Introduction
The simulation capability for Elemental mercury (Hg) distribution across vapor, liquid hydrocarbon, and water phases has been improved in PVTsim NOVA through the utilization of the original formulations of the Peng-Robinson 76/78 and Soave-Redlich-Kwong equations of state. A cubic modeling framework was deliberately chosen over specialized models for modeling Hg as the former allows for the model parameters to be easily integrated into PVTsim as well as external simulation platforms.
To maintain simplicity, constant binary interaction parameters (kij’s) have been strategically applied when appropriate. The model encompasses a diverse array of hydrocarbon components, inorganic gases, water, and common hydrate inhibitors.
Hg Pure Component Properties
The critical temperature (Tc) and critical pressure (Pc) values for Hg were adopted from Kozhevnikov et al. (1996) and Huber et al. (2006). The acentric factors for PR78 and SRK were adjusted to match Huber et al.’s correlation. In the temperature range of 273.15 K to 900.15 K, a good representation of the Huber et al. correlation was achieved, with an average absolute relative deviation (AARD) of 1.3% and a maximum absolute relative deviation (MARD) of 2.0% for PR78, and an AARD of 4.1% and MARD of 6.4% for SRK. Table 1 summarizes the mercury Tc, Pc, acentric factor, and the vapor pressures AARD% against Huber et al. correlation (also detailed in Figure 1).
| EoS | Tc (K) | Pc (MPa) | Acentric factor | AARD% |
| PR78 | 1764 | 167 | -0.1805 | 1.3 |
| SRK | 1764 | 167 | -0.21 | 4.1 |
Hg Solubility in Hydrocarbon Components and Inorganic Gases
For components C2, C3, and CO2, optimal constant kij values have been derived to replace the temperature-dependent expressions from Chapoy et al. Table 2 presents the C2, C3, and CO2 kij values with Hg.
Meanwhile, for other components as shown in Table 3, the constant kij values determined by Chapoy et al. have been employed.
| Component | kij | |
| PR78 | SRK | |
| CO2 | 0.345 | 0.345 |
| C2 | 0.08 | 0.076 |
| C3 | 0.055 | 0.059 |
The Hg solubility data in binary and multicomponent systems used for verification purposes primarily originates from the same sources referenced in the supplementary material of Chapoy et al. (2020a), along with additional data presented in the Chapoy et al. (2020a) paper itself. Table 3 summarizes the results for binary systems, which demonstrate good to acceptable accuracy across all components. Utilizing a constant kij for CO2 incurs a modest cost while maintaining accuracy.
| EoS | PR78 | SRK | ||
| Comp | AARD% | MARD% | AARD% | MARD% |
| N2 | 9.5 | 37.3 | 9.3 | 38.0 |
| CO2 | 10.4 | 31.2 | 10.6 | 23.6 |
| C1 | 5.4 | 30.5 | 5.7 | 33.9 |
| C2 | 6.9 | 20.8 | 7.2 | 21.6 |
| C3 | 6.9 | 14.2 | 7.6 | 16.3 |
| iC4 | 9.8 | 47.8 | 23.5 | 57.9 |
| nC4 | Only data above 457 K. No comparisons made. | |||
| iC5 | 5.3 | 5.3 | 2.1 | 2.1 |
| nC5 | 8.5 | 24.8 | 6.9 | 21.9 |
| nC6* | 12.7 | 27.5 | 5.3 | 19.2 |
Hg Solubility in Multi Component Mixtures.
The solubility of Hg in multicomponent mixtures indicates good to acceptable accuracy as presented in Table 4. It is important to note that most of the data points represent the solubility of Hg in vapor, while only a few represent the solubility of Hg in liquid. None of the data points provide information on the partitioning (solubility) of Hg between vapor and liquid phases. Furthermore, the available data in the literature do not include components heavier than nC6, which means that the solubility of Hg in condensate or oil-like mixtures is not represented.
| EoS | PR78 | SRK | ||
| Mix (main components) | AARD% | MARD% | AARD% | MARD% |
| MIX 1 (89% C1, 6% C2) | 8.1 | 20.9 | 9.2 | 24.5 |
| MIX 2 (75% C1, 10% C2, 9% CO2) | 7.6 | 15.6 | 9.6 | 20.3 |
| MIX 3 (69% CO2, 26% C1) | 9.5 | 25.0 | 11.0 | 29.2 |
| Mix 1 in Table 1 in Chapoy et al. (2020b) (32.4% nC4, 33.5% nC5, 34.1% nC6) | 2.5 | 5.2 | 4.5 | 7.2 |
| Mix 2 in Table 1 in Chapoy et al. (2020b) (59.4% C3, 40.6% iC4) | 8.2 | 23.4 | 9.1 | 25.0 |
| Mix 3 in Table 1 in Chapoy et al. (2020b) (88.1% C1, 6.2% C2) | 8.3 | 25.0 | 8.9 | 25.7 |
As an illustration, Figure 2 shows the PVTsim MIX 1 Hg solubility predictions with PR78 versus experimental data at -30°C, 0°C, 25°C, and 50°C in a single plot. Hg solubilities were also extrapolated to 100°C, which shows that model predictions appear reasonable up to typical reservoir conditions. At higher temperature, the Hg solubility in the vapor phase is higher. As pressures increase, the solubilities tend to decrease and sometimes pass through a minimum. This effect is more prominent at low temperatures.
Hg Solubility in H2O
PVTsim uses the critical temperatures, critical pressures, and acentric factors for H2O presented in Table 5.
| Component | Critical Temperature (K) | Critical Pressure (MPa) | Acentric Factor |
| H2O | 647.3 | 22.089 | 0.3440 |
The H2O PR76/78 kij expression proposed by Koulocheris (2021) was adopted in PVTsim while the SRK kij expression was derived using the data set provided by Gallup et al. for Hg solubility in H2O. Tables 6 and 7 present the derived kij expression and the associated accuracy achieved.
| Component | PR76/ Koulocheris | SRK |
| H2O | -0.084172 + 0.002422 ∙ T | -0.092356 + 0.002475 ∙ T |
| EoS | PR/PR78 | SRK | ||
| Component | AARD% This work | MARD% This work | AARD% This work | MARD% This work |
| H2O | 2.2 | 9.1 | 1.7 | 3.9 |
Table 8 shows that the temperature range of the data for H2O encompasses typical reservoir temperatures. This is important as H2O is commonly present in produced reservoir fluids.
| Component | Tmin (K) | Tmax (K) | No of points |
| H2O | 273.15 | 373.15 | 8 |
Hg Solubility in Hydrate Inhibitors
PVTsim uses the critical temperatures, critical pressures, and acentric factors for MeOH, MEG, DEG, and TEG presented in Table 9.
| Component | Critical Temperature (K) | Critical Pressure (MPa) | Acentric Factor PR78 | Acentric Factor PR76/SRK |
| MeOH | 512.6 | 8.096 | 0.55226 | 0.55900 |
| MEG | 720.0 | 9.000 | 0.52933 | 0.53470 |
| DEG | 681.0 | 4.661 | 1.10105 | 1.20110 |
| TEG | 710.15 | 3.313 | 1.16490 | 1.28740 |
Tables 10 and 11 present the kij expressions and corresponding accuracies for the data provided by Yamada et al. The simulation accuracy achieved consistently falls within the range of experimental uncertainties for all cases.
| Component | PR78 | SRK |
| MeOH | -0.1294 + 0.00197 ∙ T | -0.1578 + 0.00210 ∙ T |
| MEG | -0.2807 + 0.00267 ∙ T | -0.3014 + 0.00278 ∙ T |
| DEG | -0.4033 + 0.00273 ∙ T | -0.4009 + 0.00278 ∙ T |
| TEG | -0.5249 + 0.00290 ∙ T | -0.5114 + 0.00294 ∙ T |
| EoS | PR78 | SRK | ||
| Component | AARD% | MARD% | AARD% | MARD% |
| MeOH | 3.9 | 5.2 | 4.1 | 4.8 |
| MEG | 4.3 | 5.0 | 4.3 | 6.0 |
| DEG | 7.6 | 12.6 | 7.6 | 12.5 |
| TEG | 3.1 | 4.4 | 3.1 | 4.3 |
All solubility data for Hg in hydrate inhibitors, obtained from Yamada et al. (2021), are presented in Table 12. The data collected is confined to a narrow temperature range at atmospheric pressure. While the validity of the kij expressions strictly applies within this temperature range, it should be noted that the hydrate inhibitors are typically introduced downstream where the temperature (and pressure) is to the lower side. Additionally, in liquid-liquid equilibrium, solubility exhibits minimal dependence on pressure. Test simulations indicate negligible solubility increases (<0.1%) when transitioning from 0.1 to 1 MPa, <1% from 0.1 to 10 MPa, and <10% from 0.1 to 100 MPa. Therefore, the influence of pressure becomes significant somewhere between 10 and 100 MPa. Although this increase in solubility does not necessarily imply an increase in simulation uncertainty, the magnitude of the increase lacks verification through experimental data.
| Component | Tmin (K) | Tmax (K) | No of points |
| MeOH | 298.2 | 333.3 | 4 |
| MEG | 303.3 | 333.2 | 4 |
| DEG | 303.2 | 333.2 | 4 |
| TEG | 303.2 | 333.4 | 4 |
Conclusion
The PVTsim modeling capability on the solubility of elemental Hg has been improved with the introduction of new model parameters for a wide range of hydrocarbon components, inorganic gases, and aqueous substances. Specifically, binary interaction parameters (kij values) are optimized for the original formulations of the Soave-Redlich-Kwong, Peng-Robinson 1976, and Peng-Robinson 1978 equations of state. While a constant kij is sufficient for hydrocarbon components and inorganic gases, it was found that an expression linear in temperature is needed for an accurate representation of interactions with aqueous components.
References
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Chapoy, A., Ahmadi, P., Yamada, J. et al. 2020. Elemental mercury partitioning in high pressure fluids: Part 2: Model validations and measurements in multicomponent systems. Fluid Phase Equilibria 523: 112773. doi: https://doi.org/10.1016/j.fluid.2020.112773
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