PEH:Phase Behavior of H2O Hydrocarbon Systems

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume I – General Engineering

John R. Fanchi, Editor

Copyright 2007, Society of Petroleum Engineers

Chapter 11 – Phase Behavior of H₂O + Hydrocarbon Systems

E.D. Sloan, SPE, Center for Hydrate Research, Colorado School of Mines

Pgs. 499-531

ISBN 978-1-55563-108-6
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The phase behavior of H₂O + hydrocarbon mixtures differs significantly from the vapor/liquid equilibria of normal hydrocarbons in two ways: the aqueous and hydrocarbon components usually separate, with very low mutual solubility; and hydrates often form with water and hydrocarbons smaller than n-pentane. Water generally is avoided because it is incombustible, and hydrate solids usually are avoided because their presence creates flow assurance difficulties.

When hydrocarbon contacts water, the two components separate into two phases in which the mutual component solubility is less than 1.0 mol% at ambient conditions. This splitting of phases affects almost all treatments of H₂O + hydrocarbon systems and is caused by the different molecular attractions within water and hydrocarbons. Hydrocarbon molecules have a weak, noncharged attraction for each other, while water attracts other water molecules through a strong, charged hydrogen bond.

Because hydrogen bonds are significantly stronger than those between hydrocarbon molecules, hydrocarbon solubility in water (and that of water in hydrocarbons) is very small. Hydrogen bonds are responsible for most of the unusual properties water displays. One example is water’s very high heat of vaporization, which absorbs large amounts of heat and buffers many hydrocarbon reservoir temperatures. Another example is the very high normal boiling point water has relative to its molecular weight.

This chapter discusses H₂O + hydrocarbon phase equilibria in macroscopic terms, such as temperature, pressure, concentration, and phase diagrams—more easily applied by the engineer—because a quantitative molecular prediction of H₂O + hydrocarbon phase behavior is beyond the current state of the art. Quantitative predictions of macroscopic phase behavior are illustrated by example, along with a few results from hand calculations, though the many excellent commercial phase equilibria computer programs now available largely have eliminated the need for the hand calculations. This chapter also explains qualitative trends, to help the engineer to understand the implications of temperature, pressure, and composition changes. Such a qualitative understanding and a few hand calculation methods serve as an initial check on the quantitative predictions of computer programs.

This chapter is divided into three main sections. The first section covers phase definitions and the Gibbs phase rule, which are used to define the problem. Only the two most common concerns are treated in this section; for a rigorous discussion of H₂O + hydrocarbon phase diagrams, see Harmens and Sloan. The second section goes on to cover the simplest case—that of an H₂O + hydrocarbon mixture when all phases are fluid, as vapor and/or liquid, and without hydrate formation. This H₂O + hydrocarbon equilibrium without hydrates exists at high temperature or low pressure or when only large (greater in size than n-pentane) hydrocarbon components are present.

Because of the importance of hydrates in H₂O + hydrocarbon equilibria, however, the largest and third section of this chapter deals with systems containing small hydrocarbon molecules (<9Å) that form hydrates with water. This is an important section—hydrates are the most common solid-phase problem in flow assurance. They are solid crystalline compounds that typically plug flow channels, valves, drillstrings, blowout preventers, etc.; therefore, hydrate-formation regions normally are avoided. A chapter on emerging technologies related to flow assurance and hydrates is in the Emerging and Peripheral Technologies section of this Handbook.

Phase Definitions and the Gibbs Phase Rule

Phases are homogeneous regions of matter—gas, liquid, or solid—that can be analyzed using common tools such as pressure gauges, thermocouples, and chromatographs. In this chapter, phases are distinct homogeneous regions larger than 100 μm. The shorthand used here for the various phases are:

• HC = hydrocarbon, typically with a very low (<1%) water concentration.
• I = pure ice.
• L = liquid that is either water (L_W) or hydrocarbon (L_HC).
• V = vapor that is always a single phase, never splitting.
• W = liquid water, usually of high (>99%) purity, except where indicated.
• H = hydrate or solid.

The order of phase listing is by decreasing water concentration. For example, the listing order L_W > H > V > L_HC means that hydrates (H) contain less water than the liquid water phase (L W ), but more water than vapor (V), which in turn contains more water than liquid hydrocarbon (L_HC).

The Gibbs phase rule for nonreacting systems provides the most convenient method for determining how many intensive variables are important in phase equilibria. The Gibbs phase rule states:

....................(11.1)

where F = number of intensive variables (e.g., pressure, temperature, single phase composition) required to define the system (known as the degrees of freedom); C = number of components; and P = number of phases.

For example, when excess gas (excess so that its composition does not change) contacts water to form hydrates, there are three phases (P = 3, namely L_W + H + V) and two components (C = 2, namely water and a gas of constant composition), so that F = 1; only one intensive variable (either pressure, temperature, or one phase composition) is needed to define the system. If this system is uniquely specified at a given pressure, for example, the identical temperature, and same individual phase compositions always will occur for the initial components at that pressure, when three phases are present. This system definition assures the engineer of uniqueness, so that the identical equilibrium phase behavior will be achieved. If gas also condenses (P = 4, with the addition of L_HC), however, or the gas quantity is small enough to change composition (such that C > 2), then the F = 1 restriction no longer holds.

As a second example, consider again the case of a constant composition hydrocarbon vapor in equilibrium with water, so that C = 2. With two phases (V + L_W), by the Gibbs phase rule the degrees of freedom are two (F = 2), so that for this example, both temperature and pressure are needed to determine the water composition in the hydrocarbon at conditions under which the two phases coexist. In contrast to the single variable required for three-phase systems in the above paragraph, with this case of two phases and two components, the saturated water concentration in the hydrocarbon (or water dewpoint) is determined by two variables. The water content in a hydrocarbon vapor is correlated with temperature and pressure in Sec. 11.3.1 below. Identical restrictions apply to the hydrocarbon content in the water phase, also considered briefly in Sec. 11.3.1.

The same restriction of F = 2 applies when a constant composition liquid hydrocarbon exists in equilibrium with liquid water. However, because both phases (L_W + L_HC) are dense, very large pressure changes are required to influence the water content of the hydrocarbon. In general, when condensed phases coexist, temperature and concentrations have a much greater influence than does pressure. With liquid hydrocarbon and water, the temperature controls the mutual solubility (i.e., the concentration of the water in the hydrocarbon liquid, as well as the concentration of the hydrocarbon in the liquid water). The mutual solubility of water and liquid hydrocarbons is correlated with temperature in Sec. 11.3.2 below.

The Gibbs phase rule is discussed further in Chap. 7 of the General Engineering section of this Handbook.

Equilibrium of H₂O + Hydrocarbon Systems Without Hydrates

This section considers two equilibrium conditions. First, it investigates the point at which, at a given temperature and pressure, water becomes saturated in either hydrocarbon vapors or hydrocarbon liquids and forms a separate fluid phase. Second, it considers the point at which hydrocarbon becomes saturated in liquid water and forms a separate hydrocarbon phase. Thus, both water and hydrocarbon dewpoints are represented as the maximum solubility of each phase in the other.

The discussion in this section assumes that hydrates will not form; prevention of hydrate formation requires a high temperature, a low pressure, or that all hydrocarbons be larger than n-pentane (9Å). Prediction of hydrate formation is covered in Sec. 11.4 of this chapter, whereas the discussion of nonhydrate-forming systems in this section provides a basis for understanding the subsequent equilibria of hydrocarbons and water.

Water Solubility (Dewpoint) in a Hydrocarbon Gas

The chart by McKetta and Wehe (Fig. 11.1) acceptably correlates the water content of hydrocarbon gases as a function of temperature and pressure. Because F = 2, two intensive variables are needed to specify the system. At a given temperature and pressure, the user can determine the saturated water content of gases, the point at which a liquid water phase will precipitate. For this reason Fig. 11.1 frequently is called the water dewpoint chart. Before using Fig. 11.1, however, note that:

• Water content is given in H₂O lbm/MMscf of gas at 60°F and 1 atm.
• Remarkably, the chart can be used for any hydrocarbon gas or gas mixture, regardless of gas composition. However, the water content should be multiplied by a slight correction factor for gas gravity (gas gravity = gas molecular weight divided by air molecular weight). Larger correction factors are required for sour (H₂S + CO₂) gases.
• To construct the chart, data from several investigators were measured at high (> 50 lbm/MMscf) water contents and extrapolated (as ln water content vs. temperature) along isobaric lines of constant pressure to lower water content.
• While the semilogarithmic plot adequately correlates data for gases at higher water contents, the correlation cannot be extrapolated to lower water content (< 20 lbm/MMscf) because the lines bend sharply downward at the hydrate formation temperature and pressure.
• Dashed lines in Fig. 11.1 represent metastable equilibrium of water in the vapor, giving a metastable water content that is higher than the equilibrium water content of gas in equilibrium with hydrates, the stable condensed phase at lower temperatures.
• Fig. 11.1 should not be used for low water concentrations; instead, use a computer program, as indicated in Sec. 11.4.2 below.

Despite its limitations, Fig. 11.1 is very useful and provides a check against high water content values calculated by commercial phase equilibria computer programs.

• 

  Fig. 11.1 – Water content of hydrocarbon gases (from McKetta and Wehe). C_s = correction factor for salinity, C_G = correction factor for gas gravity.

No similar measurements and charts are available for determining the hydrocarbon content in water vapor, with a separate liquid hydrocarbon phase. To approximate this at low pressures, an engineer may use the rule of thumb that hydrocarbon liquid will condense when the hydrocarbon partial pressure equals its vapor pressure. This calculation rarely is performed, however, because water’s hydrogen bonds cause water vapor pressure to be lower than that of many hydrocarbons. At temperatures below 100°C, only alkanes with carbon numbers above seven (n-C₈H₁₈⁺) have lower vapor pressures than water, because of water’s strong hydrogen bonds.

For this reason, it is much more common for water to precipitate from a hydrocarbon vapor in gas/petroleum operations than it is for hydrocarbon to precipitate from a low-pressure water vapor. Therefore, Fig. 11.1 is most practical for determining water solubility in hydrocarbon vapor.

Mutual Solubility of Liquid Water and Liquid Hydrocarbons

Tsonopoulos correlated mutual liquid solubility of liquid water and well-defined liquid hydrocarbons (normal alkanes, 1-alkenes, alkylcyclohexanes, and alkylbenzenes) for molecules that are too large (>9Å) to form hydrates. Solubilities in more general liquids (e.g., petroleum fractions) are not in the open literature and can be approximated using well-defined hydrocarbon fluid solubilities or their mixtures. The correlations for such fluids are given in four parts in this section:

• Solubility of hydrocarbons in liquid water at 298 K.
• Solubility of hydrocarbons in liquid water as a function of temperature.
• Solubility of water in liquid hydrocarbons at 298 K.
• Solubility of water in liquid hydrocarbons as a function of temperature.

Pressure does not significantly affect the mutual solubilities of liquids.

Solubility of Hydrocarbon in Liquid Water at 298 K. Solubility of Hydrocarbon in Liquid Water at 298 K. Because of dissimilarity in bonds between water and hydrocarbon, the mole fraction of well-defined hydrocarbon in water at 298 K always is very small, ranging from a high of 5 × 10^–4 for alkylbenzenes with a carbon number of 6 (N_c = 6), to a low of 2 × 10^–9 for nonane, a normal alkane. Even with these low water concentrations, at the same carbon number, the hydrocarbon in water concentrations decrease in the order of alkylbenzenes > alkylcyclohexanes > linear 1-alkenes > normal alkanes, as shown in Fig. 11.2. For a given chemical type, larger molecules always are less soluble in water than are smaller molecules.

• 

  Fig. 11.2 – Solubility of hydrocarbons in water at 298.15 K (from Tsonoupoulos).

The correlation for the mole fraction of hydrocarbons in water (x_HC-W) at 298 K is:

....................(11.2)

where N_c = the carbon number, and a, b, and c = constants as given in Table 11.1. For normal alkanes, the correlation does not fit well after N_c = 11.

• 

  Table 11.1

Solubility of Hydrocarbon in Liquid Water as a Function of Temperature. Liquid hydrocarbon solubility in water generally increases with temperature; however, there appears to be a minimum in solubility that ranges from 291 K for alkylbenzenes to 303 K for alkanes. As the temperature moves below these minimum values, the hydrocarbon concentration in water increases.

These solubilities change enough that the temperature effects for each compound must be treated individually. The hydrocarbon mole fraction for hydrocarbon liquids (x_HC-W) in water, as a function of temperature (T) in K, is well-described by the correlation:

....................(11.3)

where a, b, and c = constants for normal alkanes, as given in Table 11.2. For constants for individual 1-alkenes, alkylcyclohexanes, and alkylbenzenes, see Tsonopoulos.

• 

  Table 11.2

Solubility of Water in Liquid Hydrocarbons at 298 K. The solubility of water in hydrocarbon liquids at 298 K, like that of hydrocarbons in liquid water, is small, ranging from 3.2 × 10^–4 for ethane to 3 × 10^–3 for alkylbenzenes (N_c = 6), as shown in Fig. 11.3. The solubility of water in liquid hydrocarbons decreases in the following order for the same N_c: alkylbenzenes > linear 1-alkenes > normal alkanes > alkylcyclohexanes.

• 

  Fig. 11.3 – Solubility of water in hydrocarbons at 298.15 K (from Tsonopoulos).

The correlation for mole fraction of water in liquid hydrocarbons for well-defined fluids is:

....................(11.4)

where a, b, and c = constants as given in Table 11.3.

• 

  Table 11.3

Solubility of Water in Liquid Hydrocarbons as a Function of Temperature. Unlike the three above solubility correlations, the solubility of water in hydrocarbons increases dramatically with temperature. At high temperatures (> 500 K) the solubility of water in hydrocarbons can exceed 0.1 mole fraction, and may not be negligible, as with some of the above concentrations. These solubilities change so dramatically that the temperature solubility of each compound must be treated individually. The correlation of the mole fraction of water in liquid hydrocarbons as a function of temperature (K) is:

....................(11.5)

where a and b = constants as given in Table 11.4 for normal alkanes, as well as the heat of solution (H₁) defined as the enthalpy of water in the hydrocarbon solution minus that of pure liquid water. Consult Tsonopoulos for constants and ranges for individual 1-alkenes, alkylcyclohexanes, and alkylbenzenes.

• 

  Table 11.4

Equilibrium of H₂O + Hydrocarbon Systems With Hydrates

For systems containing both water and small (<9Å) hydrocarbons, hydrates are an important part of the phase diagram. This section addresses phase equilibria with hydrates, and is divided into two subsections: hydrate structures, stability, and measurements (Sec. 11.4.1); and phase equilibria and calculations involving hydrates (Sec. 11.4.2). A discussion of hydrates relative to such issues as safety, flowline blockage, gas storage, seafloor stability, and energy recovery is offered in the Emerging and Peripheral Technologies section of this Handbook.

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. 11.4. 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. 11.4 – 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 11.5 shows properties of these three common unit crystals.

• 

  Table 11.5

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. 11.4 and Table 11.5, 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.

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).

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.

Three experimental tools are used for nondestructive hydrate phase measurements: diffraction tools, such as X-ray or neutron, Raman spectroscopy, and 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 H₂O + 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. 11.5a) .
• Gas + single condensate + water systems (e.g., H₂O + C₂H₆, C₃H₈, or i-C₄H₁₀) in which the hydrocarbon may be vapor or liquid (Fig. 11.5b).
• Systems with gas + mixed oil/condensate + water (Fig. 11.5c).
• Systems with inhibitors (Fig. 11.5d).

Pressure/temperature diagrams for each of the above system types are discussed in the next four sections of 11.4.2. The section following those presents hand calculation methods for estimating hydrate equilibria.

• 

  Fig. 11.5a – Pressure/temperature diagram for methane + water or nitrogen + water systems in the hydrate region (from Sloan).

• 

  Fig. 11.5b – Pressure/temperature diagram of hydrocarbon single components with upper quadruple points (from Sloan).

• 

  Fig. 11.5c – Pressure/temperature diagram for multicomponent natural gas + water systems (from Sloan).

• 

  Fig. 11.5d – 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. 11.5a, 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. 11.5a, 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, and 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. 11.6 and Table 11.6 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.

....................(11.6)

where p = pressure, in kPa; a and b = constants; and T = temperature, in K, as shown in Table 11.6.

• 

  Table 11.6

When using Eq. 11.6, 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 11.7), where L_W-H-V cannot exist.

• 

  Table 11.7

The pressures and temperatures in Fig. 11.5a 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. 11.5b is slightly more complex than Fig. 11.5a, for systems such as ethane + water, propane + water, isobutane + water, or 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. 11.5a 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. 11.5b 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 11.7 shows measured upper quadruple points for simple natural gas components. Q₂ is the origin for two additional 3-phase lines: a vertical L_W-H-L_HC line that is very incompressible and an 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, by line L_W-H-V at conditions between Q₁ and Q₂, and by 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 11.7 lie on a straight line between Q₁ and Q₂, on a semilogarithmic plot (ln p vs. 1/T_a). As discussed below in the Hand Calculations of Hydrate Formation Conditions section, 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. 11.5b, 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 (H-V, H-L_HC, and I-H) for hydrate equilibrium with phases that are not liquid water. 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. 11.5a. 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 in Sec. 11.4.1 apply.

For natural gases that contain oils or mixed condensates, however, the upper portion of the diagram is more like that in Fig. 11.5b. 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. 11.5b.

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. 11.5b, broadens to become an area, such as that labeled CFK in Fig. 11.5c. 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. 11.5d. 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. 11.5d is equivalent to line AQ₁Q₂B in Fig. 11.5b, with three slopes that change at the quadruple points.

In Fig. 11.5d, 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. 11.5d 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. 11.5d has omitted the lines analogous to the three 3-phase lines in Fig. 11.5b (I-L_W-H, which would intersect Fig. 11.5d‘s AQ₁Q₂B at Q₁, and 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. 11.5a) and systems with a liquid hydrocarbon region (as in Fig. 11.5c), 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:

....................(11.7)

where ΔT = hydrate temperature depression from the equilibrium temperature at a given pressure, °F); M = molecular weight of the inhibitor; and 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. The Hand Calculations of Hydrate Formation Conditions section below 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.

Hand Calulations of Hydrate Formation Conditions. The most accurate predictions of hydrate formation conditions are made using commercial phase equilibria computer programs such as ASPEN, HYSYS, Multiflash, Process II, and PVTsim.* These programs are of two types: those which enable the prediction of the pressure and temperature at which hydrates begin to form (incipient hydrate formation programs), and those which predict all phases and amounts at higher pressures and lower temperatures than the incipient hydrate formation point (flash programs, or Gibbs energy minimization programs).

Of these two program types, the flash/Gibbs type is gaining pre-eminence because its predictions are available in the phase diagram interior (where many systems operate), whereas the incipient type provides the P/T points of hydrate initiation. At present, state-of-the-art programs are transitioning to the flash/Gibbs free-energy type.

The basis for both program types is a hydrate equation-of-state (EOS). A clear, prescriptive method for constructing the hydrate flash program has recently been published. The hydrate flash program usually is so complex as to require two or more man-years of single-minded effort to construct a robust version of the program. For this reason and because of readily available commercial programs, engineers usually elect to use those rather than construct another program. (For more details about the hydrate EOS, however, see Chap. 5 of Sloan.)

When gathering critical prediction results for a design, however, it is important to check the program results by hand to determine whether the program has made an unusual prediction. This section offers some hand-calculation techniques for this type of evaluation.

Which Hydrate Conditions Are Calculable by Hand? Not all hydrate conditions are calculable by hand. The Three-Phase L W -H-V Calculations, Estimating the Total Amount of MeOH or MEG to Inject to Inhibit Hydrates, and Hydrate Formation on Expansion Across a Valve or Restriction sections below give hydrate formation hand calculations along the three-phase (L_W-H-V) system and for three-phase (L_W-H-V) hydrate formation on wet gas expansion, as through a valve.

The other three-phase regions (e.g., L_W-H-L_HC and I-H-V) are less important, and methods presented in Three-Phase L_W-H-V Calculations are suitable for checking the accuracy of a computer program in the L_W-H-V region as an indication of the quality of the other three-phase predictions. Four-phase (L_W-H-V-L_HC) hand calculation methods are not available, and one generally must rely on computer methods for this most common flow assurance hydrate concern. Recent work by Hopgood shows that hydrate prediction programs commonly are in error by as much as 5°C for hydrate formation conditions in black oils; this is an area of current research.

For the two-phase regions of hydrate equilibria, such as those shown schematically in the Gas + Pure Condensate + Water Systems (e.g., H₂O + C₂H₆, C₃H₈, or i-C₄H₁₀) section above (i.e., V-H, L_HC-H, and I-H), the key question is that of water content: how much water can a vapor or liquid hydrocarbon phase hold before hydrates will precipitate? Just as knowing the V and L_HC saturation conditions allows the engineer to avoid solid hydrate formation, determining the I-H region (below 273 K) lets the engineer avoid ice or hydrate formation, both of which cause flow problems. Unfortunately, however, for hydrate precipitation from a vapor or liquid hydrocarbon, there is no water content hand calculation analogous to either Fig. 11.1 (for V-L_W water dewpoints) or Fig. 11.3 (for L_HC-L_W water dewpoints).

Three Phase L_W-H-V Calculations. There are several ways to do hand calculations for three-phase L_W-H-V conditions:

• For pure hydrate guests (e.g., CH₄, C₂H₆, C₃H₈, and i-C₄H₁₀), Eq. 11.6 can be used with the constants in Table 11.6, noting the range of application. A somewhat less accurate semilogarithmic interpolation can be performed between the two quadruple points listed for pure components in Table 11.7, as briefly discussed in Gas + Pure Condensate + Water Systems (e.g., H₂O + C₂H₆, C₃H₈, or i-C₄H₁₀) .
• For gas mixtures, a relatively low pressure is required for hydrate formation. For example, at a typical seafloor temperature of 277 K, hydrates will form in a natural gas system if free water is available and the pressure is greater than 1.2 MPa. Hydrate formation data at 277 K were averaged for 20 natural gases, and the average formation pressure was 1.2 MPa. Of the 20 gases, the lowest formation pressure was 0.67 MPa for a gas with 7.0 mol% C₃H₈, while the highest value was 2.00 MPa for a gas with 1.8 mol% C₃H₈. At temperatures below 277 K, pressures below the 1.2 MPa average are required.
• Although it is not presented in this section, the Katz K_VH value method can be used for hydrate formation condition estimation from gas mixtures. Hydrate K_VH values (defined as a component’s mole fraction divided by that in the hydrate) for each gas component are used to determine a hydrate dewpoint for a gas of constant composition. As with the more common DePriester vapor/liquid values (K_VL), the hydrate K_VH values are functions of temperature and pressure. The K_VH method is not considered here for two reasons. First, at a given temperature and pressure, the method gives the same K_VH value, regardless of hydrate type, even though the K_VH value should be a strong function of crystal type. Second, the number of plots (>11) for the corrected method is unwieldy. See Sloan for details and examples of the original K_VH method, including an extension to hydrate formation from water and liquid hydrocarbon (L_W+L_HC+H).
• A more compact, accessible method for hydrate formation from water and gas mixtures is the gas gravity method. Presented in detail below, the gas gravity method is suitable for calculation of L_W-H-V equilibrium pressures and temperatures at the point of hydrate formation. Although the method is only up to 75% accurate in pressure, it gives a fast initial estimate and has the advantage of being extended easily to expansion calculations for hydrate formation from wet gases.

The gas gravity method is the simplest method for quantifying the hydrate formation temperature and pressure. Gas gravity is defined as the molecular weight of the gas divided by that of air. To use the chart shown in Fig. 11.6, calculate the gas gravity and specify the lowest temperature of the pipeline/process. The pressure at which hydrates will form then is read directly from the chart at that gas gravity and temperature.

• 

  Fig. 11.6 – Pressure/temperature curves for predicting hydrate formation (from Katz).

To the left of every line, hydrates will form with a gas of that gravity. At pressures and temperatures to the right of every line, the system will be hydrate-free. The following example, modified from Katz’s original work, illustrates chart use.

* ASPEN and HYSYS are products of AspenTech. Multiflash is a product of Infochem Services Ltd, London. Process II is a product of Simsci-Esscor, Lake Forest, California. PVTsim is a product of CalSep, Houston.

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Example 11.1 A gas is composed of (mol%) 92.67% methane, 5.29% ethane, 1.38% propane, 0.182% i-butane, 0.338% n-butane, and 0.14% pentane. When free water is present with the gas, find:

• The pressure at which hydrates form at 283.2 K (50°F).
• The temperature at which hydrates form at 6.8 MPa (1,000 psia).
• The highest gas gravity without hydrate formation, when the pressure is 4.76 MPa (700 psia) and the temperature is 289 K (60°F).

Solution: The gas gravity (γ_g) is calculated as 0.603, using the average molecular weight calculated in Table 11.8 and Eq. 11.8:

....................(11.8)

where = the total molecular weight of the gas in the mixture and M_a = the molecular weight of air. Using this gas gravity number to read Fig. 11.6 indicates that:

• At 50°F, the hydrate formation pressure is 450 psia at a gas gravity of 0.603.
• At 1,000 psia, the hydrate formation temperature is 61°F at a gas gravity of 0.603.
• At 700 psia and 60°F, gases with gravity below 0.69 are not expected to form hydrates.
• Caution: this method is only approximate for several reasons:
• Fig. 11.6 was generated for gases containing only hydrocarbons and should be used with caution for gases with substantial amounts of CO₂, H₂S, or N₂.
• The curves should not be extrapolated to temperatures below 273 K (32°F) or to pressures above 2.72 MPa (4,000 psia)—the data limits upon which the gas gravity plot is based.
• For the hydrate equilibrium temperature (T_eq) and pressure (p_eq), the estimated inaccuracies for 0.6 gravity gas are at a maximum of ±7°F or ±500 psia.

• 

  Table 11.8

Over the 60 years since the generation of the chart in Fig. 11.6, the development of more accurate hydrate data and prediction methods have led to the gravity method being used as a first estimate or a check, rather than as a principle method, despite its ease of calculation. The introduction of the Hand Calculations of Hydrate Formation Conditions section above discusses the computer programs available, which are the current and most accurate method for prediction of hydrate conditions.

Most commonly now, perhaps, the gas gravity chart is used to check the conditions at which a flowline fluid will enter the hydrate formation region. Such a calculation requires a second multiphase fluid flow simulator, such as OLGA or Pipephase.* A discussion of such simulators is beyond the scope of this chapter, however.

Estimating the Total Amount of MeOH or MEG to Inject to Inhibit Hydrates. The amount of injected MeOH or MEG needed to inhibit hydrate formation is the total of the amounts that reside in three phases: aqueous liquid, hydrocarbon vapor, and liquid hydrocarbon. The inhibitor in the hydrocarbon vapor and liquid hydrocarbon phases has no effect—hydrate inhibition occurs only in the aqueous phase—but this inefficiency is unavoidable.

The Hammerschmidt equation (Eq. 11.7) provides the MeOH or MEG concentration in the aqueous phase. With that inhibitor concentration as a basis, the amount of inhibitor in the vapor or liquid hydrocarbon phases is estimated by:

....................(11.9)

where K is a function of inhibitor used and the phase into which it partitions [e.g., (K_V) MeOH or (K_L)_MEG]; a and b = constants for the two most common inhibitors, MeOH and MEG, as listed in Table 11.9; and T = temperature, in °R.

• 

  Table 11.9

With Eq. 11.9, one can calculate the total amount of hydrate inhibitor needed, as shown below in Ex. 2. Note that the fourth (missing) value of (K_V)_MEG in the above table is taken as zero because the amount of ethylene glycol lost to the vapor phase is too small to measure. Although these expressions for the inhibitor partitioning are the most current, inhibitor partitioning is an active research area, for which new equations and constants will be developed over the coming few years.

* OLGA is a product of Scandpower AS, Oslo, Norway (2000). Pipephase is a product of Invensys, Inc., Lake Forest, California (2004).

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Example 11.2 A pipeline with the gas composition below has inlet pipeline conditions of 195°F and 1,050 psia. The gas flowing through the pipeline is cooled to 38°F by the surrounding water. The gas also experiences a pressure drop to 950 psia. Gas exits the pipeline at a rate of 3.2 MMscf/D. The pipeline produces condensate at a rate of 25 B/D, with an average density of 300 lbm/bbl and an average molecular weight of 90 lbm/lbm mol. Produced free water enters the pipeline at a rate of 0.25 B/D.

Find the rate of methanol injection that will prevent hydrates in the pipeline for a natural gas composed of (mol%) 71.60% methane, 4.73% ethane 1.94% propane, 0.79% n-butane, 0.79% n-pentane, 14.19% carbon dioxide, and 5.96% nitrogen.

The basis for these calculations is 1.0 MMscf/D. Methanol will exist in three phases: water, gas, and condensate. The steps in the solution are:

1. Calculate hydrate formation conditions using the gas gravity chart (Fig. 11.6).
2. Calculate the wt% MeOH needed in the free-water phase.
3. Calculate the free (produced and condensed) H₂O/MMscf of natural gas.
4. Calculate the methanol needed in the aqueous phase.
5. Calculate the methanol lost to the gas phase.
6. Calculate the methanol lost to the liquid hydrocarbon phase.
7. Sum the amounts in steps 4, 5, and 6 for the total methanol needed.

Step 1—Calculate hydrate formation conditions using the gas gravity chart. Start by calculating the gas gravity (γ_g) , using Eq. 11.8 and the data in Table 11.10:



At γ_g = 0.704, the gas gravity chart shows the hydrate temperature to be 65°F at 1,050 psia.

• 

  Table 11.10

Step 2—Calculate the wt% MeOH needed in the free-water phase. Recall the Hammerschmidt equation (Eq. 11.7):



where ΔT = the hydrate temperature depression from the equilibrium temperature at a given pressure (65°F – 38°F = 27°F); M = molecular weight of the inhibitor (methanol = 32.0); and W = wt% of the inhibitor in the free-water phase. Rearranging the Hammerschmidt equation to find W:



yields that 27 wt% of methanol is needed in the free-water phase to provide hydrate inhibition at 1,050 psia and 38°F (highest pressure, lowest temperature) for this gas.

Step 3—Calculate the mass of liquid water/MMscf of natural gas. a) Calculate the mass of condensed H₂O. In the absence of a water analysis, use the water content chart (Fig. 11.1) to calculate the amount of water in the vapor/MMscf. By this chart, 1,050 psia and 195°F, the inlet gas water content is 600 lbm/MMscf. At 950 psia and 38°F, the exiting gas contains 9 lbm/MMscf of water. The difference between the original water and the water remaining in the gas is the mass of liquid water from condensation: 600 – 9 = 591 lbm/MMscf.

b) Calculate the mass of produced H 2 O flowing into the line. Convert the produced water of 0.25 B/D to lbm/MMscf:



c) Calculate the total mass of water/MMscf of gas. Sum the condensed and produced water:



Step 4—Calculate the rate of methanol needed in the aqueous phase. With 27.0 wt% methanol required to inhibit the free-water phase, and the mass of water/MMscf calculated at 618.4 lbm in the free-water phase, the mass (m) of MeOH/MMscf is



Solving this equation yields m =228.7 lbm MeOH in the water phase. The mole fraction MeOH in the free-water phase (x_MeOH-W) is:



The mole fraction MeOH in the free-water phase is x_MeOH-W = 0.172.

Step 5—Calculate the MeOH lost to the gas phase. The distribution constant of MeOH in the gas is calculated by Eq. 11.9 to be 38°F (497.7°R), relative to the methanol in the water:



The mole fraction of MeOH in the vapor (y_MeOH)_-V is:



The daily gas rate is 8,432 lbm mol [= 3.2 × 10⁶ scf/(379.5 scf/lbm mol), where an scf is at 14.7 psia and 60°F], so that the MeOH lost to the gas is 4.29 lbm mol (= 0.000509 × 8,432) or 137.3 lbm/D. Because the calculation basis is 1 MMscf/D, the amount of MeOH lost is 42.9 lbm/MMscf (= 137.3 lbm/3.2 MMscf).

Step 6—Calculate the amount of MeOH lost to the condensate.



The mole fraction MeOH in condensate (x_MeOH-HC) is:



The condensate rate is 26.0 lbm mol/MMscf (= 25 B/D × 300 lbm/bbl × 1 lbm mol/90 lbm × 1 d/3.2 MMscf), so that the amount of MeOH in condensate is 0.0314 lbm mol/MMscf [= 0.001207 × 26/(1 – 0.001207)], or 1.0 lbm/MMscf).

Step 7—Sum the total amount of MeOH/MMscf. The amounts of MeOH in Ex. 2 are shown in Table 11.11.

• 

  Table 11.11

This example illustrates the fact that a significant amount of MeOH partitions into the vapor and liquid hydrocarbon phases. The calculation could be done equally well for MEG, substituting appropriate constants in Eq. 11.9. See Sloan for further examples of MeOH and MEG partitioning.

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Hydrate Formation on Expansion Across a Valve or Restriction. When water-wet gas expands rapidly through a valve, orifice, or other restriction, hydrates form because of rapid gas cooling by Joule-Thomson (constant enthalpy) expansion. Hydrate formation with rapid expansion from a wet line is common in fuel gas or instrument gas lines. In well-testing, startup, and gas lift operations, hydrates can form with high pressure drops, even with a high initial temperature, if the pressure drop is very large. This section provides an initial hand calculation method for situations when hydrates will form upon rapid expansion. Sloan (pp. 21 ff ) contains a more accurate computer calculation method and discussion.

If a gas expands rapidly through a valve or restriction, the fluids will cool much faster than with heat transfer, possibly causing the system to enter the hydrate formation regime at the valve/restriction discharge. Two rapid expansion curves for the same 0.6-gravity gas are shown in Fig. 11.7. Intersections of the gas expansion curves with the hydrate formation line limits the expansion discharge pressures from two different high initial P/T conditions, labeled Gas A and Gas B.

• 

  Fig. 11.7 – Intersection of free expansion curves with hydrate-formation region for 0.6-gravity gases (from Katz).

In Fig. 11.7, the curves determine the restriction downstream pressure at which hydrate blockages will form for a given upstream pressure and temperature. Gas A expands from 13.6 MPa (2,000 psia) and 316 K (110°F) until it strikes the hydrate formation curve at 0.53 MPa (780 psia) and 287 K (57°F), so 0.53 MPa (780 psia) represents the limit to hydrate-free expansion. Gas B expands from 12.2 MPa (1,800 psia) and 322 K (120°F) to intersect the hydrate formation curve at a limiting pressure of 1.97 MPa (290 psia) and 279 K (42°F). In expansion processes, the upstream temperature and pressure are known, but the discharge temperature usually is unknown, and a downstream vessel normally sets the discharge pressure.

Cooling curves such as the two in Fig. 11.7 were determined for constant enthalpy (Joule-Thomson) expansions, obtained from the First Law of Thermodynamics for a system flowing at steady state, ignoring kinetic and potential energy changes:

....................(11.10)

where ΔH₂ = the enthalpy difference across the restriction (downstream to upstream), Q = the heat added, and W_s = shaft work obtained at the restriction. Normal flow restrictions (e.g., valves and orifices) have no shaft work, and because rapid flow approximates adiabatic operation, both W_s and Q are zero. The result is constant enthalpy (ΔH₂ = 0) operation on expansion.

Katz generated charts to determine the hydrate-free limit to gas expansion, combining the gas gravity chart (Fig. 11.6) and the gas enthalpy/entropy charts by Brown to determine Fig. 11.7‘s hydrate formation line and cooling lines labeled Gas A and Gas B, respectively. Interestingly, Brown’s charts also could be used with Fig. 11.6 to determine the limits to wet gas expansion across an isentropic device such as a nozzle or turboexpander; however, that has not been done.

Cautioning that the charts apply to gases of limited compositions, Katz provided constant enthalpy expansion charts for gases of 0.6, 0.7, and 0.8 gravities, shown in Figs. 11.8 , 11.9 , and 11.10, respectively. The abscissa (x-axis) in each figure represents the lowest downstream pressure without hydrate formation, given the upstream pressure on the ordinate (y-axis) and the upstream temperature (a parameter on each line).

Note that maxima in Figs. 11.8 through 11.10 occur at the upstream pressure of 40.8 MPa (6,000 psia), the Joule-Thomson inversion pressure. At pressures above 6,000 psia, these gases will cool on expansion.

The following three examples of chart use are from Katz’s original work.

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Example 11.3a To what pressure can a 0.6-gravity gas at 13.6 MPa (2,000 psia) and 311 K (100°F) be expanded without danger of hydrate formation?

According to Fig. 11.8, the maximum pressure of gas expansion is 7.14 MPa (1,050 psia).

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Example 11.3b

How far can a 0.6-gravity gas at 13.6 MPa (2,000 psia) and 333 K (140°F) be expanded without hydrate formation?

Fig. 11.8 shows that there is no intersection with the 333 K (140°F) isotherm. Hydrates will not form upon expansion to atmospheric pressure.

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Example 11.3c

A 0.6-gravity gas is to be expanded from 10.2 MPa (1,500 psia) to 3.4 MPa (500 psia). What is the minimum initial temperature that will permit the expansion without danger of hydrates?

Fig. 11.8 shows that 310 K (99°F) is the minimum initial temperature to avoid hydrates.

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Figs. 11.8 through 11.10 incorporate the inaccuracies of the gas gravity charts from which they were derived. As indicated in the Three-Phase L_W-H-V Calculations section above, the 0.6-gravity chart (used for both hydrate formation and gas expansion) may have inaccuracies of ±3.4 MPa (500 psia). Accuracy limits for these expansion curves have been tested by Loh et al., 23 who found, for example, that the allowable 0.6-gravity gas expansion from 23.8 MPa (3,500 psia) and 338 K (150°F) should be 2.8 MPa (410 psia), rather than the value of 4.76 MPa (700 psia) given by Fig.11.8.

• 

  Fig. 11.8 – Permissible expansion of a 0.6-gravity natural gas without hydrate formation (from Katz).

• 

  Fig. 11.9 – Permissible expansion of a 0.7-gravity natural gas without hydrate formation (from Katz).

• 

  Fig. 11.10 – Permissible expansion of a 0.8-gravity natural gas without hydrate formation (from Katz).

*

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

Conclusions

The fundamental reason an engineer should consider the equilibria is the possible existence of a water phase, in which hydrates can form, causing multiphase flow, flow blockage, and other engineering challenges. Flowline blockages can cause losses of millions of dollars of income while blockage remediation is occurring. The most accurate prediction methods allow avoidance of flowline blockages. With this review of the topic of H₂O + hydrocarbon equilibria and the hand-calculation methods provided in this chapter, the engineer should be able to determine whether the computer calculation is within the accuracy bounds of the hand-calculation methods and, if not, whether the circumstances require a more accurate computer calculation. For a more complete exposition of the hydrate calculation methods, see Makogon and Sloan.

Nomenclature

a	=	constant
b	=	constant
c	=	constant
C	=	in the Gibbs phase rule, the number of components in a nonreacting system
CG	=	correction factor for gas gravity
CS	=	correction factor for salinity
Cv	=	vapor composition
F	=	in the Gibbs phase rule, the number of intensive variables required to define a nonreacting system (degrees of freedom)
H1	=	the enthalpy of water in the hydrocarbon solution minus that of pure liquid water, Btu/lbm
H2	=	enthalpy difference across a valve or restriction, Btu/lbm
K	=	amount of inhibitor in the vapor or liquid hydrocarbon phases
(KL)MEG	=	liquid distribution coefficient, , of MEG, dimensionless
(KL)MeOH	=	liquid distribution coefficient, , of MEOH, dimensionless
KVH	=	a Katz’s value term, defined as a component’s mole fraction divided by that in the hydrate
KVL	=	DePriester’s vapor/liquid value, defined as a component’s mole fraction divided by that in the liquid
(KV)MEG	=	vapor distribution coefficient, , of MEG, dimensionless
(KV)MeOH	=	vapor distribution coefficient, , of MEG, dimensionless
m	=	mass, lbm
M	=	molecular weight
Ma	=	the molecular weight of air
	=	the average molecular weight of a gas in a mixture
Nc	=	carbon number
p	=	pressure, psia
peq	=	pressure, hydrate equilibrium, psia
P	=	in the Gibbs phase rule, the number of phases in a nonreacting system
Q	=	heat added to a system flowing at steady state, Btu/hr
T	=	temperature, °F
Ta	=	temperature, absolute,°F
Teq	=	temperature, hydrate equilibrium, °F
W	=	wt% of the inhibitor in the free-water phase
Ws	=	shaft work
xHC-W	=	mole fraction for hydrocarbon in liquid water
xMeOH-HC	=	mole fraction MeOH in condensate
xMeOH-W	=	mole fraction MeOH in the free-water phase
xW-HC	=	mole fraction for water in liquid hydrocarbon
yMeOH-V	=	mole fraction of MeOH in vapor
z	=	mole fraction of a component in mixture
γg	=	gas gravity
∆T	=	hydrate temperature depression below the equilibrium temperature at a given pressure, °F

References

SI Metric Conversion Factors

Å	×	1.0*	E – 01	=	nm
atm	×	1.013 250	E + 05	=	Pa
bbl	×	1.589 873	E – 01	=	m3
Btu	×	1.055 056	E + 00	=	kJ
°C		°C + 273		=	K
°F		°F + 459.67/1.8		=	K
°F		(°F – 32) / 1.8		=	°C
ft3	×	2.831 685	E – 02	=	m3
lbm	×	4.535 924	E – 01	=	kg
psia	×	6.894 757	E + 00	=	kPa
°R	×	5/9		=	K
U.S. gal	×	3.785 412	E – 03	=	m3

*

Conversion factor is exact.