Determination of Compressed Liquid Densities for CO₂ + n-Decane Using a Vibrating Tube Densimeter

Abstract

Understanding the density of CO₂ + n-decane is crucial for designing and operating CO₂ capture, transport, and storage. The safety and effectiveness of CO₂ burial is directly affected by the density of CO₂ + n-decane mixtures. The liquid densities of CO₂(1) + n-decane(2) mixtures with mole fractions of CO₂ x₁ = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured using a vibrating tube densimeter. The combined expanded uncertainties of density with a level of confidence of 0.95 are estimated to be 0.6 kg·m⁻³. A total of 221 compressed liquid densities of CO₂(1) + n-decane(2) mixtures along the five isotherms between T = (283 and 363) K with pressures up to 100 MPa were presented. The densities of mixtures were correlated by the modified Tait equation, resulting in absolute average deviations between the experimental and calculated values of 0.028%, 0.013%, 0.017%, 0.044%, and 0.042%. In addition, the isothermal compressibility, isobaric thermal expansivity, and excess molar volume were derived from the modified Tait equation.

1. Introduction

The greenhouse gas emissions of CO₂, CH₄, and N₂O generated by the power industry, agriculture, livestock farming, fuel combustion, natural gas extraction, and natural gas transportation have a significant impact on the global climate, ecosystems, environment, and life on earth [1,2,3,4]. Due to the irreversibility of climate change and its threat to human survival, mitigating climate change has become a hot topic. As the main greenhouse gas, the reduction and utilization of CO₂ is of the utmost importance [5]. At present, CO₂ capture and storage technology (CCS) or the thermocatalytic conversion of CO₂ into liquid fuels and chemicals are considered as the effective means of greenhouse gas emission reduction [6,7,8]. CCS combined with Enhanced Oil Recovery (EOR) is a proven technique, which may not only considerably reduce greenhouse gas emissions but can also effectively enhance crude oil recovery [9,10]. During the process of burying oil reservoirs, CO₂ migrates into the pores of rocks and dissolves when it comes into contact with crude oil. After the of crude oil and CO₂ mix in the formation, the density of the mixture will change, which will affect the natural transportation of CO₂ within the reservoir, thereby affecting the safety and effectiveness of the burial. Due to the complex composition of crude oil, single-component hydrocarbons or simple mixtures of several-component hydrocarbons can be used as substitutes [11].

Accurate knowledge of the thermodynamic properties of CO₂ + n-decane mixtures plays a significant role in the design and operation of CO₂ conditioning and transport [12,13]. A change in the density of CO₂ + n-decane mixtures will influence the movement of CO₂ under the oil reservoir, which has a significant impact on the oil displacement efficiency and the safe storage of CO₂. Extensive experimental density data for CO₂ + n-decane mixtures have been reported [14,15]. The densities of CO₂ + n-decane mixtures have been investigated, as shown in

Table 1. Summary of density data for CO₂(1) + n-decane(2) mixtures.

Reference	x1	T/K	p/MPa	Method	Expanded Uncertainty/kg∙m−3
Cullick and Mathis [16]	0.15–0.85	310–403	7–35	VTD	0.5
Bessiéres et al. [17]	0.15–0.84	308–368	20–40	VTD	0.2
Zúñiga-Moreno et al. [18]	0.05–0.97	313–363	1–25	VTD	0.2
Fandiño et al. [19]	0.30–0.95	283–398	10–120	VTD	0.7
Song et al. [11]	0.23–0.87	303–353	8–19	MSB	0.48
Nourozieh et al. [20]	0.07–0.37	373	1–6	VTD	1.0
Kariznovi et al. [21]	0.09–0.51	323	1–6	VTD	1.0
Kandil et al. [22]	0.21–0.73	313–410	3–76	VTD	2.0
Zambrano et al. [23]	0.30–0.95	283–393	10–100	VTD	1.8
Yang et al. [24]	0.60–0.87	303–373	1–80	VTD	0.6

. Cullick and Mathis [16] measured the density of CO₂ + n-decane mixtures at 310–403 K, and 7–35 MPa with a vibrating tube densimeter (VTD). Bessières et al. [17] used a VTD to measure the densities of CO₂ + n-decane mixtures at 308–368 K and 20–40 MPa. Zúñiga-Moreno et al. [18] carried out tests on the density of CO₂ + n-decane mixtures at 313–363 K and 1–25 MPa using a VTD. Fandiño et al. [19] reported the densities of CO₂ + n-decane mixtures measured by a VTD at 283–398 K and 10–120 MPa. Song et al. [11] studied the densities of CO₂ + n-decane mixtures at 303–353 K and 8–19 MPa with a magnetic suspension balance (MSB). Nourozieh et al. [20] and coworkers (Kariznovi et al. [21]) investigated saturated liquid density at 323 K and 373 K using a VTD. Kandil et al. [22] provided the density of CO₂ + n-decane mixtures at 313–410 K and 3–6 MPa. Zambrano et al. [23] conducted tests on the density of CO₂ + n-decane mixtures at 283–393 K and 10–100 MPa using a VTD. Yang et al. [24] measured the densities of CO₂ + n-decane mixtures using a VTD at 303–373 K and 1–80 MPa. The literature survey shows that density data for CO₂ + n-decane mixtures mainly focus on low-pressure areas. The density data for mixtures at high pressures are still insufficient.

In this study, the densities of CO₂ + n-decane mixtures were measured with a VTD at temperatures ranging from 283 K to 363 K, and pressures between 10 and 100 MPa. The density data in this study were analyzed using the modified Tait equation. Furthermore, the thermodynamics properties of the mixtures were derived. The purpose of this study is to provide a basis of data and theoretical support for the CO₂ sequestration and resource utilization.

2. Samples and Methods

2.1. Samples

n-decane and CO₂ were purchased from Aladdin Chemistry Co. Ltd., Shanghai, China and Jining Xieli Special Gas Co., Ltd., Jining, China, respectively. The stated mass fraction purities of n-decane and CO₂ were higher than 0.99 and 0.99999, respectively. n-decane was used without further purification. The CO₂ was degassed through three freeze–pump–thaw cycles [25,26]. The purities of the samples were not further checked. The specifications of the samples are listed in

Table 2. Specification of samples.

Chemical Name	Source	CAS No.	Molar Mass g/mol	Stated Mass Fraction Purity	Purification Method
CO2	Jining Xieli Special Gas	124-38-9	44.01	>0.99999	Freeze-pump-thaw cycle
n-Decane	Aladdin	124-18-5	142.28	>0.99	none

.

2.2. Apparatus and Sample Preparation

Figure 1 presents a schematic diagram of the experimental system. The liquid densities were analyzed using an Anton Paar VTD (DMA HPM). The VTD was displayed in our previous publications [27,28,29,30,31]. The combined expanded uncertainty U_c values were U_c(T) = 16 mK, U_c(p) = 0.062 MPa (p ≤ 60 MPa), U_c(p) = 0.192 MPa (60 MPa < p < 140 MPa), and U_c(ρ) = 0.6 kg·m⁻³ with a confidence level of 0.95 (k = 2). A sample preparation section was designed for biphasic mixtures (see bottom right corner of Figure 1). Details on sample preparation are available in our previous studies [24]. The combined expanded uncertainty of the mole fraction was U_c(x) = 0.005 (k = 2).

3. Results and Discussion

3.1. Experimental Density Data

The densities of the CO₂(1) + n-decane(2) mixtures with mole fractions of CO₂ x₁ = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured at temperatures ranging from 283 K to 363 K and pressures up to 100 MPa. The experimental data are listed in Table S1 in the Supplementary Materials. The deviations in the densities of the n-decane between the experimental data and values calculated using Equation (1) are shown in Figure 2. The information on density measurements taken for n-decane is summarized in

Table 3. Summary of density data for n-decane.

Year	Author	Purity	Method	T/K	p/MPa	Uncertainty
1940	Nysewander et al. [38]	na	Volume measurements	294–344	0.1–25	na
1940	Sage et al. [39]	na	Volume measurements	294–394	1–69	na
1970	Synder et al. [40]	na	Brideman-type sylphon bellows piezometer	298–358	0.1–656	na
1978	Peña et al. [41]	>99 mol%	Piezometer	298–333	0.1–41	na
1986	Gate et al. [42]	99.4 mol%	Two flow VTD	298–368	0.1–20	na
1991	Banipal et al. [32]	/	VTD	318–373	0.1–10	na
1992	Susnar et al. [33]	99.6%	VTD	294.35	0.1–35	0.02%
2004	Troncoso et al. [34]	99 mol%	VTD	283–328	0.1–40	0.1%
2005	Zúñiga-Moreno et al. [18]	>99%	VTD	313–363	1–25	0.1%
2009	Segovia et al. [35]	99%	VTD	283–398	0.1–70	0.2%
2009	Valencia et al. [36]	99.9%	VTD	283–323	0.1–60	0.2%
2012	Quevedo-Nolasco et al. [37]	99.7 mol%	VTD	313–363	1–25	0.03%
2013	Nourozieh et al. [20]	99 mass%	VTD	323	0.1–10	0.3%
2021	Yang et al. [24]	99.5 mass%	VTD	303–373	1–80	0.2%

. It can be noted that the relative deviations in the experimental data from the calculated values obtained from the modified Tait equations are mostly lower than 0.6%. The data from references [17,18,19,20,24,32,33,34,35,36,37] with relative deviations of within ±0.6% are in satisfactory agreement with our correlation. These density data were obtained with a VTD. However, the larger deviations come from earlier literature [38,39,40,41]. The experimental data obtained by Nysewander et al. [38] and Sage et al. [39] were measured through a volume measurement. Synder et al. [40] and Peña et al.’s experimental data [41] were obtained with a piezometer. From this Figure and Table 3, it seems that the deviation can be explained by the accuracy of the different measurement methods.

Figure 3 shows the densities of CO₂(1) + n-decane(2) mixtures at 283–363 K. It can be concluded that the density values of the mixtures smoothly increase with increasing pressure and mole fraction of CO₂ and decrease with increasing temperature. It is worth noting that the slopes of the density curve increase with increasing mole fraction of CO₂. The density curves for different mole fractions of CO₂ intersect under specific temperatures and pressures. For example, the liquid densities of the mixtures with a mole fraction of 0.2032 and 0.7589 are equal at 363 K and approximately 15 MPa. This intersection between the trends is largely due to the differences in molecular size, non-hydrogen atoms fraction, and critical temperature for mixture components [24].

The deviations in density between the experimental data and the values calculated using Refprop 10.0 [43] are plotted in Figure 4. It is important to note that the deviations in the experimental data and the literature values are generally within ±2.0%. The deviations in the data obtained by Zambrano et al. [23] exhibit scattered deviations around the baseline within ±1.5%. The deviations in the data obtained by Bessières et al. [17] and Kandil et al. [22] are within ±1.6%. The deviations in the data obtained by Yang et al. [24] are within ±2.0%. The density data measured by Song et al. [11] have a maximum deviation of 2.2%. These results reveal that the measurement results are reasonably acceptable.

3.2. Modified Tait Equation

In order to ease the application of our method in practical engineering, the following modified Tait equation was used to correlate the measured densities of each CO₂ + n-decane mixture:

$$\rho \left(T,p\right)={\displaystyle \frac{{\rho }_0\left(T\right)}{1-C\ln \left(\left(B\left(T\right)+p\right)/\left(B\left(T\right)+0.1\right)\right)}}$$

(1)

with

$${\rho }_0\left(T\right)=A_0+A_{1}T+A_2{T}^2+A_3{T}^3$$

(2)

$$B\left(T\right)=B_0+B_{1}T+B_2{T}^2$$

(3)

where the A_i, B_i, and C parameters correlated with the experimental density data.

To test the deviation between the experimental data and the calculated values, the Absolute Average Deviation (AAD), the Maximum Absolute Deviation (MAD), and the Standard Deviation (σ) were evaluated:

$$AAD/\%={\displaystyle \frac{100}{N-m}}{\displaystyle \sum _{i=1}^N\left|\frac{{{\rho }_i}^{\exp }-{{\rho }_i}^{\mathrm{calc}}}{{{\rho }_i}^{\exp }}\right|}$$

(4)

$$MAD/\%=Max\left(100\left|{\displaystyle \frac{{{\rho }_i}^{\exp }-{{\rho }_i}^{\mathrm{calc}}}{{{\rho }_i}^{\exp }}}\right|\right)$$

(5)

$$\sigma =\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^N{\left({{\rho }_i}^{\exp }-{{\rho }_i}^{\mathrm{calc}}\right)}^2}}{N-m}}}$$

(6)

where N and m represent the amount of experimental data and the number of modified Tait equation parameters, respectively. ${\rho }_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}$ and ${\rho }_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{c}}$ denote the experimental density and the density values calculated using Equation (1), respectively. The modified Tait equations’ parameters and statistical deviations are shown in

Table 4. Parameters and deviations in density correlation.

Parameters	x1 = 0	x1 = 0.2032	x1 = 0.4434	x1 = 0.7589	x1 = 0.8947
A0/g·cm−3	0.86080	1.03703	1.40990	−0.01853	4.40805
A1/g·cm−3·K−1	−8.51553 × 10−6	−1.41571 × 10−3	−4.63320 × 10−3	8.91860 × 10−3	−3.40563 × 10−2
A2/g·cm−3·K−2	−1.95868 × 10−6	2.03202 × 10−6	1.23117 × 10−8	−2.61347 × 10−5	1.17519 × 10−4
A3/g·cm−3·K−3	1.62432 × 10−9	−2.33131 × 10−9	−1.40789 × 10−10	1.73563 × 10−8	−1.48211 × 10−7
B0/MPa	344.951	366.422	327.392	452.091	271.332
B1/MPa·K−1	−1.20993	−1.41645	−1.32612	−2.32403	−1.466625
B2/MPa·K−2	1.09394 × 10−3	1.45102 × 10−3	1.36670 × 10−3	3.00725 × 10−3	1.98299 × 10−3
C	9.12134 × 10−2	9.15440 × 10−2	8.94176 × 10−2	9.64531 × 10−2	9.71727 × 10−2
σ/g·cm−3	3.456 × 10−5	1.112 × 10−4	1.401 × 10−4	4.567 × 10−5	4.183 × 10−5
AAD/%	0.028	0.013	0.017	0.044	0.042
MAD/%	0.075	0.033	0.040	0.065	0.059

.

3.3. Derived Thermodynamics Properties

The isothermal compressibility, κ_T, was calculated with the modified Tait Equation (1), which was calculated by [29]:

$${\kappa }_{\mathrm{T}}\left(T,p\right)=\left({\displaystyle \frac{1}{\rho }}\right)\left({\displaystyle \frac{\partial \rho }{\partial p}}\right)={\displaystyle \frac{C}{\left(1-C\ln \left(\frac{B\left(T\right)+p}{B\left(T\right)+0.1}\right)\right)\left(B\left(T\right)+p\right)}}$$

(7)

We suppose that ${\rho }_{\mathrm{p}}\left(T\right)=a_0+a_{1}T+a_2{T}^2+a_3{T}^3$, the isobaric thermal expansivity, α_p, was determined

$${\alpha }_{\mathrm{p}}=-{\displaystyle \frac{a_1+2a_{2}T+3a_3{T}^2}{a_0+a_{1}T+a_2{T}^2+a_3{T}^3}}$$

(8)

The isothermal compressibility and isobaric thermal expansivity of the mixtures are listed in Table S2 (provided as Supplementary Materials) and illustrated in Figure 5 and Figure 6. The isothermal compressibility and isobaric thermal expansivity of the CO₂ + n-decane mixtures increase with increasing CO₂ concentration.

The excess molar volume was obtained using the following equation:

$$V_{\mathrm{m}}^{\mathrm{E}}={\displaystyle \frac{x_1{M}_1+\left(1-x_1\right)M_2}{{\rho }_{\mathrm{mix}}}}-x_1{\displaystyle \frac{M_1}{{\rho }_1}}-\left(1-x_1\right){\displaystyle \frac{M_2}{{\rho }_2}}$$

(9)

where ρ₁ and ρ₂ represent the density of the pure components obtained from Refprop 10.0 [43] and this work, respectively. The excess molar volumes were calculated and are presented in Table S2 (provided as Supplementary Materials). A comparison of the excess molar volumes with the Helmholtz EoS at 343 K is shown in Figure 7. The negative values of the excess molar volume resulted from the filling effects and the dispersion interaction between CO₂ and the n-decane molecules. It is important to note that a deviation of 0.12% in density will generate a deviation of 0.10–0.25 cm³·mol⁻¹ in excess molar volume [44]. This difference could be a result of the precision in measuring the density.

4. Conclusions

CCS combined with EOR is a promising technique to reduce CO₂ concentration, alleviate climate change, and promote the transformation to a renewable economy. During the process of reservoir burial, CO₂ will dissolve in the rock pores when it comes into contact with crude oil. After CO₂ dissolves into crude oil, the density of the crude oil will change, which will affect the natural transport of CO₂ in the reservoir, thereby affecting the safety and effectiveness of burial. It is vital to study the thermodynamic properties of mixtures formed by CO₂ dissolution in crude oil.

In this work, the experiment was carried out with a VTD at 283–363 K and 10–100 MPa. Experimental density data for CO₂(1) + n-decane(2) mixtures with mole fraction x₁ = 0, 0.2030, 0.4434, 0.7589, and 0.8947 were complemented by this work. The experimental data for CO₂ + n-decane mixtures were compared with values from the literature and showed a good agreement. The experimental densities were fitted with the modified Tait equation with an AAD lower than 0.1%. Based on the experimental data, the isobaric thermal expansivity, isothermal compressibility, and excess molar volume were determined. Overall, this study aims to provide a basis of data and theoretical support for the CO₂ sequestration and resource utilization.

Based on the work completed in this study, further work should be carried out on the following aspects:

(1)

The composition of crude oil is complex, and single-component hydrocarbons or simple mixtures are not sufficient to represent crude oil. Therefore, it is necessary to study the densities of CO₂ + multicomponent alkane mixtures and CO₂ + crude oil using a high-pressure VTD.

(2)

In the future, the density equations for CO₂ + alkane mixtures can be further developed by combining the Helmholtz equation of state and mixing rules. Specialized mixing rules and applicable equations can thus be developed.

(3)

The temperature range, pressure range, and system used in the experimental apparatus can be further expanded. The experimental system used in this work had a temperature range from 283 K to 363 K, and a pressure of up to 100 MPa. In the future, the temperature system can be improved to expand the experiment to a higher temperature range and a higher pressure range. The densities of other mixtures can be obtained by using this experimental apparatus.