The thermodynamic stability of clathrate hydrate. Encaging non-spherical propane molecules

The thermodynamic stability of a clathrate hydrate encaging non-spherical molecules has been investigated by examining the free energy of cage occupancy. In the present study, a generalized van der Waals and Platteeuw theory is extended to treat the rotational motion of guest molecules in clathrate hydrate cages. The vibrational free energy of both guest and host molecules is divided into harmonic and anharmonic contributions. The anharmonic free energy associated with the non-spherical nature of the guest molecules is evaluated as a perturbation from the spherical guest. Predicted thermodynamic properties are compared with measured values. It is shown that this anharmonic contribution is important in the free energy of the hindered rotation of the guests.     

Soft-core potentials in thermodynamic integration: comparing one- and two-step transformations

Molecular dynamics-based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This "singularity" problem can be addressed with "soft-core" potential functions which keep pairwise interaction energies finite for all configurations and provide smooth free energy curves. "One-step" transformations, in which electrostatic and van der Waals forces are simultaneously modified, can be simpler and less expensive than "two-step" transformations in which these properties are changed in separate calculations. Here, we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters α(LJ) and β(C) controlling the behavior of the soft-core Lennard-Jones and Coulomb potentials and compare one- and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates.     

Avoiding the van der Waals endpoint problem using serial atomic insertion

In the past analyses of the so-called van der Waals end point problem focused on thermodynamic integration. Here we investigate which of the recommendations, such as the need for soft-core potentials, are still valid when Bennett's acceptance ratio method is used. We show that in combination with Bennett's acceptance ratio method intermediate states characterized by the coupling parameter λ can be replaced by intermediate states in which Lennard-Jones interactions are turned on or off on an "atom by atom" basis. By doing so, there is no necessity to use soft-core potentials. In fact, one can compute free energy differences without dedicated code, making it possible to use any molecular dynamics program to compute alchemical free energy differences. Such an approach, which we illustrate by several examples, makes it possible to exploit the tremendous computational power of the graphics processing unit.     

Absolute binding free energy calculations of CBClip host–guest systems in the SAMPL5 blind challenge

Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett’s acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94 kcal/mol and an average unsigned error of 3.41 kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments.     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.     

Hydrate dissociation conditions for gas mixtures containing carbon dioxide,hydrogen, hydrogen sulfide,nitrogen, and hydrocarbons using SAFT

A new method, a molecular thermodynamic model based on statistical mechanics, is employed to predict the hydrate dissociation conditions for binary gas mixtures with carbon dioxide, hydrogen, hydrogen sulfide, nitrogen, and hydrocarbons in the presence of aqueous solutions. The statistical associating fluid theory (SAFT) equation of state is employed to characterize the vapor and liquid phases and the statistical model of van der Waals and Platteeuw for the hydrate phase. The predictions of the proposed model were found to be in satisfactory to excellent agreement with the experimental data.     

Gas hydrates in low water content gases: Experimental measurements and modelling using the CPA equation of state

In this communication, new experimental data are reported for the water content of methane and two synthetic gas mixtures in equilibrium with hydrates at pressures range from 5 to 40 MPa and temperature down to 251.65 K. The measurements have been made on equilibrated samples taken from a high-pressure variable volume hydrate cell using a new analyser based upon tuneable diode laser absorption spectroscopy (TDLAS) technology. A statistical thermodynamic approach, with the Cubic-Plus-Association equation of state, is employed to model the phase equilibria. The hydrate-forming conditions are modelled by the solid solution theory of van der Waals and Platteeuw. The thermodynamic model was used to predict the water content of methane and synthetic gases in equilibrium with gas hydrates.     

Thermodynamic equations of state from molecular solvation

A general expression of the canonical partition function for mixture fluids in terms of solvation free energy is presented. Following the same approach as set forth in generalized van der Waals theory, we show that the physical assumptions made in existing thermodynamic models from the perspective of molecular solvation can be prevailed. For example, the temperature dependence on the coordination number, i.e. the number of solvent molecules surrounding the solute, has an impact not only on the temperature dependence of the solvation free energy but on the non-linear solvent reaction field response as well. More importantly, the new formulation provides a unified scheme for deriving the commonly used equations of state (EOS) and newly developed COSMO-type liquid activity coefficient models. We show that from this new formulation it is possible to develop a new class of thermodynamic models that behave like existing EOS and liquid models in the low and high-density limits, respectively.     

Pathway dependence of the efficiency of calculating free energy and entropy of solute–solute association in water

In this study we investigate two alternative pathways to compute the free energy and the entropy of small molecule association (ΔF_assoc and ΔS_assoc) in water. The first route (direct pathway) uses thermodynamic integration as function of the distance R between the solutes. The mean force and the mean covariance of the force with the energy in solution are calculated from molecular dynamics simulation followed by integration of these quantities with respect to the reaction coordinate R. The alternative approach examined (solvation pathway) would first remove the solutes from the solution using thermodynamic integration as function of a solvation coupling parameter λ, change the solute–solute distance in vacuo and then solvate back the solute pair at the new separation distance. The system studied was a pair of CH₄ molecules in water. We investigate the influence of the CH₄–water interaction strength on the obtained ΔF_assoc and ΔS_assoc values by changing van der Waals and Coulomb interaction and evaluated the accuracy and efficiency for the two pathways. We find that the direct route seems more suitable for the calculation of free energies of hydrophobic solutes while the solvation pathway performs better when calculating entropy changes for solutes that have a stronger interaction with the solvent.     

The generalized van der waals partition function. I. basic theory

Sandler, S.I., 1985. The generalized van der Waals partition function. I. Basic theory. Fluid Phase Equilibria, 19:233-257 In this paper we provide a new derivation of the generalized van der Waals partition function for pure fluids and mixtures, and show how this partition function can be used as a basis for understanding equations of state, their mixing rules, and excess free energy (activity coefficient) models. The results presented here clarify some of the confusion which presently exists in the literature concerning the ramifications of local composition thermodynamic models, and provide the theory for papers to follow which combine the generalized van der Waals partition function and our computer simulation results to obtain new, statistical mechanical-based thermodynamic models.     

Experimental and thermodynamic modelling of systems containing water and ethylene glycol: Application to flow assurance and gas processing

Accurate knowledge of hydrate phase equilibrium in the presence of inhibitors is crucial to avoid gas hydrate formation problems and to design/optimize production, transportation and processing facilities. In this communication, we report new experimental dissociation data for various systems consisting of methane/water/ethylene glycol and natural gas/water/ethylene glycol. A statistical thermodynamic approach, with the Cubic-Plus-Association equation of state, is employed to model the phase equilibria. The hydrate-forming conditions are modelled by the solid solution theory of van der Waals and Platteeuw. The thermodynamic model was used to predict the hydrate dissociation conditions of methane and natural gases in the presence of distilled water or ethylene glycol aqueous solutions. Predictions of the developed model are validated against independent experimental data and the data generated in this work. A good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.     

Modeling heating curve for gas hydrate dissociation in porous media

A method for modeling the heating curve for gas hydrate dissociation in porous media at isochoric conditions (constant cell volume) is presented. This method consists of using an equation of state of the gas, the cumulative volume distribution (CVD) of the porous medium, and a van der Waals-Platteeuw-type thermodynamic model that includes a capillary term. The proposed method was tested to predict the heating curves for methane hydrate dissociation in a mesoporous silica glass for saturated conditions (liquid volume = pore volume) and for a fractional conversion of water to hydrate of 1 (100% of the available water was converted to hydrate). The shape factor (F) of the hydrate-water interface was found equal to 1, supporting a cylindrical shape for the hydrate particles during hydrate dissociation. Using F = 1, it has been possible to predict the heating curve for different ranges of pressure and temperature. The excellent agreement between the calculated and experimental heating curves supports the validity of our approach.     

Enveloping distribution sampling: a method to calculate free energy differences from a single simulation

The authors present a method to calculate free energy differences between two states A and B "on the fly" from a single molecular dynamics simulation of a reference state R. No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state R which is designed such that the subset of phase space important to it is the union of the parts of phase space important to A and B. Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interaction perturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replica-exchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to A and B, respectively. This can be explained by the total absence of phase space overlap of A and B in these two cases.     

On the thermodynamic stability of clathrate hydrates IV: double occupancy of cages

We have extended the van der Waals and Platteeuw theory to treat multiple occupancy of a single cage of clathrate hydrates, which has not been taken into account in the original theory but has been experimentally confirmed as a real entity. We propose a simple way to calculate the free energy of multiple cage occupancy and apply it to argon clathrate structure II in which a larger cage can be occupied by two argon atoms. The chemical potential of argon is calculated treating it as an imperfect gas, which is crucial to predict accurate pressure dependence of double occupancy expected at high pressure. It is found that double occupancy dominates over single occupancy when the guest pressure in equilibrium with the clathrate hydrate exceeds 270 MPa.     

Impact of Low-Dosage Inhibitors on Clathrate Hydrate Stability

Summary: Development of more capable low-dosage hydrate inhibitors (LDHI) is of crucial importance to oil and gas industry. Those efforts have been severely hindered so far by lack of clear understanding of molecular-level mechanisms, both thermodynamic and kinetic, which make certain chemical compounds into efficient inhibitors. An accurate representation of intermolecular potentials between polymeric low dosage inhibitors and hydrate-water-gas surfaces is essential for modelling systems containing these components. A two-stage computational study was undertaken of two proven LDHIs, polyvinylpyrrolidone (PVP) and polyvinylcaprolactam (PVCap), in aqueous solutions under various conditions. We have first carried out ab initio density functional theory (DFT) calculations for PVP and PVCap polymers with molecular weight spanning from monomers to polymeric chains. Molecular dynamics were then employed to investigate thermodynamic and kinetic processes that affect hydrate nucleation and growth. Comparison with experiments has also shown that calculated potential is able to mimic the characteristic behaviour of methane hydrate and PVP complexes.     

Two approaches for modelling hydrate growth

We consider two different approaches to model growth of CO₂ hydrate, phase field theory and a model based on cellular automata. The two approaches are applied to simulations of hydrate growth from supersaturated aqueous solution of CO₂. The thermodynamic models for the solution properties are derived from experimental solubility data while the hydrate thermodynamics is based on adsorption theory with reference properties derived from molecular simulations. We show that the cellular automata approach has the benefit of being much more computationally efficient, and are still giving results which are consistent with results from the phase field theory.     

基于PC-SAFT方程研究多孔介质中水合物相平衡的预测模型

对多孔介质中水合物的形成条件预测模型进行了研究.利用微扰链-统计缔合流体理论状态方程(PC-SAFT)结合van der Waals-Platteuw模型和毛细管Kelvin模型,建立了用于多孔介质水合物体系的相平衡预测模型.在此模型基础上,针对甲烷水合物和CO2水合物对界面张力作了进一步的研究.根据多孔介质水合物相平...     

Ensemble variance in free energy calculations by thermodynamic integration: theory, optimal "Alchemical" path, and practical solutions

Thermodynamic integration is a widely used method to calculate and analyze the effect of a chemical modification on the free energy of a chemical or biochemical process, for example, the impact of an amino acid substitution on protein association. Numerical fluctuations can introduce large uncertainties, limiting the domain of application of the method. The parametric energy function describing the chemical modification in the thermodynamic integration, the "Alchemical path," determines the amplitudes of the fluctuations. In the present work, I propose a measure of the fluctuations in the thermodynamic integration and an approach to search for a parametric energy path minimizing that measure. The optimal path derived with this approach is very close to the theoretical minimum of the measure, but produces nonergodic sampling. Nevertheless, this path is used to guide the design of a practical and efficient path producing correct sampling. The convergence with this practical path is evaluated on test cases, and compares favorably with that of other methods such as power or polynomial path, soft-core van der Waals, and some other approaches presented in the literature.     

Experimental determination and modeling of structure II hydrates in mixtures of methane+water+1,4-dioxane

Hydrate phase equilibrium conditions were measured with a Cailletet apparatus in the pressure range 2<14 MPa. The investigated 1,4-dioxane concentrations were 1, 2, 5, 7, 10, 20 and 30 mol% relative to water. The results show that adding 1,4-dioxane up to concentrations of 6 mol%, about the stoichiometric ratio of large sII cages to water (1/17), reduced the equilibrium pressure of hydrate formation. Adding 1,4-dioxane beyond 6 mol% caused a slow increase of the equilibrium pressures. The hydrate phase equilibria data were modeled as equilibrium between a liquid phase of water and 1,4-dioxane, with a small amount of methane, and a sII hydrate of 1,4-dioxane and methane. The chemical potential of the hydrate phase was described using the van der Waals and Platteeuw theory. Activity coefficients of the liquid phase were calculated by a van Laar relation, based on literature 1,4-dioxane+water VLE data. The predicted equilibrium pressures calculated were within 5% of the data up to a concentration of 20 mol% 1,4-dioxane relative to water.