-29 /*Valor minimo de la concentracion*/

#define Cte gases 8314 /*Constante de los gases J/kmol K */

#define MW Mal 406.7 /*Peso molecular maltenos kg/kmol */

#define MW Asp 1092.8 /*Peso molecular asfaltenos kg/kmol */

#define Den Mal 983.2 /*Densidad de maltenos kg/m3 */

#define Den Asp 1158 /*Densidad de asfaltenos kg/m3 */

#define Vol Total 5.067075e-4

Domain **domain reactant = r->domain reactant;

real *stoich reactant = r->stoich reactant;

int *reactant = r->reactant;

int i;

int sp id;

int dindex;

real Presion;

59

Appendix A. User defined functions (UDFs) 60

real Sg;

real So;

real PO2;

real Mol;

real xO2;

real x mal;

real ID gas;

real xi;

real MW Oil;

real Den Oil;

Thread *t reactant;

real ci;

real T;

real V = C VOLUME(c,t);

/* Calculo del coeficiente de reaccion */

*rr = 1;

for (i=0; i < r->n reactants; i++)

sp id = reactant[i];

if (sp id ==-1) sp id = 0;

dindex = DOMAIN INDEX(domain reactant[i]);

t reactant = THREAD SUB THREAD(t,dindex);

T = C T(c,t reactant);

Mol = mw[dindex][sp id];

if (Mol == 32)

Presion = C P(c,t);

ID gas = dindex;

xO2 = (yi[dindex][sp id]/32)/((yi[dindex][sp id]/32)+((1-yi[dindex][sp id])/28));

PO2 = xO2*Presion;

*rr *= pow(PO2,0.4246);

else

So = C VOF(c,t reactant);


x mal = yi[dindex][sp id];

xi = (x mal/MW Mal)/((x mal/MW Mal) + ((1-x mal)/MW Asp));

MW Oil = xi*MW Mal + (1-xi)*MW Asp;

Den Oil = xi*Den Mal + (1-xi)*Den Asp;

ci = Porosidad*So*xi*Den Oil/MW Oil;

*rr *= ci;

*rr *= A*exp(-E activacion/(Cte gases*T));

*rr = *rr;

A.2 Reaction rate of asphaltenes oxidation (R2)


#include <stdio.h>

DEFINE HET RXN RATE(reac het asph,c,t,r,mw,yi,rr,rr t)

#define A 2.133e-10 /*Factor de frecuencia 1/Pa-4.7627 s */













int i;

int sp id;

int dindex;

real Presion;


real Sg;

real So;

real PO2;

real Mol;

real xO2;

real x asp;

real xi;

real MW Oil;

real Den Oil;

Thread *t reactant;

real ci;

real T;


*rr = 1;



if (sp id ==-1) sp id = 0;





if (Mol == 32)

Presion = C P(c,t);


PO2 = xO2*Presion;

*rr *= pow(PO2,4.7627);

else


x asp = yi[dindex][sp id];

xi = (x asp/MW Asp)/((x asp/MW Asp) + ((1-x asp)/MW Mal));

MW Oil = xi*MW Asp + (1-xi)*MW Mal;


Den Oil = xi*Den Asp + (1-xi)*Den Mal;


*rr *= ci;


*rr = *rr;

A.3 Reaction rate of maltenes pyrolysis (R3)


DEFINE HET RXN RATE(reac pyr mal,c,t,r,mw,yi,rr,rr t)

#define A 9.092e12 /*Factor de frecuencia 1/s */












int i;

int sp id;

int dindex;

real Presion;

real Sg;

real So;

real xi;


real MW Oil;

real Den Oil;

Thread *t reactant;

real ci;

real T;

*rr = 1;



if (sp id ==-1) sp id = 0;





xi = (yi[dindex][sp id]/MW Mal)/((yi[dindex][sp id]/MW Mal) + ((1-yi[dindex][sp id])/MW Asp));

MW Oil = xi*MW Mal + (1-xi)*MW Asp;

Den Oil = xi*Den Mal + (1-xi)*Den Asp;


*rr *= ci;


*rr = *rr;

A.4 Reaction rate of asphaltenes pyrolysis to produce coke(R4)


#include <stdio.h>

DEFINE HET RXN RATE(reac pyr asph1,c,t,r,mw,yi,rr,rr t)














int i;

int sp id;

int dindex;

real Presion;

real Sg;

real So;

real Den Oil;

real xi;

real MW Oil;

Thread *t reactant;

real ci;

real T;

*rr = 1;



if (sp id ==-1) sp id = 0;





xi = (yi[dindex][sp id]/MW Asp)/((yi[dindex][sp id]/MW Mal) + ((1-yi[dindex][sp id])/MW Asp));




*rr *= ci;



*rr = *rr;

A.5 Reaction rate of asphaltenes pyrolysis to produce gases(R5)


DEFINE HET RXN RATE(reac pyr asp2,c,t,r,mw,yi,rr,rr t)













int i;

int sp id;

int dindex;

real Presion;

real Sg;

real So;

real Den Oil;

real xi;

real MW Oil;

Thread *t reactant;

real ci;

real T;


*rr = 1;



if (sp id ==-1) sp id = 0;





xi = (yi[dindex][sp id]/MW Asp)/((yi[dindex][sp id]/MW Mal) + ((1-yi[dindex][sp id])/MW Asp));




*rr *= ci;


*rr = *rr;

A.6 Reaction rate of coke oxidation (R6)


#include <stdio.h>

DEFINE HET RXN RATE(reac het coke,c,t,r,mw,yi,rr,rr t)

#define A 2.04e-7 /*Factor de frecuencia 1/Pa s */










int i;

int sp id;

int dindex;

real Presion;

real Sg;

real Sc;

real xO2;

real Mol;

real PO2;

Thread *t reactant;

real ci;

real T;


*rr = 1;



if (sp id ==-1) sp id = 0;





if (Mol == 32)

Presion = C P(c,t);


PO2 = xO2*Presion;

*rr *= pow(PO2,1);

else

Sc = C VOF(c,t reactant);

ci = Porosidad*Sc*1380/13.13;

*rr *= ci;



*rr = *rr;

A.7 Evaporation of water


#include <stdio.h>

DEFINE HET RXN RATE(user evap react,c,t,r,mw,yi,rr,rr t)

#define C 8.89513e7

#define D 3.81644e3

#define E -227

#define MW water 18

#define Den vapor 1

#define Den water 1000

#define Diff 2e1 /* 1/s */




int i;

int sp id;

int dindex;

real Presion;

real Sg;

real Sw;

real Mol;

real yH2O;

real x H2O;

real Keq;

real Ceq g;

real P;

real C g;

Thread *t reactant;

real ci;


real T;

*rr = 1;



if (sp id ==-1) sp id = 0;




P = C P(c,t);


if (Mol == 18)

Sg = C VOF(c,t reactant);

yH2O = (yi[dindex][sp id]/18)/((yi[dindex][sp id]/18)+((1-yi[dindex][sp id])/28));

else

Sw = C VOF(c,t reactant);

x H2O = 1;

Keq = 0.133*C*exp(-D/(T-E))/P;

Ceq g = Keq*Sw*Den water/MW water;

C g = Sg*yH2O*Den vapor/MW water;

if (Ceq g > C g)

*rr *= Diff*(Ceq g - C g);

else

*rr *= 0;

*rr = *rr;


A.8 Condensation of water


#include <stdio.h>

DEFINE HET RXN RATE(user cond react,c,t,r,mw,yi,rr,rr t)

#define C 8.89513e7

#define D 3.81644e3

#define E -227

#define MW water 18

#define Den vapor 1

#define Den water 1000

#define Diff 2e1 /* m2/s */




int i;

int sp id;

int dindex;

real P;

real Sg;

real Sw;

real Mol;

real yH2O;

real x H2O;

real Keq;

real Ceq g;

real C g;

Thread *t reactant;

real ci;

real T;

*rr = 1;




if (sp id ==-1) sp id = 0;




P = C P(c,t);


if (Mol == 18)


yH2O = (yi[dindex][sp id]/18)/((yi[dindex][sp id]/18)+((1-yi[dindex][sp id])/28));

else

Sw = C VOF(c,t reactant);

x H2O = 1;

Keq = 0.133*C*exp(-D/(T-E))/P;

Ceq g = Keq*Sw*Den water/MW water;

C g = Sg*yH2O*Den vapor/MW water;

if (C g > Ceq g)

*rr *= Diff*(C g - Ceq g);

else

*rr *= 0;

*rr = *rr;


A.9 Evaporation of maltenes


#include <stdio.h>

DEFINE HET RXN RATE(user evap mal react,c,t,r,mw,yi,rr,rr t)

#define C 1.4196e8

#define D 6.5623e3

#define E -80.1

#define MW malt 406.7

#define Den vapor 1

#define Den malt 983

#define Diff 0.53 /* 1/s */




int i;

int sp id;

int dindex;

real P;

real Sg;

real So;

real Mol;

real yMal;

real x mal;

real Keq;

real Ceq g;

real C g;

Thread *t reactant;

real ci;

real T;

*rr = 1;



if (sp id ==-1) sp id = 0;





P = C P(c,t);


if (Mol == 406.7)


yMal = (yi[dindex][sp id]/406.7)/((yi[dindex][sp id]/406.7)+((1-yi[dindex][sp id])/28));

else


x mal = (yi[dindex][sp id]/406.7)/((yi[dindex][sp id]/406.7)+((1-yi[dindex][sp id])/1092.8));

Keq = 0.133*C*exp(-D/(T-E))/P;

Ceq g = Keq*0.412*So*x mal*Den malt/MW malt;

C g = 0.412*Sg*yMal*Den vapor/MW malt;

if (Ceq g > C g)

*rr *= Diff*(Ceq g - C g);

else

*rr *= 0;

*rr = *rr;


A.10 Condensation of maltenes


#include <stdio.h>

DEFINE HET RXN RATE(user cond mal react,c,t,r,mw,yi,rr,rr t)

#define C 1.4196e8

#define D 6.5623e3

#define E -80.1

#define MW malt 406.7

#define Den vapor 1

#define Den malt 983

#define Diff 0.53 /* m2/s */




int i;

int sp id;

int dindex;

real P;

real Sg;

real So;

real Mol;

real yMal;

real x mal;

real Keq;

real Ceq g;

real C g;

Thread *t reactant;

real ci;

real T;

*rr = 1;



if (sp id ==-1) sp id = 0;





P = C P(c,t);


if (Mol == 406.7)


yMal = (yi[dindex][sp id]/406.7)/((yi[dindex][sp id]/406.7)+((1-yi[dindex][sp id])/28));

else


x mal = (yi[dindex][sp id]/406.7)/((yi[dindex][sp id]/406.7)+((1-yi[dindex][sp id])/1092.8));

Keq = 0.133*C*exp(-D/(T-E))/P;

Ceq g = Keq*So*x mal*Den malt/MW malt;

C g = Sg*yMal*Den vapor/MW malt;

if (C g > Ceq g)

*rr *= Diff*(C g - Ceq g);

else

*rr *= 0;

*rr = *rr;

A.11 Permeability of the gas phase


DEFINE PROFILE(Permeabildad gas, t, i)


#define Permeabilidad 12000 /*Permeabilidad del medio (unidades md)*/

#define Swc 0.05 /*Saturacion residual del agua*/

#define Sgc 0.05 /*Saturacion residual del gas*/

cell t c;

int domain id;

int porous zone id;

real Sg;

real Sw;

real So;

real Krg;

real Per efectiva;

Domain *phase domain;

Thread *phase1 thread, *phase2 thread, *phase3 thread;

/* Fase gaseosa */

domain id = 2;

phase domain = Get Domain(domain id);

porous zone id = 11;

phase1 thread = Lookup Thread(phase domain,porous zone id);

/* Fase aceite */

domain id = 3;




/* Fase agua */

domain id = 4;




begin c loop(c,t)

Sg = C VOF(c,phase1 thread);

So = C VOF(c,phase2 thread);

Sw = C VOF(c,phase3 thread);

if (Sg < 0.49)


Krg = 0.016*Sg + 0.0001;

Per efectiva = Krg*Permeabilidad;

else if (Sg >= 0.49 && Sg<0.79)

Krg = 0.193*Sg - 0.086;


else

Krg = 0.16*Sg - 0.06;


C PROFILE(c,t,i) = (1e15)/Per efectiva;

end c loop(c,t)

A.12 Permeability of the oil phase


DEFINE PROFILE(Permeabildad aceite, t, i)



#define Sor 0.1 /*Saturacion residual del aceite*/

cell t c;

int domain id;

int porous zone id;

real Sg;

real Sw;

real So;

real Kro;

real Krw;

real Krg;

real Krow;


real Krog;

real Per efectiva;



/* Fase gaseosa */

domain id = 2;




/* Fase aceite */

domain id = 3;




/* Fase agua */

domain id = 4;




begin c loop(c,t)




if (Sw < 0.65)

Krw = 0.0598*Sw + 0.0001;

Krow = -1.405*Sw + 1;

else

Krw = 0.2312*Sw -0.1113;

Krow = -0.2469*Sw + 0.247;


if (Sg < 0.49)

Krg = 0.016*Sg + 0.0001;

Krog = -1.628*Sg + 1;

else if (Sg >= 0.49 && Sg<0.79)

Krg = 0.193*Sg - 0.086;

Krog = -0.631*Sg + 0.511;

else

Krg = 0.16*Sg - 0.06;

Krog = -0.0596*Sg + 0.0597;

Kro = (Krow + Krw)*(Krog + Krg) - (Krw + Krg);

if (Kro <=1e-8)

Kro = 1e-4;

Per efectiva = 12000*Kro;


end c loop(c,t)

A.13 Permeability of the water phase


DEFINE PROFILE(Permeabildad agua, t, i)



#define Sor 0.1 /*Saturacion residual del aceite*/


cell t c;

int domain id;

int porous zone id;

real Sg;

real Sw;

real So;

real Krw;

real Per efectiva;



/* Fase gaseosa */

domain id = 2;




/* Fase aceite */

domain id = 3;




/* Fase agua */

domain id = 4;




begin c loop(c,t)




if (Sw < 0.65)

Krw = 0.0598*Sw + 0.0001;

Per efectiva = Krw*Permeabilidad;


else

Krw = 0.2312*Sw -0.1113;

Per efectiva = Krw*Permeabilidad;


end c loop(c,t)

A.14 Temperature ramped


DEFINE PROFILE(wall Temp,t,i)

face t f;

real T;

begin f loop(f,t)

real Tiempo = RP Get Real(”flow-time”);

T = (100*Tiempo/3600) + 300;

F PROFILE(f,t,i) = T;

end f loop(f,t)

A.15 Viscosity of the maltenes


DEFINE PROPERTY(viscosidad mal,c,t)

real visc;

real T = C T(c,t);

visc = (1.9359e-8)*exp(5642.2/T);


return visc;

A.16 Viscosity of the asphaltenes


DEFINE PROPERTY(viscosidad asph,c,t)

real visc;

real T = C T(c,t);

visc = (4.892e-28)*exp(33420/T);

return visc;

A.17 Mixing law for the viscosity of the oil phase


DEFINE PROPERTY(mix law visc,c,t)

real sum = 0.;

int i;

Material *sp;

real visc;

real visc mix;

Property *prop;

real T = C T(c,t);

mixture species loop(THREAD MATERIAL(t),sp,i)

prop = (MATERIAL PROPERTY(sp));

visc = generic property(c,t,prop,PROP mu,T);

sum += C YI(c,t,i)*log(visc);

visc mix = exp(sum);

return visc mix;


A.18 Mixing law for the density of the oil phase


DEFINE PROPERTY(mix law dens,c,t)

real sum = 0.;

int i;

Material *sp;

real dens;

real dens mix;

Property *prop;

real T = C T(c,t);

mixture species loop(THREAD MATERIAL(t),sp,i)

prop = (MATERIAL PROPERTY(sp));

dens = generic property(c,t,prop,PROP rho,T);

sum += C YI(c,t,i)/dens;

dens mix = 1/sum;

return dens mix;

A.19 Pressure profiles


#include <stdio.h>

DEFINE PROFILE(Pressure5,t,i)

real x[ND ND];

real pos z;

face t f;

real P;

begin f loop(f,t)

F CENTROID(x,f,t);

pos z = x[2];


P = 2000*pos z;

F PROFILE(f,t,i) = P;

end f loop(f,t)

Appendix B

0-D model

B.1 Data analysis

function Fig = Graficas Belgrave();

close all

clear all

clc

RTO = Celda Cinetica Belgrave();

%Analisis de datos %

t(:,1) = RTO.x/3600;

N Coke(:,1) = RTO.y(1,:); N Mal(:,1) = RTO.y(2,:); N Asp(:,1) = RTO.y(3,:);

N Agua(:,1) = RTO.y(4,:); N H2Og(:,1) = RTO.y(5,:); N Gas(:,1) = RTO.y(6,:);

N O2(:,1) = RTO.y(7,:); N N2(:,1) = RTO.y(8,:); N Mal g(:,1) = RTO.y(9,:);

x O2 = N O2./(N O2 + N Gas + N H2Og + N Mal g + N N2);

x Gas = N Gas./(N O2 + N Gas + N H2Og + N Mal g + N N2);

x H2Og = N H2Og./(N O2 + N Gas + N H2Og + N Mal g + N N2);

x Mal g = N Mal g./(N O2 + N Gas + N H2Og + N Mal g + N N2);

x N2 = N N2./(N O2 + N Gas + N H2Og + N Mal g + N N2);

x mal = N Mal./(N Mal + N Asp);

x asp = N Asp./(N Mal + N Asp);

% Analisis de datos %

Prop = Propiedades Belgrave();

Param.Vol Total = 5.067075e-4; %Volumen total (m3)

C Coque = N Coke*Prop.MW Coke/Param.Vol Total/1000; %kg/m3

86

Appendix B. 0-D model 87

So = (0.001*N Mal*Prop.MW Mal/Prop.Den Mal + ...

0.001*N Asp*Prop.MW Asp/Prop.Den Asp)/(0.412*Param.Vol Total);

B.2 Main code

function RTO = Celda Cinetica Belgrave();

close all

clear all

clc

%%% Condiciones de operacion y de entrada

Param.Vol Total = 5.067075e-4; %Volumen total (m3)

Param.Porosidad = 0.412;

Param.Vol Poroso = Param.Vol Total*Param.Porosidad; %Volumen Poroso (m3)

Param.Sg 0 = 0.75; %Fraccion de volumen ocupado por el gas

Param.So 0 = 0.25; %Fraccion de volumen ocupado por el oil

Param.Sw 0 = 0.00; %Fraccion de volumen ocupado por el agua

Param.Sc 0 = 0;

Param.T0 = 300; %Temperatura inicial (K)

Param.P = 4100; %Presion del sistema kPa

Param.P in = 101.3; %Presion de entrada kPa

Param.Dif H2O = 1e-5;

Param.Dif Mal = 1e-6;

Param.R = 8314.47; %Constante de los gases (J/kmol K) o (m3 Pa/kmol K)

Param.v0 = 2.25e-5; %Flujo de aire de entrada (m3/s)

Param.x Mal 0 = 0.9151; %Fraccion molar de maltenos

Param.x Asp 0 = 0.0849; %Fraccion molar de asfaltenos

Param.x O2 0 = 0; %Fraccion molar de oxıgeno

Param.x N2 0 = 1; %Fraccion molar de nitrogeno

Param.x O2 in = 0.21; %Fraccion molar de oxıgeno, entrada

Param.x N2 in = 0.79; %Fraccion molar de nitrogeno, entrada

Cond 0 = Condiciones iniciales(Param);

%Condiciones iniciales.

x 0 = zeros(9,1);

x 0(1) = 0; %Coque inicial (mol)

x 0(2) = Cond 0(2); %Maltenos iniciales (mol)


x 0(3) = Cond 0(1); %Asfaltenos iniciales (mol)

x 0(4) = Cond 0(5); %Agua inicial (mol)

x 0(5) = 0; %H2Og inicial (mol)

x 0(6) = 0; %Gas inicial (mol)

x 0(7) = Cond 0(3); %O2 inicial (mol)

x 0(8) = Cond 0(4); %N2 inicial (mol)

x 0(9) = 0; %Mal g inicial (mol)

M = zeros(9,9);

for i = 1:4

M(i,i)= 1;

end

Options = odeset(’RelTol’, 1e-6, ’AbsTol’, 1e-6, ’Mass’,M,’MassSingular’,’yes’,...

’MStateDependence’,’strong’);

RTO = ode15s(@Celda,[0 21600],x 0,Options,Param);

function f = Celda(t,x,Param);

f = zeros(9,1);

N Coke = x(1); N Mal = x(2); N Asp = x(3); N Agua = x(4);

N H2Og = x(5); N Gas = x(6); N O2 = x(7); N N2 = x(8); N Mal g = x(9);

%%%%%%%% Condiciones del sistema %%%%%%%

P = 1000*Param.P; % (Pa)

P ext = 1000*Param.P in; %(Pa)

Vol Total = Param.Vol Total;

Vol Poroso = Param.Vol Poroso;

R = Param.R;

T = (100/3600)*t + 300;

%%%%%%% Propiedades de los compuestos %%%%%

Prop = Propiedades Belgrave();

%%%% Fracciones molares gas %%%%%

x O2 = N O2/(N H2Og + N Gas + N O2 + N N2 + N Mal g);

x H2Og = N H2Og/(N H2Og + N Gas + N O2 + N N2 + N Mal g);

x Mal g = N Mal g/(N H2Og + N Gas + N O2 + N N2 + N Mal g);

x Gas = N Gas/(N H2Og + N Gas + N O2 + N N2 + N Mal g);

x N2 = N N2/(N H2Og + N Gas + N O2 + N N2 + N Mal g);


%%%% Fracciones molares aceite %%

x mal = N Mal/(N Mal + N Asp);

x asp = N Asp/(N Mal + N Asp);

%%% Densidad molar de aceite %%%%%%%

MW Oil = Prop.MW Mal*x mal + Prop.MW Asp*x asp; %kg/kmol

Den Oil = 1/(x mal/Prop.Den Mal + x asp/Prop.Den Asp); %kg/m3

DenMolar oil = 1000*Den Oil/MW Oil; %mol/m3

%%%% Saturacion de las fases %%%%%%

Param.So = ((N Mal + N Asp)/DenMolar oil)/Vol Poroso;

Param.Sw = 0.001*N Agua*Prop.MW H2O/(Prop.Den Agua*Vol Poroso);

Param.Sc = 0.001*N Coke*Prop.MW Coke/(Prop.Den Coke*Param.Vol Poroso);

Param.Sg = 1 - Param.Sw - Param.So - Param.Sc;

%%%%%% Flujo de entrada y de salida %%%%%%%%%

Inlet = Flujo entrada(Param);

%%%%%%% Equilibrio de fases %%%%%%%%%%%%

Trans H2O = Equilibrio Belgrave(T, P, x H2Og,Param);

Trans Mal = Equilibrio Belgrave Maltenos(T, P, x mal, x Mal g,Param);

%%%%%%%%%%%%% Velocidades de reaccion %%%%%%%%%%%%%%%%

Rxn = Mecanismo Belgrave(T, P, x mal, x asp, x O2, Param);

%%%%%% Ecuaciones %%%%%%%%%

f(1) = Vol Total*(83.223*Rxn(2) + 101.537*Rxn(5) - Rxn(6)); %Balance de coque

f(2) = Vol Total*(-Rxn(1) - Rxn(4)) - Trans Mal; % Balance Maltenos

f(3) = Vol Total*(0.372*Rxn(1) - Rxn(2) - Rxn(3) + 0.4726*Rxn(4) - Rxn(5)); %Bal-

ance de asphaltenos

f(4) = -Trans H2O;

f(5) = Vol Total*0.565*Rxn(6) - N H2Og + Trans H2O; %Balance de Vapor de agua

f(6) = Vol Total*(37*683*Rxn(3) + Rxn(6)) -N Gas; %Balance de Gas

f(7) = Vol Total*(-3.431*Rxn(4) - 7.513*Rxn(5) - 1.232*Rxn(6)) + Inlet(1) - N O2;

%Balance de O2

f(8) = Inlet(2) - N N2; %Balance de N2

f(9) = Trans Mal; %Balance de Maltenos en el gas

return


B.3 Initial conditions

function Cond 0 = Condiciones iniciales(Param);

Prop = Propiedades Kapadia Extendido();

DenMolar Mal = 1000*Prop.Den Mal/Prop.MW Mal; %mol/m3

DenMolar Asp = 1000*Prop.Den Asp/Prop.MW Asp;

Den O2 0 = Prop.MW O2*Param.P*1000/(Param.R*Param.T0); %Densidad oxıgeno

(kg/m3)

Den N2 0 = Prop.MW N2*Param.P*1000/(Param.R*Param.T0); %Densidad

nitrogeno (kg/m3)

y Mal 0 = Param.x Mal 0*Prop.MW Mal/(Param.x Asp 0*Prop.MW Asp + ...

Param.x Mal 0*Prop.MW Mal); %Fraccion masica

y Asp 0 = Param.x Asp 0*Prop.MW Asp/(Param.x Asp 0*Prop.MW Asp + ...

Param.x Mal 0*Prop.MW Mal); %Fraccion masica

y O2 0 = Param.x O2 0*Prop.MW O2/(Param.x O2 0*Prop.MW O2 + ...

Param.x N2 0*Prop.MW N2); %Fraccion masica

y N2 0 = Param.x N2 0*Prop.MW N2/(Param.x O2 0*Prop.MW O2 + ...

Param.x N2 0*Prop.MW N2); %Fraccion masica

Den oil = 1/(Param.x Mal 0/Prop.Den Mal + ...

Param.x Asp 0/Prop.Den Asp); %Densidad (kg/m3)

Den Gases 0 = 1/(Param.x O2 0/Den O2 0 + ...

Param.x N2 0/Den N2 0); %Densidad (kg/m3)

MW Oil 0 = Param.x Mal 0*Prop.MW Mal + ...

Param.x Asp 0*Prop.MW Asp; %(kg/kmol)

DenMolar Oil 0 = 1000*Den oil/MW Oil 0; % (mol/m3)

% Calculo de las cantidades masicas iniciales de cada compuesto

Masa oil 0 = Param.Vol Poroso*Param.So 0*Den oil; %Masa de crudo (kg)

Masa Gases 0 = Param.Vol Poroso*Param.Sg 0*Den Gases 0; %Masa de gases (kg)

Masa Agua 0 = Param.Vol Poroso*Param.Sw 0*Prop.Den Agua; %Masa de agua (kg)

Masa Asp 0 = Masa oil 0*y Asp 0;

Masa Mal 0 = Masa oil 0*y Mal 0;

Masa O2 0 = Masa Gases 0*y O2 0;

Masa N2 0 = Masa Gases 0*y N2 0;

% Calculo de las cantidades molares iniciales de cada compuesto

Moles Asp 0 = Masa Asp 0/Prop.MW Asp; %Moles de Asp (kmol)

Moles Mal 0 = Masa Mal 0/Prop.MW Mal;


Moles O2 0 = Masa O2 0/Prop.MW O2;

Moles N2 0 = Masa N2 0/Prop.MW N2;

Moles Agua 0 = Masa Agua 0/Prop.MW H2O;

Cond 0(1) = 1000*Moles Asp 0;

Cond 0(2) = 1000*Moles Mal 0;

Cond 0(3) = 1000*Moles O2 0;

Cond 0(4) = 1000*Moles N2 0;

Cond 0(5) = 1000*Moles Agua 0;

B.4 Inlet flow

function Inlet = Flujo entrada(Param);


Den O2 in = Prop.MW O2*Param.P*1000/(Param.R*Param.T0); %Densidad

(kg/m3)

Den N2 in = Prop.MW N2*Param.P*1000/(Param.R*Param.T0); %Densidad

(kg/m3)

y O2 in = Param.x O2 in*Prop.MW O2/(Param.x O2 in*Prop.MW O2 + ...

Param.x N2 in*Prop.MW N2); %Fraccion masica

y N2 in = Param.x N2 in*Prop.MW N2/(Param.x O2 in*Prop.MW O2 + ...

Param.x N2 in*Prop.MW N2); %Fraccion masica

Den Gases in = 1/(Param.x O2 in/Den O2 in + ...

Param.x N2 0/Den N2 in); %Densidad (kg/m3)

% Calculo del flujo molar de entrada

Masa Entrada = Param.v0*Den Gases in; %Flujo masico (kg/s)

Masa Entrada O2 = Masa Entrada*y O2 in; %Flujo masico (kg/s)

Masa Entrada N2 = Masa Entrada*y N2 in; %Flujo masico (kg/s)

Moles Entrada O2 = Masa Entrada O2/Prop.MW O2; %Flujo molar (kmol/s)

Moles Entrada N2 = Masa Entrada N2/Prop.MW N2; %Flujo molar (kmol/s)

Inlet(1) = 1000*Moles Entrada O2; %Flujo molar (mol/s)

Inlet(2) = 1000*Moles Entrada N2; %Flujo molar (mol/s)


B.5 Equilibrium water

function Trans H2O = Equilibrio Belgrave(T, P, x H2Og,Param);


Keq H2O = 0.133*8.89513e7*exp(-3816.44/(T-46.13))/P;

x H2Oeq = Param.Sw*Keq H2O;

Trans H2O = (Prop.Den Agua/Prop.MW H2O)*Param.Dif H2O*log((1-x H2Og)/(1-x H2Oeq));

B.6 Equilibrium maltenes

function Trans Mal = Equilibrio Belgrave Maltenos(T, P, x mal, x Mal g,Param);


Keq Mal = 0.133*1.4196e8*exp(-6562.3/(T-193.02))/P;

x mal eq = Param.So*x mal*Keq Mal;

if x mal eq < 0

x mal eq = 0;

end

Trans Mal =(1/Prop.MW Mal)*Param.Dif Mal*log((1-x Mal g)/(1-x mal eq));

B.7 Mechanism Belgrave

function Rate = Mecanismo Belgrave(T, P, x mal, x asp, x O2, Param);

%%%%% Mecanismo de reaccion propuesto por Belgrave

%%%%% Rate = Rata de reaccion para las 6 reacciones propuesta por Belgrave

%%%%% Rate = mol/s m3 Totales

%%%%% 1 = pirolisis maltenos

%%%%% 2 = pirolisis asfaltenos - produccion de coque

%%%%% 3 = pirolisis asfaltenos - produccion de gases

%%%%% 4 = oxidacion de maltenos

%%%%% 5 = oxidacion de asfaltenos

%%%%% 6 = oxidacion de coque

%%%%% T = Temperatura (K)


%%%%% P = Presion (Pa)

%%%%% Param = Porosidad, Fraccion vol de coque y saturacion de aceite

%%%%% Parametros %%%%%%%%


MW Oil = Prop.MW Mal*x mal + Prop.MW Asp*x asp; %Peso molecular (kg/kmol)

Den Oil = 1/(x mal/Prop.Den Mal + x asp/Prop.Den Asp); %Densidad (kg/m3)

DenMolar oil = 1000*Den Oil/MW Oil; %Densidad molar(mol/m3)

DenMolar coke = 1000*Prop.Den Coke/Prop.MW Coke; %Densidad molar(mol/m3)

Porosidad = Param.Porosidad;

So = Param.So;

Sc = Param.Sc;

Sg = Param.Sg;

PO2 = P*x O2; % Presion parcial de O2 (Pa)

%%%%%%% Constantes cineticas %%%%%%

A = [9.1e12; 4.06e9; 1.362e9; 6.819e3; 2.133e-10; 2.04e-7];

E = [2.35e8; 1.772e8; 1.763e8; 8.673e7; 1.856e8; 3.4763e7]; %J/kmol

R = Prop.R;

Temp = T;

k = A.*exp(-E./(R*Temp));

%%%%%% Velocidades de reaccion %%%%%%

Rate(1) = k(1)*Porosidad*So*DenMolar oil*x mal;

Rate(2) = k(2)*Porosidad*So*DenMolar oil*x asp;

Rate(3) = k(3)*Porosidad*So*DenMolar oil*x asp;

Rate(4) = k(4)*Porosidad*So*DenMolar oil*x mal*(PO2) 0.4246;

Rate(5) = k(5)*Porosidad*So*DenMolar oil*x asp*(PO2) 4.7627;

Rate(6) = k(6)*Porosidad*Sc*DenMolar coke*(PO2);

B.8 Properties of the pseudo-components

function Prop = Propiedades Belgrave();

Prop.R = 8314.47;

Prop.MW Mal = 406.7; %Peso molecular maltenos (kg/kmol)

Prop.MW Asp = 1092.8; %Peso molecular asfaltenos (kg/kmol)

Prop.MW Coke = 13.13; %Peso molecular coque (kg/kmol)


Prop.MW Agua = 18; %Peso molecular agua (kg/kmol)

Prop.MW Gas = 43.2; %Peso molecular gases (kg/kmol)

Prop.MW O2 = 32; %Peso molecular oxıgeno (kg/kmol)

Prop.MW N2 = 28; %Peso molecular nitrogeno(kg/kmol)

Prop.Den Mal = 983.2; %Densidad maltenos (kg/m3)

Prop.Den Asp = 1158; %Densidad asfaltenos (kg/m3)

Prop.Den Coke = 1380; %Densidad coque (kg/m3)

Prop.Den Agua = 1000; %Densidad agua (kg/m3)

Appendix C

Simulation of the reactor at 5

atm and simulation of the airflow

in a prototype for the study of

the ISC

C.1 Simulation of the reactor at 5 atm

In this simulation the conditions and the mesh of the Figure 5.9 were used, only the

conditions at the outlet was changed for a pressure of 500 kPa. Because the fluid dynamic

it was evaluated previously and the effect of the pressure is negligible in this case, only

the result of the species produced and the oxygen uptake is shown.

Figure C.1 show the species in the gas phase and the oxygen uptake. In this case it was

observed some differences in the behavior of the species at those found in Figure 5.15.

At low temperatures, two peak were observed in the oxygen uptake, which are attributed

at the maltenes oxidation and the asphaltenes oxidation, respectively. Meanwhile, at 41

atmospheres (Figure 5.15) only one peak was observed at low temperatures. Another

difference, it was the delay in the maximum peaks in the case of a pressure of 5 atm,

which it is logic because the dependency in the reactions rates with the partial pressure

of oxygen. Finally, another consequence of the lower values of the partial pressure of

oxygen was the lower values in the molar fraction of the gases produced in comparison

with the case of 41 atm.

95

Appendix X. Simulation of the reactor at 5 atm and simulation of the airflow in aprototype for the study of the ISC 96

Figure C.1: Prediction of the mole fraction of the species that can be measured inthe core at 5 atm.

C.2 Simulation of the airflow in the prototype camera

In the simulation of the prototype that is planning to construct, the objective was to

evaluated the residence time and the percentage of gas that leaves the core by the slits

with the aim to determine if this amount is significative and affect the concentration of

the species in the measurement with laser techniques.

Figure C.2 show the geometry of the prototype simulated in this case, that include parts

as the core holder, the chamber, the inlet, the outlet and the core.

The simulation in this case made in a structured mesh of 104000 nodes, consisted in the

injection of air at the core and only the fluid-dynamic was studied in this case.

Figure C.3 show the mesh used in this case, the boundary conditions used in this case

were: a mass flow inlet, wall conditions, interior conditions and outlet pressure. The

steady-state simulation consider the injection of air that pass by a pipe that is commu-

nicated with the core where the oil would stay in the test. The core that is slotted has

connection with the interior of the chamber through the slits and has a connection with

a pipe, that is the place through which the air can leave the chamber.

In Figure C.4 the residence time of the different pathways of the air in the chamber

was plotted. It was observed that in some cases, the air takes up 3 hours to leave the


Chamber

Outlet

Inlet Core

Core holder

Slits

Figure C.2: Chamber prototype geometry

Figure C.3: Mesh used in the simulation of the flow air in the chamber prototype


Figure C.4: Time of streamlines in the chamber.

chamber, being this time significative in comparison with the time of a test carried out

in this type of devices.

Although, the residence time is high in some cases the next parameter evaluated was

the percentage of the air that leaves the core by the slits. In this case the results showed

that only the 0.024 % of the inlet flow passed through the slits to the interior of the

chamber. This percentage is too low and decreases the possibilities of interference in the

laser measurements by the gases stuck in the interior of the chamber.

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