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

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 %

Derivation of a Langmuir type of model to describe the intrinsic growth rate of gas hydrates during crystallisation from gas mixtures

International audienceGas hydrates are crystalline water based solids composed of a three-dimensional network of water molecules. They form a network of cavities in which molecules of light gases can be encapsulated depending on their size and affinity. Gas hydrates can, by their nature, not be classified as chemical compounds since they do not possess a definite stoechiometry. In contrast they have to be regarded as solid solution phases, the stoechiometry of which is not fixed but depends on the composition of the surrounding liquid. At equilibrium, the composition dependence of the hydrate phase can be described by means of the classical van der Waals and Platteeuw model (van der Waals and Platteeuw, 1959). In the framework of the model, Langmuir constants are used for expressing the relative ability of light components to get enclathrated within the cavities. The work consists in considering again the enclathration of host species, not at thermodynamic equilibrium, but during the crystallisation process taking place under non-equilibrium conditions. It aims at proposing a new formulation for the hydrate composition as a function of new intrinsic constants which are based on Langmuir kinetic constants

Clathrate hydrate equilibrium data for gas mixture of carbon dioxide and nitrogen in the presence of an emulsion of cyclopentane in water.

International audienceCarbon dioxide and nitrogen gas separation is achieved through clathrate hydrate formation in the presence of cyclopentane. A phase diagram is presented in which the mole fraction of CO2 in the gas phase is plotted against the mole fraction of CO2 in the carbon dioxide + nitrogen + cyclopentane mixed hydrate phase, both defined with respect to total amount of CO2 and N2 in the respective phase. The curve is plotted for temperatures ranging from 283.5 K to 287.5 K and pressures from 0.76 MPa to 2.23 MPa. The results show that the carbon dioxide selectivity is moderately enhanced when cyclopentane is present in the mixed hydrate phase. Carbon dioxide could be enriched in the hydrate phase by attaining a mole fraction of up to 0.937 when the corresponding mole fraction in the gas mixture amounts to 0.507. When compared to the three phase hydrate-aqueous liquid-vapor equilibrium in the ternary system {water + carbon dioxide + nitrogen}, the equilibrium pressure of the mixed hydrate is reduced by 0.95 up to 0.97. The gas storage capacity approaches 40 m3 gas*m-3 of hydrate. This value turns out to be roughly constant and independent of the gas composition and the operating conditions

Prototyping of a real size air-conditioning system using a tetra-<i>n</i>-butylammonium bromide semiclathrate hydrate slurry as secondary two-phase refrigerant - Experimental investigations and modelling // Prototypage d'un système de conditionnement d'air de taille réelle utilisant un coulis d'hydrate de semi-clathrate de tétra-<i>n</i>-butyl ammonium comme frigoporteur diphasique - Etudes expérimentales et modélisation

International audienceAmong innovative processes developed in the field of refrigeration systems, technologies are encountered which are based on the application of Phase Change Materials (PCM) for the storage and transportation of energy. PCM are often provided by means of slurries. In the air-conditioning system presented here, a slurry of semi-clathrate hydrate crystals based on Tetra-n-Butyl-Ammonium Bromide (TBAB) is used as secondary refrigerant. The production of the slurry can be smoothed over day and night. Upon storage, the slurry can be distributed to end users, and melted to recover the cooling capacity. By adaption of a standard refrigeration technology, it is at first demonstrated that an air-conditioning system can be established by replacing the standard refrigeration fluid by a slurry of TBAB based semi-clathrate hydrate. Furthermore, the study attempts to model the settling of particles within the storage tank, aiming at gaining some insight in their complex migration processes obtained during the production and distribution steps

Gas hydrate equilibria for CO2–N2 and CO2–CH4 gas mixtures—Experimental studies and thermodynamic modelling

International audienceIn this paper, a set of experimental data on the phase equilibrium of gas hydrates in the presence of binary gas mixtures comprising CO2 is presented. The procedure established allows for the determination of both the composition of the gas phase as well as the hydrate phase without the need to sample the hydrate. The experimental results obtained in these measurements have been described by means of the classical model of van der Waals and Platteeuw. The values of internal parameters of the reference state and the Kihara parameters have been re-discussed and their interdependency is pointed. Finally the new set of parameters is validated against experimental data from other sources available in the literature, or invalidated against other sources. Finally, we conclude on the difference of experimental data between laboratories. The differences are not on the classical (pressure, temperature, gas composition) data which appear equivalent between laboratories. The difference stands on the measurement composition of the hydrate phase

Oxidation kinetics of a Ni-Cu based cermet at high temperature

The oxidation kinetics of a cermet composed of Ni–Cu alloy and nickel ferrite was studied by thermogravimetry at 960 °C under oxygen in the range 0.5–77 kPa. After an initial mass increase up to 15 g/m2 due to oxidation of surface metallic particles, the mass change was attributed to both outwards NiO growth and internal oxidation. Above 40 g/m2, the NiO scale thickness remained constant and the oxidation kinetics followed a complete parabolic law. The variations of the kinetic rate with oxygen partial pressure allowed to propose mechanisms, rate-controlling steps and kinetic laws in both transient and long term oxidation periods

Gas hydrate equilibria for CO₂-N₂ and CO₂-CH₂ gas mixtures, experiments and modelling

International audienceCO2 capture in industry is regarded as a possible tool that is suitable for reducing the global carbon emissions. The gases emitted by industry are by definition localized at the plants, like steelmaking plants, gas or coal power plants, chemical plants or natural gas production plants. Facing the variety of gases to be treated with regard to their quantities, qualities (mainly the CO2 content, but also the presence of minor impurities such as H2S, SO2, NOX....), and conditions of pressure and temperature, different strategies and technologies need to be developed to minimize the cost of the process. Hydrate technology could be used as an alternative approach to remove green house gases, and this is the route we try to develop here. A preliminary costing has revealed the process to be competitive for high concentrated mixtures of CO2 containing N2 such as found in exhaust gases of steel making plants at atmospheric pressure. This work presents a set of experimental data on the hydrate liquid vapour equilibria encountered in the mixtures of CO2-N2 and CO2-CH2 with pure water. We present in detail our experimental procedure by which the gas composition can be measured directly, whereas the hydrate composition is to be calculated from a mass balance. Furthermore we have tried to validate our experimental data by using the classical van der Waals and Platteeuw model with internal parameters found in the literature. These parameters are the so-called macroscopic parameters (i.e. macroscopic parameters from Table 3 which refer to a classical thermodynamic approach) and the so-called Kihara parameters (referring to a statistical thermodynamic approach). Due to large deviations between the modelled values obtained in the way described above and the experimental results, we have re-fitted the internal parameters, essentially by retaining a set of macroscopic parameters from Handa and Tse and re-fitting the Kihara parameters from our experimental results. Finally the new set of parameters is validated against experimental data from other sources available in the literature, or falsified against other sources

Clathrate Hydrate Equilibrium Data for the Gas Mixture of Carbon Dioxide and Nitrogen in the Presence of an Emulsion of Cyclopentane in Water

Carbon dioxide and nitrogen gas separation is achieved through clathrate hydrate formation in the presence of cyclopentane. A phase diagram is presented in which the mole fraction of CO₂ in the gas phase is plotted against the mole fraction of CO₂ in the carbon dioxide + nitrogen + cyclopentane mixed hydrate phase, both defined with respect to total amount of CO₂ and N₂ in the respective phase. The curve is plotted for temperatures ranging from 283.5 K to 287.5 K and pressures from 0.76 MPa to 2.23 MPa. The results show that the carbon dioxide selectivity is moderately enhanced when cyclopentane is present in the mixed hydrate phase. Carbon dioxide could be enriched in the hydrate phase by attaining a mole fraction of up to 0.937 when the corresponding mole fraction in the gas mixture amounts to 0.507. When compared to the three phase hydrate–aqueous liquid–vapor equilibrium in the ternary system {water + carbon dioxide + nitrogen}, the equilibrium pressure of the mixed hydrate is reduced by 0.95 up to 0.97. The gas storage capacity approaches 40 m³ gas·m^–3 of hydrate. This value turns out to be roughly constant and independent of the gas composition and the operating conditions