Thermodynamic properties and phase transtions in the H2O/CO2/CH4 system

The availability of free energy densities as functions of temperature, pressure and the composition of all components is required for the development of a three-component phase field theory for hydrate phase transitions. We have broadened the extended adsorption theory due to Kvamme and Tanaka (J. Phys. Chem., 1995, 99, 7114) through derivation of the free energy density surface in case of CO(2) and CH(4) hydrates. A combined free energy surface for the liquid phases has been obtained from a SRK equation of state and solubility measurements outside hydrate stability. The full thermodynamic model is shown to predict water-hydrate equilibrium properties in agreement with experiments. Molecular dynamics simulations of hydrates in contact with water at 200 bar and various temperatures allowed us to estimate hard-to-establish properties needed as input parameters for the practical applications of proposed theories. The 5-95 confidence interval for the interface thickness for the methane hydrate/liquid water is estimated to 8.54 A. With the additional information on the interface free energy, the phase field theory will contain no adjustable parameters. We provide a demonstration of how this theory can be applied to model the kinetics of hydrate phase transitions. The growth of hydrate from aqueous solution was found to be rate limited by mass transport, with the concentration of solute close to the hydrate approaching the value characterizing the equilibrium between the hydrate and the aqueous solution. The depth of the interface was estimated by means of the phase field analysis; its value is close to the interface thickness yielded by molecular simulations. The variation range of the concentration field was estimated to approximately 1/3 of the range of the phase field.     

Kinetics and mechanism of the formation of CO2 hydrate

This article proposes a mechanism of CO₂ hydrate formation taking into account both diffusion and reaction, and gives an analysis of its kinetics. The most important assumptions on the model are that water dissolves into liquid CO₂ and reacts to form CO₂ hydrate, and that the hydrate blocks the dissolution and diffusion of water. Computational simulations were conducted, and the model proposed explains well the many observations on the CO₂ hydrate formation in previous articles. It is concluded that liquid CO₂ disposed in a deep ocean will form a very thin film of CO₂ hydrate, and this will greatly control the CO₂ diffusion in the ocean. © 1993 John Wiley & Sons, Inc.     

Gas hydrate equilibrium dissociation conditions in porous media using two thermodynamic approaches

We employ two thermodynamic approaches, based on the equal fugacities and the equal activities, to predict the gas hydrate equilibrium dissociation conditions in the porous media. The predictions are made for the hydrate systems, CH₄/H₂O, C₂H₆/H₂O, C₃H₈/H₂O, CO₂/H₂O, CH₄/CO₂/H₂O, C₃H₈/CH₄/C₂H₆/H₂O, and CH₄/CH₃OH/H₂O. For the non-hydrate phase, we used the Trebble–Bishnoi equation in the fugacity approach and the Soave–Redlich–Kwong equation in the activity approach. For the hydrate phase, the van der Waals–Platteeuw model incorporated with the capillary model of Llamedo et al. [M. Llamedo, R. Anderson, B. Tohidi, Am. Mineral. 89 (2004) 1264–1270] was used in the two approaches. The predictions are found to be in satisfactory to good agreement with the experimental data. The predictive ability of the fugacity approach is better than that of the activity approach.     

An efficient model for the prediction of CO2 hydrate phase stability conditions in the presence of inhibitors and their mixtures

A thermodynamic model for the prediction of CO₂ hydrate phase stability conditions in the presence of pure and mixed salts solutions and various ionic liquids (ILs) is developed. In the proposed model van der Waals and Platteeuw model is used to compute the hydrate phase, Peng–Robinson equation of state (PR-EoS) for the gas phase and the Pitzer–Mayorga–Zavitsas-Hydration model is employed to calculate the water activity in the liquid water phase. This model is an extension of the model developed by Tumba et al. (2011) for the prediction of methane and CO₂ hydrate phase stability conditions in the presence of tributylmethylphosphonium methylsulfate IL solution. Shabani et al. (2011) mixing rule is modified by incorporating the water–inhibitor (salt/IL) interaction parameter to calculate the water activity in mixed salt solutions. The model predictions are also calculated using the Pitzer–Mayorga model separately and compared with predictions of the developed model. The model predictions are compared with experimental results on the phase stability of CO₂ hydrate in the presence of ILs, pure and mixed salts as reported in literatures. The ILs are chosen from imidazolium cationic family with various anion groups such as bromide (Br), tetrafluoroborate (BF₄), trifluoromethanesulfonate (TfO), and nitrate (NO₃) and the common salts such as NaCl, KCl and CaCl₂. Good agreement between the developed model predictions and the literature data is observed. The overall average absolute deviation (AARD%) with Pitzer–Mayorga–Zavitsas-Hydration model is observed to be within ±1.36% while Pitzer–Mayorga model accuracy were about ±1.44 %. Further, the model is extended to calculate the inhibition effect of selected inhibitors (ILs and salts) on CO₂ hydrate formation.     

Equilibrium conditions for CO2 hydrate in porous medium

Experimental phase equilibrium conditions data for carbon dioxide (CO₂) hydrate in porous medium with the presence of sodium chloride (NaCl) solution were investigated in this study. The experimental data were generated using graphic-method in presence of solutions contained (0, 0.2, 0.4, 0.6, and 0.8) mol/L NaCl. The results indicated the increase of NaCl concentration caused the enhancement in the equilibrium pressure of CO₂ hydrate as the pore size and the temperature were kept the same. Effects of NaCl solutions on CO₂ hydrate equilibrium conditions could be neglected when the temperature is lower than ice point. An improved model was used to predict CO₂ hydrate equilibrium conditions, and the predictions showed good agreement with experimental measurements.     

Study of the pseudo-steady-state kinetics of CO2 hydrate formation and stability

This article describes a dynamic model for formation and stability of CO₂-hydrate on the interface of liquid CO₂(LCO₂) and ocean water at large depths. Experimental results indicate that a thin film of hydrate naturally forms on the interfaces between LCO₂ and water, and inhibits diffusion between the two phases. Experiments further shows that the flux of CO₂ through the hydrate film is dependent of the CO₂-concentration in the ambient sea water. The model proposed here explains these phenomena by introducing four major mechanisms; diffusion of water to the LCO₂-phase, formation of hydrate in the LCO₂-hydrate interface, decay of hydrate in the water-hydrate interface, and diffusion of CO₂ through the water phase. The model explains the CO₂ flux not by diffusion through the hydrate film, but suggest a mechanism of continuous hydrate formation and decay. The overall effect is a “moving,” pseudo-steady-state hydrate film due to transport of CO₂ through the film. The film velocity is dependent of liquid-liquid diffusivity parameters and reaction constant, and lacking experimental values of these parameters, an order–of-magnitude analysis is done by fitting the model to experimentally obtained data for the overall film velocity. The motivation for this work is to elucidate options for CO₂ depositions in deep oceans, of which liquid CO2 sequestration is believed to be one of the most feasible. Spreading of CO₂ from a liquid CO₂-lake and associated lowering of pH in the ecosystem surrounding the lake is of large concern. The work presented here concludes that diffusion of CO₂ in the ocean is largely reduced by the hydrate film and suggests that hydrate formation may alleviate some of the environmental concerns regarding deep ocean sequestration of liquid CO₂. © 1994 John Wiley & Sons, Inc.     

Hydrate capture CO2 from shifted synthesis gas,flue gas and sour natural gas or biogas

CO₂ capture by hydrate formation is a novel gas separation technology, by which CO₂ is selectively engaged in the cages of hydrate and is separated with other gases, based on the differences of phase equilibrium for CO₂ and other gases. However, rigorous temperature and pressure, high energy cost and industrialized hydration separator dragged the development of the hydrate based CO₂ capture. In this paper, the key problems in CO₂ capture from the different sources such as shifted synthesis gas, flue gas and sour natural gas or biogas were analyzed. For shifted synthesis gas and flue gas, its high energy consumption is the barrier, and for the sour natural gas or biogas (CO₂/CH₄ system), the bottleneck is how to enhance the selectivity of CO₂ hydration. For these gases, scale-up is the main difficulty. Also, this paper explored the possibility of separating different gases by selective hydrate formation and reviewed the progress of CO₂ separation from shifted synthesis gas, flue gas and sour natural gas or biogas.     

Multiscale approach to CO2 hydrate formation in aqueous solution: phase field theory and molecular dynamics. Nucleation and growth

A phase field theory with model parameters evaluated from atomistic simulations/experiments is applied to predict the nucleation and growth rates of solid CO(2) hydrate in aqueous solutions under conditions typical to underwater natural gas hydrate reservoirs. It is shown that under practical conditions a homogeneous nucleation of the hydrate phase can be ruled out. The growth rate of CO(2) hydrate dendrites has been determined from phase field simulations as a function of composition while using a physical interface thickness (0.85+/-0.07 nm) evaluated from molecular dynamics simulations. The growth rate extrapolated to realistic supersaturations is about three orders of magnitude larger than the respective experimental observation. A possible origin of the discrepancy is discussed. It is suggested that a kinetic barrier reflecting the difficulties in building the complex crystal structure is the most probable source of the deviations.     

Modeling of (vapor + liquid) equilibrium and enthalpy of solution of carbon dioxide (CO2) in aqueous methyldiethanolamine (MDEA) solutions

A thermodynamic model was used to estimate enthalpy of solution of carbon dioxide (CO₂) in methyldiethanolamine (MDEA) aqueous solutions. The model was based on a set of equations for chemical equilibria, phase equilibria, charge, and mass balances. Non-ideality in the liquid phase was taken into account by interaction parameters fitted to (vapor + liquid) equilibrium data.The enthalpies of solution of CO₂ were derived from the model using classical thermodynamic relations and were compared to experimental values obtained in previous works.     

A cross-association model for CO2-methanol and CO2-ethanol mixtures

A cross-association model was proposed for CO₂-alcohol mixtures based on the statistical associating fluid theory (SAFT). CO₂ was treated as a pseudo-associating molecule and both the self-association between alcohol hydroxyls and the cross-association between CO₂ and alcohol hydroxyls were considered. The equilibrium properties from low temperature-pressure to high temperature-pressure were investigated using this model. The calculated p-x and p-ρ diagrams of CO₂-methanol and CO₂-ethanol mixtures agreed with the experimental data. The results showed that when the cross-association was taken into account for Helmholtz free energy, the calculated equilibrium properties could be significantly improved, and the error prediction of the three phase equilibria and triple points in low temperature regions could be avoided.     

Understanding the Solid Solution–Aqueous Solution Equilibria in the KCl + RbCl + H<Subscript>2</Subscript>O System from Experiments,Atomistic Simulation and Thermodynamic Modeling

The solid solution–aqueous solution (SSAS) equilibria in the KCl + RbCl + H₂O system were redetermined at 298.15 K. The experimental data for (K,Rb)Cl were consistent with the formation of a continuous solid solution without miscibility gaps. The Schreinemakers’ wet residues method and an XRD quantitative analysis technique based on the Vegard approach were applied to determine the chemical composition of the solid solution phase of (K,Rb)Cl. The compositions of (K,Rb)Cl derived from the Vegard approach are in accordance with those from the wet residues method. The thermodynamic properties of mixing of the (K,Rb)Cl solid solution were theoretically predicted using atomistic simulations. From these simulations, a regular solution behavior is recognized that is consistent with the knowledge of the thermodynamic properties of mixing of (K,Rb)Cl obtained from SSAS equilibrium studies, but the predicted regular solution model parameter A ₀ is significantly larger than that regressed from the SSAS equilibrium data. Finally, a thermodynamic model was developed for representing the SSAS equilibria and element partitioning in the KCl + RbCl + H₂O system as a function of temperature that can be used for predicting the SSAS equilibria in the studied system over the temperature range 273.15–373.15 K.     

Phase behaviour of tri-n-butylmethylammonium chloride hydrates in the presence of carbon dioxide

The phase behaviour of the system water?Ctri-n-butylmethylammonium chloride (TBMAC)?CCO₂ was investigated by pressure-controlled differential scanning calorimetry in the range 0?C10?mol% TBMAC in water and at CO₂ pressures ranging from 0 to 1.5?MPa. In the absence of CO₂, an incongruent melting hydrate, which estimated composition corresponds to TBMAC·30H₂O, crystallizes at temperatures below ?13.6?°C and forms with ice a peritectic phase at approximately 3.9?mol% TBMAC. In the presence of CO₂ at pressures as low as 0.5?MPa, curves evidenced the presence of an additional phase exhibiting congruent melting at temperatures that are strongly pressure dependent and significantly higher than those of hydrates obtained without CO₂. This new phase, whose enthalpy of dissociation and CO₂ content increase slightly with CO₂ pressure, was identified as a mixed semi-clathrate hydrate of TBMAC and CO₂ of general formula: (TBMAC?+?xCO₂)·30H₂O.     

Predicting hydrate stability zones of petroleum fluids using sound velocity data of salt aqueous solutions

Predicting hydrate stability zones of petroleum fluids from the aqueous phase properties can have a practical application as measuring these properties is normally easier than hydrate phase equilibrium measurement and can reduce experimental costs and efforts. In this work, the possibility of estimating hydrate stability zone from sound velocity data of salt aqueous solutions is investigated using a feed-forward artificial neural network method with a modified Levenberg–Marquardt algorithm. The method considers the changes of sound velocity in salt (NaCl, KCl, NaBr, KBr, BaCl₂, MgCl₂, Na₂SO₄, HCOONa) aqueous solution with respect to sound velocity in pure water and therefore there is no need to have a quantitative analysis of the aqueous solution. Independent data (not used in training and developing of the method) are used to examine the reliability of this tool. The predictions of this method are in acceptable agreement with independent experimental data, demonstrating the reliability of this tool for estimating the hydrate stability zone in the presence of salt aqueous solutions.     

Determination of NMR Lineshape Anisotropy of Guest Molecules within Inclusion Complexes from Molecular Dynamics Simulations

Nonspherical cages in inclusion compounds can result in non‐uniform motion of guest species in these cages and anisotropic lineshapes in NMR spectra of the guest. Herein, we develop a methodology to calculate lineshape anisotropy of guest species in cages based on molecular dynamics simulations of the inclusion compound. The methodology is valid for guest atoms with spin 1/2 nuclei and does not depend on the temperature and type of inclusion compound or guest species studied. As an example, the nonspherical shape of the structure I (sI) clathrate hydrate large cages leads to preferential alignment of linear CO₂ molecules in directions parallel to the two hexagonal faces of the cages. The angular distribution of the CO₂ guests in terms of a polar angle θ and azimuth angle ? and small amplitude vibrational motions in the large cage are characterized by molecular dynamics simulations at different temperatures in the stability range of the CO₂ sI clathrate. The experimental ¹³C NMR lineshapes of CO₂ guests in the large cages show a reversal of the skew between the low temperature (77 K) and the high temperature (238 K) limits of the stability of the clathrate. We determine the angular distributions of the guests in the cages by classical MD simulations of the sI clathrate and calculate the ¹³C NMR lineshapes over a range of temperatures. Good agreement between experimental lineshapes and calculated lineshapes is obtained. No assumptions regarding the nature of the guest motions in the cages are required.     

Kinetics on the dissolution of CO2 into water from the surface of CO2 hydrate at high pressure

Kinetic study on the dissolution of CO₂ from the surface of a liquid CO₂ droplet in water was conducted, and a mechanism of the decay of CO₂ hydrate was proposed. The model was applied to the experimental data which showed that the radius of liquid CO₂ droplets in water reduced linearly with time. It was proved that the dissolution rate of CO₂ into water is dominated by the decay of CO₂ hydrate on the surface of the droplet. The rate constant of the decay of CO₂ hydrate was estimated to be 1.25 × 10^?6 m s^?1. From a viewpoint of liquid CO₂ disposal in the deep ocean, it is predicted that the thin membrane of CO₂ hydrate at the interface between seawater and liquid CO₂ will control the dissolution of CO₂ into seawater. © 1995 John Wiley & Sons, Inc.     

Determination of Minimum Miscibility Pressure of CO2–Oil System: A Molecular Dynamics Study

CO₂ enhanced oil recovery (CO₂-EOR) has become significantly crucial to the petroleum industry, in particular, CO₂ miscible flooding can greatly improve the efficiency of EOR. Minimum miscibility pressure (MMP) is a vital factor affecting CO₂ flooding, which determines the yield and economic benefit of oil recovery. Therefore, it is important to predict this property for a successful field development plan. In this study, a novel model based on molecular dynamics to determine MMP was developed. The model characterized a miscible state by calculating the ratio of CO₂ and crude oil atoms that pass through the initial interface. The whole process was not affected by other external objective factors. We compared our model with several famous empirical correlations, and obtained satisfactory results—the relative errors were 8.53% and 13.71% for the two equations derived from our model. Furthermore, we found the MMPs predicted by different reference materials (i.e., CO₂/crude oil) were approximately linear (R² = 0.955). We also confirmed the linear relationship between MMP and reservoir temperature (T_R). The correlation coefficient was about 0.15 MPa/K in the present study.     

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part II: Binary mixtures with CO2

In Part I of this series of articles, the study of H₂S mixtures has been presented with CPA. In this study the phase behavior of CO₂ containing mixtures is modeled. Binary mixtures with water, alcohols, glycols and hydrocarbons are investigated. Both phase equilibria (vapor-liquid and liquid-liquid) and densities are considered for the mixtures involved. Different approaches for modeling pure CO₂ and mixtures are compared. CO₂ is modeled as non self-associating fluid, or as self-associating component having two, three and four association sites. Moreover, when mixtures of CO₂ with polar compounds (water, alcohols and glycols) are considered, the importance of cross-association is investigated. The cross-association is accounted for either via combining rules or using a cross-solvation energy obtained from experimental spectroscopic or calorimetric data or from ab initio calculations. In both cases two adjustable parameters are used when solvation is explicitly accounted for. The performance of CPA using the various modeling approaches for CO₂ and its interactions is presented and discussed, comparatively to various recent published investigations. It is shown that overall very good correlation is obtained for binary mixtures of CO₂ and water or alcohols when the solvation between CO₂ and the polar compound is explicitly accounted for, whereas the model is less satisfactory when CO₂ is treated as self-associating compound.     

Thermodynamic modeling for clathrate hydrates of ozone

We report a theoretical study to predict the phase-equilibrium properties of ozone-containing clathrate hydrates based on the statistical thermodynamics model developed by van der Waals and Platteeuw. The Patel–Teja–Valderrama equation of state is employed for an accurate estimation of the properties of gas phase ozone. We determined the three parameters of the Kihara intermolecular potential for ozone as a = 6.815 · 10⁻² nm, σ = 2.9909 · 10⁻¹ nm, and ε · k_B⁻¹ = 184.00 K. An infinite set of ε–σ parameters for ozone were determined, reproducing the experimental phase equilibrium pressure–temperature data of the (O₃ + O₂ + CO₂) clathrate hydrate. A unique parameter pair was chosen based on the experimental ozone storage capacity data for the (O₃ + O₂ + CCl₄) hydrate that we reported previously. The prediction with the developed model showed good agreement with the experimental phase equilibrium data within ±2% of the average deviation of the pressure. The Kihara parameters of ozone showed slightly better suitability for the structure-I hydrate than CO₂, which was used as a help guest. Our model suggests the possibility of increasing the ozone storage capacity of clathrate hydrates (∼7% on a mass basis) from the previously reported experimental capacity (∼1%).     

Phase field modeling of CH4 hydrate conversion into CO2 hydrate in the presence of liquid CO2

We present phase field simulations to estimate the conversion rate of CH(4) hydrate to CO(2) hydrate in the presence of liquid CO(2) under conditions typical for underwater gas hydrate reservoirs. In the computations, all model parameters are evaluated from physical properties taken from experiment or molecular dynamics simulations. It has been found that hydrate conversion is a diffusion controlled process, as after a short transient, the displacement of the conversion front scales with t(1/2). Assuming a diffusion coefficient of D(s) = 1.1 x 10(-11) m(2) s(-1) in the hydrate phase, the predicted time dependent conversion rate is in reasonable agreement with results from magnetic resonance imaging experiments. This value of the diffusion coefficient is higher than expected for the bulk hydrate phase, probably due to liquid inclusions remaining in the porous sample used in the experiment.