Alternative Routes to Hydrate Formation during Processing and

Article Cite This: J. Chem. Eng. Data 2018, 63, 832−844

pubs.acs.org/jced

Alternative Routes to Hydrate Formation during Processing and Transport of Natural Gas with a Significant Amount of CO2: Sleipner Gas as a Case Study Bjørn Kvamme* and Solomon Aforkoghene Aromada Department of Physics and Technology, University of Bergen, Allegaten 55, 5007 Bergen, Norway ABSTRACT: Carbon dioxide from the Sleipner gas field in the North Sea has now been injected into the Utsira Formation for more than 20 years. A million tons of carbon dioxide per year is transported and injected. Conditions of temperatures and pressures in the injection pipeline as well as inside the reservoir are outside hydrate-forming conditions. Transport pipelines, on the other hand, are subject to low temperatures and high pressures, which can potentially lead to hydrate formation. In this work, we examine some possible routes to hydrate formation and the consequences for maximum amounts of water that can be permitted to follow the gas. A conventional hydrate risk evaluation involves calculation of water dew point concentrations in the gas as an upper tolerance limit for preventing liquid water to drop out from the gas and eventually form hydrates. Pipelines are rusty even from the moment they are placed on the seafloor in the North Sea. Initially this rust consists of various forms of iron oxides. Hematite (Fe2O3) is one of the most stable of these and is used as a model for rust in this work. A second route to hydrate formation involves adsorption of water on rusty surfaces. Earlier work in the open literature indicates that the chemical potential of adsorbed water may be substantially lower than the chemical potential of liquid water at the same temperature and pressure. This opens up a path for heterogeneous hydrate nucleation toward the pipeline walls. The chemical potential of the first few adsorbed water layers (roughly 1 nm) is too low for them to form hydrates, but outside of that the liquid structure is similar to that of liquid water and can form hydrates. The estimated maximum water content that can be permitted on the basis of the water dew point was found to be on the order of 20 times higher than the amount that would be tolerated if adsorption on hematite were the tolerance criterion. This ratio is similar for the original Sleipner gas with carbon dioxide and the hydrocarbon phase after separation of the carbon dioxide. As expected, the difference is not substantial in absolute tolerance given that the carbon carbon dioxide content is less than 3.5 mol %. Another aspect is the possibility of forming more than one type of hydrate. The dominating components in the mixture are methane, ethane, and carbon dioxide, which are structure I formers. The presence of 3 mol % propane and 0.25 mol % isobutane will have a substantial impact on the dew point curve and thus also the whole phase envelope of the system. The solubility of water in condensed hydrocarbon is qualitatively different and increases with pressure, in contrast to the solubility in supercritical methane. However, the relative tolerance limits between the dew point criterion and the adsorption criterion is found to be on the same order of magnitude as for the gas mixture. The pipeline walls are typically the coldest regions of the pipeline and rarely exceed 280 K for the North Sea seafloor. Sensitivity analyses of the maximum tolerance for water as a function of propane content in methane and in carbon dioxide are also conducted and confirm the relative tolerance limits.

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INTRODUCTION Water is always produced together with hydrocarbons from the reservoir and also flows with the hydrocarbons into the processing plant for treatment. The presence of this water in natural gas mixtures during processing and transport of natural gas mixtures raises a serious concern because under highpressure and low-temperature conditions, by implication of the second law of thermodynamics (entropy), water molecules can organize to form an ice-like lattice (three-dimensional structure) with cavities (cages). Molecules of hydrocarbon gases and volatile liquids in addition to some inorganics like carbon dioxide and hydrogen sulfide, which are termed guest molecules, can be entrapped in the cavities to form nonstoichiometric crystalline compounds called clathrate hydrates © 2018 American Chemical Society

or natural gas hydrates. These hydrates can grow to plug processing equipment and/or transport pipelines. In this study, we evaluate the risk of hydrate formation based on the upper limit of water content that can be permitted in a multicomponent natural gas mixture with a substantial amount of carbon dioxide. Sleipner gas from the North Sea forms a perfect case study for this work because the natural gas from the Sleipner gas field contains a significant amount of CO2 and both structure I and structure II hydrocarbon guest molecules, which represents a practical industrial situation. Received: November 11, 2017 Accepted: January 29, 2018 Published: February 5, 2018 832

DOI: 10.1021/acs.jced.7b00983 J. Chem. Eng. Data 2018, 63, 832−844

Journal of Chemical & Engineering Data

Article

hydrate crystal nucleus from ever attaining the critical size, and thus, stable growth may not commence. Another problem that can compound the issue of hydrate growth is heat transport. The fact that methane has poor thermal conductivity relative to liquid water clusters and hydrate before hydrate is formed1 implies that there will be a challenge of transporting the exothermic heat of hydrate formation away from the system, and this could also critically restrict the hydrate formation rate. Solid surfaces will also indirectly affect hydrate formation that occurs, for instance, at the interface between the methane-rich gas and the aqueous phase adsorbed on solid wall surfaces covered with rust, as in the case of the internal walls of processing equipment and transport pipelines. This possible effect of water-wetting surfaces on the phase transitions must not be ignored merely for the reason that the gas phase will dominate as far as the mass is concerned.1 Hydrate nucleation and growth may take place either when both water and hydrate formers are adsorbed on the rusty surface or when water alone is present in the adsorbed phase and hydrate-forming species are imported from the methane-rich phase. Although hydrate formation will not occur directly on hematite surfaces because of the incompatibility between the distribution of partial charges of hydrogen and oxygen in the lattice and atom charges in the hematite surface, hematite nevertheless works as a catalyst that removes water from the bulk gas by means of an adsorption mechanism, thereby providing a separate water phase for hydrate formation, which takes place slightly outside the first two or three water layers with a thickness of around 1 nm. Thermodynamically, a third pathway for hydrate formation exists.1,2 It involves hydrates forming directly from water dissolved the natural gas stream. However, because of the low concentration of water dissolved in the bulk gas together with limitations on heat and mass transport, it is improbable for hydrates to form through this pathway. Therefore, this alternative pathway is not considered for investigation in this work. Nevertheless, if surface stress from flow does not impact the water/hydrocarbon system at all, subsequently the quick formation of a hydrate film at the water−hydrocarbon interface would take place, which would very rapidly block further transport of molecules of hydrate formers and water through the hydrate film (very low coefficient of diffusivity). Therefore, hydrates would form from the molecules of hydrate formers dissolved in water and could also form from water dissolved in the gas, which then would take advantage of nucleation on the hydrate surface. However, in the case of flow with turbulent shear forces, this is not practical. Another difference between the flowing case and the case of a stationary constant-volume, constant-mass experiment in the laboratory is that new mass is continuously supplied. Consequently, the limiting situation where the water is completely consumed, causing hydrate formation to stop, does not exist. This paper presents the application of our novel thermodynamic scheme for investigation of different routes to hydrate formation utilizing the ideal gas as the reference state for all components in all phases, including the hydrate phase. This thermodynamic scheme is used to investigate the upper limit of water content that can be tolerated in a multicomponent natural gas with a substantial amount of CO2 (using Sleipner gas as a case study) without the risk of hydrate formation during processing and transport. Two alternative pathways to hydrate formation, the traditional dew point route and that of water adsorbed on the hematite (rusty) surface of the internal

Gas processing involves several unit operations that can create thermodynamic conditions that are conducive for hydrates to form. Typical examples are compressors that increase pressure, turbines that lead to gas cooling, and lowtemperature flash tanks. In the North Sea, where the Sleipner gas field is located, oil and gas transport operations involve about 8000 km of (rusty) pipelines laid on the seafloor with a typical temperature range of 272 to 279 K and a pressure range of 5000 to about 30 000 kPa. These conditions are favorable for the formation of hydrates from the water and gas system when a free water phase exists. Even though hydrates formed in transport pipelines can be removed applying a number of technologies, the simplest possible approach is to prevent the risk of hydrate formation. This is achieved by evaluating the upper limit of water content that can be permitted in the natural gas stream during processing and transport. A very important question at this point is “what level of water concentration can be tolerated without the risk of water dropping out of the hydrocarbon system?” The process of hydrate formation in a system of natural gas with substantial admixtures of impurities, for example water and carbon dioxide as in this study, is complex and involves competing phase transition mechanisms and routes, where both kinetics and thermodynamics have a significant function. The conventional technique applied by industry to evaluate the risk of hydrate formation at present is based on the assumption that hydrates will form if water drops out of the gas stream during processing or transport. Therefore, this method involves estimating the dew point temperature of the specific natural gas mixture. We refer to this approach as the water dropout or dew point route to hydrate formation. However, there is a problem with this viewpoint: it absolutely disregards the fact that the existence of rust (hematite) on the internal walls of the pipeline and some processing equipment will make water adsorption sites available and consequently provide an alternative route for hydrate formation (the hematite route). Hematite is the most dominant and one of the most thermodynamically stable forms of rust. The problem is even more complex1 because hydrate formation from natural gas in industrial situations like pipeline transport and processing cannot successfully attain equilibrium as a result of limitations imposed by either the Gibbs phase rule or mass and heat transport limitations. The Gibbs phase rule is given as τ = n − π + 2, where τ is the number of degrees of freedom (i.e., the number of defined independent thermodynamic variables in the system), π is the number of actively coexisting phases, and n is the number of active components in terms of hydrate phase transitions. If we chose a simple scenario where only one hydrate-forming guest molecule is present in a system containing bulk gas and water, say methane and water for illustration, with the existence of a hydrate nucleus, we will have three actively coexisting phases (π = 3) and two active components (n = 2). According to the Gibbs phase rule, there should be just one degree of freedom (τ = 1) for the system to reach equilibrium. However, the system will never attain equilibrium because for a real system like the industrial case under consideration, involving a flowing stream, hydrodynamics and hydrostatics, including phase transitions, which involve heat exchange, the local pressure and temperature are specified; this implies that even for the simplest system with one guest molecule (methane), the system will not attain equilibrium. Furthermore, mass transport limitations and low concentration of water in methane could hinder the 833



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(MD) results for water in different phases (empty hydrates, liquid water, and ice).6 In equilibrium systems, both phase distributions and compositions can be evaluated by minimization of free energy, and it is not a critical issue to choose a reference state for different components in different phases for equilibrium systems, provided that thermodynamic models are available. However, in nonequilibrium systems, the most favorable phase distributions locally, together with thermodynamic preferences for each component to move across phase boundaries to other phases, can be determined by a free energy analysis, and it is convenient to use the ideal gas as the reference state in order to make sure that we have the same reference value for the free energy of every phase present in the estimation of the chemical potentials of all components irrespective of the phase, as presented in eq 1:

walls of process equipment and pipeline, are investigated using our novel approach discussed below.

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SLEIPNER GAS FROM THE NORTH SEA Natural gas from the Sleipner gas field (precisely the Sleipner Vest (West in English) gas field, from the Sleipner B installation) is very appropriate for this work. The Sleipner Vest gas field is located in the central part of the Norwegian North Sea with a water depth of approximately 110 m, but the reservoir depth is about 3450 m.3 The natural gas mixture from Sleipner Vest contains a substantial amount of propane and some isobutane, which are structure II hydrate guest molecules, and the amount of CO2 is also significant. Consequently, CO2 is removed from the produced gas during processing and injected into the Utsira Formation in the North Sea (over 16 million tons of CO2 have been stored in the Utsira Formation since 1996).4 All of these operations involve installations that include equipment for gas processing and pipelines for transport. The wellstream from Sleipner B is routed through pipelines laid mostly on the seafloor of the North Sea to Sleipner A for processing. The processed gas is transported to the market through the Gassled pipeline system (which is the largest offshore gas transmission system in the world)5 operated by the Norwegian Gassco. The daily gas export, which is put at 369 000 000 m3,5 is transported normally at high pressures ranging from 50 to about 300 bar. In addition, the temperatures to which these pipelines are exposed on the seafloor of the North Sea are low, about 272 to 279 K. These low-temperature and elevated-pressure conditions to which the transported natural gas mixtures with CO2 are exposed are within hydrate formation conditions.1 Under these conditions, there is a propensity for natural gas mixtures to form hydrates6 on the internal walls of pipelines and processing equipment during transport and processing, respectively; gas processing operations are normally performed at low temperatures and high pressures too. Table 1 presents the normalized concentrations of only the structure I and structure II hydrate-forming components in Sleipner gas.

μj (T , P , y) − μjideal gas (T , P , y) = RT ln ϕj(T , P , y) lim(ϕi) → 1

(1)

where ϕj is the fugacity coefficient for component j in a given phase, R is the universal gas constant and y is the vector of gasphase mole fractions. The chemical potential of the ideal gas comprises the trivial mixing term for mixing of ideal gases at constant pressure. For the liquid state, another reference state is used to evaluate the chemical potential of component j as an intermediate step. This is given in eq 2, generally known as symmetric excess: μj (T , P , x) − μjideal liquid (T , P , x) = RT ln γj(T , P , x) lim(γj) → 1

molar concentration

molar concentration after CO2 separation

methane (CH4) ethane (C2H6) propane (C3H8) isobutane (i-C4H10) carbon dioxide (CO2)

0.8448 0.0876 0.0304 0.0025 0.0347

0.8752 0.0907 0.0315 0.0026 −

when xj → 1 (2)

where γj is the activity coefficient for component j in the liquid mixture and x is the vector of liquid-phase mole fractions. Here as well the chemical potential of the ideal liquid includes the trivial ideal mixing term together with the pure liquid value. When eq 2 is applied to water, the ideal gas reference state can suitably be applied also when the chemical potential of pure liquid water is evaluated from molecular interaction models by means of MD simulations. In this work, we utilized data from ref 6. In the case of gas components with low solubility in water, like the hydrocarbon components under consideration here, “infinite dilution” of the gas in water is a more apt liquid reference state for the components. Therefore, the asymmetric excess formulation is appropriate. It is called asymmetric excess as a consequence of the fact that the limit of the activity coefficient for component j tends to 1 as the mole fraction xj decreases to 0, as shown in eq 3:

Table 1. Normalized Concentrations of Components in Sleipner Gas7 guest molecule

for ideal gas

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FLUID THERMODYNAMICS To successfully reach thermodynamic equilibrium, the temperatures, pressures, and chemical potentials of all coexisting phases must be the same across all phase boundaries. Despite the fact that equilibrium is not attainable, applying a quasiequilibrium method helps us to evaluate the thermodynamic benefits of different pathways of formation/dissociation of hydrate as asymptotic limits of possible stability for each given phase transition. Residual thermodynamics by application of the Soave−Redlich−Kwong (SRK) equation of state8 is used for all components in all phases, including hydrate, liquid water, and ice. This was executed by the use of molecular dynamics

μjH2O(T , P , x) − μjH2O, ∞(T , P , x) = RT ln[x jH2OγjH2O, ∞(T , P , x)]

lim(γjH2O, ∞) → 1

when xj → 0

(3)

HO μj 2

where is the chemical potential of component j in water, H O,∞ ∞ represents infinite dilution, and γj 2 is the activity coefficient of component j in the aqueous phase based on the same reference state. Estimation of values of the infinite834



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dilution chemical potentials with the ideal gas as the reference state can be achieved by means of MD simulations and use of the Gibbs−Duhem relation.2,9 The first and second laws of thermodynamics would demand that the available mass of every component and the total mass have to be distributed over all possible phases that are able to coexist under specific local pressure and temperature conditions, on the condition that thermodynamic properties of all phases can also be specified and evaluated outside of equilibrium. This evaluation will be quite uncomplicated for most of the fluid phases being considered, but the hydrate phase needs special consideration; it has been comprehensively evaluated by Kvamme and coworkers.2,10 Thus, minimization of the free energy and obtaining values for local phase distributions complying with the first and second laws of thermodynamics become equally straightforward by combining the thermodynamic formulations for fluids in eqs 1, 2, and 3 with hydrate nonequilibrium formulations from Kvamme and co-workers.2,10 A number of algorithms capable of implementing this approach are available in the open literature. Apart from the case of hydrates, the relevant pressures and temperatures will chiefly correspond to the liquid state, and the cases/situations considered here involve very low mutual solubilities and/or low concentrations. The approximation shown in eq 4 therefore should consequently prove to be satisfactorily accurate for most industrial applications where hydrate formation is a risk factor:

hij = e−β(μi

ki (kJ/mol)

⎠

small cavities −43.813648521031130 106.808557472676400 −175.329170034438500 152.610688932900800 −40.106958584295300 −63.620921270476180

Table 3. Coefficients ki in the Equation Δginc = ∑5i=0ki(Tc/T)i for the Cases of Isobutane and n-Butane Filling the Large Cavities in Structure IIa ki (kJ/mol)

HYDRATE THERMODYNAMICS The chemical potential of water in a hydrate is evaluated with the statistical mechanical model for water in a hydrate, which is a typical Langmuir-type adsorption model, used as presented by Kvamme and Tanaka.6 The Kvamme and Tanaka form, unlike that of van der Waals and Platteuw,11 considers the lattice movements and corresponding effects of different guest molecules as well as collisions between guest molecules and water that are sufficiently strong to have an effect on water motions. A rigid lattice is presumed by the van der Waals and Platteuw model, and it assumes that guest j does not affect water movements in the lattice. The Kvamme and Tanaka form is given in eq 5:6

j=1

large cavities −5.094627553540807 78.912901663868380 −320.706071041342300 −92.801071078869710 216.614508964751100 271.063786771121300

Tc in the equation is the critical temperature (Tc = 190.56 K for CH4).

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⎞

i 0 1 2 3 4 5 a

where the superscript i denotes different phases with low solubility and the subscript j refers to different components.

∑ hij⎟⎟

(6)

Table 2. Coefficients ki in the Equation Δginc = ∑5i=0ki(Tc/T)i for the Case of CH4 Inclusion in Structure II Hydratea

(4)

nguest

−Δgijinc)

where β = 1/RT and Δginc ij is the free energy of inclusion of guest molecule j in cavity i.12 The temperature dependence of inc Δginc = ∑5i=0ki(Tc/T)i, where Tc is the ij can be expressed as Δg critical temperature. Values of the coefficients ki for various guests and cavities are given in Tables 2 and 3.

μji (T , P , x) ≈ μji , ∞(T , P , x) + RT ln[xjiγji , ∞(T , P , x)]

⎛ 2 ⎜1 + RT v ln μH(H)O = μH(0,H) − ∑ i ⎜ 2 2O ⎝ i=1

H

i

isobutane

n-butane

0 1 2 3 4 5

59.299832852181710 −9.753377879788639 −23.981753808902050 −52.725437864730400 4.444622217080790 15.164119111906450

0.5181470228744305 −0.7458577910404459 −35.525356419904710 −11.943295481885760 2.143179555611181 7.239783088451416

a

Tc in the equation is the critical temperature (Tc = 407.81 K for isobutane and 425.13 K for n-butane).

At equilibrium, the chemical potential of component j in the hydrate phase (H) must be same as the chemical potential of component j in the (parent) phase from which it has been extracted.1 The chemical potentials of all of the gas components of the hydrate are estimated by employing eq 1. However, the usual equilibrium approximation that most hydrate simulators utilize assumes a free hydrate-former phase (gas, liquid, fluid) in which every component’s chemical potential is generally estimated by an equation of state and the resulting chemical potential required in eq 6 for the cavity, as shown in eq 7: 2 ⎛ ⎜1 + RT v ln − μH(0,H) ∑ i ⎜ 2O i=1 ⎝

(5)

nguest

⎞

j=1

⎠

∑ hij⎟⎟

water (T , P) + RT ln[xi ,H2Oγi ,H O(T , P , x)] = μi pure ,H O

where H denotes the hydrate phase, μH(H) is the chemical 2O potential of water in the hydrate, μH(0,H) is the chemical potential 2O of water in the empty clathrate structure, vi is the fraction of cavity type i per water molecule, hij is the canonical cavity partition function of component j in cavity type i, and nguest is the number of guest molecules in the system. The unit cell of structure I hydrate has 46 water molecules, and structure I hydrate has two small and six large cavities; consequently, vsmall cavity = 1/23 and vlarge cavity = 3/23. Equation 6 is used to evaluate the canonical partition function:

2

2

(7)

The estimation of the chemical potential of water in the empty chlatrate (hydrate) structure is implemented utilizing the model of Kvamme and Tanaka.6 This model has proven or been verified to have predictive capabilities; consequently, it makes any empirical formulations of these chemical potentials unnecessary and maybe unphysical because of the fact that the chemical potential is a fundamental thermodynamic property. We approximated the right-hand side of eq 7 as pure water for the reason that no ions are in the water, just limited amounts of 835



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dissolved gases. The consequence would be only a minor shift in the chemical potential of liquid water. For instance, at 15 000 kPa and 274 K the correction is −0.07 kJ/mol, and although it is slightly greater for 20 000 and 25 000 kPa, it is still not dramatic enough for the purpose of this study. Equation 8 has proven or been verified to be beneficial for estimating the free energy change corresponding to a hydrate phase transition, ΔgH: nH H

Δg = δ ∑ xjH(μjH − μjP ) (8)

j=1

where H refers to the hydrate phase of molecule j and P is the parent phase of molecule j. Equation 9 expresses the relation between the filling fraction, mole fraction, and cavity partition function: θij =

xijH vj(1 − x T)

=

hij 1 + ∑j hij

Figure 1. Experimental and predicted equilibrium curves for isobutane. The solid line shows estimated results, and asterisks (*) are experimental values from ref 26.

(9)

where xT is the total mole fraction of all guests in the hydrate, θij is the filling fraction of component j in cavity type i, and xHij is the mole fraction of component j in cavity type i.

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VALIDATION OF THEORETICAL MODEL We do not have the intention to tune the empirical model parameters since the priority is to keep the statistical mechanical model6 free of adjustable parameters in all terms, in addition to the empty hydrate chemical potentials and the chemical potentials for ice and liquid water. Consequently, a reasonable qualitative agreement is quite acceptable for the purpose of this project. We have applied our new approach and compared the results with those obtained using the classical technique employed by the industry to investigate the maximum concentration of water that can be permitted to prevent the risk of hydrate formation when both structure I and structure II hydrate hydrocarbon guest molecules with carbon dioxide are present during processing and transport of natural gas. This has not been investigated previously. Natural gas from several gas fields contains in addition to methane other components such as ethane, propane, and isobutane and sometimes significant amounts of CO2, as in the case of gas from the Sleipner gas field in the North Sea, which is being investigated in this study. Experimental data for hydrate equilibria involving multicomponent hydrocarbon gas mixtures with CO2 as one of the components, especially for several temperature−pressure data points at constant concentration, are not common in the literature. In 1992, Adisasmito and Sloan13 stated that there were no previous data for binary mixtures containing carbon dioxide and either ethane or isobutane in the literature. Thus, the estimates of hydrate equilibrium pressures for both multicomponent and binary mixtures together with that of pure CO2 from our theoretical model have been compared mainly with experimental data from only Adisasmito and Sloan13 and Adisasmito et al.,14 as presented in Figures 1 to 7. However, in Figure 3 our estimates are compared with several experimental data sets.14−20 Our model has been validated for both structure I and structure II hydrate-forming hydrocarbon components (methane, ethane, propane, and isobutane) together with their binary and ternary mixtures.21 It is pertinent to understand that when comparing results from our model and experimental data, the estimation of the

Figure 2. Experimental and predicted equilibrium curves for three different hydrocarbon systems, two of which contain CO2. The order of mole fractions (given in parentheses for each system) is CH4, C2H6, C3H8, i-C4, n-C4, CO2. For the first system (A), asterisks (*) are experimental values,13 and the solid curve shows the predicted values. The composition of this system is (0.7662, 0.1199, 0.0691, 0.0182, 0.0266, 0). For the second system (B), plus signs (+) are experimental values, and the dashed line shows the predicted values. The composition of this system is (0.5255, 0.0812, 0.0474, 0.0319, 0.0188, 0.314) . For the third system, circles (○) are experimental values, and the dot-dashed line shows the predicted values. The composition of this system is (0.2442, 0.0399, 0.0307, 0.0075, 0.0092, 0.6685).

free energy of inclusions was done using MD simulations, and we did not tune the model as explained above. In addition, it is imperative to recall that the formation of more than one hydrate having distinct properties (compositions, densities, and free energies) does result from multicomponent gas mixtures. The first and second laws of thermodynamics dictate that hydrate formation commences first with the most stable hydrate, and the formation of a variety of hydrate compositions will subsequently occur. This minimum-free-energy direction is 836



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Figure 3. Estimated equilibrium pressures for pure CO2 compared to experimental data.14−20

Figure 6. Equilibrium curves for the initial 65% propane/35% CO2 system.13 The dot-dashed curves are for hydrates from the resulting gas and liquid mixtures after phase separation at a temperature of 278.5 K. The upper dot-dashed curve is for a resulting phase consisting of 38.87% propane and 61.13% CO2, while the lower one is for 86.02% propane and 13.98% CO2. The solid curve is the initial composition showing the change in pressure during the crossing into the two phase region at 278.50 K. It should be noted that the propane-rich fraction also splits into a gas/liquid fraction at slightly higher temperature than the initial mixture. After the phase split, the most stable hydrate phase almost coincides with the structure I estimates for the propane-rich system (lower dashed curve). Structure I estimates are illustrated using dashed curves assuming no propane entering structure I. The upper dashed curve is for the 38.87% propane/61.13% CO2 mixture, and the lower one is for the 86.02% propane/13.98% CO2 mixture. Asterisks (*) are experimental data.

Figure 4. Estimated equilibrium pressures for a gas mixture containing 86% methane and 14% CO2 compared to experimental data.14

Figure 7. Estimated equilibrium pressures for a gas mixture containing 79.3% isobutane and 20.7% CO2 compared to experimental data.13

of course constrained by access to mass (hydrate formers and water) and sufficient heat transport capacities. For hydrates forming at a gas−water interface, heat transport is very fast through liquid water, typically 2−3 orders of magnitude faster than mass transport (diffusion) through liquid water.22 Hydrate formation from dissolved hydrate formers is therefore typically kinetically constrained by mass transport. Hydrate formation from water dissolved in gas is thermodynamically possible and

Figure 5. Estimated equilibrium pressures for a gas mixture containing 80% ethane and 20% CO2 compared to experimental data.13

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feasible for water in CO22 but not feasible in terms of access to water from a very dilute solution in CO2. Getting rid of the heat of hydrate formation through the surrounding CO2 gas or liquid is an additional limiting constraint. Condensation of water from CO2 on an initial hydrate layer formed at the water−CO2 interface is feasible and likely. This formation is possible down to a water concentration in CO2 at which the chemical potential for water in CO2 equals the hydrate water chemical potential. While the thermodynamic aspects of hydrate formation are governed by the combined first and second laws of thermodynamics and heat transport (and associated enthalpy change for the phase transition), the access to mass is a more complex issue. Obviously the formation of hydrate at a gas−water interface is being supplied with guest molecules available on the water surface and at an associated supersaturated water interface. These concentrations are not the same as the “bulk” gas concentration, and in a nonequilibrium situation the chemical potential of the “bulk” gas is different from that of adsorbed gas molecules. The reader is referred to the paper by Kvamme23 for an example of selective adsorption of CO2 on water from a CO2/N2 mixture. For a multicomponent natural gas mixture like Sleipner gas, hydrate formation will commence with structure II hydrate guest molecules (propane and isobutane) first, and then the hydrate structure I guest molecules will finally form hydrate. Therefore, it is only structure II hydrate that forms in the case presented in Figure 1, but it is more probable that the hydrate formed at the end for the cases presented in Figures 2, 6, and 7 will be a combination of hydrates from both structures I and II having varying compositions of the initial guest molecules from the gas or liquid. Only structure I hydrate can result from Figures 3, 4, and 5. For our system under consideration, both propane and isobutane would occupy the large cavities of structure II, whereas because of their small size, methane molecules would fill mainly the small cavities of structure I, while ethane and CO2 would be entrapped in the large cavities of structure I. Since in structure II the ratio of small to large cavities is high, various hydrate compositions of both structures I and II can result. Phase field theory (PFT) is a feasible scheme for analyzing the coupling of phase transition thermodynamics to the mass- and heat-transport dynamics in a nonequilibrium system.24,25 PFT simulations are time-consuming, but coupled with MD simulations for thermodynamics, interface characteristics, and transport properties, PFT is a very powerful concept for evaluation of nonequilibrium systems with competing phase transitions. For practical purposes and for schemes that can more readily be implemented as extensions of current industrial hydrate risk evaluation software, the use of residual thermodynamics for all components in all phases, including hydrate phase,6 makes it very transparent for comparing free energies of various phases, including various hydrate phases. In comparisons of experimental data with predictions, it is important to stress that the model parameters involved in the water chemical potential are based on interaction parameters for molecules and well-established mixing rules. Thus, we do not expect a perfect match with experimental data. Anyone wanting to use the computational schemes described here may use their own software and tune the Langmuir constants or associated interaction parameters involved in the evaluation of the Langmuir constants. Some schemes are based on differences in chemical potential of water between liquid water (or ice) and empty hydrate water for a given structure. It is not recommended that these parameters be treated as

adjustable parameters since these are fundamental properties of water. Frequently enthalpy differences between liquid water (or ice) and empty clathrates are also tuned. Since there is a fundamental relationship between the enthalpy and the partial derivative of μ/T with respect to temperature, caution also has to be taken in order to avoid thermodynamic inconsistencies. We are of course not arguing that other groups should use our models6 for empty clathrate water chemical potentials and chemical potential for water as liquid or ice. Even small computers and various free MD codes make it easy for anyone to calculate their own values for this. In Figure 2 we compare experimental values and theoretical estimates for three structure II systems. These are denoted as systems A, B, and C in ref 13. As mentioned above, we do not expect a perfect match, and as can be seen from Figure 2, there are deviations of significance for the lower-temperature regions, except for the system without CO2, which is in fairly good agreement. Nevertheless, the agreement is fair enough for qualitative analysis of various routes that can lead to hydrate formation. All three systems show a small jump in hydrate stability pressure between 278 and 279 K. We have not analyzed this jump in detail since it is not very critical for the qualitative analysis in this work. It could be due to changes in partial molar densities of the various components of the gas mixtures (which enter ideal gas chemical potential calculations) or changes in the estimated fugacity coefficients for the components (which enter the residual chemical potential). The propane/CO2 system examined by Adisimoto and Sloan13 appears to be more complex in terms of phase transitions. We have examined this system using various equations of state and in-house software as well as commercial software. In all of these studies, this system undergoes phase transitions for some of the higher temperatures. Therefore, it might be worthwhile to experimentally re-examine this system. Interestingly enough, the predicted equilibrium pressures are in perfect accordance with the gas phase for regions of conditions (pressure and temperature) before the phase split, and hydrate formed from the condensed liquid and water after the phase split. See the caption of Figure 6 for more details.

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RESULTS AND DISCUSSION Alternative Approaches for Evaluating the Risk of Hydrate Formation for Sleipner Gas from the Reservoir. The initial step in hydrate risk analysis for a particular gas mixture containing hydrate-forming hydrocarbon components (in this work, both structure I and II components) and inorganics (CO2 in this study) during processing or pipeline transport at a certain pressure and temperature is to evaluate the upper limit of water content that can be tolerated in the gas or liquid system before water can condense out. The classical approach for hydrate risk analysis has been based on the mole fraction of water in the gas or liquid at the water dew point. Two other alternative pathways have been considered in more recent analyses.1,2 The first of these alternative pathways involves water condensing out as an adsorbed phase on the rusty (denoted as hematite) internal walls of the pipeline. The other alternative route to hydrate formation involves hydrate forming directly from water dissolved in the hydrate-former phase. Despite the fact that this latter alternative to the classical route seems to be feasible thermodynamically in the hydrateforming systems examined in those studies,1,2 both mass transport and heat transport pose a huge limitation. Thus, the route where hydrate forms directly from dissolved water is 838



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extremely improbable compared with both the classical (dew point) water dropout approach and the alternative approach involving adsorption of water on hematite (rusty) surfaces. Therefore, our investigation in this study does not include the third alternative but only considers the classical dew point approach and that of water adsorbed on the hematite surface. The final limits of water content have to be sufficiently low to stay in the natural gas being transported from Sleipner A through the Gassled pipeline system to the receiving terminals on the continent. The final water content in the CO2 transported from the Sleipner T facility for storage in the Utsira Formation in the North Sea also has to be necessarily low. In the North Sea, the seafloor temperature typically ranges from 272 to 279 K, and the operating pressure also ranges from around 5000 to about 25 000 kPa. Hence, our investigation is confined to these temperature and pressure ranges. Our novel thermodynamic scheme for investigation of different routes to hydrate formation using the ideal gas as the reference state for all of the components in all phases, including hydrate phase, has been applied to investigate the maximum limit of water content that can be permitted in Sleipner gas from the North Sea. The composition of Sleipner gas is presented in Table 1. Figures 8

Figure 9. Maximum concentration of water that can be permitted in Sleipner gas (with CO2) before water is adsorbed on hematite.

Figure 10. Maximum concentration of water that can be permitted in Sleipner gas (without CO2) before liquid water drops out.

Figure 8. Maximum concentration of water that can be permitted in Sleipner gas (with CO2) before liquid water drops out.

structure I hydrate guest molecules, methane and CO2, the safe limit of water content decreases as the pressure increases. This is same for the Sleipner gas investigated because it is methane (or structure I hydrate)-dominated. However, the presence of the heavier structure II hydrate guest molecules, propane and isobutane, makes the maximum mole fraction of water that can be tolerated in the Sleipner gas stream relatively insensitive to an increase in pressure from 13 000 to 25 000 kPa, unlike the case of the pure components methane and CO2. As presented in Figures 16 to 19, the heavier hydrocarbons, pure propane and pure isobutane, also exhibit opposite trends because of the high-density nonpolar phase at high pressures. Generally, for both routes to hydrate formation there is a significant reduction in the gap/difference between the pressure curves between 5000 and 9000 kPa and between 9000 and 13 000 kPa. However, the curves for particularly the last two higher pressures, 21 000 and 25 000 kPa (to be precise), for methane overlap, and for CO2 the last three higher-pressure

to 11 qualitatively illustrate the safe limits of water content for Sleipner gas before and after CO2 is separated out of the bulk, with both the classical dew point liquid water dropout approach and the alternative route that involves adsorption of water on the surfaces of the internal walls of process equipment and transport pipelines covered with rust (hematite). There is almost no differencein fact, the difference between the upper limits of water content for the Sleipner gas with CO2 and that without CO2 is less than 0.1%. This is true because in both cases the system is methane-dominated, the CO2 molar concentration is only approximately 0.035, and both methane and CO2 exhibit similar trends at all pressures investigated, as can be seen in Figures 12 to 15. There is only a very insignificant shift in the absolute values of the water dropout mole fractions, with methane having very slightly higher values compared with CO2. In the case of the pure components of 839



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Figure 11. Maximum concentration of water that can be permitted in Sleipner gas (without CO2) before water is adsorbed on hematite.

Figure 13. Maximum concentration of water that can be permitted in pure methane before adsorption of water on hematite occurs.

Figure 14. Maximum concentration of water that can be permitted in pure CO2 before liquid water drops out.

Figure 12. Maximum concentration of water that can be permitted in pure methane before liquid water drops out.

adsorbed on hematite is over 18 times lower than the value of the water mole fraction with the classical dew point approach that is currently applied by the industry. This explains why hydrates may still form in industrial processes if only the dew point approach is used as a measure to operate safe from hydrate formation. Therefore, the alternative route to hydrate formation involving adsorption of water on rusty surfaces (making a free water phase available for hydrate nucleation) cannot be ignored if the risk of hydrate formation without addition of inhibitors or applying other costly measures during processing and pipeline transport of natural gas from the North Sea may be avoided. On the other hand, it is not possible for initial hydrate nuclei to attach directly to the surface of the rust (hematite) because of the low chemical potential of adsorbed water. The hydrate formed will be bridged (as a minimum) by three to four layers of structured water on the surface of the hematite. This alternative route to hydrate formation through adsorption on hematite absolutely dominates in examining the risk of water dropping out from the gas mixtures (and pure

curves almost completely overlap, which indicates higher density impact with CO2. In Figures 8 to 12, almost all of the last four higher-pressure curves (13 000 to 25 000 kPa) overlap. The reason for this is that the differences at the higher pressures are almost insensitive to pressure as a consequence of the high-density nonpolar phase of especially the higher hydrocarbons at the high pressures already mentioned above. Comparing Figures 8 to 11 with Figures 12 to 15 reveals the impact of the densities of the heavier hydrocarbons at higher pressures. The presence of the heavier hydrocarbons also results in a slight shift in the absolute values of the upper limit of the allowable mole fractions of water even at 5000 and 9000 kPa. In the subsequent sections, sensitivity analysis of the mole fractions of water that can be permitted at varying concentrations of the higher hydrocarbons propane and isobutane (structure II guest molecules) are investigated. For the two routes investigated with the Sleipner gas system, the safe limit of water mole fraction with the route of water 840



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Figure 15. Maximum concentration of water that can be permitted in pure CO2 before adsorption of water on hematite occurs.

Figure 17. Maximum concentration of water that can be permitted in pure propane before adsorption of water on hematite occurs.

Figure 16. Maximum concentration of water that can be permitted in pure propane before liquid water drops out.

Figure 18. Maximum concentration of water that can be permitted in pure isobutane before liquid water drops out.

components investigated) to form a separate water phase and ultimately result in hydrate formation. This can be understood from the fact that the average chemical potential of the water adsorbed on hematite (rusty surfaces) could be about 3.4 kJ/ mol less than the chemical potential of liquid water and thermodynamics favors lower chemical potential. Impact of Varying Concentration of Propane on the Maximum Water Content without the Risk of Hydrate Formation for Methane/Propane and Carbon Dioxide/ Propane Binary Gas Mixtures. The maximum mole fractions of water that can be permitted at various concentrations of propane (structure II guest molecules) in methane/propane and CO2/propane binary mixtures have been investigated for pressures of 5000, 9000, and 13 000 kPa, as presented in Figures 20 to 25. These pressures were chosen because of the high-density nonpolar phase at higher pressures and the presence of propane (a heavier hydrocarbon), which makes the mole fraction of water insensitive to increases in pressure as

discussed in the previous section. The analysis was performed for temperatures of 274, 278, and 280 K at each pressure and for both the classical dew point approach and the route of adsorbed water on hematite surface. At 5000 kPa, the trends show a decline in the permitted maximum water content with increasing concentration of propane for both binary mixtures at all of the temperatures investigated. This is a result of the highdensity nonpolar phase at high pressures, which makes propane exhibit the opposite trend compared with methane and CO2, as discussed in the previous section and as can be seen by comparing Figures 16 and 17 with Figures 12 and 13. Thus, as the mole fraction of propane increases, because of the opposite trend compared with methane and CO2, it is expected that the nonpolar heavy hydrocarbon will act to draw down the upper limit of water content that can be tolerated in the gas mixture until it totally dominates or dictates the trend. 841



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Figure 19. Maximum concentration of water that can be permitted in pure isobutane before adsorption of water on hematite occurs.

Figure 21. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before water is adsorbed on hematite at 5000 kPa.

Figure 20. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before liquid water drops out at 5000 kPa.

Figure 22. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before liquid water drops out at 9000 kPa.

The difference between the trends for both binary mixtures in absolute values of permitted maximum mole fraction of water also widens with increasing concentration of propane and with increasing temperature. However, higher pressures of 9000 and 13 000 kPa exhibit quite different trends even though there is a reduction in safe limits of water mole fraction with an increase in the concentration of propane. For 9000 kPa, the curves almost flatten from a propane molar concentration of 0.35, where the impact of propane tends to dominate and the gap between the curves starts to close up. This starts from a propane molar concentration of 0.25 for the 13 000 kPa scenario (see Figures 20 to 25). The differences in maximum water content between the mixtures are higher with the classical dew point route analysis compared with the alternative route of absorbed water on hematite (rust). The maximum water

content that can be tolerated from the classical dew point liquid water dropout approach for these binary gas mixtures is over 17 times higher than that of the route of absorbed water on hematite.

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CONCLUSION Alternative approaches for examining the risk of hydrate formation based on the maximum mole fraction of water that can be tolerated in a natural gas stream have been investigated using Sleipner gas from the North Sea of Norway as a case study. We have applied a novel Sleipner gas comprising both structure I and structure II hydrate formers and a significant amount of carbon dioxide. About 1 million metric tons of CO2 is separated out at the Sleipner T facility and injected into the Utsira Formation annually. The thermodynamic conditions of 842



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Figure 23. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before water is adsorbed on hematite at 9000 kPa.

Figure 25. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before water is adsorbed on hematite at 13 000 kPa.

mixture of iron oxides and in this study was modeled as hematite (Fe2O3), which is one of the most thermodynamically stable forms of rust. These rusty surfaces provide water adsorption sites that can also lead to hydrate formation. However, hydrate formation cannot occur directly on the surfaces covered by hematite because the distribution of partial charges of hydrogen and oxygen in the lattice are incompatible with the atom charges in the rusty (hematite) surface. The chemical potential of the first few adsorbed water layers (about 1 nm) is too low for hydrates to form, but outside of that the liquid structure is similar to that of liquid water and can form hydrates. The rusty surfaces work as a catalyst that helps take water out of the gas stream via the mechanism of adsorption, and hydrate formation can ensue slightly outside of the first few layers of water with a thickness of roughly 1 nm. Estimates in this work indicate that it is more probable for free water to be made available for hydrate formation through the alternative route involving adsorption on hematite than the classical dew point route currently used by the industry. The safe limit of water mole fraction with the classical dew point method is over 18 to 19 times higher than the values estimated using the alternative approach of adsorption water onto hematite. This is the case because the average chemical potential of the water adsorbed on hematite could be around 3.4 kJ/mol more negative than the chemical potential of liquid water and thermodynamic processes strive toward minimum free energy. Therefore, hydrate nucleation and growth could still occur in industrial processes if only the dew point approach is used as a measure for operation safe from hydrate formation. Sensitivity analysis of the maximum tolerance for water as a function of concentration of propane in methane/propane and carbon dioxide/propane binary gas mixtures was also conducted and also confirmed the relative tolerance limits. The typical trend exhibited by methane, methane-dominated Sleipner gas, and carbon dioxide is decline in the upper limit of water with increasing pressure. The heavier hydrocarbons (ethane, propane, and isobutane) exhibit the opposite trend compared with CH4 and CH4-dominated gas mixtures, where the permitted maximum water content increases with

Figure 24. Maximum concentration of water that can be permitted in methane/propane and CO2/propane binary gas mixtures before liquid water drops out at 13 000 kPa.

temperature and pressure in the injection pipeline and inside the reservoir are not inside the range of hydrate stability conditions. However, the natural gas transport pipelines are exposed to the low temperatures of the seafloor, and operations are performed at high pressures. Processing operations also involve low temperatures and elevated pressures. Therefore, a possible risk of hydrate formation exists. The typical technique the industry currently applies to examine the risk of hydrate formation is based on estimation of the water dew point concentration for the gas in question as a maximum allowable limit of water content to avoid the risk of liquid water condensing out from the gas and subsequently resulting in hydrate formation. Evaluation totally based on this approach absolutely disregards other possible alternative routes to hydrate formation. An alternative route to hydrate formation involves adsorption of water from the gas stream onto rusty surfaces. Transport pipelines are rusty before they are mounted together and laid on the seafloor in the North Sea. Rust is a 843



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(6) Kvamme, B.; Tanaka, H. Thermodynamic stability of hydrates for ethane, ethylene, and carbon dioxide. J. Phys. Chem. 1995, 99, 7114− 7119. (7) Johansen, G. R. Optimization of offshore natural gas field development. Master’s Thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, 2010. https://daim.idi. ntnu.no/masteroppgaver/006/6256/masteroppgave.pdf. (8) Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27, 1197−1203. (9) Kvamme, B.; Kuznetsova, T.; Jensen, B.; Stensholt, S.; Bauman, J.; Sjøblom, S.; Lervik, K. N. Consequences of CO2 solubility for hydrate formation from carbon dioxide containing water and other impurities. Phys. Chem. Chem. Phys. 2014, 16, 8623−8638. (10) Kvamme, B.; Qasim, M.; Baig, K.; Kivelä, P. H.; Bauman, J. Hydrate phase transition kinetics from Phase Field Theory with implicit hydrodynamics and heat transport. Int. J. Greenhouse Gas Control 2014, 29, 263−278. (11) van der Waals, J. H.; Platteuw, J. C. Clathrate Solutions; Interscience Publishers: New York, 1959; Vol. 2. (12) Sloan, E. D. Fundamental principles and applications of natural gas hydrates. Nature 2003, 426, 353−363. (13) Adisasmito, S.; Sloan, E. D., Jr. Hydrates or hydrocarbon gases containing carbon dioxide. J. Chem. Eng. Data 1992, 37 (3), 343−349. (14) Adisasmito, S.; Frank, R. J., III; Sloan, E. D., Jr. Hydrates of carbon dioxide and methane mixtures. J. Chem. Eng. Data 1991, 36 (1), 68−71. (15) Robinson, D.; Metha, B. Hydrates in the propanecarbon dioxide−water system. J. Can. Pet. Technol. 1971, DOI: 10.2118/7101-04. (16) Larson, S. D.. Phase studies of the two component carbon dioxide−water system involving the carbon dioxide hydrate. Doctoral Dissertation, University of Illinois, Urbana, IL, 1955. (17) Deaton, W. M.; Frost, E. M., Jr. Gas Hydrates and Their Relation to the Operation of Natural Gas Pipelines; Report No. BM-Mon-8; Bureau of Mines, Helium Research Center: Amarillo, TX, 1946. (18) Unruh, C. H.; Katz, D. L. Gas hydrates or carbon dioxidemethane mixtures. JPT, J. Pet. Technol. 1949, 1 (04), 83−86. (19) Vlahakis, J.; Chen, H.; Suwandi, M.; Barduhn, A. The growth rate of ice crystals: Properties of carbon dioxide hydrate, a review of properties of 51 gas hydrates. Syracuse Univ. Res. Dev. Rep. 1972, 830, 56−86. (20) Ohgaki, K.; Makihara, Y.; Takano, K. Formation of CO2 hydrate in pure and sea waters. J. Chem. Eng. Jpn. 1993, 26 (5), 558−564. (21) Kvamme, B.; Aromada, S. A. Risk of Hydrate Formation during the Processing and Transport of Troll Gas from the North Sea. J. Chem. Eng. Data 2017, 62 (7), 2163−2177. (22) Svandal, A. Modeling hydrate phase transitions using mean-field approaches. Ph.D. Dissertation, University of Bergen, Bergen, Norway, 2006. (23) 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 (3), 1280−1295. (24) Kvamme, B.; Graue, A.; Aspenes, E.; Kuznetsova, T.; Gránásy, L.; Tóth, G.; Pusztai, T.; Tegze, G. Kinetics of solid hydrate formation by carbon dioxide: Phase field theory of hydrate nucleation and magnetic resonance imaging. Phys. Chem. Chem. Phys. 2004, 6 (9), 2327−2334. (25) Tegze, G.; Gránásy, L.; Kvamme, B. Theoretical modeling of the conversion of methane hydrate into carbon dioxide hydrate. Phys. Chem. Chem. Phys. 2007, 9, 3104. (26) Rouher, O. S.; Barduhn, A. J. Hydrates of iso- and normal butane and their mixtures. Desalination 1969, 6, 57−73.

increasing pressure. This manifestation can be explained as a result of the high-density nonpolar phase at the high pressures for the C2+ compounds. The nonpolar heavier hydrocarbons (especially of structure II hydrate formers) will act to draw down the maximum concentration of water that can be tolerated in the gas mixture to a point where they completely dominate or dictate the trends. The safe limit of water to prevent the risk of hydrate formation during processing and pipeline transport of CO2 is only very slightly less than that for CH4 if operations are carried out at hydrate formation conditions of temperature and pressure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bjørn Kvamme: 0000-0003-3538-5409 Solomon Aforkoghene Aromada: 0000-0002-9054-4604 Notes

The authors declare no competing financial interest.

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NOMENCLATURE C2+ – higher hydrocarbons (ethane, propane, and isobutane) T – temperature Tc – critical temperature P – pressure of parent phase μ – chemical potential H – hydrate ΔG – free energy change R – universal gas constant ϕ – fugacity coefficeint γ – activity coefficient x – vector of liquid-phase mole fractions y – vector of gas-phase mole fractions h ij – canonical cavity partition function of component j in cavity type i Δginc ij – free energy of inclusion of guest molecule j in cavity type i θij – filling fraction of component j in cavity type i β – reciprocal of gas constant times temperature xT – total mole fraction of all guests in the hydrate τ – number of defined independent thermodynamic variables for the system n – number of active components in terms of hydrate phase transitions π – number of actively coexisting phases

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REFERENCES

(1) 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. (2) 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. (3) http://www.norskpetroleum.no/en/facts/field/sleipner-vest/ (accessed May 4, 2017). (4) https://www.statoil.com/en/what-we-do/norwegian-continentalshelf-platforms/sleipner.html (accessed May 7, 2017). (5) http://njordgasinfra.no/gassled/ (accessed May 12, 2017). 844


Alternative Routes to Hydrate Formation during Processing and

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