Fuel 143 (2015) 194–201

Contents lists available at ScienceDirect

Fuel

journal homepage: www.elsevier .com/locate / fuel

Molecular dynamics simulation on volume swelling of CO2–alkanesystem

http://dx.doi.org/10.1016/j.fuel.2014.11.0460016-2361/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +86 053286983366.E-mail address: zhangjun.upc@gmail.com (J. Zhang).

Bing Liu a, Junqin Shi a, Baojiang Sun b, Yue Shen a, Jun Zhang a,⇑, Xu Chen a, Muhan Wang a

a School of Science, China University of Petroleum, Qingdao 266580, Shandong, Chinab School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, Shandong, China

h i g h l i g h t s

�Molecular dynamics simulation was first used to address CO2–alkane swelling.� Volume swelling coefficients from simulation are in well agreement with experiments.� Swelling mechanism was investigated by process, structure and interaction energy.� Effects of pressure and temperature on volume swelling were interpreted.� Simplification of alkane molecular structure promotes volume swelling.

a r t i c l e i n f o

Article history:Received 17 August 2014Received in revised form 20 September2014Accepted 16 November 2014Available online 26 November 2014

Keywords:Volume swellingCO2–alkane systemDispersion interactionMolecular simulation

a b s t r a c t

The microscopic mechanism of the volume swelling of CO2–alkane (decane, octane, hexane and cyclohex-ane) systems and the effects of temperature, pressure and alkane structure on the volume swelling ofCO2–alkane systems are investigated by performing molecular dynamics simulation. It is shown thatthe increase in pressure, the reduction in temperature and the straight-chain structure of the alkaneare of benefit to the volume swelling of CO2–alkane systems by calculating the volume swelling coeffi-cient; CO2 in supercritical state plays a dominant role in the volume swelling of CO2–alkane systems.The microscopic process of the volume swelling of CO2–decane system shows that the increase in theaverage separation distance between decane molecules and the stretch of decane molecules result inthe volume swelling of decane as CO2 dissolve into decane. The calculations of interaction energies inCO2–decane system indicate that the interaction between CO2 and decane molecules is responsible forthe volume swelling of CO2–alkane system. Further study on the interaction between CO2 and decanemolecules shows that the dispersion interaction, resulting in the different solubility of CO2 in alkanes,is the essence of the volume swelling for CO2–alkane system. This work is a good start on understandingthe mechanism of alkane swelling influenced by CO2 at the molecular level and provides useful informa-tion for guiding CO2 enhancing oil recovery.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction considerably lower the oil viscosity and expand the oil volume,

Combining geological CO2 storage and CO2 flooding to enhanceoil recovery (EOR) has been attracting both industrial and scientificinterest because of the growing concern about global warming andshortage of energy supply [1–4]. When CO2 is injected intooil-bearing reservoirs and dissolved in crude oil, there appearfavorable characteristics of CO2 including that the oil volumeswells, the oil viscosity is reduced, and CO2 and oil could bemiscible [1,5–9]. Even under immiscible conditions CO2 can also

leading to a significant improvement of oil recovery [1,5–9]. Mean-while, as parts of CO2 injected into the reservoirs could be seques-trated to effectively perform the geological storage of CO2 in thereservoirs, it is also an attractive solution for the fighting with glo-bal warming aiming at mitigating CO2 emission and accumulation[5,10–17].

In the petroleum industry, experimental studies and reservoirsimulations on binary systems composed of CO2 and hydrocarbonwere implemented for investigation of improving hydrocarbonrecovery [18–26]. Most of the researches focused on the oil swell-ing effect mainly caused by CO2 preferably dissolved in the lightfractions of oil and accurately quantified at reservoir conditions.David et al. [20] and Erdogan et al. [21] studied the change in the

B. Liu et al. / Fuel 143 (2015) 194–201 195

volume of different CO2–alkane systems, indicating that the excessvolume displays a sigmoidal variation with composition of CO2.The obtained solubility parameters predicted the dissolving capac-ity of CO2 in hydrocarbon. The oil swelling effect was quantified bythe volume swelling coefficient defined by Yang et al. [5,22–26].These studies indicate that the volume swelling coefficient of oilincreases with the increases of pressure and solubility of CO2 inoil. Yang et al. [5] attempted to understand the behavior of oilswelling by qualitatively analyzing the dispersion property ofCO2 in oil. However, experiments are difficult under such extremeconditions with high pressure and temperature. On the other hand,the experimental investigation of oil swelling affected by CO2 atmicroscale under reservoir conditions is still quite challenging,and it is not common to comprehensively characterize the mecha-nisms of oil swelling as CO2 is dissolved in oil.

Consequently, molecular simulation as a new means beingdeveloped fast has been increasingly applied in CO2 storage[16,27–29] and EOR approach [30,31]. It helps us to gain a betterunderstanding of the interactions taking place in a microscopiclevel and to investigate the structure, dynamics, and rheology ofa mixture system [27–29]. Recently, the interfacial property andphase equilibrium of CO2–oil systems were reported by molecularmodeling. Attempts to understand the dynamic behavior at alkane-solid surfaces have been made using molecular simulation [31–33].Zhang et al. [30] performed the configurational-bias Monte Carlosimulation in the osmotic ensemble to study CO2 solubility inoctane and its effect on octane swelling, showing the interactionbetween the octane and CO2 is the main cause of the octane swell-ing. However, to our knowledge, the work of molecular simulationreported to investigate the effect of CO2 on oil swelling is limited,the microscopic process of oil swelling and the mechanism ofinteraction between CO2 and oil are not reported from a molecularsimulation perspective. Molecular dynamics (MD) simulation canreveal the microscopic behavior of CO2 spreading into alkanesand display the configuration change of alkane molecules as CO2

dissolves in alkanes, which are useful information for analyzingthe effect of CO2 on alkane volume swelling.

Therefore, in this study, MD simulations were used to investi-gate the volume swelling of four alkanes (hexane, cyclohexane,octane and decane) influenced by CO2 dissolving in them. The pur-pose of the work is to assist in understanding the mechanisms ofthe dissolution of CO2 in alkanes and the alkane volume swellinginduced by CO2. The following content of the paper is organizedas follows. Section 2 provides the molecular models and the detailsof the simulation. In section 3, firstly, the volume swelling coeffi-cients of CO2–alkane systems are calculated under different condi-tions; then, a molecular interaction mechanism between CO2 andalkane molecules is applied to explain alkane swelling inducedby CO2; finally, the effects of pressure, temperature and the alkanestructure on the volume swelling of CO2–alkane systems are dis-cussed in detail. The study on alkane swelling at a microscopiclevel is helpful to better understand mechanisms of CO2-EOR andCO2 storage in reservoir in scientific and industrial researches.

2. Simulation method

Molecular dynamics (MD) simulations were carried out usingMaterials Studio software package with the condensed-phase opti-mized molecular potential for atomistic simulation studies (COM-PASS) force field describing all atoms in this study. COMPASS, awidely used all-atom force field based on ab initio and optimiza-tion by the experimental data, has been validated to be capableof accurately predicting structural and thermophysical propertiesfor a broad range of organic and inorganic substances includingCO2 and alkanes [34–36]. This force field includes the bonded

potential and the non-bonded potential. The total potential energyof a model system in the COMPASS force field is described by thefollowing equation [37].

E ¼ Ebond þ Eangle þ Etorsion þ Eoop þ Ecross þ EvdW þ Ecoulomb ð1Þ

where the first five terms on the right side of the equation corre-spond to bond stretching, angular bending, dihedral angle torsion,out-of-plane interactions and cross-coupling, respectively, whichconstitute the bonded potential; the last two terms on the right sideare the short-range van der Waals (vdW) interactions and the long-range electrostatic interactions, respectively, which constitute thenon-bonded potential. The vdW interactions are represented byLennard-Jones 96 function and the electrostatic interactions are cal-culated by Coulombic equation, described by the following equa-tions respectively.

EvdW ¼ D0 2R0

R

� �9

� 3R0

R

� �6" #

ð2Þ

Eele ¼ Cqiqj

eRð3Þ

where D0 is the depth of potential well, R0 is the Lennard-Jonesradius, R is the distance between the atoms, C = 332.0647 (kcal/mol) Å/e2 is the unit conversion factor, qi and qj are the partialcharges of the atoms i and j respectively, and e is the relative dielec-tric constant. In Eq. (2), the first term in the bracket describes therepulsion interaction energies and the second represents the disper-sion interaction energies.

A series of all-atom MD simulations on the CO2–alkanes binarywere performed on a system initially consisting of two indepen-dent bulk phases. The first bulk system contained initially 150 mol-ecules of alkane (hexane, cyclohexane, octane or decane). Thesecond bulk phase consisted of CO2 molecules determined by theexperimental solubility of CO2 in the alkane [5,23] shown in TablesS1 and S2 (in the supplementary material). Initially, the dimen-sions of each binary system in the x and y directions were fixedto 40 Å, while the dimension in the z direction was identified bythe densities of CO2 and alkanes. The binary systems were subjectto 3D periodic boundary conditions. The original configuration ofthe CO2–alkanes binary system was depicted in Fig. 2(a).

All simulations were carried out in the NPT ensemble for 1.5 nswith the time step of 1 fs after the energy minimization was per-formed on each system using smart minimizer approach. In allsimulations, the temperatures of the systems were controlled at318, 333, and 343 K, respectively, by the Andersen thermostatmethod; the pressures were kept at a series of values in a rangeof 0–11 MPa by the Berendsen barostat method. The long-rangeelectrostatic interactions were evaluated by the Ewald summation[38,39]. The vdW interactions were calculated using the atom-based summation with a cutoff distance of 13.5 Å. Full trajectorieswere saved and the frames were output every 1 ps for the analysisof the results.

3. Results and discussion

3.1. Volume swelling coefficient of CO2–alkane systems

To examine the effects of the pressure, the temperature and thealkane structure on the swelling of CO2–alkane systems, the vol-ume swelling coefficients, g, quantifying the alkane swelling whenCO2 dissolves into the alkane (hexane, cyclohexane, octane anddecane), were calculated. Here, g is defined as the followingequation

g ¼ V=V0 ð4Þ

Fig. 1. Volume swelling coefficients of (a) CO2–decane (black), octane (red), hexane (blue) and cyclohexane (green) systems as a function of pressure at the temperature of333 K, (b) CO2–decane systems as a function of pressure at temperatures of 318 (blue), 333 (red) and 343 K (black). The line-solid symbol represents the experimental value,the hollow symbol represents the simulated value. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2. The representative snapshots of the volume swelling for CO2–decane system. Color code: gray, carbon; red, oxygen; white, hydrogen. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version of this article.)

196 B. Liu et al. / Fuel 143 (2015) 194–201

where V is the volume of the CO2 saturated alkane at a certain tem-perature and pressure, and V0 is the volume of pure alkane at thesame temperature and at atmospheric pressure.

The calculated and experimental g [5] for the CO2–alkane sys-tems are depicted in Fig. 1 and listed in Tables S3 and S4 (in thesupplementary material). These two tables show the overwhelm-ing majority of the relative deviation between the calculated andexperimental g is less than 5%. This figure and the two tables dem-onstrate that the predicted g for all the CO2–alkane systems are ina well agreement with previous experimental data. Moreover,additional MD simulations were performed in the supplementarymaterial (Tables S5, S6 and Figs. S1–S4). The results indicate thatthe size of the simulated CO2–alkane system is big enough todepict the structural and thermophysical properties of the system,the simulation time is long enough for the system to reach its equi-librium, and the COMPASS force field is valid to calculate the inter-actions in the CO2–alkane system.

Fig. 1(a) shows that the volume of each CO2–alkane systemswells with the increase of pressure, which is due to the fact thatthe rising pressure enhances the solubility of CO2 in the alkaneas shown in Tables S1 and S2. This figure also shows that at thesame pressure and temperature, the g for straight-chain alkanes(hexane, octane, and decane) decrease with the increase of thechain length. Compared with hexane, the g of cyclohexane is rela-tively small, which is ascribed to the cyclohexane molecule with a

shape of chair rather than a straight-chain. Evident from this fig-ure, when CO2 is in the supercritical state (scCO2, Tc = 304.3 K,pc = 7.38 MPa), the g of each CO2–alkane system increases dramat-ically, indicative of significant effect of scCO2 on the swelling ofCO2–alkane systems.

Fig. 1(b) shows that the g of CO2–decane system decreases withthe increase of temperature at the same pressure. Although theincrease of temperature results in the thermal expansion of decaneand the decrease in the solubility of CO2 in decane, the effect of sol-ubility of CO2 on the swelling of decane is strong enough to effec-tively cover up the effect of the weak thermal expansion of decane.From the close inspection of Fig. 1(b), it can be seen that at a rangeof low pressure, the g of decane varies slightly as the temperaturechanges; whereas at a range of high pressure (especially above pc),the g of decane greatly changes at different temperature. The resultindicates that CO2, especially for scCO2, can be more miscible withalkane and has a larger solubility in alkane at a larger pressure.

3.2. Microscopic mechanism of the alkanes swelling

3.2.1. Microscopic process of decane swellingOne of the advantages of MD simulations method is able to

dynamically describe the microscopic process where the volumeof the CO2–alkane system varies with the time evolution, which

B. Liu et al. / Fuel 143 (2015) 194–201 197

is helpful for observing and better understanding the alkane swell-ing behavior induced by CO2 in detail. To visualize the swellingprocess of the CO2–alkane system, some representative snapshotsfor the CO2–decane system at 333 K and 8 MPa are presented inFig. 2.

Fig. 2(a) shows that decane molecules pack closely at a highdegree of aggregation due to the decane–decane interaction,resulting in a relatively small volume of the decane phase. How-ever, two free spaces, located between CO2 and decane phasesand on the surfaces of the decane phase respectively, provide theavailable space for CO2 molecules. Evident in Fig. 2(b), CO2 mole-cules have occupied the space between CO2 and the decane phaseas well as the surfaces of the decane phase, which could beascribed to the strong diffusibility of scCO2. It is the evidence thatthe decane begins swelling. As the simulation proceeds, shown inFig. 2(c), many CO2 molecules diffuse into decane and some decanemolecules also diffuse in CO2 phase. Furthermore, as more CO2

molecules dissolve in decane, shown in Fig. 2(d), it is interestingto find that many CO2 molecules gather together and form somesmall groups in decane rather than separate from each otherdirectly; simultaneously, the decane phase is divided into manysmall clusters by the CO2 groups. Consequently, the decane swellsfurther, which offers the available space for CO2 molecules again.Then, CO2 molecules in groups continue to be dispersed into dec-ane; the decane clusters are continuously divided into smallerclusters and even single molecules, indicative of the decane swell-ing until the CO2–decane system reaches the equilibrium state, asshown in Fig. 2(e) and (f).

Another contribution to the decane swelling is the change in thechain stretch of decane molecules. To visualize the chain stretch ofdecane molecules during the process of decane swelling, represen-tative snapshots for CO2 and decane molecules in the vicinity of theinterface between decane and CO2 are presented in Fig. 3, whereonly five decane molecules marked with yellow color are high-lighted for clarity. This figure shows that the five decane molecules,initially bended and entangled with other decane molecules, tendto stretch as long as possible under the action of CO2 molecules.This indicates the disentanglement and swelling of decane. Mean-while, the stretch of decane molecules means the increase in thecontact surface area between CO2 and decane molecules, whichstrengthens the interactions and the mutual dissolution of CO2

and decane.From the microscopic process of decane swelling, we see that

adding CO2 to decane results in the disentanglement and thestretch of decane molecules, which indicates the reduction in theviscosity (discussed in the supplementary material) and theenhancement in the migration of decane. It is of great benefit toCO2-EOR.

Fig. 3. Representative snapshots of CO2–decane system in the vicinity of the surface of dinterpretation of the references to color in this figure legend, the reader is referred to th

3.2.2. Radial distribution function and tortuosity distributionTo quantify the process of decane swelling, the radial distribu-

tion functions (RDFs) between different molecules and the tortuos-ity distribution of decane molecules are calculated and presentedin Figs. 4 and 5, respectively. Here, the tortuosity is defined asthe equation x ¼ ðl� l0Þ=l0, where l represents the end-to-end dis-tance of the decane molecule in the CO2–decane system, and l0 rep-resents the end-to-end distance of the decane molecule in the stateof free extension. The tortuosity distribution can be used to quan-titatively describe the stretch or bend of decane molecules.

Fig. 4(a) depicts the RDFs between carbon atoms in differentdecane molecules (C(dec)) at 333 K and 8 MPa against differentsimulation time. In Fig. 4(a), the first and second peaks of RDFsfor decane molecules at time of 50 ps locate at 5.25 Å and 9.88 Å,respectively. With time evolution, the positions of the peak andthe trough keep unchanged, but the amplitudes of the peaksdecrease clearly, which is further discussed in the supplementarymaterial. These results indicate the corresponding coordinationnumbers around one decane molecule reduce from 6.67 at 50 psto 3.61 at 1500 ps as shown in Table S7 (in the supplementarymaterial). The reduction in the coordination number implies thatdecane molecules tend to keep away from each other, and theaverage separation distance between decane molecules increases.Especially, the second peak height at 1500 ps decreases nearly toone, indicating the ordered structure of decane phase disappearsand decane molecules form more relaxed structure. In contrast,in Fig. 4(b), the increase of the peak height of the RDF between car-bon atoms in CO2 (C(CO2)) and decane (C(dec)) becomes more pro-nounced with time evolution, and the calculated coordinationnumbers of decane around one CO2 molecule increase from 1.20at 50 ps to 3.51 at 1500 ps shown in Table S7, indicating moreCO2 molecules keep close to decane molecules. Therefore, CO2 willassemble around decane molecules and lead decane molecules tobe away from each other.

Fig. 5 depicts the tortuosity distribution of decane moleculesagainst the different time at 333 K and 8 MPa. It shows that the tor-tuosity is mainly in the range from �0.30 to 0.03, corresponding tothe length of the decane molecule from 7.94 Å to 11.68 Å. It impliesthat the most decane molecules are in the state of bending orentangling with each other. However, the first large peaks enhanceand shift to the right with time, which implies that the decane mol-ecules in CO2–decane system disentangle and stretch gradually atthe action of CO2. Meantime, a shoulder peak occurs at the positionof 0 in Fig. 5, meaning that some decane molecules are almost inthe state of free extension due to the addition of CO2 to the decanephase.

From above analyses, combination of the results of RDF and tor-tuosity distribution reflects the volume swelling of CO2–decanesystem, which may be ascribed to that the interaction of CO2–dec-

ecane phase. Five decane molecules are marked with yellow colour for clarity. (Fore web version of this article.)

Fig. 4. (a) RDFs of C(dec)–C(dec) in decane molecules, (b) RDFs of C(CO2)–C(dec) at different time.

Fig. 5. Tortuosity distribution for decane molecules at different time under 333 Kand 8 MPa.

Fig. 6. Interaction energies for CO2–decane system as a function of time at 333 Kand 8 MPa.

198 B. Liu et al. / Fuel 143 (2015) 194–201

ane could compete with or overcome that of decane–decane, andthereby may be responsible for the volume swelling of decane.

3.2.3. Interaction energyThe different configurations of CO2–decane system could be

ascribed to the changing interactions of CO2–decane system. Here,

the interaction energies of CO2–CO2, CO2–decane and decane–dec-ane at different time are calculated and presented in Fig. 6. FromFig. 6, it can be seen that at the initial stage, the interaction energyof �6502 kJ/mol for decane–decane is predominant and the inter-action energy of CO2–CO2 is �2099 kJ/mol also far larger than thatof �500 kJ/mol for CO2–decane. It shows that at the initial simula-tion, a few of CO2 molecules passing through the free spacesbetween CO2 and decane phases contact with decane, having a lit-tle effect on the swelling of decane yet accumulating closely andentangling together. Thus, the diffusion of CO2 plays a crucial roleon spreading CO2 molecules towards or into decane initially.

Then, it can be seen that the interaction energy of CO2–decaneincreases dramatically, however, the interaction energy of dec-ane–decane decreases rapidly from 50 ps to 600 ps. It reveals theincrease of the average contact surface area of CO2 with the decanemolecule and the average separation distance between decanemolecules. It is deduced that CO2 molecules are preferentiallydragged by decane and dissolve into decane, causing the decaneto be apart from each other or form many clusters separated byCO2, and the decane molecule to disentangle and stretch at a highdegree. As a consequence, the volume of decane swells obviouslydue to CO2–decane interaction.

After 600 ps, it can be seen that the interaction energies of bothCO2–decane and decane–decane experience a small change andalmost keep unchanged finally, indicating that the CO2–decanesystem reaches the equilibrium state where CO2 molecules areentirely dispersed in decane. The interaction energy of CO2–decaneand that of decane–decane are comparable to each other, implyingCO2–decane interaction is responsible for the decane swellingagain. Moreover, the absolute value of the interaction energy ofdecane–decane is always larger than that of CO2–decane, whichindicates that decane–decane interaction yet controls the distribu-tion of the decane molecules in the CO2–decane system wheremany decane clusters exist.

On the basis of the information mentioned above, the process ofmicrostructure transition of decane swelling is speculated as threeprocesses: (1) CO2 diffuses and occupies the free spaces betweenCO2 and decane; (2) CO2 dissolves in decane packing closely, whichresults in a loose packing of decane; (3) Decane volume swells,resulting from the increase of both the average separation distancebetween decane molecules and the chain stretch under the interac-tion between decane and CO2. Actually, the three processes occursimultaneously and are not separated from each other in manycases.

In order to further illustrate the role of intermolecular interac-tion in decane swelling, the non-bonded interaction energies of

Fig. 7. The non-bond interaction energy components of CO2–decane system at333 K and 8 MPa.

B. Liu et al. / Fuel 143 (2015) 194–201 199

CO2–decane system, comprising the vdW interaction energy andthe electrostatic interaction energy, are presented in Fig. 7. This fig-ure shows the vdW interaction energy is predominant while theelectrostatic energy is so small as to be neglected in the totalenergy, which is ascribed to the fact that the CO2 molecule is linearand its overall dipole moment is zero, while the decane molecule isnonpolar. The vdW dispersion and repulsion energies of decane–decane are �9862 kJ/mol and 5723 kJ/mol, respectively. As forCO2–decane, the vdW dispersion and repulsion energies are�7544 kJ/mol and 4634 kJ/mol, respectively. The absolute valueof the dispersion energy is larger than that of the repulsion energy,indicating that the dispersive interaction dominates the vdW inter-action of CO2–decane system. Therefore, the dispersive interactionof CO2–decane is mainly responsible for the dissolution of CO2

molecules in decane phase and the swelling of decane.

3.3. Effects of pressure and temperature on the volume swelling

In order to clarify the effects of pressure and temperature on thestructure of CO2–alkane systems, the RDFs of C(dec)–C(dec) in dif-ferent decane molecules are depicted in Fig. 8. From the effect ofpressure in Fig. 8(a), it can be seen that the positions of the maximaand minima keep unchanged, the heights of the first peaks, how-ever, decrease with the increase of pressure. The result illustratesthat the corresponding coordination numbers, calculated inTable S8 (in the supplementary material), around one decane

Fig. 8. RDFs of C(dec)–C(dec) for (a) at the specified pressures

molecule reduce, indicating the increase of average separation dis-tance between decane molecules. On the other hand, the resultreveals the weak miscibility between CO2 and decane at low pres-sure due to the strong interaction of decane–decane preventingCO2 molecules from dissolving in decane. And then, with theincrease of pressure, because the interaction of CO2–decaneincreases and the interaction of decane–decane decreases, the mis-cibility between CO2 and decane increases, corresponding to theincrease of decane swelling.

The RDFs of C(dec)–C(dec) at the specified temperatures and8 MPa are plotted in Fig. 8(b). It can be seen that from 333 K to343 K, the positions of the maxima and the minima are keptunchanged, however, the first peaks of the RDFs increase withthe increase of temperature. The result means that more decanemolecules are around a certain decane molecule at a higher tem-perature, indicating that the average separation distance betweendecane molecules decreases. A similar conclusion is obtained inFig. S5 (in supplementary material) for the RDFs of octane at333 K and 343 K. It is interesting to note that the peaks of theRDF at 318 K are apparently higher than the corresponding peaksat other two temperatures, which indicates that the average sepa-ration distance between decane molecules is smaller. Moreover,the similar phenomenon is observed in CO2–octane system asshown in Fig. S5. The reason for the interesting phenomenon,firstly, is speculated to be that the CO2–decane system is not equil-ibrated yet or the force field has underestimated the solubility ofCO2 in decane at 318 K. Thereupon, two additional simulationswere performed at 318 K and 8 MPa: (1) a 2 ns simulation startingfrom the final configuration of the 1.5 ns for the CO2–decane sys-tem; (2) a 2.5 ns simulation for the CO2–decane system with thesolubility of CO2 decreased artificially from 0.817 to 0.667 (equalto the solubility at 333 K). The RDFs of C(dec)–C(dec) in the twoadditional simulations in Fig. S6 (in the supplementary material)are consistent with Fig. 8(b), so we negate the above speculation.And then, the abnormal phenomenon most likely arises from thedecane clusters, explained in the following. Similar to Fig. 3(d), itcan be found that at the equilibrium state of CO2–decane system,most of decane molecules entangle together and form many clus-ters as shown in Fig. S7 (in the supplementary material), and thedissolved CO2 molecules locate between these decane clusters.Thus, though the larger solubility of CO2 in decane at low temper-ature results in the larger average separation distance of clustersrepresenting the volume swelling of CO2–decane system, theweaker thermal motion of the decane molecule at low temperatureprevent large decane clusters from being separated into smallerclusters by CO2. Consequently, the RDFs in decane at 318 K exhibithigh peaks.

and 333 K, (b) at the specified temperatures and 8 MPa.

Fig. 9. (a) RDFs of the centroid–centroid between alkane molecules, (b) RDFs of C(CO2)–C(alkane) at 333 K and 8.67 MPa.

200 B. Liu et al. / Fuel 143 (2015) 194–201

3.4. Effects of the molecular structure on the volume swelling

The RDFs of the centroid–centroid between alkane molecules inCO2–hexane and CO2–cyclohexane systems are depicted inFig. 9(a). It can be seen that the first sharp peak and the secondpeak of RDFs for CO2–cyclohexane system occur at about 6.35 Åand 10.5 Å, respectively. It means cyclohexane displays an orderedstructure and the compact arrangement. For CO2–hexane system,only a low and wide peak is observed at around 6.35 Å, indicatinghexane phase possesses no ordered structure and is at loose distri-bution. Furthermore, the RDFs between C(CO2) and C(cyclohexaneor hexane) are depicted in Fig. 9(b). For CO2–hexane system, it canbe seen that the positions of the maximum and the minimum ofthe RDFs appear at 4.95 Å and 6.55 Å, respectively. However, forCO2–cyclohexane system, the locations of the maximum and theminimum of the RDFs shift to 5.25 Å and 7.65 Å, respectively,and the peaks of the RDFs are a little lower than the correspondingpeaks in CO2–hexane system. It illustrates that there is a preferen-tially ordered structure in CO2–hexane, and the average separationdistance between CO2 and hexane molecules is smaller than thatbetween CO2 and cyclohexane molecules. These results shown inFig. 9 are ascribed to the structural difference between hexaneand cyclohexane molecules. This structural difference indicatesthe different cohesive energy densities ascribed to the dispersionforce [40]. The reference [41] shows the cohesive energy densityof hexane (222.01 J/cm3) is smaller than that of cyclohexane(282.24 J/cm3), indicating the dispersion force between hexanemolecules is weaker than that between cyclohexane molecules.

Fig. 10. Tortuosity distribution for straight-chain alkane molecules in equilibriumconfiguration at 333 K and around 7.67 MPa.

This leads to that CO2 is easier to dissolve in hexane. In addition,the solubility parameters of CO2, hexane and cyclohexane are11.70 MPa1/2, 14.90 MPa1/2 and 16.80 MPa1/2, respectively, whichimplies the hexane is highly miscible with CO2 according to theidea that like dissolves like.

The effects of the chain length for the straight-chain alkane onthe volume swelling are investigated by the tortuosity distributionshown in Fig. 10. This figure shows obvious differences among thethree tortuosity distributions. The tortuosity distribution of hexanehas two higher peaks than that of octane and decane, and the posi-tion of the largest peak shifts to right with the decrease of the chainlength. These results suggest that the stretch degree of straight-chain alkane molecules and the average separation distancebetween alkane molecules decrease with the increase in the chainlength. In conclusion, the structure of an alkane molecule has sig-nificant influence on the dissolution of CO2 and the alkane volumeswelling.

4. Conclusion

We have performed the molecular dynamics simulation toinvestigate the microscopic mechanism of the volume swelling ofCO2–alkane (decane, octane, hexane and cyclohexane) systems.The results show, through the analysis of the effects of tempera-ture, pressure and alkane structure on the volume swelling ofCO2–alkane systems, that CO2 in supercritical state plays an impor-tant role in the volume swelling of CO2–alkane systems and thevolume swelling coefficients of CO2–alkane systems increase withthe increase of pressure, the reduction of temperature and the sim-plification of alkane molecular structure. The volume swellingcoefficients of CO2–alkane systems evaluated are well coincidentwith the data derived from the published experiments. The micro-scopic process of the volume swelling of CO2–decane systemshows that the increases in the stretch of decane molecules andthe average separation distance between decane molecules resultin the volume swelling of decane as CO2 molecules dissolve intodecane. The calculated interaction energies in CO2–decane systemindicate that the interaction between CO2 and decane molecules isresponsible for the volume swelling of CO2–alkane system. Fromthe study on the interaction between CO2 and decane molecules,we infer that the dispersion interaction, playing a significant rolein the solubility of CO2 in alkanes, is the dominant impact on thevolume swelling of CO2–alkane system. This work could revealthe mechanism of alkane swelling influenced by CO2 at the molec-ular level and offers insight into aspects of understanding theinteractions in CO2–alkanes systems, and thereby provide someuseful information for guiding CO2 enhancing oil recovery and

B. Liu et al. / Fuel 143 (2015) 194–201 201

the geological CO2 storage in the depleted oil reservoirs. However,crude oils are complex mixtures. Therefore, in the future, we willinvestigate the interactions in CO2-branched alkanes systems orin the CO2–aromatics systems, thereby explore the solubility ofCO2 in complex oil and the volume swelling of CO2–oil systemswith sulfur-, nitrogen- and oxygen-containing compounds.

Acknowledgements

This work is financially supported by National Natural ScienceFoundation of China (U1262202), National Basic Research Programof China (2014CB239204), China University of Petroleum (EastChina), Innovation Project (14CX05022A) and Graduate InnovationProject (14CX06089A).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.fuel.2014.11.046.

References

[1] Farajzadeh R, Andrianov A, Bruining H, Zitha PLJ. Comparative study of CO2 andN2 foams in porous media at low and high pressure–temperatures. Ind EngChem Res 2009;48:4542–52.

[2] Kuznetsova T, Kvamme B. Thermodynamic properties and interfacial tensionof a model water–carbon dioxide system. Phys Chem Chem Phys2002;4:937–41.

[3] Fujii T, Endo K, Nakagawa S, Sato Y, Inomata H, Nakao S, et al. Water saturationdependence on CO2 sorption potential of sandstones. Nat Resources2012;3:48–55.

[4] Godec ML, Kuuskraa VA, Dipietro P. Opportunities for using anthropogenic CO2

for enhanced oil recovery and CO2 storage. Energy Fuels 2013;27:4183–9.[5] Yang ZH, Li BP, Lin MP, Dong ZX. Dispersion property of CO2 in oil. 1. Volume

expansion of CO2 + alkane at near critical and supercritical condition of CO2. JChem Eng Data 2012;57:882–9.

[6] Stalkup J, Fred I. Status of miscible displacement. J Pet Technol1983;35:815–26.

[7] Klins MA. Carbon dioxide flooding: basic mechanisms and projectdesign. Boston (MA): International Human Resources DevelopmentCorporation; 1984.

[8] Li XS, Ross DA, Martin Trusler JP, Maitland GC, Boek ES. Molecular dynamicssimulations of CO2 and brine interfacial tension at high temperatures andpressures. J Phys Chem B 2013;117:5647–52.

[9] Godec M, Kuuskraa V, Van Leeuwen V, Melzer LS, Wildgust N. CO2 storage indepleted oil fields: the worldwide potential for carbon dioxide enhance oilrecovery. Energy Procedia 2011;4:2162–9.

[10] Kuznetsova T, Kvamme B. Atomistic computer simulations for thermodynamicproperties of carbon dioxide at low temperatures. Energy Convers Manage2002;43:2601–23.

[11] Li HZ, Qin JS, Yang DY. An improved CO2–oil minimum miscibility pressurecorrelation for live and dead crude oils. Ind Eng Chem Res 2012;51:3516–23.

[12] Liu YY, Wilcox J. Molecular simulation studies of CO2 adsorption by carbonmodel compounds for carbon capture and sequestration applications. EnvironSci Technol 2013;47:95–101.

[13] Sell K, Enzmann F, Kersten M, Spangenberg E. Microtomographicquantification of hydraulic clay mineral displacement effects during a CO2

sequestration experiment with saline aquifer sandstone. Environ Sci Technol2013;47:198–204.

[14] Kim Y, Wan J, Kneafsey TJ, Tokunaga TK. Dewetting of silica surfaces uponreactions with supercritical CO2 and brine: pore-scale studies in micromodels.Environ Sci Technol 2012;46:4228–35.

[15] Davis SJ, Caldeira K, Matthews HD. Future CO2 emissions and climate changefrom existing energy infrastructure. Science 2010;329:1330–3.

[16] Orr Jr FM, Taber JJ. Use of carbon dioxide in enhance oil recovery. Science1984;224:563–9.

[17] Orr Jr FM, Heller JP, Taber JJ. Carbon dioxide flooding for enhanced oilrecovery: promise and problems. JAOCS 1982;59:810–7.

[18] Li HZ, Yang DY, Li XL. Determination of three-phase boundaries of solvent–CO2–heavy oil system under reservoir conditions. Energy Fuels2013;27:145–53.

[19] Diep P, Jordan KD, Johnson JK, Beckman EJ. CO2–fluorocarbon and CO2–hydrocarbon interaction from first-principles calculations. J Phys Chem A1998;102:2231–6.

[20] David B, Henri SG, Daridon JL. Volumetric behavior of decane + carbon dioxideat high pressures, measurement and calculation. J Chem Eng Data2001;46:1136–9.

[21] Erdogan K, Holger P, Yan X. Volumetric properties of pentane + carbon dioxideat high pressires. J Chem Eng Data 1996;41:158–65.

[22] Li XL, Li HZ, Yang DY. Determination of multiphase boundaries and swellingfactors of solvent–CO2–heavy oil systems at high pressures and elevatedtemperatures. Energy Fuels 2013;27:1293–306.

[23] Mulllken CA, Sandler SI. The prediction of CO2 solubility and swelling factorsfor enhanced oil recovery. Ind Eng Chem 1980;19:709–11.

[24] Luo P, Yang CD, Gu YA. Enhanced solvent dissolution into in-situ upgradedheavy oil under different pressures. Fluid Phase Equilib 2007;252:143–51.

[25] Yang CD, Gu YA. Novel experimental technique for studying solvent masstransfer and oil – swelling effect in the vapour extraction (VAPEX) process.Canadian international petroleum conference. Calgary, Alberta, Canada; 2005.

[26] Do HD, Pinczewski WV. Diffusion controlled swelling of reservoir oil by directcontact with injection gas. Chem Eng Sci 1991;46:1259–70.

[27] Criscenti LJ, Cygan RT. Molecular simulations of carbon dioxide and water:cation solvation. Environ Sci Technol 2013;47:87–94.

[28] Zhao LL, Lin SC, Jonathan DM, Pak KY, Daniel B. Molecular dynamicsinvestigation of the various atomic force contributions to the interfacialtension at the supercritical CO2 water interface. J Phys Chem B2011;115:6076–87.

[29] Zhang H, Sherwin JS. Analysis of the subcritical carbon dioxide–waterinterface. J Phys Chem A 2011;115:6285–96.

[30] Zhang JF, Pan ZJ, Liu KY, Nick B. Molecular simulation of CO2 solubility and itseffect on octane swelling. Energy Fuels 2013;27:2741–7.

[31] Dai M, Makoto K, Liang YF, Toshifumi M. Application of molecular simulationsto CO2-EOR: phase equilibria and interface phenomena. SPE 2013;18:319–30.

[32] de Lara LS, Mateus FM, Caetano RM. Molecular dynamics studies of fluid/oilinterfaces for improved oil recovery processes. J Phys Chem B2012;116:14667–76.

[33] Makoto K, Kennichi N, Liang YF. Self-accumulation of aromatics at the oil–water interface through weak hydrogen bonding. J Am Chem Soc2010;132:18281–6.

[34] Sun H. COMPASS: an ab Initio force field optimized for condensed-phaseapplications overview with details on alkane and benzene compounds. J PhysChem B 1998;102:7338–64.

[35] Yang J, Ren Y, Tian AM. Compass force field for 14 inorganic molecules, He, Ne,Ar, Kr, Xe, H2, O2, N2, NO, CO, CO2, NO2, CS2, and SO2, in liquid phases. J PhysChem B 2000;104:4951–7.

[36] Wu GZ, He L, Chen DY. Sorption and distribution of asphaltene, resin, aromaticand saturate fractions of heavy crude oil on quartz surface: molecular dynamicsimulation. Chemosphere 2013;92:1465–71.

[37] Accelrys. Material Studio, Accelrys Software Inc., San Diego, CA; 2010.[38] Toukmaji AY, Board Jr JA. Ewald summation techniques in perspective: a

survey. Comput Phys Commun 1996;95:73–92.[39] Nymand TM. Ewald summation and reaction field methods for potentials with

atomic charges, dipoles, and polarizabilities. J Chem Phys 2000;112:6153–60.[40] Koenhen DM, Smolders CA. The determination of solubility parameters of

solvents and polymers by means of correlations with other physical quantities.J Appl Polym Sci 1975;19:1163–79.

[41] Burke J. Solubility parameters: theory and application. The Oakland Museumof California, August 1984.