1
Experimental investigation of the diffusive properties of ternary
liquid systems
Thèse de doctorat présentée en vue de l’obtention du diplôme de Docteur en Sciences de l’Ingénieur
Quentin GALAND
Directeur
Professeur Stéfan VAN VAERENBERGH
ServiceChimie Physique E.P.
Année académique
2011-‐2012
ABSTRACT
A fundamental step in the further developments of comprehensive modelling of the diffusive processes in liquids requires the possibility of obtaining reliable and accurate experimental data of the diffusion and thermodiffusion coefficients of multicomponent liquid systems. In the present work, we perform an experimental investigation of the diffusive properties of binary and ternary liquid systems. Two experimental techniques, the ‘Open Ended Capillary’
technique and the ‘Transient Interferometric Technique’ have been developed.
Those techniques have been used for the experimental characterization of several systems composed of 1,2, 3,4-‐Tetrahydrnaphtalene, Isobutylbenzene and Dodecane at ambient temperature. Those particular species were selected as a simplified multicomponent system modelling the fluids contained in natural crude oils reservoirs.
For each of these techniques, experimental set-‐ups were designed, implemented and calibrated. The procedures for identifying the ternary diffusion coefficients from the measured compositions fields were studied in details.
The Open Ended Capillary Technique was applied under gravity condition to study isothermal diffusion binary and ternary systems. Difficulties related to a new procedure for interpreting the data collected at short times of the experiments are highlighted and its implication in the generalization of the technique for the study of multicomponent systems is discussed.
The Transient Interferometric Technique was used to perform an experimental study of three binary systems under gravity conditions. It was also applied for the investigation of ternary systems under microgravity condition in the frame of the DSC on SODI experiment, which took place aboard the International Space Station in 2011. The experimental results are reported and the analysis of the accuracy of the technique is presented. The TIT is the first technique ever providing accurate experimental measurements of the complete set of diffusion and thermodiffusion coefficients for ternary liquid systems.
REMERCIEMENTS
Il est véritablement important pour moi d’introduire quelques mots dans ce texte à l’attention de toutes les personnes qui m’ont soutenu dans la préparation de ce travail.
Un très grand merci à toi Stéfan pour m’avoir encadré tout au long de ce travail.
Merci pour nos discussions, pour tes idées, pour ta patience.
Un très grand merci à vous Julie, Papa, Maman, Robin et Corentin.
Un très grand merci également à toute l’équipe du MRC, avec qui j’ai eu le plaisir de travailler et qui m’avez tant appris.
Un très grand merci à tous nos partenaires au sein du projet DSC.
Quentin
TABLE OF CONTENT
I. INTRODUCTION
………..………...……1
II. DIFFUSIVE PROPERTIES IN LIQUID SYSTEMS II.1 Diffusive processes through the TIP
II.1.1 The entropy balance………...……….………9
II.1.2 The linear relations of TIP and the Fickian formalism………...………….…..….…………
12
II.2 Molecular diffusion in ternary systems
II.2.1 The Fickian formalism for ternary systems….………...…………16
II.2.2 Specific phenomena in ternary systems….……….…………...……
16
II.2.3 Properties of the Fickian diffusion coefficients in ternary systems………...….…....…
18
II.2.4 Onsager reciprocal relations for ternary diffusion coefficients………..…….…
20
II.3 Thermodiffusion
.……….…………..………...…..22
II.4 Diffusion coefficients measurement techniques
II.4.1 Stationary measurement techniques…...………...24
II.4.2 Transient measurement techniques……….………...
25
II.4.3 Indirect measurement techniques………..………...………...
30
II.4.4 Selected ground measurement technique…...………...………...
31
III. GROUND MEASUREMENTS OF DIFFUSION COEFFICIENTS IN BINARY AND TERNARY LIQUID SYSTEMS BY THE OEC III.1 Introduction
……….………...………..………...33
III.2 Materials & Methods
III.2.1 Principle of the OEC technique…….………..………...34
III.2.2 Hydrodynamic stability………...
34
III.2.3 Mathematical formulation of the OEC technique………...
39
III.2.4 Fitting procedure……….………...
44
III.2.5 Experimental……….………...
46
III.3 Results and discussion
III.3.1 Calibration experiments……….………...
53
III.3.2 Analysis of binary OEC results……….……….………...
58
III.3.3 Analysis of ternary OEC results ……….………...
65
III.4 Conclusion
………..……..………...71
IV. MEASUREMENT OF SORET AND DIFFUSION COEFFICIENTS IN LIQUID SYSTEMS BY A TIT IV.1 Introduction
………...………..……….…...73
IV.2 The TIT technique
IV.2.1 Principle of the TIT…..……….……….……...74
IV.2.2 Application field of the TIT………..……….……...
76
IV.3 Experimental TIT set up
IV.3.1 Experimental cell………..……….……….……….……...78
IV.3.2 Thermal regulation……….………..…….……...
78
IV.3.3 Mach-‐Zehnder interferometer………..…….……...
79
IV.4 Mathematical description of the TIT
IV.4.1 Soret phase………..……….………...………..…….……...81
IV.4.2 Diffusion phase………..……….………...………...…….……...
83
IV.4.3 Optical signals interpretation………..….………...……….…..…….……...
85
IV.4.4 Estimation of the Soret coefficients………..…..….………...………..…….……...
87
IV.4.5 Fitting procedure for the estimation of the diffusion coefficients………..……...
88
IV.5 Image processing for the TIT
IV.5.1 Complex representation of a plane wave………..………..….……...90
IV.5.2 Interference pattern………..………..….……...
91
IV.5.3 ‘Fourier image processing routine’………..………...
92
IV.5.4 Scope of the Fourier interferometry…..………...
95
IV.5.5 Unwrapping………..………..………...
95
IV.6 Optical sensitivities for the TIT
IV.6.1 Nomenclature.………..……….………..………...96
IV.6.2 Contrast factors……….……...……….…….…...
97
IV.6.3 Experimental determination the ni,T………..………...
100
IV.7 Results and discussion
IV.7.1 Thermal analysis of the TIT cell………..………...……….……...
102
IV.7.2 ni,T mesurements………..……...
104
IV.7.3 Contrast factors measurement………..………..……...
108
IV.7.4 Soret and diffusion coefficients measurements………..………...……...
116
IV.8 Conclusion
………..………..………..………...……….………...……...125
V. THE DSC ON SODI EXPERIMENT
V.1 Introduction
………..……….……….…...………...127
V.2 Standard microgravity measurements of diffusion and Soret coefficients
129 V.3 Systems investigated in the DSC experiment
V.3.1 General……….……….………...………...130
V.3.2 Strategy for the choice of the compositions of the DSC systems. ………...
132
IV.3.3 Selected systems for the DSC experiment…………...………...……...
136
V.4 Materials & Methods
V.4.1 DSC experimental set up………...………...…...138
IV.4.2 Experimental procedure………...…...
143
V.4.3 Phase shifting interferometry and image processing……...………...
148
V.5 Ground Results
V.5.1 Thermal analysis of the DSC cell………...………....………...151
V.5.2 TIT with the DSC cell………...……...
152
V.6 ISS Results
IV.6.1 DSC Checkout runs results………..………...……...154
V.6.2 DSC on orbit optical calibrations………..……….…...……...
158
IV.6.3 Collected scientific data……….…..………..…...……...
163
V.6.4 Thermal analysis………..………..………..…...……...
167
V.6.5 Binary Soret and diffusion coefficients..………..………..…...……...
171
V.6.6 Ternary Soret and diffusion coefficients………...…...……...
178
V.7 Conclusion
………...…...……...185
VI. CONCLUSION
………...…...……...187
VII. REFERENCES
………...…...……...195
1
I. INTRODUCTION
The objective of the present work is the study of molecular diffusion and thermodiffusion in multicomponent liquid systems.
Molecular diffusion, often referred as isothermal diffusion, describes the species distribution changes resulting from gradients of chemical composition in the system. In the simplest case, in binary systems, diffusion explains the mass flux from a region of higher concentration to one of lower concentration and results in gradual mixing of the components in the system if no other thermodynamic force tends to separate them.
An applied temperature difference is an example of such a thermodynamic force and the observed tendency of the components to segregate is named thermodiffusion.
Both these processes play an important role in a variety of natural phenomena as well as in industrial applications and there are numerous scientific studies dealing on them since several centuries. They are described by introducing the appropriate number of diffusion and thermodiffusion coefficients for each of the molecular species of the system. These quantities and their main properties are established in details in section II.1 to II.3 where we also describe the different formalisms used to model the diffusive properties in binary and ternary systems.
The diffusion coefficients are relatively well known for binary systems as attested by the many reports found in literature on the subject of their experimental determination. Different experimental techniques exist and provide mostly fairly consistent measurements. The different experimental techniques used for the binary systems measurements are described in section II.4.
The analysis of the experimental results in binary systems reveals that the study
of diffusion brings many interesting information about the behaviour of
molecules in their chemical environment, about the interactions between the
molecules in liquid phase and about dissipation. For instance, the diffusion
coefficient in general increases when temperature increases. Diffusion depends
2
on the size and shape of molecules. The diffusion coefficients of macromolecules are often of the order of 10
-‐10m
2/s, that is one order of magnitude lower than the coefficients of small molecules. This property has been extensively studied and several correlations have been established to obtain the diffusion coefficients in dilute liquid mixtures. For instance, the correlation of Wilke and Chang is very often used in chemical engineering. It shows that the diffusion coefficients at infinite dilution can be obtained from a very simple relation, involving the temperature, viscosity and the molal volume. Diffusion also strongly depends on the molecular interactions. Several correlations have been proposed to predict the diffusion coefficients in concentrated liquid systems. In most of them, the principle is to express the diffusion coefficients in concentrated systems as functions of the coefficients in the corresponding diluted systems. Some of these correlations allow obtaining very satisfactory results for regular solutions. When the interactions between molecules are more important, these correlations must be coupled to thermodynamic models. It appears that in the present state of the art, the set of properties observed in binary diffusion are far from embedded in a specific theory. We believe that the study of multicomponent systems will reveal new evidences and will significantly contribute to the development of a comprehensive theoretical framework.
Diffusion in multicomponent liquid systems is a research area now in booming.
The study of ternary systems is of great scientific interest as it is the first step toward a better understanding of the properties of complex systems. Introducing a third component allows the study of thermodynamic couplings; in the present case, the coupling appears between similar processes: the diffusion of each of the components. In other words, in multicomponent systems, the mass flux of a component is induced by its own concentration gradient, but also by concentration gradient of the other components. The theory shows that generalizing Fick law to multicomponent systems introduces new behavior in the system, as reverse diffusion.
Diffusion in multicomponent system is described with a matrix of diffusion
coefficients. There exist very few publications that report the experimental
determination of the complete matrix of the diffusion coefficients for ternary
3
liquid systems. To the best of our knowledge, the full set of diffusion coefficients has never been measured in liquid systems involving more than three components. Indeed, the experimental study of multicomponent liquid systems involves considerable challenges from several points of view. First, the analytical techniques allowing observing the evolution of the chemical composition in multicomponent systems with sufficient accuracy are scarce and are difficult to apply to diffusion experiments. Then, the mathematical description of multicomponent diffusion also introduces a major challenge. It appears that each of the diffusion coefficients describing those systems cannot be observed individually. The analysis of experimental data to retrieve all the elements of the diffusion coefficients matrix requires implementing complex mathematical procedures and limits the precision on the identification of the coefficients.
Finally, ground measurements of the diffusive properties of liquid systems are delicate as it is difficult to avoid completely the convective mass transfer in the liquid in the presence of gravity. This difficulty can easily be circumvented in binary systems. For multicomponent, this question is much more demanding. A theoretical analysis shows that diffusive instabilities may occur in the system but the analysis itself of the hydrodynamic stability of the system during an experiment requires knowing precisely the diffusion coefficients.
In a similar way, the study of thermodiffusion allows studying the coupling between two different processes: molecular diffusion and heat diffusion.
The study of these couplings and of the phenomenological equations used to
describe them is central issues in the linear Thermodynamic of Irreversible
Processes (TIP). Experimentally, the study of thermodiffusion in binary liquid
mixtures is very problematical. The measurements of thermodiffusion
coefficients requires applying a temperature difference to the liquid and it is well
known that uncontrolled convective currents may appear in the liquid and
disturb the experiment. Many reports about the experimental determination of
the thermodiffusion coefficients in binary liquid mixtures can be found in
literature, but the discrepancies between the obtained results are sometimes
very important. Convection currents are sometimes difficult to detect and some
biased results are published. When the thermodiffusion coefficient of the system
4
is negative, the denser component migrates to the hot side of the system. In this case, it is also very difficult to perform a convection free experiment. Again, the study of multicomponent systems under gravity condition is even more complex from the experimental point of view.
A part of the present work is performed in the frame of an international research program. To overcome the difficulties in measuring the diffusive properties of liquid systems under gravity conditions, the DSC (Diffusion and Soret Coefficients) was performed under microgravity conditions. The scientific community considered the topic with interest and many partners, which includes the European Space Agency, several university research centres around the world as well as industrial partners, have come together to develop the study of the diffusive properties of liquid systems.
The original objectives of the DSC project are the experimental investigation of the thermodiffusion and molecular diffusion coefficients of ternary liquid systems. Indeed, initially, the DSC project was born from the collaboration between several academic research centres with partners from the oil industry.
The primary objective of the experiment is the characterization of the diffusive properties of a system that models the fluids contained in a natural oil reservoir.
Crude oil is essentially composed of paraffinic, aromatic and naphtenic hydrocarbons. Three chemical species were selected to represent three major families of compounds found in crude oils: 1,2,3,4 Tetrahydronaphtalene (referred as
THN) for the family of the naphtenic compounds, Isobutylbenzene(referred as IBB) for the aromatic compounds and Dodecane (referred as C
12) for the aliphatic compounds. A series of one binary system and five ternary systems of these three components has been selected for the first DSC experiment.
After consultation between the partners involved in the DSC project, several objectives were defined, among with:
•
the experimental determination of molecular diffusion coefficients and thermodiffusion coefficients in ternary liquid mixtures under microgravity conditions
The DSC results constitute the first experimental measurement of the
diffusion coefficients in ternary liquid systems with strict convection free
5
conditions. As such, they serve as benchmark results and will be used to validate the experimental techniques developed on ground.
•
the development and calibration of ground based measurement techniques for diffusion and thermodiffusion coefficients according to flight standards
The experiments performed under microgravity conditions are the results of an expensive, long and tedious work. For all these reasons, only a limited number of experiments can be organized, and only a few systems can be investigated. It is important to develop in parallel ground based measurement techniques for the measurement of the diffusive properties in liquid systems. These techniques should achieve faster experimental results for other systems.
•
the establishment of mixing rules for the diffusive properties of multicomponent systems
The study of ternary systems in microgravity also aims to develop mixing rules, both for diffusion and thermodiffusion coefficients. The idea of mixing rules is to establish predicting rules for thermodynamic quantities in complex systems (in the present case in ternary systems) from the corresponding quantities in simpler systems (the corresponding binary systems). The objective is to obtain mixing rules that could be generalized to describe more complex systems, involving four or more components.
The first step in the study of these rules requires obtaining accurate and precise experimental data of the diffusion and thermodiffusion coefficients in ternary systems.
•
the description and prediction of the molecular properties of multicomponent systems through thermodynamic and molecular dynamic models
Experimental data on diffusion and thermodiffusion coefficients allow elaborating and testing thermodynamic and molecular dynamics models.
These models could also help in describing other properties of the investigated system, such as viscosity, density, interactions parameters.
Our team in the Microgravity Research Center is involved in achieving the three
first mentioned objectives and is in charge for preparing, monitoring and
6
analysing the results of microgravity experiment. The DSC program involves several experiments. All these experiments will take place inside the SODI facility that was uploaded to the International Space Station in 2008. The DSC experiment took place in the end of 2011. Other similar experiments are planned and will be performed in the coming years.
The present thesis has been realized in the frame of the DSC project. Two main objectives were defined:
•
Developing ground measurement techniques for the experimental determination of the diffusion and Soret coefficients of ternary systems.
•
The contribution to the preparation, the mission and the interpretation of the experimental data of the DSC experiment. Also, the first experiment carried out in this thesis is the standard for following similar space missions.
Based on literature review, we selected the Open Ended Capillary Technique (OEC) to perform ground measurements of molecular diffusion coefficients. This technique is a well-‐known technique and has proven to be reliable in the study of binary systems. The principle of the OEC is to create a concentration gradient in a liquid system by placing in contact two liquids with different chemical compositions. One of the liquids is introduced in capillary tubes, which are immersed in a bath of the second liquid. Over time, the tubes are one by one extracted of the bath to analyze the chemical composition of the liquid that they contain. This is the main reason that led us to the choice of this particular experimental technique: the OEC set-‐up allows retrieving samples, and therefore to perform the composition analysis with ex situ tools. For ternary systems, the chemical composition analysis can be performed by coupling density and refractive index measurements. For some quaternary or more complex systems, quantitative composition analysis can be obtained by
1H-‐NMR. The OEC can therefore in principle be extended to the study of multicomponent liquid systems.
An OEC set up was designed. The principle of the technique is simple but its
implementation required the analysis and the tuning of several experimental
7
parameters. A new approach in the analysis of the experimental data has been proposed in order to decrease the experimental time from several weeks to a few days. The modelling of the experiment and the procedure for the analysis of the experimental data have been generalized for the study of ternary systems. All these aspects are described in section III.2.
The technique has been studied in details and calibrated through the study of water-‐ethanol binary systems. It was then applied to the study of binary and ternary systems. Experimental results are reported and important observations regarding the data interpretation are discussed in section III.3. Based on the experimental data, we observed that the precision of the OEC technique does not allow a complete characterization of ternary systems. These results led us to investigate another experimental technique.
We refer to this technique as ‘Transient Interferometric Technique’ (TIT). The TIT is an original technique for the experimental determination of both the thermodiffusion and the diffusion coefficients of liquid mixtures. The principle is to make use of the thermodiffusion effect to induce a separation of the chemical components, which is then used as the initial condition to observe molecular diffusion. A run of the experiment then consists of two phases. In the first, a temperature difference is applied to a liquid layer and the Soret coefficients are quantified by measuring the chemical separation of the components when the system reaches a steady state. During the second phase, the temperature gradient is removed and the isothermal diffusion coefficients are determined by observing the relaxation in the liquid by molecular diffusion.
The experimental set-‐up used for the TIT is described in section IV.2. The measuring cell is placed in an interferometer, which allows observing the temporal evolution of the complete 2D chemical composition fields with a high resolution. The measuring cell and the thermal regulation system are also described.
We studied the three binary systems, composed of THN, IBB and C
12, with mass
fractions of 50 percent’s of two of the components. These systems were selected
with the purpose to complement the results obtained on the systems studied in
the DSC experiment.
8
The required experimental procedures, mathematical modelling of experimental runs, data processing procedures and interpretation scheme for the TIT have been developed, both for binary and ternary systems. These aspects are detailed in section IV.4. The optical processing procedures instead are briefly described in section IV.5.
The TIT also requires measuring certain optical characteristics of the studied liquids in preliminary experiments. Two additional experimental devices have been realized to that purpose and are described in section IV.6.
Experimental results obtained with the TIT for binary systems under ground conditions are reported and discussed in section IV.7.
The TIT has also been applied for the study of ternary system during the DSC experiment. All outcomes of the DSC experiment are presented separately in section V.
In this experiment, one binary system and a series of five ternary systems composed of THN, IBB and C
12were investigated. The reasons for choosing those particular systems and their characteristics are provided in section IV.3.
The experimental set-‐up used for the on orbit experiment was designed and produced by an industrial partner in order to meet the ISS standards. It is described in section V.4. It is different from the set up used on ground for the TIT. We have studied its peculiarities and derived some important consequences to be taken into account in the analysis of the experimental data. In the microgravity campaign, a series of fifty experimental runs were performed. We document in the first part of section V.6 the course of the ISS measurement mission and a series of difficulties that arose and how they have been solved. The acquired experimental data were stored on hard drives and will be routed to ground in the coming months. However, for each run, a few images were downloaded in order to monitor the functioning of the experiment. The analysis of this partial data already allows obtaining an estimate of the measured Soret and diffusion coefficients for ternary systems, as detailed in section V.6.
All the results obtained in this work are summarized and allow us to draw conclusions in section VI.
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VI. CONCLUSION
In the present work, we conducted an experimental study of the diffusive processes in liquid systems.
Using linear Thermodynamics of Irreversible Processes (TIP), we have studied the mathematical formalisms used to describe molecular diffusion and thermodiffusion in binary and ternary systems. Linear TIP shows that multicomponent systems possess properties that do no exist in binary systems.
These result from the couplings that occur between the diffusion fluxes of the different components. These couplings can already be observed in ternary systems, since they appear as soon as more than two components are diffusing.
They also appear explicitly when generalizing the Fickian diffusion equations to ternary systems. In the Fickian formalism, isothermal diffusion in a ternary system is characterized by a matrix of four diffusion coefficients. Linear TIP shows that only three of those coefficients are independent. Indeed, it is possible to write an Onsager reciprocal relation and infer a link between the ternary Fickian coefficients. The expression of this equation has been established.
After a literature review, we selected the Open Ended Capillary (OEC) technique
to perform an experimental study of the diffusion coefficient of ternary liquid
systems. Indeed, this technique presents several fundamental qualities. The
modeling of the processes is quite simple and one-‐dimensional diffusion
equations provide an excellent description of the experimental data. Moreover,
the OEC is based on an
out-‐situ analysis of the chemical composition of thesamples. This feature is important for the generalization of the technique to the
study of multicomponent systems. We completed the design of an OEC set-‐up. An
original gravity-‐flow system was proposed and optimized to control as
accurately as possible the boundary condition of the diffusion equations during
the experiments. Different geometric characteristics of the capillary tubes have
been tested. We have shown that the calibrated set-‐up accurately reproduces
binary experimental results of the literature. The main drawback of the
technique is the duration of the experiments that reaches several weeks. We
developed a new interpretation scheme of the OEC results to obtain the diffusion
188
coefficients from the data collected at short times of the experiments. These developments have not led to successful results. They however allowed us to highlight a fundamental difficulty in the use of the OEC technique for the study of liquid systems: the imperfect modeling of the boundary condition significantly affects the interpretation of the OEC results. At the beginning of the experiments, while the composition gradient is essentially located close to the open end of the tubes, the boundary condition is not perfectly controlled. It follows that a diffusive concentration profile develops in the bath at the outlet of the tubes. We called this phenomenon a positive
ΔL effect: the length of the tubes in thediffusion equation is slightly larger than the actual length of the tubes. The development of the composition profile accumulates a delay and the data analysis leads to underestimate the diffusion coefficients. Later in the experiments, this effect fades thanks to the progressive distribution of the composition gradient lower in the tubes. When only the long time data are considered, this effect can be neglected and the OEC technique provides measurements of the diffusion coefficients of binary systems with accuracy smaller than four percent.
The technique was adapted for the study of ternary systems. For these experiments, the OEC was coupled with proton-‐NMR compositional analysis. We have developed an effective interpretation scheme to obtain the ternary diffusion coefficients from the measured compositions. In particular, we showed that the fitting procedure used to identify the ternary coefficients requires limiting the space of the mathematically admissible solutions to obtain a convergence of the optimization algorithm to a set of physically admissible coefficients. The mathematical expression of the standard deviations on the estimated coefficients was established. In doing so, we showed that the OEC technique allows identifying the diagonal diffusion coefficients while there remains a strong incertitude on the values of the cross coefficients. The effects of the cross diffusion coefficients are difficult to observe by the OEC technique.
This is probably due to the averaging of the composition profile that is
performed when the liquid of the tubes is sampled and to a slight positive
ΔLeffect at short times of the experiments.
189
The obtained value of the diffusion matrix was used to calculate the Onsager coefficients and we observed that the Onsager reciprocal relation for the ternary diffusion coefficients is verified very satisfactorily.
In complement to the OEC study, another experimental technique was investigated: the Transient Interferometric Technique (TIT). This technique involves two steps, in which both the Soret and diffusion coefficients are measured. It is based on the observation of the complete 2-‐dimensional composition fields in the liquid through an interferometric technique.
Two different experimental set-‐ups were developed for the application of this technique: a ground set-‐up has been created to obtain the diffusive properties of binary systems under gravity conditions and a flight set-‐up was developed to study ternary systems under microgravity conditions in the frame of the DSC experiment, which took place aboard the International Space Station at the end of 2011.
The DSC program was born from the collaboration between several academic research centres with partners from the oil industry. The primary objective of the experiment is the characterization of the diffusive properties of a system that models the fluids contained in a natural oil reservoir. The systems investigated in this experiment are composed of 1,2,3,4-‐Tetrahydronaphtalene, Isobutylbenzene and Dodecane; these particular chemical species were selected to represent three major families of compounds found in crude oils. In the first DSC experiment, one binary system and a series of five ternary systems were investigated. The chemical compositions of these systems were selected in order to investigate mixing rules, both for molecular diffusion and thermodiffusion coefficients.
The ground experimental set-‐up was used to characterize the three binary systems composed of 50 percent of each of these three molecular species.
The mathematical modeling of the diffusive processes involved in the TIT has
been established in details both for binary and ternary systems. The fitting
procedure to obtain the binary and ternary diffusive properties has been
developed according to the method used in the OEC technique processing. As
190
previously, the fitting takes into account the constraints required to obtain a convergence to a physically acceptable ternary diffusion matrix.
The interpretation of the TIT data requires knowing the optical sensitivities of each investigate system (these are the partial derivatives of the refractive indexes with respect to temperature and to the mass fractions of the components). Two experimental set-‐ups were developed to perfrom the experimental determination of these quantities. They were measured for the three binary systems and for all the DSC systems. For ternary systems, a sensitivity analysis on the measured contrast factors highlighted that the amplification factor strongly depends on the choice of the reference component in the contrast factors matrix. The contrast factors matrix leading to the smallest amplification factor must be used for the data analysis.
The characterization of the temperature field in the ground-‐measuring cell has been obtained experimentally. A linear temperature field was observed in the central part of the cell. We observed that lateral heat losses cause slight deformations of the temperature field close to the walls of the cell. These deformations are very small and do allow performing diffusive experiments in binary systems without observing convection in the liquid. The obtained results show that the TIT allows measuring the binary Soret coefficient with accuracy smaller than 1 percent, and the binary diffusion coefficients with accuracy smaller than 3 percent. These results clearly establish that the TIT is a very precise technique.
During the DSC mission, the measuring instrument has been recalibrated to improve the quality of the interferometric data. The experimental operations were monitored throughout the mission and the planning of the experiments was adapted to optimize the acquisition of valuable scientific data under microgravity conditions.
The major part of the experimental data acquired during the experiment was
stored on hard drives and will be routed to ground in the coming months. A
partial set of the data was transferred via telemetry in order to monitor the
functioning of the experiment during the mission and is already available. These
data represent less than 10 percent of the total DSC data. They were used to
characterize the thermal performances of the flight experimental set-‐up and to
191
obtain a preliminary assessment of the diffusive properties of the investigated system.
The temperature field in the measuring cell was characterized experimentally.
This analysis shows that the design of the flight-‐measuring cell induces important heat losses through the lateral walls of the cell. The cell being symmetrical, this means that the temperature field is also bended along the direction of the optical axis of the interferometer. This effect induces a deformation of the composition field with the thermodiffusion of the components. A complete 3-‐dimensional characterization of the temperature field must be performed upon reception of the complete data of the experiment and should be taken into account for the computation of the diffusive properties.
An important remark was formulated after analyzing the sensitivity of the TIT to the contrast factors. We observed high amplification factors for some of the DSC systems. The fitting procedure to obtain the ternary diffusion coefficients should focus directly on the optical signals rather than on the composition variables, as usually performed in literature. This method avoids multiplying the measurement noise by the amplification factor prior to the fitting.
The preliminary assessment of the diffusive properties indicates that, on the basis of the incomplete data set, the accuracy on the binary Soret coefficient, binary diffusion coefficient, the smallest ternary Soret coefficients and on the ternary diagonal diffusion coefficients is respectively of 1, 10 and 20 and 50 percent. The accuracy on the ternary cross diffusion coefficient is very low. The precision on these coefficients will be significantly improved when performing a refined analysis of the complete DSC data set. It seems reasonable to expect accuracy better than 5 and 10 percent respectively on the diagonal and cross ternary diffusion coefficients.
The general conclusions of this work are:
•
Linear TIP allows writing the Onsager reciprocal relation for multicomponent systems. These relations can be used to obtain a qualitative validation of multicomponent diffusion experiments.
•
The OEC technique can be used for the experimental investigation of the
diffusion coefficients of binary liquid systems. Calibration experiments
192
allow identifying empirically adequate experimental parameters of the experimental set-‐up. The imperfect modelling of the boundary condition was highlighted and disturbs the interpretation of the data collected during the early times of the experiments. Accordingly, a
ΔL effect isidentified at short times. The influence of this effect decrease in time and becomes negligible at long times of the experiment. The long time interpretation of the experimental data allows identifying accurately the diffusion coefficients of binary systems.
•
Coupled with
1H NMR measurements, the OEC technique can be applied for the study of multicomponent systems. However, the
ΔL effect and theaveraging of the composition during the sampling of the liquid of the tubes decrease the sensitivity of the technique in the study of ternary systems. At the present stage of our research, only the diagonal ternary diffusion coefficients can be clearly identified. Further developments should be made to the technique. A realistic description of the boundary condition could be obtained from the numerical modelling of the short times of the experiment. An additional approach could be used to increase the sensitivity of the technique to multicomponent diffusion: the study of one single system could be realized by performing two or more complementary experiments, each of these experiments starting from different initial conditions.
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In the mathematical analysis of ternary diffusion experiments, the mathematical constraints resulting from the diagonalization of the system of diffusion equation must be taken into account for the fitting procedure.
An efficient method is to impose that the system reaches a stationary state at the end of the diffusive processes.
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The experimental study of the diffusive properties of multicomponent systems is always based on a parametric identification of the coefficients.
The expressions of the standard deviations of the fitting procedure for
ternary diffusion experiments have been established carefully. The
computation of those quantities allows obtaining accurate information to
evaluate the sensitivity of the experimental technique to each individual
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diffusion coefficients. They can be used to validate any experimental technique for multicomponent diffusion.
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We demonstrated the accuracy of the TIT in the experimental determination of both the Soret and diffusion coefficients for binary liquid systems. This technique requires a careful thermal design of the measuring cell.
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We performed the experimental determination of the temperature and composition derivatives of the refractive indexes for several binary and ternary systems composed of 1,2,3,4-‐Tetrahydronphtalene, Isobutylbenzene and Dodecane. For ternary systems, we performed a sensitivity analysis of the contrast factor matrix. The contrast factor matrix leading to the smallest amplification factor must be selected for the analysis of TIT data.
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A preliminary analysis of the data collected during the DSC experiment indicates that the TIT allows measuring precisely both the Soret and diffusion coefficients of ternary systems. As soon as the complete set of data of the experiment will be available, a more refined analysis, involving the accurate description of the 3-‐dimensional temperature field and the compensation volume chamber of the measuring cell will be further developed. At the end of this analysis, all the Soret and diffusion coefficients of the investigated systems will be identified within accuracy lower than 10 percent. The TIT is the first technique ever that can achieve such results.
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These coefficients will be used to calibrate the ground-‐based measurement techniques.
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These coefficients will be used to determine suitable conditions to observe the phenomenon of reverse diffusion.
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The TIT should be used under gravity-‐conditions to investigate other ternary liquid systems. All these experimental data should be collected in a database.
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