Asymptotic modelling of crystallisation in two-layer systems. Application to methane hydrate crystallization

International audienceThe problem of gas-liquid crystallization is re-visited in the framework of a two-film model. The moments of the crystal size distribution can be derived from a differential equation system. Instead of a numerical solution, we present here a general procedure to express analytically the asymptotic behaviour of the physical system. Thanks to this formulation, influence of different parameters can be easily identified and validated on experimental data which mainly concern methane hydrate crystallization

Asymptotic Modelling of Crystallisation in Two Layers Systems. Application to Methane Hydrate Formation in Batch Reactor.

6 pagesThis paper proposes to re-visit the problem of gas-liquid crystallization in the framework of a two-layer model and with the help of data coming from experiments on methane hydrate crystallization in a semi-batch reactor. Preliminary quantitative discussion of the order of magnitude of different effects makes possible realistic simplifications in the theoretical models. In particular, the role of the interfacial film is clearly defined. As previous authors did, we use a formulation in terms of moments of the crystal size distribution, however we are not interested in the numerical solution to the corresponding differential system, but we propose a general procedure to express analytically the asymptotic behaviour of the physical system. Thanks to this formulation, influence of different parameters can be easily identified and validated on available experimental dat

Modelling of gas clathrate hydrate equilibria using the electrolyte non-random two-liquid (eNRTL) model

International audienceA thermodynamic framework for modelling clathrate hydrate equilibria involving electrolytes is presented. In this framework, the gas phase is described by using the Soave-Redlich-Kwong equation of state, while the gas solubility in the liquid phase is estimated by means of a Henry's law approach. The liquid phase non-idealities are accounted for by using the semi-empirical electrolyte non-random two-liquid (eNRTL) excess Gibbs energy model. The van der Waals and Platteeuw model is used for the hydrate phase. This three-phase equilibrium model has been implemented in a new Java-based in-house programme. The main focus of the present work is the influence of the electrolytes on the incipient hydrate forming conditions. Therefore, the most recent version of the eNRTL model is thoroughly discussed. The model equations are presented in detail to facilitate future implementation and further development of this model, since the eNRTL modelling approach is quite new in the context of gas hydrate calculations. The correctness of the programme implementation is rigorously studied and verified by comparing the results with results of selected examples in the literature. At last, calculations are performed on solid-aqueous liquid-gas phase equilibria of selected systems of the type {water + salt + gas}, {water + salt1 + salt2 + gas}, {water + salt + CH4 + CO2} and {water + salt1 + salt2 + CH4 + CO2} with salt = NaCl, KCl, CaCl2 and gas = CH4, CO2) comprising a gas clathrate hydrate phase. The results are in good agreement with experimental p-T-hydrate-liquid-gas phase equilibrium data found in the literature, with average absolute relative deviations between experimental and calculated pressures ranging from 1% to 15%

Modelling gas hydrate equilibria using the electrolyte non-random two-liquid (ENRTL) model

International audienceThe semi-empirical electrolyte NRTL (eNRTL) model, also referred to as the model of Chen, is a versatile model for the excess molar Gibbs energy, capable of describing multicomponent electrolyte systems over wide ranges of state conditions. The model represents the excess Gibbs molar energy as the sum of two contributions, the first one of which accounts for long range electrostatic forces between ions, and the second one for the short range forces between all species. In single solvent systems, the long range interaction contribution consists of a term originating from the Pitzer-Debye-Hückel (PDH) equation . A modified version of the Non-Random-Two-Liquid (NRTL) local composition model of Renon and Prausnitz accounts for the short range interaction between all the species in their immediate neighbourhood. The most general form of the eNRTL activity coefficient expressions for both, individual species as well as mean ionic quantities have been implemented in the JAVA language. Model parameters for different strong electrolytes are provided by means of a data bank in the xml file format. The program code of the model implementation has been incorporated into the program package "gashydyn" developed in our group and allowing for performing equilibrium calculations involving gas hydrate phases. The correctness of the program implementation of the eNRTL expressions has been verified by comparing the results of numerous examples with corresponding literature results, including the composition dependence of the mean ionic activity coefficient of binary salt + solvent mixtures as well as of ternary salt 1 + salt 2 + mixtures. For the ternary systems, the influence of different values for the salt-salt binary interaction parameter is illustrated. Calculations on HLV phase equilibria of ternary H2O + salt + gas and quaternary H2O + salt + gas 1 + gas 2 systems have been performed. The calculations are based upon an equation of state approach for the gas phase, the van-der-Waals and Platteeuw model for the clathrate hydrate phase and the eNRTL model to account for the liquid phase non-idealities. The results reveal that a satisfying correlation of the experimental p-T-phase equilibrium data can be achieved with results ranging from around 1 to 15 %

Modelling of the rheological behaviour of slurries used for cold transportation

National audienceSuspensions of solid crystals are used for cold transportation purposes with the aim of reducing the use of classical refrigerants. From a general point of view, the understanding and the mastering of the rheological properties of the crystal suspensions is essential for controlling the operating conditions. Water ice and Tetra-ButylAmmonium Bromide (TBAB) hydrate aqueous give rise to non-Newtonian flows. In particular Bingham-like behaviours are frequently observed. Two reasons at least can explain deviation from Newtonian characteristics: crystal agglomeration and particle

Cristallisation non-stoechiométrique et modélisation d’un flash thermodynamique : Cas des hydrates mixtes de gaz

National audienceClathrate Hydrates are ice-like compounds that can be formed under high pressure and low temperature. They are composed of water and small molecules of ‘’gas’’. Hence they are usually called gas hydrates. They are involved in a significant issue of the oil industry, the hydrate plugs in pipelines (flow-assurance), as well as gas capture and storage, air conditioning… Moreover, methane hydrates can be found in sediments in deep sea and permafrost. That is why they are also considered as a significant methane resource on earth.Since they are non-stoichiometric compounds, it is difficult to model these crystals in process simulation. Furthermore, the speed of crystallization seems to influence the hydrate composition. Therefore, a modeling of the hydrate crystallization taking into account the history of the solid formation could be an interesting tool.In this work, a successive thermodynamic flash approach is presented according to two different hypotheses: heterogeneous hydrate phase during the crystal growth, and homogeneous hydrate phase. The main idea of these procedures is to discretize the crystal growth while the hydrate volume is increasing. Hence, three phase flash calculations are performed on the system. Each time, the previous amount of hydrate that has been formed is removed (at each iteration).The results of such algorithms are compared to batch experiments at low and quick crystallization rates (Duyen et al. 2016). The flash algorithms at given temperature (only one degree of freedom) give accurate results. The predicted final pressure and the hydrate volume are calculated within 7% accuracy. Moreover, the flash calculation results with no hydrate reorganization are closer to experiments at quick crystallization rate, whereas the experiment at low crystallization rate is better predicted with the second hypothesis (reorganization of the hydrate phase during growth). This work and its results provide a more realistic and comprehensive view of gas hydrate crystallization (more details in Bouillot and Herri, 2016).Les hydrates mixtes de gaz sont des cristaux solides dont la composition n’est pas stoechiométrique. Cette spécificité entraine des difficultés de modélisation lorsque qu’un volume significatif peut être formé. Il faut dans ce cas faire l’hypothèse d’un solide homogène (cas le plus simple), ou tenir compte de l’historique de la cristallisation si on suppose qu’un cristal formé à un temps t1 ne se met pas en équilibre rapidement avec sa solution, dont la composition peut avoir varié, à un temps t2.Dans le présent travail, une approche de modélisation de la cristallisation d’hydrates mixtes de gaz est proposée. Cette approche tient compte de l’évolution du milieu au cours de la cristallisation par des calculs successifs de flash thermodynamique.Deux hypothèses sont considérées. Dans la première, les cristaux d’hydrates mixtes croissent à l’équilibre thermodynamique à chaque instant. Il en résulte un cristal non homogène. La deuxième hypothèse forte est une ré-homogénéisation de la phase hydrate au cours de la cristallisation.Ces deux approches sont comparées à des mesures expérimentales obtenues par cristallisation lente ou rapide à partir de mélange d’hydrocarbures (CO2, CH4, C2H6). Les données importantes sont notamment : la pression finale, la composition des cristaux d’hydrates et leur volume.Les résultats obtenus par simulation s’accordent bien avec les données expérimentales. Les erreurs obtenues sur la pression d’équilibre et le volume d’hydrate sont généralement inférieures à 7%. Plus particulièrement, les résultats montrent qu’une cristallisation lente est plus proche d’un cas où le cristal se réorganise (équilibre thermodynamique), tandis qu’une cristallisation rapide est mieux simulée par une croissance non homogène. Une cristallisation rapide des hydrates mixtes de gaz peut donc se produire hors équilibre thermodynamique

Thermodynamic modelling of gas semi-clathrate hydrates using the electrolyte NRTL model

International audienceIn this work a modified version of the modelling procedure of Paricaud is presented for describing the solid-liquid equilibria encountered in aqueous solutions of tri-n-butylammonium bromide (TBAB) involving a semiclathrate hydrate phase. The theoretical framework is further applied to the description of the solid-liquid-vapour three phase p-T-lines of the ternary system water + TBAB +methane at different overall TBAB concentrations. For the calculations performed on the ternary system exhibiting a gas semiclathrate hydrate phase, model parameters gained previously for the water + TBAB mixture were used. The thermodynamics of the semiclathrate hydrate phase was modelled by means of the salt hydrate model of Paricaud. For the description of the gas semiclathrate hydrate phase a combination of the salt hydrate model of Paricaud with the Waals-Platteeuw (vdW-P) theory has been applied. An unsymmetric reference frame has been employed to treat the liquid phase, i.e., Henry's constant was adopted for the ideal solubility of methane in the aqueous phase, whereas the fugacity of pure liquid water was adopted as reference state for water. The Soave Redlich Kwong equation of state was used to calculate the fugacities in the gas phase. Whereas the model of Paricaud employs the SAFT equation of state in a φ-φ-approach to account for both, liquid and gas phase non-idealities, the electrolyte NRTL (eNRTL)-GE-model has been incorporated in our modified model to describe deviations from ideality in the liquid phase. In the calculations, the temperature dependence of the eNRTL-interaction energy parameters has been neglected and instead, ENRTL-coefficients at 298.15 K have been used. The solid-liquid T-x phase diagram of TBAB was calculated at ambient pressure up to 60% stoichiometric mass fraction of TBAB. By assuming the existence of only type B hydrate a good overall correlation of experimental data found in the literature was achieved by adjusting the values for the standard molar enthalpy of the dissociation and the temperature at the congruent melting point of the semiclathrate hydrate compound. Using these values, phase boundary HLV-lines of the ternary system H2O + TBAB + methane, calculated at different stoichiometric concentrations of TBAB in the liquid phase, are displayed and compared with measured results. Average relative deviations p|/p> between experimental data and modeling results between 4 and 44 % show the applicability of the approach presented

Formation & Dissociation of Methane Hydrates in Sediments.Part I : A New Experimental Set-up for Measurements and Modelling at the Core Scale

5 pagesThe ForDiMHyS project is a program devoted to experimental studies and the model development of the kinetics of FORmation and Dissociation of Methane Hydrates in Sediments. The first part of the project that is presented hereafter is designed to obtain experimental data on hydrate formation & dissociation under in-situ temperature and pressure conditions of methane hydrate in well constrained porous materials. The second part presented in another paper (Jeannin et al., 2002) consists in modelling the flows inside the core; a specific numerical model has been developed to simulate the experimental set-up described in part one. The numerical model is 3D three phases and simulates the kinetics of hydrate dissociation and formation, taking into account the solubility of methane in water and the heat of phase transitions

Crystallisation and rheology of an hydrate slurry as secondary two-phase refrigerant for air-conditioning application

8 pagesUnder atmospheric pressure condition and temperatures between 0°C and +12°C, Tetra-n- ButylAmmonium Bromide (TBAB) aqueous solutions crystallise into hydrate slurries. These slurries seems to be well appropriate for cold storage and transportation in the case of air conditioning applications. We focus here on the crystallisation and the rheological properties of TBAB hydrates slurries. Once the crystallisation conditions described, we propose an experimental analysis of their flow behaviour. The experimental device is made up of a brushed surface heat exchanger in which the hydrates slurry is generated, and of a measurement loop. The flow behaviour of the slurry is characterised through flow rates and pressure drops measurements. We obtain flow curves of hydrates slurries depending on the volume fraction of hydrate solid particles. In the range of shear rate investigated, hydrate slurries behave as Bingham fluids. We propose a method of determining their apparent viscosities and yield shear stress versus the volume fraction of hydrates

Rheological study of an hydrate slurry for air conditionning application

Fifth International Conference on Gas Hydrates (ICGH 5), Tromdheim, Norvège, 13 au 16 juin 2005International audienceUnder atmospheric pressure condition and tempertures between 0°C and +12°C, Tetra-n-ButylAmmonium bromide (TBAB) aqueous solutions crystallise into hydrate slurries. These slurries seem to be well appropriate for cold storage and transportation in the case of air-conditionning applications. We focus here on the crystallisation and the rheological properties of TBAB hydrates slurries. Once the crystallisation conditions described, we propose an experimental analysis of their flow behaviour. The experimental device is made up of a brushed surface heat exchanger in which the hydrates slurry is generated, and of a mesasurement loop. The flow behaviour of the slurry is characterised through flow rates and pressure drops measurements. We obtain flow curves of hydrates slurries depending on the volume fraction of hydrate solid particles. In the range of shear rate investigated, hydrate slurries behave as Bingham fluids. We propose a method of determining their apparent viscosities and yield shear stress versus the volume fraction hydrates