Density and Viscosity of CO₂ Binary Mixtures with SO₂, H₂S, and CH₄ Impurities: Molecular Dynamics Simulations and Thermodynamic Model Validation

Abstract

The aim of this study is to generate density and viscosity data for carbon capture utilization and storage (CCUS) mixtures using equilibrium molecular dynamics (EMD) simulations. Binary CO₂ mixtures with SO₂ and H₂S impurities at mole fractions of 0.05, 0.10, and 0.20 were constructed. Simulations were performed across a temperature range of 223–323.15 K and at pressures up to 27.5 MPa using ms2 software. The simulation results were compared with predictions from established models. These included the Multi-Fluid Helmholtz Energy Approximation (MFHEA) for density, and the Lennard-Jones (LJ), Residual Entropy Scaling (ES-NIST), and Extended Corresponding States (SUPERTRAPP) models for viscosity. Available experimental data from the literature were also used for validation. Density predictions showed excellent agreement with MFHEA, especially for CO₂ + SO₂ mixtures, with %AARD values below 1% for 0.05 and 0.10, and 1.60% for 0.20 mole fraction SO₂. For CO₂ + H₂S mixtures, deviations also increased with impurity concentration, reaching a maximum %AARD of 4.72% at 0.20 mole fraction. Viscosity data were validated against experimental values from the literature for a CO₂ + CH₄ (xCH₄ = 0.25) mixture, showing strong agreement with both models and experiments. This confirms the reliability of the MD approach and the thermodynamic models, even for systems lacking experimental data. However, viscosity estimates showed higher uncertainty at lower temperatures and higher densities, a known limitation of the Green–Kubo method. This highlights the importance of selecting an appropriate correlation time to ensure the pressure correlation functions reach a plateau, avoiding inaccurate or uncertain viscosity values.

1. Introduction

To mitigate carbon emissions and confront global warming, one promising approach is the implementation of carbon capture, utilization, and storage (CCUS) projects [1]. A critical factor in the success of these projects is the safe and cost-effective transportation of CO₂ from the capture point to the storage or utilization location. Depending on the CO₂ source and the capture technology used, CCUS fluids may contain various impurities such as N₂, O₂, H₂, CH₄, Ar, CO, SO₂, and H₂S [2,3]. These impurities can significantly influence thermophysical properties, including vapor–liquid equilibrium (VLE), density, and viscosity [4,5,6]. Density and viscosity are particularly important for designing efficient transport systems. Density data are essential for validating equations of state and accurately estimating the mass flow rate. Viscosity, which reflects fluid’s resistance to flow, is crucial for developing thermodynamic models used in commercial software to design process facilities effectively. Two common impurities in CCUS fluids, namely H₂S and SO₂, are highly toxic and corrosive. Their presence poses serious risks to both the personnel and equipment, demanding careful consideration in system design and operation.

Many researchers have investigated the density and viscosity of CO₂ mixtures containing impurities through experimental measurements. Buddenburg and Wilke [7] were among the first to estimate viscosities of gas mixtures, including CO₂ + H₂, using properties of the pure components. They built an apparatus similar to the one used by Rankine and Smith [8] which measured viscosity relative to nitrogen by timing a falling mercury pellet that pushed gases through a capillary tube. Using equations from Rankine and Smith [8], they attempted to estimate viscosities for binary mixtures. Jackson [9] measured viscosities of CO₂ + CH₄ mixtures at 298.15 K using a platinum capillary tube viscometer. Dewitt and Thodos [10] used an unsteady-state capillary viscometer to study CO₂ + CH₄ mixtures in the dense gaseous state. Esper et al. [11] examined volumetric properties, including density, for equimolar mixtures of CO₂ + CH₄ and CO₂ + N₂. Hobley et al. [12] developed a novel capillary flow viscometer to study CO₂ + Ar mixtures. Stouffer et al. [13] applied the Burnett isochoric technique to measure densities of CO₂ + H₂S mixtures from 220 K to 450 K and at pressures up to 25 MPa. Loianno and Mensitieri [14] introduced a novel dynamic method using thermal mass flow controllers to retrieve thermodynamic data on pressure, temperature, and density for CO₂ + CH₄ gas mixtures. Li et al. [15] reviewed experimental data and theoretical models for the PVTxy properties of CO₂ mixtures relevant to CCUS. Al-Siyabi [16] investigated how impurities affect CO₂ stream properties. Locke et al. [17] introduced a clamped vibrating-wire instrument to measure viscosities of gas mixtures. Pinho et al. [18] used a microfluidic approach with HP/HT capillary devices to simultaneously measure density and viscosity. Nazari et al. [19] studied thermophysical properties, including density, for CO₂ + H₂S and CO₂ + SO₂ mixtures from 273 K to 353 K and at pressures up to 42 MPa, covering gas, liquid, and supercritical regions. Chapoy et al. [20] and Owuna et al. [21] generated extensive experimental data on density and viscosity for CO₂ + CH₄ and CO₂ + H₂ mixtures across temperatures from 238 K to 423 K and at pressures up to 80 MPa. Ahmadi et al. [22] measured density for three multicomponent CO₂ mixtures with xCO₂ values of 0.406, 0.693, and 0.987 over a temperature range of 220–422 K and at pressures up to 62 MPa. They studied mixtures with different impurities which included hydrocarbons, from methane to heptane, as well as nitrogen. Jung and Schmick [23] measured the viscosity of diluted gas systems including the CO₂ + SO₂ system in the range of 287.65 to 291.15 K. Chakraborti and Gray [24] measured gaseous mixtures containing polar gases. They studied seven binary mixtures including CO₂ + SO₂ at the 298.15 K, 308.15 K, and 353.15 K isotherms. Bhattacharyya and Ghosh [25] employed an oscillating-disk viscometer to measure viscosities of polar–quadrupolar gas mixtures. Viscosities of CO₂ + SO₂ were measured in the temperature range of 238.15 K to 308.15 K.

Our literature review shows that experimental data, especially on viscosity, are very limited for binary mixtures under extreme pressure and temperature conditions. While some density data exist [13,26,27,28], few viscosity data are available for CO₂ + SO₂ mixtures, and no viscosity data were found for CO₂ + H₂S mixtures. This is likely due to the safety considerations and hazards related to handling these fluids in laboratories. In such cases, molecular simulation offers a valuable alternative for generating semi-experimental thermodynamic data. Several researchers have used molecular simulations to study the density and viscosity of CCUS mixtures. Lachet et al. [29] calculated density, VLE, and transport properties for CO₂ + N₂O and CO₂ + NO mixtures. Xue et al. [30] examined the effect of impurities on the shear viscosity of CO₂. They used MD simulations to calculate viscosity for pure CO₂ and a CO₂ + N₂ + O₂ mixture, comparing results with theoretical models. Their findings showed that N₂ and O₂ increase viscosity when mixed with CO₂. Fernandez et al. [31] performed molecular simulations to calculate viscosity and thermal conductivity for ten real fluids. They used two-center Lennard-Jones plus point quadrupole (2CLJQ) models, with parameters fitted to VLE data. Their MD results deviated by 10% from the experimental data. They also noted the slow convergence of the Green–Kubo integral for shear viscosity at low temperatures and high densities. Aimoli et al. [32] compared different force fields and predicted thermodynamic properties, including density, for CO₂ and CH₄ under supercritical conditions up to 900 K and 100 MPa. Their results showed that force fields fitted to VLE data can also predict other properties over wide temperature and pressure ranges. MD simulations were generally more accurate than the Peng–Robinson equation of state, especially near critical conditions and high-pressure conditions. In another study, Aimoli et al. [33] predicted transport properties of CO₂ and CH₄ from 273.15 K to 573.15 K and at pressures up to 800 MPa using MD simulations in the NVT ensemble using the LAMMPS package [34]. They tested seven CO₂ models and three CH₄ models, including single-site, multi-site, rigid, and flexible types. They found that the choice of molecular model strongly affected accuracy, but flexibility had little impact. At high densities, single-site models showed a caging effect that reduced mobility and led to viscosity overestimation. They concluded that the three-site TraPPE [35] and EPM2 [36] are suitable for CO₂, while the single-site TraPPE model works best for methane. Recently, Raju et al. [37] generated a large dataset of thermophysical properties, including density and viscosity, for CO₂-rich mixtures with N₂, Ar, H₂, and CH₄ impurities using MD simulations.

Based on our literature review, most molecular simulation studies focus on calculating VLE properties. To the best of our knowledge, no viscosity data exist for CO₂ binary mixtures with SO₂ and H₂S. This gap is likely due to the hazardous nature of these components, which pose safety risks in laboratory settings. To address this limitation, the aim of this study is to generate semi-experimental data for these mixtures, which are relevant to CCUS operations. We consider impurity concentrations up to 0.20 mole fraction, slightly more than typical CCUS candidate fluids, to support future model tuning. We first validate our molecular dynamics (MD) approach using available experimental data for the viscosity of CO₂ + CH₄ mixtures (xCH₄ = 0.25). Then, new data are generated for mixtures with 0.05, 0.10, and 0.20 mole fractions of impurity. Finally, the MD results are compared with predictions from the MFHEA reference equations of state [38,39] and existing viscosity models, including Lennard-Jones (LJ) [40], Residual Entropy Scaling (SRES/ES-NIST) [41,42], and Extended Corresponding States (ECS/SUPERTRAPP) [43].

2. Theoretical Background

Molecular dynamics (MD) simulation is a powerful technique widely used across many scientific fields. In this method, molecular models describe interatomic forces, and phase space trajectories are generated by integrating classical equations of motion. The most accurate way to study thermophysical properties through simulations is to use the first-principles approaches. These involve solving the electronic structure of atomic configurations to determine interatomic forces. Such methods, introduced by Car and Parinello [44], are known as ab initio MD (AIMD) and typically rely on density functional theory (DFT). Although highly accurate, AIMD is limited to small systems with only a few hundred atoms and short simulation times typically in the picosecond (ps) range. Due to these limitations, empirical force field-based methods are often preferred. These allow simulations of much larger systems up to hundreds of thousands of atoms and longer timescales, reaching microseconds. Force fields are mathematical expressions that relate the system’s potential energy to particle coordinates. In molecular systems, interactions are divided into bonded and non-bonded types. Bonded interactions include bond stretching, angle bending, and dihedral rotations. Non-bonded interactions consist of short-range Van der Waals forces and long-range electrostatic forces.

Many functional forms exist to model these interactions. For simplicity, harmonic potentials are commonly used for bonds and angles (see Equation (1)). The 12-6 Lennard-Jones formula and Coulomb’s law are typically used for Van der Waals and electrostatic forces, respectively (see Equation (2)). In these equations, r is the distance between atoms, ϵ is the depth of the potential well (dispersion energy), and σ is the distance at which the potential is zero (often interpreted as particle size). The terms 1/r¹² and 1/r⁶ represent repulsive and attractive forces, respectively. For interactions between different atom types, the Lorentz–Berthelot combination rules [45,46] are applied. In these rules, η and ξ are binary parameters, typically set to 1 as the standard form (see Equations (3) and (4)). To improve computational efficiency, both Van der Waals and electrostatic forces are truncated using a cutoff radius (r_c).

$${\mathrm{U}}_{\mathrm{B}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{d}}=\sum {\mathrm{K}}_{\mathrm{r}}{(\mathrm{r}-{\mathrm{r}}_{\mathrm{e}\mathrm{q}})}^2+\sum {\mathrm{K}}_{\mathrm{ϴ}}{(\mathrm{ϴ}-{\mathrm{ϴ}}_{\mathrm{e}\mathrm{q}})}^2$$

(1)

$${\mathrm{U}}_{\mathrm{N}\mathrm{o}\mathrm{n}-\mathrm{b}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{d}}=4\mathsf{\epsilon }\left[{\left({\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{j}}}}\right)}^{12}-{\left({\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}}{{\mathrm{r}}_{\mathrm{i}\mathrm{j}}}}\right)}^6\right]+{\displaystyle \frac{{\mathrm{q}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{j}}}{4\mathsf{\pi }{\mathsf{\epsilon }}_0{\mathrm{r}}_{\mathrm{i}\mathrm{j}}}}\mathrm{r}<{\mathrm{r}}_{\mathrm{c}}$$

(2)

$${\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{1}{2}}\mathsf{\eta }·\left({\mathsf{\sigma }}_{\mathrm{i}\mathrm{i}}+{\mathsf{\sigma }}_{\mathrm{j}\mathrm{j}}\right)$$

(3)

$${\mathsf{ϵ}}_{\mathrm{i}\mathrm{j}}={\mathsf{\xi }·\left({\mathsf{\epsilon }}_{\mathrm{i}\mathrm{i}}{\mathsf{\epsilon }}_{\mathrm{j}\mathrm{j}}\right)}^{{\displaystyle \frac{1}{2}}}$$

(4)

Newton’s classical equations of motion, combined with advanced finite-difference methods, are used to predict particle trajectories over small timesteps. All thermodynamic and structural properties can then be obtained using statistical mechanics. For transport properties, equilibrium MD (EMD) simulations are commonly used. In EMD, the system is first allowed to reach thermodynamic equilibrium. Then, transport coefficients are calculated using the Green–Kubo or Einstein methods. Nonequilibrium MD (NEMD) is another approach for studying transport properties, with more details available in the literature [45,47]. The Green–Kubo method is widely applied in EMD simulations. It defines transport coefficients as the time integration of the autocorrelation function of a flux [46,47], as presented in Equation (5). In simple terms, the decay of correlations between instantaneous fluctuations is directly related to the transport coefficient of that property [48,49,50]. Accordingly, shear viscosity can be calculated using Equation (6).

In this equation, ${\mathrm{p}}_{\mathsf{\alpha }\mathsf{\beta }}$ is the off-diagonal component of the pressure tensor, k_B is the Boltzmann constant, and V is the system volume.

$$\mathrm{k}\propto {\int }_0^{\mathrm{\infty }}〈\dot{\mathrm{A}}\left(\mathrm{t}\right)\dot{\mathrm{A}}\left(0\right)〉dt$$

(5)

$$\mathsf{\eta }={\displaystyle \frac{\mathrm{V}}{{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}}{\int }_0^{\mathrm{\infty }}〈{\mathrm{p}}_{\mathsf{\alpha }\mathsf{\beta }}\left(\mathrm{t}\right){\mathrm{p}}_{\mathsf{\alpha }\mathsf{\beta }}\left(0\right)〉\mathrm{d}\mathrm{t}$$

(6)

A more refined version of this equation includes all independent components of the pressure tensor. This improves the statistical accuracy of the calculation [45].

Method

In this study, MD simulations were performed using ms2 software [51]. Two system sizes were considered: 1000 molecules for density calculations in the NPT ensemble, and 4000 molecules for viscosity calculations in the NVT ensemble. As viscosity is subjected to high statistical uncertainty, larger system sizes with longer simulation times are recommended [45]. However, for computational efficiency, fewer molecules were considered for density as larger systems had minimal impact on the results and only increased the computational time.

Each simulation began with energy minimization and equilibration stages, consisting of 100 and 200,000 steps, respectively. Production runs were then carried out for 1 million steps for density and 5 million steps for viscosity. A timestep of 1.2 femtoseconds (fs) was used throughout. The Gear predictor–corrector integrator [45] was applied to solve Newton’s equations of motions. Pairwise-additive 12-6 Lennard-Jones (LJ) potentials were used to model non-bonded interactions. The standard Lorentz–Berthelot combination rules [47] were applied for cross-species interactions. Viscosity was calculated using the Green–Kubo method [45,47]. The maximum correlation length was set to 6600 steps, and correlation functions were computed at every step, sampled every 5 steps, and spaced by 250 steps between successive functions. For CO₂ and CH₄, the TraPPE models were used while single-site models developed by Svehla et al. [52] were used for SO₂ and H₂S. These models are specifically designed for estimating viscosity and thermal conductivity. The force field parameters used in this study are listed in

Table 1. Force fields used in this work for density and viscosity.

	CO2 TraPPE [35]		CH4 TraPPE [53]	SO2 Svehla [52]	H2S Svehla [52]
${(ϵ}_{ab}/k_B)$ (K)	C-C	27.0	148.00	335.4	301.1
	O-O	79.0
${\sigma }_{ab}$ (Å)	C-C	2.8	3.73	4.112	3.623
	O-O	3.05
q (e)	C	+0.7	-	-	-
	O	−0.35
${ϴ}_{eq}\left(deg\right)$	O-C-O	180	-	-	-
$r_{eq}\left(\AA \right)$	C-O	1.16

.

In this study, the relative deviation and percentage average absolute relative deviation, %AARD, were calculated using the following equations:

$$\%Dev.=\left({\displaystyle \frac{Simulation/Experiment-model}{Simulation/Experiment}}\right)\times 100$$

(7)

$$\%AARD={\displaystyle \frac{1}{N}}\left({\sum }_{i=1}^N\left|{\displaystyle \frac{Simulation/Experiment-model}{Simulation/Experiment}}\right|\right)\times 100$$

(8)

Statistical uncertainties were estimated using the block averaging method [47]. Regarding viscosity, first, MD-estimated values versus the correlation time were plotted. The values in the plateau region were then converted to multiple blocks of data. The standard deviation between the average data inside each block with a 95% confidence level was reported as the expanded uncertainty. In this study up to 27 blocks, each with 50 data points, were considered for calculating standard deviations. For density, 1 million simulation times were divided into 1000 blocks of data, each with 1000 data points. The blocks selected were large enough to ensure that they are independent and do not affect the standard deviation.

3. Results and Discussion

3.1. Validation with Model Predictions and Experimental Data

A binary mixture of CO₂ + CH₄ (xCH₄ = 0.25) was selected to validate our molecular modeling. Initially, MD-estimated densities as illustrated in Figure 1a were compared against predictions from the MFHEA model [38,39]. As shown in Figure 1b for the deviation plot on density, good agreement with MFHEA was observed. In most cases, deviation was less than 2.0%, except at 273.15 K and 10.0 MPa, where 5.3% deviation due to being near the critical point (279.11 K and 8.55 MPa) was observed. Three viscosity models, namely the LJ, the ES-NIST, and the SUPERTRAPP, as well as experimental data from Chapoy et al. [20] at 238.15 K, 298.15 K, and 323.15 K, were used to further validate the MD modeling. Figure 1 shows that both the experimental data and the model predictions fall within the uncertainty bounds of the MD results, confirming the reliability of the simulation procedure.

3.2. Density

To estimate density, three isotherms of 223.15 K, 273.15 K, and 323.15 K were considered at pressures up to 25 MPa, covering the typical CCUS operating range. Initial density estimates for ms2 software were taken from the MFHEA equations of state [38,39]. Mixtures with 0.05, 0.10, and 0.20 mole fractions of impurity were studied. Figure 2a–c and Figure 2d–f show the density results for CO₂ + SO₂ and CO₂ + H₂S mixtures, respectively. Densities were evaluated in both the dense liquid and supercritical regions and compared with experimental data from the literature and MFHEA [38,39] predictions. In most MD simulations, the uncertainty was below 1 kg/m³, smaller than the symbol sizes. However, at 323.15 K and 10 MPa, uncertainties reached up to 6.88 kg/m³, possibly due to proximity to the Widom line [54,55], where the mixture fluctuates between liquid-like and gas-like behavior. Figure 3 shows the deviation plots of the MD-estimated densities compared to MFHEA model [38,39] predictions. For CO₂ + SO₂ mixtures with xSO₂ = 0.05 and 0.10, excellent agreement was observed, with %AARD values below 1% across all isotherms. Slightly higher deviations were noted for the mixture with 0.20 mole fraction SO₂. Experimental data from Nazari et al. [19] for 0.05 mole fraction SO₂ and H₂S at 273.15 K and 323.15 K and from Gimeno et al. [28] for 0.10 and 0.20 mole fraction SO₂ at 273.15 K were used for comparison. For the mixture with xSO₂ = 0.05, the %AARD values from the literature for MFHEA were 0.75% and 1.13% at 273.15 K and 323.15 K, respectively. However, in this study, lower deviations of 0.33% and 0.90% in the same conditions were observed. For CO₂ + H₂S mixtures, the literature data showed deviations of 1.60% and 0.56% from MFHEA, while MD-estimated results yielded 1.78% and 3.23% at 273.15 K and 323.15 K, respectively. Gimeno et al.’s data at 273.15 K showed %AARD values of 2.44% and 2.00% for mixtures with xSO₂ = 0.10 and 0.20, compared to 0.43% and 1.86% from MD simulations. It is important to note that their CO₂ mole fractions were 0.8969 and 0.8029, indicating impurity levels not exactly matching 0.10 and 0.20, which may explain the larger deviations from MFHEA predictions. Overall, MD-estimated densities for CO₂ + H₂S mixtures showed greater deviations than CO₂ + SO₂ mixtures, increasing with impurity concentration. This is likely due to stronger interactions between unlike species at higher impurity levels. The standard Lorentz–Berthelot mixing rule used in this study may not capture these effects accurately. Improved predictions would require specifying binary interatomic parameters, which were not included here. Density results, along with uncertainties and deviations from the MFHEA model, are presented in Table S1 through Table S6 in the Supplementary Materials.

3.3. Viscosity

Figure 4 presents MD-estimated viscosities for six binary mixtures of CO₂ with SO₂ and H₂S impurities across temperatures from 223 to 323 K and at pressures up to 25 MPa, covering both liquid and supercritical regions. These results were compared with predictions from various thermodynamic models (Appendix A). Since the reliability of the MD-estimated densities using ms2 was already investigated against MFHEA [38,39] predictions, no additional density calculations were performed. Instead, initial density values for the NVT ensemble were taken directly from the MFHEA equation of state. As with the density study, binary mixtures of CO₂ with 0.05, 0.10, and 0.20 mole fractions of SO₂ and H₂S were constructed. Three thermodynamic models were selected for comparison: Lennard-Jones (LJ) [40], Residual Entropy Scaling (SRES/ES-NIST) [41,42], and Extended Corresponding States (ECS/SUPERTRAPP) [43]. As shown in Figure 4, all models demonstrated very good agreement with the MD results. In every case, model predictions fell within the uncertainty range of the MD simulations, confirming both the accuracy of the molecular modeling and the reliability of the thermodynamic models.

For CO₂ + SO₂ mixtures, the ES-NIST model showed the smallest deviations, with %AARD values of 2.44%, 2.78%, and 2.58% for mixtures with xSO₂ = 0.05, 0.10, and 0.20, respectively. For binary mixture of CO₂ with H₂S (xH₂S = 0.05), ES-NIST also performed best with a %AARD of 2.75%. However, for mixtures with xH₂S = 0.10 and 0.20, the LJ model showed deviations up to 2.89% and 2.24%, respectively. Figure 5 presents deviation plots of MD-estimated viscosities versus pressure for all mixtures. Larger uncertainties were generally observed at low temperatures and high densities, contrasting with smaller uncertainties at higher temperatures in the supercritical region. This reflects a known limitation of the Green–Kubo method; at high densities, closely packed molecules make sampling pressure correlation functions more difficult [31,56]. Additional uncertainty arises near the critical region and along the Widom line [54,55], where fluid behavior fluctuates between liquid-like and gas-like states. As discussed in the methodology section, the Green–Kubo method calculates viscosity by integrating the pressure correlation function over time. Initially the pressure tensor components lose correlation, and the function decays, fluctuating around zero. Viscosity then grows and reaches a plateau. At longer times, statistical error accumulates, causing the plateau to break down or up. Correlation functions decay more slowly at high densities than in supercritical conditions, as also reported in previous studies [31,56] and observed here. Figure 6a–c and Figure 6d–f show the time evolution of pressure correlation functions and shear viscosity for CO₂ + H₂S mixtures. At 223 K (blue curves), slower decay and longer plateau formation are evident due to higher densities. In contrast, at 323 K (red curves), faster decay and quicker plateau formation occur. Choosing an appropriate correlation time is crucial when studying viscosity, especially at lower temperatures. A time that is too short may miss the plateau region, leading to inaccurate results, while a time that is too long may increase statistical error. Viscosity results, along with uncertainties and deviations from model predictions, are presented in Table S7 to Table S12 in the Supplementary Materials. Also,

Table 2. Summary of %AARD of MD-estimated density and viscosities against model predictions.

Mixture	x	Density	Viscosity
		MFHEA	LJ	SRES	ST
CO2 + CH4	(xCH4 = 0.25)	2.00	4.36	3.89	5.61
CO2 + SO2	(xSO2 = 0.05)	0.60	4.20	2.44	3.25
CO2 + SO2	(xSO2 = 0.10)	0.92	6.20	2.78	3.91
CO2 + SO2	(xSO2 = 0.20)	1.60	7.41	2.58	4.10
CO2 + H2S	(xH2S = 0.05)	1.69	3.98	2.75	3.67
CO2 + H2S	(xH2S = 0.10)	3.51	2.89	4.02	2.96
CO2 + H2S	(xH2S = 0.20)	4.72	2.24	8.33	5.17

presents the summary for the %AARD of the MD-estimated density and viscosity data against model predictions for all mixtures in this study.

4. Conclusions

MD simulations were performed to generate density and viscosity datasets for six binary mixtures of CO₂ + SO₂ and CO₂ + H₂S in CCUS-relevant conditions, aiming to validate existing thermodynamic models. For density, excellent agreement was found with MFHEA predictions and the literature data, especially for SO₂ mixtures, where %AARD values were below 1% for mixtures with xSO₂ = 0.05 and 0.10, and 1.60% for 0.20 mole fraction SO₂. For CO₂ + H₂S mixtures, good agreement was also achieved, particularly at xH₂S = 0.05 (1.69% deviation), though higher deviations of 3.51% and 4.72% were observed for 0.10 and 0.20 H₂S mole fractions, respectively. It was observed that %AARD (compared to MFHEA) increased with the amount of impurity, with this effect being particularly pronounced in CO₂ + H₂S systems. This highlights the significant role of cross-species interactions in influencing system behavior. Viscosity results from MD simulations were compared with three models as well as experimental data from Chapoy et al. [20] for a CO₂ + CH₄ (xCH₄ = 0.25) mixture. All comparisons showed good agreement, with model predictions and experimental data falling within the uncertainty range of MD results. This validates both the molecular modeling approach and the reliability of the models, even for mixtures lacking experimental data. Among the models, ES-NIST showed the least deviation for CO₂ + SO₂ and CO₂ + H₂S (xH₂S = 0.05) mixtures, while the LJ model performed best for CO₂ + H₂S mixtures with xH₂S = 0.10 and 0.20. In terms of uncertainty, larger values were generally observed at low temperatures and high densities, in contrast with smaller uncertainties in the supercritical region. This is a known limitation of the Green–Kubo method: at high densities, closely packed molecules make sampling pressure correlation functions more challenging. Additionally, analysis of pressure correlation functions and shear viscosity over time highlighted the importance of selecting an appropriate correlation time. A time that is too short may miss the plateau region, leading to inaccurate viscosity estimates, while a time that is too long can increase statistical error. Careful selection of this parameter is essential for reliable viscosity calculations.