Alcohols,for,hydrate,inhibition-Different,alcohols,and,different,mechanisms

Bjørn Kvamme ,Na Wei ,Jinzhou Zhao ,Shouwei Zhou ,Liehui Zhang ,Wantong Sun ,Navid Saeidi

a State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,Chengdu,610500,China

b State Key Laboratory of Natural Gas Hydrate,Beijing,10027,China

c Hyzenenergy,Laguna Hills,92656,USA

d Strategic Carbon LLC,Portsmouth,03801,USA

Keywords:Hydrate Non-equilibrium Thermodynamics Alcohols Nucleation

ABSTRACT Methanol has been used to prevent hydrate formation in industrial handling of hydrate forming mixtures containing water for many decades.Ethanol is also used for the same purpose in countries that have easy access to low price ethanol,like for instance Brasil.Common to these small alcohols is that they also have surfactant properties that will promote hydrate formation,but when added to water in sufficient amounts,the hydrate prevention characteristics will dominate.These alcohols will primarily prevent heterogeneous hydrate formation on the interface between water and a separate hydrate phase.The effect of “alcohol” on both of these routes to hydrate formation are investigated and compared to experimental data.In particular we also investigate the effects of these small alcohols on Gibbs free energy for the hydrate formed on the new,shifted,stability conditions.Gibbs free energy is generally higher than hydrate formed from pure water.Enthalpies of hydrate formation are also higher for hydrate formed from water containing alcohols.These are negative numbers,so in absolute values released formation enthalpy is lower.The presence of these alcohols in water will also prevent homogeneous hydrate formation from dissolved hydrate formers in water.Glycols have more important roles in other routes to hydrate nucleation.Heterogeneous hydrate nucleation towards mineral surfaces is feasible in different ways.Polar hydrate formers like H2S and CO2 can adsorb directly on rust,and as discussed here,are able to form hydrate from adsorbed state on rust surface.Non-polar hydrocarbons like,for instance methane might get trapped in structured water and then nucleate to hydrate.Some research on this is published and further research is in progress.Glycols have very strong attraction to rust and corresponding chemical potentials for adsorbed glycols on rust are favourable enough to facilitate phase transition from glycols dissolved in water over to adsorption.Injection of glycol in gas processing plants has been used by industry for many years and in many cases it might even be economically and technically feasible compared to expensive drying units.Exceptions are situations that will lead to water/glycol freezing.But even in multiphase transport of hydrocarbons with various water cuts,mixtures of alcohols might be a technically efficient solution in which the small alcohols may be very efficient as discussed above and glycols may go through adsorption phase transition from water solution over to glycol film on rust and prevent hydrate nucleation towards rust surface.This possible strategy requires more theoretical work as well as experimental investigation.On the basis of thermodynamic analysis and calculations of hydrate formation from different routes,it is argued that real natural and industrial systems are unable to reach thermodynamic equilibrium.It is therefore a need for a consistent thermodynamic platform with a uniform reference system for all phases.We propose and demonstrate a residual thermodynamic model system for all phases.

Natural gas hydrates are classes of composite structures in which water organize to create cavities which enclathrate small non-polar molecules like for instance CH4,C2H6,C3H8and i-C4H10.Some small slightly polar components like for instance H2S and CO2also form hydrates.The molecules that enter into cavities are called guest molecules.H2S stabilizes hydrates very good due to an average positive electronic charge facing outward towards the cavity walls [1]when rotating inside a cavity.CO2exposes an average negative field facing outwards during rotations inside a cavity.Depending on the size of guest molecules relative to available volume inside a cavity,a variety of water arrangements can be found in nature.Structure I dominates natural gas hydrates because most hydrates found in natural sediments are CH4hydrate formed from biogenic degradation of organic material in the upper crust.The smallest unit cell of structure I is a cubic box with average lengths of the sides that depend on temperature.The side lengths are approximately 1.201 nm for temperature between 0°C and 20°C.A unit cell consists of 46 water molecules that form 2 small cavities (20 water molecules) and 6 large cavities (24 water molecules).With only one guest molecule per cavity,the fraction of guest molecules per water is 1/23 for small and 3/23 for large.Typical guest molecules that form structure I hydrates are CH4,C2H6,CO2and H2S.

Structure II is different from structure I in two important ways.The largest cavity has 28 water molecules and can accommodate molecules like C3H8and i-C4H10.The small cavity in structure II is very similar to the small cavity of structure I.The second difference in structure II,as compared to structure I,is that the ratio of small cavities to large cavities in structure II is 2:1.

It would require far too much space here to discuss further details on the basic structures and properties of these two hydrate structures.And it is not needed since this type of information is compiled in several books.Two of these are the books due to Sloan and Koh [2]and Mokogon [3].These books will also contain more information on structure H,which can enclathrate guest molecules up to heptane but are fairly exotic in terms of natural occurrence.

Industrial problems with hydrate formation from hydrocarbon mixtures and water have been an important motivation for much of the hydrate research during the latest seven decades.The variety of situations that can generate hydrate problems is huge and ranges from transport of natural gas or sour gases (like for instance CO2)containing water to multiphase transport of hydrocarbons with varying amounts of free water.

The interest for natural gas hydrates as energy source has increased substantially during the latest four decades.Countries like for instance China and Japan are very actively working towards full scale hydrate production schemes.Production schemes for offshore hydrates may involve sub-sea processing and/or multiphase flow with various water cuts.

Historically small alcohols like methanol and ethanol have been used to prevent hydrate formation since addition of these types of molecules in liquid water reduces the chemical potential for liquid water.As will be discussed later,this results in higher pressure before hydrate can form for a given local temperature.Methanol totally dominates the market among these two alcohols due to price and effect on a molar basis.Exceptions are countries which produce ethanol at comparative net prices from waste products.One example is Brasil which ferments sugar cane after sugar production.

Thermodynamic hydrate inhibition as discussed above is based on the effect of dissolved alcohols on “bulk” water [10,11].Most efficient concentrations of alcohol are concentrations when alcohol is the solvent for water rather than the opposite.The transition from water as solvent over to methanol as solvent is clearly visible as a transition in a mixture dielectric constant as function of concentration of alcohol [10].

Methanol has surfactant properties because of the large methyl group,which has a limited charge per atomistic group surface.Methanol will therefore up-concentrate on an interface between a non-polar gas,like for instance methane,and water.Methanol and ethanol are fully soluble in water.When a water/alcohol mixture is brought in contact with a non-polar phase,the molecules on each side of the interface has to optimize the entropy.This results in a higher concentration of alcohol in the liquid water side of the interface,as compared to “bulk” water concentration of alcohol.And the low polar parts of the alcohol molecules will have a preference orientation towards the non-polar hydrate former phase.For methanol this is the methyl group,which has a low partial charge compared to the large surface area.For ethanol the outer methyl group is almost non-polar.Carbon dioxide has a quadrupole moment that plays a role in higher solubility of carbon dioxide in water as compared to hydrocarbon solubility.It still behaves almost non-polar as gas.The methyl group in methanol,in liquid water interface,will have a preference for orienting towards carbon dioxide.

The surfactant properties in ethanol are even more pronounced than methanol.The outer methyl group in ethanol is approximately non-polar.The methyl group attached to oxygen has a positive partial charge close to that of the methyl group in methanol.

In summary,the two small alcohols will have a hydrate promoting effect due to enhanced concentrations of these components in the interface towards a non-polar hydrate forming phase.For high concentrations of alcohols in water these effects will be small compared to the thermodynamic effects of the alcohols on water activity and the corresponding effects of increasing the pressure needed for making a hydrate for a given temperature.Gas containing water and also methanol remaining from hydrate prevention action in wells during production will need to account for alcohol content in evaluation of routes to hydrate formation.The classical hydrate risk evaluation presumes that water needs to form a separate liquid water phase.In this scheme water dew-point concentration is a critical first step.If the actual concentration of water exceeds water dew-point concentration,then a typical second step would be to calculate how much water that is expected to drop out.This can typically lead to gas drying strategy,or an alternative strategy discussed below.A second possible route to hydrate formation is by direct hydrate formation from gas and dissolved water in the gas.As discussed elsewhere [12-15],the challenge for this hydrate formation route is the mass and heat transport limitations.A third route to hydrate formation from water dissolved in gas that adsorb on solid surfaces.Pure iron is neutral to water.Stainless steel is also almost neutral because the partial charges imposed by iron and other metals are small.But steel will corrode in vicinity of water and oxygen.Iron will primarily start to create Magnetite (Fe3O4) and over some time create Hematite(Fe2O3) and iron oxide (FeO).Over longer time Hematite will dominate due to higher thermodynamic stability than the other oxygen rust types.Water has strong electrostatic connections to mineral oxides.The chemical potential of water adsorbed on various mineral oxides will therefore be significantly lower than liquid water chemical potential and any water hydrate chemical potential that can be achieved.Absorption of water from gas to rust is a third possible way that hydrate can eventually be formed from water that has dropped out of gas.

Some gas processing plant does not even have a water drying plant available.The largest gas field in Norway,Troll [16],guarantees for contracts on gas deliveries to Germany and other European countries.The gas is transported by pipeline to Kollsnes outside Bergen on the west coast of Norway and processed in a hydrocarbon dew-point plant.This simply means that the hydrocarbon dewpoint in the finals separator controls the gas delivery quality.

An alternative strategy for prevention of problems with hydrate formation for gas processing plants without an attached gas drying unit is to inject glycol at critical points in the gas processing.Such critical points may be low temperatures points after gas pressure reduction in turbines or low temperature and high pressures in dew-point separator,just to mention two cases.The question is then how the glycols actually prevent hydrate problems.

As will also be mentioned in section 2 the primary thermodynamic tools are based on residual thermodynamics.Since we are the only one that uses this reference state,it is often hard to find open journal publications to refer to.There are indeed many very good hydrate papers being published all the time.But this is a theoretical paper and results are based on a fairly unique reference system.To our knowledge,many of the calculations presented here are also unique and not implemented in other hydrate thermodynamic packages.

The main objective of this paper is to shed more light on how classes of alcohols prevent hydrate problems in industrial settings.By classes of alcohols we now mean the small alcohols(methanol,ethanol) which change water activity when added,and the higher alcohols that may have more than one important mechanism for preventing hydrate problems.

A second objective is to analyse in more detail some of the hydrate formation routes from water dissolved in gas.This includes also some new models and model calculations that hopefully can also be useful for other hydrate research groups.

A third objective is to illustrate the need for using a consistent reference system for all phases.As will be discussed in more detail,there are many different routes to hydrate formation and they all create different hydrate (different composition,different density and different Gibbs free energy).

The paper is organised as follows.Methodology is briefly discussed in the next section.In section 3 we discuss why thermodynamic equilibrium is not possible for the systems that we focus there.One reason is all the possible ways that hydrate can form and the thermodynamic fact that each route creates a different hydrate even for single former.In section 4 we present the thermodynamic framework,and also verify model calculations for systems containing alcohols.

The primary scientific tool in this work is classical thermodynamics.There are elements of statistical mechanics in the historical development of the theory for chemical potential of water in hydrate,and interactions between water and guest in the hydrate lattice.In contrast to the original derivation of van der Waal and Platteeuw[33],which presume a fixed hydrate water lattice,I[34]utilized statistical mechanics and Molecular Dynamics (MD) simulations to examine the effects of dynamic interactions between guest molecules and water movements.As an example,carbon dioxide movements interfere with water movements in the hydrate lattice and interfere specific movement frequencies.The result is a difference of roughly 1 kJ/mol when comparing dynamic hydrate approach with approximation of rigid lattice.Ethane in large cavity also disturbs water movements but less than carbon dioxide.For methane as guest,the results between a dynamic water lattice and a rigid lattice are almost zero for both small and large cavity of structure I.In summary,there are implicit results from statistical mechanics in the models utilized,including treatment of the canonical partition function in the statistical mechanical model for water.

We also utilize MD to estimate water diffusivity when dissolved in methane gas.This is applied to Fick"s law in order to evaluate mass transport kinetics during hydrate nucleation and growth directly from gas.

Hydrates in sediments are always exposed to locally defined temperature and pressure.From a thermodynamic point of view the number of independent thermodynamic variables that can be fixed in order for a multiphase system to be able to establish thermodynamic equilibrium is all the number of independent thermodynamic variables in all co-existing variables minus constraints.The constraints are all conservation laws plus equilibrium conditions.It is straightforward to count this discretely for a system of water and one hydrate former.For water and methane outside hydrate formation conditions we have 8 independent thermodynamic variables and 6 constraints [4].This means that we can and must fix two independent thermodynamic variables like for instance temperature and pressure.The system is then mathematically satisfactory and the equilibrium solution is the solubility of methane in liquid water,and the solubility of water in methane gas.If the same system is now moved into the hydrate formation region of conditions there will be an additional hydrate phase.The number of independent thermodynamic variables is now 12 and the constraints are 11.See Kvamme et al.[4]for details.This implies that only one independent thermodynamic variable can be fixed if the system should be able to establish thermodynamic equilibrium.This has been known since experiments on hydrate stability limits in temperature pressure projection started up more than 80 years ago.Depending on methodology in the specific experiment either temperature or pressure is fixed.

Despite this fundamental aspect which has been known for all these years temperature and pressure stability limit curves are used as if equilibrium can be established.The reason that we prefer to use a discrete counting of the number of degrees of freedom rather than the simple and compact form of Gibbs phase rule is that many phases of importance can easily be overlooked in the use of Gibbs phase rule.One example is hydrate formation from gas mixtures and liquid water.Since hydrate is formed from adsorbed hydrate formers,and the associated concentration of these in the liquid water interface,then multiple hydrates can be formed.Gibbs phase rule will not automatically catch this point unless liquid water adsorption is included in the phases.

The reason that we use the term stability limits rather than equilibrium curve is that there are several other stability limits.Hydrate can form homogeneously from dissolved hydrate formers in water.Since the system is not an equilibrium system as discussed above,then there are no rules on equal chemical potentials for all the components in the different phases.According to the first and second laws of thermodynamics a non-equilibrium system will aim for a distribution of phases,and compositions of these that minimize Gibbs free energy.A second hydrate stability limit for given temperature and pressure is a lowest concentration of methane in surrounding water in order to keep the hydrate stable.

The addition of homogenously formed hydrate results in zero degrees of freedom and no independent thermodynamic variables can be fixed for the system to be able to reach thermodynamic equilibrium.And the list can be much longer.Hydrate can nucleate towards solid surfaces [4]from structured water and methane.Some hydrate formers like carbon dioxide and hydrogen sulphide can adsorb directly on mineral surfaces and nucleate to hydrate with outside water.These are just some examples.What is critically important here is that the chemical potential for methane in gas phase is not the same as chemical potential of dissolved methane,or methane trapped in structured water close to a mineral surface.As discussed elsewhere [4,6,8-10],all these different routes to hydrate formation result in different hydrates.This will be illustrated later with appropriate calculations.

Number of degrees of freedom is the number of thermodynamic independent variables that must be specified for a system to be able to reach equilibrium.We prefer to use the discrete counting rather than the compact Gibbs phase rule formula because mixtures of hydrate formers increase the complexity,and even bring the system more out of possibility to reach thermodynamic equilibrium.Many of these aspects will not be captured by Gibbs phase rule.As an example consider an equimolar mixture of carbon dioxide and methane.Carbon dioxide is closer to condensation on water than methane.And carbon dioxide has a stronger attraction to liquid water surface.In more rigorous physics one example of a twodimensional adsorption theory is described by Kvamme [32].If the system is closed then the result of selective adsorption is many different hydrates,in which carbon dioxide dominate the first hydrates formed from adsorbed gas mixture.Or more correctly the liquid side interface composition of hydrate formers as function of selective adsorption.Similar physical differences apply to other routes that can lead to hydrate formation.

In summary,there is no way to establish thermodynamic equilibrium for hydrate in sediments.Theoretical philosophy on phases that can be consumed and then change the summation will not help generally since all hydrate reservoirs are in some dynamic stationary state.This is because there are so many phases that affect hydrate phase transition,including mineral surfaces.While mineral surfaces are efficient catalysts for nucleating hydrates,hydrate can never touch mineral surfaces.This has been discussed earlier but can also be discussed in terms of incompatibility between atomic charges on mineral surfaces and distribution of partial charges on waters in hydrate surface.

In view of the above thermodynamic,equilibrium is not possible for hydrates in sediments.Similar line of arguments can be established for hydrates in industrial situations and pipeline transport of hydrate formers with dissolved water or a separate water phase.

The main thermodynamic framework,and all the equations for heterogeneous hydrate formation from liquid water and a separate gas phase is given in section 4.1.In section 4.2 we provide the necessary equations for homogeneous hydrate formation from water and dissolved hydrate formers in water.Homogeneous hydrate formation from water dissolved in gas is discussed in section 4.3.Two types of hydrate formation related to mineral surfaces are discussed in sections 4.4 and 4.5 respectively.

An important motivation for this work is to bring forward fundamental thermodynamics of hydrate formation from various phases.For that reason it might be easier to illustrate this using a simple system that most hydrate researchers are familiar with;CH4hydrate.There are of course no limitations in the theory and quite many papers we refer to deal with a variety of gas mixtures,ranging from non-polar hydrocarbon mixtures to polar mixtures containing H2S and CO2.Using a single hydrate former makes it easier to illustrate and discuss variations caused by effects of alcohols.

4.1.General framework

In this work we consider five different hydrate formation routes.Only three of them are studied in detail in terms of calculations presented in this paper.For all of them we use a superscript on the symbol H for hydrate to distinguish the different hydrate formation routes.The first of these is heterogeneous hydrate formation from liquid water and a separate hydrate phase.Gibbs free energy change for that phase transition is given by equation (1) below.

If the system can reach equilibrium,then the solution to(1)is an equilibrium curve.But if the number of independent thermodynamic variables minus the constraints (mass conservation and equilibrium conditions) on the system does not balance the number of fixed independent variables then the system cannot reach equilibrium.This is well known since around 1940s when experimental group measured equilibrium curves and fixed either P or T for a single hydrate former that creates hydrate with water.For this system there is 12 independent thermodynamic variables and 11 constraints.So fixing independent thermodynamic variable makes the system mathematically solvable.But using the pressure temperature projections as equilibrium curves in the same system when 2 independent thermodynamic variables are defined,like for instance in a pipeline transport,is not correct.We may still define equation(1)as a stability limit in pressure temperature projection of all the independent thermodynamic variables.These limits are calculated by solving for each of the chemical potential difference in equation (1) being zero.For this we need appropriate thermodynamic variables.And,as will be discussed later,several different hydrate phases can form and we need a consistent reference for all phases.Using ideal gas as reference state for all components in all phases them consistency in Gibbs free energy is possible.

The thermodynamic model for water is a symmetric excess model but based on residual thermodynamics for pure water and therefor a residual thermodynamic model.

γH2Ois the activity coefficient of the liquid water as function of dissolved hydrate formers,as well as additives like methanol and salt.In the ice region then the latter term in equation (7) is zero.Molecular Dynamics simulations of ice using the TIP4P potential(see Kvamme &Tanaka [17]for reference and details) provided a temperature dependent chemical potential for water as ice at 1 bar pressure [17].Using experimental data for enthalpy of ice dissociation at 273.15 K,and specific heat capacity of liquid water then also resulted in chemical potential of liquid water above 273.15 K [6].Since liquid water is almost incompressible,it is quite trivial to correct pure water chemical potential from 1 bar to higher pressures:

Some simple models for the alcohols studied in this paper is given in Table 1 below.

Table 1 Model and parameters for water activity coefficients for equation(1)γH2O（T，xH2O）=a0+a1xH2O+a2x2H2O+a3x3H2O,ak=c0，k+

Table 1 Model and parameters for water activity coefficients for equation(1)γH2O（T，xH2O）=a0+a1xH2O+a2x2H2O+a3x3H2O,ak=c0，k+

ak Methanol Ethanol c0 c1 c2 c0 c1 c2 a0 0.74821 0.52077-0.59936 0.73743 0.51369-0.58176 a1 0.54174-0.47388 0.54721 0.53390-0.45996 0.53981 a2-0.53859 0.56767-0.52552-0.52277 0.55995-0.51009 a3 0.35068-0.53117 0.37324 0.34566-0.51558 0.36817 ak Ethylene Glycol (MEG) Triethylene Glycol (TEG)c0 c1 c2 c0 c1 c2 a0 0.59006 0.44750-0.49897 0.10473 0.19307-0.12389 a1 0.47286-0.39499 0.47783 0.15496 0.17274-0.15457 a2-0.44892 0.49855-0.43804 0.08770 0.08731 0.11456 a3 0.37487-0.44859 0.36800 0.37947 0.80576-0.82038

For the gas phase we utilize the Soave Redlich Kwong(SRK)[18]equation of state and the residual thermodynamic expression needed for equation (1) is then:

x is mole-fraction for component i andis the vector of molefractions.is the fugacity for component I in the gas (pure or mixture).

Chemical potential for water in hydrate is derived from a semigrand canonical ensemble [17]and given by:

β is the inverse of Boltzmann constant time temperature in molecular units and the inverse of the universal gas constant times temperature in molar units.The rigid water lattice version of this derivation is:

miis the molecular mass of guest molecule i,ħ is the Plank-Dirac constant.wki（Vk）is the interaction energy between guest molecule i in the cavity of type k and all surrounding molecules.Samplings from harmonic oscillator simulations provide detailed sampling of frequncy ranges of guest movements which interferes with water librational frequencies.The result is specific values for the destabilization effects due to size.The harmonic oscillator formulation is:

The second term inside the brackets is the free energy of inclusion,which is evaluated based on samplings of fluctuations from energy minimum in the cavity of type k.We plot the parameters for the free energies of inclusion in Table 1 so that our results can be reproduced by others.

With reference to the discussion above,comparison of rigid lattice results and results from equation (9) gives a destabilization effect of approximately 1 kJ/mol6.For CH4the result from equations(7-9) are approximately the same.

The filling fractions of guest i in cavity k follow straightforward from the statistical mechanical model as:

θkiis the filling fraction of component i in cavity type k

ν is fraction of cavity per water.The filling fractions in large and small are given by:

Corresponding mole-fraction water is then given by:

Gibbs free energy for the hydrate phase is also important since the stability of hydrate formed through various routes will be different can be compared through comparison of Gibbs free energies for the different hydrate phases.

Enthalpy of hydrate formation is trivially available from equation (1) using the fundamental thermodynamic relationship.

Equation (16) also applies to chemical potential for any component in any phase and then relates chemical potential to partial molar enthalpy for the specific components in the same phase.

In which p is an indicator for type of phase.In the version for enthalpy of hydrate formation from water and a separate hydrate former phase p will be hydrate(H1),liquid water phase(aq)and gas(gas) and component indices in each phase are i.For the heterogeneous liquid water/gas hydrate formation,the enthalpy of hydrate formation is given by:

The simple relationship between equations (1),(16) and (17)makes it easy to derive models for enthalpy of hydrate formation for other hydrate formation routes as well.As an example,enthalpy for homogeneous hydrate from hydrate formers dissolved in liquid water is trivially obtained by replacingwithfor all hydrate formers dissolved in water [19]as discussed in section 4.2.For homogeneous hydrate formation from water dissolved in gas then replacingwithgivesthe resultfor directhydrateformation from water dissolved in gas [15]as discussed in section 4.3.Other hydrate formation routes will be discussed later.

In Fig.1 we plot pressure temperature stability limits for hydrates formed from pure water and water containing alcohol.We plot calculated results for 15 wt% methanol and ethanol respectively.Since we did not have available experimental data for 15 wt%methanol,we plot experimental data for 10 and 20 wt%methanol.

The presence of alcohol will change the activity of water,which directly affects chemical potential of water according to equation(2).We therefore plot Gibbs free energy for the formed hydrate as well as chemical potential for water in Fig.2.Chemical potential for liquid water will be lower with the alcohol content,as seen from the dashed curves,and as is obvious from equation (2).The thermodynamic stability of the formed hydrates from water with alcohol will be less than hydrate formed from pure water.The increased pressures for hydrate formed from water containing alcohol affect both gas chemical (Fig.3) and CH4mole-fractions in hydrate (Fig.4).CH4chemical potentials enter into equation (9),which then enter chemical potential for water through the cavity partition functions in last term of equation (5).The increased CH4mole-fraction (and corresponding less water) illustrates the lower hydrate stabilities for hydrates formed from water containing alcohol.

Fig.1.Pressure temperature stability limits for pure methane hydrate created from liquid water and methane gas.Black solid is calculated for 0 alcohol.+are experimental data from Tumba et al.[21]and ×are experimental data from Sabil et al.[22],both set for 0 alcohol.Solid blue curve is calculated data for methane hydrate with 15 wt%ethanol and blue circles are experimental data from Kobayashi et al.[23].Cyan is calculated data for methane hydrate with 15 wt% methanol in water.Green circles are experimental data for 10 wt% methanol [24]in water and red circles are experimental data for 20 wt% methanol [24]in water.

Fig.2.Gibbs free energy (solid) for the hydrates formed from methane and water without alcohols (black) and with 15 wt% methanol (cyan) and ethanol (blue)respectively.Dashed curves are chemical potentials for water in the formed hydrates.Same colour codes apply.

The enthalpies of hydrate formation are affected directly through the impact of alcohol on the activity coefficient in terms of shifts in hydrate forming conditions,associated changes in gas enthalpies.And for water the effect on enthalpy is directly through equation (2),and the corresponding partial molar water enthalpy from equation (17).Ideal gas water enthalpy does not depend on pressure of course and for rigid TIP4P water model the ideal gas enthalpy is trivial from the three translational degrees of freedom and the rotational degrees of freedom.In Fig.5 we plot enthalpies of hydrate formation for the three cases of pure water and water contains 15 wt%methanol or 15 wt%ethanol respectively.Note the experimental data from Nakamura et al.[25]deviates from other experimental data.See for instance Kvamme[19,26],Kvamme et al.[27,28].Measuring enthalpies of hydrate formation (and dissociation)is very challenging.Obviously hydrate dissociation cannot be done at exactly equilibrium conditions.Utilized temperature is frequently not reported and pressure is rarely given in open publications.Yet another example is coordination numbers(number of the water per hydrate former) is sometimes calculated,rarely measured and sometimes set to fixed value without arguments on reason for the specific number.This coordination number is critical in recalculation from enthalpies per mole hydrate over to enthalpies per mole hydrate former.

Fig.3.Chemical potential for CH4 (solid) in the hydrates formed from methane and water without alcohols (black) and with 15 wt% methanol (cyan) and ethanol (blue)respectively.

Fig.4.Mole-fraction CH4 (solid) in the hydrates formed from methane and water without alcohols (black) and with 15 wt% methanol (cyan) and ethanol (blue)respectively.

Many data sets are combination of some measured properties and the use of Claussius or Claussius-Claperyron in a fugacity framework.Fugacity is defined on an individual component basis and strictly there is nothing like fugacity for a mixture.Nevertheless-there are open publications that empirically define a mixture fugacity and utilize that in calculations of enthalpies.

Fig.5.Solid curves are calculated enthalpies of hydrate formation for CH4 hydrates.Hydrates formed from methane and water without alcohols (black) and with 15 wt%methanol (cyan) and ethanol (blue) respectively.Crosses are experimental data from Nakamura et al.[25].

Finally,we should keep in mind that the use of equations(2)and(16) guarantees a consistent set of thermodynamic data for enthalpy,Gibbs free energy and entropy [6,28,29].Appendix A in Kvamme [28]provides the detailed analysis and the reasons why this consistency is essential.This paper is open access and can be downloaded for free for interested readers that want mode details.

4.2.Homogeneous hydrate formation from liquid water and dissolved hydrate formers in water

Two changes are needed in the formalism presented in section 4.1 in order to calculate hydrate formation from dissolved hydrate formers in water.The first of these is the chemical potential of hydrate formers in the range of liquid water solubility and lower limit of hydrate stability concentrations.The solubility is a rigour Henry law without the simplifications.The hydrate stability limit is the minimum concentration of hydrate former(s) in water that is needed to keep the hydrate stable.For smaller concentration than these limiting values the hydrate former is more stable in liquid water phase and the hydrate will dissolve due to chemical potential gradients.This limit is very important in natural offshore gas hydrate systems.Inflow of seawater (almost infinite dilution of hydrate formers) to hydrate filled sediments will lead to leakage fluxes from dissociating hydrates.If hydrate forming conditions are favourable at the seafloor end of the fracture then hydrate may reform and lead to a hydrate “cap” on the fracture opening.This hydrate“cap”is highly dynamic and will dissolve towards seawater for the same reason as the lower concentration limit.But in addition to that there will be hydrate dissociation due to biological consumption of hydrocarbons.These latter ecosystems are dynamically linked from microbes and all the way through small organisms up to fish.

Knowledge on these concentration limits and the dynamics of hydrate formation from below and hydrate dissociation from seafloor-side can open up for commercial use of many hydrate seeps around the world.This can be done in many ways and can even include stimulating the natural biological conversion system and harvesting proteins.A challenge is of course that biological ecosystem normally leaves CO2as a product and that can form hydrates and also lead to mineral depositions.

For methane the following model is proposed by Kvamme[19,20]:

with

where TRis temperature divided by critical temperature for methane.The maximum temperature used in the fitting is 325 K.Ideal gas as function of temperature and density is trivial to consistently calculate using the TIP4P model moments in inertia for the rotational contribution [17].

The activity coefficient for methane in water,based on the asymmetric excess convention(activity coefficient for CH4in water unity as mole-fraction CH4goes to zero) has been fitted to the following function:

where TRis reduced temperature and defined as actual T in Kelvin divided by critical temperature for methane (190.6 K).The lower summation 1,2 indicates starting from 1 and counting in steps of 2.Parameters are given by Table 3 in Kvamme et al.[20].In homogeneous hydrate formation from dissolved methane in water then equation (19) enters equation (7) (rigid water lattice) or equation(9) (dynamic water lattice) instead of gas chemical potential.

The chemical potential for CO2dissolved in water is modelled by equation (22) below.

Since the chemical potential of CO2is not necessarily,the same for dissolved CO2in water,and CO2in gas (or liquid) in a nonequilibrium situation,then hydrate formed according to equation(22) in equation (7) or (9) will be different from the first hydrate and accordingly denoted H2.

For homogeneous hydrate formation from liquid water and dissolved hydrate former then the number of degrees of freedom(Gibbs phase rule) is 2 and each specific set of temperature and pressure will have a maximum dissolved content of hydrate former according a Henry"s law type of calculation [20],and a minimum content of hydrate former is needed to keep contacting hydrate at stability.But in nature or industrial,application systems are open and both homogeneous and heterogeneous hydrate formation will occur and equilibrium cannot be achieved due to too many active phases compared to constraints (mass conservation and equilibrium conditions).Under non-equilibrium conditions there are no general thermodynamic rules that dictate the chemical potentials of hydrate forming components to be the same in different phases.On the contrary it is impossible since normally thermal equilibrium(uniform temperatures) and mechanical equilibrium (uniform pressures) will be fulfilled and then the lack of mathematical balance on number of independent thermodynamic variables and constraints after equilibrium in T and P leaves concentration in all phase to be left to the combined first and second laws of thermodynamics.Local minimum Gibbs free energy will then dictate the lowest overall (total for all phases) distribution of phases and composition in these.

Also keep in mind that there is an interface between hydrate and liquid water of roughly 1.2 nm thickness [7].In a non-equilibrium system there are no rules that say that chemical potential for each component is the same in different phases.And water adsorbed on a hydrate surface is by definition a separate phase since water density is different from“bulk”water.Hydrate formed towards an existing hydrate film on the interface between gas and liquid water is therefore not the same hydrate that will form homogeneously from“bulk” water and dissolved hydrate former.

Since we discussed homogeneous hydrate formation from dissolved CH4in water in another paper [15]we not use much space on that system in this paper.But we can still look at Gibbs free energies of these hydrates as function of alcohol concentration in water.3 D plots are easy to read quantitatively but the plots in Fig.6(pure water),Fig.7(water containing 15 wt%methanol)and Fig.8(water containing 15 wt % ethanol) illustrate that formed hydrate stability goes down with content of alcohol in water.The homogeneously formed hydrate are less stable than the corresponding(same conditions) heterogeneous hydrates (see Fig.2).The difference is not very high for pure water but very significant for water containing alcohol.

As mentioned earlier homogeneous hydrate formation from dissolved hydrate formers in water is not the most important phase transition in hydrate production schemes,although these phase transitions may play a significant role in hydrate reformation since release of CH4can lead to substantial local super saturations outside the dissociating hydrate.

4.3.Homogeneous hydrate formation from water dissolved in hydrate former phase

The classical hydrate risk evluation scheme implies that liquid water has to be formed first and the water can form heterogeneously according to the equation provided in section 4.1.Thermodynamically hydrate can form directly from gas [12].Hydrate phase transition dynamics is implicit functions of thermodynamic control(Gibbs fre energy benefit),mass transport supply dynamics,and heat transport dyanmics.Mass transport dynamics is feasible for conditions studied by Kvamme et al.[15]but more research is needed in order to conclude whether a non-polar hydrate former gas phase is able to transport away the released heat during stages of water reformation from dynamic structure in a non-polar medium over to structured configuration in a hydrate lattice.Nevertheless-the formal change needed in equation (1) is thatis replaced by chemical potential of water in gas.

Fig.6.Gibbs free energy for hydrates formed from methane dissolved in pure water.

Fig.7.Gibbs free energy for hydrates formed from methane dissolved in water containing 15 wt% methanol.

Fig.8.Gibbs free energy for hydrates formed from methane dissolved in water containing 15 wt% ethanol.

SRK [18]equation of state is generally developed for non-polar molecules but it can be used for water simply because the solubility of water in gas is extremely small.In the mixing rules for the attractive parameters the water-water contribution will vanish because it is proportional to the square of the water mole-fraction.What is then left is non-polar contributions to the fugacity coefficient.The corresponding expression for the partial molar enthalpy is then given by:

Equation(24)enters equation(18)instead offor this case.

In Kvamme et al.[15]we used water diffusivities from the nonpolar methane model in Table 2 in Kvamme et al.[15].The reason is that we have used that model for many thermodynamic calculations and wanted to check that model also for mass transport dynamics.The problem with that model for diffusivity is that it will neglect effects of water dipole moment on molecular diffusivity.We therefore plot methane diffusivity coefficients from the non-polar methane model [30]and the 5-site model (see Kvamme et al.[15]for Molecular Dynamics simulation details and model parameters).In Fig.9 we plot the calculated methane diffusivity coefficient together with experimental data and ab inito calculations.

Table 2 Coefficients dm，ki in the polynomial for free energies of inclusion;Δgki=in kJ/moles for cavity type k and guests i=CO2,CH4 and N2.TCi is critical temperature for component i.TCCO2=304.13K,TCCH4=190.56K and TCN2=126.192K.

Table 2 Coefficients dm，ki in the polynomial for free energies of inclusion;Δgki=in kJ/moles for cavity type k and guests i=CO2,CH4 and N2.TCi is critical temperature for component i.TCCO2=304.13K,TCCH4=190.56K and TCN2=126.192K.

M CO2 CH4 N2 Large Large Small Large Small Large Small T ≤283.14 T ≤283.14 1 41.52168-17.87093 .199288 17.97150-42.47683 8.85531-143.99019 2-41.96874-17.89249-28.28735-23.44013 119.24124 10.87598-95.44723 3-70.72691 17.38136-11.94528-161.81535-183.19565 25.06545 4.68052 4-11.81084-29.68940-2.66250 45.20561 128.39252 54.17078 59.13995 5 16.73045-19.90321 3.85653 36.67261-54.98784 20.64268 109.87325 6 21.91621 25.22112 3.21040 138.00217-78.55671-133.44618 113.79746 7 0 0 0 0 0-130.99357 149.13992-85.72083 139.08208 9 0 0 0 0 0-106.74770 153.82431 8 0 0 0 0 0 10 0 0 0 0 0-78.83698 141.94965

MD simulations for the 5-site methane model are in excellent agreement with experimental data and ab initio calculations.In Fig.10 we plot calculated results for diffusivity coefficient of water dissolved in CH4.Water shows the same trend as the methane molecules Diffusivity coefficients;an almost linear dependency as function of gas density.

Due to the excellent agreements for methane diffusivity coefficients as illustrated in Fig.9 it makes sense to redo the mass transport analysis [15]of the nucleation for the 5-site methane model.In Fig.11-16 we plot nucleation times for 4 super saturations in mole-fractions CH4in water;10%,20%,30% and 40%.Details on the MD simulations behind the data in Fig.9 and 10,as well as details on the calculations plotted in Fig.11-16 are given by Kvamme et al.[15].

As expected,the times for hydrate nucleation based on mass transport increase with pressure since the molecular diffusion rate decreases with gas pressure.The trend is exactly the same as for non-polar one-site model for methane as can be seen from Kvamme et al.[15].But the mass transport is slightly slower for the 5-site model.Nucleation is,however,still feasible based on mass transport and free energy benefits.As discussed by Kvamme et al.[15]it is still unclear if hydrate nucleation from water dissolved in gas is feasible in terms of heat transport kinetics.

4.4.Heterogeneous hydrate formation from liquid water and adsorbed hydrate formers

Slightly polar molecules like for instance H2S and CO2adsorb well on a variety of mineral surfaces [13,14,35-39]which are typical for industrial settings (typically rust) and various minerals in sediments containing hydrate (calcite and kaolinite) are two examples.CH4and other non-polar components are unable to compete with water in direct adsorption on mineral surfaces[4,40-42].

Fig.9.Experimentally measured Diffusivity coefficients for CH4 self-diffusion at 256.7 K (square) [32],297.0 K (circle) [32],273.15 K (diamond) [33]and 298.15(pentagram) [33],298 K (stars) [33].The data from Higgoda et al.[34]are calculated from ab initio simulations,and the three densities correspond to pressures of 50 bar(35.78 kg/m3),75 bar (55.99 kg/m3) and 100 bar (77.44 kg/m3).Crosses are the calculated results from the non-polar methane model[30].Plusses are results from the 5-site methane model [31].The MD simulations are conducted at 278 K [15].

Fig.10.Calculated Diffusivity coefficients for water dissolved in CH4.Crosses are the calculated results from the non-polar methane model [30]in Table 1.Plusses are results from the 5-site methane model[31].The MD simulations are conducted at 278 K[15].

In view of the above we see two different hydrate nucleation situations related to interactions with mineral surfaces.Hydrate nucleation with directly adsorbed hydrate former will utilize structured water close to the mineral surfaces will utilize structured water.This is qualitatively discussed in section 4.4.2 with a focus on remaining challenges that need to be addressed.Hydrate formers that get trapped in structured water are likely to utilize partly structured water[4,40-42]and“bulk”liquid water outside.This is qualitatively discussed in section 4.4.2.

4.4.1.Hydrate nucleation of adsorbed hydrate formers on mineral surfaces and structured water

Adsorption of water on mineral surfaces in nature and industry is very strong and leads to extreme water densities.Non-polar hydrocarbons are not able to compete with water in direct adsorption.H2S has a significant dipole moment that enables direct adsorption on Hematite (dominating form of oxygen rust).The quadrupole moment in CO2is active in contact with polar molecules like water and responsible for higher liquid water solubility than non-polar molecules like for instance CH4and C2H6.CO2quadrupole moment also makes it possible for CO2to adsorb on rust.

In Fig.17 we plot chemical potentials for H2S and CO2along hydrate temperature pressure stability limits and chemical potentials for the same molecules as adsorbed on a model Hematite[12]system.For the specific model systems [12-14]H2S will prefer to form hydrate rather than staying adsorbed if water can be collected from outside(“bulk”liquid water)and/or structured water slightly outside of Hematite surface can rearrange over to hydrate nuclei structure.For CO2the picture is more unclear since the chemical potential differences between adsorbed CO2(dashed red) and CO2in hydrate(solid red).We should keep in mind that these are model systems and that other interaction models may change these results.Nevertheless,the examples in Fig.17 indicates that adsorption of hydrate formers on mineral surfaces is a possible route to hydrate formation.

It is absolutely feasible to implement this route to hydrate formation in the thermodynamic framework but it would be reasonable to investigate more interaction models for these molecules.

Fig.11.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 50 bar and temperature is 278 K.Dashed lines are number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

This will not lead to definite conclusions but rather probabilities of hydrate formation.And it is not only the hydrate former interaction models but also cross interactions between hydrate former molecules and charged surface atoms on the Hematite surface.It is,however,a highly relevant and important research issue since formed hydrates cannot attach to the mineral surfaces due to the low chemical potential of adsorbed water.Solid surfaces can therefore serve as catalysts for generating hydrate nuclei that can grow (or decay) elsewhere in the system.

Fig.12.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 100 bar and temperature is 278 K.Dashed lines are number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

Fig.13.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 150 bar and temperature is 278 K.Dashed lines are number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

Fig.14.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 200 bar and temperature is 278 K.Dashed lines and number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

Fig.15.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 250 bar and temperature is 278 K.Dashed lines are number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

4.4.2.Hydrate nucleation from trapped hydrate formers and liquid water

As mentioned above non-polar hydrocarbons are unable to compete with water on direct adsorption.But what we may call a secondary adsorption is that non-polar hydrate forming molecules get trapped in structured water slightly outside the mineral surface[4,40-42].These initial hydrate nuclei tend to be dynamically stable [4,40]in the sense that the average number of methane in hydrate like structure is almost constant but the outer molecules detach and new methane enters from surrounding water [4,40].This type of situation is only feasible when the mineral and water phases are in contact with a separate methane phase,as also discussed elsewhere.This is also illustrated by similar studies without a separate hydrate former phase in contact with mineral/water system [41,42].If some layers of methane molecules are initially placed on mineral surface with water outside the a hydrate like nuclei is also formed with structured water but it dissolves again since surrounding water does not contain methane.

Fig.16.Mass transport times (logarithmic scale with basic number 10) of water as function of number of water molecules (natural logarithmic scale) is solid curve.Pressure is 300 bar and temperature is 278 K.Dashed lines are number of water molecules in critical size hydrate nuclei.Left dashed curve is for 40 mol per cent water super saturation,next is for 30 mol per cent water super saturation,then for 20 mol per cent water super saturation and the right dashed line is 10 mol per cent water super saturation.The crossings between the mass transport (solid) and the thermodynamic critical number of molecules (dashed) are the mass transport controlled nucleation times.

Fig.17.Chemical potential for H2S along H2S hydrate stability limits(black solid curve)and calculated chemical potential for adsorbed H2S on Hematite[13,14](black circles).Chemical potential for CO2 along CO2 hydrate stability limits(red solid curve).Dashed red curve is calculated chemical potential for adsorbed CO2 n Hematite [13,14].

Fig.18.Solubility mole-fractions of CH4 in water (solid curves).Black is for 273.16 K,blue is for 278 K and red is for 286 K.Minimum mole-fraction of CH4 in liquid water needed to keep contacting hydrate stable(dashed curves).Black is for 273.16 K,blue is for 278 K and red is for 286 K.

A contacting hydrate former phase will supply dissolved hydrate formers in a mole-fraction window between solubility and lowest hydrate former concentration for hydrate stability.See for instance Fig.25 in Kvamme et al.[15]for solubility as function of temperature and pressure and Fig.26 in Kvamme et al.[15]for lowest mole-fraction of CH4in surrounding water needed to keep hydrate stable.In Fig.18 below we plot solubility of CH4and hydrate stability limit mole-fractions for three temperatures as function of pressure.

Since we already have published data from the simulations of methane hydrate nucleation in water structured by mineral surface[4],we cannot use the same plots and figures here.Interested readers are referred to section 3 in Kvamme et al.[4]and Figs.4-6 in that paper.It is an open access paper so free to download.

Glycols are frequently used in drying of gas because of the low chemical potential of water dissolved in glycols.In popular language,glycols are like magnets that drive water from natural gas into glycol solution because of multiple (depending on type of glycol) hydroxyl groups that can form hydrogen bonds with water molecules.They may not be ideal as direct thermodynamic inhibitors due to high prices and some inconvenient properties like for instance high viscosity.But they are ideal for adsorption on rusty surfaces and might be an excellent alternative for processing plants that do not have a drying unit,like for instance the Troll plant[16]outside Bergen,Norway.Injection of glycols in points that are critical for hydrate formation can compensate for the missing drying unit.And since the minimum temperature in the Troll processing plant is-22°C,it is higher than freezing points of these glycols.Common for these glycols are high boiling points and correspondingly low vapour pressures.The typical glycols are MEG(mono ethylene glycol),DEG (di ethylene glycol) and TEG (tri ethylene glycol).Number of active hydroxyl groups increase from MEG to DEG to TEG.But viscosity also increases in the same order and as such some dynamic features decrease the efficiency in the same order.

Technically also glycols are thermodynamic inhibitors in the conventional way that methanol and ethanol are used today.In Fig.19 below we plot pressure temperature projection of hydrate stability limits for systems of methane/water and MEG.Agreement with experimental data is fair but could likely been improved with parameter fitting.Basis for the model(see Table 4 in Kvamme et al.[15]) and parameters are theoretical work [44-49].

Fig.19.Calculated pressure temperature stability limits for methane hydrate created from methane and water containing TEG are solid curves.Circles are experimental data from Ross and Toczylkin [43].Green is 10 wt% TEG in water,blue is 20.2 wt% TEG in water and red is 40 wt% TEG in water.Black curve is for pure water.

Fig.20.Calculated pressure temperature stability limits for methane hydrate created from methane and water containing MEG are solid curves.Circles are experimental data from Robinson and Ng[50].Blue is 10 wt%MEG in water and red is 30 wt%MEG in water.Black curve is for pure water.

Similar calculations for MEG are plotted in Fig.20 together with experimental data [50].

In Fig.21 we plot Gibbs free energies of hydrate formation for methane hydrate created from pure water and the various concentrations of TEG in Fig.19.The created hydrates in presence of TEG are less stable than hydrates created from pure water and methane although differences are moderate for the actual concentrations of TEG in these particular examples.Similar calculations for MEG are plotted in Fig.22.The changes in hydrate stability with MEG are fairly similar to those of TEG in Fig.21.

Finally,we can also examine the impact of these glycols on enthalpies of hydrate formation in Figs.23 and 24.We do expect a flattening of enthalpies of hydrate formation for the high pressures and maybe even a slight decrease.It is hard to evaluate if the deceases in enthalpies of hydrate formation for the high temperatures and high pressures are realistic for 40 wt% TEG.Results for MEG in Fig.24 seems realistic.

Fig.21.Calculated Gibbs free energies for methane hydrate created from methane and water containing TEG are solid curves.Green is 10 wt% TEG in water,blue is 20.2 wt%TEG in water and red is 40 wt% TEG in water.Black curve is for pure water.

Fig.22.Calculated Gibbs free energies for methane hydrate created from methane and water containing MEG are solid curves.Blue is 10 wt%MEG in water and red is 30 wt%MEG in water.Black curve is for pure water.

The important advantages of glycols,as compared to the small alcohols methanol and ethanol,are their high boiling points and strong attraction to Hematite [44,49].Ab initio adsorption energy for MEG on Hematite from Hartree Fock(HF)using the 3-21G basis set [49]was calculated to 282.3 kJ/mol.The calculated result from Density Functional Theory(DFT)using the B3LYP functionals,with the Ahlrichs-pVDZ basis set,was found to be 246.0 kJ/mol.Interested readers are directed to Olsen et al.[49]for the finer details of the calculations as well as more information on free energies and adsorption structures.Adsorption of MEG,DEG(di-ethylene glycol)and TEG all adsorbed stronger on Hematite than on Calcite and primary adsorption was through the hydroxyl hydrogens.

In summary,injection of glycol at critical points in a processing plant or a pipeline can be a feasible solution for hydrate prevention if a drying unit is not available and if temperatures do not get lower than the freezing points of these glycols.The formation of an adsorbed film of glycol towards a rusty pipeline will be able to extract water from a gas in a similar fashion as gas drying units based on glycols.Similar might apply to liquid hydrocarbon systems containing hydrate formers but it is not a feasible strategy for multiphase transport containing significant water cuts.

Fig.23.Calculated Enthalpy of hydrate formation for methane hydrate created from methane and water containing TEG are solid curves.Green is 10 wt%TEG in water,blue is 20.2 wt%TEG in water and red is 40 wt%TEG in water.Black curve is for pure water.

Fig.24.Calculated Enthalpy of hydrate formation for methane hydrate created from methane and water containing MEG are solid curves.Blue is 10 wt%MEG in water and red is 30 wt% MEG in water.Black curve is for pure water.

Hydrates can form from any different phases.Specifically,we have demonstrated heterogeneous hydrate formation from gas/water interface,homogeneous hydrate formation from dissolved hydrate formers in water and also homogeneous hydrate formation from water dissolved in gas.Heterogeneous hydrate nucleation from adsorbed hydrate formers(H2S and CO2)on mineral surfaces has been discussed with reference to theoretical adsorption studies.Also hydrate nucleation from non-polar hydrate formers that get trapped in water that is structured by mineral surfaces is feasible.The reason for listing all of these different routes to hydrate formation is that all these hydrates are different.They have different compositions and different levels of stability in terms of Gibbs free energy.And the enthalpy of hydrate formation for the various hydrate formation routes varies substantially depending on which phases the hydrate formers and the water comes from.We have demonstrated that a residual thermodynamic scheme provides a simple and direct route for enthalpy of hydrate formation that can be applied to any hydrate formation route for which it is possible to calculate chemical potentials for water and hydrate formers.This route to consistent values of Gibbs free energy and enthalpy also provides for realistic estimations of hydrate entropies,which is critical in evaluations of strategies for hydrate dissociation.And since all phases have the same reference state (ideal gas for all components),then direct comparison of free energies for the different phases is feasible and free energy minimization is easy and transparent across phase boundaries.And this is needed since real systems in industry and nature cannot reach full thermodynamic equilibrium simply because there are too many possible phases (and all independent thermodynamic variables) compared to constraints (mass conservations and equilibrium conditions).Even for simple systems with one hydrate former ins separate phase,water and one hydrate phase experimental researchers knew that only one independent thermodynamic variable,like for instance temperature or pressure,could be defined if thermodynamic equilibrium should be achieved.It is therefore somewhat strange that researchers use these equilibrium curves for situations in which have both T and P are defined.Since hydrate can form and dissociate through several different routes,it therefore makes more sense to discuss hydrate stability limits in various sets of independent thermodynamic variables.

Small alcohols like methanol and ethanol dominate the markets for thermodynamic inhibition.The presence of these alcohols in water shifts the hydrate formation conditions but also reduces the stability of formed hydrate in the new conditions.These alcohols have significant surfactant properties [20]when water containing these alcohols is in contact with a separate non-polar phase.Amount of alcohols needs to be high enough to dominate above these surfactant effects.

Glycols can be used as thermodynamic inhibitors also in multiphase transport containing separate water phase.A very important advantage of these glycols is the strong adsorption on rust,and very high boiling points compared to the small alcohols.Injection of glycols in critical (with reference to risk of hydrate formation)points during transport or processing of natural gas is a feasible option in situations for which gas drying units are not available.Glycol films on rust surfaces will extract water from gas.Limitations are freezing points of these glycols.

In multiphase pipeline transport of hydrocarbons containing various water cuts the two most important routes to hydrate nucleation are heterogeneous hydrate nucleation on hydrocarbon/water interface and heterogeneous hydrate nucleation towards rust.Methanol or ethanol is efficient in addressing the first one.The strong adsorption of glycols on rust makes these alcohols efficient for prevention of hydrate nucleation towards rust.Even if glycols are added to liquid water in a mixture with small alcohols,there will be a thermodynamic driving force for these alcohols to extract from water to rust.More studies are needed along the lines in Olsen et al.[49]in order to systemize rust adsorption chemical potential for various glycols,and a systematic calculation of combined thermodynamics and mass balances.In chemical engineering language this will be like a flash calculation between water and adsorption phase on rust.Since this is a phase transition between condensed a simple temperature correlation of adsorbed chemical potential for the different glycols will be sufficient.See for instance adsorbed chemical potential for water on rust [12]as one example.

Finally,we have demonstrated a thermodynamic toolbox for detailed analysis of hydrate formation and dissociation in natural systems as well industrial systems.Many possible scenarios of hydrate formation,dissociation and reformation are possible and a comprehensive and consistent thermodynamic toolbox will assist in making proper designs of hydrate production schemes or better hydrate risk analysis for industrial systems.

Hydrate formation and dissociation during transport and processing are very complex processes that involve many possible phase transitions.There are several routes to hydrate formation and they all create different hydrates.Independent thermodynamic variables include temperatures,pressures and concentrations in all phases.The difference between number of independent variables and constraints (mass conservation and equilibrium conditions) is the number of independent thermodynamic variables that must be defined for thermodynamic equilibrium to be possible.If more or less thermodynamic variables are fixed then the system is mathematically undetermined and thermodynamic equilibrium is not possible.This is a well-known fact from the early times of hydrate equilibrium measurements.Only one thermodynamic variable can be fixed for equilibrium between liquid water,one hydrate former and hydrate.Still people use these curves as equilibrium curves when both temperature and pressure are fixed by local conditions in a processing plant or a pipeline.As illustrated here,and in a number of open papers,various hydrate formation routes lead to different hydrates.This is visible from the statistical mechanical model for water in hydrate which has been used by most hydrate researchers since 1970"s.If it is assumed that thermal equilibrium(uniform temperatures) and mechanical equilibrium (uniform pressures)will establish,it is straightforward to demonstrate that it is not possible fulfil the equal chemical potential equations due to a lack of balance between number of independent mole-fractions in all phases and number of equations for chemical equilibrium.There is a need for a more complete thermodynamic platform that is not only able to calculate hydrate formation but also is able to calculate hydrate dissociation according to a variety of possible ways.Hydrate can dissociate if temperature and/or pressure is brought outside stability limits.But hydrate will also dissociate towards pure water even if temperature and pressure is inside hydrate stability limits.Hydrate can sublimate is exposed to a dry hydrocarbon mixture.Even rust surfaces have a dual thermodynamic effect on hydrate.Rust surfaces act as a catalyst for hydrate nucleation but hydrates are not able to attach to the surfaces because of very low chemical potential for water.

Small alcohols like for instance methanol are efficient hydrate inhibitors in sufficient amounts to overcome the surfactant effects of methanol when water is exposed to a hydrate former phase.Methanol and ethanol will primarily act on hydrate formation between water and a separate phase containing the hydrate formers,and on hydrate formation from dissolved hydrate formers in water.During gas transport they can also act on various routes to hydrate formation from water in gas since these small alcohols will also dissolve in gas.Glycols,on the other hand,will efficiently adsorb on rust.Injection of glycol will therefore be an efficient hydrate prevention action when drying units are not available and temperatures above glycol freezing points.Films of glycol on rust surfaces will extract water from gas.But even for multi-phase transport with various water cuts,a mixture of small alcohols and glycols might be efficient since glycols will have a thermodynamic driving force to extract out to adsorption on rust.More research is needed on development of the thermodynamic data and the following logistics of incorporating glycol adsorption phase transition into the thermodynamic hydrate package.

We have published a significant number of papers on various routes to hydrate formation from water dissolved in gas.Two of these involves direct water dropout as liquid or as adsorption on rust.The third route is direct hydrate formation from dissolved water in gas.We have used molecular dynamics simulations to estimate water diffusivity coefficient when dissolved in methane at different pressures,ranging from 50 bar to 300 bar.We have not found any data to compare with for the water diffusion but methane diffusivity coefficients in this system are in excellent agreement with available experimental data and ab initio calculations.It is demonstrated that direct hydrate nucleation is feasible from a thermodynamic point of view,as well as from a mass transport point of view.It is still uncertain whether heat transport makes this route to hydrate formation feasible.Research work is in progress on addressing this issue.

Acknowledgements

The authors are grateful for financial support through 111 Project (No:D21025),National Key Research and Development Program (No:2019YFC0312300),National Natural Science Foundation Item of China (No:U20B6005-05,51874252 and 5177041544),Open Fund Project of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (No:PLN2021-02 and PLN2021-03).

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