Risk of Hydrate Formation during the Processing and Transport of Troll

Article pubs.acs.org/jced

Risk of Hydrate Formation during the Processing and Transport of Troll Gas from the North Sea Bjørn Kvamme* and Solomon Aforkoghene Aromada Department of Physics and Technology, University of Bergen, Allegaten 55, 5007 Bergen, Norway ABSTRACT: The North Sea is covered by close to 8000 km of pipelines transporting hydrocarbons. Pressures are high, and temperatures are generally low. Temperatures can be as low as 272 K in the north, due to seawater salinity, and rarely exceed 279 K for the southernmost pipelines. The most common procedure for hydrate risk analysis involves the calculation of the water dew point for a gas mixture containing water. Pipelines are normally covered by rust even before they are put in place. Rust is a mixture of iron oxide, and one of the most stable is hematite, Fe2O3. Because of the distribution of partial charges on the hematite surface, adsorbed water will be highly structured, resulting in low chemical potentials and a low adsorption energy for the water molecules. The adsorbed water on the walls is thermodynamically cold in terms of the functional derivative of the internal energy of the adsorbed layer with respect to the entropy of the adsorbed layer. This fact adds on top of the walls being the coldest region of the pipeline due to the cooling toward outside seawater. The low chemical potential of adsorbed water and incompatibility of partial charges between hematite and the hydrate surface will not permit hydrate to directly attach to the surface of the walls, but the walls can serve as nucleation surfaces, and hydrates formed can be bridged by structured water layers to the rusty pipeline surface. Earlier studies for various simple hydrocarbon systems indicate that the tolerance for water content based on dew point might be 20 times higher than the water content corresponding to water adsorbing from gas onto solid hematite surface. In this study we apply a similar comparison for a real hydrocarbon mixture for the first time, using composition data which is openly available for the Troll gas from the North Sea. Since the average chemical potential of adsorbed water can be as much as 3.4 kJ/mol lower than the liquid water chemical potential, this route to hydrate formation dominates completely in determining the risk of water dropping out from the gas and eventually forming a hydrate.

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INTRODUCTION Processing and transportation are important integral aspects of natural gas operations. This is because natural gas is mostly produced from places (e.g., offshore, swamps, and hinterland forests) which are far from its market, and processing is important to meet market quality requirements. The transportation of natural gas from reservoir to processing plants and for supply delivery terminals is primarily done by the use of pipelines. As of 2010, there was a total of 1,942,669 km of pipelines1 in the world transporting natural gas, crude oil, or petroleum products. In the North Sea in particular, about 96 billion standard cubic meters of gas is transported annually through over 7800 km long pipelines which are laid mainly on the seafloor and consequently exposing them to low temperatures of about 275−279 K.2 A large quantity of natural gas is transported through these pipelines at elevated pressures but at low temperatures. With availability of free water, these are the right conditions that can likely lead to the risk of formation and deposition of ice-like substances known as clathrate hydrates or natural gas hydrates, NGHs, on the pipelines and thereby may result in eventual plugging of pipelines and process equipment. This is a great flow assurance challenge to the oil and gas industries. Natural gas hydrate also exits naturally; it is mainly found usually trapped under clay or shale (sealing formations) in © XXXX American Chemical Society

sediments, or permafrost having more but varying sealing added to the frozen layers above the hydrate zones. The source of naturally occurring methane-rich gas hydrate is from the biogenic degradation of organic materials just some hundreds of meters on top of the Earth’s crust, as opposed to the case of the thermogenic degradation of organic materials at a greater depth in the Earth’s crust to release hydrocarbons. In the offshore of Norway, the compositions of natural gas that is produced reveal the distinct origins of the hydrocarbons. At the Troll gas field which is examined in this study, the gas produced has a high content (mole fraction) of methane with some amount of ethane and heavier hydrocarbons. Consequently, on the limited amount of C2+ present (which is not valuable), there is therefore no justification for extra investment in a processing (separation) plant to operate at extremely low temperatures. Thus, the Troll separation plant is simply a dewpoint separation plant operating at 6900 kPa with the minimum temperature of 251.15 K. However, the separation plant for the gas from Kvitebjørn, also at Kollsnes (outside of Bergen), operates at a lower temperature of 203.15 K at 6900 kPa. This is because the content of C2+ (ethane and heavier hydrocarbons) Received: March 14, 2017 Accepted: May 24, 2017

A

DOI: 10.1021/acs.jced.7b00256 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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permitted in the gas stream during processing and transport for a specific range of pressures and temperatures. The most typical approach for gas dehydration is by absorption in glycol. But the glycol dehydration approach can only be applied for temperatures not lower than 248.15 K. Separation temperatures lower than 248.15 K will require mostly adsorption technology. This study is carried out to investigate the upper limit of water that can be allowed in Troll gas from the North Sea based on the traditional technique of the water dew point, in addition to the maximum content of water that can be accepted based on water adsorbing onto hematite (rusty) surfaces. The Troll field is located in the northern part of the North Sea covering an area of about 750 km2, and it is approximately 65 km2 west of Kollsnes, the landing site just outside of Bergen.3 The largest gas field discovered in the North Sea is the Troll gas field (the reservoir is 1400 m below sea level); thus, it is of very crucial importance to Norwegian gas production. Troll gas makes up 40 percent of all the gas reserves on the Norwegian continental shelf. The Troll A platform and the gas processing plant at Kollsnes together with the pipelines transporting hydrocarbons from the platform to the onshore processing plant all make up Troll gas. Norwegian Shell was in charge of the development of the first phase of Troll gas before Statoil became the operator as from 1996. The composition of the Troll gas used in this study has been obtained from Ebbrell.4 The composition data contain components C1 to C7+, toluene, xylene, nitrogen, and carbon dioxide. But this work is focused only on the hydrocarbons that commonly form hydrate structure I and structure II. Therefore, only methane, ethane, propane, and isobutane data are required, and the necessary normalization of the composition of these four components has been done.

in this gas is high enough and, thus, valuable enough to justify having a separation plant with more complexity to handle such lower temperature conditions. The final separator for the Troll gas is a major critical point where the formation of hydrate or ice is likely to occur consequent on its operations at such low temperatures. In the gas phase, a structure I hydrate dominated by methane is expected. The liquid outlet of the final separator will contain a high concentration of ethane. Thus, at the liquid outlet (liquid phase) an ethane dominated structure I hydrate is expected. However, the presence of remarkable amount of propane (though limited compared to C1 and C2) could cause the formation of some structure II hydrate to occur, which would form first before the structure I hydrate. If the structure II hydrate eventually results in the Troll gas separation process, it could be small since the propane and isobutane concentrations in the gas would be relatively small. Besides the transport of natural gas from the fields offshore like Troll and Snøhvit. in Norway, pipelines are also used in transport to Germany for further distribution. For markets that are far away, the transportation of natural gas is typically accomplished by shipping as liquefied natural gas (LNG) or compressed natural gas (CNG), but usually more costly. Liquefied natural gas from Snøhvit, which is offshore at the northern part of Norway, was meant to supply the United States of America (USA) market before the USA commenced a large scale gas production from shale. The conditions for both transport (North Sea seafloor temperatures is 275−279 K under high pressure, up to 25 000−30 000 kPa for transport to the continents) and the separation of natural gas at processing plants like the Troll plant (295.15 K and 6900 kPa) are within the region for hydrate to form with the availability of free water, or if water can drop out from the gas as separate phase(s) thereby being available for possible hydrate formation. At the receiving depots, the pressures vary, and it depends on the transport velocity required and additional infrastructure to process the gas, petrochemistry, or transport distribution. In this work, the pressure range applied is 5000 to 25 000 kPa, because pressures during processing and transport of natural gas in the North Sea fall within this range. If free water or separate water phase is present or condenses out from dissolved water in the gas, the condition stated already are right for hydrate to possibly form. As has been mentioned earlier, natural gas also has some other light hydrocarbons and nonhydrocarbons, small amounts relative to methane. Meanwhile, hydrogen sulfide gives stabilization efficiently well to the hydrate such that the presence of even a very small amount of it would shift the hydrate formation conditions to lower pressures and/or higher temperatures. On the other hand, the stabilization influence of nitrogen on the hydrate cages is limited. Its effect is the dilution of the natural gas, and this adjusts the conditions for the hydrate to form at higher pressures and/or lower temperatures. Hydrate could form from a separate water phase and guest molecules in the hydrocarbon gas stream, and this can eventually grow to substantial ice-like plugs that can severely impede the flow of gas and in worst situation result in blocking the entire pipeline cross-section and damaging the pipeline or equipment. The best solution is, thus, dehydration or the removal of water from the gas to a level (mole fraction) which below that which can lead to making a separate water phase available. To determine the amount of water that is required to be removed to avoid the risk of hydrate formation, it is crucial to estimate the maximum water content that should be

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ROUTES TO HYDRATE FORMATION It is typical that the gas stream from the reservoir always contains water. A three-phase separator is first applied to separate water from the hydrocarbon stream. The least amount of water that is in the hydrocarbon stream as it flows into the processing plant prior to the removal of the water phase is the saturation concentration. Usually, some more water is dissolved and dispersed in nano to micro droplets in the gas stream as a result of hydrodynamics. This water can drop out from the gas stream and form a separate water phase, and this depends on the local conditions of temperature and pressure, composition of the gas, and the amount (mole fraction) of water in the hydrocarbon stream. The risk of hydrate formation is conventionally done on the basis of availability of free water (separate water phase) as liquid droplets made available through condensation from the gas mixture during processing and transport. This method involves the estimation of the water dew-point pressure for a particular residual volume of water in hydrocarbons. The evaluation of the amount of water that would condense out of the hydrocarbon gas stream is done based on whether the dewpoint pressure at the local temperature is within the expected pressure and temperature of the stability region of hydrate. This technique does not consider the situation where water could condense out from the hydrocarbon gas mixture stream by the process of adsorption on the internal walls of processing equipment or that of pipeline used for transport of the hydrocarbons. Steel of different quality or compositions is the material generally used in manufacturing both pipelines and most oil and gas treatment equipment. These wall surfaces of the steel materials used for both the processing equipment and pipelines B



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field to production field. The water would come out with hydrocarbons as a separate water phase and as water that is dissolved in the gas phase and liquid phase of the hydrocarbons. The processing of gas involves a number of unit operations/ equipment that can give rise to thermodynamic conditions which are right for hydrates to form. Some examples are turbines that cause cooling of gas like in the case of cryogenic processing of gas and low-temperature flash tanks. In the North Sea, operating pressures with respect of delivery pressures to the processing (separation) plants and from the separation plants to the continents (markets) or at connection points vary in range as mentioned in above. The seafloor temperatures are normally between 272 and 279 K. The North Sea natural gas transport conditions range from pressures of 5000 to 25 000 kPa. Thus, if free water could be made available by dropping out of the gas through either condensation or adsorption, these temperature and pressure conditions are favorable for hydrates to form during the transport of gas in the North Sea. What is critical then is to know how much water can be permitted in the gas without the risk of dropping out to form a free water phase. There are several technologies that could be used to remove hydrates from pipelines; nevertheless, the simplest approach to prevent hydrate from forming is to evaluate the maximum limit of water concentration that can be tolerated in natural gas in the course of transport and processing. The typical classical technique applied by the industries is to estimate the water dew point pressures for local temperatures. The maximum limit of water content before liquid water can condense out of the gas stream can be estimated for each local temperature and pressure during the transport and processing. The calculated maximum amount of water that can be permitted in the gas forms the basis for design of gas dehydration (water removal) systems. Water can also drop out from the gas through the mechanisms of adsorption onto hematite that usually cover the surface of pipeline and consequently cause hydrate to form heterogeneously from water layers slightly outside.2 The initial step to manage hydrate formation is to estimate the particular temperature−pressure conditions favorable for hydrate to form from gas in a specific system. But the necessary further step to evaluate the maximum content of water that should be permitted in gas during its processing and pipeline transport to avoid the risk of hydrate formation is a very complex problem. This is because of the competing phase transition process and the several distinct routes to the formation of hydrates, where both kinetics and thermodynamics play a very important role. The dynamic situation comes to be even more complex because the hydrates formed in the hydrocarbons transport pipelines are not able to attain thermodynamic equilibrium consequent on the limitations of Gibbs phase rule. The chemical potentials of different hydrate forming components are not the same but are different across all the phase boundaries in a nonequilibrium situation. We applied free energy analysis in this our study owing to the fact that hydrate formed from different phases will have different free energies due to the different chemical potential of hydrate formers (guest molecules). For equilibrium situation, the conventional technique employed to evaluate for equilibrium is to calculate (at the same time) the conditions for equilibrium, conservation of mass, and conservation of energy. While in the case of nonequilibrium the combined first and second laws of thermodynamics are used in place of the equilibrium conditions by means of certain

are usually covered by rust. Water can drop out and form a separate water phase available for hydrate formation through either the process of condensation or adsorption on solid surfaces (normally on the surfaces of pipelines covered with rust). These two processes or routes are investigated in this work. In this study, the Troll gas, which comprise the platform A, processing plant at Kollsnes, and transport conditions, are investigated by examining these two routes to hydrate formation mentioned above: the route that involves condensation of water from the gas phase to form free water phase which together with the guest molecules from the gas phase subsequently form hydrate; and the route where a free water phase is made available through the process of adsorption of water from the gas phase onto the rusty surfaces of pipelines. Hydrate cannot form directly on hematite (rusty) surfaces due to the incompatibility between the distribution of partial charges of hydrogen and oxygen in the lattice and atom charges in the hematite (rusty) surface. However, the hematite will act as a catalyst for pulling out the water from the gas through adsorption mechanism; subsequently, the formation of hydrate can then occur slightly outside of the first two or three water layers of approximately one nanometre. Rust is formed from iron and oxygen under the influence of or exposure to water. It is a mixture of a number of different oxides of iron such as magnetite (Fe3O4), hematite (Fe2O3), and iron oxide (FeO). Even though magnetite usually forms very early, in the long run it is hematite that is most dominant, one of the most thermodynamically stable forms of ordinary rust. By ordinary rust we refer to different oxides of iron formed by the exposure of iron to water and oxygen. Impurities of components such as carbon dioxide and hydrogen sulfide can cause conversions over to iron carbonates and different iron and sulfur components. Theoretically, there is a third route where the formation of hydrate can also occur directly from the water that is dissolved in the hydrocarbon gas stream, but consequently on the low concentration of the water (and limitations in heat and mass transport), it is unlikely for hydrate formation to occur via this route. Thus, this route will not be investigated in this study. However, if the surface stress from flow does not affect the water/hydrocarbon system at all, afterward a rapid formation of hydrate film on the water/hydrocarbon interface would occur and would very quickly block further transport of guest molecules and waters through the hydrate film (very low coefficient of diffusivity). In that case, hydrate would form from the guest molecules dissolved in water and could form from water dissolved in gas, which then would benefit from nucleation on the hydrate surface. But considering a flowing case with turbulent shear forces, this is not a realistic occurrence. A further difference between a flowing case and a case of a stationary constant volume and constant mass experiment in laboratory is that there is a continuous supply of new mass. Therefore, the limiting situation where the water is totally consumed resulting in stoppage/cessation of hydrate formation does not exist. Kvamme et al.2 has presented comprehensive probable routes to hydrate formation, together with likely routes to hydrate dissociation during pipeline transport of natural gas based on changes in free energy associated with the different phase transitions.

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EVALUATION OF THE RISK OF HYDRATE FORMATION The content of water that accompanies hydrocarbons from offshore or onshore production reservoirs varies from production C



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THERMODYNAMICS This system in consideration cannot attain equilibrium. This is trivially known for the simplest system of one hydrate former, for instance methane, in a separate phase and liquid water. With two components and three phases (after hydrate formation) only one thermodynamic variable can be specified for equilibrium to be possible. In a flowing pipeline hydrodynamics and hydrostatics as well as phase transitions involving heat exchange determine local pressure and temperature so even for the simplest system equilibrium is not possible. Even this simple example system is more complex since a hydrate film will slow down transfer of methane gas to contact liquid water and the other way around. But the hydrate can also form from dissolved methane in water and even from water dissolved in methane. This latter option is not very likely in terms of mass transport and heat transport. Since the system is not in equilibrium, the chemical potentials for hydrate former (methane) are not the same in gas and as dissolved in water. By the statistical mechanical relationship between chemical potential for hydrate formers entering the hydrate clathrate and the chemical potential of water in the hydrate,7 it is straightforward to verify that each of these hydrate phases have a different composition, different density, and different free energy. By fundamental thermodynamics, they are therefore unique phases. The number of degrees of freedom according to Gibbs phase rule is therefore further reduced and system even more over-determined. The system only gets even more complex when more hydrate formers are added since the first and second laws will dictate that lowest free energy phases forms first given that these routes does not involve penalties in mass as heat transport. Practically this implies that any additions of ethane, propane, and isobutane will result in a variation of hydrate phases. The initial formation of hydrates dominated by the larger hydrocarbons does not involve penalties in terms of mass transport since they will, by simple thermodynamic considerations,8 condense out first on the water/hydrocarbon surface. To attain thermodynamic equilibrium, the temperatures, pressures, and chemical potentials of all components must be equal in all coexisting phases, as given by eqs 3 to 5 below. Thermal equilibrium:

strategies for minimizing free energy locally under constraints of conservation of both mass and energy. In consideration of formation and dissociation of hydrate, the modeling of every phase transition is accomplished as pseudo reactions in consistent with changes in free energies as driving force for phase transition and coupled dynamically to mass transport and heat transport.5 Equation 1 is used to evaluate the free energy changes in connection with all phase changes: H,i H,i p ΔGi = δ[x wH,i(μwH,i − μwp ) + xgas (μgas − μgas )]

(1)

where x = composition, H = hydrate phase, i = phase transition scenario, μ = chemical potential, p = liquid, gas, adsorbed phases, δ = +1 for hydrate formation and −1 for hydrate dissociation, and w = water. For a nonequilibrium situation, we need to remember that the chemical potentials for hydrate formers (guest molecules) in different phases are not the same but are different. This indicates that the chemical potentials for the hydrate formers in the hydrate will also be different, as can be observed from a Taylor expansion from an equilibrium point.6 The hydrate phase change, be it formation or dissociation, is a nanoscale process governed kinetically by what occurs on a thin interface of generally three to four water layers, that is approximately 1−1.5 nm. Thus, the implicitly coupled mass transport is a molecular scale diffusion transport. This diffusion is coupled to hydrodynamics of the flow situation by the support of mass from the larger surrounding. The enthalpy of formation is required to be transported out for hydrate formation. While in the case of hydrate dissociation, it requires a supply of heat by heat transport from the larger surrounding. The absolute value of the heat necessary to be transported is consistently given from eq 1 by the trivial thermodynamic relationship: ΔG ∂⎡⎣ RTi ⎤⎦ P , N⃗

∂T ΔG ∂⎡⎣ RTi ⎤⎦ P , N⃗

∂T

= −RT 2ΔHi

=−

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(2)

RT 2 ΔHi

T (I) = T (II) = T (III)... = T

where ΔHi = enthalpy change associated with a certain route i to hydrate formation. T = temperature in Kelvin, and N⃗ = vector of mole numbers in the system, and R = gas constant = 8.3143 J/mol·K. This can be calculated numerically and analytically on the basis of the models for chemical potentials incorporated. The real heat transport dynamics, coupled implicitly to the phase change thermodynamics as expressed in eq 1, is distinct for each phase change and given by the feasible directions to transport away the hydrate formation heat. For the case of hydrate formation slightly outside of the first water molecules on a pipeline wall, the heat is transported fast toward the adsorbed water layer and subsequently then through the pipeline walls. The formation of hydrate on the interface of water adsorbed on hematite would thus have rapid heat transport, likewise for hydrate formed from dissolved or adsorbed guest molecules in this layer. Heat transport possibly will be 2−3 orders of magnitude more rapidly than mass transfer,7 therefore, there is no rate limiting process for these two routes to hydrate formation.

(3)

Newton’s law, mechanical equilibrium: P(I) = P(II) = P(III)... = P

(4)

Chemical equilibrium: μ(I) = μ(II) = μ(III)... = μ

(5)

The superscripts I, II, and III further represent phase index for every of the coexisting phases in consideration. Even though equilibrium is not possible, applying a quasiequilibrium method allow us evaluate the thermodynamic benefits of different routes of either formation or dissociation of hydrate through eqs 3 to 5 as asymptotic limits of possible stability for each given phase transition. Residual thermodynamics by application of the Soave− Redlich−Kwong (SRK) equation of state9 is used for all components in all phases: hydrate, liquid water, and ice inclusive. This was executed by the use of molecular dynamics results for water in different phases (empty hydrates, liquid water, and ice).10 D



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Figure 1. The top curve shows the estimated equilibrium pressures for the hydrate formed from methane and water, as compared to experimental data.11−13 The bottom curve is the molar free energy for the hydrate () and water chemical potential (---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

Figure 2. The top curve shows the estimated equilibrium pressures for hydrate from ethane as compared to experimental data.14−16 The bottom curve shows the molar free energy for the hydrate (−) and water chemical potential (---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

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FLUID THERMODYNAMICS The estimation of the chemical potential of component i in gas is accomplished using

μi (T , P , x ⃗) − μiideal liquid (T , P , x ⃗) = RT ln γi(T , P , x ⃗)

μi (T , P , y ⃗ ) − μiideal gas (T , P , y ⃗ ) = RT ln ϕi(T , P , y ⃗ )

where lim γi → 1.0 when x i → 1.0

lim(ϕi) → 1.0 for ideal gas

(7)

(6)

Also, the ideal liquid term includes the trivial ideal mixing term in addition to the pure liquid value.

where ϕi refers to fugacity coefficient for component i in particular phase and y⃗ stands for the mole fraction vector of the gas. Here, the chemical potential of the ideal gas contains the trivial mixing term due to entropy change of mixing ideal gases at constant pressure and total temperature.

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ASYMMETRIC EXCESS The solubility of methane, ethane, and higher hydrocarbons in water is limited; thus, it is proper to use a reference state of infinite dilution as stated in eq 8.

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AQUEOUS THERMODYNAMICS The calculation of pure water chemical potential is established on samplings from molecular dynamics (MD) simulations.10

μi (T , P , x ⃗) − μi∞(T , P , x ⃗) = RT ln[x iγi∞(T , P , x ⃗)] where lim γi∞ → 1 when x i → 0

SYMMETRIC EXCESS The chemical potential of component i in the water phase is modeled as

(8)

where μ∞ i = chemical potential of component i in water at infinite dilution, γi∞ = activity coefficient of component i in the E



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Figure 4. The top curve shows the estimated equilibrium pressures for hydrate from isobutane as compared to experimental data.20 The bottom curve is the molar free energy for the hydrate (solid ) and water chemical potential (dashed ---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

Figure 3. The top curve shows the estimated equilibrium pressures for hydrate from propane as compared to experimental data.16−19 The bottom curve is the molar free energy for the hydrate (solid ) and water chemical potential (dashed ---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

where H = hydrate phase, μHw = chemical potential of water in hydrate, μ0,H w = chemical potential of water in empty hydrate structure, vk = fraction of cavity type k per water molecule, and hik = canonical cavity partition function of component k in cavity type j. Equation 11 gives the canonical partition function:

aqueous phase based on the same reference state, and R = universal gas constant. The solubility of methane and that of ethane are each very low and may therefore be approximated as independent. Thus, eq 9 could be applied together with eq 8. It has proven satisfactorily accurate for most industrial applications where the risk of hydrate formation is a factor. μi,j(T , P , x )⃗ ≈ μi,j∞(T , P , x ⃗) + RT ln[xi , jγi,j∞(T , P , x ⃗)]

hik = e β(μi

EQUILIBRIUM THERMODYNAMICS OF HYDRATE The chemical potential of component i in hydrate phase should be equal to the component’s chemical potential in the phase it is extracted from2 at equilibrium. Water absolutely dominates the dew point in this work. Equation 12 is applied for evaluation of hydrate formation for the route of liquid water dropped out. Nevertheless, the chemical potential of all gas components (guest molecules) of hydrate are evaluated utilizing eq 6 in the case of water dissolved in gaseous phase.

HYDRATE THERMODYNAMICS The typical Langmuir type of adsorption model is used for chemical potential for water in hydrate, however, in the form derived by Kvamme and Tanaka10 which as well provides consideration for lattice movements and corresponding impacts of different guest molecules:

∑

RTvk ln(1 +

∑ hik) i

(11)

■

■

k = 1.2

−Δgikinc)

where β = inverse of the gas constant times temperature and Δginc ik = impact on hydrate water from inclusion of the guest molecules i in the cavity k.

(9)

where subscript i refers to a phase with low solubility for component j.

μwH = μw0,H −

H

(10) F



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Figure 5. The top curve shows the estimated equilibrium curve as compared to experimental data21 for 28.6 mol % isobutane and rest methane. The bottom curve is the molar free energy for the hydrate (solid ) and water chemical potential (dashed ---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

μw0,H −

∑ k = 1.2

RTVk ln(1 +

Figure 6. The top curve is the estimated equilibrium pressures for hydrate from 72.9% ethane and 27.1% propane as compared to experimental and smoothed data.14 The bottom curve is the molar free energy for the hydrate (solid) and water chemical potential (dashed) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

water ∑ hik) = μi pure (T , P ) ,H2O i

+ RT ln[xi ,H2Oγi ,H2O(T , P , x ⃗)]

nH H

ΔG = δ ∑ xiH(μi H − μiP )

(12)

(13)

i=1

The chemical potential of empty hydrate structure is evaluated from the model described by Kvamme and Tanaka.10 This model has proven to have predictive capabilities; consequently, it causes any empirical formulations to be unnecessary and may be unphysical because chemical potential is a fundamental thermodynamic property. In this work the right-hand side of eq 12 is approximated by pure water. The consequence would be merely a slight shift in chemical potential of liquid water. For example, at 1500 kPa and 274 K the correction is −0.07 kJ/mol, though marginally greater for 20 000 and 25 000 kPa; nonetheless, it is still not dramatic for the purpose of this work. However, eq 13 has proven beneficial for the estimation of free energy change related to a hydrate phase transition ΔGH

where H = hydrate phase of molecule i, P = parent phase of molecule i (the phase from which the guest molecule comes from. For equilibrium situations it is the hydrate guest former phase in equilibrium with hydrate and water as liquid or ice. Equation 14 gives the relation between the filling fraction, the mole fractions, and cavity partition function as follows: θik =

x ikH h ik = v k(1 − x T) 1 + ∑i h ik

(14)

where xT = total mole fraction of all guests in the hydrate. θik = filling fraction of component in cavity type k. xHik = mole fraction of component i in cavity type k. G



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Figure 7. The top curve is the estimated equilibrium pressures for hydrate from 65.8% ethane and 34.2% propane as compared to experimental and smoothed data.14 The bottom curve is the molar free energy for the hydrate (solid) and water chemical potential (dashed) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

Figure 8. The top curve is the estimated equilibrium pressures for hydrate from 28% ethane and 72% propane as compared to experimental and smoothed data.14 The bottom curve is the molar free energy for the hydrate (solid) and water chemical potential (dashed) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

VERIFICATION OF THE MODEL Our model has previously been applied in the investigation of structure I hydrate from mainly methane, ethane, carbon dioxide, and hydrogen sulfide.2 In this study, our investigation of the limit of water concentration in the gas stream is more comprehensive; it has been extended further to cover structure II hydrate formation and gas stream with both binary and ternary mixtures of sI and sII guest molecules of hydrocarbons. Free energy and water chemical potential are also estimated in this work. There was no attempt to fit interaction parameters to replicate experimental data. This is because the priority is to keep the statistical mechanical model10 free of adjustable parameters in all terms, together also with empty hydrate chemical potentials and chemical potentials for ice and liquid water. Nevertheless, anyone who intends to make use of the scheme and analysis presented in this work could make adjustment to their own models at their discretion. It is imperative to

study the qualitative agreements between estimates from our model systems10 and established experimental data. We observed a satisfactory agreement between the estimates of hydrate equilibrium with our model and experimental data from well-known literature without using any empirical data fitting. We therefore infer that the deviations is sufficiently acceptable to show the upper limit of water concentration tolerable in hydrocarbons gas stream during processing and transport for various situations that result in hydrate formation; especially, results are very satisfactory for the range of significant temperatures of 273−280 K. The hydrate equilibrium estimates obtained with our model compared with some experimental data for pure components (Figures 1−4), binary mixtures (Figures 5−9), and ternary mixtures (Figures 10 and 11). As an illustration of the relative stability of the various hydrates, plots of molar free energy for each hydrate are shown along with the chemical potential of water for the same hydrates.

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H



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Figure 9. The top curve is the estimated equilibrium pressures for hydrate from 85% ethane and 15% propane as compared to experimental data.14 The bottom curve is the molar free energy for the hydrate (solid ) and water chemical potential (dashed ---) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

Figure 10. The top curve is the estimated equilibrium pressures for hydrate from 17.4% methane, 70.5% ethane, and 12.1% propane as compared to experimental data14 (dissociation condition). The bottom curve is the molar free energy for the hydrate (solid) and water chemical potential (dashed) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa).

Figures 1−4 show the equilibrium curves for hydrates formed from pure hydrocarbon phase and water. Figures 5−9 show the equilibrium curves of binary mixtures of hydrocarbons. Figures 10 and 11 show the equilibrium curves of ternary mixtures of hydrocarbons. It is important in this context to keep in mind that these equilibrium calculations are based on free energies of inclusion (see eq 11) calculated from molecular dynamics simulations according to procedures due to Kvamme and Tanaka.10 As such, any perfect match with experimental data for real systems is not expected. In view of this the calculated results are in very good agreement with experimental data and more than sufficient for hydrate risk analysis of real industrial hydrocarbon systems.

content of water in the gas or liquid hydrocarbon system before water drop out is the first step of a hydrate risk analysis. In classical hydrate risk analysis this has been the water mole fraction in the hydrocarbon at water dew point. In more recent analysis2,6 an alternative route of water dropping out as adsorbed phase on a rusty pipeline (rust represented as hematite) has also been considered. Even a third route of direct hydrate formation from water dissolved in the hydrate former phase has been evaluated.2,6 While this route appears to be thermodynamically feasible in hydrate forming systems investigated in those studies, limitations in mass transport and heat transport appear to be massive. Direct hydrate formation from dissolved water is therefore highly unlikely compared to other routes that can lead to hydrate formation. The final limits of water content have to be low enough to stay in the transport gas from Kollsnes gas processing plant and all of the way to the receiving terminal at the continent. Seafloor temperatures in the North Sea rarely exceed 279 K.

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HYDRATE RISK ANALYSIS OF TROLL GAS: UPPER LIMIT OF WATER CONTENT IN THE GAS TO PREVENT HYDRATE FORMATION For a given hydrocarbon system in a process or pipeline transport system at a given pressure and temperature, the maximum I



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Figure 12. Maximum water content before liquid water drops out from the well-head fluid (Troll gas). Curves from top to bottom correspond to pressures of 5000 kPa, 9000 kPa, 13 000 kPa, 17 000 kPa, 21 000 kPa, and 25 000 kPa, respectively.

Figure 11. The top curve is the estimated equilibrium pressures for hydrate from 36.4% methane, 54.1% ethane, and 9.5% propane as compared to experimental data14 (dissociation condition). The bottom curve is the molar free energy for the hydrate (solid) and water chemical potential (dashed) as a function of temperature for the equilibrium pressures in the top curve (1 bar = 1 × 102 kPa). Figure 13. Maximum water content before the adsorption of water on hematite occurs for the well-head fluid (Troll gas). Curves from top to bottom correspond to pressures of 5000 kPa, 9000 kPa, 13 000 kPa, 17 000 kPa, 21 000 kPa, and 25 000 kPa, respectively.

Table 1. Molar Composition of Troll Gas4a well-head fluid components methane, C1 ethane, C2 propane, C3 isobutane, iC4

Separator 1

Separator 1b

Separator 1c

273.15 K and 274.15 K and 274.15 K and 274.15 K and 7000 kPa 7000 kPa 7000 kPa 7000 kPa 0.959213 0.034936 0.003115 0.002736

0.959708 0.034704 0.003024 0.002564

0.861300 0.075100 0.063600

Four experimental tests were carried out by Statoil to determine the composition of Troll gas, and the results of tests 3 and 4 are considered to be most reliable. Separator 2 was not considered because of its temperature and pressure conditions of 261.15 K and 4620 kPa, respectively. This temperature is below the typical hydrate formation temperature. However, Separator 1 conditions are 274 K and 7000 kPa which are favorable for hydrate formation, thus, we investigated the upper limit of water that could be permitted in the gas stream without the risk of hydrate formation together with that of the well-head fluid. For the well head, pipeline transport conditions were applied. Temperature and pressure values of 273.15 K and 7000 kPa conditions exactly were particularly demanded by Statoil for the Thornton Research Centre analysis.4 We are aware that transport pressures range between 5000 and 25 000 kPa; thus the analysis in this work covers this pressure range.

0.541133 0.458867

a

Only hydrate forming hydrocarbon components have been considered. bThe molar composition of components after methane is separated out of the gas stream. cThe molar composition of components after methane and ethane are separated out of the gas stream.

Our model has been applied to a real situation, the Troll gas from the North Sea.4 The compositions of the well-head fluid and that of Separator 1 of the Troll gas from the Statoil (Norway) in-flow performance test 44 have been used in this work (see Table 1). J



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be allowed during processing and transport of the gas containing the remaining three components was estimated as presented in Figures 16 and 17. A further evaluation was also done assuming all the ethane was separated out leaving only the heavier components of propane and isobutane. The estimates of the latter are shown in Figures 18 and 19. Figures 12 to 19 have illustrated the maximum amount of water that can be permitted in hydrocarbon gas streams without the risk of hydrate formation during processing and transport. As mentioned earlier, both routes were considered: the water dew-point approach, which is the conventional route currently used by the industry where free water condenses out of the gas stream, and the route where free is adsorbed on the hematite that covers the internal surface of processing equipment and transport pipelines. The investigation is based on Troll gas. All estimates show that it is more likely for free water to be made available by adsorption on hematite than the conventional dew-point route. These analyses show that there is still the risk of hydrate formation even below the upper limit of water content estimated by the usual approach (water dew point). Considering the route of adsorption on hematite in the temperature range of 274−280 K, only about 5−6% of the dewpoint approach estimated maximum water contents should be permitted in hydrocarbon gas stream during processing and pipeline transport of hydrocarbon gas streams to avoid formation of hydrate. The gas mixtures with only the heavier hydrocarbons (without methane) exhibit opposite maximum water tolerance compared to the methane dominated Troll gas stream within the pressure range investigated. The higher the pressure is, the higher the maximum amount of water that can be allowed without the risk of hydrate formation, but it is opposite for the methane-rich Troll gas. Moreover, for the gas mixture containing only the C2+, the higher the number of carbon in each component’s molecule, the higher the allowable amount of water without the risk of hydrate formation. Consequently, the maximum amount of water that can be permitted to avoid the formation of hydrate in the gas stream from separator 1 (containing just propane and isobutane) after methane and ethane are separated out is around 24−37% higher than that of the fluid at the liquid outlet of Separator 1, having ethane, propane, and isobutane within the pressure range of 5000−25 000 kPa and temperature range of 274− 280 K. Thus, the sensitivity of these C2+ on the Troll are further investigated in the following section.

Our estimates are presented in Figures 12 to 15. Table 2 has the allowable water content of the Troll gas at 274.14 and 280 K.

Figure 14. Maximum water content before liquid water drops out from Troll gas at Separator 1. Curves from top to bottom correspond to pressures of 5000 kPa, 9000 kPa, 13 000 kPa, 17 000 kPa, 21 000 kPa, and 25 000 kPa, respectively.

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Figure 15. Maximum water content before the adsorption of water on hematite occurs from Troll gas at Separator 1. Curves from top to bottom correspond to pressures of 5000 kPa, 9000 kPa, 13 000 kPa, 17 000 kPa, 21 000 kPa, and 25 000 kPa, respectively.

SENSITIVITY ANALYSIS OF CONCENTRATION OF COMPONENTS ON MAXIMUM WATER CONTENT THAT SHOULD BE PERMITTED IN TROLL GAS DURING PROCESSING AND TRANSPORT The effect of higher molar concentration of each components of the C2+ (hydrate forming higher hydrocarbons) on the maximum permitted amount of water in Troll is investigated at 274 and 280 K and within the pressure range of 5000−25 000 kPa used in this work. The results are presented in Figures 20 to 25. The Troll gas is methane-dominated gas; thus, the characteristic behavior at these conditions shows methane dominance, with permitted water content being higher at lower pressures and reducing with increasing pressures. Consequent on opposite characteristics exhibited by the C2+ as seen above, increasing the concentration of ethane to 10% results in a slight change from the characteristics of a methane-dominated gas to a C2+ dominated gas from around 17 000 to 25 000 kPa, thereby

The two routes to hydrate formation have been evaluated. It can be observed in Figures 12 to 15 that the gap (or difference) between the pressure curves decreases from between 5000 and 9000 kPa to 21 000 and 25 000 kPa. In fact, the curves for the last two higher pressures, 21 000 and 25 000 kPa to be precise, overlap. This is due to the fact that differences at the highest pressures are almost insensitive to pressures due to the high density. With assumption that all of the methane is separated out of the Troll gas stream in Separator 1, leaving the heavier hydrate forming hydrocarbon components, that is, ethane, propane, and isobutane, the compositions of the remaining components were normalized, and the maximum water concentration that could K



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Table 2. Maximum Water Content Permitted without the Risk of Hydrate Formation for Troll Gas and Pure Components of Hydrocarbons pressure (kPa) routes well-head fluid

Separator 1 fluid

liquid outlet of Separator 1 fluid (i.e., C2, C3 and C4)

C3 and iC4 (with C2 out)

dew point hematite dew point hematite dew point hematite dew point hematite dew point hematite dew point hematite dew point hematite dew point hematite

temperature (K) 273 K 280 K 274.14 K 280 K 274.14 K 280 K 274.14 K 280 K

Figure 16. Maximum water content before liquid water drops out from the gas stream after separator 1 containing 86.1% of ethane, 7.5% of propane, and 6.4% of isobutane (Troll gas). Curves from top to bottom correspond to pressures of 25 000 kPa, 21 000 kPa, 17 000 kPa, 13 000 kPa, 9000 kPa, and 5000 kPa, respectively.

5000

9000

13 000

17 000

21 000

25 000

0.001194 0.000062 0.001822 0.000102 0.001194 0.000062 0.001823 0.000102 0.000271 0.000014 0.000397 0.000022 0.000335 0.000017 0.000482 0.000027

0.000753 0.000039 0.001148 0.000065 0.000754 0.000039 0.001148 0.000065 0.000430 0.000022 0.000624 0.000035 0.000548 0.000029 0.000787 0.000044

0.000618 0.000032 0.000934 0.000052 0.000618 0.000032 0.000934 0.000052 0.000557 0.000029 0.000806 0.000045 0.000724 0.000038 0.001038 0.000058

0.000577 0.000030 0.000860 0.000048 0.000577 0.000030 0.000860 0.000048 0.000661 0.000034 0.000953 0.000054 0.000870 0.000045 0.001247 0.000070

0.000568 0.000030 0.000839 0.000047 0.000568 0.000030 0.000839 0.000047 0.000746 0.000039 0.001074 0.000060 0.000991 0.000052 0.001419 0.000080

0.000571 0.000030 0.000837 0.000047 0.000571 0.000030 0.000837 0.000047 0.000816 0.000043 0.001173 0.000066 0.001091 0.000057 0.001562 0.000088

Figure 17. Maximum water content before the adsorption of liquid water on hematite occurs from the gas stream after separator 1 containing 86.1% of ethane, 7.5% of propane, and 6.4% of isobutane (Troll gas). Curves from top to bottom correspond to pressures of 25 000 kPa, 21 000 kPa, 17 000 kPa, 13 000 kPa, 9000 kPa, and 5000 kPa, respectively.

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slightly raising the allowable water limit. A further increase of ethane concentration to 15% and 20% in the gas stream does not result in change in the pressure at which C2+ dominance commences (i.e., about 17 000 kPa). Both propane and isobutane at a 10% molar concentration show similar characteristics with ethane at approximately 17 000 kPa. That is, C2+ dominance also commences as from around 17 000 kPa with the maximum permitted amount water slightly more than that of ethane, the effect of isobutane being higher than propane. However, the increase of propane further to 15% and 20% results shifting in the pressure at which the dominance of C2+ commences from around 17 000 to 13 000 kPa. For isobutane, the impact is more as the pressure at which the change from methane dominance to C2+ dominance occurs shifts backward with increasing molar concentration. At 10%, it is around 17 000 kPa, and at 15%, it is 13 000 kPa, while it is 9000 kPa at 20%.

CONCLUSION The processing and transport of natural gas involves conditions of low temperatures and high pressures which are inside the hydrate formation region. In this work we focus on the Troll gas from the North Sea and conditions which covers the conditions of temperature and pressure representative for transport from Kollsnes gas processing plant to the continent. Locally in a pipeline temperatures and pressures are given by the fluid dynamics, and the critical question is actually how much water that can be in the gas before drop out. Classically this has been calculated by the water dew point. If the actual mole fraction of water exceeds the dew point mole fraction, locally the water will condense out, and hydrate can form from liquid water and the hydrate formers in the gas if the local temperature and pressure L



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Figure 18. Maximum water content before liquid water drops out from the gas stream after further separation, leaving only propane and isobutene with molar concentrations of 0.54 and 0.46, respectively (Troll gas). Curves from top to bottom correspond to pressures of 25 000 kPa, 21 000 kPa, 17 000 kPa, 13 000 kPa, 9000 kPa, and 5000 kPa, respectively.

Figure 20. Maximum water content before liquid water drops out of gas streams at a temperature of 274.14 K with 10% ethane, 0.31% propane, 0.27% isobutane, and the rest is methane; 10% propane, 3.5% ethane, 0.27% isobutane, and the rest is methane; 10% isobutane, 3.5% ethane, 0.31% propane, and the rest is methane; Troll gas well-head fluid (1 bar = 1 × 102 kPa).

Figure 19. Maximum water content before the adsorption of liquid water on hematite occurs from the gas stream after further separation leaving only propane and isobutane with molar concentrations of 0.54 and 0.46, respectively (Troll gas). Curves from top to bottom correspond to pressures of 25 000 kPa, 21 000 kPa, 17 000 kPa, 13 000 kPa, 9000 kPa, and 5000 kPa, respectively.

Figure 21. Maximum water content before liquid water drops out of gas streams at a temperature of 280 K with 10% ethane, 0.31% propane, 0.27% isobutane, and the rest is methane; 10% propane, 3.5% ethane, 0.27% isobutane, and the rest is methane; 10% isobutane, 3.5% ethane, 0.31% propane, and the rest is methane; Troll gas well-head fluid (1 bar = 1 × 102 kPa).

are inside the hydrate formation region for the actual hydrocarbon system. Recently also another route to liquid water drop out has been discussed in open literature. Rust consists of a variation of iron oxides, with hematite (Fe2O3) as one of the most thermodynamically stable iron oxide forms. Earlier work in open literature indicates that adsorbed water on hematite may have a chemical potential which is 3.4 kJ/mol lower than the liquid water and would condense out. In this work we therefore also investigate the maximum limits of water in the gas before water adsorption on hematite. For all components in all phases, including hydrate, we utilize residual thermodynamics. This is possible due to available chemical potentials for

ice, liquid water, and water in empty hydrate structures calculated from molecular dynamics simulations. Free energies of various guest molecules inside cavities are also evaluated from molecular dynamics simulations. Results for hydrate equilibrium curves are in good agreement with experimental data for pure hydrate formers, as well as binary and ternary mixtures. Corresponding plots of hydrate free energy and water chemical potential for the various hydrates are also plotted to illustrate the differences in thermodynamic stability. According to the first and second laws of thermodynamics, the most stable hydrates will form first from a multicomponent mixture, under constraints of mass and heat transport. As expected, there are M



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substantial changes in free energy for various hydrates formed from the experimental mixtures which we have compared with. In a follow-up study, we intend to conduct a detailed free energy analysis investigation on dynamic hydrate formation from multicomponent mixture. The purpose is to visualize the nonuniform hydrate formation aspect in real situations. Troll is the largest gas field offshore Norway. The gas is processed at Kollsnes gas processing plant. We have applied the analysis of water drop out as liquid water or as adsorbed on hematite for four different mixtures related to the Troll hydrocarbon system. Two trends are very clear. Drop out as water adsorbed on hematite dominates totally as compared to water dew-point

calculations. For the Troll well-head fluid, the tolerance of water mole-fraction in gas is roughly 20 times the similar tolerance limit if adsorption on hematite is used. The solubility of water in hydrocarbons is sensitive to the density and composition of the system. For the heavier fractions the solubility of water in the hydrocarbon increases, and the tolerance for water increases accordingly, in contrast to the light systems in which water tolerance limit decrease with increasing pressure. This is also illustrated through a sensitivity analysis. Even though the results clearly indicated that hematite dominates water drop out and is likely very important in hydrate nucleation, the low chemical potential of adsorbed water makes it impossible for N



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(11) Maekawa, T. Equilibrium conditions for gas hydrates of methane and ethane mixtures in pure water and sodium chloride solution. Geochem. J. 2001, 35, 59−66. (12) Adisasmito, S.; Frank, R. J.; Sloan, E. D. Hydrates of carbon dioxide and methane mixtures. J. Chem. Eng. Data 1991, 36, 68−71. (13) Svartas, T.; Fadnes, F. Methane hydrate equilibrium data for the methane-water-methanol system up to 500 bara. In The Proceedings of the Second International Offshore and Polar Engineering Conference, San Francisco, CA, 1992. (14) Holder, G.; Hand, J. Multiple-phase equilibria in hydrates from methane, ethane, propane and water mixtures. AIChE J. 1982, 28, 440−447. (15) Englezos, P.; Bishnoi, P. R. Experimental study on the equilibrium ethane hydrate formation conditions in aqueous electrolyte solutions. Ind. Eng. Chem. Res. 1991, 30, 1655−1659. (16) Deaton, W.; Frost, E., Jr Gas hydrate composition and equilibrium data. Oil Gas J. 1946, 45, 170−178. (17) Englezos, P.; Ngan, Y. T. Incipient equilibrium data for propane hydrate formation in aqueous solutions of sodium chloride, potassium chloride and calcium chloride. J. Chem. Eng. Data 1993, 38, 250−253. (18) Robinson, D. B.; Metha, B. R. Hydrates in the propane-carbon dioxide-water system. J. Can. Pet. Technol. 1971, 10, 33−35. (19) Kubota, H.; Shimizu, K.; Tanaka, Y.; Makita, T. Thermodynamic properties of R13 (CClF3), R23 (CHF3), R152a (C2H4F2), and propane hydrates for desalination of sea water. J. Chem. Eng. Jpn. 1984, 17, 423−429. (20) Rouher, O. S.; Barduhn, A. J. Hydrates of iso- and normal butane and their mixtures. Desalination 1969, 6, 57−73. (21) Wu, B. J.; Robinson, D. B.; Ng, H. J. Three and Four Phase Hydrate Forming Conditions in Methane-Isobutane-Water System. J. Chem. Thermodyn. 1976, 8, 461−469.

initial hydrate nuclei to attach directly to the surface of the hematite. As a minimum the formed hydrate will be bridged by 3−4 layers of structured water on the hematite surface.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bjørn Kvamme: 0000-0003-3538-5409 Notes

The authors declare no competing financial interest.

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LIST OF SYMBOLS T, Temperature P, Pressure μ, Chemical potential H, hHydrate ΔG, Free energy change P, Parent phase R, Universal gas constant Φ, Fugacity coefficeint γ, Activity coefficient x⃗, Mole fraction of liquid y,⃗ Mole fraction of gas vk, Fraction of cavity type k per water molecule h, Cavity partition function Δgikinc, Free energy of inclusion of the guest molecules i in the cavity k θik, Filling fraction of component i in cavity type k β, Inverse of gas constant times temperature xT, Total mole fraction of all guests in the hydrate

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REFERENCES

(1) Chartsbin. Total Length of Pipelines for Transportation by Country; http://chartsbin.com/view/1322 (accessed on Jan 16, 2017). (2) Kvamme, B.; Kuznetsova, T.; Bauman, J. M.; Sjöblom, S.; Kulkarni, A. A. Hydrate Formation during Transport of Natural Gas Containing Water and Impurities. J. Chem. Eng. Data 2016, 61, 936− 949. (3) Statoil. Troll; https://www.statoil.com (accessed on Dec 20, 2016). (4) Ebbrell, H. K. . The composition of Statoil (Norway) gas well, 1984. Available online: http://www.npd.no/engelsk/cwi/pbl/wellbore_ documents/127_05_31_6_6_The_Composition_of_Statoil_Gas_ Well.pdf (accessed on Dec 20, 2016). (5) Jemai, K.; Kvamme, B.; Vafaei, M. T. Theoretical studies of CO2 hydrates formation and dissociation in cold aquifers using RetrasoCodeBright simulator. WSEAS Trans. Heat Mass Transfer 2014, 9. Available online: http://hdl.handle.net/1956/9247 (accessed on Jan 13, 2017). (6) Kvamme, B.; Kuznetsova, T.; Kivelæ, P.-H.; Bauman, J. Can hydrate form in carbon dioxide from dissolved water? Phys. Chem. Chem. Phys. 2013, 15, 2063−2074. (7) Svandal, A. Modeling hydrate phase transitions using mean-field approaches. PhD dissertation for the Degree Philosophiae Doctor, University of Bergen, 2006. (8) Kvamme, B. Thermodynamic Limitations of the CO2/N2 Mixture Injected into CH4 Hydrate in the Ignik Sikumi Field Trial. J. Chem. Eng. Data 2016, 61, 1280−1295. (9) Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27, 1197−1203. (10) Kvamme, B.; Tanaka, H. Thermodynamic Stability of Hydrates for Ethane, Ethylene, and Carbon Dioxide. J. Phys. Chem. 1995, 99, 7114−7119. O


Risk of Hydrate Formation during the Processing and Transport of Troll

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