Methane hydrate formation and decomposition: Structural studies vianeutron diffraction and empirical potential structure refinementHelen Thompson, Alan K. Soper, Piers Buchanan, Nawaf Aldiwan, Jefferson L. Creek et al. Citation: J. Chem. Phys. 124, 164508 (2006); doi: 10.1063/1.2191056 View online: http://dx.doi.org/10.1063/1.2191056 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v124/i16 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

THE JOURNAL OF CHEMICAL PHYSICS 124, 164508 �2006�

Methane hydrate formation and decomposition: Structural studiesvia neutron diffraction and empirical potential structure refinement

Helen Thompsona�,b� and Alan K. SoperISIS Facility, Rutherford Appleton Laboratory, Didcot, Oxon OX11 0QX, United Kingdom

Piers Buchananc� and Nawaf AldiwanDepartment of Chemistry, Kings College London, Strand, London WC2R 2LS, United Kingdom

Jefferson L. CreekChevron Energy Technology Company, Houston, Texas 77002

Carolyn A. Koha�,d�

Colorado School of Mines, Center for Hydrate Research, Chemical Engineering Department,Golden, Colorado 80401

�Received 19 January 2006; accepted 7 March 2006; published online 27 April 2006�

Neutron diffraction studies with hydrogen/deuterium isotope substitution measurements areperformed to investigate the water structure at the early, medium, and late periods of methaneclathrate hydrate formation and decomposition. These measurements are coupled with simultaneousgas consumption measurements to track the formation of methane hydrate from a gas/water mixture,and then the complete decomposition of hydrate. Empirical potential structure refinement computersimulations are used to analyze the neutron diffraction data and extract from the data the waterstructure in the bulk methane hydrate solution. The results highlight the significant changes in thewater structure of the remaining liquid at various stages of hydrate formation and decomposition,and give further insight into the way in which hydrates form. The results also have importantimplications on the memory effect, suggesting that the water structure in the presence of hydratecrystallites is significantly different at equivalent stages of forming compared to decomposing.These results are in sharp contrast to the previously reported cases when all remaining hydratecrystallites are absent from the solution. For these systems there is no detectable change in the waterstructure or the methane hydration shell before hydrate formation and after decomposition. Based onthe new results presented in this paper, it is clear that the local water structure is affected by thepresence of hydrate crystallites, which may in turn be responsible for the “history” or “memory”effect where the production of hydrate from a solution of formed and then subsequently meltedhydrate is reportedly much quicker than producing hydrate from a fresh water/gas mixture. © 2006American Institute of Physics. �DOI: 10.1063/1.2191056�

I. INTRODUCTION

Clathrate hydrates are solid inclusion compounds com-prising hydrogen-bonded water cages which trap small guestmolecules, such as methane, carbon dioxide, or propane.1,2

There are three main clathrate hydrate structures, known assI, sII, and sH, which vary in the type and number of cavitiesthey contain per unit cell. The size of the guest species gen-erally determines the structure type that is formed �see Refs.1 and 2 for more details�. For example, methane hydrate willform sI hydrate, while a larger molecule such as propane willform sII hydrate and an even larger molecule such as meth-ylcyclohexane will form sH when methane is also present.1

Gas clathrate hydrates generally form at high pressure�typically 5–35 MPa� and low temperature �typically277–288 K�.

a�Authors to whom correspondence should be addressed.b�Electronic mail: h.thompson@rl.ac.ukc�Present address: Meteorological Office, Fitzroy Road, Exeter, Devon, EX1

3PB, U.K.d�

Electronic mail: ckoh@mines.edu

0021-9606/2006/124�16�/164508/12/$23.00 124, 1645

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

Gas clathrate hydrates have a number of industrial andtechnological applications. Gas hydrates occur naturally indeepwater subsea oil and gas pipelines when the fluid in thepipeline is subjected to high pressures and low temperatures.Hydrate formation can lead to blockage of the pipelines andsubsequent catastrophic economic and safety hazards.1,2 Thediscovery3 of natural deposits of methane hydrate in oceanicand permafrost regions has led to the increasing interest inrecovery and production of methane from these naturalhydrates.4 Even the most conservative estimates suggest thatthe amount of methane held within these natural hydrateminerals is twice that of all fossil fuels combined.4 Coupledwith this current drive to recover energy from these naturalhydrate deposits are the concerns of seafloor stability5 andclimate change.6,7 Other technological applications of gashydrates include energy storage of natural gas8,9 andhydrogen10,11 within clathrate materials, desalination of sea-water using hydrate particles,12 and gas separations.13,14

Fundamental understanding of the hydrate formation anddecomposition processes on a molecular level is important in

advancing the above technologies. In particular, controlling

© 2006 American Institute of Physics08-1

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-2 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

hydrate formation and decomposition is key to preventingindustrial pipeline blockages due to hydrates, assessing theeconomic feasibility of producing methane from natural hy-drate deposits, and releasing energy from hydrate storagematerials safely and efficiently.

One component of the hydrate formation and decompo-sition processes is the widely reported and debated phenom-enon of the “memory” effect. This is where the time requiredto form hydrates from a fresh water/gas mixture is found tobe significantly longer than that prepared from a solution ofpreviously formed and then subsequently meltedhydrate.1,15–18 The shortened time for hydrate formation inthe latter case is attributed to water retaining a memory ofthe melted hydrate. While some reports suggest that thismemory is due to residual water structure remaining in thesolution after hydrate has melted,1,19–22 other reports attributethis phenomenon rather to dissolved gas remaining in solu-tion after hydrate melts.15

Nerheim et al.23 used dynamic light scattering �photocor-relation spectroscopy� to examine the effect on hydratenuclei/cluster size distributions of forming hydrate from afresh water/gas system versus from an aqueous solution ofpreviously melted hydrate. In these studies they found thatthe history or memory of melted hydrate in liquid water isremoved after a period of time �1 h when dissociated at277 K and atmospheric pressure and 12 h when dissociatedat higher pressures�. During gas hydrate formation �preparedfrom a 94 mol % methane/6 mol % propane gas mixture� acritical size of hydrate nuclei between 5 and 30 nm was ob-served �cf. Englezos et al.24 who estimated critical nuclei of6–34 nm diameters�. Dissociation of the hydrate was per-formed over 7 days at 299 K �2–3 °C outside the hydratestability region�. During hydrate melting a “stable” state wasreached which survived for a significant period of time priorto total dissociation. This stable state gave rise to two par-ticle size distributions centered at 50 and 1800 nm. The dis-tribution centered at 50 nm was suggested to reflect criticalnuclei associated with the dissociation process, while thatcentered at 1800 nm was attributed to gas bubbles or impu-rities. After 7 days of melting and on complete dissociationof the hydrate, the scattered intensity was found to be higherthan that prior to hydrate formation. The authors suggestedthat this intensity difference may be due to low concentra-tions of gas bubbles, remnants from the dissociated hydrate,or residual crystal-like networks. However, it was recognizedthat the size of residual crystal-like networks would be toosmall to be detected with light scattering.

Few molecular-level studies have been performed on thememory effect of hydrates. Buchanan et al.18 recently usedneutron diffraction studies to show that, provided all detect-able hydrate crystallites �up to 1 vol %� are removed fromsolution, the water structure is not changed significantly for afresh water/gas system compared to a water/gas systemformed from previously melted hydrate. The results alsoshowed that the crystalline hydrates were persistent in solu-tion during the decomposition process and required up to 8 hto be removed at 294 K and 14.5 MPa.

Uchida et al.25 used Raman spectroscopy to examine the

hydration structure in aqueous solutions containing bulk hy-

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

drate crystals. They monitored the methane ��C–H� stretch-ing vibration at different distances from the hydrate-solutioninterface. Methane hydrate exhibits two ��C–H� peaks ataround 2914 and 2904 cm−1 for methane in the large andsmall cages, respectively. The results showed that the posi-tions of the ��C–H� peaks changed significantly on movingfrom the hydrate crystal interface through the solution, de-creasing from around 2914 to around 2911.5 cm−1 on mov-ing from 0 to 0.5 mm from the hydrate-solution interface.Further than around 0.5 mm from the hydrate-solution inter-face, the ��C–H� peak position was around 2910 cm−1 cor-responding to the position for methane in water without hy-drate crystals present. Based on these results, the authorssuggested that the hydrate crystals cause “semistable cage-like” entities in aqueous solution and that these entities aredifferent to those of the hydration shell.

In this paper we track the hydrate formation and decom-position processes on a molecular level. Using empirical po-tential structure refinement �EPSR� computer analysis of theneutron diffraction data we determine the changes in the wa-ter structure encapsulated in hydrate crystallites during theequivalent phases of hydrate formation and decomposition.These results have implications in the widely reported anddebated memory effect phenomenon.

II. METHODS

A. Experiment: Neutron diffraction data of hydrateformation and decomposition

Neutron diffraction measurements have been performedon Small Angle Neutron Diffractometer for Amorphous andLiquid Samples �SANDALS� at the ISIS facility to track theformation and decomposition stages of methane hydrate. Fulldetails of the experimental setup are given in Ref. 18. Thesamples were prepared at a constant pressure of 14.5 MPaand an initial temperature of 293 K. The temperature wasthen dropped to 279 K �8 K below the formation line ofmethane/D2O hydrate at this pressure�,18 and diffraction pat-terns were recorded every 0.5 h, to follow the formation ofthe hydrate crystal. The hydrate was considered “fullyformed” once the methane gas consumption had reached itsmaximum, and no further increase in the height of the Braggpeaks was observed.

The structural changes during the decomposition processwere also carefully monitored. By increasing the temperatureto 292 K �5 K above the methane hydrate melting line�,complete dissociation took place slowly over a period of12 h. Neutron diffraction measurements were again recordedevery 0.5 h to track the decomposition process.

These measurements were performed for two isotopiccompositions: CD4–D2O and CH4–D2O. The degree ofcrystallinity within each sample, x, was ascertained by fittingthe part-formed data to a sum of the data for the fully formedhydrate and the data for the 0% formed methane-water liquid

18

mixture,

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-3 Methane hydrate formation and decomposition J. Chem. Phys. 124, 164508 �2006�

F�Q�part-formed = x�F�Q�100% formed� + �1 − x�

��F�Q�0% formed� . �1�

The degree of crystallinity as determined by this methodwas, in general, found to be within 10% of the degree ofhydrate formation expected by monitoring the gasconsumption.18

B. EPSR simulation details

EPSR simulation26 is a useful tool in interpreting diffrac-tion data. EPSR is essentially a Monte Carlo simulation of asystem, in which iterative refinement of atomic potentialsdrive the simulated structure until it becomes consistent withthe available diffraction data. The resulting configuration al-lows three-dimensional structural properties of the system tobe investigated in detail.

EPSR has been widely used to interpret data on a varietyof amorphous materials.26–28 In theory, the technique shouldbe transferable to crystalline systems exhibiting long-rangeorder, and given an infinite box size, the Fourier transforma-tions used in EPSR to convert from g�r� to S�Q� would stillbe valid. However, we are limited by computer power andspeed to being able to model configurations with a maximumbox side of 60–70 Å. For this reason, the neutron diffractiondata for the 100% formed case were convoluted with a func-tion dependent on the box size of 60 Å, to account for thecrystalline long-range order extending beyond the length ofthe box. The form of the convolution function was takenfrom Ref. 29. In a crystalline system, the g�r� is long ranged,although the EPSR simulation will only be able to calculatethe g�r� out to a half of the box size. The simulated g�r� istherefore equivalent to the long-range g�r� multiplied by astep function �m�r�=1 for 0�r�L /2, and 0 otherwise�. TheFourier transform of the simulated g�r�, Fsim�Q�, is thereforethe measured Fexpt�Q� convoluted with the Fourier transformof m�r�, leading to a broadening of the measured Braggpeaks. This is the function which must be used for compari-son with the simulated F�Q�. This structure factor is calcu-lated via

Fsim�Qj� =1

�� Fexpt�Qi�

�� sin��Qi − Qj�L/2

�Qi − Qj�−

sin��Qi + Qj�L/2

�Qi + Qj��dQi. �2�

The data for the 100% formed crystal structure weremodeled using EPSR, with the initial atomic coordinates de-rived from SI hydrate crystal x-ray and neutron diffractiondata.30,31 This sI structure comprises a unit cell of 12 Å,containing 46 water molecules and 8 methane molecules fill-ing both the 2 small and 6 large cages. The simulation cellsize used was 60 Å, �large in order to allow the maximumresolution for calculating the simulated Bragg peaks�. Theneutron diffraction data were convoluted with a function de-pendent on the box size of 60 Å, �using Eq. �4�� to accountfor the crystalline long-range order extending beyond thelength of the box. The atomic positions were then allowed to

relax during the course of the simulation, causing the initial

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

crystal to become more disordered, although it did not meltor form a purely amorphous structure, as can be seen by thepresence of the long-range correlations in the partial pairdistribution functions plotted. This was achieved by limitingthe step size for each molecule translation, such that the sys-tem was unable to surmount the energy barrier for such amelting process.

A further challenge is attempting to model the part-formed hydrate data, which incorporates both long-rangecrystalline structure and underlying amorphous structure.Here we are limited by the maximum size of the systemwhich we are able to simulate on a fully atomistic level. Itwould be implausible to attempt to extract long-range corre-lations from a relatively small atomic configuration which isonly part crystalline, or indeed to begin with a crystallineconfiguration and attempt to “melt” a part of it, while pre-serving some degree of long-range order.

To overcome this complication, the data for each per-centage of hydrate formation were separated into a “crystalphase” F�Q� and a “liquid phase” F�Q�. This would thenallow the data from each of the two phases �methane-waterliquid and methane hydrate� to be incorporated into two in-dependent simulations.

The total liquid F�Q� was generated using

liquid F�Q�

=�total F�Q� − x�100 % formed crystal F�Q���

�1 − x�,

�3�

where x is the degree of crystallinity.Similarly, the total crystal F�Q� was created using

crystal F�Q�

=�total F�Q� − �1 − x��0 % formed liquid F�Q���

x.

�4�

The crystal structure factors for each of the part-formedmethane hydrate samples were created as a check on theestimate, x, for the degree of hydrate formation. In each case,the crystal F�Q�’s had the same Bragg peak heights as the100% formed samples after subtraction of the liquid struc-ture factor, thus confirming the reliability of the above meth-ods, �3� and �4�, for separating the data for the liquid andcrystal phases. The methane hydrate decomposition datawere analyzed using a similar method to the hydrate forma-tion data, again by fitting a sum of the fully formed and fullydecomposed data to determine the degree of crystallinity.

The data for the liquid phases of part-formed methanehydrate were modeled via EPSR, using a randomized startingconfiguration with a concentration of 1 methane molecule to100 water molecules, at a density of 0.1 at. Å−3. The simu-lation comprised 808 molecules in total, in a box of side29.0044 Å. It should be noted that each liquid phase data set

is modeled with a box which has no crystalline component,

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-4 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

and therefore does not take explicit account of water-crystallite correlations. The initial potentials for the methanemolecule were taken from Ref. 32, and the water model usedthe SPC/E �simple point charge–extended� water potentials.33

III. RESULTS

The methane hydrate total structure factors during for-mation and decomposition, after corrections for the back-ground, absorption, multiple scattering and self-scattering,are shown in Figs. 1 and 2. These data were then separatedinto the crystal and liquid structure factors using the methodoutlined in Sec. II, for each percentage formed. The sepa-rated liquid structure factors are presented in Figs. 3 and 4:the absence of significant Bragg peaks in the liquid structurediffraction pattern is evidence that once formed the crystalhydrate pattern did not change appreciably. �Note that in thecase of some of the part-decomposed �60%, 70%, and 80%crystalline� liquid structure factors, some small peaks remainwhere it was not possible to subtract the crystal structurefactor exactly�.

For each part-formed sample, the crystal structure factoris very similar apart from a small background level. For thisreason, it is suggested that any structural changes occurringas methane hydrate forms and decomposes take place in theliquid phase rather than the crystal phase. For the fully deu-

FIG. 1. Total structure factors for the methane hydrate formation stages: �a�CD4–D2O and �b� CH4–D2O.

teriated sample, the height of the principal peak in the liquid

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

structure factor decreases significantly in the part-formedstages �Fig. 3�a��, as compared to the 0% formed methane-water mixture before hydrate formation or after hydrate de-composition. In addition, the data for the protiated methanesamples show increased low-Q ��1.2 Å−1� scattering withincreasing amounts of hydrate formed. Bearing in mind thatin the CH4–D2O sample, there is a larger contrast in terms ofscattering cross section between the protiated methane andthe deuteriated water, the observed low-Q scattering suggestspossible segregation of methane hydrate �higher methaneconcentration� and methane-water liquid �lower methaneconcentration�, giving rise to regions of confined methane-water liquid within the samples. This effect of increased low-Q scattering has also been observed in the total structurefactors of Vycor: a porous network of silica glass,34 and intertiary-butanol-water solution,35 where small angle neutronscattering reveals clustering at mesoscopic length scales. Themethane hydrate was decomposed at temperatures of up to5 °C above the dissociation temperature, and the confinedwater effect can also be observed at these temperatures�14–19 °C� as the hydrate decomposes.

The detailed analysis of this proposed confinement of themethane-water system is given as follows. Using the formal-ism outlined in the Appendix, we have formed a uniformatom distribution function, which takes account of the fact

FIG. 2. Total structure factors for the methane hydrate decompositionstages: �a� CD4–D2O and �b� CH4–D2O.

that the methane-water liquid is excluded from the crystal-

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-5 Methane hydrate formation and decomposition J. Chem. Phys. 124, 164508 �2006�

line hydrate regions of the sample, and therefore will “see” alocal number density which is significantly higher than theaverage liquid density. The calculation assumes that the wa-ter molecules are randomly distributed within spherical poreswith a specified radius R and with separation D. These uni-form atom distribution functions were then multiplied by thetotal pair distribution function G�r� from the EPSR simula-tion of the 0% formed methane-water solution. Then a Fou-rier transform to Q space was applied to the “confined”G�r�gu�r� radial distribution function,

F�Q� =4��

Q� rG�r�gu�r�sin Qrdr , �5�

where � is the local atomic number density.The resulting F�Q�’s are shown in Fig. 5 and can be seen

to have a broadened principal peak compared with the origi-nal F�Q�. The pore separations were chosen to be consistentwith the degree of hydrate formation; however, the structurefactors calculated assuming a single, isolated pore showedlittle difference to those calculated assuming an ensemble ofpores. We shall now turn to computer simulation to gainfurther insight into the possible processes behind hydrateformation/decomposition.

A. Hydrate crystal simulation

The fit to the methane hydrate crystal is shown in Figs. 6

FIG. 3. The liquid structures of the part-formed methane hydrate after sub-traction of the crystal structure.

and 7, shows the atomic configuration initially and after

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

EPSR refinement. For both the deuteriated and protiatedmethane–heavy-water samples, the simulation has provided aclose fit to the measured hydrate structure. The long-rangeorder is preserved as the simulation progresses, as can beseen in the partial pair correlation functions �Figs. 8 and 9�,where the structural oscillations extend beyond �20 Å.Looking at the C–OW and C–HW distributions from the ini-tial configuration, the methane resides in both small andlarge water cages with radii of 3.95 and 4.33 Å, respectively.Upon disordering the crystal, the hydration shell C–OW dis-tribution becomes broader. Although the change in this peakshape gives the appearance that the C–OW distance becomessmaller, in fact, the mean C–OW distance remains the same.

The C–C and OW–OW distances �Fig. 9� maintain simi-lar average values, although over a broader range as the crys-tal has become more disordered. This disordering has alsoled to a broadening of the OW–OW–OW bond angle distri-bution, defined as in Fig. 10. The change in this bond angledistribution is illustrated in Fig. 11: the initial simulation cellshows the most probable bond angles to be at �107° and125°. After the simulation has run its course, the most likelybond angle remains around 107°, but there is also a smallprobability of OW–OW–OW arrangements at an angle of�51°. This distribution is not unlike that for the liquidphases of methane hydrate formation/decomposition, to

FIG. 4. The liquid structures of the part-decomposed methane hydrate aftersubtraction of the crystal structure.

which we shall turn our attention in the following section.

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-6 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

B. Simulation of the liquid phases of methanehydrate formation

The EPSR fits to the part-formed liquid phase data setsare shown in Fig. 12. The employment of the empirical po-tential allows the simulation to obtain a close fit to the data.The misfits evident in the CH4–D2O graph are due only tobackground levels, rather than any significant differences instructure between the simulation and the data.

The simulations here are again able to reproduce theexperimental data. We notice a broadening in the principalpeak with the degree of hydrate formation. We propose thatthis is indicative of the way in which methane hydrate forms:namely, that the crystal grows from several nucleation sites,eventually “self-trapping” the remaining methane-water so-lution.

A comparison of the liquid phase data for the part-formed methane hydrate and the structure factors calculatedfor bulk methane-water solution confined in pores shows thatthe observed broadening of the principal peak is consistentwith the remaining methane hydrate solution becoming self-trapped in smaller and smaller pores, from �15 Å at 50%hydrate formation down to �5 Å at 80% hydrate formation�Fig. 5�.

Figure 13 shows several of the atom-atom partial paircorrelation functions arising from the EPSR simulations of

FIG. 5. Comparison of the resulting total structure factors after confinementin pores of radii 5–15 Å, with the liquid phases of part-formed methanehydrate samples.

the liquid phases of the part-formed methane hydrate. Given

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

the very low concentration of methane present, the dominantcontribution from the data is due to water-water correlations.The OW–OW, OW–HW, and HW–HW distributions show anincrease in the height of the peak relating to the nearestneighbor correlations with the degree of hydrate formation.This is a further signature of water clustering or confinement:because the local density of the water molecules in confine-ment becomes greater than the average density of water inthe solution, any pair correlation functions will also show alarger amplitude at lower r, following the shapes of the uni-form atom radial distribution functions �see the Appendix�.

Further to this, the OW–OW–OW bond angle distribu-tion plotted in Fig. 14 shows significant changes as the hy-drate forms. With increasing hydrate formation, we observean increase in the “trigonal” water distribution at 53°, and ashift of the “tetrahedral” distribution to slightly higher anglesfrom 97° to 101°, suggesting an increase in the degree oftetrahedrality. It could also mean that there is an increase inpentagonal or hexagonal rings, as per Fig. 11, i.e., the wateris starting to order to be ready for hydrate formation. There-fore we observe both ordering �growth of tetrahedrality� anddisordering �growth of trigonal peak� effects.

The initial data, together with the changes to the water-water distribution as shown by the EPSR simulations, lead usto propose that methane hydrate begins to form at severalpositions in the sample and grows in such a way as to trapthe remaining methane-water solution in small pores. These

FIG. 6. The EPSR fits to the fully formed methane hydrate crystal.

pores decrease in size as more methane hydrate is formed

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-7 Methane hydrate formation and decomposition J. Chem. Phys. 124, 164508 �2006�

around the pore wall, leading to still sharper water-waterreal-space distributions, and a broader principal peak in themethane-water solution total structure factors. It is then ofinterest to investigate whether methane hydrate decomposi-tion occurs in a similar way: whether the hydrate melts toleave small cavities of methane-water solution, or whetherthe melting process begins in one region only and decompo-sition proceeds from that point.

C. Simulation of the liquid phases of methanehydrate decomposition

Figure 15 shows the fits to the liquid phase data as thehydrate decomposes. For the 50%–80% crystalline samples,only the CD4–D2O data have been fitted, to avoid replicat-

FIG. 7. The EPSR atomic configuration �a� initial setup, �b� after potentialrefinement.

ing the spurious oscillations which are more significant in the

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

CH4–D2O data. Again, the application of the empirical po-tential drives the simulation to fit the experimental data moreclosely.

The pair correlation functions for OW–OW, OW–HW,and HW–HW arising from the EPSR simulations of the liq-uid phases of the partly-decomposed methane hydrate areshown in Fig. 16. The trend in the water-water correlations inthe decomposing cases is similar to the “hydrate forming”simulations: the first OW–OW peak becomes less sharp asthe hydrate decomposes. Moreover, in the 70%–80% part-decomposed stages, the first OW–OW nearest neighbor peakis sharper than its equivalent part-formed counterpart duringthe formation stage. This same effect can be seen in theOW–HW and HW–HW pair correlation functions. Thesefindings all suggest that the hydrate decomposes in a similarmanner to hydrate formation—that melting occurs in smallpockets between regions of hydrate crystal. The sharper firstshell peaks also imply that this confinement of the meltedhydrate happens to a greater extent upon decompositioncompared to formation.

The OW–OW–OW bond angle distribution �Fig. 17�gives a decrease in the trigonal peak upon hydrate decompo-sition, which also moves inwards from �55° at 80% crystal-linity to 52° at 50%, 25%, and 0% crystallinities. Concur-rently, the tetrahedral peak moves inwards from 109° at 80%crystallinity to 99° at 0% crystallinity. Again, some degree of

FIG. 8. Partial pair correlation functions for methane-water correlationsC–OW and C–HW in the methane hydrate crystal, before and after EPSRsimulation.

hysteresis between formation and decomposition is evident:

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-8 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

the variations in the bond angle probabilities and the shifts inpeak positions are greater during the decomposition phasethan the formation phase.

IV. DISCUSSION

The structure of the methane-water liquid remaining insamples of part-formed methane hydrate is shown to be sig-nificantly altered from that of bulk methane-water liquid.The salient features are the broadening of the principal dif-fraction peak with the percentage of hydrate formed in boththe deuteriated and protiated methane structure factors, andthe rise at low Q in the protiated methane structure factors.Comparing the structure factors calculated for bulk methane-water solution confined in spherical pores, with the liquidphase structure factors for the part-formed methane hydrate,shows that the broadening of the principal peak can be at-

FIG. 9. Partial pair correlation functions for C–C and OW–OW in the meth-ane hydrate crystal, before and after EPSR simulation.

FIG. 10. Determination of the angle distribution from the water-water

correlations.

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

tributed to the remaining methane-water liquid becoming oc-cluded in pores from �15 to �5 Å radius, in going from50% to 80% crystallinity.

The water-water partial pair distribution functions, cal-culated from the EPSR simulations for the part-formed/part-decomposed methane hydrate, are also markedly differentfrom those for bulk water. We see an increase in the nearestneighbor OW–OW, OW–HW, and HW–HW peaks with in-creasing hydrate formation. These trends are consistent withthe local water density becoming greater than the averagewater density, owing to confinement in pores formed by the

FIG. 11. The angle distribution OW–OW–OW �with OW–OW distancesbeing between 2.2 and 3.5 Å� in the methane hydrate crystal, before andafter EPSR simulation.

FIG. 12. EPSR fits to the liquid phases of part-formed methane hydrate.

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-9 Methane hydrate formation and decomposition J. Chem. Phys. 124, 164508 �2006�

surrounding hydrate crystal. Furthermore, the OW–OW–OWangle distribution shows an increase in the trigonal peakheight and a shift of the tetrahedral peak towards higherangles, with increasing degree of crystallinity, i.e., we seeconcurrent ordering �growth of tetrahedrality� and disorder-ing �growth of trigonal peak� of the intermolecular waterstructure. The growth in tetrahedrality perhaps indicates thebeginning of the water molecules reordering into pentagonal/hexagonal rings,2 ready for hydrate formation.

It is clear then that the structure of the remainingmethane-water liquid enclosed by hydrate crystallites, duringboth formation and decomposition of the hydrate, is signifi-

FIG. 13. Partial pair correlation functions for OW–OW, OW–HW, andHW–HW in the liquid phases of methane hydrate formation.

cantly altered from the structure of bulk methane-water liq-

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

uid. The changes in the water-water radial distribution func-tion and the OW–OW–OW angle distribution are morepronounced during hydrate decomposition than during theformation stage. These results suggest that the hydrate crys-tal begins to form at several points in the sample, and thecrystal grows in such a way as to trap the remainingmethane-water liquid in small pores of 5–15 Å radius. Simi-lar structural changes upon decomposition suggest that thehydrate also starts to melt from several points, again givingrise to pockets of melted hydrate confined by the remaininghydrate crystal matrix.

FIG. 14. Angle distribution for OW–OW–OW �with OW–OW distancesbeing between 2.2 and 3.5 Å� in the liquid phases of methane hydrateformation.

FIG. 15. EPSR fits to the liquid phases of part-decomposed methane

hydrate.

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-10 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

Previous neutron diffraction work on methane hydrate18

has shown there to be no detectable change in the bulkmethane-water liquid structure before hydrate formation andafter hydrate decomposition, provided that all crystalliteshave been removed from solution. However, severalreports1,15–17 present evidence for a “memory effect” inwhich the time taken to form hydrate from a freshly preparedmethane-water solution is much longer than that from a pre-viously melted hydrate. We propose that since the localmethane-water liquid structure is markedly affected by thepresence of hydrate crystallites, this could be the cause of the

FIG. 16. Partial pair correlation functions for OW–OW, OW–HW, andHW–HW in the liquid phases of methane hydrate decomposition. The thin-ner lines show the equivalent partial pair correlation functions during thehydrate formation stage.

so-called memory effect. Any system which has not quite

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

reached equilibrium after being held at a temperature justabove the melting temperature is likely to contain small re-gions of hydrate crystallites �which can persist in solution foran extended period of time18�, around which the water struc-ture is locally modified, possibly with an increased numberof pentagonal and hexagonal rings. This would then allowthe methane-water solution to be able to reform the hydratecrystal more readily.

V. CONCLUSIONS

In this paper we have investigated the changes in theliquid structure of methane-water solution, along the crystalformation and decomposition lines. We have shown that thepresence of hydrate crystallites affects the local water struc-ture, in a manner which is analogous with the confinement ofwater within spherical pores of radius 5–15 Å, depending onthe degree of formation. The confinement of the water leadsto sharper peaks at low r in the radial distribution functions,due to the local density being higher than the average densityof the liquid. This in turn leads to a broadening of the prin-cipal peak in the measured total structure factors. In addition,we have observed an increase in the “trigonal”OW–OW–OW angle distribution and a shift of the “tetrahe-dral” peak to higher angles with the degree of hydrate for-mation. These findings lead us to propose that methane hy-drate crystal begins to form at several places within thesample, in such a way as to trap or “confine” the remainingmethane-water liquid in small pores.

The reported effects are more pronounced as the meth-ane hydrate decomposes, suggesting a hysteresis in the struc-ture between formation and decomposition. This may explainthe widely reported formation and decomposition hysteresisloops observed using macroscopic pressure measurements.1,2

Again, it is likely that methane hydrate decomposes in asimilar way: melting occurs at several points within thesample, leaving regions of confined methane-water liquid.

Since the water structure is shown to be affected by crys-tallites being present in solution, the so-called “memory ef-fect” �in which hydrate forms more readily from the melted

FIG. 17. Angle distribution OW–OW–OW �with OW–OW distances beingbetween 2.2 and 3.5 Å� in the liquid phases of the methane hydrate decom-position. The thinner lines show the equivalent angle distribution during theformation stage.

crystal than from a freshly prepared methane-water solution�

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-11 Methane hydrate formation and decomposition J. Chem. Phys. 124, 164508 �2006�

could be explained by a low concentration of hydrate crys-tallites remaining in solution after the hydrate appears tohave melted. This leads to a locally modified water structure,which in turn allows the hydrate to reform more quickly.

ACKNOWLEDGMENTS

The authors acknowledge fundings from EPSRC and theChevron Energy Technology Company. The authors alsothank Keith Hester and Robin Westacott for their contribu-tions to this work. Technical help from John Dreyer, R.Done, C. Goodway, and J. Bones is also acknowledged.

APPENDIX: EXCLUDED VOLUME CORRECTIONFOR WATER CONFINED IN PORES IN HYDRATE

We refer to Ref. 36. The aim is to reproduce approxi-mately what happens to the water structure when it becomesrestricted to only a fraction of the volume of the sample. Wesuppose the pores are spherical of radius R and volume �p

= 43�R3. Equation �14� of Ref. 36 gives the basic uniform

atom distribution for this case, namely,

gu�r� =n̄p

n̄gp�r� +

1

vp� dugc�r − u�gp�u� , �A1�

where

gp�r� = �1 −3

4

r

R+

1

16� r

R�3

for r � 2R

0 for r � 2R �A2�

is the spherical pore radial distribution function,37 and for thepresent purposes the pore-pore centers radial distributionfunction is given by

gc�r� = �0 for r � D

1 for r � D ,� �A3�

and n̄p and n̄ are the atomic number densities of the fluid inthe pores and in the sample as a whole, respectively. It isbecause n̄p� n̄ that the uniform atom distribution rises abovethe asymptotic limit at low r.

Writing �Ref. 36�

Sp�Q� =1

vp� exp�iQ · r�gp�r�dr

= 9� sin QR − QR cos QR

�QR�3 �2

�A4�

and �following Eq. �12� in Ref. 36�

Su�Q� = n̄� exp�iQ · r�gu�r�dr

= n̄pvp�Sp�Q� + Hc�Q�Sp�Q� + Nc��Q�� , �A5�

where Nc is the number of pore centers in the sample,

Hc�Q� = nc� exp�iQ · r��gc�r� − 1�dr , �A6�

and nc is the number density of pores. For convenience we3

can set nc�3/4�D , i.e., approximately the inverse of the

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

average amount of space between pore centers. Using �A3�we obtain

Hc�Q� = 3�QD cos QD − sin QD

�QD�3 � , �A7�

which goes to the limit −1 at Q=0. Equations �A5�, �A4�,and �A7� allows us to perform the convolution in Eq. �A1� inQ space and so obtain the uniform atom distribution, �A1�,by Fourier inversion of �A5�. This is done numerically in twostages: first, the sum Sp�Q�+Hc�Q�Sp�Q� is Fourier trans-formed, then 1.0 is added to the result corresponding to theFourier transform of the � function in �A5�. This gives theuniform atom distributions, gu�r�, shown in Fig. 18 for arange of pore sizes. The relative values of R and D can bedetermined from the fact that the volume fraction of thesample occupied by the liquid �approximately �1−x�, wherex is the percentage hydrate in the sample� is given by Vf

=nc�p=R3 /D3. Hence the adjustable parameter is R with Dfixed by Vf.

Note that since the pores may overlap, the use of �A3� isnot strictly correct: in reality the pore-pore distribution willhave a much broader edge than the sharp cutoff implied by�A3�. To circumvent this difficulty we will normally set R�D /2, i.e., the pore radius is set greater than or equal to halfthe mean separation of the pores. When the convolution,�A1�, is performed, this will have the effect of producing anoverly smeared distribution as would occur if the pore-poredistribution had a broad edge.

1 E. D. Sloan, Jr., Clathrate Hydrates of Natural Gases, 2nd ed. �MarcelDekker, New York, 1998�.

2 C. A. Koh, Chem. Soc. Rev. 31, 157 �2002�.3 K. A. Kvenvolden, Marine of Gas Hydrates Geochemical Evidence Vol.1 �Butterworths, Boston, 1983�.

4 E. D. Sloan, Nature �London� 426, 353 �2003�.5 A. V. Egorov, K. Crane, P. R. Vogt, and A. N. Rozhkov, Geo-Mar. Lett.

19, 68 �1999�.6 G. R. Dickens, Chem. Geol. 157, 335 �1999�.7 J. P. Kennett, K. G. Cannariato, I. L. Hendy, and R. J. Behl, MethaneHydrates in Quaternary Climate Change: The Clathrate Gun Hypothesis�American Geophysical Union, Washington, D. C., 2002�.

8

FIG. 18. Uniform atom radial distribution functions obtained for pore radiiof 5–15 Å, at varying pore center–pore center distances.

Y. Saito, T. Kawasaki, T. Okui, T. Kondon, and R. Hiraoka, Second

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

164508-12 Thompson et al. J. Chem. Phys. 124, 164508 �2006�

International Conference on Natural Gas Hydrates, Toulouse, 2–6 June1996 �unpublished�, p. 459.

9 A. A. Khokhar, J. S. Gudmundsson, and E. D. Sloan, Fluid PhaseEquilib. 151, 383 �1998�.

10 W. L. Mao, H. K. Mao, A. F. Goncharov, V. V. Struzhkin, Q. Z. Guo, J.Z. Hu, J. F. Shu, R. J. Hemley, M. Somayazulu, and Y. S. Zhao, Science297, 2247 �2002�.

11 L. J. Florusse, C. J. Peters, J. Schoonman, K. C. Hester, C. A. Koh, S. F.Dec, K. N. Marsh, and E. D. Sloan, Science 306, 469 �2004�.

12 J. P. Osegovic, S. A. Holman, S. R. Tatro, L. A. Brazel, A. L. Ames, M.C. Evans, and M. D. Max, Proceedings of the Fifth International Confer-ence on Gas Hydrates 4. Current and Future Technology, 2004 �unpub-lished�, p. 1224.

13 S. P. Kang and H. Lee, Environ. Sci. Technol. 34, 4397 �2000�.14 K. Ostergaard, B. Tohidl, A. Danesh, R. Burgass, A. Todd, and T. Baxter,

Ann. N.Y. Acad. Sci. 912, 832 �2000�.15 M. Rodger, Ann. N.Y. Acad. Sci. 912, 474 �2000�.16 S. Takeya, A. Hori, T. Hondoh, and T. Uchida, J. Phys. Chem. B 104,

4164 �2000�.17 R. Ohmura, M. Ogawa, K. Yasuka, and Y. J. Mori, J. Phys. Chem. B 107,

5289 �2003�.18 P. B. Buchanan, A. K. Soper, H. Thompson, R. E. Westacott, J. L. Creek,

G. Hobson, and C. A. Koh, J. Chem. Phys. 123, 1 �2005�.19 M. Bylov and P. Rasmussen, Chem. Eng. Sci. 52, 3295 �1997�.20 R. Ohmura, T. Shigetomi, and Y. Mori, Ann. N.Y. Acad. Sci. 912, 958

�2000�.21 I. L. Moudrakovski, A. A. Sanchez, C. I. Ratcliffe, and J. A. Ripmeester,

J. Phys. Chem. B 105, 12338 �2001�.22

S. Gao, W. Chapman, and W. House, Proceedings of the Fifth Interna-

Downloaded 11 Mar 2013 to 150.108.161.71. Redistribution subject to AIP lic

tional Conference on Gas Hydrates 1 �Kinetics and Transport Phenom-ena�, 2005 �unpublished�, p. 252.

23 A. R. Nerheim, T. M. Svartaas, and E. J. Samuelsen, Proceedings of theFourth International Offshore and Polar Engineering Conference, Osaka,10–15 April 1994 �unpublished�, Vol. 1, p. 323.

24 P. Englezos, N. Kalogerakis, P. D. Dholabhai, and P. R. Bishnoi, Chem.Eng. Sci. 42, 2647 �1987�.

25 T. Uchida, R. Okabe, K. Gohara, S. Mae, Y. Seo, H. Lee, S. Takeya, J.Nagao, T. Ebinuma, and H. Narita, Can. J. Phys. 81, 359 �2003�.

26 A. K. Soper, Chem. Phys. 202, 295 �1996�.27 A. K. Soper, Mol. Phys. 99, 1503 �2001�.28 D. T. Bowron, J. L. Finney, and A. K. Soper, J. Phys. Chem. B 102, 3551

�1998�.29 D. A. Keen, RMC Modelling of Silica Phases in “Local Structure from

Diffraction” �Plenum, Michigan, 1998�.30 R. K. McMullan and G. A. Jeffery, J. Chem. Phys. 42, 2725 �1965�.31 C. Gutt, B. Asmussen, W. Press, M. R. Johnson, Y. P. Handa, and J. S.

Tse, J. Chem. Phys. 113, 4713 �2000�.32 W. L. Jorgensen, J. D. Madura, and C. J. Swenson, J. Am. Chem. Soc.

106, 6638 �1984�.33 H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91,

6269 �1987�.34 F. Bruni, M. A. Ricci, and A. K. Soper, J. Chem. Phys. 109, 1478 �1998�.35 J. L. Finney, D. T. Bowron, R. M. Daniel, P. A. Timmins, and M. A.

Roberts, Biophys. Chem. 105, 391 �2003�.36 A. K. Soper, J. Phys.: Condens. Matter 9, 2399 �1997�.37 O. Glatter and O. Kratky, Small Angle X-ray Scattering �Academic, New

York, 1992�.

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions