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Some aspects of hydrate formation and wetting
Journal of Colloid and Interface Science 321 (2008) 130–141 www.elsevier.com/locate/jcis
Some aspects of hydrate formation and wetting P. Fotland ∗ , K.M. Askvik StatoilHydro ASA, Research Center Bergen, Norway Received 25 October 2007; accepted 18 January 2008 Available online 29 January 2008
Abstract Experimental observations of gas hydrate formation have shown that, in the initial nucleation and crystallization process, water–oil emulsions may be generated, destabilized or even inverted. These phenomena are consistent with the effects of particles on emulsions. In this work we relate experimental observations of hydrate formation to the phenomenon of wettability. It is shown that details of hydrate wetting are important for both the morphology and the kinetics of the formed hydrates. For the cases of hydrate lenses and spheres, it is shown that the various wetting states can be illustrated and analyzed by using wetting diagrams. Metastability is a function of the surface energies of the hydrate formation, i.e., the wetting state, and it is shown that in some cases metastability vanishes, and thus hydrates nucleates instantly at all positive driving forces. The magnitude of buoyancy and turbulence forces acting on a hydrate sphere are compared to the capillary force and it is concluded that capillary energy dominates when the hydrate spheres is less than 1 mm. © 2008 Elsevier Inc. All rights reserved. Keywords: Hydrates; Wettability; Metastability; Agglomeration
1. Introduction The formation of hydrates and its relation to production and transport of crude oil has been described and discussed in a number of articles and books [1–5]. Hydrate formation in pipelines and process equipment continues to be a phenomenon related both to hazard and high cost. The usual hydrate strategy states that positive driving forces for hydrate formation should be avoided. The basis of the strategy is that once the driving forces are positive the system will immediately generate a solid hydrate plug and production is shut down. Many operators find that in practice this is not always the case, hence the strategy is too conservative. Considerable amounts of chemicals can be saved by changing the strategy. In turn, a less conservative strategy may lead to developments that may have otherwise have been abandoned [6]. The presence of crude oil is known to have some impact on the hydrate formation. Oil in general consists of a large number of different chemical groups of molecules. The largest group is normally the hydrocarbons which again may be subdivided into * Corresponding author.
E-mail address: [email protected] (P. Fotland). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.01.031
groups like paraffins, naphtenes and aromatics [9]. In addition to hydrocarbons, there are solubility classes like asphaltenes and resins, and also well defined groups like acids and bases. Each oil is a unique mixture of these components which will define the physical properties of the crude like, density, viscosity, surface tension, diffusion, etc. For instance, some oils contain natural compounds that act as anti-agglomerants [10]. In one particular case some of these components have been identified to reside in the acid fraction [11]. Changing the acid content using this particular fraction will dramatically change the morphology of the formed hydrates but will only cause a negligible change in the equilibrium properties. The use of kinetic inhibitors and anti-agglomerants have exactly this effect, by either increasing the sub-cooling or forming solid dispersions, respectively. So, the presence of components that are, for practical purposes, inert with regard to the equilibrium conditions, may have a significant effect on the morphology of the hydrate phase. In many the cases the fluid phases are emulsified. The nature of the emulsion, i.e., water-in-oil or oil-in-water emulsion, as well as the wetting state of the hydrates will affect the hydrate formation in distinctly different ways. Therefore, emulsions in different oils may promote or inhibit the formation of hydratelumps [18].
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Table 1 The table contains an overview of the experimental observation and reference to corresponding figures
Fig. 1. The figure shows the sapphire crystal, and the stirrer which is to be mounted on top of the piston and inserted into the cell. The inner diameter of the cell is 26 mm and the length is 67 mm.
It is known that sub-cooling is often necessary to form hydrates. This observation points to the phenomenon of metastability and is a general effect observed when a new phase is formed. For instance, liquid water may be cooled to about −40 ◦ C at 1 bar, before freezing, and heated to about 279 ◦ C before boiling [7]. The cause of metastability derives from the ratio of surface to volume of the new phase. When the new phase is nucleating, the surface to volume ratio is large, therefore the sum of the changes in surface energy and chemical potential may be positive. This effect creates an energy barrier and as a consequence the nucleation rate will be slow, and kinetics become important [8]. In order to elucidate the above topics, continued research on the various aspects of hydrate formation is important to the oil industry. In this paper, some observations on hydrate formation is discussed from a wetting point of view. Concepts like morphology and induction time will be connected to basic wetting parameters, i.e., surface energies and contact angles. The effect of hydrates on emulsions will be discussed as well as the relative effects of gravity, turbulence and capillarity. The results have been obtained by applying standard surface chemistry and the classical theory of nucleation, to the phenomenon of hydrate formation. 2. Experimental observations 2.1. Setup Details of the experimental setup have been described elsewhere [19]. The main part of the setup is a cylindrical cell fitted with a sapphire section and a movable piston. The length of the sapphire cell is 67 mm while the inner diameter is 26 mm, yielding a visible volume of approximately 35.6 cm3 while the total volume is 100 cm3 . When fluids are loaded, volume adjustments are used to regulate the pressure. The cell is equipped with a stirrer, fitted on top of the piston, to ensure the desired equilibrium condition. Fig. 1 shows a picture of the cell and the stirrer. The cell is placed in an air bath and the temperature is monitored both in the air as well
Observation No.
Description
Figures
1
Complete phase inversion from water-in-oil to oil-in-water emulsion
Figs. 2 and 3
2
Oil-in-water emulsification upon hydrate formation
Figs. 4 and 5
3
The degree of aggregation, i.e., morphology seems to vary, a few oils create fully dispersed hydrates
Fig. 6
4
Initial hydrate formation seems to be either in bulk or at the interface, there is no evidence to support preferential formation at setup materials
Fig. 7
5
Without sufficient mixing, hydrate formation tend to stop because a hydrate layer leads to local depletion of hydrate formers
Fig. 7
as inside the cell. Temperature controls, pressure controls, and the piston are connected to a computer for remote and automatic control. The temperature can be varied between −40 and 200 ◦ C and the maximum pressure is 700 bar. The materials that are in contact with the fluids are mainly: stainless steel, sapphire crystal, and plastics and Teflon from gaskets. The surfaces roughness range from smooth to irregular and knife sharp edges. 2.2. Observations During routine measurements and research on hydrate behavior of a large number of both oil and gas condensates systems, some valuable observations have been made, over a period of several years. Below is a list of some of these observations which are important with regard to the discussions and considerations of this paper: Each observation is more thoroughly described below and Table 1 contains a list of the observations with reference to figures. Observation 1 (inversion) has been seen for a large number of systems during routine measurements. Fig. 2 shows stillimages from video recordings. Picture A of Fig. 2 shows the stirred water-in-oil emulsion system. In pictures B and C hydrates have formed and the emulsion seems bi-continuous. In picture D the inversion to oil-in-water is complete. Fig. 3 shows the corresponding volume–time recordings. The sudden drop in volume corresponds to hydrate formation. The main contribution to the volume change is due to the fact that gas molecules in the clathrates of the hydrate phase occupies less volume than in the gas phase. The volume change from picture A to D corresponds to insignificant amounts of water being converted to hydrates. Thus a very small amount of hydrates has a dramatic effect on the dynamics of the system. Observation 2 (emulsification) is similar and consistent to observation 1. In picture A of Fig. 4 is seen the water phase with the stirrer running and an oil phase being dragged into the water by the propeller action of the stirrer. The stirrer is not able to emulsify the water–oil system. As the system cools with time,
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Fig. 2. The figure shows that hydrate formation induces full emulsion inversion. Picture A shows a water-in-oil emulsion before hydrate has formed. Pictures B and C show the emulsions immediately after hydrate formation and during inversion. Picture D shows the inverted emulsion, i.e., oil-in-water. The volume/time development is shown in Fig. 3. The water content is 70% with regard to volume of the liquid phases at 1 bar, i.e., the water cut.
Fig. 3. The figure shows part of the volume/time development for the experiment where the pictures in Fig. 2 were taken. The letters refer to letters in Fig. 2 and show that the emulsion inversion occurs as only a negligible amount of hydrates has been formed.
the volume decreases according to the curve in Fig. 5. In picture B the oil–water interface has become rigid and deformed which are typical signs of hydrate formation. In picture C, the oil is beginning to emulsify as large drops of oil is dispatched into the water phase. In this particular system the hydrate formation stopped because a layer of hydrates prevented sufficient mass-transport between water and gas. In other systems that have been observed, a complete oil-in-water emulsion is formed during the initial stages of hydrate formation.
Morphology of formed hydrates is important with regard to the rheological properties of the resulting multi-phase solid suspension. Observation 3 (morphology) is illustrated in Fig. 6. Picture A of Fig. 6 shows an oil where the plugging tendency is significant while picture B shows an oil where a colloidal suspension of hydrate particles forms. The former case needs a more conservative hydrate strategy than the latter. Initially, hydrate formation is seen at the oil–water or oil–gas interface or in the bulk water phase (see Fig. 7). Hydrate formation may also occur in the oil phase, however due to opacity this is visually difficult to detect. Thus although the experimental setup contains a large number of different surfaces, observation 4 shows that the hydrates seem to nucleate at the interface between the aqueous and oil–gas phases. This is important with regard to where and how the hydrate phase nucleate and grow both in this system as well as in full sized pipelines. In observation 5 is emphasized that unless the stirring/turbulence in the system ensures good mixing, the hydrate formation will stop due to local depletion of hydrate formers and formation of a hydrate (layer). In other words, the driving force decrease to zero in the vicinity of the hydrates and the system is no longer in a state of overall thermodynamic equilibrium. Thus the hydrate layer has become an effective internal restraint and the total system may be classified as a composite system with an internal barrier to mass exchange [12]. This is important for a full sized pipeline. In the event of an unplanned shut-down, the situation in Fig. 7 may be realistic. The hydrate growth may stop due to internal barriers created by growing hydrates. As the line is restarted the growth may start again as new interfaces
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Fig. 5. The figure shows the volume–time development of the pictures in Fig. 4. The curve indicates no detectable amounts of hydrate formation. The turbulence in the system is too low to induce fresh interfaces, thus hydrate formation stops. The negative slope is due to a decreasing temperature.
Fig. 4. The figure shows that hydrate breaks apart and emulsify an otherwise separated well-defined oil–water interface. The volume–time development is shown in Fig. 5.
are created following turbulence and mixing. However, driving forces will usually decrease due to increasing temperature. As indicated above, stirring in the sense of full homogenization and/or mixing of the phases, is likely to remove this effect. As will be shown later, the above observations can be explained by the wetting properties of the total system. 3. Hydrate formation at the water–oil interface 3.1. Assumptions and system descriptions In order to simplify subsequent analysis some assumptions should be clarified. During the formation of a new phase either homogeneously in bulk, or heterogeneously at an interface, the phase grows
Fig. 6. The figure shows two oils giving widely different hydrate morphology. The upper picture shows a large lump of hydrates floating between oil and water. The lower picture shows a creamy dispersion of hydrates.
from molecular size of the order 10−10 m to the macroscopic visible size of 10−4 m. This is 6 orders of magnitude and it is assumed that the new phase may take the geometrical forms of lenses or spheres at all of these length scales. The wetting state of the system consisting of a hydrate phase, an aqueous and a hydrocarbon phase is defined by specifying the surface energies between the phases. Once the energies have
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Fig. 7. The figure shows that hydrate form mainly at the water gas interface and that formation stops due to slow diffusion unless mechanical forces are stronger.
been defined, the fractional area of the hydrate phase covered by water or oil at equilibrium is defined. It will be shown that the capillary force dominates when the particles are small, but the effects of wetting can be observed at any level. The actual shape of the nuclei and crystallites may be different than assumed herein, but that will not affect the arguments concerning the wetting, only the geometrical arrangements. It is therefore assumed that as the nuclei grow at the interface with defined wetting angles toward both phases, the surface energies dictate the position of the nuclei. The exact nature and shape of the nuclei are not known. In order to cover both fluid and solid cases, the two simplest geometrical arrangements, i.e., fluid lens and solid sphere, have been chosen. It will be shown that the there are no fundamental differences regarding the results and conclusions. For a discussion of the classical nucleation theory approximation and the complications therein we refer to Drossinos and Kevrekidis [13] and Ruckenstein and Djikaev [14]. For thorough discussions on nucleation in general we refer to Debenedetti [7] and Kashchiev [8]. In addition, any effects of line tension are not discussed in this paper, but there are several papers available in the literature on the topic [15–17]. The majority of observations referred to, are in crude oil systems. As mentioned in the introduction, crude oil consists of a large number of components. Particularly the pentane insoluble (asphaltene) and propane insoluble (resin) fractions may contain surface active agents. These fractions may be in the range of 20–30 wt% of the crude or for heavy oils even more.
So, once crude oil has been added to the system a large and unknown fraction of surfactants has been added. These crude oil surfactants have a tendency to change wettability of any material and also reduce the oil–water interfacial tension. The surface tension of the liquid n-alkanes versus water is in the range 45–55 mN/m, while crude oil–water is usually as low as 15–25 mN/m. The oil-indigenous surfactants will adsorb to any available surface. Thus, the surface energies will be lowered for all involved surfaces. Due to the high concentration of surfactants in oil, the system will not be as critically dependent upon small impurities as pure-component system of gas–water or model oil–water is. Therefore, measurement of metastability and induction time are probably less prone to errors that are dependent upon reproducibility of the system composition, when using a crude oil system. In multiphase flow systems at least four phases may be present before hydrates form. These phases are normally; aqueous phase, liquid hydrocarbon phase, gaseous hydrocarbon phase and a crystalline wax phase. Thus, hydrates will constitute the fifth phase. Hydrates will most likely form in the surface region of water. Neglecting environments like the pipe wall, water will have interfaces toward gaseous or liquid hydrocarbon. Due to gravity, the main part of the interface will be water–oil, however some water droplets may interface directly to the gas phase. Whether the interface is water–oil or water–gas does not change the wettability arguments, but the later arguments regarding buoyancy and turbulence is only sensible if the interface is water–oil. 3.2. Lenses The criteria for equilibrium of a lens residing at an fluid– fluid interface, can be formulated mechanically by equating the sum of the surface forces to zero. For a hydrate nucleus or crystallite shaped like a lens at the interface we may write [20] σow + σho + σhw = 0,
(1)
where σ denotes the surface force, where the magnitude is σ and the subscripts ow, ho, and hw denotes oil–water, hydrate– oil, and hydrate–water, respectively. Equation (1) is illustrated by the Neumann triangle which is shown in Fig. 8. The figure shows a wetting state defined by Eq. (1) and the particular values of the surface energies. These parameters defines the shape of the lens, in this case the lens is slightly more water than oil wet. This is because the hydrate–oil energy is higher than the hydrate–water energy, thus leading to γ < α. In general for triangles, the length of any side must be less than the sum of the two remaining, i.e., σow σhw + σho ,
σho σow + σhw ,
σhw σho + σow , (2)
the equality sign is only valid when two of the angles become 0 and the third π . The particular situations where the equalities are valid describe spreading of one phase between the two others. The Neumann triangle is then collapsed to a line. The three expressions that emerge are known as Antonow’s rules. These rules are exact expressions for the case of spreading:
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Fig. 8. Lens at the interface with tensions and the Neumann triangle drawn to scale. The wetting state is marked by a dashed circle in the wetting diagram of Fig. 9.
σow = σhw + σho hydrate spreading between oil and water,
(3a)
σho = σow + σhw water spreading between hydrate and oil,
(3b)
σhw = σho + σow oil spreading between hydrate and water.
(3c)
Equation (3b) describes the situation where water is spontaneously spreading on hydrates. This case is often assumed to be true for hydrates, and in water–gas systems it might be, although we are not aware of any conclusive evidence to support this. Equation (3c) is the situation where oil is the wetting phase. Any contact between hydrates and the oil phase will cause oil to spontaneously cover the hydrate surface. A film of oil will probably stop further growth as water is prevented to contact the hydrate surface. Hydrates spreading at the interface between oil and water is described by Eq. (3a). The concept of solids spreading on a fluid phase is perhaps counter-intuitive. It is however, merely a way of describing the phenomenon that the two fluid–hydrate contacts are energetically preferable compared to situations involving fluid–fluid contact. Later it is shown that this case implies zero induction time. The three equations describing spreading of one phase between the two others are special cases. All the wetting states is described by Eq. (1). This equation may be rewritten in a number of ways, for instance if we rearrange Eq. (1) and square both sides: ( σho + σhw )2 = (− σow )2 we get cos β =
2 σow
2 − σho
2 − σhw
2σho σhw
.
(4)
Similar expressions can also be formed for angles α and γ . So, a set of three equations can be derived (see below) but these are not independent [20]. Equation (4) may be regarded as Young’s equation extended for lenses at interfaces. In order to comprehend the above equation it is useful to draw a wetting diagram. This diagram determines the wetting angles once each interfacial tension has been fixed. Fig. 9 shows the wetting diagram
Fig. 9. Wetting map showing the lines of constant angles α, β, and γ . The oil– water interfacial tension is 30 mN/m. The dashed circle refers to realization of the lens in Fig. 8.
for the general three phase case. It can be adapted to hydrates by assuming that the microscopically freshly formed hydrate phase will grow in accordance with Eq. (1). The boundaries of the wetting states are given by Eq. (3). The lines inside are defined by constant angles α, β, and γ of Eq. (1). For instance, one line of constant β are formed by assigning constant values to β and σow and then rearrange Eq. (4) to get 2 cos2 β − σ 2 + σ 2 . σho = −σhw cos β ± σhw (5) ow hw By setting σow = 30 mN/m one obtains the β-curves of Fig. 9. Care must be taken to interpret the correct sign of the square root. By setting β = 0 and β = π , Antonow’s expressions are again recovered. For the water angle γ we may again rearrange Eq. (1) into: ( σow + σhw )2 = (− σho )2 to get 2 + σ 2 + 2σ σ cos γ σho = ± σow (6) ow hw hw and last, for the angle α we rearrange Eq. (1) into: ( σow + σho )2 = (− σhw )2 and get 2 cos2 α − σ 2 + σ 2 . σho = −σow cos α ± σow (7) ow hw As is evident from Fig. 8 the sum of the angles must be 2π . It can also be seen that, since the water and hydrocarbon phases are of a priori equal importance, there is symmetry around the axis: σho = σhw . Similar diagrams to Fig. 9 were previously adopted by Mori [21] for gas bubbles. Wetting diagrams are merely graphical illustrations of all possible wetting states. In the case of Fig. 9 the oil–water interfacial tension is kept constant. The point encircled by a dashed line corresponds to the lens of Fig. 8, thus we are at the exact point where the lines of α = 160◦ , β = 100◦ , and γ = 100◦ intersect. These particular angles for a lens corresponds to the
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surface energies that can be read from the diagram, and are listed in Fig. 8 as σow = 30 mN/m, σho = 30 mN/m, and σhw = 11 mN/m. By moving in the diagram one may determine angles and surface energies and thereby realize all possible wetting states for the given value of the oil–water interfacial tension. The wetting states are bounded on three sides by Antonow’s expressions. The work needed to form the new hydrate phase at the interface or in the bulk is usually written as [8] W (n) = −ng + ϕ(n) + ϕs (n) − ϕs,o ,
(8)
where n is the number of units in the nucleus, g is the driving force, which is defined positive within the hydrate stable region, ϕ is the interfacial energy of the new phase, ϕs is the interfacial energy of the interface after lens-formation, and ϕs,o is the interfacial energy before lens-formation. By geometric and energy consideration it can be shown that Eq. (8) can be written as W (n) = −ng + n2/3 cσe ,
(9)
where c is a constant and the effective surface energy, σe is defined by 1 σe = (1 + cos γ )2 (2 − cos γ ) 4 1/3 sin γ 3 2 (1 + cos α) (2 − cos α) σhw . + (10) sin α It follows from Eq. (9) that if the effective surface energy is zero then metastability disappears. The effective surface energy is a measure of the change in the system surface energy upon hydrate formation. From Eq. (10) the effective surface energy becomes zero when the angles γ and α both are zero. Physically this is the situation of hydrates spreading at the interface and we are at Antonow’s expressions which are visualized in Fig. 9. It should be remarked that the ratio (sin γ / sin α) seems to be undefined when the angles α and γ are 0 or π . However, the ratio will approach −1 as the angles approach 0 and π , respectively. This can be seen by using L’Hospital’s rule: lim
γ ,α→0,π
sin γ cos γ = lim = −1. sin α γ ,α→0,π cos α
(11)
In summary, by using Eq. (10), we write (α = π, β = π, γ = 0)
⇒
σe = σhw
water spreading, (α = π, β = 0, γ = π)
oil spreading.
of critical nuclei size is no longer meaningful because all nuclei is super-critical. This will always be the case if the sum of the surface energy after phase formation is equal to the surface energy before phase formation. According to Eq. (8) we may write the criterion as ϕ(n) + ϕs (n) − ϕs,o = 0.
(13)
A zero or negative effective surface energy is normally only possible for heterogeneous nucleation. In homogeneous nucleation the only surface term is φ(n) which is usually larger than zero. The effective surface energy σe , is plotted in the wetting diagram of Fig. 10. Again the area of mixed wetting is bounded by Antonow’s expressions. The figure links effective surface energy and wetting. Because σe is directly connected to the energy barrier of hydrate nucleation, Fig. 10 connects concepts like induction time to the wetting state of the system. As the effective surface energy increases the barrier increases and the induction time will increase, thus higher sub-cooling or increased supersaturation is needed in order to form hydrates.
(12a) ⇒
3.3. Hydrate spheres
σe = 0
hydrate “spreading,” (α = 0, β = π, γ = π)
Fig. 10. Wetting map showing the lines of constant effective energy for the case of a lens (σe ). At low surface energies we have hydrates spreading and zero effective surface energy. At high and low σho we have water and oil spreading, respectively. The dashed circle shows the lens geometry of Fig. 8 and indicates that the effective energy is approximately 8 mN/m for this case. The oil–water interfacial tension is 30 mN/m.
(12b) ⇒
σe = σho (12c)
It should be mentioned that Eq. (12c) is obtained by symmetry. As mentioned, when σe = 0, metastability vanishes because the work W (n) = −ng will be negative or zero for all positive driving forces. The maximum work is at n = 0, and the concept
In the case where the hydrates are perceived as spherical even though they grow at an interface, the equations are simplified due to the spherical geometry. Antonow’s expressions (3) are still valid, except for the case where hydrates are spreading, so the set is reduced to the following two equations: σho = σow + σhw
water spreading,
σhw = σho + σow
oil spreading.
(14)
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Fig. 11. The figure shows a hydrate sphere at a given wetting state at the interface between oil and water. The tensions are drawn to scale. This wetting state is indicated in the wetting diagram of Fig. 12 by a dashed circle.
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Fig. 13. The figure shows the effective surface energies for a sphere. At low surface energies the effective surface energy becomes zero and hydrate will form spontaneously. At high and low σho we have water and oil spreading, respectively. The dashed circle indicates the geometry of Fig. 11 and that the effective surface energy is approximately 17 mN/m. The oil–water interfacial tension is 30 mN/m.
Investigating the work function as for the lens case of Eq. (8), leads to the following expression for σe : 1 σe = σhw − σow (1 + cos γ )2 . (16) 4 The work needed for a new phase to form becomes negative when σe = 0. We may write
Fig. 12. The figure shows the wetting diagram of the hydrate sphere at the interface. The dashed circle indicates the geometry shown in Fig. 11. The oil–water interfacial tension is 30 mN/m.
In addition, at equilibrium we have Young’s equation which reads σho − σhw = σow cos γ
(15)
which is seen to reduce to Antonow’s for the cases where γ = 0 and γ = π , respectively. All possible geometric realizations for a sphere at the interface between two fluids are between these two extremes (for a given σow ). One particular geometrical configuration is shown in Fig. 11. The sphere, of radius r, is immersed a given distance ho into the oil phase and the remaining part is immersed hw into the water phase. Fig. 12 shows the lines of constant water angle γ , in the wetting diagram of the sphere. The diagram is much simpler than in the lens case due to constancy of β = π and the fact that γ = π − α. The lines in Fig. 12 indicate not only constant γ but also constant difference σho − σhw .
1 σhw = σow (1 + cos γ )2 . (17) 4 The plot of constant values for σe for the case of the sphere is shown in Fig. 13. It is interesting to see that for the lens case the mixed wetting area is defined by Antonow’s expressions (3), which also coincides with the area where σe can be defined (see Figs. 9 and 10). The case for spheres shows that according to Young’s equation (15), we may realize mixed wetted spheres along every line in the diagram of Fig. 12. However, when we examine the effective surface energy σe , then it is seen that one may obtain negative values which at first seems unphysical. As mentioned, the effective surface energy of the system is a measure of the change in surface energy upon hydrate formation, and as such σe may become zero or negative. Hence the energy barrier to hydrate formation may become zero or negative. When this barrier is zero or negative hydrate formation will be spontaneous. In summary we have 1 σhw > σow (1 + cos γ )2 4 1 σhw = σow (1 + cos γ )2 4
positive energy barrier,
(18a)
zero energy barrier “Antonov,” (18b)
1 σhw < σow (1 + cos γ )2 negative energy “barrier,” (18c) 4 where the equality sign will is an analogue for Antonow’s rule in the case of solid spheres.
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If we introduce some foreign material that have large surface energy toward water, then hydrate formation may be spontaneously induced. With regard to Eq. (18) we may say that we introduce a water–material surface energy which may be much higher than the water–oil surface energy. Therefore Eq. (18c) will be effective and hydrates will form spontaneously and thereby the system energy is reduced. A common example is to put dry grains of sand in a supersaturated solution of freon/water or tetra-hydro-furan/water mixture. If however, the same material, i.e., sand grains, was equilibrated in the mixture, then the surface energy would be lowered due to reactions between the surface and the fluids and the effect will vanish or be much less dramatic (ref. observation 4: interface). For the case of flow in pipelines, sand and other mineral particles will be wetted by water and oil, and thus either hydrolyzed by the water phase at a given pH or adsorbed by oil components like asphaltenes and wax. Therefore it is to be expected that hydrate formation will take place mainly at the oil–water interface also in pipelines. 4. Morphology 4.1. Turbulence, bouancy, and capillarity Hydrate growth is mainly at the interface between the aqueous and hydrocarbon phases. This can be due to mixed wetting and/or local driving forces during growth. Hence, in order to determine whether the particle will stay at the interface or not during growth we examine simple expressions for the forces. If it is assumed that there is a certain degree of turbulence in the system, either sustained by flow in a pipeline or by simple stirring in a closed cell, then the particles will be subjected to turbulent forces in addition to the capillary and buoyant forces. In the following discussion forces acting vertically is considered positive. Furthermore the shear force is assumed negligible due to small velocity gradients far from the pipe wall. The sum of the forces will determine the trajectory of the particle. Such calculations are outside the scope of this article but we may calculate the importance of the various forces in the vertical direction. Assuming spherical particles, the turbulent force that acts on the particle by the fluid can be written as [22] Ft = 0.18πρh u2 r 2 f,
(19)
where ρh is the hydrate density, u is the mean fluid velocity, r is the particle radius, and f is the friction factor which may be defined by, f = 0.316/Re0.25 , where Re is the Reynolds number for single phase pipe flow and is given by Re = ρud/η, where η is the fluid viscosity, d is the pipe diameter, and, finally, ρ is the fluid density. The turbulent force on the particle is dependent upon the fluid properties of the phase in which it is immersed. However, for the present discussion it is sufficient to assume that this phase is always the water phase. In contrast to the turbulent energy which may remove the particle from the interface, gravity may act to keep the particle at the interface. This is due to the fact that solid hydrates in petroleum systems often have densities intermediate to the values
of oil and water. Densities of oil varies from light condensates with densities possibly lower than 500 kg/m3 to heavy crude which has a densities from 930 kg/m3 and upward. Since hydrates have densities from 920 kg/m3 they will most likely float in heavy oil. The buoyancy of a particle partly submerged in oil and water is Fb = (ρh − ρw )gVw + (ρh − ρo )gVo ,
(20)
where Vw and Vo are the volumes of the part of the sphere which is submerged in water and oil, respectively. The sum of the volume in the oil and in the water must be equal to total volume of the hydrate sphere, Vh with radius r (see Fig. 11). So, by use of Vh = Vw + Vo we get Fb = (ρhw Vh − ρow Vo )g,
(21)
where ρhw and ρow are the differences in density between hydrate–water and oil–water, respectively. The volume of the spherical cap can be substituted by Vo = π(rh2o − h3o /3)
πg 3 Fb = (22) 4r ρhw − 3rh2o − h3o ρow . 3 Finally, we consider the capillary force on the particle which can be taken directly from Young’s equation as Fc = −2πr(σow cos γ − σho + σhw ),
(23)
where the immersion depth ho and the wetting angle γ is connected by ho = r(1 − cos γ ). Considering only the vertical component, Fcv , we can write the vertical capillary force component as Fcv = Fc sin γ . The particle experience the sum of these forces Fp = Fcv + Fb + Ft . When the sum equals zero (Fp = 0) the system is at equilibrium. Keeping the radius constant one may determine how the total force varies as a function of immersion depth ho . Fig. 14 shows the individual forces and the sum plotted as a function of the immersion depth normalized by the particle diameter, hon = ho /2r. It can be seen that at a particle radius of 0.1 m buoyancy (Fb ) is dominating because the buoyancy force is approximately equal to the total particle force. At a radius of 0.01 m the buoyancy and capillary forces are in the same range and no single force is dominating. Finally, at r = 0.001 m the capillary force is seen to be of equal magnitude as the total particle force. Thus, capillarity dominates completely. As the hydrate particles grow, bouancy and capillarity determines the location of the particle. Particles smaller than 0.01 m will be largely dominated by the wetting properties. This balance of the forces will have impact on the hydrate particle size distributions. The effect may be illustrated by increasing the density of the oil phase to ρo = 940 kg/m3 , which is equivalent to an API of 19. The results are shown in Fig. 15. With the current wetting properties (Table 2 and Fig. 11) the particle is bound to the interface as long as the radius is sufficiently small. The lower graph of Fig. 15 shows that the sum of the forces are zero for a given value ho meaning that the particle is at equilibrium at the interface. The two upper upper graphs show that when the radius is increased to 0.01 m buoyancy removes the particle from the interface. Therefore, hydrates will continue growth at the interface until buoyancy removes it. In
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Fig. 14. The figure shows the forces acting on the particle. The top figure shows that the bouancy force is the main contributor to the total force. The middle figure shows that at a radius of 0.01 m the buoyancy and capillary forces are of the same magnitude. Finally, the lower figure shows that at a radius of 0.001 m the capillary force dominates. Table 2 The table lists the parameter values used for calculating the curves of Figs. 14 and 15. Superscripts 1 and 2 refer to Figs. 14 and 15, respectively Property
Value
ρw , density water (kg/m3 ) ρo , density oil (kg/m3 ) ρh , density hydrate (kg/m3 ) σow , oil/water surface energy (N/m) σho , hydrate/oil surface energy (N/m) σhw , hydrate/water surface energy (N/m) η, viscosity water (Pa s) d, pipe diameter (inches) U , volume flow (m3 /day)
998.0 800.01 940.02 920.0 0.030 0.035 0.020 0.001 8.0 2500
the oil phase hydrate growth will occurs at a different rate than at the interface or in the water phase. In this particular case where the hydrate particle is mostly water wet (see Fig. 11) it will probably be sticky in the oil phase. Due to the different paths toward equilibrium, the morphology of the resulting equilibrated system will be different. It should be remarked that the true equilibrium state is unique, and cannot vary according to the path but the present variations, although visually large may be considered energetically small.
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Fig. 15. The figure shows the forces acting on the particle. The equilibrium position is determined by the point where the total force Fp is zero. As the particle grows it gradually extends into the oil phase until it is completely immersed in oil due to bouancy.
4.2. Emulsions Systems composed of oil and water are often characterized by the water cut. The water cut is defined as the water volume fraction of the produced liquids at 15 ◦ C and 1 bar. The definition is well suited to a stirred cell where it is possible to mix all fluids thoroughly, as well as to produced fluids. The water cut is important because it is used as a parameter to characterize the emulsion properties. However, for systems flowing in a pipe, the amounts of water locally have to be related to the degree of turbulence locally. It is therefore possible to observe both oil-in-water emulsions, water-in-oil emulsions, and inversion states for a pipe line system at constant water cut. For the present discussion we assume that we have either water-in-oil or oil-in-water emulsions, and the water cut is left to be defined for any given case. In the following analysis the theory of particle stabilized emulsions has been utilized [23–25]. There are two aspects of hydrates and emulsions, first the impact of hydrates on the emulsion characteristics and second the effect of emulsions on the hydrate growth. Hydrate nuclei and crystallites will be wetted at the interface according to the surface energies previously discussed.
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Table 3 The table contains an overview of the initial emulsion state and the effects of hydrate formation for water wetted and oil wetted hydrates Initial state
Water wetted γ < π/2
Oil wetted γ > π/2
Water-in-oil
Destabilizing, separation, inversion to oil-in-water. Inhibits hydrate growth before inversion. Aggregate formation likely
Stabilizing, break up of droplets and more interface generated. Hydrate growth is instantly promoted. Dispersion is probable
Oil-in-water
Stabilizing and possible break up of droplets. New interface forms in water and hydrate growth will probably accelerate. Eventual aggregation is likely
Destabilizing, droplets will grow and oil separate from water. Eventually inversion may occur. Initially hydrate growth is inhibited due to decreasing interfacial area
Separated/stratified
Oil-in-water emulsion may form. Interfacial area increases thus hydrate growth is promoted. Aggregation is likely
Water-in-oil emulsions may be generated. Increasing interfacial area promotes hydrate growth. Dispersions due to oil wetting is likely
First we assume that the flow regime is such that there is a water-in-oil emulsion locally and that water wetted hydrates (γ < π/2) nucleate at this location. The main volume of the particles will then be inside the water droplet and the droplet will be destabilized. The droplet size distribution will then tend toward a higher mean value thus promoting separation and eventually, if possible, phase inversion (ref. observations 1 and 2: inversion and emulsification). Initially, the interfacial area will decrease due to droplet growth and it is to be expected that hydrate formation will be temporarily inhibited. Because the hydrates are water wetted any contact with water will lead to growth and it is likely that aggregates will form. If the hydrates are oil wetted (γ > π/2) then the water droplets will be further stabilized and may even break up to form smaller droplets. This effect will lead to an increase in the interfacial area and accelerated hydrate growth. Droplet contact with water will not cause aggregation to the same extent as at lower wetting angles, thus one may expect dispersions to form (ref. observation 3: morphology). Second, we assume that an oil-in-water emulsion has formed locally and that water wetted (γ < π/2) hydrates are forming. The hydrates will stabilize the emulsion and even promote break up of droplets thereby increasing the interfacial area and accelerate the hydrate growth. The hydrates are water wetted therefore aggregation is likely to take place. If the hydrates are oil wetted (γ > π/2) then the droplets will be destabilized and interfacial area will decrease until phase inversion takes place. Hydrate growth will therefore be temporarily inhibited. The process will most likely lead to a dispersion of hydrates. As described above, the initial emulsion state is important with regard to the hydrate growth, and the wetting state determines the direction of the changes, i.e., toward aggregation or dispersion. In a flow regime where the rates are too low to emulsify the phases the flow may be stratified or layered. Hydrate formation at the interface may then induce emulsification. The produced emulsions will be a function of the hydrate wettability. Thus water wetted (γ < π/2) hydrates will produce oil-in-water emulsions and vice versa. It is worth noticing that although one process leads to aggregates while the other leads to dispersion, both will enhance hydrate growth due to formation of new interfaces. The different scenarios and instances involving emulsions and hydrates are summarized in Table 3.
Fig. 16. The figure illustrates how movements in the wetting diagram may induce morphology changes at constant effective surface energy or vice versa. The oil–water interfacial tension is 30 mN/m.
5. Kinetics and agglomeration From the previous section we can deduce that by increasing the value of surface energy term in the work function, it is possible to manipulate the kinetics. It is to be expected that the induction time will increase as the work needed to form the new phase increase, i.e., as the effective surface energy increases. This has been illustrated by the diagonal arrow from lower left to upper right in Fig. 16. If we keep the surface energy term constant and vary the wetting angles, i.e., moving along the other diagonal of Fig. 16, we either end up at oil spreading or water spreading on hydrates. The morphology of the hydrates is expected to be dependent upon the wetting state. Oil wetted hydrates will form a dispersion of hydrates while water wetting will form aggregates [26]. The diagram in Fig. 16 connects wetting, kinetics and morphology showing exactly how parameters should be manipulated in order to achieve either dispersions or long induction times or both. 6. Conclusions During nucleation of hydrates at an interface or in the bulk of a phase, the detailed state of wetting is a key factor in determining the fate of the freshly formed crystallites.
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Depending on flow and turbulence, water wetted hydrates will most likely lead to large aggregates of hydrates while oil wetted hydrates will lead to flowable dispersions. At certain conditions the limit of metastability can be defined by the effective surface energies for a given geometry. Equating the effective surface energy term of the work function to zero, will define the metastability limit. Capillary forces dominates both turbulence and gravity when the hydrate crystallites are less than 10−3 m in diameter. Acknowledgments The authors thank Norsk Hydro for the permission to publish these results. Thanks also to Sylvi Hoiland, Arne Valle and Finn Gunnar Nielsen for helpful discussions regarding this work. References [1] E.D. Sloan, Clathrates Hydrates of Natural Gases, second ed., Dekker, New York, 1998. [2] Y.F. Makogon, Hydrates of Natural Gas, PennWell, Tulsa, 1981. [3] E. Berecz, M. Balla-Achs, Gas Hydrates, Elsevier, Amsterdam, 1983. [4] B. Beauchamp, C. R. Geosci. 336 (2004) 751–765. [5] H. Davy, Philos. Trans. R. Soc. 110 (1811) 155–162. [6] E.D. Sloan, Fluid Phase Equilib. 228–229 (2005) 67–74. [7] P.G. Debenedetti, Metastable Liquids, Concepts and Principles, Princeton Univ. Press, Princeton, NJ, 1996. [8] D. Kashchiev, Nucleation Basic Theory with Applications, Butterworth– Heinemann, Oxford, 2000. [9] K.S. Pedersen, P.L. Christensen, Phase Behavior of Petroleum Fluids, CRC Press, Boca Raton, FL, 2007.
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[10] F.H. Fadnes, Fluid Phase Equilib. 117 (1996) 186–192. [11] S. Hoiland, A.E. Borgund, T. Barth, P. Fotland, K.M. Askvik, Wettability of freon hydrates in crude oil/brine emulsions: The effects of chemical additives, in: Proceedings of the Fifth International Conference on Gas Hydrates, Trondheim, June 13–16, 2005. [12] J.W. Tester, M. Modell, Thermodynamics and Its Applications, Prentice Hall, New York, 1997. [13] Y. Drossinos, P.G. Kevrekidis, Phys. Rev. E 67 (2003). [14] E. Ruckenstein, Y.S. Djikaev, Adv. Colloid Interface Sci. 118 (2005) 51– 72. [15] A. Amirfazli, A.W. Neumann, Adv. Colloid Surface Sci. 110 (2004) 121– 141. [16] B. Widom, Colloids Surf. A 239 (2004) 141–144. [17] A.I. Rusanov, A.K. Shchekin, D.V. Tatyanenko, Colloids Surf. A 250 (2004) 263–268. [18] T. Austvik, X. Li, L.H. Gjertsen, in: G.D. Holder, P.R. Bishnoi (Eds.), Gas Hydrates, Challenges for the Future, in: Annals of the New York Academy of Sciences, vol. 912, 2000. [19] L.H. Gjertsen, F.H. Fadnes, in: G.D. Holder, P.R. Bishnoi (Eds.), Measurements and Prediction of Hydrate Equilibrium Conditions, in Gas Hydrates, Challenges for the Future, in: Annals of the New York Academy of Sciences, vol. 912, 2000. [20] J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity, Clarendon Press, Oxford, 1982. [21] Y.H. Mori, Int. J. Multiphase Flow 11 (1985) 571–576. [22] A. Valle, Three phase gas–oil–water flow, Ph.D. thesis, Imperial College London, 2000. [23] D.E. Tambe, M.E. Sharma, Adv. Colloid Interface Sci. 52 (1994) 1–63. [24] R. Aveyard, B.P. Binks, J.H. Clint, Adv. Colloid Interface Sci. 100–102 (2003) 503–546. [25] B.P. Binks, S.O. Lumsdon, Phys. Chem. Chem. Phys. 2 (2000) 2959– 2967. [26] S. Hoiland, K.M. Askvik, P. Fotland, E. Alagic, T. Barth, F.H. Fadnes, J. Colloid Interface Sci. 287 (2005) 217–225.
Some aspects of hydrate formation and wetting P. Fotland ∗ , K.M. Askvik StatoilHydro ASA, Research Center Bergen, Norway Received 25 October 2007; accepted 18 January 2008 Available online 29 January 2008
Abstract Experimental observations of gas hydrate formation have shown that, in the initial nucleation and crystallization process, water–oil emulsions may be generated, destabilized or even inverted. These phenomena are consistent with the effects of particles on emulsions. In this work we relate experimental observations of hydrate formation to the phenomenon of wettability. It is shown that details of hydrate wetting are important for both the morphology and the kinetics of the formed hydrates. For the cases of hydrate lenses and spheres, it is shown that the various wetting states can be illustrated and analyzed by using wetting diagrams. Metastability is a function of the surface energies of the hydrate formation, i.e., the wetting state, and it is shown that in some cases metastability vanishes, and thus hydrates nucleates instantly at all positive driving forces. The magnitude of buoyancy and turbulence forces acting on a hydrate sphere are compared to the capillary force and it is concluded that capillary energy dominates when the hydrate spheres is less than 1 mm. © 2008 Elsevier Inc. All rights reserved. Keywords: Hydrates; Wettability; Metastability; Agglomeration
1. Introduction The formation of hydrates and its relation to production and transport of crude oil has been described and discussed in a number of articles and books [1–5]. Hydrate formation in pipelines and process equipment continues to be a phenomenon related both to hazard and high cost. The usual hydrate strategy states that positive driving forces for hydrate formation should be avoided. The basis of the strategy is that once the driving forces are positive the system will immediately generate a solid hydrate plug and production is shut down. Many operators find that in practice this is not always the case, hence the strategy is too conservative. Considerable amounts of chemicals can be saved by changing the strategy. In turn, a less conservative strategy may lead to developments that may have otherwise have been abandoned [6]. The presence of crude oil is known to have some impact on the hydrate formation. Oil in general consists of a large number of different chemical groups of molecules. The largest group is normally the hydrocarbons which again may be subdivided into * Corresponding author.
E-mail address: [email protected] (P. Fotland). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.01.031
groups like paraffins, naphtenes and aromatics [9]. In addition to hydrocarbons, there are solubility classes like asphaltenes and resins, and also well defined groups like acids and bases. Each oil is a unique mixture of these components which will define the physical properties of the crude like, density, viscosity, surface tension, diffusion, etc. For instance, some oils contain natural compounds that act as anti-agglomerants [10]. In one particular case some of these components have been identified to reside in the acid fraction [11]. Changing the acid content using this particular fraction will dramatically change the morphology of the formed hydrates but will only cause a negligible change in the equilibrium properties. The use of kinetic inhibitors and anti-agglomerants have exactly this effect, by either increasing the sub-cooling or forming solid dispersions, respectively. So, the presence of components that are, for practical purposes, inert with regard to the equilibrium conditions, may have a significant effect on the morphology of the hydrate phase. In many the cases the fluid phases are emulsified. The nature of the emulsion, i.e., water-in-oil or oil-in-water emulsion, as well as the wetting state of the hydrates will affect the hydrate formation in distinctly different ways. Therefore, emulsions in different oils may promote or inhibit the formation of hydratelumps [18].
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Table 1 The table contains an overview of the experimental observation and reference to corresponding figures
Fig. 1. The figure shows the sapphire crystal, and the stirrer which is to be mounted on top of the piston and inserted into the cell. The inner diameter of the cell is 26 mm and the length is 67 mm.
It is known that sub-cooling is often necessary to form hydrates. This observation points to the phenomenon of metastability and is a general effect observed when a new phase is formed. For instance, liquid water may be cooled to about −40 ◦ C at 1 bar, before freezing, and heated to about 279 ◦ C before boiling [7]. The cause of metastability derives from the ratio of surface to volume of the new phase. When the new phase is nucleating, the surface to volume ratio is large, therefore the sum of the changes in surface energy and chemical potential may be positive. This effect creates an energy barrier and as a consequence the nucleation rate will be slow, and kinetics become important [8]. In order to elucidate the above topics, continued research on the various aspects of hydrate formation is important to the oil industry. In this paper, some observations on hydrate formation is discussed from a wetting point of view. Concepts like morphology and induction time will be connected to basic wetting parameters, i.e., surface energies and contact angles. The effect of hydrates on emulsions will be discussed as well as the relative effects of gravity, turbulence and capillarity. The results have been obtained by applying standard surface chemistry and the classical theory of nucleation, to the phenomenon of hydrate formation. 2. Experimental observations 2.1. Setup Details of the experimental setup have been described elsewhere [19]. The main part of the setup is a cylindrical cell fitted with a sapphire section and a movable piston. The length of the sapphire cell is 67 mm while the inner diameter is 26 mm, yielding a visible volume of approximately 35.6 cm3 while the total volume is 100 cm3 . When fluids are loaded, volume adjustments are used to regulate the pressure. The cell is equipped with a stirrer, fitted on top of the piston, to ensure the desired equilibrium condition. Fig. 1 shows a picture of the cell and the stirrer. The cell is placed in an air bath and the temperature is monitored both in the air as well
Observation No.
Description
Figures
1
Complete phase inversion from water-in-oil to oil-in-water emulsion
Figs. 2 and 3
2
Oil-in-water emulsification upon hydrate formation
Figs. 4 and 5
3
The degree of aggregation, i.e., morphology seems to vary, a few oils create fully dispersed hydrates
Fig. 6
4
Initial hydrate formation seems to be either in bulk or at the interface, there is no evidence to support preferential formation at setup materials
Fig. 7
5
Without sufficient mixing, hydrate formation tend to stop because a hydrate layer leads to local depletion of hydrate formers
Fig. 7
as inside the cell. Temperature controls, pressure controls, and the piston are connected to a computer for remote and automatic control. The temperature can be varied between −40 and 200 ◦ C and the maximum pressure is 700 bar. The materials that are in contact with the fluids are mainly: stainless steel, sapphire crystal, and plastics and Teflon from gaskets. The surfaces roughness range from smooth to irregular and knife sharp edges. 2.2. Observations During routine measurements and research on hydrate behavior of a large number of both oil and gas condensates systems, some valuable observations have been made, over a period of several years. Below is a list of some of these observations which are important with regard to the discussions and considerations of this paper: Each observation is more thoroughly described below and Table 1 contains a list of the observations with reference to figures. Observation 1 (inversion) has been seen for a large number of systems during routine measurements. Fig. 2 shows stillimages from video recordings. Picture A of Fig. 2 shows the stirred water-in-oil emulsion system. In pictures B and C hydrates have formed and the emulsion seems bi-continuous. In picture D the inversion to oil-in-water is complete. Fig. 3 shows the corresponding volume–time recordings. The sudden drop in volume corresponds to hydrate formation. The main contribution to the volume change is due to the fact that gas molecules in the clathrates of the hydrate phase occupies less volume than in the gas phase. The volume change from picture A to D corresponds to insignificant amounts of water being converted to hydrates. Thus a very small amount of hydrates has a dramatic effect on the dynamics of the system. Observation 2 (emulsification) is similar and consistent to observation 1. In picture A of Fig. 4 is seen the water phase with the stirrer running and an oil phase being dragged into the water by the propeller action of the stirrer. The stirrer is not able to emulsify the water–oil system. As the system cools with time,
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Fig. 2. The figure shows that hydrate formation induces full emulsion inversion. Picture A shows a water-in-oil emulsion before hydrate has formed. Pictures B and C show the emulsions immediately after hydrate formation and during inversion. Picture D shows the inverted emulsion, i.e., oil-in-water. The volume/time development is shown in Fig. 3. The water content is 70% with regard to volume of the liquid phases at 1 bar, i.e., the water cut.
Fig. 3. The figure shows part of the volume/time development for the experiment where the pictures in Fig. 2 were taken. The letters refer to letters in Fig. 2 and show that the emulsion inversion occurs as only a negligible amount of hydrates has been formed.
the volume decreases according to the curve in Fig. 5. In picture B the oil–water interface has become rigid and deformed which are typical signs of hydrate formation. In picture C, the oil is beginning to emulsify as large drops of oil is dispatched into the water phase. In this particular system the hydrate formation stopped because a layer of hydrates prevented sufficient mass-transport between water and gas. In other systems that have been observed, a complete oil-in-water emulsion is formed during the initial stages of hydrate formation.
Morphology of formed hydrates is important with regard to the rheological properties of the resulting multi-phase solid suspension. Observation 3 (morphology) is illustrated in Fig. 6. Picture A of Fig. 6 shows an oil where the plugging tendency is significant while picture B shows an oil where a colloidal suspension of hydrate particles forms. The former case needs a more conservative hydrate strategy than the latter. Initially, hydrate formation is seen at the oil–water or oil–gas interface or in the bulk water phase (see Fig. 7). Hydrate formation may also occur in the oil phase, however due to opacity this is visually difficult to detect. Thus although the experimental setup contains a large number of different surfaces, observation 4 shows that the hydrates seem to nucleate at the interface between the aqueous and oil–gas phases. This is important with regard to where and how the hydrate phase nucleate and grow both in this system as well as in full sized pipelines. In observation 5 is emphasized that unless the stirring/turbulence in the system ensures good mixing, the hydrate formation will stop due to local depletion of hydrate formers and formation of a hydrate (layer). In other words, the driving force decrease to zero in the vicinity of the hydrates and the system is no longer in a state of overall thermodynamic equilibrium. Thus the hydrate layer has become an effective internal restraint and the total system may be classified as a composite system with an internal barrier to mass exchange [12]. This is important for a full sized pipeline. In the event of an unplanned shut-down, the situation in Fig. 7 may be realistic. The hydrate growth may stop due to internal barriers created by growing hydrates. As the line is restarted the growth may start again as new interfaces
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Fig. 5. The figure shows the volume–time development of the pictures in Fig. 4. The curve indicates no detectable amounts of hydrate formation. The turbulence in the system is too low to induce fresh interfaces, thus hydrate formation stops. The negative slope is due to a decreasing temperature.
Fig. 4. The figure shows that hydrate breaks apart and emulsify an otherwise separated well-defined oil–water interface. The volume–time development is shown in Fig. 5.
are created following turbulence and mixing. However, driving forces will usually decrease due to increasing temperature. As indicated above, stirring in the sense of full homogenization and/or mixing of the phases, is likely to remove this effect. As will be shown later, the above observations can be explained by the wetting properties of the total system. 3. Hydrate formation at the water–oil interface 3.1. Assumptions and system descriptions In order to simplify subsequent analysis some assumptions should be clarified. During the formation of a new phase either homogeneously in bulk, or heterogeneously at an interface, the phase grows
Fig. 6. The figure shows two oils giving widely different hydrate morphology. The upper picture shows a large lump of hydrates floating between oil and water. The lower picture shows a creamy dispersion of hydrates.
from molecular size of the order 10−10 m to the macroscopic visible size of 10−4 m. This is 6 orders of magnitude and it is assumed that the new phase may take the geometrical forms of lenses or spheres at all of these length scales. The wetting state of the system consisting of a hydrate phase, an aqueous and a hydrocarbon phase is defined by specifying the surface energies between the phases. Once the energies have
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Fig. 7. The figure shows that hydrate form mainly at the water gas interface and that formation stops due to slow diffusion unless mechanical forces are stronger.
been defined, the fractional area of the hydrate phase covered by water or oil at equilibrium is defined. It will be shown that the capillary force dominates when the particles are small, but the effects of wetting can be observed at any level. The actual shape of the nuclei and crystallites may be different than assumed herein, but that will not affect the arguments concerning the wetting, only the geometrical arrangements. It is therefore assumed that as the nuclei grow at the interface with defined wetting angles toward both phases, the surface energies dictate the position of the nuclei. The exact nature and shape of the nuclei are not known. In order to cover both fluid and solid cases, the two simplest geometrical arrangements, i.e., fluid lens and solid sphere, have been chosen. It will be shown that the there are no fundamental differences regarding the results and conclusions. For a discussion of the classical nucleation theory approximation and the complications therein we refer to Drossinos and Kevrekidis [13] and Ruckenstein and Djikaev [14]. For thorough discussions on nucleation in general we refer to Debenedetti [7] and Kashchiev [8]. In addition, any effects of line tension are not discussed in this paper, but there are several papers available in the literature on the topic [15–17]. The majority of observations referred to, are in crude oil systems. As mentioned in the introduction, crude oil consists of a large number of components. Particularly the pentane insoluble (asphaltene) and propane insoluble (resin) fractions may contain surface active agents. These fractions may be in the range of 20–30 wt% of the crude or for heavy oils even more.
So, once crude oil has been added to the system a large and unknown fraction of surfactants has been added. These crude oil surfactants have a tendency to change wettability of any material and also reduce the oil–water interfacial tension. The surface tension of the liquid n-alkanes versus water is in the range 45–55 mN/m, while crude oil–water is usually as low as 15–25 mN/m. The oil-indigenous surfactants will adsorb to any available surface. Thus, the surface energies will be lowered for all involved surfaces. Due to the high concentration of surfactants in oil, the system will not be as critically dependent upon small impurities as pure-component system of gas–water or model oil–water is. Therefore, measurement of metastability and induction time are probably less prone to errors that are dependent upon reproducibility of the system composition, when using a crude oil system. In multiphase flow systems at least four phases may be present before hydrates form. These phases are normally; aqueous phase, liquid hydrocarbon phase, gaseous hydrocarbon phase and a crystalline wax phase. Thus, hydrates will constitute the fifth phase. Hydrates will most likely form in the surface region of water. Neglecting environments like the pipe wall, water will have interfaces toward gaseous or liquid hydrocarbon. Due to gravity, the main part of the interface will be water–oil, however some water droplets may interface directly to the gas phase. Whether the interface is water–oil or water–gas does not change the wettability arguments, but the later arguments regarding buoyancy and turbulence is only sensible if the interface is water–oil. 3.2. Lenses The criteria for equilibrium of a lens residing at an fluid– fluid interface, can be formulated mechanically by equating the sum of the surface forces to zero. For a hydrate nucleus or crystallite shaped like a lens at the interface we may write [20] σow + σho + σhw = 0,
(1)
where σ denotes the surface force, where the magnitude is σ and the subscripts ow, ho, and hw denotes oil–water, hydrate– oil, and hydrate–water, respectively. Equation (1) is illustrated by the Neumann triangle which is shown in Fig. 8. The figure shows a wetting state defined by Eq. (1) and the particular values of the surface energies. These parameters defines the shape of the lens, in this case the lens is slightly more water than oil wet. This is because the hydrate–oil energy is higher than the hydrate–water energy, thus leading to γ < α. In general for triangles, the length of any side must be less than the sum of the two remaining, i.e., σow σhw + σho ,
σho σow + σhw ,
σhw σho + σow , (2)
the equality sign is only valid when two of the angles become 0 and the third π . The particular situations where the equalities are valid describe spreading of one phase between the two others. The Neumann triangle is then collapsed to a line. The three expressions that emerge are known as Antonow’s rules. These rules are exact expressions for the case of spreading:
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Fig. 8. Lens at the interface with tensions and the Neumann triangle drawn to scale. The wetting state is marked by a dashed circle in the wetting diagram of Fig. 9.
σow = σhw + σho hydrate spreading between oil and water,
(3a)
σho = σow + σhw water spreading between hydrate and oil,
(3b)
σhw = σho + σow oil spreading between hydrate and water.
(3c)
Equation (3b) describes the situation where water is spontaneously spreading on hydrates. This case is often assumed to be true for hydrates, and in water–gas systems it might be, although we are not aware of any conclusive evidence to support this. Equation (3c) is the situation where oil is the wetting phase. Any contact between hydrates and the oil phase will cause oil to spontaneously cover the hydrate surface. A film of oil will probably stop further growth as water is prevented to contact the hydrate surface. Hydrates spreading at the interface between oil and water is described by Eq. (3a). The concept of solids spreading on a fluid phase is perhaps counter-intuitive. It is however, merely a way of describing the phenomenon that the two fluid–hydrate contacts are energetically preferable compared to situations involving fluid–fluid contact. Later it is shown that this case implies zero induction time. The three equations describing spreading of one phase between the two others are special cases. All the wetting states is described by Eq. (1). This equation may be rewritten in a number of ways, for instance if we rearrange Eq. (1) and square both sides: ( σho + σhw )2 = (− σow )2 we get cos β =
2 σow
2 − σho
2 − σhw
2σho σhw
.
(4)
Similar expressions can also be formed for angles α and γ . So, a set of three equations can be derived (see below) but these are not independent [20]. Equation (4) may be regarded as Young’s equation extended for lenses at interfaces. In order to comprehend the above equation it is useful to draw a wetting diagram. This diagram determines the wetting angles once each interfacial tension has been fixed. Fig. 9 shows the wetting diagram
Fig. 9. Wetting map showing the lines of constant angles α, β, and γ . The oil– water interfacial tension is 30 mN/m. The dashed circle refers to realization of the lens in Fig. 8.
for the general three phase case. It can be adapted to hydrates by assuming that the microscopically freshly formed hydrate phase will grow in accordance with Eq. (1). The boundaries of the wetting states are given by Eq. (3). The lines inside are defined by constant angles α, β, and γ of Eq. (1). For instance, one line of constant β are formed by assigning constant values to β and σow and then rearrange Eq. (4) to get 2 cos2 β − σ 2 + σ 2 . σho = −σhw cos β ± σhw (5) ow hw By setting σow = 30 mN/m one obtains the β-curves of Fig. 9. Care must be taken to interpret the correct sign of the square root. By setting β = 0 and β = π , Antonow’s expressions are again recovered. For the water angle γ we may again rearrange Eq. (1) into: ( σow + σhw )2 = (− σho )2 to get 2 + σ 2 + 2σ σ cos γ σho = ± σow (6) ow hw hw and last, for the angle α we rearrange Eq. (1) into: ( σow + σho )2 = (− σhw )2 and get 2 cos2 α − σ 2 + σ 2 . σho = −σow cos α ± σow (7) ow hw As is evident from Fig. 8 the sum of the angles must be 2π . It can also be seen that, since the water and hydrocarbon phases are of a priori equal importance, there is symmetry around the axis: σho = σhw . Similar diagrams to Fig. 9 were previously adopted by Mori [21] for gas bubbles. Wetting diagrams are merely graphical illustrations of all possible wetting states. In the case of Fig. 9 the oil–water interfacial tension is kept constant. The point encircled by a dashed line corresponds to the lens of Fig. 8, thus we are at the exact point where the lines of α = 160◦ , β = 100◦ , and γ = 100◦ intersect. These particular angles for a lens corresponds to the
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surface energies that can be read from the diagram, and are listed in Fig. 8 as σow = 30 mN/m, σho = 30 mN/m, and σhw = 11 mN/m. By moving in the diagram one may determine angles and surface energies and thereby realize all possible wetting states for the given value of the oil–water interfacial tension. The wetting states are bounded on three sides by Antonow’s expressions. The work needed to form the new hydrate phase at the interface or in the bulk is usually written as [8] W (n) = −ng + ϕ(n) + ϕs (n) − ϕs,o ,
(8)
where n is the number of units in the nucleus, g is the driving force, which is defined positive within the hydrate stable region, ϕ is the interfacial energy of the new phase, ϕs is the interfacial energy of the interface after lens-formation, and ϕs,o is the interfacial energy before lens-formation. By geometric and energy consideration it can be shown that Eq. (8) can be written as W (n) = −ng + n2/3 cσe ,
(9)
where c is a constant and the effective surface energy, σe is defined by 1 σe = (1 + cos γ )2 (2 − cos γ ) 4 1/3 sin γ 3 2 (1 + cos α) (2 − cos α) σhw . + (10) sin α It follows from Eq. (9) that if the effective surface energy is zero then metastability disappears. The effective surface energy is a measure of the change in the system surface energy upon hydrate formation. From Eq. (10) the effective surface energy becomes zero when the angles γ and α both are zero. Physically this is the situation of hydrates spreading at the interface and we are at Antonow’s expressions which are visualized in Fig. 9. It should be remarked that the ratio (sin γ / sin α) seems to be undefined when the angles α and γ are 0 or π . However, the ratio will approach −1 as the angles approach 0 and π , respectively. This can be seen by using L’Hospital’s rule: lim
γ ,α→0,π
sin γ cos γ = lim = −1. sin α γ ,α→0,π cos α
(11)
In summary, by using Eq. (10), we write (α = π, β = π, γ = 0)
⇒
σe = σhw
water spreading, (α = π, β = 0, γ = π)
oil spreading.
of critical nuclei size is no longer meaningful because all nuclei is super-critical. This will always be the case if the sum of the surface energy after phase formation is equal to the surface energy before phase formation. According to Eq. (8) we may write the criterion as ϕ(n) + ϕs (n) − ϕs,o = 0.
(13)
A zero or negative effective surface energy is normally only possible for heterogeneous nucleation. In homogeneous nucleation the only surface term is φ(n) which is usually larger than zero. The effective surface energy σe , is plotted in the wetting diagram of Fig. 10. Again the area of mixed wetting is bounded by Antonow’s expressions. The figure links effective surface energy and wetting. Because σe is directly connected to the energy barrier of hydrate nucleation, Fig. 10 connects concepts like induction time to the wetting state of the system. As the effective surface energy increases the barrier increases and the induction time will increase, thus higher sub-cooling or increased supersaturation is needed in order to form hydrates.
(12a) ⇒
3.3. Hydrate spheres
σe = 0
hydrate “spreading,” (α = 0, β = π, γ = π)
Fig. 10. Wetting map showing the lines of constant effective energy for the case of a lens (σe ). At low surface energies we have hydrates spreading and zero effective surface energy. At high and low σho we have water and oil spreading, respectively. The dashed circle shows the lens geometry of Fig. 8 and indicates that the effective energy is approximately 8 mN/m for this case. The oil–water interfacial tension is 30 mN/m.
(12b) ⇒
σe = σho (12c)
It should be mentioned that Eq. (12c) is obtained by symmetry. As mentioned, when σe = 0, metastability vanishes because the work W (n) = −ng will be negative or zero for all positive driving forces. The maximum work is at n = 0, and the concept
In the case where the hydrates are perceived as spherical even though they grow at an interface, the equations are simplified due to the spherical geometry. Antonow’s expressions (3) are still valid, except for the case where hydrates are spreading, so the set is reduced to the following two equations: σho = σow + σhw
water spreading,
σhw = σho + σow
oil spreading.
(14)
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Fig. 11. The figure shows a hydrate sphere at a given wetting state at the interface between oil and water. The tensions are drawn to scale. This wetting state is indicated in the wetting diagram of Fig. 12 by a dashed circle.
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Fig. 13. The figure shows the effective surface energies for a sphere. At low surface energies the effective surface energy becomes zero and hydrate will form spontaneously. At high and low σho we have water and oil spreading, respectively. The dashed circle indicates the geometry of Fig. 11 and that the effective surface energy is approximately 17 mN/m. The oil–water interfacial tension is 30 mN/m.
Investigating the work function as for the lens case of Eq. (8), leads to the following expression for σe : 1 σe = σhw − σow (1 + cos γ )2 . (16) 4 The work needed for a new phase to form becomes negative when σe = 0. We may write
Fig. 12. The figure shows the wetting diagram of the hydrate sphere at the interface. The dashed circle indicates the geometry shown in Fig. 11. The oil–water interfacial tension is 30 mN/m.
In addition, at equilibrium we have Young’s equation which reads σho − σhw = σow cos γ
(15)
which is seen to reduce to Antonow’s for the cases where γ = 0 and γ = π , respectively. All possible geometric realizations for a sphere at the interface between two fluids are between these two extremes (for a given σow ). One particular geometrical configuration is shown in Fig. 11. The sphere, of radius r, is immersed a given distance ho into the oil phase and the remaining part is immersed hw into the water phase. Fig. 12 shows the lines of constant water angle γ , in the wetting diagram of the sphere. The diagram is much simpler than in the lens case due to constancy of β = π and the fact that γ = π − α. The lines in Fig. 12 indicate not only constant γ but also constant difference σho − σhw .
1 σhw = σow (1 + cos γ )2 . (17) 4 The plot of constant values for σe for the case of the sphere is shown in Fig. 13. It is interesting to see that for the lens case the mixed wetting area is defined by Antonow’s expressions (3), which also coincides with the area where σe can be defined (see Figs. 9 and 10). The case for spheres shows that according to Young’s equation (15), we may realize mixed wetted spheres along every line in the diagram of Fig. 12. However, when we examine the effective surface energy σe , then it is seen that one may obtain negative values which at first seems unphysical. As mentioned, the effective surface energy of the system is a measure of the change in surface energy upon hydrate formation, and as such σe may become zero or negative. Hence the energy barrier to hydrate formation may become zero or negative. When this barrier is zero or negative hydrate formation will be spontaneous. In summary we have 1 σhw > σow (1 + cos γ )2 4 1 σhw = σow (1 + cos γ )2 4
positive energy barrier,
(18a)
zero energy barrier “Antonov,” (18b)
1 σhw < σow (1 + cos γ )2 negative energy “barrier,” (18c) 4 where the equality sign will is an analogue for Antonow’s rule in the case of solid spheres.
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If we introduce some foreign material that have large surface energy toward water, then hydrate formation may be spontaneously induced. With regard to Eq. (18) we may say that we introduce a water–material surface energy which may be much higher than the water–oil surface energy. Therefore Eq. (18c) will be effective and hydrates will form spontaneously and thereby the system energy is reduced. A common example is to put dry grains of sand in a supersaturated solution of freon/water or tetra-hydro-furan/water mixture. If however, the same material, i.e., sand grains, was equilibrated in the mixture, then the surface energy would be lowered due to reactions between the surface and the fluids and the effect will vanish or be much less dramatic (ref. observation 4: interface). For the case of flow in pipelines, sand and other mineral particles will be wetted by water and oil, and thus either hydrolyzed by the water phase at a given pH or adsorbed by oil components like asphaltenes and wax. Therefore it is to be expected that hydrate formation will take place mainly at the oil–water interface also in pipelines. 4. Morphology 4.1. Turbulence, bouancy, and capillarity Hydrate growth is mainly at the interface between the aqueous and hydrocarbon phases. This can be due to mixed wetting and/or local driving forces during growth. Hence, in order to determine whether the particle will stay at the interface or not during growth we examine simple expressions for the forces. If it is assumed that there is a certain degree of turbulence in the system, either sustained by flow in a pipeline or by simple stirring in a closed cell, then the particles will be subjected to turbulent forces in addition to the capillary and buoyant forces. In the following discussion forces acting vertically is considered positive. Furthermore the shear force is assumed negligible due to small velocity gradients far from the pipe wall. The sum of the forces will determine the trajectory of the particle. Such calculations are outside the scope of this article but we may calculate the importance of the various forces in the vertical direction. Assuming spherical particles, the turbulent force that acts on the particle by the fluid can be written as [22] Ft = 0.18πρh u2 r 2 f,
(19)
where ρh is the hydrate density, u is the mean fluid velocity, r is the particle radius, and f is the friction factor which may be defined by, f = 0.316/Re0.25 , where Re is the Reynolds number for single phase pipe flow and is given by Re = ρud/η, where η is the fluid viscosity, d is the pipe diameter, and, finally, ρ is the fluid density. The turbulent force on the particle is dependent upon the fluid properties of the phase in which it is immersed. However, for the present discussion it is sufficient to assume that this phase is always the water phase. In contrast to the turbulent energy which may remove the particle from the interface, gravity may act to keep the particle at the interface. This is due to the fact that solid hydrates in petroleum systems often have densities intermediate to the values
of oil and water. Densities of oil varies from light condensates with densities possibly lower than 500 kg/m3 to heavy crude which has a densities from 930 kg/m3 and upward. Since hydrates have densities from 920 kg/m3 they will most likely float in heavy oil. The buoyancy of a particle partly submerged in oil and water is Fb = (ρh − ρw )gVw + (ρh − ρo )gVo ,
(20)
where Vw and Vo are the volumes of the part of the sphere which is submerged in water and oil, respectively. The sum of the volume in the oil and in the water must be equal to total volume of the hydrate sphere, Vh with radius r (see Fig. 11). So, by use of Vh = Vw + Vo we get Fb = (ρhw Vh − ρow Vo )g,
(21)
where ρhw and ρow are the differences in density between hydrate–water and oil–water, respectively. The volume of the spherical cap can be substituted by Vo = π(rh2o − h3o /3)
πg 3 Fb = (22) 4r ρhw − 3rh2o − h3o ρow . 3 Finally, we consider the capillary force on the particle which can be taken directly from Young’s equation as Fc = −2πr(σow cos γ − σho + σhw ),
(23)
where the immersion depth ho and the wetting angle γ is connected by ho = r(1 − cos γ ). Considering only the vertical component, Fcv , we can write the vertical capillary force component as Fcv = Fc sin γ . The particle experience the sum of these forces Fp = Fcv + Fb + Ft . When the sum equals zero (Fp = 0) the system is at equilibrium. Keeping the radius constant one may determine how the total force varies as a function of immersion depth ho . Fig. 14 shows the individual forces and the sum plotted as a function of the immersion depth normalized by the particle diameter, hon = ho /2r. It can be seen that at a particle radius of 0.1 m buoyancy (Fb ) is dominating because the buoyancy force is approximately equal to the total particle force. At a radius of 0.01 m the buoyancy and capillary forces are in the same range and no single force is dominating. Finally, at r = 0.001 m the capillary force is seen to be of equal magnitude as the total particle force. Thus, capillarity dominates completely. As the hydrate particles grow, bouancy and capillarity determines the location of the particle. Particles smaller than 0.01 m will be largely dominated by the wetting properties. This balance of the forces will have impact on the hydrate particle size distributions. The effect may be illustrated by increasing the density of the oil phase to ρo = 940 kg/m3 , which is equivalent to an API of 19. The results are shown in Fig. 15. With the current wetting properties (Table 2 and Fig. 11) the particle is bound to the interface as long as the radius is sufficiently small. The lower graph of Fig. 15 shows that the sum of the forces are zero for a given value ho meaning that the particle is at equilibrium at the interface. The two upper upper graphs show that when the radius is increased to 0.01 m buoyancy removes the particle from the interface. Therefore, hydrates will continue growth at the interface until buoyancy removes it. In
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Fig. 14. The figure shows the forces acting on the particle. The top figure shows that the bouancy force is the main contributor to the total force. The middle figure shows that at a radius of 0.01 m the buoyancy and capillary forces are of the same magnitude. Finally, the lower figure shows that at a radius of 0.001 m the capillary force dominates. Table 2 The table lists the parameter values used for calculating the curves of Figs. 14 and 15. Superscripts 1 and 2 refer to Figs. 14 and 15, respectively Property
Value
ρw , density water (kg/m3 ) ρo , density oil (kg/m3 ) ρh , density hydrate (kg/m3 ) σow , oil/water surface energy (N/m) σho , hydrate/oil surface energy (N/m) σhw , hydrate/water surface energy (N/m) η, viscosity water (Pa s) d, pipe diameter (inches) U , volume flow (m3 /day)
998.0 800.01 940.02 920.0 0.030 0.035 0.020 0.001 8.0 2500
the oil phase hydrate growth will occurs at a different rate than at the interface or in the water phase. In this particular case where the hydrate particle is mostly water wet (see Fig. 11) it will probably be sticky in the oil phase. Due to the different paths toward equilibrium, the morphology of the resulting equilibrated system will be different. It should be remarked that the true equilibrium state is unique, and cannot vary according to the path but the present variations, although visually large may be considered energetically small.
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Fig. 15. The figure shows the forces acting on the particle. The equilibrium position is determined by the point where the total force Fp is zero. As the particle grows it gradually extends into the oil phase until it is completely immersed in oil due to bouancy.
4.2. Emulsions Systems composed of oil and water are often characterized by the water cut. The water cut is defined as the water volume fraction of the produced liquids at 15 ◦ C and 1 bar. The definition is well suited to a stirred cell where it is possible to mix all fluids thoroughly, as well as to produced fluids. The water cut is important because it is used as a parameter to characterize the emulsion properties. However, for systems flowing in a pipe, the amounts of water locally have to be related to the degree of turbulence locally. It is therefore possible to observe both oil-in-water emulsions, water-in-oil emulsions, and inversion states for a pipe line system at constant water cut. For the present discussion we assume that we have either water-in-oil or oil-in-water emulsions, and the water cut is left to be defined for any given case. In the following analysis the theory of particle stabilized emulsions has been utilized [23–25]. There are two aspects of hydrates and emulsions, first the impact of hydrates on the emulsion characteristics and second the effect of emulsions on the hydrate growth. Hydrate nuclei and crystallites will be wetted at the interface according to the surface energies previously discussed.
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Table 3 The table contains an overview of the initial emulsion state and the effects of hydrate formation for water wetted and oil wetted hydrates Initial state
Water wetted γ < π/2
Oil wetted γ > π/2
Water-in-oil
Destabilizing, separation, inversion to oil-in-water. Inhibits hydrate growth before inversion. Aggregate formation likely
Stabilizing, break up of droplets and more interface generated. Hydrate growth is instantly promoted. Dispersion is probable
Oil-in-water
Stabilizing and possible break up of droplets. New interface forms in water and hydrate growth will probably accelerate. Eventual aggregation is likely
Destabilizing, droplets will grow and oil separate from water. Eventually inversion may occur. Initially hydrate growth is inhibited due to decreasing interfacial area
Separated/stratified
Oil-in-water emulsion may form. Interfacial area increases thus hydrate growth is promoted. Aggregation is likely
Water-in-oil emulsions may be generated. Increasing interfacial area promotes hydrate growth. Dispersions due to oil wetting is likely
First we assume that the flow regime is such that there is a water-in-oil emulsion locally and that water wetted hydrates (γ < π/2) nucleate at this location. The main volume of the particles will then be inside the water droplet and the droplet will be destabilized. The droplet size distribution will then tend toward a higher mean value thus promoting separation and eventually, if possible, phase inversion (ref. observations 1 and 2: inversion and emulsification). Initially, the interfacial area will decrease due to droplet growth and it is to be expected that hydrate formation will be temporarily inhibited. Because the hydrates are water wetted any contact with water will lead to growth and it is likely that aggregates will form. If the hydrates are oil wetted (γ > π/2) then the water droplets will be further stabilized and may even break up to form smaller droplets. This effect will lead to an increase in the interfacial area and accelerated hydrate growth. Droplet contact with water will not cause aggregation to the same extent as at lower wetting angles, thus one may expect dispersions to form (ref. observation 3: morphology). Second, we assume that an oil-in-water emulsion has formed locally and that water wetted (γ < π/2) hydrates are forming. The hydrates will stabilize the emulsion and even promote break up of droplets thereby increasing the interfacial area and accelerate the hydrate growth. The hydrates are water wetted therefore aggregation is likely to take place. If the hydrates are oil wetted (γ > π/2) then the droplets will be destabilized and interfacial area will decrease until phase inversion takes place. Hydrate growth will therefore be temporarily inhibited. The process will most likely lead to a dispersion of hydrates. As described above, the initial emulsion state is important with regard to the hydrate growth, and the wetting state determines the direction of the changes, i.e., toward aggregation or dispersion. In a flow regime where the rates are too low to emulsify the phases the flow may be stratified or layered. Hydrate formation at the interface may then induce emulsification. The produced emulsions will be a function of the hydrate wettability. Thus water wetted (γ < π/2) hydrates will produce oil-in-water emulsions and vice versa. It is worth noticing that although one process leads to aggregates while the other leads to dispersion, both will enhance hydrate growth due to formation of new interfaces. The different scenarios and instances involving emulsions and hydrates are summarized in Table 3.
Fig. 16. The figure illustrates how movements in the wetting diagram may induce morphology changes at constant effective surface energy or vice versa. The oil–water interfacial tension is 30 mN/m.
5. Kinetics and agglomeration From the previous section we can deduce that by increasing the value of surface energy term in the work function, it is possible to manipulate the kinetics. It is to be expected that the induction time will increase as the work needed to form the new phase increase, i.e., as the effective surface energy increases. This has been illustrated by the diagonal arrow from lower left to upper right in Fig. 16. If we keep the surface energy term constant and vary the wetting angles, i.e., moving along the other diagonal of Fig. 16, we either end up at oil spreading or water spreading on hydrates. The morphology of the hydrates is expected to be dependent upon the wetting state. Oil wetted hydrates will form a dispersion of hydrates while water wetting will form aggregates [26]. The diagram in Fig. 16 connects wetting, kinetics and morphology showing exactly how parameters should be manipulated in order to achieve either dispersions or long induction times or both. 6. Conclusions During nucleation of hydrates at an interface or in the bulk of a phase, the detailed state of wetting is a key factor in determining the fate of the freshly formed crystallites.
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Depending on flow and turbulence, water wetted hydrates will most likely lead to large aggregates of hydrates while oil wetted hydrates will lead to flowable dispersions. At certain conditions the limit of metastability can be defined by the effective surface energies for a given geometry. Equating the effective surface energy term of the work function to zero, will define the metastability limit. Capillary forces dominates both turbulence and gravity when the hydrate crystallites are less than 10−3 m in diameter. Acknowledgments The authors thank Norsk Hydro for the permission to publish these results. Thanks also to Sylvi Hoiland, Arne Valle and Finn Gunnar Nielsen for helpful discussions regarding this work. References [1] E.D. Sloan, Clathrates Hydrates of Natural Gases, second ed., Dekker, New York, 1998. [2] Y.F. Makogon, Hydrates of Natural Gas, PennWell, Tulsa, 1981. [3] E. Berecz, M. Balla-Achs, Gas Hydrates, Elsevier, Amsterdam, 1983. [4] B. Beauchamp, C. R. Geosci. 336 (2004) 751–765. [5] H. Davy, Philos. Trans. R. Soc. 110 (1811) 155–162. [6] E.D. Sloan, Fluid Phase Equilib. 228–229 (2005) 67–74. [7] P.G. Debenedetti, Metastable Liquids, Concepts and Principles, Princeton Univ. Press, Princeton, NJ, 1996. [8] D. Kashchiev, Nucleation Basic Theory with Applications, Butterworth– Heinemann, Oxford, 2000. [9] K.S. Pedersen, P.L. Christensen, Phase Behavior of Petroleum Fluids, CRC Press, Boca Raton, FL, 2007.
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[10] F.H. Fadnes, Fluid Phase Equilib. 117 (1996) 186–192. [11] S. Hoiland, A.E. Borgund, T. Barth, P. Fotland, K.M. Askvik, Wettability of freon hydrates in crude oil/brine emulsions: The effects of chemical additives, in: Proceedings of the Fifth International Conference on Gas Hydrates, Trondheim, June 13–16, 2005. [12] J.W. Tester, M. Modell, Thermodynamics and Its Applications, Prentice Hall, New York, 1997. [13] Y. Drossinos, P.G. Kevrekidis, Phys. Rev. E 67 (2003). [14] E. Ruckenstein, Y.S. Djikaev, Adv. Colloid Interface Sci. 118 (2005) 51– 72. [15] A. Amirfazli, A.W. Neumann, Adv. Colloid Surface Sci. 110 (2004) 121– 141. [16] B. Widom, Colloids Surf. A 239 (2004) 141–144. [17] A.I. Rusanov, A.K. Shchekin, D.V. Tatyanenko, Colloids Surf. A 250 (2004) 263–268. [18] T. Austvik, X. Li, L.H. Gjertsen, in: G.D. Holder, P.R. Bishnoi (Eds.), Gas Hydrates, Challenges for the Future, in: Annals of the New York Academy of Sciences, vol. 912, 2000. [19] L.H. Gjertsen, F.H. Fadnes, in: G.D. Holder, P.R. Bishnoi (Eds.), Measurements and Prediction of Hydrate Equilibrium Conditions, in Gas Hydrates, Challenges for the Future, in: Annals of the New York Academy of Sciences, vol. 912, 2000. [20] J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity, Clarendon Press, Oxford, 1982. [21] Y.H. Mori, Int. J. Multiphase Flow 11 (1985) 571–576. [22] A. Valle, Three phase gas–oil–water flow, Ph.D. thesis, Imperial College London, 2000. [23] D.E. Tambe, M.E. Sharma, Adv. Colloid Interface Sci. 52 (1994) 1–63. [24] R. Aveyard, B.P. Binks, J.H. Clint, Adv. Colloid Interface Sci. 100–102 (2003) 503–546. [25] B.P. Binks, S.O. Lumsdon, Phys. Chem. Chem. Phys. 2 (2000) 2959– 2967. [26] S. Hoiland, K.M. Askvik, P. Fotland, E. Alagic, T. Barth, F.H. Fadnes, J. Colloid Interface Sci. 287 (2005) 217–225.