S Content on Thermodynamic Stability of Hydrate Formed from CO

Article pubs.acs.org/jced

Effect of H2S Content on Thermodynamic Stability of Hydrate Formed from CO2/N2 Mixtures Bjørn Kvamme,* Eirik Iden, Jørgen Tveit, Veronica Veland, Mojdeh Zarifi, and Khadijeh Qorbani Department of Physics and Technology, University of Bergen, Allegaten 55, 5007 Bergen Norway ABSTRACT: Huge resources of energy in the form of natural gas hydrates are widely distributed worldwide in permafrost sediments as well as in offshore sediments. A novel technology for combined production of these resources and safe long-term storage of carbon dioxide is based on the injection of carbon dioxide injection into in situ methane hydrate-filled sediments. This will lead to an exchange of the in situ methane hydrate over to carbon dioxide-dominated hydrate and a simultaneous release of methane gas. Recent theoretical and experimental results indicate that the conversion from natural gas hydrate to carbon dioxide hydrate and mixed carbon dioxide/methane hydrate follows two primary mechanisms. Direct solid state transformation is possible, but very slow. The dominating mechanism involves formation of a new hydrate from injected carbon dioxide and associated dissociation of the in situ natural gas hydrate by the released heat. Nitrogen is frequently added in order to increase gas permeability and to reduce blocking due to new hydrate formation, and will as such also reduce the relative impact of the fast mechanism on the conversion rates. In addition to carbon dioxide also other sour gases, such as hydrogen sulfide, may follow the carbon dioxide from the sour gas removal process. Hydrogen sulfide is a very aggressive hydrate former. It is abundant in various amounts in thermogenic hydrocarbon systems. In this work we investigate the sensitivity of possible additions of hydrogen sulfide in carbon dioxide/nitrogen mixtures, and how the ability to form new hydrate changes with the additions of hydrogen sulfide. This analysis is applied to four case studies: (1) Bjørnøya gas hydrate basin, (2) the Nankai field in Japan, (3) the Hikurangi Margin in New Zealand, and (4) a gas hydrate basin in South-West Taiwan. The hydrate saturations found in these fields vary over a range from 25−80%. Pressures range from 4−22.6 MPa and temperatures from 275.15−292.77 K. For all these ranges of conditions, even 1% H2S will substantially increase the ability to form new hydrate from an injected CO2/N2 mixture containing H2S. Except for the most shallow of the reservoirs (Bjørnøya) 1% H2S results in formation of a new hydrate for all concentrations of CO2 in N2 above 1%. Implementation of results from this work into a reservoir simulator is a natural follow-up which can shed light on the macroscopic consequences in term of possible local blocking of the flow due to content of H2S. The mass transport, mass balances, and energy balances in a reservoir simulator are also needed for a more detailed evaluation on how the content of H2S and CO2 changes over time and location in the reservoir due to various processes in addition to hydrate formation. H2S and CO2 dissolves significantly in pore water, and also adsorbs well on various sediment minerals.

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INTRODUCTION Injection of carbon dioxide into sediments containing methane hydrates will lead to conversion of in situ methane hydrate over to CO2 hydrate1−3 and mixed CO2/CH4 hydrate.4−6 This concept of simultaneous long-term CO2 storage with the associated release of methane for new energy production is a win−win situation. Two primary mechanisms for this conversion have been discussed in the open literature.4,5,7,8 Various laboratories have utilized NMR9 in experiments for monitoring the hydrate exchange processes. Reported conclusions9 indicate that the conversion follows a solid state exchange mechanism. Slow mass transport through hydrate is the main kinetic limitation involved in this mechanism. Formation of a new CO2 hydrate from injected CO2 and free water in the pores4,5 is a second mechanism. The heat released from forming CO2 hydrate will then contribute to dissociation of the in situ methane hydrate. Since CO2 is a thermal insulator as compared to liquid water and hydrate, the heat released from © 2017 American Chemical Society

the new hydrate formation will essentially be transported through the water toward the in situ CH4 hydrate. Mixing N2 into the CO2 reduces the thermodynamic driving force for the formation of a new hydrate from injection gas and free water in the pores. The filling of large cavities in structure I hydrate will be dominated by CO2 while some N2 will enter the small cavity. Gas permeability increases proportionally to the N2/CO2 ratio, and this is one reason for adding N2. Formation of new hydrate from free pore water and injection gas reduces proportionally to the increasing N2/CO2 ratio. A high N2/CO2 ratio will therefore also reduce blocking of gas flow paths through the reservoir due to the new hydrate formation. Because of the combined first and second laws of thermodynamics the most stable hydrates will form first. One Received: January 10, 2017 Accepted: April 3, 2017 Published: April 7, 2017 1645

DOI: 10.1021/acs.jced.7b00027 J. Chem. Eng. Data 2017, 62, 1645−1658

Journal of Chemical & Engineering Data

Article

equilibrium curves for the same fluid mixtures without H2S. It is therefore expected that also formation of a new hydrate from an injection gas of CO2 and N2 will be significantly affected by H2S following the CO2 from sour gas removal processes. The question is how much H2S is needed in order to create new hydrate from CO2/N2 mixtures that may contain as much as 80% by volume N2. The H2S molecule can exist in both small and large cavities, which means that it can enter both structures I and II hydrates. H2S is a polar molecule with a dipole moment of 0.97 D at 25 °C, which means that the S atom is more electronegative than the hydrogen atoms. The water dipole moment is 1.84 D at 25 °C, and the average negative charge on oxygen is correspondingly larger than the negative charge on sulfur in H2S. The center of mass in H2S is dominated by the heavy sulfur as compared to the associated hydrogens. When H2S rotates in hydrate cavities, the positive hydrogen atoms will be exposed toward the average negatively charged cavity walls (Kvamme and Førrisdahl9), as illustrated by Figure 1 above. The corresponding average

result of this is that CO2 will gradually be extracted from the gas phase and form CO2 in structure I hydrate. CO2 is superior to both CH4 and N2 in stabilization of the large cavity. Some CO2 might enter the small cavity, but the thermodynamic benefit is very small and negligible in comparison to available CH4 and N2. There are at least two routes that can lead to heterogeneous nucleation of a CO2-dominated hydrate. Adsorption of CO2 on mineral surfaces and/or in structured water adsorbed on mineral surfaces is one possibility, but the most commonly considered is CO2 hydrate formation on water/CO2 interfaces. The thermodynamic driving force for this hydrate formation is the free energy benefit for water and CO2 to enter into a hydrate structure rather than remaining in their original phases. Adding N2 to CO2 will change the chemical potential of CO2, and also reduce the availability of CO2 (mass transport aspect). A first question arises as to how far CO2 concentration in the gas can be reduced before the gas is no longer able to create a new hydrate. CO2 separated from hydrocarbon streams will frequently also contain significant amounts of H2S due to thermogenic decomposition of organic material in the deep crust. The most common technology for separating sour gases from hydrocarbons uses amine solutions. This can be MDEA (methyl diethanol amine), which is a weak base but does not have any reaction with CO2 over to carbamate. MDEA is utilized in separating CO2 from the natural gas produced at the Sleipner platform in the North Sea.10 The separated CO2 is then injected into the Utsira formation.11,12 Owing to the base properties of MDEA, H2S and other sour gases also will follow the CO2 and thus also follow into the injection. North Sea systems are fairly lean in H2S, typically in the ppm range. Other hydrocarbon sources around the world which have a higher content of hydrocarbons from thermogenic sources will typically have high concentrations of H2S due to anaerobic degradation of sulfur in organic material. The basic properties are also in amines that react with CO2 and form carbamates. Mixed amine solutions, as for example MDEA and a reactive amine, will also lead to separation of H2S over to the CO2 phase. This type of mixed solutions is used when a higher purity of the natural gas is needed. As for example, in the Snøhvit plant10 in the north of Norway, where high methane purity is needed due to the liquified natural gas plant for methane. Since H2S is a very aggressive hydrate former a second question arises. How will additions of H2S to CO2/N2 mixtures affect the ability to form new hydrate from the injection gas and thus retain a fast mechanism for release of CH4 from in situ CH4 hydrate. By adding H2S to the N2/CO2 mixture, the new hydrate will become more stable. H2S will occupy both small and large cavities in structure I hydrates. A special feature of H2S compared to nonpolar hydrate formers is the impact of the dipole moment. The rotation of H2S inside a cavity exposes an average positive charge outward. The average charge of the cavity walls are negative inward in the cavity. This is due to the negative water oxygen located at the center of water molecules in the water lattice, and the distribution of the positive hydrogens (Kvamme and Førrisdahl9). The efficient stabilization of hydrate by H2S can be seen from the experimental equilibrium curves for hydrate formed from pure H2S and water. Even small amounts of H2S added to a fluid mixture of hydrate formers, such as small hydrocarbons, will significantly change hydrate equilibrium curves compared to hydrate

Figure 1. Schematic 2D illustration of H2S behavior in a hydrate cavity9 Red are water oxygens in cavity walls, and gray indicates water hydrogens that would prefer to line along the water connection. The other hydrogens will have variable tipping (in and out of cavity). On the average the sampled net balance9 is a negative electrostatic field inward in the cavity. Since H2S has a positive center on the central S (orange) the rotational modes of H2S in the cavity result in an average positive electrostatic field facing outward toward the cavity walls.

Coulumbic attraction adds to the short-range water−hydrogen sulfide interactions and leads to the high stabilization of hydrate by H2S which is well-known from experiments (see later sections of the paper). In this article the primary focus is on structure I hydrate. Structure I hydrates consist of H2O molecules ordered in a hexagonal lattice, surrounding the guest molecule. Structure I consists of two 512 cavity types and six 51262 cavity types, while structure II consists of 16 516 cavity types and eight 51264 cavity types (Sloan, 2003).13 The 512 cavity (pentagonal dodecahedra) has 12 faces of pentagonal bonded water molecules, denoted as a small cavity with an average cavity radius of 3.95 Å for structure I and 3.91 Å for structure II. The 51262 cavities (hexagonal face) are needed to keep the 512 hydrogen bonds from breaking, denoted as a large cavity with an average cavity radius of 4.33 Å. For the 51264 cavities, found in structure II, the average cavity radius is 4.73 Å. All structures need to fill their free cavity space, and the hexagonal faces relieve the strain from the 512 cavity, by adding two hexagonal faces in structure I and four in structure II. Structure I consists of two small and six large cavities, and 46 H2O molecules. This cavity structure is preferred by guest molecules such as methane, ethane, carbon dioxide, and hydrogen sulfide. H2S occupies both the small and large cavities in structure I. The large cavities in structure II are not able to benefit from the H2S dipole moment to the same extent as structure I small and large cavities. In the case of 1646



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temperature of 276 K.21 The pressure gradient is 0.01 MPa/ m.21 Temperature gradient is 0.039 °C/m.21 There are two primary objectives of this paper. As mentioned above, there is a general need for a complete thermodynamic model description of these CO2/CH4/N2/H2S systems that can be implemented in reservoir simulation software for modeling hydrate production using CO2-based injection technologies. Evaluating pipeline transport in these multicomponent mixtures also requires an appropriate thermodynamic description of these gas mixtures, including also the risk of hydrate formation. The second main goal of the paper is to shed light on some possible special features related to the addition of H2S to mixtures of N2 and CO2. In particular how various amounts of H2S can influence the possibilities for simultaneous CO2 storage as hydrate and associated release of CH4 from in situ CH4 hydrate. To accomplish this the focus is on conditions that will favor formation of a new hydrate from the injection gas since the solid state conversion mechanism is far too slow to be of any practical interest for either CO2 storage or CH4 release. The specific ranges of conditions (temperature, pressure) have been retrieved from field data from the four cases chosen for this particular study (Tables 1 to 4). It should be

CO2/N2 mixtures with H2S then N2 and H2S are able to enter both cavity types of structure I while we approximately disregard filling of CO2 in the small cavity. The thermodynamic benefits of CO2 entering the small cavity of structure I is questionable. So at least in a very dynamic situation with multiple choices for CO2 to enter various phases inside a pore (dissolve in pore water, adsorb on minerals, enter large cavity of structure I, adsorb on in situ CH4 hydrate) this seems like a fair first approximation. Case Studies. As mentioned before, natural gas hydrates are widely distributed worldwide in permafrost sediments and offshore sediments. The case studies chosen here are from four different offshore locations. Pressure and temperature regions are tabulated for each case. 1. Bjørnøya Gas Hydrate Basin, Norway. Bjørnøya is a gas hydrate basin located in the southwest of the Barents Sea. Gas hydrate at Bjørnøya overlays a gas zone.11 The gas has a thermogenic source and has migrated from deep sediments. The average water depth in the Barents Sea is about 230 m, while inferred gas hydrate occurrence takes place at a water depth of 395 to 400 m.14 The thickness of the hydrate stability zones varies from approximately 155 to 170 m depending on the water depth.15 The maximum and minimum hydrate saturation are expected to be between 47% and 26%.14 A variable amount of hydrocarbons heavier than methane is expected to be present since the source is thermogenic. The analysis will mainly be discussed in terms of methane hydrate since the relative amount of higher hydrocarbons is unknown. Nevertheless, a specific mixture containing heavier hydrocarbons also is included in the thermodynamic stability analysis. 2. The Nankai field, Japan. The world’s first offshore gas hydrate production was conducted at the β-MHCZ site located in northwestern slope of the Daini−Astumi Knoll in March 2013.16 Area of the testing site is approximately 12 km2. Water depth in this area ranges from 857 to 1405 m.17 The hydrate bearing zone is found in a turbidite formation composed of different layers. Average depth of the hydrate layer from the seafloor is 307 m. The hydrate layer thickness is estimated to vary between 50−70 m, with an approximate hydrate thickness of 62 m.18 Sandy layers showed hydrate saturations of 50−80%, compared to muddy layers, which had hydrate saturations of 0−10%. (This can be explained by the fact that sandy layers have larger pore space and therefore are more favorable for hydrate formation).16 Average temperature gradient ≈ 0.0318 °C/m, pressure is estimated from a hydrostatic pressure gradient of 35 000 ppm saline water.18 3. The Hikurangi Margin, New Zealand. The East Coast Basin, located at the Hikurangi Margin,20 east of the North islands is currently considered the economically most promising gas hydrate province in New Zealand. Seismic data shows evidence for gas hydrate bearing sands. An approximate 200 m thick hydrate layer was found about 380 m below the seafloor. One location is predicted to consist of high permeable channel sands with a gas hydrate saturation of approximately 25%.20 The temperature gradient is 0.029 °C/m. Water depth is 1680 m, and the seafloor temperature is 275.95 K.20 4. A Gas Hydrate Basin in Southwest of Taiwan. A hydrate basin has been located in the submarine accretionary wedge offshore of southwestern Taiwan. The approximate 104 m thick hydrate layer was found about 200 m below the seafloor.21,22 The water average depth is 1666 m,23,24 with a seafloor

Table 1. Ranges of Pressures and Temperatures for Bjørnøya Gas Hydrate Basin.14,12

initial pressure temperature

at the top of the hydrate layer

at the bottom of the hydrate layer

4 MPa 275.15 K

7 MPa 285.65 K

Table 2. Ranges of Pressures and Temperatures for the Nankai Field




13.05 MPa17−19 285.81 K16,17,19

13.67 MPa17−19 287.78 K16,17,19

Table 3. Ranges of Pressures and Temperatures for the Hikurangi Margin20




20.6 MPa 286.97 K

22.6 MPa 292.77 K

Table 4. Ranges of Pressures and Temperatures for the Hydrate Basin in the Southwest of Taiwan




18.75 MPa 283.8 K

19.79 MPa 287.9 K

emphasized that the systems are analyzed with reference to pure water. There are three reasons for this. One is that the salinity can vary substantially between different hydrate filled sediments in offshore and permafrost hydrate reservoirs. The other reason is that the addition of salinity would require a model for the impact of salinity on the activity coefficient of water. It would even be possible to incorporate this by simple shifts of the water chemical potential according to the impact of salinity. And finally the third reason is that the salinity in the water surrounding a growing new hydrate will change 1647



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where the superscripted ∞ stands for the infinite dilution. This particular convention is known as the nonsymmetric excess convention because the limit of the activity coefficient for the component i will approach unity as the mole fraction vanishes. One way to estimate values based on the ideal gas reference state for these infinite dilution chemical potentials is through molecular dynamics simulations and the application of the Gibbs−Duhem relation.7,8 Provided that thermodynamic properties of all phases can also be specified and evaluated outside of equilibrium, the first and second laws of thermodynamics would require that the available mass of each component, and the total mass, should be distributed over all possible phases able to coexist under given local pressure and temperature conditions. This evaluation will be fairly straightforward for most of the fluid phases under consideration. The only phase requiring special attention will be the hydrate phase, which is discussed extensively in Kvamme et al.5,8 Combining thermodynamic formulations for fluids in eqs 1 to 3 with hydrate nonequilibrium formulations from Kvamme et al.5,8 makes it fairly straightforward to minimize the free energy and obtain estimates for local phase distributions obeying the first and the second law of thermodynamics. Several algorithms capable of implementing this approach are available in the open literature. Situations considered here imply very limited solubility and/ or limited concentrations. The solubility of H2O in CO2/N2 is very low. In view of this fact, the following approximation should prove sufficiently accurate for pure liquid CO2 (or CO2 with small amounts of N2 but still in liquid) limit:

proportional to the consumption of water into hydrate. But the dilution of this water with increased salinity through mixing with water from surrounding sediments will be highly individual for each reservoir. As such, the results presented here are conservative estimates intended to illustrate some important qualitative aspects of adding hydrogen sulfide and nitrogen to the carbon dioxide. The paper is organized as follows. The thermodynamic models are described in the next section, followed by a section for verification of the model systems through comparison with experimental data. Thermodynamic stability limits of different hydrates under influence of various surrounding fluids are discussed in subsections, leading to a final conclusion section.

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THEORY Fluid Thermodynamics. If thermodynamic equilibrium can be achieved, then the temperatures, pressures, and chemical potentials of all coexisting phases have to be uniform across all phase boundaries. Minimizing free energy can be used to find phase distributions and compositions in equilibrium systems. For nonequilibrium systems a free energy analysis can be used to find the most beneficial phase distributions locally, as well thermodynamic preference for individual components to move across phase boundaries to other phases. For equilibrium systems the choice of reference state for different components in different phases is not critical, as long as thermodynamic models are available. For nonequilibrium systems it will be convenient to have the same reference state for the free energy of all phases. The calculation of chemical potentials of all components in the different phases based on ideal gas as the reference state is then formulated as μi (T , P , y ⃗ ) − μi

ideal gas

μi,j(T , P , x ⃗) ≈ μi,j∞(T , P) + RT ln[xi , jγi∞ (T , P , x ⃗)] ,j

(T , P , y ⃗ ) = RT ln ϕi(T , P , y ⃗ )

where subscript i refers to components; subscript j denotes the phase. In the context of this work, j is CO2 in case of the CO2 phase, H2O for the aqueous phase, and H is the solid hydrate phase. For water dissolved in gas mixtures of CO2 and N2 the solubility is low enough to approximately cancel the water/ water term in the attractive parameter so, at the cost of some rigor, rough estimates of liquid water drop-out can also be achieved.8 Equilibrium Thermodynamics of Hydrate. The statistical mechanical model for water in hydrate25 yields the following equation for chemical potential of water in hydrate:

(1)

where ϕi is the fugacity coefficient for component i in a given phase. The ideal gas term on left-hand side also includes the ideal gas mixing term due to entropy of mixing ideal gases at constant temperature and pressure. Another reference state for the chemical potential of a liquid state component i will also be used as an intermediate step: μi (T , P , x ⃗) − μiideal liquid (T , P , x )⃗ = RT ln γi(T, P, x ⃗) (2)

lim(γi) = 1.0

μwH = μw0,H −

when (x i) → 1.0

RTvk ln(1 +

∑ hik) i

(5)

where superscript H denotes the hydrate phase and superscript 0 stands for the empty hydrate. vk is the fraction of cavity of type k per water molecule. For structure I hydrate, νk = 1/23 and 3/23 for small cavities (20 water molecules) and large cavities (24 water molecules), respectively. hik is the canonical partition function for cavities of type k containing a “guest” molecule of type i and is given by hik = e β(μi

H

−Δgikinc)

(6)

where β is the inverse of the gas constant times temperature while Δginc jk reflects the impact on hydrate water from the inclusion of the guest molecule i in the cavity.13 At equilibrium, chemical potential μHi has to be identical to the chemical potential of molecule i in the phase from which it has been extracted. The hydrate content of all gas components can be estimated by applying eq 1 to calculate their chemical potential

μi (T , P , x ⃗) − μi∞(T , P , x ⃗) = RT ln[xiγi∞(T , P , x ⃗)] (3)

= 1.0

∑ k = 1,2

where γi is the activity coefficient for component i in the liquid mixture. The ideal mixing term is included in the chemical potential of ideal liquid on the left-hand side. Equation 2, as applied to water, can also be based on ideal gas reference state when the chemical potential of pure water liquid water is calculated from molecular interaction models using molecular simulations. More specifically, data from Kvamme and Tanaka25 are employed. The formulation in eq 2 is normally called symmetric excess. For gases with low solubility in water infinite dilution of the component in water is a more appropriate liquid reference state for those components:

lim(γi∞)

(4)

when x i → 0 1648



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when dissolved in the methane phase. The typical equilibrium approximation used in most hydrate reservoir simulators is given by eq 7 below within the assumption of a free hydrate former phase (gas, liquid, fluid) in which each component chemical potential is normally calculated by an equation of state and the resulting chemical potential needed in eq 6 for the cavity partition functions in eq 7 can then be calculated from eq 1. μw0,H −

∑

RTvk ln(1 +

k = 1,2

=

(T , μi purewater ,H2O

θik =

xikH hik = vk(1 − x T) 1 + ∑i hik

where θik is the filling fraction of component in cavity type k. xHik is the mole fraction of component i in cavity type k, xT is the total mole fraction of all guests in the hydrate, and vk is, as defined above, the fraction of cavities per water of type k. Computed free energies of guest inclusion in the large cavity of structure I have been fitted to a series in inverse reduced temperature.

∑ hik) i

P) + RT ln[xi ,H2Oγi ,H2O(T , P , x ⃗)]

5

Δg inclusion =

(7)

(10)

where Tc is the critical temperature of the guest molecule in question. See Tables 1, 2, and 3 for CO2, CH4, and N2, respectively. Critical temperatures for the three different guest molecule types are given in the figure captions. There is some different experimental evidence (see for instance Kuhs et al.26) that CO2 also enters the small cavity, but during our MD studies, we did not find that it gives any net stabilizing effect of the hydrate. For most CO2 models we have tested the hydrate structure collapses. Whether CO2 will enter the small cavities in a highly dynamic situation of flow still remains experimentally unverified. The cavity partition function of CO2 in a small cavity (eq 6) is close to zero anyway. The free energy of inclusion in eq 4 can be estimated according to Kvamme and Tanaka (1995).25 Thermodynamic consistency has been a high priority throughout this work. It was not our intention to adjust any parameters to fit experimental data. Molecular dynamics simulations reported in this work were restricted to extending the approach of Kvamme and Tanaka25 to larger hydrate systems and additional temperatures between 273.16 and 280 K, which is the temperature range in this study. Updated parameters for free energy of inclusion of H2S are given in Table 5 and free energy parameters for CH4, CO2, and

nH H

i=1

⎡ Tc ⎤i ⎥ T⎦

∑ ki⎣⎢ i=0

The chemical potential of water in the empty hydrate structure as estimated according to Kvamme and Tanaka13 has been verified to have predictive capabilities. Empirical formulations for these chemical potentials are therefore redundant and maybe unphysical since chemical potential is a fundamental property. Throughout this study we approximate the right-hand side of eq 7 by pure water since there are no ions in the water and only limited amounts of dissolved gases. This approximation will imply a limited shift to the chemical potential of liquid water as corrected for dissolved CO2. For example the correction at 150 bar and 274 K will be −0.07 kJ/ mol and slightly higher for 200 and 250 bar but still not dramatic for the purpose of this study. The free energy change related to a hydrate phase transition, ΔGH can be written as ΔG = δ ∑ xiH(μi H − μi p )

(9)

(8)

Superscript H in eq 8 denotes hydrate phase property or mole-fraction while p denote similar for parent phase for the molecule i. The sum runs over all components in the hydrate phase. δ is 1 for hydrate formation and −1 for hydrate dissociation. Hydrate formation, for instance, will at minimum require that the free energy change be negative. But more rigorously it will also require that the implications of the gradients of free energy in all independent thermodynamic variables must result in negative free energy changes. For example, methane hydrate will form as long as the conditions of temperature and pressure are inside the hydrate stability zone, but stability of this hydrate will also depend on the concentration of hydrate formers in liquid water, as well as the water chemical potential in hydrate former phase(s). In a pressure, volume, temperature experiment the water phase will naturally saturate in hydrate formers with reference to hydrate properties. So unless the water is replaced by undersaturated water this effect is not always seen, but can be very important in real flowing situations for which the water phase may not have sufficient time to saturate with hydrate formers, due to liquid and fluid transport flux dynamics. The description of hydrate thermodynamic properties outside equilibrium due to Kvamme et al.5 can be utilized for this purpose to follow free energy gradients until the CO2/N2 phase has been mostly depleted of the most aggressive hydrate former, carbon dioxide. The analysis of eq 6 will also require the knowledge of hydrate composition. This can be found by applying statistical thermodynamic theory to the adsorption model for hydrate (left-hand side of eq 10); the composition will be given by

Table 5. Coefficient of Δginclusion (eq 10) in the Case of Hydrogen Sulfide Inclusion in Structure I. Critical Temperature for H2S is 373.4 K k (kJ/mol)

large cavity

small cavity

0 1 2 3 4 5

−9.867851530796533 × 10−001 −5.091001628046955 × 10−001 −41.197126767481830 −13.013675083152700 5.462790477011296 8.535406376549272

−35.841596491485960 75.644235713727100 −49.924309029873280 −31.868805469546190 −1.638643733127986 12.738557911032440

N2 can be found elsewhere.27,28 Parameters for empty hydrates and ice were not significantly affected and the parameters of Kvamme and Tanaka25 were applied. Estimates for the chemical potential of liquid water were extended from 273.15 K by means of thermodynamic relationships and experimental data on enthalpy of dissociation and liquid water heat capacities. For more details, see Kvamme and Tanaka.25

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VERIFICATION OF THE MODEL SYSTEMS No experimental data for the composite hydrate consisting of CO2, H2S, and N2 were found in the open literature. In most of the North Sea hydrocarbon systems the H2S content is low, typically in the ppm range. So at least one experimental data set 1649



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Figure 2. Estimated and experimental hydrate equilibrium curve for a system of 99% CO2 and 1% H2S. Solid line, our estimate; asterisk, experimental data from Chen et al.29.

Figure 4. Estimated and experimental hydrate equilibrium curve for a system of 89.6% CH4, and 10.4% H2S. Solid line, our estimate; asterisk, experimental data from Mohammadi and Richon.30

Figure 3. Estimated and experimental hydrate equilibrium curve for a system of 90% CO2 and 10 mol % H2S. Solid line, our estimate; asterisk, experimental data from Chen et al.29

Figure 5. Estimated and experimental hydrate equilibrium curve for a system of 88.89% CH4 and 11.11% H2S. Solid line, our estimate; asterisk, experimental data from Ward et al.31

from Chen et al.27 can be used for comparison (see Figure 2 for a plot of model estimates versus experimental data). In comparing estimates and experimental data it is very important to keep in mind two aspects. First of all it is important to keep in mind that the free energy of inclusions was calculated by molecular simulations without tuning of the model. And the second thing is that several mixtures do form more than one hydrate. According to the first and second laws of thermodynamics the most stable hydrates form first and then a variety of hydrate compositions will follow. So for many experimental mixtures it is not given that the final hydrate is uniform. It is more likely that it is a mixture of several hydrates

with varying composition of the initial hydrate formers from gas or liquid. It is not our intention to tune empirical model parameters so even fair qualitative agreement is sufficient for the main focus of this paper. The comparison in Figure 3 can potentially be a mixture of both structures I and structure II. CO2 stabilizes the large cavity of structure I well, while H2S stabilizes the small cavities of both structures I and II well. Given the larger ratio of small to large cavities in structure II this can give rise to various hydrate compositions of both structures I and II. It is beyond the scope of this work to analyze the free energy differences in detail. At this stage this is just a hypothesis which needs verification or falsification. But since residual thermodynamics (ideal gas as 1650



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Figure 6. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 40 and 70 bar for Bjørnøya. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in CO2/N2 mixture. This case is for 0% H2S added to the hydrate mixture.


almost the same composition as in Figure 4 but for a higher temperature range is plotted in Figure 5. The MD simulations for the free energy of inclusion have mainly been conducted for up to 280 K so the highest temperatures are to be considered as extrapolations. It is very important in this context that the cavity partition functions for these molecules, including also H2S, has been derived from molecular simulations of model systems rather than fit empirical models to experimental data. Other schemes which use the chemical potential difference method (difference between pure liquid water and empty hydrate) will likely have enough flexibility to fit these experimental data well enough since the chemical difference at a reference state is frequently treated as an empirical fitting parameter along with fitting of temperature dependency through the enthalpy of the same difference. Fitting of these parameters and molecular interaction parameters in the Langmuir constants toward these experimental data (and potentially additional exper-

reference) is used for all components in all phases, as discussed in the thermodynamic section, it is feasible to examine these aspects in detail. And work is ongoing related to another project. The experimental values are also quite interesting in this respect since there appear to be no (almost) experimental difference in equilibrium pressures for two very different temperatures. Since the dominating mechanism for the CH4/CO2 hydrate swap process goes through the formation of a new hydrate from incoming gas it is not obvious that any significant amounts of H2S ever mixes in with CH4 under reservoir conditions. Nevertheless, a comparison between experimental data and estimates is given in Figure 4 below. As also discussed for the CO2/H2S systems above, the distribution of hydrates generated from the gas mixture is rather unclear, but a free energy analysis will be able to shed some light on this. As for the focus of this paper the estimates are considered as good enough. Another experimental data set for 1651



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Figure 9. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 130 and 140 bar for the Nankai field. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in CO2/N2 mixture. This case is for 0% H2S added to the hydrate mixture.

potential of liquid water, water in hydrate formed from CH4 and water in hydrate formed from CH4 (80 mol %), C2H4 (12 mol %), and C3H6 (8 mol %). In these calculations, it is approximated that the guest molecules establish equilibrium between hydrate and gas, and that released methane arising as a result of heat generated by the new hydrate formation does not mix but escapes by buoyancy through separate pathways. Hydrate Stability for Mixtures of CO2/N2/H2S. To simplify the analysis of these figures, H2O in CH4 and H2O in CH4, C2H6, and C3H6 will be referred to as hydrate 1 and hydrate 2, respectively. The estimated water chemical potentials in hydrate, liquid water, hydrate 1 and hydrate 2 for pressures representative to the four cases, with regard to the upper and lower hydrate level, are plotted in Figures 6 to 17. This analysis will focus on CO2 hydrate stability, compared to hydrate 1 (green dashed line), with different H2S compositions. Liquid water (red dashed line) and hydrate 2 (blue dashed), are only for reference. When the CO2 hydrate32 (solid lines) has a lower

imental data) is likely to reproduce experiments well. Rather than doing this it was decided to accept the differences and stick to the theoretical models based on molecular dynamics simulations. The main focus of this paper is, after all, to investigate qualitatively how the presence of H2S may shift the limits of N2 in CO2 which makes hydrate formation possible. If this analysis is of interest and value for a more detailed study, then also new experimental data on hydrate formations from CO2/N2/H2S systems should be conducted. Verification of the CO2/N2 system has been conducted separately in published papers,27,28 and similar for H2S hydrate and mixtures with H2S, although without the presence of N2. Within the scope of this work we consider the comparisons between estimates and theoretical predictions as illustrated above, and similar comparisons published by Kvamme et al.27,28 Limits of Hydrate Stability for Mixtures of CO2/N2/ H2S. In the next section we investigate the stability of hydrates from different CO2/N2/H2S ratios with reference to chemical 1652



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identical, so the analysis is the same for both pressures. For 130 and 140 bar and 0% H2S (Figure 9), the exchange process will occur for gas mole fraction of CO2 above approximately 7.5 mol % at 280 K and above 4 mol % CO2 in gas at 288 K. By adding 1% H2S (Figure 10), and keeping the N2/CO2 relationship constant, the exchange process will occur above approximately 1.8% gas mole fraction of CO2 at 280 K and at any mole percent at 288 K for 130 and 140 bar. By adding 5% H2S (Figure 11), the exchange process will occur at any gas mole fraction of CO2 at temperatures ranging from 275 to 285 K for hydrate 1 and hydrate 2. After the conduction of this study it was brought to our attention that more accurate and up-to-date information on the Nankai Trough is available through two new papers which were published after this study, Yamamoto et.al.33 and Konno et al.34 Although there are some limited adjustments in the range of conditions, the information from these new papers do not change the analysis significantly.

chemical potential than hydrate 1, an exchange process will occur. Hydrate 1 will dissociate through solid state diffusion, releasing methane, creating CO2 hydrate. Bjørnøya Gas Hydrate Basin, Norway. For 40 bar and 0% H2S (Figure 6), the exchange process will occur for gas mole fraction of CO2 above approximately 19 mol % at 275 K and above 3 mol % CO2 in gas at 285 K. Corresponding values for 70 bar are 13% and 3.5%, respectively. By adding 1% H2S (Figure 7), and keeping the N2/CO2 relationship constant, immediate changes can be observed. Now, for 40 and 70 bar the exchange process will occur for 0% gas mole fraction of CO2 at the given temperatures. By adding 5% H2S (Figure 8), similar observations are observed, where the exchange process will occur at any gas mole fraction of CO2 at temperatures ranging from 275 to 285 K for hydrate 1. Hydrate 2 is more relevant with 5% H2S. The Nankai Field, Japan. The initial pressures in the upper and lower hydrate baring layers in the Nankai field are almost 1653



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Figure 12. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 200 and 230 bar for Hikurangi Margin. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in CO2/N2 mixture. This case is for 0% H2S added to the hydrate mixture.

Figure 13. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 200 and 230 bar for Hikurangi Margin. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in the CO2/N2 mixture. This case is for 1% H2S added to the hydrate mixture.

The Hikurangi Margin, New Zealand. For 200 bar and 0% H2S (Figure 12), the exchange process will occur for gas mole fraction of CO2 above approximately 4.5 mol % at 285 K and above 2.5 mol % CO2 in gas at 288 K. By adding 1% H2S (Figure 13), and keeping the N2/CO2 relationship constant, similar observations as for Bjørnøya are observed. The exchange process will occur for 0 mol % gas mole fraction of CO2 at the given temperatures. The results observed by adding 5% H2S, shown in Figure 14, are very extreme, which is the cause of extreme pressures and temperatures in the hydrate baring layers. The exchange process will occur at any gas mole fraction of CO2 at temperatures ranging from 285 to 293 K for hydrate 1 and hydrate 2. A Gas Hydrate Basin in Southwest Taiwan. Similar to the Nankai field, the initial pressure for the upper and lower hydrate baring layers for the hydrate basin in southwest Taiwan are almost identical, so the analysis is the same for both pressures. For 180 and 200 bar and 0% H2S (Figure 15), the

exchange process will occur for the gas mole fraction of CO2 above approximately 5.2 mol % at 283 K and above 4 mol % CO2 in gas at 288 K. By adding 1% H2S (Figure 16), and keeping the N2/CO2 relationship constant the exchange process will occur for 1% gas mole fraction of CO2 at 283 K and any mole percent at 288 K for both pressures. By adding 5% H2S (Figure 17), the exchange process will occur at any gas mole fraction of CO2 at temperatures ranging from 283 to 288 K for hydrate 1 and hydrate 2. The results obtained by the simulation, show that the addition of H2S to the CO2/N2 mixture reduces the chemical potential of water in hydrate substantially. The formation of a new hydrate from the injection gas will lead dissociation of in situ CH4 hydrate, and improve the mass transport rate through the hydrate. Only a small percentage of H2S will alter the stability conditions for the injected gas mixture. As a consequence of the first and second laws of thermodynamics the most stable hydrates will form first, if conditions of mass1654



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Figure 14. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 200 and 230 bar for Hikurangi Margin. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in CO2/N2 mixture. This case is for 5% H2S added to the hydrate mixture.

Figure 15. Estimated water chemical potential in hydrate (solid), liquid water (red dash), liquid water with CH4 (green dash), and liquid water with a mixture of gases (CH4, C2H6, C3H8) (blue dash) as a function of temperature for 180 and 200 bar for southwest Taiwan. The solid line from the top: 1%, 2%, 5%, 10%, 40%, 70%, 80% CO2 by volume in CO2/N2 mixture. This case is for 0% H2S added to the hydrate mixture.

in dissociating the in situ CH4 hydrate. This second mechanism will therefore be several orders of magnitude faster since it is a liquid state transport process, in contrast to the solid state conversion mechanism. Adding N2 to the injected CO2 has been proposed in order to increase gas permeability and limit blocking of the pores due formation of new hydrate. In a recent pilot plant study28 the content of N2 was as much as 77% by volume. Thermodynamic stability of hydrates is a function of all independent thermodynamic variables. In addition to temperature and pressure this includes concentrations of all components that enter the hydrates, in all the coexisting phases. There are lower limits for concentration of CO2 in CO2/N2 injection gas which makes formation of new hydrate thermodynamically impossible. Amounts and types of inorganic gases following the hydrocarbons depend on the relative amounts of thermogenic hydrocarbons in the stream. Thermogenic conversion of sulfur under anaerobic conditions deep down in the crust ends up as H2S. During sour gas

and heat-transport permit. Follow up studies will be needed to evaluate how fast the formation of new hydrate will be and correspondingly possible blocking in the initial stages before the content of H2S and CO2 is reduced in the injection gas. A possible way to examine this is through reservoir simulation using a reactive transport simulator like RCB,35−40 which can be extended to studies of this type of systems that involves a variety of hydrates being formed.

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CONCLUSIONS

Injection of CO2 into CH4 hydrate will lead to an exchange process in which the in situ CH4 hydrate will be replaced by a mixed hydrate, in which CO2 dominates filling of the large cavity in the structure I hydrate. This process is possible through a direct solid state exchange, which is very slow and practically not interesting. In a second mechanism CO2 forms a new hydrate from injection gas and free water in the pores. The released heat from the formation of this new hydrate will assist 1655



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Nankai offshore Japan and then two fairly deep fields offshore Taiwan and New Zealand, respectively. For the most shallow gas hydrate (Bjørnøya) almost 30% CO2 in N2 is needed at 40 bar pressure and 280 K for the hydrate water chemical potential to be lower than the liquid water chemical potential. For the same temperature and 70 bar pressure the same limit for CO2 content is reduced to 6%. H2S at 1% reduces these limits of CO2 to 9% and 1%, respectively. With 5% H2S all concentrations of CO2 in N2 from 1% to 80% lead to formation of new hydrate for both 40 and 70 bar and temperatures from 275 to 280 K. The higher range of pressures in the Nankai case to between 130 and 140 bar reduces the necessary content of CO2 to about 2% at 280 K. Even 1% H2S added to the CO2/N2 mixture makes new hydrate formation possible for all temperatures between 280 and 288 K. As expected the minimum CO2 content needed for creation of a new hydrate in the two deep reservoirs is low. Roughly 5% CO2 is enough to make a new hydrate even at temperatures of

removal H2S will normally follow CO2 in a product stream which needs to be handled or utilized. The primary purpose of this study was to shed more light on whether the addition of H2S to a CO2/N2 mixture would significantly change the ability for the injection gas to form a new hydrate. For this purpose we utilize a thermodynamic analysis based on comparison of chemical potential for hydrate water as a function of variations in content of N2 and H2S, and liquid water chemical potential. In addition we also compare the chemical potential of water in two different hydrates, the first being a pure CH4 hydrate representative of biogenic source. The second hydrate is formed from a gas characteristic of thermogenic gas, with significant amounts of ethane and propane. Four different hydrate fields have been chosen for this purpose. The conditions of temperature and pressure in these fields vary over significant ranges of temperatures and pressure; from a fairly shallow field offshore Norway (Bjørnøya) to 1656



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293 K and pressures between 200 and 230 bar. For 1% H2S this number is reduced to 1%. The pressure range is slightly lower for the Taiwan reservoir, 180 to 200 bar, and limits for minimum CO2 content about 5% in N2 to form new hydrate. Even 1% H2S addition results in new hydrate formation for the whole range of CO2 concentrations between 1% and 80%. The relative stability of methane hydrate is not directly relevant for a mechanism in which heat is generated from formation of a new hydrate, but it is not given that the released CH4 mixes in with the incoming CO2/N2 mixture due to separating barriers of liquid water and newly formed hydrate. Potential reformation of CH4 is, however, possible in competition with hydrate formation from incoming gas. The variations in water chemical potential for the pure CH4 hydrate, in the limited temperature ranges, are small. Mixtures of CO2/ N2 containing between 2% and 5% CO2 will be competitive with reformation of CH4 hydrate. The general trend is that the deeper is the hydrate reservoir, the smaller is the amount of CO2 in the N2 needed to form a new hydrate and thus facilitate a fast mechanism for release of in situ CH4 hydrate. Except for in the case of the Bjørnøya reservoir even a concentration of 1% H2S shifts the ability to form a new hydrate from pore water and the injection gas substantially and essentially for all concentrations of CO2 above 1%. But formation of a new hydrate will not be uniform since the most stable hydrates form first, under constraints of masstransport and heat-transport. This can lead to a reduction of H2S and CO2 in the injected gas though the reservoir. Additional solvation of sour gases in the pore water and adsorption on mineral surfaces are other processes which will consume H2S and CO2. Implementation of results and thermodynamic models from this work into a reservoir simulator is one way to proceed with a follow up study which also couples in mass-transport and mass-balances as well as heat-transport. Work in this direction is in progress.

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K = ratio of mole-fraction gas versus mole-fraction liquid of the same component (gas/liquid K-values) Ni = number of molecules N = number of phases in the Gibbs phase rule P = pressure [Pa] P0 = reference pressure [Pa] r = distance [m] R = molar gas constant [kJ/(K mol)] T = temperature [K] vj = no. of type j cavities per water molecule vm = molar volume [m3/mol] V̅ r = molar volume of rth component [m3/mol] V̅ clath = volume of clathrate [m3] x = mole fraction in liquid or adsorbed, arrow on top denote vector y = mole fraction in gas, arrow on top denote vector yw = mole fraction of water Y = residual chemical potential per Kelvin z = mole fraction α = liquid (water) phase fraction β = inverse of the gas constant times temperature μ = chemical potential [kJ/mol] μ0,H = chemical potential for water in empty hydrate w structure [kJ/mol] θkj = fractional occupancy of cavity k by comp γ = activity coefficient ϕ = fugacity coefficient

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mojdeh Zarifi: 0000-0002-5625-8348 Khadijeh Qorbani: 0000-0003-2991-9806 Notes

The authors declare no competing financial interest.

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NOMENCLATURE C = number of components in the Gibbs phase rule EP = potential energy [kJ/mol] F = number of degrees of freedom in the Gibbs phase rule F = free energy [kJ/mol] f = free energy density [kJ/(mol m3)] f i = fugacity [Pa] g(r) = radial distribution function (RDF) G = Gibbs free energy [kJ/mol] Δginc kj = Gibbs free energy of inclusion of component k in cavity type j [kJ/mol] H = enthalpy [kJ/mol] hkj = cavity partition function of component k in cavity type j k = constants in polyonomial fitting of free energies of guest inclusion in eq 10. 1657



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