Bjørn Kvmme ,Nvid Seidi

a Hyzenenergy,26701 Quail Creek,Laguna Hills,CA,92656,USA

b Strategic Carbon LLC,20 Ladd St.,Suite 200,Portsmouth,NH 03801,USA

c State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,Xindu Road No.8,Chengdu,610500,China

ABSTRACT The global amount of energy contained in natural gas hydrates is huge,maybe as much as twice all known conventional fossil fuel resources.Unlike the worldwide distribution of conventional fossil fuels,hydrocarbons trapped in water as hydrate is also available in countries with limited conventional hydrocarbon resources.The development towards lower global emissions of greenhouse gases requires new strategies for the use of hydrocarbons,whether they are available as conventional resources,or in the form of natural gas hydrates.In this work we outline some possible strategies of utilizing hydrocarbon energy resources in a clean and environmentally friendly way.The use of carbon dioxide for producing hydrates is not new.Results from several experimental studies are available.In this work we shed more light on thermodynamic limitations and the need for additives in order to make the approach technically efficient.Through thermodynamic analysis we show that up to 20 mol per cent N2 is feasible in a CO2/N2 injection gas based on ability to form a new hydrate with free pore water and the released enthalpy needed to dissociate in situ CH4 hydrate.Surfactant is also needed in order to keep the injection gas front free of blocking hydrate films.Small alcohols like methanol and ethanol have surfactant properties.It is demonstrated that even 10 wt% ethanol in liquid pore water still makes it feasible to create a new hydrate from injection gas containing 20 mol per cent N2.Consequences of other components than CH4 in the hydrate are also discussed.And in practical cases with a well-defined source of CO2 it is also important to investigate impact of other components like for instance H2S on the stability of injection gas hydrate,as well as changes in enthalpy of hydrate formation.Another key element of this work is the conversion of produced hydrocarbons over to hydrogen and carbon dioxide using steam cracking.The technology for this is very old and in daily use.

Keywords:Hydrate Non-equilibrium Thermodynamics Kinetics

1.Introduction

Despite rapid development of renewable energy it seems unlikely to replace the eighty per cent fossil fuel share within the next few generations.The worldwide amount of natural gas trapped in the form of hydrate is huge.Estimates[1]indicate that energies of CH4trapped in this ice-like crystalline form(hydrates)may be as much as twice all known reserves of conventional sources of fossil fuel.These hydrates are not thermodynamically stable in porous media and relate to physical trappings(clay,shale or ice).The fact that these hydrate deposits exist is evidence of safe sealing during geological time scales since penetration of groundwater into CH4hydrate would lead to hydrate dissociation.Many hydrate reservoirs are connected to conventional hydrocarbon reservoirs,for instance in the Messoyakha field[2,3].Since early 1970's the accumulated gas production from this field is 430 bcf,of which roughly half is interpreted as produced from hydrate layers on top of the gas filled section.

Many different technologies have been proposed for the production of natural gas hydrates.The Messoyakha field[2,3]is a natural pressure reduction method with a free gas cap.It started as a conventional gas production but pressure monitoring(increased pressure after some time of gas production)revealed that gas was also released from hydrate.Pressure oscillations during later years also confirmed one of the challenges of pressure reduction.Geothermal gradients and small thermal gradients due to Joule-Thomson effects are not sufficient to supply the necessary heat for hydrate dissociation.This is also observed in pilot plant studies in Alaska[4-7].The first offshore pilot plant study was conducted offshore Japan in 2012 but froze down after 6 days[8,9].The second text was planned for 6 months but froze down after 24 days[10].

Thermal stimulation through injection of steam or hot water was also tested in Alaska[4-7,9].It is feasible technically but far too expensive for commercial use.

A critical bottle neck in the hydrate dissociation is transport of hydrate formers across a thin interface(1.2 nm)between liquid water and hydrate[11-13].This interface is a physical necessity due to electrostatic balance between fairly fixed partial charges on hydrate water surface and the dynamic water molecules outside.The extremely slow diffusivity coefficient close to the hydrate side of this interface limits mass transport supply during growth of hydrate,and also limits the release and transport of guest molecules during dissociation.Even though the phase transition is on nano scale it is the inner core of the hydrate phase transition dynamics and the interface reproduce itself rapidly(nano scale in time)during hydrate phase transitions.Any efficient hydrate production method has to“attack”the hydrogen bonds.As mentioned above the Joule-Thomson effect cools down the hydrate,and the geothermal gradients are limited.Pumping out liquid water and/or gas from a hydrate reservoir will change the fluids in contact with the hydrate and can lead to some other routes for hydrate dissociation.Sublimation of hydrate towards gas may not be very likely but hydrate exposed to water containing less methane than needed to keep hydrate stable[11-18]is viable.During a dynamic situation of hydrate particles moving around in pores also collisions with pore walls will dissociate hydrate.All mineral oxides are water wetting and structures water to extreme water densities in adsorbed layers[19-28].Corresponding chemical potentials of water in the first three adsorption layers are far lower than what is possible for hydrate water.In this respect mineral surfaces act as thermodynamic hydrate inhibitors.But hydrate formers like H2S and CO2can adsorb on mineral surfaces[23-28]and form hydrate[29,30].Methane is unable to adsorb directly on mineral surfaces in competition with water.But methane can get trapped in water which is structured by the mineral surfaces,and then nucleate to hydrate[11,20-23].This dual nature of mineral surfaces,acting as thermodynamic inhibitors while at the same time acting as catalysts for hydrate nucleation,is important in local hydrate reformation and also in many other aspects.Any efficient hydrate production method needs to affect the hydrogen bonds chemically and/or thermally.Injection of substantial amounts of thermodynamic inhibitors,like for instance methanol,is efficient but costly.

It is beyond the scope of this work to review all proposed methods for producing hydrate.The focus of this work is to examine possible concepts in which it is possible to store CO2safely while at the same time being technically and economically to produce clean energy.In that sense the focus is shifted form primary energy focus towards safe CO2storage and it might be relevant to look at options that are currently in use.

Norway has in many senses been a pioneer in underground storage of CO2.Sleipner oil field offshore Norway has been producing 1Mton CO2per year since 1996,which is stored in aquifer layers in Utsira.STATOIL(now EQUINOR)started this project based on a CO2emission tax of 50 US$per ton.This was the basis for the maximum cost of the project.0.7 Mtons of CO2per year from Snøhvit(Northern Norway)is stored in sediments below the Snøhvit hydrocarbon reservoir.The cost of separation,transport and storage is a reduction of the net value of the produced hydrocarbons in these two projects.The most recent project in Norway is the separation of 1.3 Mton CO2per year from cement industry and other industry in eastern part of Norway.The separated CO2will be shipped to a site close to the city of Bergen and piped for underground aquifer storage in an aquifer formation[31].The Norwegian government is putting in 25 Billion NOK(roughly 3 Billion US$)into the project.

One of the critical elements related to aquifer storage of CO2is storage integrity,which to a large extent is related to the existence of sealing formations(layers of clay,shale or other impermeable structures)that prevents CO2from leaking vertically into the ocean.After 25 years of injection into Utsira,and horizontal spreading of CO2plume there is still no verified answers on whether there are CO2leakages to the ocean or not.Natural gas hydrate reservoir with high hydrate pore saturation,on the other hand,have proven sealing structures that has kept the hydrate inside for millions of years.Hydrate reservoirs with low hydrate saturation will typically be in a dynamic situation in which hydrates are continuously dissociated by incoming seawater and low(relative)formation of new hydrate from upcoming gas.A reservoir with substantial fracture systems towards seafloor is not suitable for injection of CO2for storage in the form of hydrate.

Third largest Norwegian gas field,Ormen Lange,is located in the Storegga region below hydrate filled sediments.More recent mappings of Norwegian offshore hydrate have focused on Nyegga[32]and lately also the Barents Sea[33,34].These are just examples on hydrate deposits offshore Norway.And Nyegga[32]is an example of a hydrate reservoir with low hydrate saturation(below 15% of pore volume).Norway has been a net exporter of conventional oil and gas for 5 decades and the interest for mapping Norway offshore hydrate resources have been limited.

Many other countries have been mapping hydrate resources with a focus on possibility as a future energy source.References[1-5,9]contain typical examples of hydrate reservoirs with details on geological structures and trapping(sealing)formations.This information is not needed in this work and no review of this type of information will be provided here.We discuss a general concept that has to be adapted to each specific site depending on premises related to the actual site.The first major difference is between onshore and offshore hydrates.Then there are very many factors like depths,hydrate distribution in terms of thickness of hydrate layers and horizontal spreading,fracture systems and hydrate dynamics,upcoming hydrate fluxes and biogenic and thermogenic sources.In many cases biogenic layers of hydrate is blocking for available thermogenic sources.In other cases like Nyegga[32]the dissociation towards incoming seawater has been massive over long times and the gas that comes out is a mixture of biogenic and thermogenic gas.

The concept of CO2exchange with in situ CH4hydrate is not new.We have conducted experimental and theoretical work on this approach for 3 decades.And so has many other groups.There are numerous publications on experimental studies.We do not refer to these studies.That also includes our own experimental studies so there is no discrimination.It would simply take away too much of the focus of this work.

The primary objective of this work is to illustrate possible ways to combine CO2/CH4swapping with steam cracking of the produced gas,and how this can be assembled in a zero emission cycle.

A secondary objective of this work is to discuss some important thermodynamic aspects of the process.This is very important since it appears that many studies are designed on a“trial and error”basis without prior analysis of the thermodynamic limitations of the concept.The only conducted pilot plant study on using CO2/N2[35,36]is not an exception.Amount of N2utilized in the projects was too much relative to the ability for injection gas to form a new hydrate with the free pore water[37].

A third objective is to shed light on some confusion around the conversion mechanism.Fundamental atomistic experiments have to be conducted at atmospheric pressure and very low temperatures to get into the hydrate formation conditions[38-40].The formation of CH4hydrate from powdered ice and CH4gas is challenging by itself in terms of unconverted ice covered by hydrate.The conversion process with CO2is also very different from liquid water region since there is no dynamic liquid water side of the interface.

A fourth objective is to illustrate why there is a need for a consistent thermodynamic reference system for all phases.Generally there are too many active phases of significance and importance for hydrate in natural sediments for the system to be able to reach thermodynamic equilibrium.Then it is even more important that Gibbs free energy for the various water phases is comparable in terms of stability.Different hydrate formation routes lead to different hydrates(different composition,different densities and different free energies).

A fifth objective is related to the objectives above.There are some misunderstandings on the relative stability of CH4hydrate and CO2hydrate.This is due to comparison of pressure pemperature limits for hydrate formation rather than comparing Gibbs free energies for the hydrates.Temperature and pressure are only two of many independent thermodynamic variables.Gibbs free energy is the relevant phase stability thermodynamic variable and enthalpy is the first law dependent variable.

Steam conversion of released CH4to H2and CO2(for reinjection and storage as hydrate)is an old technology invented by Norsk Hydro more than 100 years ago(1913)and even available on ship[41],likely it is also feasible for sub-sea installation.The original technology has been continuously further developed and extended over to cracking higher hydrocarbons.The process is in daily industrial use in the production of ammonia as part of fertilizer production.For this reason,we do not devote any space for discussing the method in detail and rather focus on the more complex hydrate system.

The paper is organized as follows.The methodologies utilized in the work are briefly described in section 2.A brief overview of the concept is described in section 3.A thermodynamic analysis of the technical feasibility is provided in section 4.The paper is concluded with a brief discussion in section 5 and our conclusions in section 6.

2.Methodology

The primary scientific methods in this work are classical thermodynamics and statistical mechanics.The statistical mechanics is limited to application of earlier published models and derivatives of these.But these models are also derived in order to achieve models for other thermodynamic properties.The fundamental details behind the original derivation from statistical mechanics are also important.Mass transport is utilized in combination with classical nucleation theory from physics.Results from molecular dynamics is also utilized for properties of water in different phases as well as concentration profiles of hydrate forming molecules across interfaces between liquid water and hydrate.These results are based on earlier publications and not methods directly used in this work.Similar applies to models for diffusivity coefficients of hydrate forming molecules across the interface between liquid water and hydrate.

3.Schematics for a zero emission concept for combined safe CO2 storage and clean energy(H2)production from hydrate and conventional hydrocarbon sources

The main cycle we discuss in this work involves production of hydrocarbons,cracking of hydrocarbons to H2and CO2and safe storage of the CO2in the form of hydrate while at the same time releasing CH4from in situ natural gas hydrate.The reason that we discuss natural gas hydrate as CH4hydrate is that most natural gas hydrates originate from biogenic gas and are almost pure CH4hydrate.Many of these biogenic hydrate occurrences are,however,also sitting on the top of thermogenic hydrocarbon sources.Over time hydrate production from these sources will get into a situation of mixed hydrates with gradually more fraction of thermogenic gas.Cracking of other small hydrocarbons is also very easy and there is no need for a separate discussion on the cracking aspect.But we will discuss some other consequences of thermogenic gas later.

A substantial number of different technologies for cracking CH4to hydrogen are available.Some technologies are more mature than others.We focus on steam cracking,which is well established and has been in commercial use since 1913.This is our choice of method simply because we can utilize the steam by-product.In section 3.1 we briefly mention some recent papers of CH4cracking.This is mostly included for cost estimates.

In section 3.2 we discuss some thermodynamic aspects of the exchange from in situ CH4hydrate over to CO2hydrate in the sediments.The main goal of this section is to verify the thermodynamic models utilized in the thermodynamic analysis in section 4 and also to examine some infrastructure implications.The latter includes hydrate risk analysis related to transport of produced gas as well as injection gas.A few points on reservoir completion strategy are discussed qualitatively in section 3.3.

3.1.Cracking of hydrocarbons

There are a huge number of publications in open literature on various technologies for cracking hydrocarbons.In the context of this work we do not need a comprehensive review of all these methods.What is important here are the costs,and how the cracking method can be utilized for the total process.In view of this the recent paper by Ayodele et al.[42]provides a sufficient overview of various technologies for Hydrogen production from CH4and related costs.

Steam cracking is a two stage process in which the first stage is a cracking of CH4to CO(+small amounts of CO2)and H2using steam with temperatures in the range of 700-1100°C and pressures ranging from 3 to 25 bar.The specific conditions depend on how this first step and the second step,the water-gas shift,are designed and the specific choice of catalyst for the second step.The net ideal chemical balance for the two steps is that one molecule methane and two molecules water is converted to one CO2and four molecules H2.The energy needed for the two stage steam cracking is about 165 kJ/mol[42-51].The energy needed for thermal cracking of methane to elementary carbon and hydrogen is around 75 kJ/mol,but produces about half the hydrogen than steam cracking.The produced elementary carbon might have a market but in this project we are more interested in the net steam export.

An important motivation for these plots is that we need a thermodynamic platform for hydrate production analysis that can account for non-equilibrium and many different routes to hydrate.

A second motivation for these plots is the role of mineral surfaces in hydrate nucleation.Solid conversion of CH4with CO2as observed in ice range[38-40]is not feasible since it is extremely slow.Since the hydrate saturation is less than 85% of pore volume there is always free liquid in the pores.Even in Alaska permafrost the average hydrate saturation is closer to 75%.Offshore hydrate reservoirs are normally subject to fracture systems that bring in seawater which dissociate hydrate.It is therefore rare to find offshore hydrate reservoirs with hydrate saturation as high as 75%.The formation of new hydrate from liquid water in the pores,and injection gas,gives rice to new exchange mechanism.Some associated questions are:

(1)Is it thermodynamically feasible to make a new hydrate from liquid water and the injection gas according to first and second law(Gibbs free energy)?

(2)Is the released energy form the hydrate formation sufficient to dissociate the in situ CH4hydrate according to first law(Enthalpy)?

(3)Injection of CO2into water wetting sediment structures containing hydrate is a challenge and N2has been mentioned as a possible additive to increase gas injection permeability.How does addition of N2affect formation of new hydrate and released energy?

(4)How can we reduce blocking of pores due to formation of new hydrate?

In contrast to most academic and commercial codes for calculation of pressure and temperature equilibrium curves we use classical thermodynamics and modeling of guest water interaction contribution to the cavity partition functions.The model is described in more detail in section 4.The reference model used in most other codes is based on empirical fitting of the difference between chemical potential of pure liquid water and chemical potential in empty hydrate.In addition the interaction between water in the hydrate and guest molecules in the cavities are fitted to experimentally data.See for instance Kvamme et al.[18]for more details on the reference method versus residual thermodynamics utilized in this work.Since we do not fit parameters we do need to verify our predictions.Three different sources of experimental data[63-65]have been used for verifications of structure I hydrates formed from mixtures of CH4and C2H6.In Fig.3 we plot calculated temperature pressure hydrate stability limits.If the system could reach equilibrium then this would be equilibrium curves.But since the number of routes to hydrate formation and dissociation are quite many thermodynamic equilibrium is not possible.The number of constraints(conservation laws and equilibrium constraints)is higher than number of independent thermodynamic variables and there is no unique mathematical solution to the constraining equations[11].Another reason to verify the model is that the pressure temperature calculations based on chemical potentials for all components,with ideal gas as reference state for all components in all phases,verifies modeling of Gibbs free energy that we need later in the concept evaluations.The combined first and second laws for a multiphase system can be written as:

min in front of the bracket means that the term inside will strive to reach towards a global minimum.Inside the bracket the unequal sign indicates that the pathway towards minimum will follow steps that lead to lower Gibbs free energy.S is entropy,V is volume and the line below denote extensive variable.Superscript m is a phase index and phases is the total number of active phases that distribute all the masses.is chemical potential for component i in phase m.is the mole numbers of component i in phase m.Pressures and temperatures will normally reach equilibrium even in a non-equilibrium system.If we neglect hydrate formation from water solution for now and assume that equilibrium between gas,water and hydrate can be reached then adding the mass balance to equation(1)and results in the equation for the hydrate equilibrium curve;

Superscript H denotes hydrate,superscript aq denotes liquid water phase and superscript gas denotes the hydrate former phase.

In Fig.4 we compare our calculated results for very ethane rich mixtures with the experimental data from Holder and Grigorio[64].

In Fig.5 we plot calculated results and experimental data from Deaton and Frost[63]and in Fig.6 we plot calculated results and experimental data from McLeod and Campbell[65].

Hydrate formation from dissolved hydrate formers can be important over long time scales.But the concentration limits for hydrate stability that is associated with these hydrates might be more important in terms of hydrate production analysis.Gas leaking to the seafloor at hydrate formation condition will dissociate towards seawater that is under saturated with hydrate former.The enthalpies[71]needed for the hydrate dissociation can be found from Fig.11.The enthalpies of homogeneous hydrate formation from dissolved hydrate formers in water are substantially smaller in absolute value since the guest molecules are transferred from a similar water arrangement in liquid water as the cage inside hydrate.We actually find that the average water coordination number around a methane molecule in liquid water is around 20 based on Molecular Dynamics simulations with TIP4P[77]for water and OPLS[78]for CH4.For CH4there is a significant change in hydrate formation enthalpies from mole-fractions close to hydrate stability limit and up towards liquid solubility mole-fractions.The range of hydrate formation mole-fractions for homogeneous hydrate formation is very limited for CO2at this temperature and pressure.But the change in enthalpies of hydrate formation is more than 3 kJ/mol,from solubility mole-fraction and down to molefraction that is close to hydrate stability limit.

We are not going to discuss potential hydrate formation problems in section 4 and it might therefore be appropriate to check maximum water content that can be permitted for the injection gas and the produced gas.The water in the gas can drop out in three possible ways.The classical hydrate risk evaluation during transport of gas in pipelines is based on the dew-point concentration of water as the first point of liquid water being available for hydrate formation.A second possibility is that hydrate can form directly from dissolved water in the gas.The low solubility of water in the gas,and also the limited heat transport capabilities of a non-polar gas,will make that option less probable.Both in terms of mass transport and heat transport capacity for getting rid of the hydrate formation enthalpy.Thirdly water can adsorb directly from gas onto rust on the pipeline surface.

Injection gas can be dried on top-side using conventional glycol drying,or Zeolite systems.These are well-established technologies and need no further discussion here.Some molecular level details related to glycol drying can be found elsewhere[82-84],and some molecular level studies on Zeolite drying[19,85,86]are available for details on the principles of that method.

Produced gas will enter production pipelines after transport through water filled sediments.There might therefore be free water droplets as well as dissolved water.In a sub-sea completion it might be possible with local drying.In the context of this work,however,we are not going into possible technical solutions.

The differences in water dew-points between water dissolved in methane or CO2and CO2with 20 mol per cent N2is limited.The most important is that the tolerance for water content based on water dew-point mole-fraction is roughly 18 to 19 times higher than a water content tolerance based on water adsorption on rust.

3.3.Some practical details on completion and setup

The Ignik Sikimu pilot was,as mentioned,conducted with far too much N2.Another problem is that a“huff and puff”approach was utilized.The problem with this approach is that the injection gas(CO2/N2mixture)was injected over a certain period and then the system was shut down before pressure was released again and the gas was sampled.In a real exchange system,in which released heat from formation of a new hydrate from injection gas and free water is sufficient to dissociate the in situ CH4hydrate it is important to create“escape”pathways for released CH4.Otherwise the released CH4will mix with the injection gas and mess up the concept.As a minimum this means one production well kept at slightly lower pressure than the local reservoir pressure,and then of course also lower than injection well pressure.And of course this sampling/production well needs to be located in a reasonable distance from the injection well so that CH4will find it's way to the well.Much is actually accomplished once the hydrate is dissociated since the partial molar density of CH4is low and buoyancy will assist in transport of released CH4.The absolutely best would be a network of producing wells.This would not be economically feasible with conventional drilling technology.TIOS(A TechnipFMC and Island Offshore Subsea Company)have developed a simple drilling riserless coil tubing technology that can save the costs of drilling to a fraction of conventional drilling.This is accomplished using tubing rather than the expensive process of connecting shorter lengths of pipelines to required length.The technology has been verified through a number of projects and the latest test was a successful drilling to 3000 m between Bjørnøya and Jan Mayen as a project for the Norwegian Petroleum directory in the autumn of 2020.The low cost involved in this type of technology can make it beneficial to drill even more than one injection well also.The cost per well goes down proportional to the number of wells since the cost of rigging and getting the ship in place in the area will be shared on each well.A schematic illustration of the drilling ship is given in Fig.14 below.

4.Thermodynamic analysis and technical feasibility

In section 4.1 we give a brief description of the thermodynamic framework used in this work,and as illustrated through examples in section 3.2.This thermodynamic platform is the basis for a more detailed analysis of the exchange from in situ CH4hydrate over to CO2hydrate in section 4.2.

4.1.Thermodynamic framework

In this work we utilize classical thermodynamics.The reason for that choice is quite many and some reasons are discussed elsewhere[13,15,18].A fundamental limitation of the fugacity scheme is that it is basically only defined on a component basis.I.e.:

The chemical potential in equation(3)needs to be integrated from a reference state to a real value.In classical thermodynamics the most common reference states are 1)ideal gas(Residual Thermodynamics),2)pure liquid(Symmetric Excess Thermodynamics)and 3)infinite dilution in a solvent(Asymmetric Excess Thermodynamics).All entropy related thermodynamic properties will have an ideal mixing as part of the integration scheme.For the Residual Thermodynamic scheme the entropy of ideal mixing at constant temperature and pressure arises from the change in pressure for each ideal gas from P to partial pressure for the actual component in the ideal gas mixture.Similar applies to the other schemes.

Note that our scheme is based on chemical potential for pure liquid water,ice and empty hydrate lattice of structure I and II[87]from Molecular Dynamics simulations using TIP4P[77].Through these samplings ideal gas chemical potential comes directly from samplings in momentum space(velocities)and residual energies from configurational space(interaction energies).And since TIP4P is a rigorous water model the rotational momentums are only functions of moments of inertia for the water model and the actual temperature and pressure.Translational momentums are trivial from molecular mass.The equations for the ideal gas chemical potential can be found in any textbook on physical chemistry and need no dedicated space here.Practically this means that also liquid water phase is a residual thermodynamic scheme in which water activity coefficient is the correction for non-ideal liquid mixture.Generally we also utilize Molecular Dynamics(MD)simulations for modelling infinite dilution chemical potentials[88,89]and also then use residual scheme for infinite dilution as reference state.

Chemical potential for water in hydrate is also on a residual basis scheme since the empty hydrate water chemical potential is sampled from MD.

μkiis chemical potential for molecule type i in cavity type k.It is assumed that small and large cavities are at equilibrium so that:

I.e.for a system at equilibrium the chemical potential for a guest molecule in a cavity is equal to the chemical potential for the same molecule in the other cavities in the hydrate.Δgk1is the free energy change for inclusion for guest molecule i in a cavity of type k.

The most typical example is a hydrate former phase(gas,liquid,supercritical)in contact with liquid(or ice)water.Under favorable conditions hydrate will form heterogeneously on the interface.For these three phases there are 12 independent thermodynamic variable,3 conservation laws and 8 conditions of equilibrium.We can then fix only one independent thermodynamic variable.Most common choices are T or P.For this particular case equation of equilibrium we have:

for the equilibrium between the gas and the hydrate the chemical potential for the guest that enters hydrate is the same as in the original phase.The iexpression can be found in the last column of Table 1 for chemical potential as well as for fugacity needed in the more common formulations.

Table 1 Model and parameters for water activity coefficients for equation(1).

Figures(3)-(8)are calculated by solving equal chemical potential for pure liquid water(activity coefficient of water equal to 1):

Equation(8)presume,as given by equation(7),that chemical potential for gas components is the same as chemical potential for the same components in hydrate in hydrate;see equations(5)and(6).SubscriptH2Odenotes water.Superscript aq denotes liquid water phase and superscipt0,Hdenotes empty hydrate lattice.Equation(8)is solved for pressure at defined(chosen)temperature using calculated fugacity coefficients from Soave Redlich Kwong(SRK)[90].Ideal gas chemical potential for models of methane(spherical)and ethane(linear with well defined average bond length)is trivial.

Fig.7 is just the resulting hydrate free energies calculated from the solutions of equation(8)for all the systems plotted in Fig.3 according to:

The compositions of the hydrates are given by the fillingfractions of the different cavities,which is given by the statisticalmechanical model as derived from the semi grand canonocal ensemble[87].

θkiis the filling fraction of componentiin cavity typek.Also:

where ν is the fraction of cavity per water for the actual cavity type,as indicated by subscripts.The corresponding mole-fraction water is then given by:

Figure(8)is constructed by solving equation(14)below for given mole-fraction alcohols in the water.The mole-fraction vector on the left hand side is the composition of the liquid water phase and superscript gas is now inserted on the mole-fraction vector for the gas on the right hand side.A simple model for the activity coefficients are given in Table 1 below.

Fig.9 gives the resulting Gibbs free energies according to equation(9)from the solutions of equation(14)for the conditions and alcohol concentrations in Fig.8.

As discussed earlier a system with one hydrate former phase,liquid water phase and minimum one hydrate phase cannot reach thermodynamic equilibrium when both T and P are defined.Peacticallt this means that if thermal and mechanical equilibrium is satisfied then there is no mathematical rule that says that chemical potential are the same in all phases are the same.Quite the opposite.It is actually mathematically impossible.Composition of hydrate formed homogeneously from dissolved hydrate former is therefore different from the heterogeneously formed hydrate.And by thermodynamic definition it is therefore a separate phase.

Hydrate can form in between the solubility of hydrate former in water,which is given by the solution of equation(15)below.

Models for infinite dilution chemical potentials for CH4and CO2,and for activity coefficients with infinite dilution reference state are given elsewhere and will not be repeated here.These are actually treated slightly different since CO2is more soluble than CH4but also since infinite dilution properties of CO2from open sources and better suitable for a residual scheme based on infinite dilution density.For details the reader is directed to Kvamme[12].The model for CH4is given by equations(35)to(37)in Ref.[12]while the model for CO2is given by equations(38)to(40)in Ref.[12].The free energies of inclusions,Δgkiare also available in Ref.[12].

Hydrate can form from liquid solubility according to the solutions to equation(15)and down to minimum mole-fraction needed to keep hydrate stable(Fe3O4)is normally very abundant initially when pipelines corrode outside but over time the amount of Hematite increases relative to Magnetite and Irin oxide(FeO)because of higher thermodynamic stability.For the time being a representation of rust with Hematite seems fair enough within other uncertainties.

The only reason that SRK[90]is useable for water in equations(17)and(18)is that the direct water-water contributions in the attractive part of SRK is practically zero due to the square of very low mole-fractions water(see Figs.12 and 13)in the gas.And even cross-

I.e.Once hydrate has fomed from dissolved hydrate former then that can only happen if the chemical potential for water in hydrate is lower than liquid water chemical potential.And the smallest possible liquid water concentration for hydrate formation is when equation(16)approaches equal sign.

In Fig.16 we plot solubility of CH4in water along with minimum hydrate stability limits.Similar plots for CO2are given in Fig.17.In situ CH4hydrates in sediments are locally exposed to fixed temperature and pressure and cannot reach thermodynamic equilibrium but reside in a state of stationary situation.This also applies even if there is no free gas since mineral surfaces are active towards hydrate,as discussed before.And hydrates nucleated towards mineral surfaces have different compositions than hydrates formed heterogeneously towards gas and homogeneously from dissolved hydrate former.Surrounding water methane mole-fractions are therefore likely to be close to those in Fig.16 b).

For most offshore hydrate reservoirs seawater leak in through fractures.As a result hydrate dissociate towards incoming seawater since chemical potential for CH4at infinite dilution in water is lower than chemical potential for CH4concentrations in Fig.16 b).If there is no supply of new gas from below then the hydrate will be depleted over time.Many offshore hydrate reservoirs with fair to high hydrate saturation are in stationary balance between dissociation from incoming water and formation of new hydrate from incoming gas below.

Figs.12 and 13 are constructed by calculating the minimum water mole-fraction in gas(or liquid)that results in water drop-out.For water dew-point at defined T and P then mole-fraction water is solved from same chemical potential in liquid water that drops out as in gas:

An average chemical potential for water adsorbed on Hematite(Fe2O3)was derived[57]from samplings of adsorbed water energies for the three first water layers and thermodynamic integration to achieve corresponding chemical potential for water.

Equation(18)is used to calculate water adsorption limits in Figs.12 and 13.Hematite is a dominating form of rust.Magnetite interactions with water are small.In unpublished work we have also examined the use of virial equation using rigorous integrations for calculations of second and third virial equation.We utilized TIP4P[77]and the calculations confirm that the direct effect water-water interactions fade out due to low water mole-fractions.

The route to enthalpy changes,from the residual thermodynamic scheme described in this work is fairly straightforward.The fundamental relationship between Gibbs free energy and enthalpy also applies to a relationship between chemical potential and partial molar enthalpy.And of course then it also applies for differences in these quantities for a phase transition.

Differentiation of equation(8)gives the following results for partial molar enthalpy of water in hydrate[71,73,74]:

and from Fig.15 for liquid water:

The enthalpy of hydrate formation is then:

Looking at the last term on the right hand side of(21)we distinguish between guest in a separate gas.Since the guest in this case is described by residual thermodynamics for both phases then:

In Table 2 we provide the necessary equations for(22),and in Table 3 we list the associated parameters as calculated from Monte Carlo simulations[91,92].The term“parent phase”is used to label the phase from which the hydrate former is coming.

Fig.10 is constructed using the scheme on left hand side of Table 2 while the results in Fig.11 are constructed using numerical differentiation of the actual equations for chemical potentials of dissolved hydrate formers.As expected the enthalpies of formation from solution are smaller since the difference in guest situation is more limited.A liquid water surrounding environment in water solution is not that very different from hydrate cavity in terms of average interaction energy(and related chemical potential).For heterogeneous hydrate from gas and liquid water the guest molecules are surrounded by other gas molecules.Although the density changes the difference in hydrate formation enthalpy is higher than the formation enthalpy from dissolved hydrate formers.And Table 2 can be extended to hydrate formation from other“parent phases”.This includes hydrate formers coming from direct adsorption on minerals as illustrated by Figs.1 and 2,or secondary(trapped in structured water)adsorbed guest molecules as discussed in more details elsewhere[11,20-22].More work is needed in order to make this route for hydrate nucleation more“streamlined”and feasible for hydrate thermodynamics software.So far we have mainly utilized thermodynamic integration for calculations of chemical potentials.Chemical potential for water as ice and water in empty hydrates were calculated using harmonic oscillator approach and oscillations from minimum energy state.Average chemical potential for adsorbed water as utilized through equation(18)also works well.For this the adaptive biasing force(ABF)scheme[93,94]is more appropriate.See for instance Refs.[25-28,95,96].Some caution on temperature control is needed however.ABF is an entropy based method and the special dynamics of the mineral/water interactions and movements.It is therefore necessary to understand the complex dynamic behavior,and to analyze the calculated results with caution and proper analysis of bias.Appendix 1 is included to shed light on the challenges of entropy generation and thermostat control on simulations.

Table 2 Enthalpy changes for guest molecules from“parent phase”to hydrate phase.

Table 3 Sample residual energies,UR,and cavity occupation volumes for.CH4 and CO2.

4.2.Conversion of in situ natural gas hydrate to CO2 hydrate for combined energy production and safe long terms storage of CO2

Most of the natural gas hydrates are almost pure methane hydrate(biogenic gas origin).Thermogenic gas will create very different mixtures of hydrates.Propane,and possibly iso-butane,will dominate the adsorption on liquid water[37]as a pre-stage to hydrate nucleation.N-butane will not enter hydrate structure II but will also adsorb on liquid water and affect adsorbed chemical potentials of hydrate formers on the liquid water surface.The first hydrate formed will have high content of propane(and i-C4H10if present)in a structure II hydrate and then gradually there will be structure I when all structure II hydrate formers(mainly propane and iso-butane)have been depleted.The effect of the propane phase transition at around 278.5 K will have an artificially extreme impact on the pressure temperature stability limit curve.The best way to handle systems containing propane would be to calculate composition of adsorbed hydrate formers on water and then use that as a basis.It will be feasible to set up a model system with defined mass of gas and then consider gradual selective adsorption and hydrate formation until all propane is depleted and the system turns into a structure I mixture.

In Fig.19 we plot Gibbs free energies for the same systems as in Fig.18.As mentioned above propane will totally out-compete ethane and methane in selective adsorption on liquid water.Based on the distribution of large and small cells in structure II the ideal composition will be that propane fills all the large 1/3 of the cavities,and get help from some filling of methane in the small cavities.But then again the formation of hydrate is from adsorbed hydrate formers and not bulk gas,and it is not given that there will be optimum filling of small cavities.The adsorption aspect becomes even more pronounced beyond the propane phase transition temperature.It might be feasible to conduct a flash calculation and evaluate hydrate phase transitions from the resulting two hydrate formation phases.In view of all the different possibilities for the propane containing mixtures we stick to CH4and the 20 mol per cent C2H6system as model systems for in situ hydrate.

In Fig.22 we plot Gibbs free energy for the systems in Fig.21.We now see a bit more difference from the effect of adding N2.Pure CO2hydrate is the thermodynamically most stable but even with 20 mol per cent N2in CO2/N2mixture the injection gas forms more stable hydrate than even the system with 20 mol per cent C2H6in CH4/C2H6mixture.

The lower free energy for the hydrate formed from injection gas containing up to 20 mol per cent N2in the CO2/N2mixture has several significant implications.One of these is that the first hydrate to dissociate when the ion concentration increases is the two hydrocarbon hydrates.And the ion concentration in the pore will increase when water is extracted into a new hydrate formed from free pore water and injection gas.

As mentioned alcohols are surfactants due to the limited polarity of methyl groups in the alcohols.Ethanol is more surfactant than methanol and also more environmentally friendly.Despite this fact injection of methanol is being considered as a possible production method due to the low price of methanol.It is well known from pilot scale experiments[109]that small amounts of methanol act as hydrate promotors and accelerators.There are also several experimental studies that confirm the same but not needed to spend space on in the context of this work.See also Kvamme et al.[66]for a more detailed discussion on the reason for methanol efficiency on the water/hydrate former phase interface.

The important issue here is to examine how addition of small amounts of methanol or ethanol affects the stability of the formed hydrate.We therefore examine three different concentrations of alcohol.5 wt% methanol in the free pore water would correspond to methanol mole-fraction in water of 0.02873.5 wt% ethanol corresponds to a mole fraction ethanol in water of 0.02016.We also examine an ethanol mole-fraction of 0.04032 in water.

There are many reflections that can be made on these plots.The common misunderstanding that a solid state conversion is also the mechanism for the liquid state region of water is not possible based on our own experiments during 2 decades of experiments and 3 decades of theoretical evaluations.It would simply be far too slow to be able to explain experimental data in the liquid region[110,111].As mentioned in the introduction we will generally not discuss experiments here because we frequently see that essential details regarding the exchange mechanism is not described in the papers and/or the experiments are conducted in a way so that the natural mechanism is influenced by boundary limits.And to be fair with other groups the two references above are the only of our own experiments that we refer to and we refer to them without experimental details.See also[112,113]for meso scale modelling(Phase Field Theory,PFT)of the system.These theoretical results confirm a rapid heat transport mechanism as long as there is available free water in the pores.When free water is consumed then a slow solid state conversion almost stops the conversion(extremely slow progress).

Sour gases separated from hydrocarbon systems can also contain H2S,which will increase the stability of the injection gas as well as increase the absolute value of hydrate formation enthalpy.

The other type of additive needed for the injection system is a surfactant.There are a number of criteria for a suitable surfactant but due to patent right it is not suitable to discuss in this paper.Some of the effects we desire,however,are discussed in Kvamme et al.[66].Alcohols,as used for examples here can be efficient additives because they also break hydrogen bonds in hydrate and liquid water/hydrate interface.But they also dissolve fast in the liquid water and distribute in the sediments.Basically we seek ppm range of surfactants that do not significantly affect hydrate stability limits but act between the injection gas front and the liquid water.At this stage we utilize various types of molecular modelling approaches to find the right surfactant.At first we are not limited to environmentally friendly surfactants but rather focus on efficiency.In the second step we aim for natural substances which can have similar functionality while also being environmentally friendly.The actual substances that we develop for this purpose will be patented and for this reason we will not discuss details at this stage.

6.Conclusions

The use of CO2for combined storage of CO2,and the associated release of CH4from in situ CH4hydrate is thermodynamically feasible.Far too often experiments are conducted on a trial and error basis rather than conducting thermodynamic analysis in order to narrow down the range of various variables.One example is the impact of N2addition to CO2on stability of formed hydrate in terms of Gibbs free energy.And the second important thing is the available enthalpy of hydrate formation from the injection gas as heat source for dissociating in situ hydrate.Since most natural gas hydrates are almost pure CH4then up to 20 mol per cent N2in CO2/N2mixture is thermodynamically feasible evenwith up to 10 mol per cent ethanol in the free pore water.This is of course unrealistically high concentration of alcohol.More dedicated efficient ppm range surfactants are more desirable.Work in in progress on development of such surfactants.Steam conversion of the produced hydrocarbons is a maturetechnologyand technicallyeasy toimplement.This opens up for a circle in which the separated CO2from the steam cracking is reinjected for further CH4production.In principle this can be an efficient solution also for onshore hydrate sources in remote areas since the only deliverable is either hydrogen for pipeline transport,or energy production on site for export in the form of electricity.Conversion to ammonia,or other chemicals,that can either serve as energy source,or be utilized for useful products are also possible.The steam cracking was developed in Norway more than 100 years ago as part of fertilizer production.

Storing CO2in a natural gas hydrate reservoir requires that the hydrate reservoir is properly sealed.Hydrate saturation is one indicator for this since low hydrate saturation typically implies that hydrate dissociation toward incoming seawater through fracture systems is higher than formation of new hydrate from upcoming gas.Other signs are pockmarks,and in many cases bubbling gas.High hydrate saturation and few or none of the sign of gas leakage through surface of seafloor are good initial signs that the hydrate reservoir is properly sealed,and has kept hydrate safe in place for geological time scale in similar way as the role of shale and sealing caps that traps conventional hydrocarbon resources.In contrast aquifer storage of CO2depends on a mapping of sealing structures prior to selection of storage formation.Resolution of monitoring tools is one limitation and another limitation is the long travel times over many years of injection.1 million ton CO2per year as injected in Utsira offshore Norway is a small amount compared to amounts of CO2from a power plant.There is no doubt that this yearly injection since 1996 implies that the CO2has migrated far outside the boundaries of Norway and might have reached UK.It is fairly unknown how the sealing structures are on that side of the North Sea.Storing CO2as hydrate removes this uncertainty.And the value of the produced CH4more than compensates for the costs.This is true whether CH4is converted to hydrogen or not.But the steam conversion to hydrogen is a smart way to utilize remote hydrate resources since the cycle generates CO2to keep the energy cycle going.Some of the onshore hydrate resources in China,as one example,are in very remote areas.The possibility that the CH4from hydrate can produce energy,as well as fertilisers,can even open up for new possibilities in geographic areas that has so far not been considered as useful.

Declaration of competing interest

It is hereby declared that the submission involves no conflict of interests with other people or institutions.

Appendix 1.Heat generation and heat consumption during water adsorption on mineral surfaces

Definition of Systems

We now consider a simple case in which a water wetting mineral is exposed to water under liquid water conditions(temperatures above freezing point).Similar consideration will apply under ice conditions since ice will not be able to directly attach to the mineral surface.The reason is the incompatibility between average partial charges locations in ice surface,and distribution of atomic charges in the mineral surface atoms.The mineral/interface/ice system is,however,different in structure and dynamics than mineral/interface/liquid water system.And it is outside the scope of this work.

The system(s)is now defined as a mineral slab and the water and surroundings(o)is everything outside.The usual combination of first and second laws leads us to the basic expression:

in which M is used as shortening for the dependencies of location in terms of a three-dimensionless position vector,and time t as in the parenthesis on the left hand side.H is the intensive system Hamiltonian,T is absolute temperature,P is pressure,V is molar volume and N is number of molecules.

With all terms on right hand side equal to zero equation(A1)gives the micro-canonical ensemble and temperature is a result rather than an independent variable.Strictly speaking equation(A1)should be rewritten accordingly.

Using equation(A1)in the micro canonical ensemble forab initiocalculations of partial charges of a uniform fluid exposed to vacuum is theoretical fair due to the properties of vacuum(perfectly heat insulating etc.).Making a rerun with an applied field imitating for instance water will implicitly involve heat transport which is not sampled and remain unverified in impact.So for this case strictly speaking only the two latter terms of right hand side can be deleted.

Quantum mechanical simulations of for instance adsorption energies in the NVT ensemble(constant number of moles,constant volume and constant temperature)will also involve a similar type of heat exchange with the surroundings in order to keep the average temperature fixed during the phase transition(adsorption).This may not be very critical to the sampling of average adsorption energy but might be far more critical on development of entropy[97]and resulting free energy of adsorption.

Equation(A1)defines the impact of boundary conditions between the system and surroundings and will be on top of the internal constraints on the system.Combination of(A1)and a similar equation for the surroundings under the usual conservation laws leads to the usual conditions of equilibrium and corresponding analysis of whether the system will phase split or not under the given conditions.The internal constraints(inside system)make this an open system.An extensive formulation of(A1)would then lead to a split into a system of a Hamiltonian for liquid multiplied by the corresponding liquid distribution and a similar term for the gas.This will involve a linear algebraic summation that involves the partial molar of the Hamiltonian with respect to each different component.

In this non-uniform system the mineral surface is not movable and practically(in case of approximated rigid solid)a structured set of interacting particles at fixed positions in the grid system.The local Hamiltonian as function of distance from the mineral surface z and position in the xy plane parallel to the mineral surface will be non-uniform with local energies lowest in best adsorption configuration.This will also correspond to locations of lowest entropies.And in summary the local Hamiltonian is characterized by local temperature,local partial molar volume and local chemical potential.This implies also that the adsorbed layer(approximated as roughly 4 water layers based on our observations for water adsorbed on some different mineral surfaces).Formally this implies that the whole adsorbed layer is a continuous coupled set of different phases(structure and average density unique as function of local positions).It also implies that in the subsets of the macro-canonical ensemble there are no interchangeable molecules in the adsorbed layer for each specific number of molecules within the adsorbed layer.

Heat generation,consumption and transport

As discussed in previous section the system itself is now an open system exposed to interaction between system and surroundings as given by equation(A1).In order to avoid rewriting equation(1)we now let“s”be the adsorbed section(roughly 4 water layers)and the rest is then approximated as uniform liquid water and denoted as“o”.But as discussed above the adsorbed section is by formal definitions a continuous section of,in theory,infinite number of phases since structure and density vary continuously in this section.For distances z from the solid surface it is therefore convenient(although local positions are uniquely defined by the position vector)to introduce an index k counting layers in z-direction.

We can now write:

If we slice the whole adsorbed section into smaller discrete approximated“phases”then equation(A2)involve a linear algebraic equation that couples the average Hamiltonians to entropies,volumes and masses.This slicing,and corresponding dependency on neighbour slices,implies an iterative linear algebraic solution.But for qualitative illustration purposes let's just use the following approximation merely to illustrate the main message of this appendix:

and then reformulate(A2)into:

Molar volumes are small.Although we cannot omit the middle term on right hand side let's rather focus on the more important contributions and use:

Using a simplified Fick's law based on concentration(inverse molecular density for pure water):

in which X and Yare the lengths of the simulation box in the two axes perpendicular to z and even though the diffusivity coefficientDw,zwill vary in these two directions depending on the impact of the charge distributions on the solid surface we may consider this as an average value useable enough for the purpose of this note.Insertion of(A6)into(A5)gives:

and defining a dynamic entropy change of the slice k as:

we end up with the local average absolute temperature in slice k as:

Diffusivity in z direction will be sensitive to the distance from the mineral surface but can be evaluated although the quality of sampling statistics might be a challenge.And also other parts of the latter term is challenging to quantify with acceptable statistical accuracy.Nevertheless - returning to the first term this is the obvious term that will result from any freezing process(or the opposite).Heat released during freezing must be transported away and equation(A9)(within all simplifications above)defines local absolute temperature to the gradients of local system Hamiltonian with respect to local entropy gradients.This will of course be related to local heat transport capability(conduction,convection,radiation)and result in a heat flow in the z-direction that will be different from similar heat flow in the x and y directions.

Thermostat challenges in highly non-uniform systems

A sound way to design a thermostat for MD is to evaluate natural oscillations in temperature in the NVE ensemble and assign proper thermostat values for translational and rotational modes.This is feasible for small rigid molecules,like for instance TIP4P for water,when using a quaternion approach[97-103].In the final end ergodicity actually means the ability to mimic the canonical partition function in momentum space,which involves Boltzmann integrals over all the different momentums in the systems of molecules,and associated atoms.

Algorithms based on atomistic treatment of external forces,and rearrangements to molecules based on intramolecular constraints(intramolecular forces),will generally not make it feasible with more than one thermostat control parameters.The range in dynamics of the various kinetic modes that single parameter is going to control makes it impossible to even get close to ergodicity.

The challenge is even more complex for an adsorption in which water may arrange to densities in the order of three times liquid water in the first adsorbed layer[24-28.82,85,86,95,96]and then transit over to a very different liquid like dynamics,and structure,roughly 6 water layers outside.

Physically the best model for a thermostat in the first layer?might be based on a“spring”like model while liquid water is still conventional fast liquid water dynamics.A compromise might be a hybrid thermostat,in which a“spring”behaviour based thermostat in the adsorbed layer is gradually scaled over to a conventional Nose-Hover thermostat[104]over a distance of 6 water layers(roughly 1.8 nm).