Multicomponent Shale Oil Flow in Real Kerogen Structures Via Molecular Dynamic Simulation

energies

Article Multicomponent Shale Oil Flow in Real Kerogen Structures via Molecular Dynamic Simulation

Jie Liu 1,2 , Yi Zhao 3, Yongfei Yang 1,2,* , Qingyan Mei 3, Shan Yang 3 and Chenchen Wang 4

1 Key Laboratory of Unconventional Oil and Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao 266580, China; [email protected] 2 Research Centre of Multiphase Flow in Porous Media, School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China 3 Exploration and Development Research Institute of PetroChina Southwest Oil and Gas Field Company, Chengdu 610041, China; [email protected] (Y.Z.); [email protected] (Q.M.); [email protected] (S.Y.) 4 Hubei Cooperative Innovation Centre of Unconventional Oil and Gas, Yangtze University, Wuhan 430100, China; [email protected] * Correspondence: [email protected]

Received: 5 July 2020; Accepted: 22 July 2020; Published: 24 July 2020

Abstract: As an unconventional energy source, the development of shale oil plays a positive role in global energy, while shale oil is widespread in organic nanopores. Kerogen is the main organic matter component in shale and affects the flow behaviour in nanoscale-confined spaces. In this work, a molecular dynamic simulation was conducted to study the transport behaviour of shale oil within kerogen nanoslits. The segment fitting method was used to characterise the velocity and flow rate. The heterogeneous density distributions of shale oil and its different components were assessed, and the effects of different driving forces and temperatures on its flow behaviours were examined. Due to the scattering effect of the kerogen wall on high-speed fluid, the heavy components (asphaltene) increased in bulk phase regions, and the light components, such as methane, were concentrated in boundary layers. As the driving force increased, the velocity profile demonstrated plug flow in the bulk regions and a half-parabolic distribution in the boundary layers. Increasing the driving force facilitated the desorption of asphaltene on kerogen walls, but increasing the temperature had a negative impact on the flow velocity.

Keywords: ﬂow; shale oil; kerogen; molecular simulation

1. Introduction The development of shale oil has ameliorated global energy shortages, and many countries have launched programmes to investigate various development approaches [1–3]. However, the complex structure of nanopores in shale and the different components in shale oil hinder the further study of shale oil flow behaviours [4,5]. The sizes of pores in shale range from nanometres to micrometres, but experimental nanoscale studies are restricted to laboratory assessments [6–12]. Molecular dynamic (MD) simulations are often used to study the fluid behaviours within nano-confined spaces [13]. MD simulations are based on Newtonian mechanics and can be used to calculate a system’s thermodynamic quantities and other macroscopic properties. Shale is mainly composed of organic and inorganic matter [14–16]. The inorganic matter contains quartz and clay minerals. As a source of oil, kerogen is the main component of organic matter [17]. Thus, the flow behaviour of shale oil in realistic kerogen channels needs to be investigated.

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BousigeBousige et et al. al. [18] [18] produced produced a a realistic molecular kerogenkerogen modelmodel usingusing thethe generalised generalised phonon phonon densitiesdensities of of states. states. Ungerer Ungerer et et al. al. [19] [19] classified classified kerogen moleculesmolecules intointo fourfour typestypes ofof maturity maturity and and constructedconstructed corresponding corresponding structures. structures. It is didifficultfficult forfor shale shale oil oil to to flow flow in in a kerogena kerogen matrix matrix as aas result a result of ofkerogen’s kerogen’s dense dense matrix matrix structure structure [20], so[20], the so reasonable the reasonable construction construction of kerogen of channelskerogen ischannels necessary. is necessary.During the During kerogen the matrix kerogen generation matrix generation process, the process, insertion the of repulsiveinsertion dummyof repulsive particles dummy can produceparticles canporous produce models porous [21,22 models]. Perez [21, et al.22]. [8 ]Perez blended et al. a fluid[8] blended mixture a with fluid kerogen mixture monomers with kerogen and simulatedmonomers andthe simulated annealing the process, annealing and the process, fluid moleculesand the fluid gathered molecules as clusters. gathered Kerogen as clusters. monomers Kerogen form monomers organic formframeworks. organic frameworks. However, it However, is difficult it tois obtaindifficult clear to obtain transport clear characteristics transport characteristics in irregular in channels. irregular channels.Carbon nanotubesCarbon nanotubes (CNTs) and(CNTs) graphene and graphene slits are commonslits are common flow channel flow modelschannel [ 7models,23], but [7, the 23], flow but therate flow can rate be overestimated can be overestimated on ultra-smooth on ultra-smooth surfaces. surfaces. In multicomponent In multicompone fluids,nt heterogeneous fluids, heterogeneous density densitydistribution distribution characteristics characteristic cannots cannot be produced be produced on smooth on smooth surfaces. surfaces. Due to Due thedriving to the driving force’s eforce’sffect, effect,the velocity the velocity profile profil tendse tends to plug to inplug smooth in smooth channels channels rather rath thaner parabolas than parabolas on rough on wallsrough [ 24walls]. Thus, [24]. Thus,constructing constructing flow flow channels channels with with kerogen kerogen is a more is a more reasonable reasonable choice. choice. TheThe flow flow channel’s channel’s boundary boundary condition condition affects affects the slipslip length [[25].25]. Due toto thethe presencepresence of of slippage, slippage, Darcy’sDarcy’s law law is is invalid invalid in in nanoscale nanoscale fluid fluid flows flows [20, [20, 2626].]. TheThe slippageslippage eeffectffect cancan be be characterised characterised using using thethe slip slip length length concept, concept, which which is defined is defined as the as thedistance distance between between the solid the solid surface surface and the and point the pointwhere thewhere velocity the extrapolation velocity extrapolation is zero [27]. is zeroMartini [27 ].et Martinial. [27] found, et al. [at27 a] found,low driving at a lowforce, driving the movement force, the of onlymovement a few molecules of only a fewalong molecules a wall, called along a a “defect wall, called slip” a in “defect a nonlinear slip” in mode. a nonlinear At a high mode. driving At a highforce, alldriving of the force,fluid molecules all of the fluid adjacent molecules to the adjacent liquid–solid to the interface liquid–solid contribute interface to contribute“global slip.” to “global Conversely, slip.” onConversely, a rough kerogen on a rough wall, kerogen the boundary’s wall, the boundary’scavity can trap cavity some can molecules. trap some molecules. In addition, In fluid addition, molecules fluid impingemolecules protrusions impingeprotrusions on the interface, on the decelerating interface, decelerating the velocity the in velocity the boundary in the boundarylayer [28-30]. layer However, [28–30]. toHowever, the best toof theour best knowledge, of our knowledge, very few veryreports few in reports the literature in the literature discuss multicomponent discuss multicomponent shale oil slippage.shale oil slippage. InIn this this study, study, we we constructed constructed a a kerogen kerogen slit [[3311-33]–33] and used aa nonequilibriumnonequilibrium molecularmolecular dynamic dynamic (NEMD)(NEMD) simulation simulation to to analyse analyse the the flow flow behaviour behaviour of of shale oil. We alsoalso examinedexamined thethe eeffectsffectsof of the the drivingdriving force force and and temperature, temperature, and and the the simulation simulation re resultssults were were fitted fitted using using the the Poiseuille Poiseuille formula formula by dividingby dividing the thechannel channel into into two two sections. sections. We We calcul calculatedated the the flow flow rate rate using boundaryboundary layerslayers underunder multicomponentmulticomponent shale shale oil oil conditions. conditions.

2.2. Methodology Methodology

2.1.2.1. Molecular Molecular Models Models InIn this this study, study, type type Ⅱ-C II-C kerogen kerogen monomers monomers were were used used to tocons constructtruct realistic realistic organic organic slits slits because because the Ⅱthe-C kerogen II-C kerogen tended tended to be present to be present in organic-rich in organic-rich shales [19]. shales We [used19]. Wea simplified used a simpliﬁed shale oil component shale oil modelcomponent including model different including molecular diﬀerent weight molecular models weight(C1, C4, models C8, C12, (C1, methylbenzene, C4, C8, C12, asphaltene)[8, methylbenzene, 33, 34].asphaltene) The details [8, 33and,34 ].structures The details of andthe kerogen structures molecules of the kerogen and shale molecules oil models and shaleare provided oil models in are the Supportingprovided in Information, the Supporting and Information,the model of andthe slit the system model is of shown the slit in system Figure is 1. shown There inwere Figure 26,8991. There atoms inwere the entire 26,899 system. atoms inThe the dimensions entire system. of the The simulation dimensions box were of the 40 simulation Å3 × 50 Å3 box× 200 were Å3, and 40 Å each3 50 kerogen Å3 × × matrix200 Å 3contained, and each 15 kerogen kerogen matrix monomers. contained 15 kerogen monomers.

FigureFigure 1. 1. MolecularMolecular model model of of the the kerogen kerogen slits slits constructe constructedd with a kerogenkerogen matrixmatrix andand multicomponent multicomponent shale oil. Molecular colours: red, kerogen; black, asphaltene; grey, methylbenzene; purple, n-dodecane; shale oil. Molecular colours: red, kerogen; black, asphaltene; grey, methylbenzene; purple, n-dodecane; mauve, n-octane; pink, n-butane; green, propane; yellow, ethane; blue, methane. mauve, n-octane; pink, n-butane; green, propane; yellow, ethane; blue, methane.

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WeWe used used a a polymer polymer consistent consistent force force field field (PCFF) for all of the molecules [[19,19,35 35,,36 36],], and and described described thethe Van Van der der Waals Waals interactions usingusing Lennard–JonesLennard–Jones (LJ)(LJ) potentials.potentials. TheThe parameters parameters between between di differentfferent moleculesmolecules were were calculated calculated using Waldman–Hagler combiningcombining rulesrules [37[37].]. TheThe EwaldEwald method method was was adoptedadopted to to compute compute the the electrostatic potential [[38].38]. TheThe boundaryboundary conditionsconditions in in three three directions directions were were periodic,periodic, and and the the cut-off cut-off distancedistance was was 12 12 Å. Å.

2.2.2.2. Simulation Simulation Methods Methods TheThe large-scale large-scale atomic/molecular atomic/molecular massively massively parallel parallel simulator simulator (LAMMPS) (LAMMPS) package package distributed distributed by Sandiaby Sandia National National Laboratories Laboratories was wasused used for the for molecular the molecular simulations simulations [39]. [The39]. MD The simulation MD simulation in the NVEin the (The NVE number (The number of atoms, of volume atoms, volumeand energy and of energy system of remain system constant.) remain constant.) ensemble ensemble was conducted was forconducted 50 ps to relax for 50 the ps system’s to relax the configuration. system’s configuration. The NPT (The The number NPT (The of atoms, number pressure of atoms, and pressure temperature and oftemperature system remain of system constant.) remain ensemble constant.) was ensemble then performed was then (P performed = 30.0 MPa ( Pand= 30.0 T = MPa300 K) and forT 100= 300 ps. K)We putfor 100the ps.simulation We put thesystem simulation into the system NVT into (The the numb NVTer (The of atoms, number volume of atoms, and volume temperature and temperature of system remainof system constant.) remain ensemble constant.) at ensemble T = 300 K at forT =200300 ps K to for achieve 200 ps an to achieveequilibrium an equilibrium system. The system. timesteps The of thetimesteps NVE, NPT, of the and NVE, NVT NPT, ensemble and NVT simulations ensemble were simulations 0.5 fs, 0.5 were fs, and 0.5 fs,1.0 0.5 fs, fs,respectively. and 1.0 fs, respectively. WeWe conducted conducted NEMD NEMD simulations with thethe drivingdriving forceforce along along the the streaming streaming direction. direction. A A constant constant forceforce was was applied applied to to each each atom ratherrather thanthan aa pressurepressure gradient gradient because because longitudinally longitudinally homogeneous homogeneous pressurepressure can can be be maintained maintained with with a aconstant constant field field [40]. [40]. The The NEMD NEMD simulations simulations were were conducted conducted in inthe NVTthe NVTensemble ensemble at 300 at 300K for K for18 18ns, ns, and and we we collected collected the the last last 6 nsns ofof trajectoriestrajectories for for analysis. analysis. The The temperaturetemperature was was maintained maintained by by a a Nosé–Hoover Nosé–Hoover thermost thermostatat perpendicular toto thethe flowflow directiondirection [ 41[41,,42 42],], whichwhich reduced reduced the the effect effect of thermal motion onon thethe velocityvelocity ininthe theflow flow direction. direction. During During the the simulation, simulation, asas shown shown in in Figure Figure 2,2, we we froze froze the the kerogen kerogen matrix matrix layer layer (KML) (KML) and and controlled controlled the the temperature temperature (300 (300 K) ofK) the of therough rough adsorption adsorption layer layer (RAL) (RAL) [29, [29 43],,43], wh whichich made made the kerogenkerogen interfaceinterface flexibleflexible [ 44[44].]. We We discusseddiscussed these these layers layers in in the the Section Section 3.1. 3.1 The. The free free slit slitlayer layer (FSL) (FSL) was wasdivided divided into a into bulk a bulkphase phase region andregion boundary and boundary layer, which layer, are which discussed are discussed in Section in Section3.3. By averaging3.3. By averaging the velocity the velocity and number and number of atoms inof the atoms bins inthat the were bins parallel that were to the parallel flow direction, to the flow we direction, obtained the we velocity obtained and the density velocity profiles and density [27]. To reduceprofiles errors, [27]. To the reduce simulations errors, thewere simulations calculated were three calculated times independently three times independently with the same with initial the condition.same initial condition.

FigureFigure 2. 2. TheThe density density profile proﬁle of of kerogen. The dashed lineline segmentssegments representrepresent the the kerogen kerogen matrix matrix layer layer (KML),(KML), rough rough adsorption adsorption layer layer (RAL), (RAL), and and free free slit slit layer layer (FSL) (FSL) systems. systems.

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Energies 2020, 13, x FOR PEER REVIEW 4 of 12 3. Results and Discussions 3. Results and Discussions 3.1. Heterogeneous Density Distribution Analysis 3.1. Heterogeneous Density Distribution Analysis As shown in Figure2, to more clearly describe the flow behaviour, we divided the system into three As shown in Figure 2, to more clearly describe the flow behaviour, we divided the system3 into regions according to kerogen’s density profile. The KML density fluctuated at 1.1–1.2 g cm− [18,22,32]. · −3 Thethree FSL regions was definedaccording as to the kerogen’s free space density without prof kerogen,ile. The KML and density the RAL fluctuated was comprised at 1.1–1.2 of g·cm the cavities [18, and22, 32]. protrusions The FSL ofwas the defined kerogen as betweenthe free space the KML without and kerogen, FSL. The and widths the RAL of the was FSL, comprised RAL, and of KMLthe cavities and protrusions of the kerogen between the KML and FSL. The widths of the FSL, RAL, and were 5 nm, 1.5 nm, and 2.5 nm, respectively. The roughness of the kerogen matrix’s two walls differed KML were 5 nm, 1.5 nm, and 2.5 nm, respectively. The roughness of the kerogen matrix’s two walls as a result of its amorphous structure, so we only used half of the system to analyse the shale oil fluid’s differed as a result of its amorphous structure, so we only used half of the system to analyse the shale properties. Due to the random molecular thermal motion effects, there were always slight errors in the oil fluid’s properties. Due to the random molecular thermal motion effects, there were always slight shale oil’s distribution. The kerogen wall friction also played a role in the difference between the two errors in the shale oil’s distribution. The kerogen wall friction also played a role in the difference halves,between but the the two friction halves, was but notthe ourfriction focus. was not our focus. UsingUsing NEMDNEMD simulations, we we simulated simulated the the shal shalee oil oil flow flow through through the the kerogen kerogen slit slit under under the the drivingdriving force’sforce’s eeffect.ffect. Figure 33aa showsshows thatthat the shaleshale oil density profile profile varied varied considerably considerably at at different di fferent drivingdriving forces.forces. There were two density peaks peaks in in the the boundary boundary layer layer at at a alow low driving driving force, force, consistent consistent withwith ourour previousprevious research research [33]. [33]. The The density density profiles profiles presented presented as a as single a single peak peak in the in middle the middle of the of slit the slitat a at larger a larger driving driving force. force. The The difference difference in inthe the density density was was small small below below a adriving driving force force of of 5 5× 1010−4 4 × − kcalkcal/(mol·Å)./(mol Å). FigureFigure3 3bb shows shows thatthat thethe methanemethane densitydensity distribution peaked peaked in in the the RAL RAL region, region, and and the the · asphaltene’sasphaltene’s density peak was was distributed distributed in in the the FSL. FSL.

(a) (b)

Figure 3. NEMD simulations: (a) The density profile of the fluid at different driving forces. (b) Figure 3. NEMD simulations: (a) The density profile of the fluid at different driving forces. (b) The 4 The density profile of the shale oil’s components assessed by the NEMD simulations. F = 40 10− density profile of the shale oil’s components assessed by the NEMD simulations. F = 40 ×× 10−4 kcal/(mol Å). T = 300 K. kcal/(mol·Å).· T = 300 K. Due to the high flow speed caused by the driving force, the shale oil molecules collided with the Due to the high flow speed caused by the driving force, the shale oil molecules collided with the kerogen protrusion and had a diffuse scattering behaviour, forming a velocity component perpendicular kerogen protrusion and had a diffuse scattering behaviour, forming a velocity component to the streaming direction [43,45]. The perpendicular velocity component enriched the shale oil in the perpendicular to the streaming direction [43, 45]. The perpendicular velocity component enriched the bulk phase, as shown in Figure3b, especially in the asphaltene with its complex and large molecular shale oil in the bulk phase, as shown in Figure 3b, especially in the asphaltene with its complex and structure. The diffuse scattering reduced the density in the interface [43]. large molecular structure. The diffuse scattering reduced the density in the interface [43]. Notably,Notably, the density density profile profile remained remained steady steady under under the different the different driving driving forcesforces on the onsmooth the smooth walls walls[7], and [7], it and was it wasdifficult diffi tocult obtain to obtain a heterogeneous a heterogeneous distribution distribution because because the smooth the smooth wall could wall couldnot notprovide provide a vertical a vertical force force from from the wall the wallto the to fluid. the fluid.This characteristic This characteristic was similar was similarto blood to flow blood in the flow inblood the bloodvessels; vessels; haemoglobin haemoglobin concentrates concentrates in the incentral the central area and area ionic and ionicliquid liquidconcentrates concentrates at the at theboundary boundary [46, [ 4647].,47 By]. Bycomparing comparing the the results results of ofdifferent different driving driving forces, forces, that that the the density density profiles profiles of of asphalteneasphaltene and methane were were opposite, opposite, which which was was important important for for calculating calculating the theflow flow rate. rate.

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3.2.3.2. Sensitivity Analysis Analysis

3.2.1.3.2.1. Effect Eﬀect of of the the Driving Driving Force Force on on the the Flow Flow Behaviour Behaviour in inthe the Kerogen Kerogen Slit Slit

To investigate the the driving driving force’s force’s effects, effects, we weconducted conducted the NEMD the NEMD at driving at driving forces from forces 15 from× 10−4 15 kcal/(mol·Å)10 4 kcal/(mol to 40Å) × 10 to−4 40 kcal/(mol·Å).10 4 kcal /Unlike(mol Å). conventional Unlike conventional parabola and parabola plug profiles and plug [36], profiles Figure 4a [36 ], × − · × − · Figureshows 4thata shows the velocity that the distribution velocity distribution was a trapezoid was a with trapezoid two arched with twowaists arched at high waists driving at highforces. driving The forces.heterogeneity The heterogeneity of the shale ofoil the caused shale an oil interesting caused an interestingflow conformation. flow conformation. According to According the previous to the previousdensity analysis, density analysis,the asphaltene the asphaltene concentrated concentrated in the bulk in the region, bulk region,while the while methane the methane enriched enriched the theboundary boundary layer layer at high at highdriving driving forces. forces. In this Incase, this as case, a result as aof result cohesion, of cohesion, the asphaltene the asphaltene formed clusters formed clusterswith a molecular with a molecular pore network pore networkand trapped and trappedsome sm someall molecules. small molecules. The linear The alkanes linear sheared alkanes easily. sheared easily.The orientation The orientation property property of the alka ofnes the was alkanes observed was by observed solation byforce solation experiments force experiments[48, 49]. However, [48,49 ]. it was hard to change the configuration of the asphaltene cluster with the shear friction, so the bulk However, it was hard to change the configuration of the asphaltene cluster with the shear friction, so velocity was flat. the bulk velocity was flat.

(a) (b)

Figure 4. Velocity profiles: (a) The velocity profile of the shale oil at different driving forces. (b) The velocityFigure 4. profile Velocity in theprofiles: boundary (a) The layer. velocityT = 300profile K. of the shale oil at different driving forces. (b) The velocity profile in the boundary layer. T = 300 K. In the boundary layer, the methane enrichment made the velocity profile approximately parabolic. BasedIn on the the boundary platform layer, and the twomethane halves enrichment of the parabolic made the velocity velocity profile, profile we approximately divided the FSL parabolic. into two regionsBased on (the the bulkplatform phase and and the boundarytwo halves layers)of the para andbolic fit the velocity velocity profile, and we flow divided rate [ 50the]. FSL The into platform two regionregions was (the the bulk bulk phase phase and (0–12.5 boundary Å), layers) and the and halves fit th ofe velocity the parabola and flow were rate the [50]. boundary The platform layers region (12.5–25 Å).was Consequently, the bulk phase using (0–12.5 the Å), Poiseuille and the equation,halves of wethe quantitativelyparabola were analysedthe bounda thery flowlayers behaviour. (12.5–25 Å). Consequently, using the Poiseuille equation, we quantitatively analysed the flow behaviour.4 The velocity in the boundary layer increased homogeneously over forces of 30 10− kcal/(mol Å), × −4 · as shownThe velocity in Figure in 4theb. Byboundary increasing layer the increased driving homogeneously force, the fluid over molecules forces of had 30 more× 10 kinetickcal/(mol·Å), energy, leadingas shown to in stronger Figure 4b. scattering By increasing effects. the Figure driving5 demonstrates force, the fluid that molecules the driving had more force kinetic had a energy, positive leading to stronger scattering effects. Figure 5 demonstrates that the driving force had a positive effect 4 effect on the asphaltene density in the bulk phase, and the density profile stabilised beyond 30 10− on the asphaltene density in the bulk phase, and the density profile stabilised beyond 30 × ×10−4 kcal/(mol Å). Due to the strong scattering, the asphaltene density peaks in the RAL were diminished. kcal/(mol·Å).· Due to the strong scattering, the asphaltene density peaks in the RAL were diminished. However, the asphaltene still adsorbed in the RAL and formed density peaks at driving forces below 30 However, the asphaltene still adsorbed in the RAL and formed density peaks at driving forces below 10 4 kcal/(mol Å). Therefore, the constant distribution of the asphaltene density facilitated a steady ×30 × −10−4 kcal/(mol·Å).· Therefore, the constant distribution of the asphaltene density facilitated a steady increase in velocity. increase in velocity.

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FigureFigure 5. 5. TheThe density density profile profile of of the asphaltene at didifferentfferent drivingdriving forces.forces.T T= =300 300 K. K. The The dashed dashed blue blue Figure 5. The density profile of the asphaltene at different driving forces. T = 300 K. The dashed blue lineslines are are the the borders borders of of the the KML, KML, RAL, RAL, and and FSL. FSL. lines are the borders of the KML, RAL, and FSL. 3.2.2. Effect of the Temperature on the Flow Behaviour in the Kerogen Slit 3.2.2.3.2.2. Effect Effect of of the the Temperature Temperature on the Flow BehaviourBehaviour in in the the Kerogen Kerogen Slit Slit We compared the velocity profiles of the shale oil subjected to different temperatures, as shown WeWe compared compared the the velocity velocity profiles of thethe shaleshale oil oil subjected subjected to to different different temperatures, temperatures, as shownas shown in in in Figure6a. In general, the fluid had a higher velocity as the temperature increased because the FigureFigure 6a. 6a. In In general, general, the the fluidfluid hadhad a higher velocivelocityty as as the the temperature temperature increased increased because because the the stronger stronger stronger thermal motion facilitated the reduction in viscosity. However, the velocity decreased and the thermalthermal motion motion facilitatedfacilitated thethe reduction inin viscviscosity.osity. However,However, the the velocity velocity decreased decreased and and the the asphaltene’s density profiles were gentler as the temperature increased, as shown in Figure6. asphaltene’sasphaltene’s density density profiles profiles werewere gentler asas thethe temperature temperature increased, increased, as as shown shown in inFigure Figure 6. 6.

(a) (b) (a) (b) Figure 6. Effect of the Temperature: (a) The fluid velocity profiles at different temperatures. (b) The asphaltene’sFigure 6. Effect density of the at Temperature: different temperatures. (a) The fluidF = velocity30 10 profiles-4 kcal/(mol at differentÅ). temperatures. (b) The × · Figureasphaltene’s 6. Effect density of the at Temperature:different temperatures. (a) The fluidF = 30 velocity × 10-4 kcal/(mol·Å). profiles at different temperatures. (b) The asphaltene’sThe higher density temperature at different of thetemperatures. single component F = 30 × 10-4 fluid kcal/(mol·Å). reduced its viscosity. In the confined nanoslits,The higher the temperature temperature aff ectedof the the single shale componen oil’s heterogeneoust fluid reduced density its distribution.viscosity. In Thethe asphalteneconfined clusternanoslits,The behaved higher the temperatur astemperature a complexe affected molecularof the the single shale network. componenoil’s heterogeneous The strongert fluid reduced thermal density motiondistribution.its viscosity. increased The In asphaltene thethe distanceconfined nanoslits,betweencluster behaved the temperatur asphaltene as a complexe atoms, affected molecular expanding the shale network. theoil’s asphalteneTh heterogeneouse stronger cluster thermal density and motion increasing distribution. increased its concentrationThethe distanceasphaltene clusterinbetween the behaved boundary the asphaltene as layer, a complex asatoms, shown molecular expanding in Figure network. the6b. asphaltene Thus, The the stronger cluster higher and thermal temperature increasing motion its weakened increasedconcentration the the density indistance the betweendistributionboundary the layer, asphaltene heterogeneity, as shown atoms, in Figure and expanding the 6b. fluid Thus, the in the asphaltene the higher boundary temperature cluster layer and wasweakened increasing mixed the with its density concentration more distribution asphaltene in the boundarymolecules,heterogeneity, layer, increasing asand shown the the fluid frictionin Figure in betweenthe 6b. boundary Thus, the the kerogen lahiyergher andwas temperature asphaltene.mixed with weakened Therefore, more asphaltene the the density high temperaturemolecules, distribution heterogeneity,hadincreasing a negative the and efrictionffect the on betweenfluid the shale in thethe oil kerogen flow,boundary with and asphaltene laasphaltene.yer was clustersmixed Therefore, inwith the the more nanochannels. high asphaltene temperature molecules, had a increasingnegative effectthe friction on the shalebetween oil flow, the withkerogen asphaltene and asphaltene. clusters in theTherefore, nanochannels. the high temperature had a negative effect on the shale oil flow, with asphaltene clusters in the nanochannels.

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3.3.3.3. Slip Slip Analysis Analysis and and Fitting Fitting

3.3.1.3.3.1. Slip Slip Length Length Analysis Analysis of of the the Transport Transport Condition Condition TheThe slip slip occurred occurred in in the the nanochannels, nanochannels, which which was was confirmed confirmed by by many many studies studies [25, [25 51-53].,51–53 ].The The slip lengthslip length was affected was affected by the by slip the wall slip location, wall location, so we soselected we selected the slip the boundary slip boundary at the interface at the interface between thebetween FSL and the FSLRAL and [54]. RAL Because [54]. Becausethe kerogen the kerogen protrusi protrusionon created created extra extraflow flowresistance resistance in the in RAL, the destabilisingRAL, destabilising the flow, the the flow, flow the in flow the inFSL the was FSL on wasly affected only aff ectedby the by viscosity the viscosity and driving and driving force. force. WeWe calculated calculated the slip length using LLss = usurfsurf/(/du(du//drdr),), where where LLss isis the the slip slip length, length, usurfsurf isis the the velocity velocity at theat theslip slip wall, wall, and and du/drdu is/dr theis thevelocity velocity gradient gradient at the at interface the interface [55]. [ As55]. shown As shown in Figure in Figure 7, the7 ,slip the length slip 4 length increased steadily over a driving force of 30 −4 10 kcal/(mol Å). Below a driving force of 25 −4 increased steadily over a driving force of 30 × 10× kcal/(mol·Å).− Below· a driving force of 25 × 10× 10 4 kcal/(mol Å), the slip length increased unstably. Because the asphaltene was still adsorbed at the kcal/(mol·Å),− the· slip length increased unstably. Because the asphaltene was still adsorbed at the boundaryboundary at at low low driving driving forces, forces, the the adsorption adsorption affected affected the the slip slip at the boundary.

FigureFigure 7. 7.The The slipslip lengthlength atat di differentﬀerent driving driving forces. forces.T T= = 300300 K.K.

3.3.2.3.3.2. Segment Segment Fitting Fitting on on the the Flow Flow Behaviour Behaviour in in the the Kerogen Kerogen Slit Slit DueDue to to the the extremely heterogeneousheterogeneous density andand velocity,velocity, itit waswas di difficultﬃcult to to obtain obtain a constanta constant boundaryboundary layer layer viscosity. viscosity. We We attainedattained aa linearlinear viscosityviscosity distributiondistribution byby separating separating the the regions regions and and calculatingcalculating the the shear shear stress stress and and shear shear velocity, velocity, resp respectively,ectively, in in the the boundary boundary layer layer using using Equations Equations (1)– (1)–(4) [56,57], (4) [56, 57], Z z P(z) = F z n(z0)dz0 (1) '' PFn(z)= 0 (z )dz (1) 0 du γ(z) = (2) dudz γ (z) = (2) dzP(z) η(z) = (3) (z) −Pγ(z) η(z) = − (3) where n is the ﬂuid density, z is the distance from theγ (z) centre of the slit, P is the shear stress, F is the driving force, γ is the shear velocity, u is the velocity, and η is the viscosity. We calculated a series of 3 P whereshale oiln is density the fluid values density, in parallel z is the bins distance of 4 from5 w binthenm centreusing of then(z islit,) = P isN ithe/(4 shear5 stress,wbin), whereF is the × × × × drivingwbin is theforce, width γ is ofthe the shear bins velocity, and Ni isu theis the number velocity, of atomsand η in is the the bins. viscosity. The viscosity We calculated distribution a series is of expressed as shale oil density values in parallel bins of 45××w nm3 using nN(z )=×× / (4 5 w ) , where η(zbina) η(zw) z a ii bin η(z) = η(za) − − (4) wbin is the width of the bins and Ni is the number− ofNbin atoms ·inw thebin bins. The viscosity distribution is expressedwhere a = asw /2 b, as shown in Figure8. a is half of the length of the half-bulk phase layer, b is half − of the length of the boundary layer, and w isηη the(z slit ) - width. (z ) Nbin− is the number of bins, η(za) is the ηη aw⋅ z a viscosity on the border between the(z) bulk = (z phasea ) - layer and boundary layer, and η(zw) is the viscosity(4) at Nwbin bin

Energies 2020, 13, x FOR PEER REVIEW 8 of 12 where aw=−/2 b, as shown in Figure 8. a is half of the length of the half-bulk phase layer, b is half η ofEnergies the length2020, 13 of, 3815 the boundary layer, and w is the slit width. Nbin is the number of bins, (za ) 8 is of 12the η viscosity on the border between the bulk phase layer and boundary layer, and (zw ) is the viscosity atthe the interface interface between between the the FSL FSL and and RAL. RAL. We We obtained obtained the the viscosity viscosity distribution distribution in in the the boundary boundary layer layer η η byby averaging averaging the the difference diﬀerence between between η((zzaa) )and andη (zw(z) asw ) expressed as expressed in Equation in Equation (4). (4).

FigureFigure 8. 8. TheThe separate separate fitting fitting of ofthe the fluid fluid velocity velocity profile. profile. F =F 30= ×30 10−410 kcal/mol.4 kcal/mol. (The (Thedashed dashed red line red is × − theline fitting is the in fitting the free in thelayer free wi layerth the withsame the velocity same velocitywhere z = where 12.5Å.z The= 12.5Å. dashed The blue dashed line is blue theline separation is the betweenseparation the betweenboundary the and boundary bulk phase and layers. bulk phase Half of layers. the velocity Half of profile the velocity is in the profile FSL). is in the FSL).

TheThe velocity velocity of of the the Poiseuille Poiseuille flow ﬂow modified modiﬁed by by the the slip slip is is expressed expressed in in Equation Equation (5) (5) [7], [7],

2 2 nF(z)n(z)F 2 ww u(=−z) = (2z − − wLs) (5) uwL(z)( (z) s ) (5) 2(z)−η2η z − 44 − where the w is the slit width. The velocity in the boundary layer is expressed in Equation (6). where the w is the slit width. The velocity in the boundary layer is expressed in Equation (6). ( ) nF(z)n z F 2 2 u1(=−z) = [( −z a22) −b − bLs] (6) ubbL1(z)(z [(z) a)s ] (6) 2(z)−η2η − − − Equation (7) expresses the velocity of the bulk phase layer where z is equal to a. Equation (7) expresses the velocity of the bulk phase layer where z is equal to a.

nF(zn( )za)F 2 ubbL(zu2( )z=−a) = a ( −( b2 − bLs ) (7) 2 as−η2η(za) − − (7) 2(z)a Although the linear distribution of the viscosity cannot perfectly describe the real viscosity, the Although the linear distribution of the viscosity cannot perfectly describe the real viscosity, the velocity profile presented in Figure8 calculated using the NEMD simulations fully fit with Equation velocity profile presented in Figure 8 calculated using the NEMD simulations fully fit with Equation (6) (6) and Equation (7). and Equation (7). The FSL flow rate is integrated using Equation (6) and Equation (7), as expressed in Equation (8): The FSL flow rate is integrated using Equation (6) and Equation (7), as expressed in Equation (8):

nF(z)n(z)F 22 2 nF(zn(z )a)F Q=+++Q = b2 ()b ( bLb + Ls) + a abbLab( ()b + Ls) (8) ηη2η(z) 3 ss2η(za) (8) 2(z) 3 2(z)a Substituting Equation (4) into Equation (8) obtains Substituting Equation (4) into Equation (8) obtains    2  Fb Nbinwbinn(z)b2( 3 b + Ls) n(za)a(b + Ls)  Q =  Nwn(z) b ( bL+ ) +  (9)  bin bin s +  Fb 2 Nbinwbinη(za) [η(za3) η(zw)] (z a) nabL(zas )η( za) ) Q =+− − · − (9) 2Nwηηη (z)-[] (z)-(z)⋅−() z a η (z) where Q is the flow rate. Comparedbin bin with a the flow a rate w using the NEMD simulations, a as demonstrated in  Equation (10), Figure9 shows that the separate fitting worked well for the heterogeneous shale oil flow.

Xz2 QMD = ∆z u MD(zi) (10) · 1 z1 Energies 2020, 13, x FOR PEER REVIEW 9 of 12 where Q is the flow rate. Compared with the flow rate using the NEMD simulations, as demonstrated in Equation (10), Figure 9 shows that the separate fitting worked well for the heterogeneous shale oil flow.

z2 = QzuzMD ·()1 MD i (10) Energies 2020, 13, 3815  9 of 12 z1

FigureFigure 9. 9. TheThe segmentation segmentation fitting fitting of of the the fluid fluid flow flow rate rate (half (half of of the the fluid) fluid) at at different different driving forces. T = 300= 300 K. Some K. Some error error bars bars are aresmaller smaller than than the thescatter scatter size. size.

ForFor the the different different interfaces interfaces in in the the kerogen kerogen matrix, we selected halfhalf ofof thethe systemsystemto tofit fit the the flow flow rate. rate. FigureFigure 99 demonstratesdemonstrates that the monotonicallymonotonically increasingincreasing flow flow rate rate was was a a result result of of the the increased increased driving driving 4 force.force. However, However, the the different different slopes slopes inin the the flow flow rate rate vs. vs. the the driving driving force force at 30 at × 30 10−410 kcal/(mol·Å)− kcal/(mol wereÅ) × · anwere unexpected an unexpected finding. finding. AsAs shown shown in in Figure Figure 55,, the density peakpeak ofof thethe asphalteneasphaltene in in the the RAL RAL slowly slowly decreased, decreased, suggesting suggesting 4 thatthat the the asphaltene asphaltene molecules molecules desorbed fromfrom thethe RALRAL and and flowed flowed into into the the bulk bulk phase phase below below 30 30 10× 10− −4 × kcal/(mol·Å).kcal/(mol Å). Figure Figure 99 demonstrates demonstrates that that the the flow flow rate rate increased increased at ata higher a higher rate rate below below the thedriving driving force · 4 offorce 30 × of 10 30−4 kcal/(mol·Å),10− kcal/(mol so Å),the so stronger the stronger driving driving force force facilitated facilitated the therecovery recovery of asphaltene of asphaltene in inthe × · boundarythe boundary layer. layer.

4.4. Conclusions Conclusions InIn this this work, work, using using MD MD simulations, simulations, we we studied studied the the flow flow behaviour behaviour of of multicomponent multicomponent shale shale oil oil in realisticin realistic kerogen kerogen nanoslits. nanoslits. Compared Compared with with previous previous static static adsorption adsorption results, wewe foundfound opposite opposite densitydensity distributions distributions for for asphaltene asphaltene and and methane. methane. TheThe asphaltene asphaltene increased increased in the in bulk the bulkphase phase layer, whilelayer, the while methane the methane concentrated concentrated in the in theboundary boundary layer. layer. Due Due to to kerogen’s eeffects,ffects, high-velocityhigh-velocity asphalteneasphaltene more more easily easily scattered scattered in the bulk phase. The fastfast transportationtransportationof of shale shale oil oil demonstrated demonstrated a a differentdifferent flow flow behaviour. behaviour. The The asph asphaltenealtene group was constrainedconstrained inin thethe bulkbulk phase phase region region and and behaved behaved asas a aplug plug flow, flow, and and the the velocity velocity profile profile in in the the bo boundaryundary layer layer presented presented as as a a half half of of a a parabola. parabola. TheThe driving driving force force had had a a positive eeffectffect onon thethe shaleshale oiloil velocity. velocity. TheThe densitydensity distribution distribution of of 4 asphaltene remained steady beyond the driving force of 30 −4 10 kcal/(mol Å), while it showed a asphaltene remained steady beyond the driving force of 30 × 10× kcal/(mol·Å),− while· it showed a slightly denserslightly peak denser at a peak smaller at a driving smaller force. driving As force. the te Asmperature the temperature increased, increased, due to the due stronger to the stronger thermal motion,thermal the motion, asphaltene’s the asphaltene’s density distribution density distribution was relatively was gentle. relatively Thus, gentle. the boundary Thus, the layer boundary viscosity increasedlayer viscosity and then increased the velocity and then decreased the velocity in the decreased slit. This incharacteristic the slit. This is characteristicunusual in macro-flow, is unusual inbut themacro-flow, asphaltene but cluster the asphaltene cohesion clusterincreased cohesion the intern increasedal friction the internalof the shale friction oil ofin the the shale nano-confined oil in the channel.nano-confined channel. AccordingAccording to to the the different different velocity velocity profiles profiles in thethe bulkbulk phasephase andand boundaryboundary layer, layer, we we employed employed thethe Poiseuille Poiseuille equation equation to to fit fit the the velocity and flowflow rate,rate, respectively.respectively. AsAs aa resultresult of of the the asphaltene asphaltene 4 desorption, the slope of the flow rate maintained a higher value below the driving force of 30 10 -4 desorption, the slope of the flow rate maintained a higher value below the driving force of× 30×10− kcal/(mol Å). Calculating the viscosity of multicomponent shale oil remains challenging, especially in · nano channels. This study proposed a new perspective on shale oil transport.

Author Contributions: J.L. did the data curation and wrote the original draft. Y.Y. provided the software and computing resources, and designed the simulation. Y.Z., Q.M. and S.Y. provided general supervision and formal analysis. C.W. analyzed the resulting data and did the validation. All authors have read and agreed to the published version of the manuscript. Energies 2020, 13, 3815 10 of 12

Funding: This research was funded by: the National Natural Science Foundation of China (No. 51674280, 51704033, and 51950410591), Shandong Provincial Natural Science Foundation (ZR2019JQ21), PetroChina Innovation Foundation (No. 2018D-5007-0210), and the Programme for Changjiang Scholars and Innovative Research Teams in University (IRT_16R69). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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