International Conference on Gas Hydrates (ICGH) (6th : 2008)

STUDY OF THE KINETICS OF FORMATION OF TRICHLOROFLUORO-METHANE HYDRATES AND METHANE HYDRATES IN WATER-IN-OIL… Dalmazzone, Didier; Hamed, Néjib; Clausse, Danièle; Pezron, Isabelle; Luong, Anh-Tuan Jul 31, 2008

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Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.  STUDY OF THE KINETICS OF FORMATION OF TRICHLOROFLUOROMETHANE HYDRATES AND METHANE HYDRATES IN WATER-IN-OIL EMULSION BY MICROCALORIMETRY Didier Dalmazzone, Néjib Hamed UER de Chimie et Procédés Ecole Nationale Supérieure de Techniques Avancées 32, boulevard Victor, 75739 Paris cedex 15 FRANCE Danièle Clausse, Isabelle Pezron, Anh-Tuan Luong Département Génie des Procédés – UA TIMR Université de Technologie de Compiègne B.P. 20529, 60206 Compiègne cedex FRANCE Christine Dalmazzone Institut Français du Pétrole 1-4, avenue de Bois Préau, 92852 Rueil Malmaison cedex FRANCE ABSTRACT Differential scanning calorimetry has been used to study the kinetics of formation of clathrate hydrates in the systems water-CCl3F and water-CH4, in which the water phase was dispersed in an oil phase in the form of an emulsion. CCl3F hydrates were formed at ambient pressure and constant temperatures of -10, -15 and -20 °C. The results showed that the crystallization of both ice and hydrate are in competition at the lowest temperature, whereas only hydrate is formed at 10 or -15 °C. CH4 hydrates were studied using a high-pressure DSC in the range 10 to 40 MPa, at various temperatures. At high driving force, the heat peak related to the formation of hydrates has a regular and symmetric shape, and its height and width depend on the gas pressure and sub cooling degree. At near equilibrium conditions, hydrate formation can be delayed by several hours, but is still clearly observable. A model based on crystal growth theory coupled with a statistical law to take into account the germination in micro sized droplets is proposed. Keywords: gas hydrates, kinetics, emulsion, drilling fluid, DSC NOMENCLATURE A area below the heat flow signal [mJ] C methane concentration [mol.l-1] d number of dimensions of the crystallization process G linear growth velocity [m.s-1]   K kg n n0  constant in Avrami-Erofeev model kinetic constant for crystal growth [m.s-1] amount of unconverted water [mol] initial amount of water [mol]  Corresponding author: Phone: +33 1 45 52 63 16 Fax +33 1 45 52 83 22 E-mail:  Ndrop P T t Vm    Hdiss T ()           number of droplets in emulsion sample pressure [MPa] temperature [K, °C] time [s, min] hydrate molar volume [m3.mol-1] adjustable parameter in AvramiErofeev model enthalpy of dissociation [kJ/mol] sub-cooling degree [K] induction time distribution law hydration number of hydrate standard deviation of induction time distribution [s] time of induction [s] average time of induction [s] rate of conversion  INTRODUCTION Studying the formation of gas hydrates in waterin-oil emulsion is of interest for two main purposes. First, there are industrial applications in which the formation of hydrates in emulsion might lead to severe safety and economic troubles. In previous works, we demonstrated that, when the required thermodynamic conditions are reached, gas hydrates readily crystallize in the dispersed aqueous phase contained in offshore drilling fluids [1]. The occurrence of gas hydrate formation in deep offshore drilling operations has been described [2] and hydrate inhibition in drilling fluids is the object of many investigations [3-5]. Another application of hydrates in emulsion has been proposed [6, 7] in order to facilitate the study of gas hydrate kinetics of formation by taking advantage of the dispersion of the water phase. Because of its stochastic behavior, hydrate nucleation requires a great number of experiments to allow statistical treatment. In a water-in-oil emulsion, each water droplet is an isolated microsized sample, in which the nucleation takes place independently of the remainder of the population. Thus, detecting the hydrate formation in an emulsion sample would provide a statistical response from one single experiment. Several techniques may be used to follow the hydrate formation in emulsion, among which dielectric spectroscopy [8] and differential scanning calorimetry (DSC). The later has long been recognized as particularly suitable for studying crystallization in emulsion [9, 10], and it has been applied to model hydrate investigations [11, 12].  The main advantage of using model hydrates is that they form at ambient pressure. Another important feature is that, unlike methane hydrate, model hydrates such as tetrahydrofurane or trichlorofluoromethane (CCl3F) hydrates have the same structure (sII) than the hydrates encountered in natural processes, which are usually formed from natural gas. DSC studies have been undertaken on CCl3F hydrate, which is known to melt at +8.5 °C, in order to investigate the kinetics of formation of hydrates in water-in-oil emulsions at atmospheric pressure [12]. DSC coupled with X-ray diffraction experiments [13] have shown that during a steady cooling from +20 °C to -60 °C, ice crystallized within the micro sized droplets at approximately -40 °C. Hydrates were not detected during cooling but they formed on subsequent warming, simultaneously with ice melting, and dissociated at approximately 5 °C It was observed in previous studies that dispersed water may crystallize above -40°C when the emulsion is maintained in isothermal conditions between -40 °C and 0 °C [9]. Hydrate formation is expected to exhibit similar behavior. Nevertheless, there is a lack of data to choose the temperature, since the formation of CCl3F hydrate has not yet been detected during a steady cooling in the above described conditions. As ice crystallizes around 40 °C in micro sized emulsion, this temperature is considered as a lower limit if one wants to avoid competitive crystallization of both solids. In the present contribution, the results obtained at -10°C, -15°C and -20°C will be presented. Controlled pressure DSC was first used a few years ago to measure the thermodynamic stability of gas hydrates in water-in-oil emulsion [14, 15], and high-pressure DSC has then been specially developed [16] to allow investigating gas hydrates at pressures close to the hydrostatic pressure encountered at deep ocean bottom. At the former International Conference on Gas Hydrates [6], we presented the first results obtained using this new apparatus in the investigation of the kinetics of formation of methane hydrates in a deep offshore drilling fluid. In this paper will be presented more complete results obtained at low and high driving force conditions. Two models, developed to represent the hydrate kinetics of formation in both types of experiments, will be described.  EXPERIMENTAL CCL3F hydrates The emulsions were prepared using deionized water containing 3 wt. % NaCl as the dispersed phase, Exxsol D80 as the continuous phase, and Berol 26 as non-ionic surfactant. Exxsol D80 is a mixture of aliphatic and cycloaliphatic hydrocarbons with 10-13 carbons. Berol 26 is a commercial name for tetraoxyethylene nonylphenyl ether (C9-Ph-(OEt)4). The concentration of Berol 26 was 4 vol. % with respect to the total oil phase (Exxsol D 80 and CCl3F). The proportions of chemicals used were chosen to fit the theoretical stoechiometry of CCl3F hydrate: CCl3F.17 H2O. The aqueous solution was first dispersed in oil at room temperature using a homogenizer Polytron PT 3000 at 10 000 rpm during 10 min. Then, the emulsion was cooled down to 0ºC. Finally, liquid CCl3F was added to the emulsion under gentle stirring in order to avoid emulsion destabilization and CCl3F evaporation. The aqueous phase to oil phase ratio of the final mixture was 58:42 (wt/wt), 60:40 in volume. Thermal analysis was performed using a Setaram DSC 111 calorimeter. 30µl samples were taken from the emulsion and introduced in several aluminum vessels. One of the vessels was immediately placed into the calorimeter, the temperature of which had been previously set to the desired value. The energy release due to the formation of solid in the dispersed water phase was recorded versus time at constant temperature for a given duration period, and then the sample was heated in order to record the melting of the solid phases formed. Meanwhile, the remaining vessels were placed into a thermostat in order to avoid locking up the calorimeter during large periods of time. From time to time a cell was taken from the thermostat and introduced into the calorimeter, the temperature of which being the same as the thermostat one. The cell was then immediately submitted to a heating program to record the melting of the solid phases formed during the stay in the thermostat. CH4 hydrates Deep off shore drilling fluids were used for the formation of methane hydrates. Each fluid is an emulsion of a solution of CaCl2 dispersed into an oil phase that contains various types of solids in suspension. The compositions of the fluids are given in Tables 1 and 2. The brine-to-oil ratio was 70%/30% in volume and the concentration of  CaCl2 in water varied from 10 to 20 % in weight as shown in Table 2. The experimental procedure has been described in [7] and [16]. A µDSCVII differential microcalorimeter from SETARAM (Fig. 1), fitted with two 0.5 cm3 high-pressure vessels having a maximum operating pressure of 40 MPa, was used. An ISCO 100DM syringe pump provided gas feeding with constant regulated pressure and the pressure was controlled using a 0-70 MPa gauge from Druck. The temperature range of operation of the DSC is 223 K to 393 K.  Phase  Compound Base oil Fluid loss Water-inreducer oil Wetting agent emulsion Emulsifier CaCl2 brine Lime Lipophilic clay Solids Weighting agent  Amount 800 ml (642 g) 19.26 g 5.78 g 13.48 g 200 ml 2.60 g 11.30 g 385.00 g  Table 1. Composition of the drilling fluids  Mass [g] Fluid #1 Fluid #2 Fluid #3 water 195.4 192.3 188.7 CaCl2 21.7 33.9 47.2 CaCl2 wt% 10 15 20 Table 2. Composition of the brine  Figure 1. High pressure DSC  RESULTS AND DISCUSSION Model hydrates The warming thermograms obtained (Fig. 2) after staying at –10°C and –15 °C show progressive melting signals, the apex of which appear around 8 °C (hydrate melting temperature), but no ice melting peak around 0°C. We thus concluded that the sole hydrate was formed during the isotherm period at either -10 °C or -15 °C. The amount of hydrate may be deduced from the areas of the melting signals [13]. It was found that 62% of the maximum theoretical mass of hydrates that could be formed at -10 °C, and 75 % of the amount that could be formed at -15 °C, were actually obtained. These discrepancies could come from incomplete hydrate formation, but also from difficulties in determining the baseline for signal integration. Indeed, as hydrate melting starts at the very beginning of the heating, the correct delimitation of the signal is subject to uncertainties. Nevertheless, these results show that the amount of hydrate formed during a given period of time (90 minutes in all experiments reported) at a given temperature decrease as that temperature gets closer to the hydrate-liquid-vapor equilibrium. Concerning the experiment performed at -20°C, it appears that the melting signal shape is different. We attribute the first signal at around 0°C to ice melting followed by the hydrate dissociation. Therefore during storage at -20°C, both ice and hydrate are formed by under cooling breakdown. From these experiments, it appears first that it is possible to obtain the hydrate formation versus time at a fixed temperature without the ice formation. This situation is different from the one  obtained during a steady cooling and heating cycle, which showed that the hydrate was formed from melting ice during heating. To explain this competition between the formations of ice and hydrate, complementary experiments are now being undertaken using DSC coupled with X-ray diffraction to get more information about the solid compound formed versus time at a fixed temperature.  -60  -2 0 °C -80  -1 00 H e a t flo w (m W )  After re-homogenizing the fluid during five minutes by means of an Ultra Turrax T8 homogenizer at 10 000 rpm, a 50 to 60 mg sample was introduced into the experimental vessel and weighted with a precision of 10-5 g. A new sample was used for each experiment, and the reference vessel was left empty. Once inserted into the calorimetric block and connected to the gas panel, the two vessels were first purged by slow methane sweeping to evacuate the air, then pressurized to the experimental pressure and left during 30 minutes to allow sample saturation. Each run consisted in a fast cooling down to a temperature corresponding to a given under cooling degree T, followed by an isotherm of variable duration. Finally, the sample was heated at 1 K/min until complete dissociation of hydrates.  -1 5 °C -1 20  -1 0 °C  -1 40  -1 60  -1 80  -2 00 -15  -1 0  -5  0  5  10  15  20  T e m p era tu re (°C )  Figure 2. Model hydrate dissociation thermograms  Methane hydrates Figure 3 presents a thermogram recorded during a DSC experiment under methane pressure. It is composed of three steps: 1. fast cooling down to the temperature of the isothermal sequence; the heat flow signal recorded during this step is meaningless; 2. isothermal sequence; after an induction period, the heat release due to the hydrate formation appears as a wide peak; 3. warming up to ambient temperature; the hydrate dissociation heat is recorded during this sequence. The shape and regularity of the formation peak, as well as the duration of the induction period, strongly depend on the operating conditions. In order to get comparable results, we define the sub cooling degree as the difference between the temperature of hydrate-liquid-vapor equilibrium at the given operating pressure and the temperature of the isothermal step. This value T is considered as representative of the driving force for hydrate crystallization. To compute the equilibrium  5  300  T = 20 K T = 22 K T = 25 K T = 30 K  3  2  Heat flow Temperature  4  4  mW  Heat flow / mW  temperature at the experimental pressure, it was necessary to take into account the effect of the salt concentration in the aqueous phase. We used classical thermodynamic modeling [14] to obtain these values.  1  290 Formation peak  0 0  270  -2  3600 t/s  Figure 3. Thermogram recorded during a DSC run, showing the isothermal formation of hydrate followed by its dissociation upon warming up  7200  9000  18  5400  16 Heat flow / mW  1800  5400  Figure 4. Hydrate formation peaks recorded at 20 MPa CH4 pressure at various sub cooling degrees  260 0  3600 t/s  Dissociation peak -4  1800  280  14  T = 20 K T = 23 K T = 25 K T = 30 K  12 mW  mW  0  T/K  K  Heat flow / mW  2  10 8 6 4 2 0  0  1800  3600  5400  t/s  Figure 5. Hydrate formation peaks recorded at 40 MPa CH4 pressure at various sub cooling degrees 11  10  P = 20 MPa P = 30 MPa P = 40 MPa  9  ()  ln ()  Figures 4 and 5 present the hydrate formation peaks recorded at various T at 20 and 40 MPa CH4 pressure, respectively. It can be seen that the peaks are more regular and sharper at high pressure. At a given pressure, the peaks get wider and the induction time increases as the sub cooling decreases. Below approximately 25 K of sub cooling, the induction period literally explodes. In Fig. 6 is reported the logarithm of the induction time  (in seconds) as a function of the sub cooling degree. Two trends clearly appear:  at high driving force, for sub cooling degrees above 23 K, the induction time varies slightly with T and the pressure;  at low driving force, below 23 K of sub cooling, the induction time increases sharply as the temperature gets closer to the equilibrium. It can be concluded from these results that the crystallization of methane hydrates in water-in-oil emulsion requires a sub cooling of about 20 K or more, to proceed with reasonable speed.  8  7  6  5  12  14  16  18  20  22  24  26  28  30  32  T / K  Figure 6. Logarithm of induction period duration versus sub cooling degree at various CH4 pressures  Low driving force model The model used to represent the trend of hydrate formation peaks recorded at low driving force is based on the Avrami-Erofeev equation [18-19]: χ  1  exp   K t   dβ     (1)  where the rate of conversion  is expressed as the proportion of the initial amount of water n0 that has been converted to hydrate at time t: χ   n0  n  A (t )  (4)  A  where A(t) represents the area of the formation peak truncated at time t and A the total area.  2  0  -2  hydrate formation peak  -4  -6  0  20000  40000  60000  80000  t/s  Figure 7. Thermogram recorded at very low driving force: T = 14 K  (2)  n0  From Eq. 3, it is possible to obtain the parameters K, d and  by linear regression on the function:  n is the amount of remaining free water at time t. K is a constant, d represents the dimensions of the crystallization process and can take integer values between 1 and 3, and  is a parameter added by Erofeev [19] to take into account the possibility of multiple step mechanism of crystallization. As that equation does not account for the induction period, we introduced the term  defined as the time elapsed between the beginning of the isothermal stay and the onset of hydrate formation signal: χ  1  exp   K  t  τ     exp ( t )   Heat flow / mW  MODELING Experimental results lead to the conclusion that modeling the kinetics of formation of methane hydrate in emulsion requires two different approaches, depending on whether the crystallization is conducted at low, or at high driving force [17]. For low driving forces, we chose a model that is well suited for reactionlimited crystallization. For high driving forces, we used an expression of the hydrate formation rate in a single water droplet based on the classical crystallization theory, combined with a statistical distribution of induction times to account for the droplets population.  dβ     (3)  Figure 7 presents the heat flow recorded during an experiment conducted at a sub cooling degree of 14 K. With such a low driving force, the hydrate formation started after more than 12 hours, and it lasted for approximately 5 hours. We integrated the heat flow signal in order to get the experimental rate of conversion:    1 ln  ln   1  exp        f ln( t   )     Fig. 8 reports the variation of the above function and the parameters of the regression function that were determined. From these results the parameters of Avrami-Erofeev equation may be obtained: d  3 d  β  3, 4 9      β  0, 4 9 ln K   3 0, 7 2   14  K  4, 5 8 .1 0  Figure 9 gives a comparison between the experimental and modeled rate of conversion. Experimental rate of conversion was obtained by integrating the heat flow signal, and dividing the result by the total heat released during the formation peak, according to Eq. 4.  2   C  G  kg   1 C   eq   ln(ln(1/(1-χexp)))  0  p  (5)  -2  A balance on the water converted to hydrate leads to the following expression of the water consumption rate:  -4 -6  Linear regression y = 3,49 x - 30,72 2 R = 0,99  -8  2  dn   -ν  dt 6  7  8  9  1 Vm  10   C  n  n 3 kg  - 1  .4 π  0 V m  (6) C   8π   eq   ln(t-  After numerical integration of Eq. 6, the rate of conversion may be expressed from Eq. 2. Figure 10 presents the rate of conversion obtained using  = 6, kg = 10-5 ms-1 and various values for the over saturation C / Ceq.  Figure 8. Determination of the regression parameters 1,0 Experiment Model  1,0  0,6  0,4  0,2  0,8  C/Ceq = 1,5 C/Ceq = 3 C/Ceq = 5  conversion  Rate of conversion  Rate of conversion  0,8  0,6  0,4 0,0 45000  50000  55000  60000  t/s  Figure 9. Rate of conversion  versus time corresponding to the thermogram in Fig.7. Comparison between experiment and model computation  High driving force model Crystal growth equations in one single water droplet were first established using the following hypothesis:  The concentration of methane in the oil phase is constant.  The concentration of methane in the water droplets is constant.  The linear growth rate G is constant versus time.  The hydrate formation in the droplet follows a mono-nucleation process. The expression for the linear growth velocity was taken from Pic [20]:  0,2  0,0 100  1000 t/s  Figure 10. Conversion rate in a single droplet versus time obtained from Eq. 6 and 2  It can be seen that, depending on the value of C / Ceq, there is a period of variable duration during which the conversion is very slow, and thus could not be detected by any technical means. This is not an induction period however, since in each case we assume that nucleation occurred at time 0. Nevertheless, if the curves in Fig. 10 are very close in shape to the experiments at the beginning of hydrate formation, they do not correspond to the experimental reality at the end of the process, where the slope should decrease smoothly down to zero. In order to get more realistic representations, it is necessary to account for the fact that each  droplet in the emulsion sample is an independent reactor. Therefore, nucleation is likely to occur in each droplet at a different time. We chose to combine the single-droplet model of Eq. 6 with a normal distribution of induction times, expressed by the following equation: 2      1,0  (7)  where () is the number of droplets in which the nucleation takes place at time , Ndrop the total  (c) 0,8  (b)  conversion      Rate of conversion   ( )  N drop       exp   2 2 2   1  the formation of a supercritical nucleus is delayed by a time that follows a statistical distribution, followed by a period during which the crystal growth is too slow to be detected.  0,6  (a)  0,4  number of droplets in the sample,  the average induction time and  the standard deviation of the distribution. Figure 11 presents three different  0,2  0,0  distributions with  = 500, 1000 and 2000 s.  0  1000  2000  3000  4000  5000  6000  t/s  Figure 12. Conversion rate in the emulsion obtained by combining the single droplet model and the three distributions of induction times illustrated in Fig. 11  200  (a)  Nb. of droplets  150  (b) 100  1,0  (c)  0  1000  2000  3000  4000  5000  t/s  Figure 11. Various normal distributions of induction times  0,8 Experiment Model  conversion  0  Rate of conversion  50  0,6  0,4  0,2  Combining the single droplet conversion equation (Eq. 6) and the distribution of induction times (Eq. 7) was realized by numerical summation and resulted in the curves presented in Fig. 12. As shown in Fig. 13 to 15, it is possible to represent not only the exact shape of the experimental conversion curves, but also the induction period, by adjusting the parameters C / Ceq, kg,  and . The parameters used to draw the curves are given in Table 3. According to this model, the extremely variable induction period observed in DSC experiments would only be an apparent one. It would be in fact composed of a real induction time, during which  0,0 0  200  400  600  800  1000  t/s  Figure 13. Rate of conversion versus time at 30 MPa CH4 pressure, T = 30 K. Comparison of experimental and modeling results  1,0 Experiment Model  Rate of conversion  0,8  conversion  0,6  0,4  0,2  0,0 0  1000  2000  3000  4000  t/s  Figure 14. Rate of conversion versus time at 20 MPa CH4 pressure, T = 25 K. Comparison of experimental and modeling results  1,0  Experiment Model  0,6 conversion  Rate of conversion  0,8  0,4  0,2  0,0 0  2000  4000  6000  8000  10000  12000  t/s  Figure 15. Rate of conversion versus time at 11 MPa CH4 pressure, T = 20 K. Comparison of experimental and modeling results  Fig. 13 14 15  PCH4 MPa 30 20 11  T K  kg m.s-1  30 25 20  -5  2.10 1.10-5 1.10-5  C     C eq  s  7 4 1.5   s  20 30 1000 400 2800 2200  Table 3. Experimental conditions and modeling parameters corresponding to the illustrations reported in Fig. 13 to 15  CONCLUSION The present contribution presents results of DSC investigations on the kinetics of hydrate formation in water-in-oil emulsions. Two different systems were studied: tetrachlorofluoromethane hydrate forms at ambient pressure and has thus been used as a model for natural gas hydrate, as well as any other structure II hydrate; methane hydrate formation in deep offshore drilling fluids has been studied using high-pressure micro DSC. Both series of experiment show the strong influence of the driving force, measured by the sub cooling degree, i.e. the difference between the temperature of experiment and the equilibrium temperature. This dependence resulted in induction periods that varied from a few minutes to more than twelve hours when the sub cooling decreased from 30 to 14 Kelvin. Two different trends were identified: a so called “high” driving force regime, where the induction period varied slightly with sub cooling, and a “low” driving force regime, where it became extremely dependent of sub cooling. Two different models were thus proposed to represent the experimental results corresponding to the two regimes. The Avrami-Erofeev equation proved to correctly represent the experimental results obtained at low driving force. A model based on classical theory of crystal growth coupled with a statistical distribution of induction times was developed for high driving force modeling. In both cases the model results exhibit a good agreement with the experiments and allow reproducing the rate of conversion measured versus time. The next step of the modeling will be to correlate the parameters to the experimental conditions in order to get predictive models.  REFERENCES [1] Dalmazzone C, Herzhaft B, Dalmazzone D. Characterization of hydrate formation in drilling muds using Differential scanning Calorimetry (DSC). In: Proceedings of 4th International Conference on Gas Hydrates, Yokohama, Japan, May 19-23, 2002. [2] Barker JW, Gomez RK. Formation of hydrates during deepwater drilling operations. Journal of Petroleum Technology 1989; 41: 297. [3] Ebeltoft H, Yousif M, Soergaard E. (1997), Hydrate control during deep water drilling: overview and new drilling fluids. In: Proceedings of the SPE Annual Technical Conference and  Exhibition, SPE 38567, San Antonio, Texas, October 5-8, 1997. [4] Power D, Slater K, Aldea C, Lattanzi S. Gas hydrate inhibited water-based muds for ultradeepwater drilling. In: Practical Solutions for Drilling Challenges, Proceedings of AADE National Technology Conference, Houston, Texas, April 1-3 2003. [5] Fu B, Neff S, Mathur A, Bakeev K. Novel low dosage hydrate inhibitors for deepwater operations. In: Proceedings of the SPE Annual Technical Conference and Exhibition, SPE 71472, New Orleans, Louisiana, September 30-October 3, 2001. [6] Dalmazzone D., Dalmazzone C., Hamed N., Herzhaft B., Rousseau L. HP DSC investigations of the kinetics of gas hydrate formation: application to drilling fluids. In: Proceedings of 5th International Conference on Gas Hydrates, Trondheim, Norway, June 13-16, 2005. [7] Dalmazzone D., Hamed N., Dalmazzone C., Rousseau L. Application of high pressure DSC to the kinetics of formation of methane hydrate in water-in-oil emulsion. Journal of Thermal Analysis and Calorimetry 2006; 85: 361-368. [8] Jakobsen T., Sjöblom J., Ruoff P. Kinetics of gas hydrate formation in w/o emulsion. The model system trichlorofluoromethane / water / non-ionic surfactant studied by dielectric spectroscopy. Colloids and Surfaces A: Physicochemical and Engineering Aspects 1996; 112: 73-84. [9] Clausse D, Babin L., Broto F., Aguerd M., Clausse M. Kinetics of ice nucleation in aqueous emulsion. Journal of Physical Chemistry 1983; 87(21): 4030-4034. [10] Clausse D. Thermal behavior of emulsions studied by differential scanning calorimetry. Journal of Dispersion Science and Technology 1999; 20: 315. [11] Koh C. A., Westacott R. E., Zang W., Hirachand K., Creek J. L., Soper A. K. Mecanisms of gas hydrate formation and inhibition. Fluid Phase Equilibria 2002; 194-197: 143-151. [12] Fouconnier B. Calorimetry study of trichlorofluoromethan hydrate formation in emulsion : a model system for the study of gas hydrates. Ph. D. Thesis, Université de Technologie de Compiègne, France, July 18th, 2002. [13] Fouconnier B., Komunjer L., Ollivon M., Lesieur P., Keller G., Clausse D. Study of CCl3F hydrate formation and dissociation in W/O emulsion by differential scanning calorimetry and  X-ray diffraction. Fluid Phase Equilibria 2006; 250(1-2): 76-82. [14] Kharrat M., Dalmazzone D. Experimental Determination of Stability Conditions of Methane Hydrate in Aqueous Calcium Chloride Solutions Using High Pressure Differential Scanning Calorimetry. Journal of Chemical Thermodynamics 2003; 35: 1489-1505. [15] Dalmazzone D, Clausse D, Dalmazzone C, Herzhaft B. The stability of methane hydrates in highly concentrated electrolyte solutions by differential scanning calorimetry and theoretical computation. American Mineralogist 2004; 89: 1183-1191. [16] Le Parlouër P., Dalmazzone C., Herzhaft B., Rousseau L., Mathonat C. Characterisation of gas hydrate formation using a new high-pressure micro-DSC. Journal of Thermal Analysis and Calorimetry 2004; 78: 165-172. [17] Hamed N. Study of the kinetics of formation of methane hydrates in offshore drilling fluids by high-pressure calorimetric analysis. Ph. D. Thesis, Ecole des Mines de Paris, France, November 10th, 2006. [18] Avrami M. Kinetics of phase change. Journal of Chemical Physics 1939; 7: 1103-1112. [19] Erofeev B.V. In De Boer J.H., editor. Reactivity of solids, Proc. 4th Int. Symp., Elsevier, Amsterdam, 1961. [20] Pic J.-S. Study of the mechanism of operation of a kinetic inhibitor on the crystallization of methane hydrate. In Science des Processus Industriels et Naturels, Ecole Nationale Supérieure des Mines, Saint-Etienne, France, 2000.  


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