## November 2019

## Process Optimization

# Accurate prediction of phase equilibrium properties—Part 2

Phase equilibrium properties, such as bubble point, hydrocarbon dewpoint, water dewpoint, phase envelope, two-phase compositions, compressibility factor, hydrate equilibrium properties, etc., for hydrocarbon mixtures have been calculated accurately using the Peng-Robinson cubic equation of state by implementing constant and temperature-dependent binary interaction parameters in the Van der Waals mixing rule.

Phase equilibrium properties, such as bubble point, hydrocarbon dewpoint, water dewpoint, phase envelope, two-phase compositions, compressibility factor, hydrate equilibrium properties, etc., for hydrocarbon mixtures have been calculated accurately using the Peng-Robinson cubic equation of state by implementing constant and temperature-dependent binary interaction parameters in the Van der Waals mixing rule.

These phase equilibrium properties find usage in the design and operation of all kinds of hydrocarbon equipment, such as hydrocarbon pipelines, hydrocarbon pumps, pressure vessels, hydrocarbon storages and distillation columns. Phase equilibrium properties are also required in upstream oil and gas activities like well simulation and oil and natural gas production. Atmospheres of various heavenly bodies are made of hydrocarbons, such as methane (CH_{4}), ethane (C_{2}H_{6}), propane (C_{3}H_{8}), etc., and inorganic gases like nitrogen (N), carbon dioxide (CO_{2}) and hydrogen sulfide (H_{2}S). Simulation of these atmospheres also requires knowledge of phase equilibrium properties.

A new vapor liquid equilibrium (VLE) software^{a} has been developed using basic calculation tools like MS Excel and Visual Basic for Applications (VBA, macro programming) to accurately calculate various phase equilibrium properties. The Peng-Robinson cubic equation of state and Van der Waals mixing rule, using a combination of temperature-dependent and constant binary interaction parameters, are used for these calculations.

Part 1 (October 2019) discussed how the proprietary phase equilibrium software^{a} is designed to give accurate phase equilibrium properties for any mixture of nonpolar or mildly polar hydrocarbons and inorganic gases up to a maximum number of 112 components in the hydrocarbon mixture.

Gas hydrate equilibrium properties for mixtures of nonpolar or mildly polar hydrocarbons and inorganic gases existing with water and including at least one hydrate former can be calculated using the phase equilibrium software. It uses temperature-dependent binary interaction parameters, as per the Enhanced Predictive Peng Robinson 78 (E-PPR78) equation, to calculate component fugacity. These parameters are used in an accurate and reliable statistical thermodynamic model for clathrates developed by Van der Waals and Platteeuw in 1959 to predict gas hydrate equilibrium curves and properties for any mixture of non-polar or mildly polar hydrocarbons and inorganic gases existing with water and including at least one hydrate former.^{6}

Hydrate-forming components included in the phase equilibrium software are CH_{4}, C_{2}H_{6}, C_{3}H_{8}, n-butane, i-butane, ethylene, propylene, cyclopropane, acetylene, N, H_{2}S, CO_{2}, carbon monoxide (CO), argon and oxygen. Additionally, the effects of hydrate inhibitors, such as salts (LiCl, NaCl, KCl, CsCl, CaCl_{2 }and MgCl_{2}); salt mixtures; organic liquids (methanol, ethylene glycol, ethanol, 1-propanol, 2-propanol, t-butyl alcohol and glycerol); sugars (deoxyribose, ribose, fructose, sucrose, glucose and maltose); urea; and formamide can be included in the calculation of gas hydrate equilibrium properties, using the phase equilibrium software.

## Gas hydrate properties

Gas hydrate equilibrium properties calculated using the phase equilibrium software include:

- Equilibrium temperature
- Hydrocarbon liquid and vapor phase compositions
- Aqueous phase composition in cases where aqueous phase exists
- Hydrate phase composition
- Fraction of hydrocarbons in liquid phase
- Type of hydrates formed (S I or S II)
- Hydration number of hydrates formed
- Density of hydrates formed.

Gas hydrate equilibrium properties are calculated at intervals of 0.4 bar, beginning with 0.4 bar and ending at 800 bar (**FIG. 4** and **TABLE 5**). Apart from calculating hydrate equilibrium temperature values and gas hydrate properties throughout the gas hydrate equilibrium curve, the phase equilibrium software also calculates hydrate equilibrium temperature values and gas hydrate properties at any desired pressure value below 800 bar.

The calculation of the fraction of hydrocarbon mixture converted to gas hydrates, the composition of gas hydrates formed, and other properties of formed gas hydrates at temperatures below the gas hydrate equilibrium temperature at the system pressure are desirable in the prediction of pipeline blockage due to hydrate formation. These calculations are also required in the use of the gas hydrate concept in the separation of hydrocarbon mixtures. The phase equilibrium software can calculate the fraction of gas hydrocarbon mixture present in gas, liquid or two-phase form converted to gas hydrate at a temperature value lower than the gas hydrate equilibrium temperature at the system pressure. This applies to any mixture of non-polar or mildly polar hydrocarbons or inorganic gases containing at least one hydrate former. It also calculates the final hydrate, liquid and vapor composition; the average hydration number; the average hydrate density; and the total fraction of initial mixture of water and hydrocarbons/inorganic gases converted to gas hydrates. Additionally, it calculates the gas hydrate equilibrium curve and gas hydrate equilibrium properties at the system pressure (< 800 bar).

If gas hydrates are formed from a hydrocarbon mixture at a temperature slightly lower than the equilibrium hydrate formation temperature at the system pressure, then a small amount of hydrates will form and some hydrocarbon mixture will convert to hydrates. The composition of hydrate formers in the hydrate phase will be different from the composition of hydrocarbon mixture in the gas or liquid phase, resulting in a change in composition of the hydrocarbon mixture in the gas or liquid phase after a small amount of hydrates form. This results in the separation of the hydrocarbon mixture.

Therefore, the phase equilibrium software can be used for hydrate-based gas separation (HBGS) calculations. This new composition will require a lower hydrate equilibrium temperature to form hydrates and will result in the formation of hydrates of different properties, such as type, density, hydration number, composition, etc. The phase equilibrium software continuously calculates hydrate properties at decreasing temperature values, until the desired temperature is reached.

## Additional calculations

Binary VLE curves, such as the concentration diagram (x-y plot), temperature concentration diagram (T-x-y plot) and enthalpy concentration diagram (H-x-y plot) used in the McCabe Thiele and Ponchon Savarit methods to design binary distillation columns, can be calculated using the phase equilibrium software. Binary VLE curves for any binary mixture of non-polar or mildly polar hydrocarbons and inorganic gases at a column operating pressure value of less than the lower critical pressure among the critical pressures of the two pure components of the binary mixture can be calculated using the phase equilibrium software.

Rigorous and more accurate, basic, stage-by-stage design calculations for binary and multicomponent distillation columns can be performed using the phase equilibrium software to calculate minimum reflux ratio, number of equilibrium stages in the rectification and stripping sections, equilibrium temperature of various stages, and liquid and vapor compositions at various stages. The phase equilibrium software calculates the minimum reflux ratio and attainable distillate composition using the Underwood correlation, as well as the overall column efficiency, actual number of stages, column diameter and column height for the distillation column being designed to separate binary and multicomponent mixtures. Distillation column design calculations for the separation of multicomponent mixtures of any number of non-polar or mildly polar hydrocarbons and inorganic gases (up to a maximum limit of 112 components at an operating pressure lower than the lowest critical pressure among the critical pressures of the pure components included in the binary or multicomponent mixture for suitably chosen light-key and heavy-key components) can be performed using the phase equilibrium software.

Various thermodynamic properties (enthalpy change from standard conditions, entropy change from standard conditions, Gibbs free energy change from standard conditions, specific heat at constant pressure, specific heat at constant volume, specific heat ratio, sonic speed, isobaric thermal expansivity and the Joule-Thomson coefficient) throughout the phase envelope curve at intervals of 0.4 bar for pure non-polar or mildly polar hydrocarbons and inorganic gases and their mixtures, including a maximum of 112 components, can be calculated using the phase equilibrium software.

Heavier components in oil and natural gas samples are sometimes characterized as pseudo components. Critical properties of these pseudo components are not documented like normal components, but are instead calculated theoretically based on experimentally determined properties of these fractions (e.g., density, boiling point). These critical properties, such as critical pressure, temperature and volume, and acentric factor, enable the pseudo components to be considered as normal components in phase equilibrium calculations. The proprietary software can include up to 40 pseudo components and can calculate phase envelope, two-phase compositions, hydrate equilibrium curve and properties, and water dewpoint curve for hydrocarbon mixtures, including these pseudo components.

Ammonia (NH_{3}) is being widely used as a refrigerant because of its excellent thermos-physical properties and ozone-friendly characteristic. VLE properties of mixtures containing NH_{3} are desirable in numerous design calculations. The Peng-Robinson cubic equation of state being used in various calculation modules of the phase equilibrium software gives accurate results of VLE properties only for mixtures of nonpolar or mildly polar compounds, whereas NH_{3} is highly polar in nature. Therefore, the Peng-Robinson equation in its usual form cannot be used to find VLE properties of mixtures containing NH_{3}.

However, temperature-dependent binary interaction parameters can be calculated for pairs containing NH_{3} with few non-polar compounds or water, and used in the Peng-Robinson equation to calculate VLE properties of mixtures containing NH_{3}. As temperature-dependent binary interaction parameters can be calculated for pairs containing NH_{3} with CH_{4}, nitrogen (N_{2}), argon (Ar), hydrogen (H_{2}) and water (H_{2}O), VLE properties can be calculated for binary or multi-component mixtures of CH_{4}, N_{2}, Ar, H_{2}, NH_{3} and H_{2}O. The various calculation modules of the phase equilibrium software that can be used for binary or multi-component mixtures of NH_{3} with CH_{4}, N_{2}, Ar, H_{2} and H_{2}O include:

- Bubble point temperature calculator
- Dewpoint temperature calculator
- Bubble point pressure calculator
- Dewpoint pressure calculator
- Two-phase composition calculator
- Phase envelope calculator
- Thermodynamic properties calculator.

As the phase equilibrium software is made using basic calculation tools, such as MS Excel and VBA (macro programming), and is executed on a laptop computer of standard configuration, it can be slow in its execution. However, the emphasis of the phase equilibrium software is not on giving instant results, but rather on providing extremely extensive and accurate results.

Graphical results of the phase equilibrium software are also provided in Part 1 of this article, which appeared in the October issue. **HP**

**NOTES**

^{a} EQ-COMP vapor liquid equilibrium (VLE) software

**LITERATURE CITED**

^{6} Sloan, Jr., E. D. and C. Koh, *Clathrate Hydrates of Natural Gases,* 3rd Ed., CRC Press, September, 2007.

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