#
The Effect of Oil Properties on the Supercritical CO_{2} Diffusion Coefficient under Tight Reservoir Conditions

^{*}

^{†}

## Abstract

**:**

_{2}in cores that are saturated with different oil samples, under reservoir conditions. In theory, a mathematical model that combines Fick’s diffusion equation and the Peng-Robinson equation of state has been established to describe the mass transfer process. In experiments, the pressure decay method has been employed, and the CO

_{2}diffusion coefficient can be determined once the experimental data match the computational result of the theoretical model. Six oil samples with different compositions (oil samples A to F) are introduced in this study, and the results show that the supercritical CO

_{2}diffusion coefficient decreases gradually from oil samples A to F. The changing properties of oil can account for the decrease in the CO

_{2}diffusion coefficient in two aspects. First, the increasing viscosity of oil slows down the speed of the mass transfer process. Second, the increase in the proportion of heavy components in oil enlarges the mass transfer resistance. According to the results of this work, a lower viscosity and lighter components of oil can facilitate the mass transfer process.

## 1. Introduction

_{2}and geological CO

_{2}storage [1,2,3]. CO

_{2}is usually injected into geological formations to improve oil recovery and to store and sequester the greenhouse gas in the atmosphere through the interaction of CO

_{2}with the crude oil, which restricts CO

_{2}molecules in the pores of the rock, and the reaction of CO

_{2}molecules with mineral grains. The main purpose of CO

_{2}EOR is to produce more hydrocarbons from oil reservoirs [4,5,6,7,8]. Therefore, a full understanding of the behavior of CO

_{2}under reservoir conditions has always been one of the main interests of researchers and the petroleum industry. There are several processes involved in the CO

_{2}EOR, i.e., diffusion of CO

_{2}into the crude oil in the porous rocks [9,10,11,12,13,14,15,16,17,18,19], the chemical reaction of CO

_{2}with formation minerals [20,21], and rock mechanics caused by pore pressure changes [22]. Only the first process of CO

_{2}diffusion in porous media is considered in this study, which has theoretical importance and meaning for applications in the petroleum industry.

_{2}, CO

_{2}, CH

_{4}[28], C

_{2}H

_{6}, C

_{3}H

_{8}, or a mixture gas) diffusion coefficient in crude oil. These methods include the pressure decay method, X-ray computer-assisted tomography (CAT) method, magnetic resonance imaging (MRI) method [29,30], dynamic drop volume analysis (DPDVA), and pore-scale network modeling method. All of these methods have advantages and flaws:

_{4}in isopentane with a constant pressure method in a Pressure-Volume-Temperature (PVT) system. Sigmund [32] also used this method to study the binary dense gas diffusion coefficients under reservoir conditions. Islas-Juarez et al. [33] set up an experimental device to determine the effective diffusion coefficient of N

_{2}in a sandpack model. They devised a special setting to sample crude oil that was dissolved with N

_{2}in their porous model. The samples were then analyzed by gas chromatograph, and the gas concentration in the oil phase was determined. The corresponding diffusion coefficient was determined by matching the mathematical diffusion model with the experimentally measured concentration curve. The main shortcomings of the direct testing method for the solvent diffusion coefficient are that it is both time and labor consuming, which results in an expensive process.

_{2}–crude oil systems with DPDVA technology and measured solvent diffusivity in heavy oil under reservoir pressure and temperature. The DPDSA is a special method that correlates the oil swelling effect due to the mass transfer from the solvent into crude oil to the interfacial tension reduction between the oil and the solvent phases.

_{2}diffusion coefficients in bulk crude oils and in cores that are saturated with formation fluids have had wide concern recently due to the popularity of CO

_{2}EOR. Many significant studies have been conducted in this field, while few attempts have been made to analyze the effect of crude oil properties on the CO

_{2}diffusion process. In this paper, a generalized methodology has been developed to determine the diffusion coefficient of supercritical CO

_{2}for cores that are saturated with different crude oils, under reservoir conditions. In theory, a mathematical model that describes the mass transfer process of CO

_{2}in crude-oil-saturated cores has been established and combines the Peng-Robinson equation of state (PR EOS) and Fick’s diffusion equation. Experimentally, the pressure decay method has been employed to determine the diffusion coefficient. The pressure of the CO

_{2}phase in the annular space of the diffusion cell was monitored and recorded during the mass transfer process of CO

_{2}into the oil-saturated low-permeable cores. Once the difference between the tested and calculated pressure decay curves reached a minimum value, the diffusion coefficient of CO

_{2}could be determined. In addition, the influence of oil properties on the CO

_{2}diffusion coefficient has also been analyzed.

## 2. Experimental Section

#### 2.1. Materials

^{3}and 1.34 mPa∙s under 50 °C and atmospheric pressure, respectively. The crude oil used in this work was collected from Changji Oilfield in Xinjiang Province (China). The crude oil sample is dead oil without sands and brine, whose density measured with a densitometer (DMA 4200M, Anton Paar, Graz, Austria) was 936.8 kg/m

^{3}under 50 °C and atmospheric pressure. The viscosity, which was measured by a rheometer (MCR 302, Anton Paar), is 1770.91 mPa∙s under the same conditions. The component distributions of both the kerosene and crude oil were determined with gas chromatography (GC), and the result is depicted in Figure 1. The CO

_{2}used in this work was purchased from Tianyuan Co., Ltd. (Qingdao, China) and has a purity higher than 99.99 mol %. Artificial cores with a permeability that ranged from 0.096 to 0.103 mD were used as porous media in this work and were compressed with sand particles. The diameters of the sand particles in the cores were restricted to a tiny range, which can ensure the homogeneity and isotropy of the cores. The parameters of the cores used in this work are tabulated in Table 1.

_{2}diffusion coefficients. To simplify the model and analysis, artificial cores are introduced to eliminate the influence of this factor. Therefore, the effects of heterogeneity and anisotropy are ignored in this study.

#### 2.2. Apparatus

_{2}diffusion experiments are conducted in a diffusion cell located in a water bath to keep a constant temperature for all the experiments. The core is placed in the center of the diffusion cell, and CO

_{2}is introduced into the cylinder. The pressure of the CO

_{2}decreases due to the diffusion of CO

_{2}into the core. The pressure decay of the CO

_{2}in the diffusion cell during each experiment is monitored and recorded by a pressure transducer, which can be used for diffusion coefficient calculation.

#### 2.3. Experimental Procedures

_{2}diffusion coefficients in the oil-saturated cores are described as follows:

- (a)
- Clean and dry the core for the experiment, put it into an intermediate container and vacuum for 10.0 h. Then, the oil sample is injected into the intermediate container at room temperature until the pressure of the oil sample reaches 15.0 MPa; maintain this pressure for 48.0 h to ensure that the core pores are completely saturated with crude oil.
- (b)
- Seal the two ends of the oil-saturated core with epoxy resin and aluminum foil to ensure that CO
_{2}can diffuse only through the side surface of the core. - (c)
- Connect the apparatus that is required for the diffusion experiment according to Figure 2. After testing the air tightness of the diffusion cell, place the core in it. Replace the air in the diffusion cell with low pressure CO
_{2}. - (d)
- Put the diffusion cell and CO
_{2}container into the water bath at the required temperature for 4.0 h, and open valve 5 to monitor the pressure in the CO_{2}container. - (e)
- When the pressure inside the CO
_{2}container is stable, open valves 2, 3 and 4 to inject CO_{2}into the diffusion cell. Close valves 3 and 4 quickly after the pressure in the diffusion cell and CO_{2}container reach a balance, and record the pressure decay in the diffusion cell. - (f)
- When the pressure in the diffusion cell does not change, finish the diffusion experiment. Slowly open all valves, release the fluid in the diffusion cell, and clean the equipment for the next set of experiments.

## 3. Mathematical Model

#### 3.1. Diffusion Model in Porous Media

_{2}can diffuse only in the radial direction of the core. The mathematical model used in this study includes Fick’s diffusion equation and PR EOS to describe the diffusion process from the CO

_{2}phase to the cores being saturated with different oil samples. The mass transfer of CO

_{2}is considered by the diffusion equation, while the phase behavior between CO

_{2}and the oil sample is described by PR EOS. Several assumptions that were adopted for this mathematical model are elaborated below:

- (1)
- Cores are homogenous and isotropic, i.e., the influences of different cores are ignored.
- (2)
- Oil saturates all pores in the cores, i.e., oil saturation is 100%.
- (3)
- CO
_{2}concentration at the side surface of the core is constant during the diffusion process. - (4)
- (5)
- The convection flow caused by the density difference is ignored.
- (6)
- The CO
_{2}transfer process occurs only in the radial direction. - (7)
- There is no heat exchange during the diffusion process.

_{2}in oil-saturated porous media. A velocity item is introduced into the equation to consider the influence of oil swelling due to CO

_{2}dissolution:

_{2}in the oil sample, mol/m

^{3}, t is diffusion time, s, u is the flow velocity that is generated by the volume expansion of the oil sample, m/s, r is the distance to the central axis of the core, m, and D is the effective diffusion coefficient of CO

_{2}in the oil-saturated core, m

^{2}/s.

_{0}is the radius of the core, m, $\overline{c}$ is the dimensionless concentration, c

_{0}is the saturation concentration of CO

_{2}in crude oil under experimental conditions, mol/m

^{3}, τ is dimensionless time and $\overline{u}$ is the dimensionless velocity.

#### 3.2. Peng-Robinson Equation of State (PR EOS)

_{2}pressure of the diffusion cell is recorded for the pressure decay method, and the pressure prediction thus affects the accuracy of the CO

_{2}diffusion coefficient. PR EOS is introduced in this paper, and the interaction between CO

_{2}and the oil sample is considered, which increases the calculation accuracy of the annular pressure and diffusion coefficient. PR EOS is a third-order equation with two constants that were proposed by Peng and Robinson [57]. It is a semi-empirical model that is widely applied in the petrochemical industry, and it describes the phase behavior and phase equilibrium of multicomponent systems. PR EOS requires the specific parameters of the components in the system and the binary interaction parameters (BIPs) between each component. PR EOS can be expressed by Equations (6) and (7):

^{3}/mol, T

_{c}is the critical temperature, K, and P

_{c}is the critical pressure, Pa. α is a function of the relative temperature and acentric factor.

_{2}system [59,60]. The parameters of the pseudo-components were determined with a series of empirical models [61,62,63,64,65,66,67,68], and the specific data are listed in the results section.

#### 3.3. Determination of the Diffusion Coefficients

_{2}diffusion coefficient is determined by fitting the experimental and calculated data with particle swarm optimization (PSO). The calculated pressure-time (p-t) curve can be adjusted to minimize the error with a measured p-t curve by optimizing the value of the diffusion coefficient, according to Equation (2). The CO

_{2}diffusion coefficient is determined once the value of the objective function reaches a minimum, which is shown in Equation (8):

_{Ei}and t

_{Ci}are the experimental and calculated times, respectively. For the calculated p-t curve, the pressure values can be determined with the following steps:

- (1)
- Determine CO
_{2}concentration distribution in the core. - (2)
- Calculate the mole composition in the annular space of the diffusion cell according to the amount of swelled oil and dissolved CO
_{2}. - (3)
- Determine the pressure value by solving PR EOS with data that are obtained in step 2.

_{2}diffusion coefficients. In a global regression, all experimental data points are used, and a constant coefficient is obtained to describe the average rate of mass transfer. In the early stage and later stage regressions, part of the data points is employed to calculate the diffusion coefficients, and two diffusion coefficients are obtained to describe the rate of mass transfer in the early and later stages, respectively. The relevant contents will be elaborated in the Results section.

## 4. Results and Discussion

#### 4.1. Characterization of the Oil Samples

_{2}diffusion coefficient. The viscosity-temperature curves of the oil samples are presented in Figure 4, and the viscosity of each oil sample at the experimental temperature is marked in the figure (the pentagram symbols). The carbon distributions of the oil samples that were determined with the method in the literatures [55,59] are illustrated in Figure 5. It is notable that the carbon distributions of kerosene and crude oil are determined with the above method, and the carbon distribution of mixed oil is determined by combining the carbon distribution of the two oils according to their mixing ratio. The detailed process can be described with Equation (9):

_{i}, ${z}_{i}^{c}$ and ${z}_{i}^{k}$ are the mole friction of component i in the mixed oil, crude oil and kerosene samples, respectively, and n

^{c}and n

^{k}are the mole numbers of crude oil and kerosene, respectively.

_{9}account for a tiny part of those oil samples (<1%), which means that there is no obvious extraction effect during the mass transfer process [56,59,60]. The components of the CO

_{2}phase were analyzed by a GC method after the diffusion experiments, and no hydrocarbons were found in the CO

_{2}phase. The GC analysis result agrees with our previous work [55] and proves that neglecting the extraction effect is reasonable. According to the figure, from oil samples A to E, the number of light components (C

_{9}–C

_{15}) decreases, while the amount of heavy components (heavier than C

_{18}) increases gradually. Multiple pseudo-components are introduced in this work to replace the entire carbon distribution to characterize the oil samples, which greatly reduces the computational cost [60]. The pseudo-component parameters are tabulated in Table 2. The tendencies and values of the data in Table 2 are analogous to our previous work [55], which proves the reliability of the parameters. The binary interaction parameter (BIP) matrix is listed in Table 3 and describes the interactions among the components in the system. BIPs between hydrocarbons are set at 0 according to [61,69]. Moreover, only the parameters of oil sample A are given in Table 2 and Table 3; the parameters of the other oil samples are presented in the Appendix A.

#### 4.2. Solution of the Diffusion Model in the Oil-Saturated Cores

_{2}diffusion process in the oil-saturated porous media can be characterized by concentration and velocity profiles, which are obtained by solving the diffusion mathematical model that is proposed in Section 3.1 [54,55]. The CO

_{2}concentration profile during the diffusion process is presented in Figure 6, where black curves identify the CO

_{2}concentrations at different space and time grids.

_{2}amount in the core at a specific time point, and the area between two curves can characterize the increment of CO

_{2}during this period of time. According to Figure 6, the CO

_{2}concentration at the central axis ($\overline{r}=0$) almost reaches 0.5 when dimensionless time is 0.2, and the area between the curve and the x-axis show that the average CO

_{2}concentration was above 0.7 at this moment (the red dashed line in Figure 6). The tendency shows that most of the CO

_{2}diffuses into the oil-saturated core at the early stage of the diffusion process. Moreover, the area of the colored region between two curves decreases with the increase in dimensionless time, which shows that the increase in CO

_{2}in the core gradually slows down, i.e., the speed of mass transfer slows down. Therefore, the diffusion process is divided into two stages, namely, an early stage with a high diffusion rate and a later stage with a lower diffusion rate, which is identical to our previous work [55].

_{2}, is relatively high. The following decrease in velocity characterizes the relatively slow diffusion rate in the later stage. Thus, Figure 6 and Figure 7 complement and confirm one another. It should be noted that the velocity difference between the outer part and inner part of the core is obvious at an early stage; then, the difference decreases gradually, which shows CO

_{2}diffusing from the outer part to the inner part of the core. More details have already been elaborated in our previous work.

#### 4.3. Effect of the Oil Properties on the Diffusion Coefficient

_{2}diffusion process in oil-saturated tight cores under reservoir conditions. The diffusion coefficient of CO

_{2}is determined with the experimental pressure recording and mathematical model that is listed in Section 3, and the pressure curves of the diffusion experiments with different oil samples are depicted in Figure 8. Except for the experimental data, the global fitting (red line) with a constant diffusion coefficient and the piecewise fitting (blue and violet dashed lines) with variable diffusion coefficients are also given in Figure 8. Although there are some differences between the results of the global regression of the different experiments (see Figure 8a,b), which can be attributed to experimental and calculation errors, the value of the goodness-of-fit in each set of experiments shows that both regression methods have acceptable accuracy. This value also shows that the piecewise regression has a better result than the global regression. The highly precise result of the piecewise fitting agrees with the literature [70,71] that suggests that the diffusion coefficient is a variable during the diffusion process, and it also proves the reliability of the conclusions in Section 4.2.

_{2}diffusion coefficients in tight porous media that is saturated with different oil samples, at 70 °C and 15.29–15.36 MPa, are illustrated in Figure 9. In the experimental range of this study, the diffusion coefficients obtained with the global regression range from 55.325 × 10

^{−10}to 107.886 × 10

^{−10}m

^{2}/s. For the piecewise regression, the diffusion coefficients range from 74.975 × 10

^{−10}to 128.925 × 10

^{−10}m

^{2}/s at the early stage and from 39.389 × 10

^{−10}to 89.462 × 10

^{−10}m

^{2}/s at the later stage. The figure also shows that the CO

_{2}diffusion coefficient decreases gradually from oil samples A to F, and the decreasing tendency can be attributed to the following two factors:

_{2}diffusion coefficient is depicted in Figure 10. The figure shows that a lower viscosity can facilitate the CO

_{2}diffusion process, which agrees with the negative relationship between the two parameters that are proposed in the literature [59,74,75,76]. Moreover, Figure 9 and Figure 10 also show the obvious tendency of the diffusion coefficients at different stages. The diffusion coefficient at the early stage is always higher than the average level (global regression), while the diffusion coefficient at the later stage is always lower than the average level. The coefficient that is determined without PR EOS is minimal because it ignores the interaction of oil and CO

_{2}. It is notable that the experimental data form a good linear trend in the semilogarithmic coordinate system.

_{2}[73,75].

_{2}in each oil sample, which is determined with a two-phase equilibrium calculation [78,79,80], is presented in Figure 12 and reflects the capacity of oil to accommodate CO

_{2}. Furthermore, the CO

_{2}solubility of each pseudo-component at 15.3 MPa and 70 °C is depicted in Figure 13. Figure 12 and Figure 13 show that the CO

_{2}solubility decreases with the increase in the proportion of heavy components in oil, i.e., the resistance for CO

_{2}diffusing into oil increases [55]. Thus, the increase in the proportion of heavy components restricts the diffusion process from two aspects. First, it improves the viscosity of oil, which indirectly decreases the diffusion coefficient [81]. Second, heavy components directly increase the mass transfer resistance. Moreover, the resistance effect of heavy components also accounts for the deviation between the experimental data and the exponential model in Figure 11.

#### 4.4. Comparison

_{2}diffusion coefficient in this paper are compared with the data in the literature, and both are listed in Table 4.

_{2}diffusivity that was obtained in this paper is somewhat larger than the CO

_{2}diffusivity in the literature. However, it is still within a reasonable range, and the differences in the data in the different papers can be attributed to several reasons. First, the experimental pressure and temperature in this work are higher than the experimental pressure and temperature in the literature [59,60,75,76]. Thus, the larger diffusion coefficient in this study agrees with the theory that an increase in pressure or temperature facilitates the diffusion process. Second, the viscosities of the oil samples used in this work are lower than the viscosities of the heavy oils used in the literature, which contributes to the high diffusion rate. Third, the proportion of heavy components in the oil samples used in this paper is smaller (by comparing Figure 1 and other works [59,60]); thus, the resistance for CO

_{2}diffusing into oil is small [55]. Moreover, the interaction between CO

_{2}and the oil samples is characterized by PR EOS in this work, and the data that were obtained with this model are more precise.

## 5. Conclusions

_{2}in cores saturated with different oil samples, under reservoir conditions. A mathematical model that describes the mass transfer process of CO

_{2}in oil-saturated cores was established. The pressure decay method was used to determine the diffusion process. The results show that the supercritical CO

_{2}diffusion coefficient decreases gradually from oil samples A to F. It decreases from 128.92 × 10

^{−10}to 74.97 × 10

^{−10}m

^{2}/s at the early stage, decreases from 89.46 × 10

^{−10}to 39.38 × 10

^{−10}m

^{2}/s at the later stage, and decreases from 107.89 × 10

^{−10}to 55.33 × 10

^{−10}m

^{2}/s with the global regression method. The changing properties of oil can account for the decrease in the CO

_{2}diffusion coefficient in two aspects. First, the increasing viscosity of oil slows down the speed of the mass transfer process. Second, the increase in the proportion of heavy components in oil enlarges the mass transfer resistance. These findings can provide direction in predicting CO

_{2}storage potential in reservoirs and the effect of CO

_{2}EOR. Moreover, these findings can also help to optimize engineering techniques in oil fields.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Parameters in PR EOS of Oil Samples B to F

Oil No. | Pseudo-Component | Z (mol %) | MW (g/mol) | SG | T_{b} (K) | T_{c} (K) | P_{c} (kPa) | ω |
---|---|---|---|---|---|---|---|---|

B | B1 | 47.706 | 150.741 | 0.819 | 466.154 | 655.221 | 2497.765 | 0.472 |

B2 | 35.239 | 209.78 | 0.857 | 544.786 | 729.824 | 1942.549 | 0.636 | |

B3 | 17.353 | 439.464 | 0.930 | 726.081 | 886.938 | 1122.854 | 1.043 | |

C | C1 | 49.459 | 158.515 | 0.824 | 477.370 | 666.098 | 2412.984 | 0.494 |

C2 | 33.400 | 244.079 | 0.872 | 580.821 | 762.058 | 1739.855 | 0.719 | |

C3 | 17.143 | 480.992 | 0.941 | 753.344 | 909.992 | 1023.217 | 1.101 | |

D | D1 | 53.065 | 164.282 | 0.828 | 485.358 | 673.746 | 2354.775 | 0.511 |

D2 | 30.215 | 263.996 | 0.880 | 600.216 | 779.188 | 1638.055 | 0.763 | |

D3 | 16.721 | 494.173 | 0.944 | 760.992 | 916.415 | 998.275 | 1.119 | |

E | E1 | 50.339 | 164.845 | 0.829 | 486.152 | 674.510 | 2348.895 | 0.512 |

E2 | 32.411 | 268.563 | 0.882 | 604.173 | 782.621 | 1619.513 | 0.771 | |

E3 | 17.253 | 498.801 | 0.945 | 763.573 | 918.579 | 990.160 | 1.124 | |

F | F1 | 55.032 | 173.010 | 0.834 | 497.042 | 684.824 | 2272.200 | 0.535 |

F2 | 28.996 | 298.023 | 0.892 | 630.406 | 805.497 | 1492.491 | 0.831 | |

F3 | 16.736 | 519.753 | 0.949 | 774.237 | 927.510 | 958.930 | 1.148 |

Oil No. | Component | B1 | B2 | B3 | CO_{2} |
---|---|---|---|---|---|

B | B1 | 0 | 0 | 0 | 3.652 × 10^{−5} |

B2 | 0 | 0 | 0 | 3.998 × 10^{−4} | |

B3 | 0 | 0 | 0 | 4.415 × 10^{−3} | |

CO_{2} | 3.652 × 10^{−5} | 3.998 × 10^{−4} | 4.415 × 10^{−6} | 0 |

Oil No. | Component | C1 | C2 | C3 | CO_{2} |
---|---|---|---|---|---|

C | C1 | 0 | 0 | 0 | 4.181 × 10^{−6} |

C2 | 0 | 0 | 0 | 9.641 × 10^{−4} | |

C3 | 0 | 0 | 0 | 5.148 × 10^{−3} | |

CO_{2} | 4.181 × 10^{−6} | 9.641 × 10^{−4} | 5.148 × 10^{−3} | 0 |

Oil No. | Component | D1 | D2 | D3 | CO_{2} |
---|---|---|---|---|---|

D | D1 | 0 | 0 | 0 | 6.155 × 10^{−7} |

D2 | 0 | 0 | 0 | 1.338 × 10^{−3} | |

D3 | 0 | 0 | 0 | 5.353 × 10^{−3} | |

CO_{2} | 6.155 × 10^{−7} | 1.338 × 10^{−3} | 5.353 × 10^{−3} | 0 |

Oil No. | Component | E1 | E2 | E3 | CO_{2} |
---|---|---|---|---|---|

E | E1 | 0 | 0 | 0 | 1.117 × 10^{−6} |

E2 | 0 | 0 | 0 | 1.421 × 10^{−3} | |

E3 | 0 | 0 | 0 | 5.422 × 10^{−3} | |

CO_{2} | 1.117 × 10^{−6} | 1.421 × 10^{−3} | 5.422 × 10^{−3} | 0 |

Oil No. | Component | F1 | F2 | F3 | CO_{2} |
---|---|---|---|---|---|

F | F1 | 0 | 0 | 0 | 2.365 × 10^{−5} |

F2 | 0 | 0 | 0 | 1.998 × 10^{−3} | |

F3 | 0 | 0 | 0 | 5.704 × 10^{−3} | |

CO_{2} | 2.365 × 10^{−5} | 1.998 × 10^{−3} | 5.704 × 10^{−3} | 0 |

## References

- Yang, Q.; Zhong, C.; Chen, J. Computational study of CO
_{2}storage in metal–organic frameworks. J. Phys. Chem. C**2011**, 112, 1562–1569. [Google Scholar] [CrossRef] - Lydonrochelle, M.T. Amine ccrubbing for CO
_{2}capture. Science**2009**, 325, 1652–1654. [Google Scholar] - Rutqvist, J. The geomechanics of CO
_{2}storage in deep sedimentary formations. Geotech. Geol. Eng.**2012**, 30, 525–551. [Google Scholar] [CrossRef] - Holm, L.W.; Josendal, V.A. Mechanisms of oil displacement by carbon dioxide. J. Pet. Technol.
**1974**, 26, 1427–1438. [Google Scholar] [CrossRef] - Monger, T.G.; Ramos, J.C.; Thomas, J. Light oil recovery from cyclic CO
_{2}injection: Influence of low pressure impure CO_{2}and reservoir gas. SPE Reserv. Eng.**1991**, 6, 25–32. [Google Scholar] [CrossRef] - Moberg, R. The Wyburn CO
_{2}monitoring and storage project. Greenh. Issues**2001**, 57, 2–3. [Google Scholar] - Baines, S.J.; Worden, R.H. Geological storage of carbon dioxide. Rudarsko-Geološko-Naftni Zbornik.
**2004**, 28, 9–22. [Google Scholar] [CrossRef] - Wang, S.; Feng, Q.; Javadpour, F.; Xia, T.; Li, Z. Oil Adsorption in shale nanopores and its effect on recoverable oil-in-place. Int. J. Coal Geol.
**2015**, 147–148, 9–24. [Google Scholar] [CrossRef] - Zhang, Z.; Chen, F.; Rezakazemi, M.; Zhang, W.; Lu, C.; Chang, H.; Quan, X. Modeling of a CO
_{2}-piperazine-membrane absorption system. Chem. Eng. Res. Des.**2018**, 131, 375–384. [Google Scholar] [CrossRef] - Zhang, Z.; Cai, J.; Chen, F.; Li, H.; Zhang, W.; Qi, W. Progress in enhancement of CO
_{2}absorption by nanofluids: A mini review of mechanisms and current status. Renew. Energy**2018**, 118, 527–535. [Google Scholar] [CrossRef] - Yang, Y.; Qiu, L.; Cao, Y.; Chen, C.; Lei, D.; Wan, M. Reservoir quality and diagenesis of the Permian Lucaogou Formation tight ccarbonates in Jimsar Sag, Junggar Basin, West China. J. Earth Sci.
**2017**, 28, 1032–1046. [Google Scholar] [CrossRef] - Cao, M.; Gu, Y. Temperature effects on the phase behaviour, mutual interactions and oil recovery of a light crude oil–CO
_{2}system. Fluid Phase Equilib.**2013**, 356, 78–89. [Google Scholar] [CrossRef] - Du, F. An Experimental Study of Carbon Dioxide Dissolution into a Light Crude Oil. Regina. Master’s Thesis, University of Regina, Regina, SK, Canada, 2016. [Google Scholar]
- Luo, P.; Yang, C.; Gu, Y. Enhanced solvent dissolution into in-situ upgraded heavy oil under different pressures. Fluid Phase Equilib.
**2007**, 252, 143–151. [Google Scholar] [CrossRef] - Yang, D.; Gu, Y. Visualization of interfacial interactions of crude Oil-CO
_{2}systems under reservoir conditions. In Proceedings of the 14th Symposium on Improved Oil Recovery, Tulsa, OK, USA, 17–21 April 2004. [Google Scholar] - Cui, G.; Zhang, L.; Tan, C.; Ren, S.; Zhuang, Y.; Enechukwu, C. Injection of supercritical CO
_{2}for geothermal exploitation from sandstone and carbonate reservoirs: CO_{2}–water–rock Interactions and their Effects. J. CO_{2}Util.**2017**, 20, 113–128. [Google Scholar] [CrossRef] - Zhang, L.; Li, X.; Zhang, Y.; Cui, G.; Tan, C.; Ren, S. CO
_{2}Injection for geothermal development associated with EGR and geological storage in depleted high-temperature gas reservoirs. Energy**2017**, 123, 139–148. [Google Scholar] [CrossRef] - Ghasemi, M.; Astutik, W.; Alavian, S.A.; Whitson, C.H.; Sigalas, L.; Olsen, D. Determining diffusion coefficients for carbon dioxide injection in oil-saturated chalk by use of a constant-volume-diffusion method. SPE J.
**2017**, 22, 505–520. [Google Scholar] [CrossRef] - Zhang, K.; Gu, Y. New Qualitative and quantitative technical criteria for determining the minimum miscibility pressures (MMPs) with the rising-bubble apparatus (RBA). Fuel
**2016**, 175, 172–181. [Google Scholar] [CrossRef] - Izgec, O.; Demiral, B.; Bertin, H. CO
_{2}Injection into saline carbonate aquifer formations I: Laboratory investigation. Transp. Porous Media**2008**, 72, 1–24. [Google Scholar] [CrossRef] - Sayegh, S.G.; Rao, D.N.; Kokal, S.; Najman, J. Phase behavior and physical properties of lindbergh heavy oil/CO
_{2}mixtures. J. Can. Pet. Technol.**1990**, 29, 31–39. [Google Scholar] [CrossRef] - Comerlati, A.; Ferronato, M.; Gambolati, G.; Putti, M.; Teatini, P. Fluid-dynamic and gmechanical effects of CO
_{2}sequestration below the venice lagoon. Environ. Eng. Geosci.**2006**, 12, 211–226. [Google Scholar] [CrossRef] - Zhang, X.; Trinh, T.T.; Santen, R.A.V. Mechanism of the initial stage of silicate oligomerization. J. Am. Chem. Soc.
**2011**, 133, 6613–6625. [Google Scholar] [CrossRef] [PubMed] - Li, Z.; Dong, M. Experimental study of carbon dioxide diffusion in oil-saturated porous media under reservoir conditions. Ind. Eng. Chem. Res.
**2009**, 48, 9307–9317. [Google Scholar] [CrossRef] - Jia, Y.; Bian H, B.; Duveau, G.; Shao, J. Numerical analysis of the thermo-hydromechanical behaviour of underground storages in hard rock. In Proceedings of the Geoshanghai International Conference, Shanghai, China, 3–5 June 2010; pp. 198–205. [Google Scholar]
- Li, Z.; Dong, M.; Li, S.; Dai, L. A New method for gas effective diffusion coefficient measurement in water-saturated porous rocks under high pressures. J. Porous Media
**2006**, 9, 445–461. [Google Scholar] [CrossRef] - Hou, S.; Liu, F.; Wang, S.; Bian, H. Coupled heat and moisture transfer in hollow Concrete block wall filled with compressed straw bricks. Energy Build.
**2017**, 135, 74–84. [Google Scholar] [CrossRef] - Wang, S.; Feng, Q.; Zha, M.; Javadpour, F.; Hu, Q. Supercritical methane diffusion in shale nanopores: Effects of pressure, mineral types, and moisture content. Energy Fuels
**2017**, 32, 169–180. [Google Scholar] [CrossRef] - Zhao, P.; Wang, Z.; Sun, Z.; Cai, J.; Wang, L. Investigation on the pore structure and multifractal characteristics of tight oil reservoirs using NMR measurements: Permian Lucaogou Formation in Jimusaer Sag, Junggar Basin. Mar. Petrol. Geol.
**2017**, 86, 1067–1081. [Google Scholar] [CrossRef] - Wang, F.; Yang, K.; Cai, J. Fractal characterization of tight oil reservoir pore structure using nuclear magnetic resonance and mercury intrusion porosimetry. Fractals
**2018**, 2, 1840017. [Google Scholar] [CrossRef] - Hill, E.S.; Lacey, W.N. Hate of solution of propane in quiescent liquid hydrocarbons. Ind. Eng. Chem.
**1934**, 25, 1014–1019. [Google Scholar] - Sigmund, P.M. Prediction of molecular diffusion at reservoir conditions. Part I—Measurement and prediction of binary dense gas diffusion coefficients. J. Can. Pet. Technol.
**1976**, 15, 48–57. [Google Scholar] [CrossRef] - Islas-Juarez, R.; Samanego, V.F.; Luna, E.; Perez-Rosales, C.; Cruz, J. Experimental study of effective diffusion in porous media. In Proceedings of the SPE International Petroleum Conference in Mexico, Puebla, Mexico, 7–9 November 2004; pp. 781–787. [Google Scholar]
- Riazi, M.R. A new method for experimental measurement of diffusion coefficients in reservoir fluids. J. Pet. Sci. Eng.
**1996**, 14, 235–250. [Google Scholar] [CrossRef] - Upreti, S.R.; Mehrotra, A.K. Experimental measurement of gas diffusivity in bitumen: Results of carbon dioxide. Ind. Eng. Chem. Res.
**2000**, 39, 1080–1087. [Google Scholar] [CrossRef] - Zhang, Y.; Hyndman, C.L.; Maini, B.B. Measurement of gas diffusivity in heavy oils. J. Pet. Sci. Eng.
**1999**, 25, 37–47. [Google Scholar] [CrossRef] - Tharanivasan, A.K.; Yang, C.; Gu, Y. Measurements of molecular diffusion coefficients of carbon dioxide, methane, and propane in heavy oil under reservoir conditions. Energy Fuels
**2006**, 20, 2509–2517. [Google Scholar] [CrossRef] - El-Haj, R.; Lohi, A.; Upreti, S.R. Experimental determination of butane dispersion in vapour extraction of heavy oil and bitumen. J. Pet. Sci. Eng.
**2009**, 67, 41–47. [Google Scholar] [CrossRef] - Okazawa, T. Impact of concentration—Dependence of diffusion coefficient on VAPEX drainage rates. J. Can. Pet. Technol.
**2009**, 48, 47–53. [Google Scholar] [CrossRef] - Wen, Y.; Bryan, J.; Kantzas, A. Estimation of diffusion coefficients in bitumen solvent mixtures as derived from low field NMR spectra. J. Can. Pet. Technol.
**2005**, 44, 29–35. [Google Scholar] [CrossRef] - Afsahi, B. Advanced in Diffusivity and Viscosity Measurements of Hydrocarbon Solvents in Heavy Oil and Bitumen. Master’s Thesis, University of Calgary, Calgary, AB, Canada, 2006. [Google Scholar]
- Guerrero-Aconcha, U.; Salama, D.; Kantzas, A. Diffusion of n-alkanes in heavy oil. In Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, CO, USA, 21–24 September 2008. [Google Scholar]
- Wen, Y.; Kantzas, A.; Wang, G. Estimation of diffusion coefficients in bitumen solvent mixtures using X-ray CAT scanning and low field NMR. In Proceedings of the Canadian International Petroleum Conference, Calgary, AB, Canada, 8–10 June 2004. [Google Scholar]
- Wang, L.; Nakanishi, Y.; Teston, A.D.; Suekane, T. Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport. J. Fluid Sci. Technol.
**2018**, 13, 1–20. [Google Scholar] [CrossRef] - Yang, C.; Gu, Y. A new method for measuring solvent diffusivity in heavy oil by dynamic pendant drop shape analysis (DPDSA). SPE J.
**2006**, 11, 48–57. [Google Scholar] [CrossRef] - Oren, P.E.; Bakke, S.; Arntzen, O.J. Extending predictive capabilities to network models. SPE J.
**1998**, 3, 324–336. [Google Scholar] [CrossRef] - Blunt, M.J.; Piri, M.; Valvatne, P. Detailed physics, predictive capabilities and upscaling for pore-scale models of multiphase flow. Adv. Water Resour.
**2002**, 25, 1069–1089. [Google Scholar] [CrossRef] - Piri, M.; Blunt, M.J. Pore-scale modeling of three-phase flow in mixed wet systems. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 29 September–2 October 2002. [Google Scholar]
- Garmeh, G.; Johns, R.T.; Lake, L.W. Pore-scale simulation of dispersion in porous media. In Proceedings of the SPE Annual Technical Conference and Exhibition, Anaheim, CA, USA, 11–14 November 2007. [Google Scholar]
- Taheri, S.; Kantzas, A.; Abedi, J. Mass diffusion into bitumen: A sub-pore scale modeling approach. In Proceedings of the Canadian Unconventional Resources & International Petroleum Conference, Calgary, AB, Canada, 19–21 October 2010. [Google Scholar]
- De Paoli, M.; Zonta, F.; Soldati, A. Dissolution in anisotropic porous media: Modelling convection regimes from onset to shutdown. Phys. Fluids
**2017**, 29, 026601. [Google Scholar] [CrossRef] - Xu, X.; Chen, S.; Zhang, D. Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers. Adv. Water Resour.
**2006**, 29, 397–407. [Google Scholar] [CrossRef] - De Paoli, M.; Zonta, F.; Soldati, A. Influence of anisotropic permeability on convection in Porous media: Implications for geological CO
_{2}sequestration. Phys. Fluids**2016**, 28, 367–370. [Google Scholar] [CrossRef] - Li, S.; Li, Z.; Dong, Q. Diffusion coefficients of supercritical CO
_{2}in oil-saturated cores under low permeability reservoir conditions. J. CO_{2}Util.**2016**, 14, 47–60. [Google Scholar] [CrossRef] - Li, S.; Qiao, C.; Zhang, C.; Li, Z. Determination of diffusion coefficients of supercritical CO
_{2}under tight oil reservoir conditions with pressure-decay method. J. CO_{2}Util.**2018**, 24, 430–443. [Google Scholar] [CrossRef] - Li, H.; Yang, D. Determination of individual diffusion coefficients of solvent/CO
_{2}mixture in heavy oil with pressure-decay method. SPE J.**2015**, 21, 131–143. [Google Scholar] [CrossRef] - Peng, D.; Robinson, D.B. A new two-constant equation of state. Ind. Eng. Chem. Fundam.
**1976**, 15, 92–94. [Google Scholar] [CrossRef] - Zuo, J.; Zhang, D. Plus fraction characterization and PVT data regression for reservoir fluids near critical conditions. In Proceedings of the SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, QLD, Australia, 16–18 October 2000. [Google Scholar]
- Zheng, S.; Li, H.; Sun, H.; Yang, D. Determination of diffusion coefficient for alkane solvent–CO
_{2}mixtures in heavy oil with consideration of swelling effect. Ind. Eng. Chem. Res.**2016**, 55, 1533–1549. [Google Scholar] [CrossRef] - Zheng, S.; Yang, D. Determination of individual diffusion coefficients of C
_{3}H_{8}/n-C_{4}H_{10}/CO_{2}/heavy-oil systems at high pressures and elevated temperatures by dynamic volume analysis. In Proceedings of the SPE Improved Oil Recovery Conference, Tulsa, OK, USA, 11–13 April 2016. [Google Scholar] - Fateen, S.E.K.; Khalil, M.M.; Elnabawy, A.O. Semi-empirical correlation for binary interaction parameters of the Peng–Robinson equation of state with the van der Waals mixing rules for the prediction of high-pressure vapor–liquid equilibrium. J. Adv. Res.
**2013**, 4, 137–145. [Google Scholar] [CrossRef] [PubMed] - Elsharkawy, A.M. An empirical model for estimating the saturation pressures of crude oils. J. Pet. Sci. Eng.
**2003**, 38, 57–77. [Google Scholar] [CrossRef] - Pedersen, K.S.; Thomassen, P.; Fredenslund, A. SRK-EOS calculation for Crude OILS. Fluid Phase Equilib.
**1983**, 14, 209–218. [Google Scholar] [CrossRef] - Twu Chorng, H. Prediction of thermodynamic properties of normal paraffins using only normal boiling point. Fluid Phase Equilib.
**1983**, 11, 65–81. [Google Scholar] - Twu Chorng, H. An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids. Fluid Phase Equilib.
**1984**, 16, 137–150. [Google Scholar] - Kesler, M.G.; Lee, B.I. Improve prediction of enthalpy fractions. Hydrocarb. Process.
**1976**, 55, 153–158. [Google Scholar] - Danesh, A.; Xu, D.; Todd, A.C. A Grouping method to optimize oil description for compositional simulation of gas-injection processes. SPE Reserv. Eng.
**1992**, 7, 343–348. [Google Scholar] [CrossRef] - Renner, T.A. Measurement and correlation of diffusion coefficients for CO
_{2}and rich-gas applications. SPE Reserv. Eng.**1988**, 3, 517–523. [Google Scholar] [CrossRef] - Moysan, J.M.; Paradowski, H.; Vidal, J. Prediction of phase behaviour of gas-containing systems with cubic equations of state. Chem. Eng. Sci.
**1986**, 41, 2069–2074. [Google Scholar] [CrossRef] - Crank, J. The Mathematics of Diffusion; Oxford University Press: Oxford, UK, 1979. [Google Scholar]
- Zhao, R.; Ao, W.; Xiao, A.; Yan, W.; Yu, Z.; Xiao, X. Diffusion law and measurement of variable diffusion coefficient of CO
_{2}in oil. J. China Univ. Pet.**2016**, 40, 136–142. [Google Scholar] - Kavousi, A.; Torabi, F.; Chan, C.W.; Shirif, E. Experimental measurement and parametric study of CO
_{2}solubility and molecular diffusivity in heavy crude oil systems. Fluid Phase Equilib.**2014**, 371, 57–66. [Google Scholar] [CrossRef] - Behzadfar, E.; Hatzikiriakos, S.G. Diffusivity of CO
_{2}in bitumen: Pressure–decay measurements coupled with rheometry. Energy Fuels**2014**, 28, 1304–1311. [Google Scholar] [CrossRef] - Umesi, N.O.; Danner, R.P. Predicting diffusion coefficients in nonpolar solvents. Ind. Eng. Chem. Proc. Des. Dev.
**1981**, 20, 662–665. [Google Scholar] [CrossRef] - Upreti, S.R.; Mehrotra, A.K. Diffusivity of CO
_{2}, CH_{4}, C_{2}H_{6}and N_{2}in athabasca bitumen. Can. J. Chem. Eng.**2002**, 80, 116–125. [Google Scholar] [CrossRef] - Rasmussen, M.L.; Civan, F. Parameters of gas dissolution in liquids obtained by isothermal pressure decay. AICHE J.
**2009**, 55, 9–23. [Google Scholar] [CrossRef] - Hayduk, W.; Cheng, S.C. Review of relation between diffusivity and solvent viscosity in dilute liquid solutions. Chem. Eng. Sci.
**1971**, 26, 635–646. [Google Scholar] [CrossRef] - Dan, V.N.; Graciaa, A. A new reduction method for phase equilibrium calculations. Fluid Phase Equilib.
**2011**, 302, 226–233. [Google Scholar] - Leibovici, C.F.; Neoschil, J. A solution of Rachford-Rice equations for multiphase systems. Fluid Phase Equilib.
**1995**, 112, 217–221. [Google Scholar] [CrossRef] - Okuno, R.; Johns, R.T.; Sepehrnoori, K. Application of a reduced method in compositional simulation. SPE J.
**2010**, 15, 39–49. [Google Scholar] [CrossRef] - Shu, W.R. Viscosity correlation for mixtures of heavy oil, bitumen, and petroleum fractions. SPE J.
**1984**, 24, 277–282. [Google Scholar] [CrossRef]

**Figure 4.**Viscosity-temperature curves of the oil samples (the pentagram symbols are the viscosities of the oil samples under experimental conditions.).

**Figure 6.**CO

_{2}concentration profile of the cores in the diffusion process (the red line reflects the average CO

_{2}dimensionless concentration in the core at τ = 0.2.).

**Figure 8.**Pressure-time curves of the CO

_{2}diffusion experiments. (

**a**) Oil sample A, 3.30 mPa∙s; (

**b**) Oil sample B, 21.57 mPa∙s; (

**c**) Oil sample C, 31.09 mPa∙s; (

**d**) Oil sample D, 43.50 mPa∙s; (

**e**) Oil sample E, 76.81 mPa∙s; (

**f**) Oil sample F, 127.47 mPa∙s.

**Figure 9.**The CO

_{2}diffusion coefficient in tight cores saturated with different oil samples (70 °C, 15.29–15.36 MPa).

Test No. | Core Diameter (mm) | Core Length (mm) | Permeability (mD) | Porosity (%) | Initial Pressure (MPa) | Temperature (°C) |
---|---|---|---|---|---|---|

1 | 38.16 | 90.42 | 0.102 | 3.92 | 15.29 | 70 |

2 | 38.18 | 90.20 | 0.099 | 3.83 | 15.36 | 70 |

3 | 38.14 | 89.66 | 0.096 | 4.95 | 15.35 | 70 |

4 | 38.20 | 89.12 | 0.103 | 3.76 | 15.33 | 70 |

5 | 38.18 | 89.74 | 0.100 | 4.16 | 15.36 | 70 |

6 | 38.16 | 89.40 | 0.102 | 3.75 | 15.32 | 70 |

Oil No. | Pseudo-Component | Z (mol %) | MW (g/mol) | SG | T_{b} (K) | T_{c} (K) | P_{c} (kPa) | ω |
---|---|---|---|---|---|---|---|---|

A | A1 | 43.302 | 143.19 | 0.813 | 454.768 | 644.008 | 2587.222 | 0.449 |

A2 | 34.479 | 180.762 | 0.841 | 509.554 | 697.369 | 2168.917 | 0.559 | |

A3 | 22.220 | 315.116 | 0.893 | 632.112 | 806.063 | 1527.015 | 0.832 |

Oil No. | Component | A1 | A2 | A3 | CO_{2} |
---|---|---|---|---|---|

A | A1 | 0 | 0 | 0 | 1.027 × 10^{−4} |

A2 | 0 | 0 | 0 | 7.162 × 10^{−5} | |

A3 | 0 | 0 | 0 | 2.057 × 10^{−3} | |

CO_{2} | 1.027 × 10^{−4} | 7.162 × 10^{−5} | 2.057 × 10^{−3} | 0 |

**Table 4.**Data in the literature of the CO

_{2}diffusion coefficient in porous media saturated with oil.

Fluid | Viscosity (mPa∙s) | Pressure (MPa) | Temperature (K) | Permeability (mD) | Diffusion Coefficient (10^{−10} m^{2}/s) | Sources | |
---|---|---|---|---|---|---|---|

Mixed oil samples | 3.30–127.47 @343.15K | 15.29–15.36 | 343.15 | 0.096–0.103 | Early stage | Later stage | This study |

74.97–128.92 | 39.38–89.46 | ||||||

Global regression | |||||||

55.33–107.89 | |||||||

Without PR EOS | |||||||

23.63–79.37 | |||||||

Changji light oil | 7.26 @323.15K | 14.56–14.89 | 298.15–358.15 | 0.058–0.192 | Early stage | Later stage | Li et al. [54] |

67.04–164.38 | 33.82–100.37 | ||||||

N-hexadecan | 2.14 @313.15 | 2.28–6.03 | 313.15 | 80.67–227.74 | 5.98–8.01 | Li et al. [24] | |

Lloydminster heavy oil | 12,854.00 @294.55K | 3.74–3.37 | 294.55 | / | 4.30 | Zheng et al. [58] | |

Lloydminster heavy oil | 12,854.00 @294.55K | 5.40 | 317.65 | / | 14.97 | Zheng et al. [59] | |

Athabasca bitumen | 821,000.00 @298.15K | 4.00–8.00 | 323.15 | / | 2.20–8.90 | Upreti [74] | |

Lloydminster heavy oil | 23,000.00 @297.15K | 2.00–6.00 | 297.15 | / | 2.00–5.50 | Yang [45] | |

Athabasca bitumen | 106,000.00 @313.15K | 3.24 | 348.15 | / | 5.03 | Rasmussen et al. [75] |

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**MDPI and ACS Style**

Zhang, C.; Qiao, C.; Li, S.; Li, Z.
The Effect of Oil Properties on the Supercritical CO_{2} Diffusion Coefficient under Tight Reservoir Conditions. *Energies* **2018**, *11*, 1495.
https://doi.org/10.3390/en11061495

**AMA Style**

Zhang C, Qiao C, Li S, Li Z.
The Effect of Oil Properties on the Supercritical CO_{2} Diffusion Coefficient under Tight Reservoir Conditions. *Energies*. 2018; 11(6):1495.
https://doi.org/10.3390/en11061495

**Chicago/Turabian Style**

Zhang, Chao, Chenyu Qiao, Songyan Li, and Zhaomin Li.
2018. "The Effect of Oil Properties on the Supercritical CO_{2} Diffusion Coefficient under Tight Reservoir Conditions" *Energies* 11, no. 6: 1495.
https://doi.org/10.3390/en11061495