Sixty Years of the van der Waals and Platteeuw Model for Clathrate Hydrates—A Critical Review from Its Statistical Thermodynamic Basis to Its Extensions and Applications

Prediction of methane hydrate equilibrium in saline water solutions based on support vector machine and decision tree techniques

The formation of clathrate hydrates offers a powerful approach for separating gaseous substances, desalinating seawater, and energy storage at low temperatures. On the other hand, this phenomenon may lead to practical challenges, including the blockage of pipelines, in some industries. Consequently, accurately predicting the equilibrium conditions for clathrate hydrate formation is crucial. This study was undertaken to design reliable models capable of predicting the equilibrium state of methane hydrates in saline water solutions. A comprehensive collection of measured data, consisting of 1051 samples, was assembled from published sources. The prepared databank encompassed the hydrate formation temperature of methane (HFTM) in the presence of 26 different saline water solutions. A machine learning modeling was undertaken through the implementation of Decision Tree (DT) and Support Vector Machine (SVM) approaches. While both models had excellent performance, the latter achieved higher accuracy in estimating the HFTM with the mean absolute percentage error (MAPE) of 0.26%, and standard deviation (SD) of 0.78% in the validation process. Furthermore, more than 90% of the values predicted by the novel models fell within the [Formula: see text]1% error bound. It was found that the intelligent models also favorably describe the physical variations of HFTM with operational factors. An examination using the William's plot acknowledged the truthfulness of the gathered data and the suggested estimation techniques. Ultimately, the order of significance of the factors governing the HFTM was clarified using a sensitivity analysis.

Gas Hydrate Dynamics with Parameter-Free Clathrate Phase Description: Validation for Hydrate Formation and Dissociation

One of the major challenges involved in clathrate hydrate science that has remained for more than six decades lies in highly parametric clathrate phase estimation. In this contribution, a recently developed parameter-free hydrate phase statistical equilibrium model is employed for the first time to formulate the formation and dissociation dynamics of clathrates and predict their experimental observation at diverse geological conditions. This rigorous thermokinetic model takes into account various practical issues, notably hydrate formation in nanometer-sized pores (confirmed through seismic survey studies), irregularity in porous particle shape and pore size, renewal of the particle surface over which hydrate majorly forms and decays, and nth-order phase transformation. The model parameters are identified by formulating the genetic algorithm-based optimization strategy. Finally, this multicomponent hydrate model is tested by predicting the formation and decomposition data having pure water as well as saltwater with and without porous media. The proposed formulation secures a promising performance with a lower absolute average relative deviation for a wide variety of data sets over the latest hydrate models.

Mesomorphology of clathrate hydrates from molecular ordering

Clathrate hydrates are crystals formed by guest molecules that stabilize cages of hydrogen-bonded water molecules. Whereas thermodynamic equilibrium is well described via the van der Waals and Platteeuw approach, the increasing concerns with global warming and energy transition require extending the knowledge to non-equilibrium conditions in multiphase, sheared systems, in a multiscale framework. Potential macro-applications concern the storage of carbon dioxide in the form of clathrates, and the reduction of hydrate inhibition additives currently required in hydrocarbon production. We evidence porous mesomorphologies as key to bridging the molecular scales to macro-applications of low solubility guests. We discuss the coupling of molecular ordering with the mesoscales, including (i) the emergence of porous patterns as a combined factor from the walk over the free energy landscape and 3D competitive nucleation and growth and (ii) the role of molecular attachment rates in crystallization-diffusion models that allow predicting the timescale of pore sealing. This is a perspective study that discusses the use of discrete models (molecular dynamics) to build continuum models (phase field models, crystallization laws, and transport phenomena) to predict multiscale manifestations at a feasible computational cost. Several advances in correlated fields (ice, polymers, alloys, and nanoparticles) are discussed in the scenario of clathrate hydrates, as well as the challenges and necessary developments to push the field forward.

Modification of the van der Waals and Platteeuw model for gas hydrates considering multiple cage occupancy

This study reviews available van der Waals- and Platteeuw-based hydrate models considering multiple occupancy of cavities. Small guest molecules, such as hydrogen and nitrogen, are known to occupy lattice cavities multiple times. This phenomenon has a significant impact on hydrate stability and thermodynamic properties of the hydrate phase. The objective of this work is to provide a comprehensive overview and required correlations for the implementation of a computationally sufficient cluster model that considers up to five guest molecules per cavity. Two methodologies for cluster size estimation are evaluated by existing nitrogen hydrate models showing accurate results for phase equilibria calculations. Furthermore, a preliminary hydrogen hydrate model is introduced and compared with the results of other theoretical studies, indicating that double occupancy of small sII cavities is improbable and four-molecule clusters are predominant in large sII cavities for pressures above 300 MPa. This work lays the foundation for further exploration and optimization of hydrate-based technologies for small guest molecules, e.g., storage and transportation, emphasizing their role in the future landscape of sustainable energy solutions.

An Accurate Model to Calculate CO2 Solubility in Pure Water and in Seawater at Hydrate–Liquid Water Two-Phase Equilibrium

Understanding of CO2 hydrate–liquid water two-phase equilibrium is very important for CO2 storage in deep sea and in submarine sediments. This study proposed an accurate thermodynamic model to calculate CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium (HLWE). The van der Waals–Platteeuw model coupling with angle-dependent ab initio intermolecular potentials was used to calculate the chemical potential of hydrate phase. Two methods were used to describe the aqueous phase. One is using the Pitzer model to calculate the activity of water and using the Poynting correction to calculate the fugacity of CO2 dissolved in water. Another is using the Lennard–Jones-referenced Statistical Associating Fluid Theory (SAFT-LJ) equation of state (EOS) to calculate the activity of water and the fugacity of dissolved CO2. There are no parameters evaluated from experimental data of HLWE in this model. Comparison with experimental data indicates that this model can calculate CO2 solubility in pure water and in seawater at HLWE with high accuracy. This model predicts that CO2 solubility at HLWE increases with the increasing temperature, which agrees well with available experimental data. In regards to the pressure and salinity dependences of CO2 solubility at HLWE, there are some discrepancies among experimental data. This model predicts that CO2 solubility at HLWE decreases with the increasing pressure and salinity, which is consistent with most of experimental data sets. Compared to previous models, this model covers a wider range of pressure (up to 1000 bar) and is generally more accurate in CO2 solubility in aqueous solutions and in composition of hydrate phase. A computer program for the calculation of CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium can be obtained from the corresponding author via email.

Structure and thermodynamics of empty clathrate hydrates below the freezing point of water

Recently prepared as a new H2O phase, ice XVI was obtained by degassing a Ne-sII clathrate hydrate under vacuum, however very little is known of that crystalline solid under temperatures (T ≤ 220 K) and pressures (p ≤ 5000 bar) relevant for the Earth's environment and geochemistry. In this work, atomically detailed calculations using long time-scale molecular simulations, seldom paralelled before, are employed to probe empty sII clathrate hydrates. It is found that the volumetric response to an applied pressure-temperature gradient is accurately described by the Parsafar and Mason equation of state with an accuracy of at least 99.7%. Structural deformation induced upon the crystals is interpreted by monitoring the unit cell length and isobaric thermal expansivity, whilst benchmarked against previous neutron diffraction measurements of ice XVI and hexagonal ice under room pressure conditions; a critical comparison is established with other sII guest occupied lattices (CH4, CO2 and CnH2n+2 with n = 2, 3, 4), often found in permafrost regions and in the margins of continental shelves. Such an analysis reveals that empty sII frameworks are slightly more stable to thermal deformation than their sI analogues and that hexagonal ice is the structurally most stable of the condensed H2O phases addressed here. Of paramount importance for the oil and natural gas industries, heat capacities obtained from enthalpy profiles are identical for the sI and sII empty clathrates up to 2000 bar and diverge by only ∼7.3% at 5000 bar. The canonical tetrahedral symmetry of water-bonded networks is analysed in terms of an angular and a distance order parameters, which are observed to decrease (increase) as pressure (temperature) increases (decreases). The results now being reported constitute a landmark for future studies dealing with high-pressure and very low-temperature conditions, characteristic of the Earth's permafrost environment and other planetary interiors, whilst contributing to expand our knowledge regarding the recently discovered ice XVI phase.