Equilibrium of water and hydrocarbon systems with hydrates

For systems containing both water and small (<9Å) hydrocarbons, hydrates are an important part of the phase diagram. This page addresses phase equilibria with hydrates. More information about the impact of hydrate formation can be found beginning at Hydrates.

Hydrate structures, stability, and measurements

On a molecular scale, hydrates form when single, small guest molecules are encaged (enclathrated) by hydrogen-bonded water cages, which then combine as solid unit crystals in these nonstoichiometric hydrates. Hydrocarbon guest repulsions prop open different sizes of water cages, which combine to form the three well-defined unit crystal structures shown in Fig. 1.

• Cubic structure I (sI), with small (4.0 to 5.5 Å) guests, predominates in natural environments.
• Cubic structure II (sII) generally has larger (6.0 to 7.0 Å) guests and mostly occurs in man-made environments.
• Hexagonal structure H (sH) may occur in either environment, but only with mixtures of small (4.0 to 5.5 Å) and the very large (8.0 to 9.0 Å) molecules.

The smallest hydrated molecules (Ar, Kr, O₂, and N₂), with diameters of less than 4.0 Å, form sII; still smaller molecules cannot be enclathrated except at extreme pressures.

• 

  Fig. 1 – Three hydrate unit crystals and constituent cavities (from Sloan).

These three common hydrate structures each have large and small cavities.

• In all three structures, the small cavity is similar and is called a 5¹² cavity because it contains 12 pentagonal faces composed of water molecules.
• In structure I, however, the large 5¹²6² cavity has 12 pentagonal faces and two hexagonal faces and is somewhat smaller than the large 5¹²6⁴ cavity in structure II, which has four hexagonal faces and is large enough to contain molecules as large as n-butane.
• Structure H has the largest cavity—a 5¹²6⁸ that can hold molecules as large as 9.0 Å—as well as three 5¹² cavities and two unusual 4³5⁶6³ cavities with three square faces.

Table 1 shows properties of these three common unit crystals.

• 

  Table 1

Remarkably, when all hydrate cavities are filled, the three crystal types have similar component concentrations: 85 mol% water and 15 mol% guest(s). This makes hydrate formation most probable at the interface between the bulk guest and aqueous phases because hydrate component concentrations exceed the mutual water/hydrocarbon solubilities. The solid hydrate film at the interface acts as a barrier against further contact of the bulk fluid phases, and fluid surface renewal is required for continued hydrate formation. The gas concentration in hydrates is comparable to that of a highly compressed gas (e.g., methane at 273 K and 17 MPa).

In addition to the three crystal structures in Fig. 1 and Table 1, a fourth and a fifth* hydrate structure recently were found. These two new structures are omitted from this overview because hydrocarbons have yet to be found in them, but their discovery points to the probability that more hydrate structures exist. Accurate stability predictions rely on accurate knowledge of the phases present, but for now, an accurate answer to the question of how many hydrate structures exist is unavailable. Currently, one must manage with the rule of thumb that three structures are common with hydrocarbons.

*Personal communication with J.A. Ripmeester, 17 March 2000.

Hydrate stability conditions

Hydrate stability conditions, which depend on hydrate structure, usually are measured in terms of dissociation because there is much less metastability on dissociation than on formation, when the two disordered phases of gas and water must organize themselves to hydrate. Hydrate dissociation typically is detected at low pressures (<70 MPa) by visual crystal disappearance and at higher pressures by measuring the gas phase pressure increase (because of high gas concentration in the hydrate phase) or liquid phase temperature decrease or salinity decrease (because of the endothermic heat of dissociation or hydrate phase water intake).

Measuring all but the hydrate phase

Because there are several hydrate structures, however, measuring every phase except the hydrate phase can introduce large data errors. For example, recently it was proven that mixtures of methane and ethane (each an sI former as a pure guest) form sII at methane gas concentrations ranging from 77 to 99.4% at deep-sea temperature (277 K). This finding means that more than 50% of the methane + ethane hydrate data measured since 1934 incorrectly assumed the sI hydrate structure for this most common hydrocarbon binary mixture.

Nondestructive hydrate phase measurements

Three experimental tools are used for nondestructive hydrate phase measurements:

• Diffraction tools, such as X-ray or neutron,
• Raman spectroscopy,
• Nuclear magnetic resonance (NMR) spectroscopy.

Without hydrate phase measurement, one must assume the hydrate structure and properties are predicted acceptably by a mathematical model. This can lead to inaccuracies, as shown in the above case of the methane + ethane system.

Phase equilibria and calculations involving hydrates

There are four types of water and hydrocarbon equilibrium that include hydrates, as indicated in the pressure/temperature (P/T) diagrams. These equilibria types are:

• Gases, such as CH₄ or N₂, that exist only as vapor for conditions of interest (Fig. 2a)
• Gas + single condensate + water systems (e.g., water + C₂H₆, C₃H₈, or i-C₄H₁₀) in which the hydrocarbon may be vapor or liquid (Fig. 2b)
• Systems with gas + mixed oil/condensate + water (Fig. 2c).
• Systems with inhibitors (Fig. 2d).

Within Figs. 2a-d, I=pure ice, L=liquid that is either water (L_w) or hydrocarbon (L_HC), V=vapor that is always a single phase, W=liquid water (usually >99% purity), and H=hydrate or solid.

• 

  Fig. 2a – Pressure/temperature diagram for methane + water or nitrogen + water systems in the hydrate region (from Sloan).

• 

  Fig. 2b – Pressure/temperature diagram of hydrocarbon single components with upper quadruple points (from Sloan).

• 

  Fig. 2c – Pressure/temperature diagram for multicomponent natural gas + water systems (from Sloan).

• 

  Fig. 2d – Pressure/temperature diagram for H₂O + hydrocarbon systems with inhibitors (after Sloan).

Pressure/temperature diagram of a gas above its hydrocarbon dewpoint

Consider the P/T diagram in Fig. 2a, shown schematically for the methane + water system at conditions both above the solid hydrate/ice region (to the right of all lines) and below the solid region (to the left of all lines). Because methane is the major component of natural gas, this diagram provides phase behavior understanding for gas systems without a liquid hydrocarbon phase.

This diagram assumes that a flash calculation has been performed to ensure that a liquid hydrocarbon phase will not form. Furthermore, the vapor hydrocarbon phase should be large enough that it neither changes composition nor condenses, in which case the vapor composition is constant (C_v = 1). If water forms a condensed phase, however, which it frequently does, then the system is below the water dewpoint, but above the hydrocarbon dewpoint.

According to the Gibbs phase rule, a two-component system such as methane + water is represented on a P/T diagram as an area (two phases), a line (three phases), or a point (four phases). To obtain nearly straight lines, semilogarithmic plots [ln pressure (p) vs. absolute temperature (T_a)] are used.

Consider the quadruple point (Q₁) in Fig. 2a, where four phases (I-L_W-H-V) coexist. The Q₁ temperature is close to 273 K for all hydrate formers, yet the quadruple pressures vary widely, e.g.:

• 0.0113 MPa for i-C₄H₁₀
• 2.56 MPa for CH₄
• 14.3 MPa for N₂

Q₁ is the starting point for four 3-phase lines:

• The L_W-H-V line, which has P/T conditions at which water and vapor form hydrates, conditions of most interest in natural gas hydrate systems.
• The I-H-V line, which terminates at about 273 K and has a lower slope than the L_W-H-V line. Industrially, the region below 273 K is avoided, if possible, because of flow assurance problems stemming from either ice or hydrate formation.
• The I-L_W-H line, which rises vertically from Q₁, with very large pressure changes for small temperature changes, typical of incompressible phases.
• The I-L_W-V line, which connects Q₁ to the pure water triple point (I-L_W-V) (273.16 K, 0.62 kPa) and denotes the transition between water and ice without hydrate formation. Because Q₁ is close to 273 K for all natural gas systems, the I-L_W-V line extends almost vertically below Q₁ to 0.62 kPa.

Eq. 1 and Table 2' enable prediction of the most common regions of interest for simple natural gas components—the pressure and temperature conditions for both L_W-H-V and I-H-V.

....................(1)

where, as shown in Table 2,

• p = pressure, in kPa
• a and b = constants
• T = temperature, in K

• 

  Table 2

When using Eq. 1, carefully note the temperature limits. It would be a mistake, for example, to extend the prediction of the L_W-H-V region beyond the temperature of either Q₁ or Q₂ (given in Table 3), where L_W-H-V cannot exist.

• 

  Table 3

The pressures and temperatures in Fig. 2a are of interest in natural gas systems for the following reasons:

• The pressures and temperatures of the L_W-H-V and the I-H-V lines mark the limits of hydrate formation. Hydrates cannot form to the right of either line, but will form to the left of both. Because both ice and hydrates cause flow problems, a gas pipeline rule of thumb is to keep the system temperature above the ice point and to the right of the L_W-H-V line.
• The L_W-H-V line has no upper pressure or temperature limit because the methane (or nitrogen) vapor/liquid critical points (191 and 126 K, respectively) are far below Q₁. Such low critical temperatures prevent intersection of the vapor pressure line with the L_W-H-V line above 273 K, and so prevent the forming of an upper quadruple point. Similarly, a gas at conditions above its dewpoint will not have an upper point where the liquid phase occurs, and the L_W-H-V line will continue to much higher temperatures and pressures.
• No upper pressure limit to the I-L_W-H line is known. Note that these phases all are nearly incompressible, so that only a small temperature change is required to cause a very large pressure change.
• The areas between the three-phase lines represent the two-phase region held in common with the bounding three-phase lines. For instance, the area between L_W-H-V and I-H-V is the H-V region, in which hydrates are in equilibrium only with water-saturated hydrocarbon vapor. Similarly, the L_W-H two-phase region exists between L_W-H-V and I-L_W-H lines, and the I-H two-phase region exists between the I-L_W-H and I-H-V lines. The two-phase regions overlap, so that at some P/T conditions there are two 2-phase regions that differ in water composition. This seeming paradox is resolved by the fact that the three-phase lines all are not in the plane of the page, but rather have been compressed from 3D (P/T/composition) into 2D (P/T).
• The diagram schematic is the same for sI hydrate systems (CH₄ + H₂O) and sII formers (N₂ + H₂O), as well as for those of fixed natural gas mixture compositions without an L_HC phase.

Gas + pure condensate + water systems (e.g., H₂O + C₂H₆, C₃H₈, or i-C₄H₁₀)

Fig. 2b is slightly more complex than Fig. 2a, for systems such as:

• ethane + water
• propane + water
• isobutane + water
• water + either carbon dioxide or hydrogen sulfide, two common noncombustibles

If the hydrocarbon phases are maintained at the same, constant composition in both vapor and liquid phases, these systems can represent multicomponent gas and oil/condensate systems.

The systems differ from those in Fig. 2a in that they have an additional three-phase (L_W-V-L_HC) line at the upper right area of the diagram. This line is very close to the vapor pressure (V-L_HC) line of the pure hydrocarbon, because the presence of the nearly pure water phase adds a very low vapor pressure to the system. In this system, each liquid phase, L_HC and L_W, exerts its vapor pressure.

Fig. 2b shows that where the L_W-V-L_HC line intersects the L_W-H-V line is a second quadruple point (Q₂), with phases L_W-H-V-L_HC. Table 3 shows measured upper quadruple points for simple natural gas components. Q₂ is the origin for two additional 3-phase lines:

• Vertical L_W-H-L_HC line that is very incompressible
• H-V-L_HC line (of less concern)

For systems with an upper quadruple point, the hydrate region is bounded by:

• Line I-H-V at conditions below Q₁
• Line L_W-H-V at conditions between Q₁ and Q₂
• Line L_W-H-L_HC at conditions above Q₂

Hydrates will form at temperatures and pressures to the left of the region enclosed by the three lines, whereas to the right of this region, hydrates are not possible. Upper quadruple point Q₂ often is approximated as the maximum temperature of hydrate formation because line L_W-H-L_HC is approximately vertical because of the incompressibility of those three phases.

To a good approximation, P/T conditions for L_W-H-V of the pure components in Table 3 lie on a straight line between Q₁ and Q₂, on a semilogarithmic plot (ln p vs. 1/T_a). Predicting hydrate formation discusses that there is no simple way to expand the above pure lines into that for a mixture, though there are several ways to hand-calculate L_W-H-V conditions (P/T) for mixed hydrocarbon hydrate formers.

In Fig. 2b, the areas between the three-phase lines represent two-phase regions held in common with the three-phase lines.

• The P/T area bounded by three 3-phase lines (L_W-H-V, L_W-H-L_HC, and I-L_W-H) is the L_W-H region, in which hydrates are in equilibrium only with liquid water.
• Similarly, the H-V region is between the three 3-phase lines (H-V-L_HC, L_W-H-V, and I-H-V).
• Finally, the H-L_HC two-phase region exists between L_W-H-L_HC and H-V-L_HC lines, and the I-H two-phase region exists between the I-L_W-H and I-H-V lines.

Note that the last paragraph contains three 2-phase regions for hydrate equilibrium with phases that are not liquid water:

• (H-V, H-L_HC
• I-H

It is a common misconception that hydrates cannot form without a liquid water phase, yet this clearly is possible according to these diagrams. Professor Kobayashi’s laboratory at Rice U. has measured hydrate equilibria without a free-water phase for more than a quarter century, so there is no thermodynamic prohibition to hydrate formation without a free-water phase. However, the kinetics of such hydrate formation are extremely slow, so that in man-made systems and time scales, it may not be practical to consider hydrate formation without a free-water phase.

Pressure/temperature diagrams for gas + oil/condensate systems

For natural gases without a liquid hydrocarbon, the P/T phase diagram is similar to that shown in Fig. 2a. The few changes would be:

• That the L_W-H-V line would be for a fixed composition mixture of hydrocarbons rather than for pure methane
• That Q₁ would be at the intersection of the L_W-H-V line and 273 K, at a pressure lower than that for methane; and
• That the other three-phase lines (for I-L_W-H and I-H-V) would have nearly the same slope at Q₁, but Q₁ would be at a lower pressure than for methane.

Otherwise, the same points as above apply.

For natural gases that contain oils or mixed condensates, however, the upper portion of the diagram is more like that in Fig. 2b. A straight line labeled L_W-H-V represents the hydrate formation region that is equivalent to the region between Q₁ (I-L_W-H-V) and Q₂ (L_W-H-V-L_HC) in Fig. 2b.

A second significant change is that point Q₂ becomes a quadruple line. When a liquid hydrocarbon mixture is present, the L_W-V-L_HC line, to the right of Q₂ in Fig. 2b, broadens to become an area, such as that labeled CFK in Fig. 2c. This area develops because a single hydrocarbon is no longer present, so that a combination of hydrocarbon and water vapor pressures creates a broader phase-equilibria envelope. Consequently, Q₂ evolves into a line KC between Q_2L and Q_2U for the multicomponent hydrocarbon system.

Line KC might not be straight in the four-phase region, though it is drawn as such here for illustration purposes. The lower point, K’s location, is determined by the point at which the phase envelope ECFKL intersects the L_W-H-V line. To determine the upper point C, calculate the vapor/liquid equilibrium, assuming that the liquid phase (exiting the envelope at point C) is the vapor composition at point K. The resulting equilibrium (bubblepoint) vapor is plugged into a vapor/liquid water/hydrate calculation to find the upper intersection with the phase envelope ECFKL.

Pressure/temperature diagrams for systems with inhibitors

The presence of inhibitors causes a change in the P/T diagram, as illustrated in Fig. 2d. For simplicity, the diagram shows only the hydrate bounding region (to the left of line AQ₁Q₂B) for an uninhibited pure component system with upper and lower quadruple points (Q₁ and Q₂). Line AQ₁Q₂B in Fig. 2d is equivalent to line AQ₁Q₂B in Fig. 2b, with three slopes that change at the quadruple points.

In Fig. 2d, the presence of an inhibitor [e.g., methanol (MeOH)] shifts the upper two-thirds of the line Q₁Q₂B to the left, approximately parallel to the uninhibited line on a semilogarithmic plot (ln p vs. T_a). With an inhibitor however, the transition temperature from water to ice (Q₁) is decreased, so that the inhibited L_W-H-V line intersects the I-H-V at a lower point (labeled Q₁ for 10 wt% methanol and Q₁ for 20 wt% methanol). The three inhibited parallel lines represent L_W-H-V and L_W-H-L_HC equilibria at 0, 10, and 20 wt% methanol concentrations in the free-water phase.

Each line in Fig. 2d bounds hydrate formation conditions listed with a methanol concentration in the free-water phase. To the left of each line, hydrates will form with a water phase of the given methanol composition; to the right of each line, hydrates will not form. For example, when the free-water phase has 10% methanol, hydrates will not form at P/T conditions to the right of the line marked 10% MeOH. Yet, if no methanol were present, the hydrates would form at pressures and temperatures between the two lines marked 10% and 0% MeOH. Similarly, more than 20% methanol would be required to prevent hydrate formation to the left of the line marked 20% MeOH.

For clarity, Fig. 2d has omitted the lines analogous to the three 3-phase lines in Fig. 2b:

• (I-L_W-H, which would intersect Fig. 2d‘s AQ₁Q₂B at Q₁
• L_W-V-L_HC and H-V-L_HC, which would intersect it at Q₂)

Such lines are less important for hydrate formation, but join the diagram at the appropriate, shifted quadruple points. For systems without an upper quadruple point (as in Fig. 2a) and systems with a liquid hydrocarbon region (as in Fig. 2c), the hydrate boundary region, similarly, is shifted to the left of (and is approximately parallel to) the uninhibited phase lines.

Other inhibitors, such as monoethylene glycol (MEG) and salts, shift the hydrate lines similarly to the left, but to a different degree. However, methanol is the most economical inhibitor on a weight basis. Note that all inhibited L_W-H-V lines are parallel to the pure water L_W-H-V line; that is, the hydrate temperature depression (∆T) is constant, regardless of pressure. To estimate ∆T for several inhibitors in the aqueous liquid, the natural gas industry uses the original Hammerschmidt expression:

....................(2)

where:

• ΔT = hydrate temperature depression from the equilibrium temperature at a given pressure, °F)
• M = molecular weight of the inhibitor
• W = wt% of the inhibitor in the free-water phase

With the above equation, the engineer can determine how much inhibitor should be added to the free-water phase to bring the L_W-H-V line below the lowest operating temperature of the system. Before the Hammerschmidt equation can be used, however, one must determine the equilibrium temperature T_eq that is to be depressed by the inhibitor. Predicting hydrate formation covers determination of T_eq and provides a method to estimate the total amount of inhibitor to inject, including not only the inhibitor amount in the aqueous liquid as calculated here by the Hammerschmidt equation, but also the amount in the vapor and liquid hydrocarbon.

Nomenclature

a	=	constant
b	=	constant
M	=	molecular weight
p	=	pressure, psia
Q	=	heat added to a system flowing at steady state, Btu/hr
T	=	temperature, °F
W	=	wt% of the inhibitor in the free-water phase
∆T	=	hydrate temperature depression below the equilibrium temperature at a given pressure, °F

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See also

Hydrates

Phase behavior of water and hydrocarbon systems

Predicting hydrate formation

PEH:Phase Behavior of H2O Hydrocarbon Systems