energies Article Hydrate—A Mysterious Phase or Just Misunderstood? Bjørn Kvamme 1,*, Jinzhou Zhao 1, Na Wei 1 and Navid Saeidi 2 1 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Xindu Road No.8, Chengdu 610500, China; [email protected] (J.Z.); [email protected] (N.W.) 2 Environmental Engineering Department, University of California Irvine, Irvine, CA 92697, USA; [email protected] * Correspondence: [email protected] Received: 6 December 2019; Accepted: 13 February 2020; Published: 17 February 2020 Abstract: Hydrates that form during transport of hydrocarbons containing free water, or water dissolved in hydrocarbons, are generally not in thermodynamic equilibrium and depend on the concentration of all components in all phases. Temperature and pressure are normally the only variables used in hydrate analysis, even though hydrates will dissolve by contact with pure water and water which is under saturated with hydrate formers. Mineral surfaces (for example rust) play dual roles as hydrate inhibitors and hydrate nucleation sites. What appears to be mysterious, and often random, is actually the effects of hydrate non-equilibrium and competing hydrate formation and dissociation phase transitions. There is a need to move forward towards a more complete non-equilibrium way to approach hydrates in industrial settings. Similar challenges are related to natural gas hydrates in sediments. Hydrates dissociates worldwide due to seawater that leaks into hydrate filled sediments. Many of the global resources of methane hydrate reside in a stationary situation of hydrate dissociation from incoming water and formation of new hydrate from incoming hydrate formers from below. Understanding the dynamic situation of a real hydrate reservoir is critical for understanding the distribution characteristics of hydrates in the sediments. This knowledge is also critical for designing efficient hydrate production strategies. In order to facilitate the needed analysis we propose the use of residual thermodynamics for all phases, including all hydrate phases, so as to be able to analyze real stability limits and needed heat supply for hydrate production. Keywords: hydrate; non-equilibrium; production 1. Introduction The formation of hydrocarbon hydrates has been a problem for the oil and gas industry for many decades. Macroscopically these hydrates looks like ice or snow. Industrially the most important structures are structure I and structure II. The smallest symmetric unit in structure I is a cubic cell containing 46 water molecules, which creates two small cavities and six large cavities formed by hydrogen bounded water. In structure I the smallest cavities consists of 20 water molecules in the cavity walls and for the large cavity there are 24 water molecules in the cavity walls (see Figure1 for an illustration). The cavities are stabilized mainly by the volume of the molecules (repulsion) entering the cavities and weak van der Waal type attractions between the molecules in the cavity and the water molecules in the cavity walls. Molecules of limited polarity can also enter these cavities. The dipole moment of H2S leads to a positive net charge in direction outwards from center of mass when the molecules rotate in the cavity. Samplings from molecular dynamics simulations [1] show that the result of the water molecules in the cavity walls is a net negative charged Coulombic field pointing inwards in the cavity. The extra attractive coulombic energy between water and H2S[2], as compared to neutral molecules like for instance methane, is the reason why H2S is an exceptionally good hydrate former. CO2, on the other hand, has a significant quadrupole moment which results in a negative coulombic Energies 2020, 13, 880; doi:10.3390/en13040880 www.mdpi.com/journal/energies Energies 2020, 13, 880 2 of 26 Energies 2020, 13, x FOR PEER REVIEW 2 of 25 to neutral molecules like for instance methane, is the reason why H2S is an exceptionally good hydrate field in the direction outward from center of mass. The result is a Coulombic repulsion that destabilizes former. CO2, on the other hand, has a significant quadrupole moment which results in a negative the largecoulombic cavity field in structurein the direction I hydrate outward by roughlyfrom cent 1er kJ of/mole mass. hydrate The result [2 ].is Thea Coulombic large size repulsion of the CO2, relativethat to destabilizes the size of the the large large cavity cavity, in destabilizesstructure I hydrate the structure by roughly I hydrate 1 kJ/mole further hydrate with [2]. approximately The large 1 kJ/molesize of hydrate the CO2, [relative1]. These to the destabilization size of the large e ffcavity,ects are destabilizes still limited the structure compared I hydrate to the further effects with of fairly largeapproximately attractive van 1 derkJ/mole Waal hydrate attractions [1]. These between destabilization water and effects the threeare still atoms limited in compared CO2. These to the aspects are oneeffects of the of fairly reasons large that attractive CO2 is van a substantially der Waal attractions better between hydrate water former and than the forthree instance atoms in CH CO42.. This will beThese quantified aspects are in one more of the details reasons later. that AnCO2 aspectis a substantially that is rarely betterdiscussed hydrate former is the than stabilizing for instance eff ects due toCH attractions4. This will be between quantified molecules in more insidedetails later. neighboring An aspect cavities. that is rarely An olddiscussed study is this the wasstabilizing published effects due to attractions between molecules inside neighboring cavities. An old study this was by Kvamme and Lund [3] using a Monte Carlo method. These attractions between molecules in published by Kvamme and Lund [3] using a Monte Carlo method. These attractions between neighboring cavities are significant and often corrected for by empirical correction factors. Some of molecules in neighboring cavities are significant and often corrected for by empirical correction thesefactors. can be Some found of in these the bookcan be by found Sloan in andthe book Koh [by4] Sloan and will and notKoh be [4] discussed and will not in morebe discussed detail here.in more detail here. FigureFigure 1. Smallest 1. Smallest symmetrical symmetrical unit unit cell cell forfor hydratehydrate stru structurecture I is I iscubic cubic with with side side lengths12.01 lengths12.01 Å at Å at zero Celsius,zero Celsius, and and smaller smaller for for lower lower temperatures temperatures [[5,65,6]. Red Red spheres spheres illustrate illustrate a simplified a simplified monoatomic monoatomic modelmodel for methane. for methane. Water Water molecules molecules are scaledare scaled down do andwn and plotted plotted in Cyan in Cyan color. color. Black Black lines lines are are average average hydrogen bonds. The figure was plotted by Geir Huseby (Huseby, G., “Kinetiske hydrogen bonds. The figure was plotted by Geir Huseby (Huseby, G., “Kinetiske hydratinhibitorer”, MSc hydratinhibitorer”, MSc Thesis, Høgskolen i Telemark, Norway, 1995) based on coordinates from Bjørn Thesis, Høgskolen i Telemark, Norway, 1995) based on coordinates from Bjørn Kvamme as used in Kvamme as used in molecular dynamics simulations. molecular dynamics simulations. Structure II hydrate contains 16 small cavities and eight large cavities with a total of 136 water Structuremolecules IIin hydratea unit cell contains with side 16 lengths small cavities17 Å. The and small eight cavity large is cavitiessimilar to with the asmall total cavity of 136 in water moleculesstructure in a I unitbut the cell large with cavity side lengths in structure 17 Å. II The is larger small and cavity contains is similar 28 water to the molecules small cavity in thein cavity structure I butwalls. the large The large cavity cavity in structure has space IIfor is molecules larger and likecontains for instance 28 propane water molecules and iso-butane. in the In cavityorder to walls. The largelimit the cavity scope has ofspace this paper for molecules we will mostly like forfocus instance on structure propane I hydrates and iso-butane. for a variety In of order reasons. to limit the scopeMostly of because this paper the discussion we will mostly in this focuspaper onfocu structures very much I hydrates on hydrate for anon-equilibrium variety of reasons. but also Mostly becausebecause the discussion99% of natural in thisgas hydrate paper focusresources very in muchthe world on hydrateare from non-equilibriumbiogenic degradation but of also organic because 99% ofmaterial natural and gas the hydrate resulting resources hydrocarbons in the are world almost are pure from methane. biogenic CO2 degradation also makes hydrate of organic structure material I and the possible win-win situation of simultaneous CO2 storage as hydrate and release of CH4 from and the resulting hydrocarbons are almost pure methane. CO also makes hydrate structure I and the in situ hydrates is another motivation for this paper. 2 possible win-win situation of simultaneous CO storage as hydrate and release of CH from in situ Van der Waal and Platteeuw [7] used a semi-grand2 canonical ensemble to derive a Langmuir4 hydratestype isadsorption another motivationtheory in which for this water paper. molecules are fixed and rigid while molecules that enter Van der Waal and Platteeuw [7] used a semi-grand canonical ensemble to derive a Langmuir type adsorption theory in which water molecules are fixed and rigid while molecules that enter cavities (guest molecules) are open to exchange with surrounding phases. The final result of the derivation is expressed in terms of chemical potential for water in hydrate: Energies 2020, 13, 880 3 of 26 0 1 X X H O,H B C µ = µ RTvk lnB1 + hijC (1) H2O H2O − @B AC k=1,2 i where µO,H is the chemical potential for water in an empty clathrate for the given structure in H2O consideration. Historically thus value has not been calculated by theoretical methods but rather fitted to experimental data in the form of chemical potential of pure liquid water minus empty clathrate water chemical potential.