Measurements and predictions of densities and viscosities in CO2 + hydrocarbon mixtures at high pressures and temperatures: CO2 + n-pentane and CO2 + n-hexane blends

This work reports new experimental data on densities and viscosities of (CO2 + n-pentane) and (CO2 + n-hexane) mixtures at high pressures and temperatures. The densities were measured by vibrating-tube densimeter with an expanded uncertainty (k = 2) smaller than 1.8 kg·m–3 at six isotherms (from 273.15 K to 373.15 K), twelve pressures starting at 5 MPa up to 100 MPa, and at six CO2 molar compositions (from 0 to 0.6). The viscosities were measured by vibratingwire viscometer with the corresponding relative expanded uncertainty (k = 2) smaller than 0.016 at five isotherms (from 273.15 K to 373.15 K), twelve pressures (from 5 MPa up to 100 MPa), and at two CO2 molar compositions (0.1 and 0.3). The densities were fitted by the semiempirical Tammann-Tait equation for densities data and the Vogel-Fulcher-Tammann (VFT) equation for viscosity data, respectively. The Groupe Européen de Recherches Gazières (GERG-2008) equation of state was also applied for modelling the densities. Over-all robustness and reliability


Introduction
Methods of crude oil extraction can be categorized in three different stages, namely primary, secondary, and tertiary techniques. Primary oil recovery processes are limited to natural rise of hydrocarbons from the bottom of the wellbore to the surface, combined with artificial lift techniques (such as the iconic pump jack). Extraction potential by this technique is limited, only around 10 % of the reservoir´s original oil in place can be extracted by this technique.
Secondary recovery techniques prolong the productive life of an oil field by injection of water and gas to displace oil and drive it to the production wellbore, thus increasing oil recovery from 20 % up to 40 % of the original oil reservoir [1].
The ultimate way to increase oil production from an already depleted reservoir is using tertiary crude oil techniques or Enhanced Oil Recovery (EOR). This process uses heat, chemicals, or solvents and starts after primary and secondary techniques have already been deployed. The use of solvents, such as CO 2 , is a specific EOR technique consisting in injecting CO 2 into the oil reservoir to improve recoverability, reducing its viscosity, swelling the crude oil, and decreasing the interfacial tension [2]. Although this method increases operation expenses, it is compensated with a yield of more than 60 % in oil recovery.
The main objective of EOR is the recovery of residual crude oil from a reservoir. However, nowadays, this technique qualifies for a second purpose, sequestration of CO 2 with a high potential in mitigation of global warming. Many oil reservoirs have the potential to sequester a great fraction of the injected CO 2 (around 40 % to 50 %) [3] injected and this procedure generates a mixture of brine, crude oil, light hydrocarbons (natural gas liquid), and nonsequestered CO 2 stream. This CO 2 stream is treated and reinjected into the reservoir [4].
In that global scenario, the CO 2 sequestration process via EOR becomes an additional strategic technology to reduce world greenhouse gas emissions. By means of gas treatment technologies, such as carbon capture with aqueous solutions of amines, CO 2 can be captured from gas stream in natural gas processing, ammonia production, steel industry, or power plants.
For those reasons, knowledge of pVT behavior and transport properties of the mixtures (CO 2 + hydrocarbon) is mandatory for carrying out the EOR process at reservoir conditions. The first objective of this work is measuring densities and viscosities of (CO 2 + hydrocarbon) mixtures in wide ranges of pressures and temperatures, extending thus the previously reported data on densities of the binary CO 2 systems with the hydrocarbons n-decane, n-dodecane and squalene [5] to n-pentane and n-hexane. The range of measurements allows to extend the potential applications of the data since the techniques allow it.
There is still limited information on these systems in the literature. Regarding the (CO 2 + npentane) mixture, Besserer and Robinson [6] reported VLE at 277.7, 311.0, 344.2 and 377.6 K and the equilibrium-phase densities were calculated from the measured phase composition and refractive index by the Lorentz molar refractivity relationship. Kiran et al. [7] investigated the volumetric behavior of this system at pressures up to 70 MPa, five isotherms between 323 K and 423 K, and over the entire composition range including the pure compounds; they have assigned an uncertainty of 1.2 % to their measurements. Chen et al. [8] measured phase behavior and density at saturation conditions with an accuracy better than 1 kg‧m -3 , these measurements range from 312.35 K to 328.15 K and pressures up to 15 MPa. No viscosity data have been reported for this mixture so far.
As for the (CO 2 + n-hexane) mixture, Kaminishi et al. [9] measured vapor pressures and liquid densities at 273. 15, 283.15, 298.15, and 303.15 K over the entire composition range with an accuracy of 0.3 %. Tolley et al. [10] measured densities at 308.15 and 313.15 K, at pressures from 6 MPa to 12.5 MPa, and covering the entire composition range with an uncertainty of 1 kg m -3 . Wang et al. [11] reported density at the dew point at 50, 55, and 60 °C. Finally, Kian and Scurto [12] measured viscosity of compressed CO 2 -saturated n-hexane at 25, 40, and 55 °C and pressures up to 107 bar with a standard uncertainty of less than 1 %.
The measurements performed in this work will contribute to consolidating the data inventory of these two mixtures. The new data also provide an excellent opportunity to examine an overall robustness and reliability of thermodynamic models, which is the second objective of this study.

Materials
The two hydrocarbons were purchased from Sigma-Aldrich and Fluka Chemicals with the highest purity available, and CO 2 was supplied by Carburos Metálicos, Premier Líquido series.
Their characteristics are summarized in Table 1. Purities were specified by the supplier and no further purification was carried out prior to investigation in the laboratory. However, the purities of the hydrocarbons were checked by gas chromatography (GC). Paar Spain S.L.U., Madrid). Pure water and vacuum were the calibration media for this study and details of the calibration procedure are reported in a previous paper [13]. This technique is able to measure density in the range of (0 to 3000) kg·m -3 with a resolution of 10 -2 kg·m -3 . The apparatus is fully automated using the Agilent VEE Pro software as a control system and for data acquisition [14]. The density of pentane and hexane was measured to check the performance of the technique. The densimeter can be operated either with liquid mixtures (prepared by weighing and charged manually into the system) or with mixtures where one component is maintained in liquid phase using a modification of the injection system. The complete modification of the apparatus is described by Zambrano et al. [5]. The experimental uncertainties were determined according to the recommendations in the GUM [15], whose details can be found in [13]. The resulting expanded uncertainty (k = 2) is less than 1.8 kg·m -3 .
Temperature was measured by means of an ASL-F100 thermometer with two resistant sensors (Pt100), whereas pressure was determined using a digital manometer (Druck DPI 104, General Electric). Both devices were calibrated in the laboratory being traceable to national standards.
The corresponding expanded uncertainties (k = 2) are U(T) = 20 mK and U r (p) = 0.0002. primary standards. The radius of the tungsten wire was calibrated using toluene as reference fluid and the accuracy of the viscosity measurements was first checked with dodecane.
In order to measure (CO 2 + hydrocarbon) mixtures, it was necessary to modify the injection system in the same way as for the densimeter [5]. The new scheme of the experimental vibrating-wire viscometer that was operated in this work is shown in Figure 1. Properties Database (REFPROP 10) [21] software with the corresponding reference for nhexane [22], n-pentane [23], and CO 2 [24]. The molar flow rate is determined using Eq. (1): where for each component "i", n i is the molar flow, Q i is the volumetric flow given by the injection pump, ρ i is the density at the injection conditions, and M i is the molar mass.
The same filling procedure of preparing the densimeter was implemented for the viscometer.
One of the dual ISCO pumps was filled with pure hydrocarbon at 6 MPa and 313.15 K and the second pump is loaded with CO 2 at the same pressure and 283.15 K assuring liquid phase. The targeted compositions were prepared by varying the flow rate of each pump, maintaining constant pressure with the back-pressure valve. The composition uncertainty depends on the quantity of each component and was reported by Zambrano et al. [5]. In the set-up of this technique [16], the main contribution to the uncertainty budget was identified as the determination of the radius of the tungsten wire. The overall uncertainties of the viscosity measurements were recalculated considering the contribution of the mixture composition to the uncertainty at the most unfavorable case (i.e., CO 2 (1) + n-pentane (2) at the lowest temperature of 293.15 K). This procedure resulted in an increase of 0.1 % in the global uncertainty budget.
The relative expanded uncertainty of these viscosity measurements is estimated better than 0.016 for a coverage factor k = 2 at all the investigated conditions.

Density measurements
Experimental density measurements of two binary systems, (CO 2 (1) + n-pentane (2)) and (CO 2 (1) + n-hexane (2)) and the two pure hydrocarbons (n-pentane and n-hexane) were obtained at  Table 2 and Table 3, respectively.  As can be seen from the experimental data, ρ (CO2 + n-hexane) > ρ (CO2 + n-pentane) at the same conditions of pressures, temperatures, and composition. As expected, the density monotonically increases with pressure and decreases with temperature for all binary systems investigated. This phenomenon becomes more pronounced at higher CO 2 mole fractions.
As regards the effect of increasing pressure, the minimum density increase, observed for a change in pressure from 10 MPa to 100 MPa, is 8 % for the system (CO 2 + n-hexane) and 9 % for (CO 2 + n-pentane), being both at the lowest temperature (T = 273.15 K) and composition (x 1 = 0.1). In the case of the pure hydrocarbons the corresponding density increase amounts to 7 % and 8 %, respectively. The maximum density increase is shown at the highest temperature . This particular behavior was also observed for the mixture (CO 2 + n-pentane) by Kiran et al. [7]. They explain that phenomenon with "a crossover region when the density for mixtures with high carbon dioxide content becomes lower than the density for mixtures with lower carbon dioxide content". In Figures 2 and 3 with the corresponding parameters given in Table 4. The dashed lines (----) represent pure CO 2 [24]. In c) experimental data of Tolley et al. [10] are represented using grey symbols.
The current experimental data were used for testing three different equations-of-state (EoS)

models, namely the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) [29], its critical point-based revision (CP-PC-SAFT) [30] and the Groupe Européen de Recherches
Gazières (GERG-2008) reference equation of state [31,32]. The latter model is a reference equation for gases covering 21 pure components, including n-pentane, n-hexane, and CO 2 and it is widely used in industrial applications. Unlike GERG-2008, the SAFT models are not restricted to specific compounds. The details of these approaches were discussed in their initial publications [29,30]. Obviously, the precision of SAFTs in modelling densities is inferior in comparison with the system and property-specific empirical models, such as the modified Tammann So far it was found that an appropriate modelling of phase equilibria in (CO 2 + n-alkane) homologues series can be achieved by adopting a universal value of the binary parameter k 12 = 0.12 for PC-SAFT [33,34] and k 12 = 0.09 for CP-PC-SAFT [35]. Figures S1 and S2 of the Supplementary Material compare the performances of both approaches in modelling the compositions of phase equilibria and the densities of saturated phases for the systems (CO 2 + n-C n H 2n+2 ) with n = 5, 6, 7, 10, 14, and 18. It can be seen that in the cases of lighter members of the series (CO 2 + n-pentane, n-hexane, and n-heptane) the results of both approaches are rather similar. More significant differences between them can be observed for the system (CO 2 + n-decane). On the one hand, CP-PC-SAFT with the adopted k 12 value erroneously estimates the liquid-liquid phase split at 310.9 K for this system, while PC-SAFT correctly predicts the topology of phase behavior [33]. On the other hand, CP-PC-SAFT is more accurate in modelling the bubble-point data. Figure S1 also demonstrates that this advantage of CP-PC-SAFT becomes more pronounced in the cases of heavier alkane homologues, such as (CO 2 + n-tetradecane and + n-octadecane).  As seen, similarly to most other systems belonging to the (CO 2 + n-alkane) series, PC-SAFT predicts the current density data more accurately than CP-PC-SAFT. In the case of (CO 2 + npentane), all the considered models display a reasonably accurate performance. The AAD of GERG-2008 is smaller than that of both SAFT models at x 1 = 0 for the pure alkane and the low It can also be seen that, in the case of the second system (CO 2 + n-hexane), GERG-2008 precisely estimates the densities of pure n-hexane which can be expected from the intentional application areas. However, the addition of CO 2 results in substantial deterioration of its performance. So, at x 1 = 0.2 and higher, the predictions of this model become particularly inaccurate, and at x 1 = 0.6 the AAD already amounts to 13.9 % and the MAD to 16.4 %, respectively. Unlike that, both SAFT approaches continue to yield reasonably good results in the entire composition range with an AAD ≤ 1.6 % in the case of CP-PC-SAFT and ≤ 0.8 % of PC-SAFT. The corresponding MAD values also remain reasonable small. The poor performance of the GERG-2008 model can be explained by a lack of consolidated of (CO 2 + nhexane) at the time of model build-up when only the VLE data were used for fitting the parameters for this system [31]. This result emphasizes an over-all advantage of the theoretically based -and thus widely data-independent -SAFT approaches, whose predictive capabilities are stronger.
As expected, viscosities of the blend (CO 2 + hydrocarbon) monotonically decrease when temperature and molar fraction of CO 2 and they increase with pressure. At the same time, viscosities are significantly enhanced at higher pressures.
The experimental viscosity data were correlated using the modified Vogel-Fulcher-Tammann (VFT) model, Eq (8), an approach that was successfully used by other authors [36,37].
Fitting of the experimental viscosity data was performed applying the least-squares method using the Solver tool of Microsoft Excel software. The fitting results are given in Table 8 which contains the parameters, the standard deviation of the adjustment, and other statistical data. The average absolute deviation AAD is within the uncertainty of the experimental viscosities (except for the mixture CO 2 + n-pentane with a mole fraction of CO 2 = 0.1) which supports that the model is suitable to be applied for this type of mixtures. One of the objectives of this work is quantifying the viscosity decrease of the pure hydrocarbon upon the addition of CO 2 . For this purpose, a direct comparison was executed. As a result, the viscosity of n-pentane [23,38] decreases between 8 % up to 18 % with the addition of CO 2 starting with pure n-pentane up to x 1 = 0.1 and between 21 % up to 31 % ending up with x 1 = 0.3, respectively. In a similar comparison for the case of pure n-hexane [22], the viscosity decreases between 1 % up to 9 % at x 1 = 0.1 and between 18 % up to 27 % at x 1 = 0.3.
Unfortunately, literature data for both binary mixtures are very limited. Kian et al. [12] only measured the viscosity of (CO 2 + n-hexane) system at saturation conditions which is far from the p, T-conditions of our experiments at single-phase homogeneous conditions, thus making a comparison impossible.
The new viscosity data provides an opportunity to examine an accuracy of the modelling framework coupling the entirely predictive Modified Yarranton-Satyro correlation (MYS) with the CP-PC-SAFT EoS [39]. This approach aims at raw estimating the unavailable viscosity data of pure non-associative compounds and their mixtures in wide range of conditions, while MYS employs the molecular parameters of CP-PC-SAFT. In this respect it should be emphasized that the sophisticated nature of viscosity data and their strong pressure and temperature dependencies hinder development of accurate and entirely predictive models whose application does not require any input of experimental data. Despite that, the accuracy of CP-PC-SAFT+MYS approach can at times be comparable to models whose parameters are fitted to the viscosity data. In particular, Thol and Richter [40] have applied REFPROP 8 [41], two recent entropy scaling approaches [42,43] and the f-theory model [44] for estimating 12 experimental viscosity points of saturated liquid phase in CO 2 -n-hexane reported by Kian and Scurto [12]. Table 10 compares the predictions of CP-PC-SAFT+MYS for the current viscosity data with the REFPROP 10 Software [21]. As seen, although the results of REFPROP 10 are better, they also exhibit remarkable deviations from the data. In this respect, it should be emphasized that unlike CP-PC-SAFT+MYS REFPROP 10 is based on the existing experimental data. Besides that, it can be seen that the accuracies of both models deteriorate with an increase of x 1 and they perform better in a case of the n-pentane system. Remarkable, the high-temperature region has a major contribution to the deviations of CP-PC-SAFT+MYS, which can be explained by inaccuracy of this model in predicting the pertinent pure compound data. Obviously, such shortcomings can be characteristic the entirely predictive approaches.
Both mixtures were measured in a wide range of pressure (up to 100 MPa) and temperature.
The modified Tammann-Tait equation can fit the density data with standard deviations that in most cases remain within the uncertainty of the measurements. The viscosity data were successfully correlated using a modified VFT model.
In the theoretical part of this work the over-all robustness and reliability of two molecularly based approaches, namely PC-SAFT and CP-PC-SAFT in estimating data of CO 2 -n-alkane series were examined. It was found that each of them has its advantages and disadvantages in modelling phase equilibria and excess enthalpies. Despite an obvious superiority of CP-PC-SAFT in predicting speeds of sound, this model is usually slightly inferior in estimating the single-phase densities of the considered systems up to 130 MPa. Such tendency was observed also in a case of the current density data. Although both approaches yielded reasonably good predictions, PC-SAFT was found somewhat more accurate. In addition, performance of the GERG-2008 equation in estimating the densities was considered. This model also yielded nearly precise estimations of CO 2 + n-pentane and pure n-hexane. However, it was found that addition of CO 2 to n-hexane results in a progressive deterioration of its accuracy. Unlike that, both SAFT approaches yielded reasonably good results for this system in the entire composition range. These results emphasize the need of upgrading the GERG-2008 EoS with new accurate experimental data.
The results of an entirely predictive CP-PC-SAFT+MYS modelling framework and the REFPROP 10 Software for the current viscosity data were also examined. Unsurprisingly, the accuracy of REFPROP 10 was superior. However, it was found that both models exhibit remarkable deviations from the data, which increase with addition of CO 2 .