AQUAlibrium was developed for calculating the fluid phase equilibria in systems composed of natural gas (both sweet and sour, sour meaning they contain hydrogen sulfide) and acid gases (hydrogen sulfide and carbon dioxide) in the presence of water. The combination of these gases and water results in a surprising and interesting variety of phase equilibria.
The philosophy in the development of AQUAlibrium was to provide a rigorous thermodynamic model that results in the highest accuracy predictions over the range of temperature and pressure of interest to the natural gas industry. This ranges from the low pressure situations, such as an atmospheric storage tank, to high pressures, such as those encountered in reservoirs. Temperatures range from conditions where solids are encountered up to about 200°C.
This report details the development of AQUAlibrium and, in a few cases, demonstrates its accuracy. Many of the papers cited here use AQUAlibrium even though the original references do not mention it by name.
Another important aspect of AQUAlibrium is its use for performing three-phase calculations. The reader is referred to the paper on Three-Phase Equilibrium for a discussion of this phenomenon.
Indirectly, the work on AQUAlibrium began in the mid-1980s with the doctoral thesis of John Carroll. That study was a thorough review of the phase equilibria in the system hydrogen sulfide + water. Many problems were revealed with the existing literature for this system. Fortunately, resolutions were also presented.
At that time, the high-pressure fluid phase equilibria was modeled using an equation of state and the low pressure equilibria with a Henry's law approach. This work is summarized in a series of papers: Carroll and Mather (1989a,b,c) and Carroll (1990). The equation of state was very complex with temperature- and composition-dependent mixing rules. However, the equation of state was surprisingly accurate for all phases and it provided a clearer picture of the phase equilibrium in this system.
The equation of state method proved so powerful that it revealed problems with the often-quoted smoothed data of Selleck et al. (1952). From then on, particularly in the development of AQUAlibrium, the smoothed data of Selleck et al. (1952) were rejected; only their original, raw data would be used. Models built using the smoothed data of Selleck et al. (1952) are prone to error. This is one advantage of AQUAlibrium over other models. Although the fact that the smoothed data of Selleck et al. (1952) are dubious, this knowledge does not seem to have spread to the engineering community at large.
Finally a thorough description of the equilibria in the system hydrogen sulfide+water was given by Carroll (1998a,b). These papers give a through description of the various phenomena in some detail. Much of the discussion in these papers is based on calculations from AQUAlibrium.
Fig. 1 High Pressure Phase Equilibria in the System Hydrogen Sulfide + Water - from Carroll and Mather (1989a); solid curves from equation of state model
Fig. 2 Water Content of Hydrogen Sulfide at Low Pressure - curves from AQUAlibrium
The next phase was an examination of the low pressure solubility of carbon dioxide in water. The amount of data available for this system is voluminous, even at low pressure. A thorough and critical review was conducted (Carroll et al., 1991). The solubility was modeled with Henry's law, similar to that used for hydrogen sulfide.
This was perhaps the most thorough review of the low pressure solubility of carbon dioxide in water and perhaps the most thorough review of any solubility. The culmination of this work was that it is quoted in the CRC Handbook of Chemistry and Physics. This work is also discussed in the IUPAC Solubility Series (Carroll and Mather, 1996).
Carbon dioxide was the first component where the Henry's law approach at high pressure was examined in some detail (Carroll and Mather, 1992b). In this paper it was demonstrated that a form of Henry's law could be used for modeling the solubility of carbon dioxide in water for pressures up to about 100 MPa.
The accurate description of the phase equilibria in the system carbon dioxide+water was an important step in the development of AQUAlibrium.
Fig. 3 Henry's Constant for Carbon Dioxide in Water - from Carroll et al. (1991)
Fig. 4 Water Content of Carbon Dioxide in the Near-Critical Region - curves from AQUAlibrium
Over the years additional components were added to the library for AQUAlibrium. The most important of these are the hydrocarbons, which make up the bulk of natural gas. The solubility of methane, ethane, and propane in water are described in Carroll and Mather (1997b).
Fig. 5 The Solubility of Methane in Water - from Carroll and Mather (1997a), curves from AQUAlibrium
Fig. 6 The Solubility of Propane in Water - from Carroll and Mather (1997a), curves from AQUAlibrium
Butane proved to be a very difficult addition to the library. The available data were so poor that it made analysis very difficult. Again, smoothed data available in the literature were rejected for the original raw, experimental data. Unfortunately, this did not help very much. Additional, new experimental data did not clarify things either. Nonetheless, the model was used to correlate the data well within experimental error. This work is summarized in Carroll and Mather (1997a) and the curious reader should review this paper to see how bad the data are.
Fig. 7 The Solubility of n-Butane in Water at 37.8°C (note the scatter in the data) - solid curve from AQUAlibrium
Perhaps the major step in the development of AQUAlibrium was the decision to employ a split model for the phase equilibria. Henry's law would be used to model the aqueous phase and an equation of state for the non-aqueous phases (gas and non-aqueous liquid). The pleasant surprise was that this approach was accurate for modeling the compositions of the three phases encountered in these systems.
A series of papers was published describing in some detail the application of Henry's law in general (Carroll, 1999b, 1993, 1992, 1991). In these papers several versions of Henry's law were presented and it was demonstrated that a form of Henry's law could be used in regions where it was otherwise thought Henry's law was not applicable. These regions included:
- high pressure,
- soluble components,
- liquid-liquid equilibrium,
- mixtures of solvents,
- mixed solutes, and
- systems with chemical reactions
The above mentioned papers clearly demonstrate that Henry's law is much more versatile than many people think.
The split model as employed in AQUAlibrium uses the Peng-Robinson equation of state for the non-aqueous phases. Thus it was important to establish the accuracy of the equation of state for many of this system, without water present. Again a series of investigations was conducted into the equilibrium, particularly for hydrogen sulfide+hydrocarbon mixtures. It was demonstrated that the equation of state did accurately model the equilibrium in these systems (Carroll and Mather, 1995a, 1995b, 1992a, and Jou et al., 1995).
The accuracy of the Peng-Robinson equation of state was further demonstrated by Carroll (1999a) on a larger number of systems important to AQUAlibrium.
The model was also successfully applied to equilibria in the system nitrous oxide+water (Jou et al., 1992 and Jaffer et al., 1993). Admittedly, this system has limited application and thus nitrous oxide is not included in the standard component library. However, nitrous oxide exhibits behavior similar to carbon dioxide. In fact, the reason for studying nitrous oxide is because it is an analog for carbon dioxide in other experiments.
One application where AQUAlibrium has proved very useful is the design of acid gas injection schemes. This is chronicled in the series of papers Carroll (1998a,b, 1999b) and Carroll and Maddocks (1999).
The phase behavior in systems containing water plus hydrogen sulfide and/or carbon dioxide is considerably more difficult than for sweet natural gas. In particular, the acid gases are significantly more soluble in water than are the hydrocarbon components of natural gas. Furthermore, the water content of acid gases exhibits a minimum. That is, at low pressure the water content of the gas decreases with increasing pressure, which is similar to sweet gas. However, a point is reached where the water content is a minimum. At higher pressures the water content increases. AQUAlibrium accurately predicts this behavior.
AQUAlibrium was developed over several years. Careful consideration was given for the inclusion of components into the software. Undoubtedly, the biggest strength of AQUAlibrium is that only critically-reviewed data were used in its development.
AQUAlibrium was designed to fit a niche market - those that want high accuracy estimates of the phase equilibria for a select group of compounds. It is currently used by several engineering firms and academic institutions for a variety of applications.
Note: Titles and abstracts for most of these references can be found on the Publications page.
