Atomic interactions between rock substrate and water-sand mixture with and without graphene nanoshee

Journal of Molecular Liquids 323 (2021) 114610

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Atomic interactions between rock substrate and water-sand mixture with and without graphene nanosheets via molecular dynamics simulation Amirhosein Mosavi a,b, Maboud Hekmatifar c, Davood Toghraie c, Roozbeh Sabetvand d, As’ad Alizadeh e,f, Zahra Sadeghi g, Aliakbar Karimipour h,⁎ a

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam c Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran d Department of Energy Engineering and Physics, Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran e Department of Mechanical Engineering, Urmia University, Urmia, Iran f Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq g Department of Chemical Engineering, Isfahan University of Technology, Isfahan, Iran h Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam. b

a r t i c l e

i n f o

Article history: Received 8 September 2020 Received in revised form 6 October 2020 Accepted 16 October 2020 Available online 20 October 2020 Keywords: Hydraulic fracturing process Molecular dynamic simulation Nanosheet Graphene Armchair edge Zig-zag edge

a b s t r a c t In this work, we describe the atomic effects of graphene nanosheets adding to the hydraulic fracturing process by molecular dynamics method. In our simulations, we study the nanosheets type effect on the fracturing process.

For this purpose, we reported physical parameters such as temperature, potential energy, joint force, and the number of lost atoms from atomic substrates. In our approach, nanofluid, which used in hydraulic fracturing, is exactly simulated by various interatomic force fields. Our simulations show that adding graphene nanoparticles to the first fluid causes maximum atomic removal from simulated rock substrate. Numerically, after 2.5 ns, the departed atoms from rock substrate reach to 74 atoms.

Furthermore, the atomic rate of graphene nanosheets is another important parameter in hydraulic fracturing. Our molecular dynamics results show that, by 5% atomic rate of graphene nanosheets to initial fluid, the departed atoms reach to the maximum rate (101 atoms). Finally, by adding graphene nanosheets with 4 nm length, the top quality of particles departed from the rock substrate. © 2020 Elsevier B.V. All rights reserved.

1. Introduction Hydraulic fracturing is a standard and appropriate method containing the fracturing of bedrock formations. This procedure consists of sand or other proppants suspended with the aid of thickening agents, including the high-pressure injection of fracking fluid, which conclude of water, brine and petroleum will flow more freely as depicted in Fig. 1.

Small grains of hydraulic fracturing fractions hold the fractures created when the hydraulic pressure was removed [1]. Historically, the hydraulic fracturing process began in 1947. About 2.5 million performances had been performed worldwide on gas and oil wells since 2012. Over 1.000.000 of those within the united states of America [2,3]. Such treatment is essential to obtain a flow rate in coal seam gas wells, tight oil, ⁎ Corresponding author.

E-mail addresses: amirhosein.mosavi@tdtu.edu.vn (A. Mosavi), aliakbarkarimipour@duytan.edu.vn (A. Karimipour).

https://doi.org/10.1016/j.molliq.2020.114610 0167-7322/© 2020 Elsevier B.V. All rights reserved.

tight gas and shale gas [4]. In certain veins or dikes, naturally, some hydraulic fractures can form [5]. The United States changed to a most important exporter of crude oil in 2019 by Drilling and hydraulic fracturing [6], but the leakage of methane, has dramatically enhanced [7].

Enriched gas and oil production from the decade long fracking boom has flowed to lower costs for consumers [8,9].

Elements of fracking discuss that these are outweighed by the environmental influence, which concludes noise and air pollution, and groundwater and surface water contamination, along with the resulting hazards to the environment and public health [10–13]. But these harmful effects can vanish with optimized of the hydraulic fracturing process.

Wigwe et al. [14] research about the influences of fluid viscosities, injection rates on hydraulic fracturing parameters and proppant densities.

These researchers express that the injection rate of 13 bpm yielded the propped, useful prop and longest fracture length for both fractions.

The low-density proppant produced the longest effective fracture length while the high-density proppant gave the longer fracture length.

A. Mosavi, M. Hekmatifar, D. Toghraie et al.

Journal of Molecular Liquids 323 (2021) 114610

work, we study the graphene nanosheets with armchair and zig-zag edges effects on the hydraulic fracturing process with molecular dynamics (MD) simulations. MD approach is one of the significant sorts of computer simulations that can be predicting the atomic manner of various structures [27–32].

Nomenclature Fij Vij Fext m rc rij t T v Natom

interparticle force on particle i by particle j (eV/Å) interparticle potential (eV) external applied force (eV/Å) particle mass (u) cut-off distance (Å) distance between particle i and j (Å) time step (ps) temperature (K) velocity of particle (Å/ps) number of particles

2. Computational method In MD simulations, atoms are permitted to interact together and give a view of the dynamic changes of the overall atomic system. In this paper, all molecular dynamics simulations are done by using LAMMPS software presented by Sandia National Laboratories [33–36]. To using LAMMPS software to measure the atomic behaviour of water/sand mixture in the vicinity of rock substrate, rock substrate with Silicon, Iron, Aluminum, Oxygen, Sodium, Calcium, Potassium, and Magnesium atoms modelled by coarse-graining method and fixed in the bottom of the MD box, while water and atomic sand structures filled the surrounding position of volume. Computationally, sand particles with the coarse-graining method described as one particle. This sand model consists of atomic properties of each constituent atoms such as atomic mass, atomic interaction, etc. Fig. 2 displays the simulation package at the perspective faces, top and front, which were visualized by Open Visualization Tool [37]. The first atomic position prepared by Packmol atomic modeling software [38].

Technically, in this molecular dynamics simulations, periodic boundary conditions were used in x and y directions and fix one implemented in the z-direction. For creating the initial temperature of simulated structures, the NVT ensemble used in equilibrates the initial temperature of atomic structures at 300 K with dt = 1 fs time step and 0.01 temperature damping rate. This rate of temperature damping appropriate with the previous report [39]. After 2.5 ns, the simulated structure was equilibrated at the beginning temperature, then the NVT effect cancelled, and NVE one was used to the time evolution of simulated structures. To simulate the rock substrate, we use Universal Force Field (UFF) [40]. In this force field were shown as a superposition of non-bonded and bonded forces-non-bond interaction between atoms described by the Lennard-Jones (LJ) potential.

The interaction between a pair of atoms approximates by the LJ potential formula. This interatomic potential was proposed by John Lennard-Jones in 1924 [41]. This simple atomic interaction stated as below:

Greek symbols ε energy parameter in Lennard-Jones (LJ) potential σ length parameter of LJ potential ϕ interaction potential θ0 Equilibrium angle

Cao et al. [15] used implementing a different of the simultaneous perturbation stochastic approximation algorithm to optimizing the hydraulic fracturing design.

Furthermore, Jahandideh et al. [16] optimized the hydraulic fracturing design to maximize the net present value of the shale asset. Using of nanotechnology in various processes leads to their improvement and development [17]. Nanotechnology is another effective way to optimize the hydraulic fracturing process. Nanotechnology is the manipulation of materials on a nano-metric (atomic) scale. The earliest, common report of nanotechnology referred to the specific technological aim of precisely manipulating atoms for the fabrication of macroscale structures, also now referred to as molecular nanotechnology [18,19]. Carbon Nanotubes, Graphene, Graphene quantum dot, and Graphene nanosheet are some of the important atomic structure in nanotechnology [20,21].

These compounds have many applications in electrochemical sensors, electromagnetic shields, energy storage, improvement in electrical conductivity, boiling, hydraulic fracturing process, etc. [22–26]. In this

" 6 # σ 12 σ U ðrÞ ¼ 4ε r ≪ rc − rij r ij

ð1Þ

Where ε is the depth of the potential well, σ is the distance at which the potential is zero; rij is the distance between the 2 atoms. In MD simulations, both σ and ε parameters depend upon the sort of atoms in the simulation box. The length scale parameter and energy for different atoms in atomic substrate simulation are listed in Table 1 [40].

The bonded forces consist of bond angle bend and bond strength terms. Harmonic oscillator equations calculate the angle and bond strength stretch in UFF force-field as below: Er ¼

1 kr ðr−r 0 Þ 2

ð2Þ

Eθ ¼

1 kθ ðθ−θ0 Þ 2

ð3Þ

In these formulas, Kθ and Kr are harmonic oscillator constants. θ0 and r0 are the atomic bond length and equilibrium value of angles. For H2O molecules, we used the SPC model in our MD simulations. The interaction between water molecules is simulated using an LJ potential.

These interaction parameters for atomic water structure reported in below [42,43]:

Fig. 1. The schematic of the common hydraulic fracturing process.

2

A. Mosavi, M. Hekmatifar, D. Toghraie et al.

Journal of Molecular Liquids 323 (2021) 114610

Oxygen mass = 15.9994 u.

Hydrogen mass = 1.008 u.

Oxygen charge = −0.820.

Hydrogen charge = 0.410.

LJ interaction epsilon for Oxygen-Oxygen = 0.1553 kcal/mol.

LJ interaction sigma for Oxygen-Oxygen = 3.166 Å.

LJ interaction epsilon and sigma of Oxygen- Hydrogen and Hydrogen - Hydrogen = 0.0.

Equilibrium bond length of Oxygen- Hydrogen = 1.0 Å.

Equilibrium angle of Hydrogen -Oxygen- Hydrogen = 109.47°.

Furthermore, graphene nanosheets in our MD simulations described

by Tersoff potential [44,45]. The most common expression of the Tersoff potential represented as below, E¼

1 ∑∑V 2 i i≠j ij

ð4Þ

V ij ¼ f C r ij f R r ij þ bij f A r ij

ð5Þ

In Eq. (5), fR is a two-body term, and fA includes three-body interactions. The summations in the formula are overall neighbours j and k of atom i within a cut-off distance Rc = R + D. Furthermore, the potential between the particles V(rN) is assumed for each pair of particles. Therefore, for N particles,

V r N ¼ ∑∑V r ij

ð6Þ

i<j

Previous reports show that the UFF force field can be used for various structures and elements of the periodic table [30]. Further, Tersoff potential is an appropriate choice for carbon nanostructures such as graphene nanosheets, carbon nanotube, etc. [44,45]. To calculate the particle movements by simulation time, Newton's second law's equation in atomic level is applied as the gradient of interatomic potential in below equations, 2

F i ¼ ∑F ij ¼ mi i≠j

d ri dt

2

¼ mi

dvi dt

F ij ¼ −grad V ij

ð7Þ ð8Þ

From the above equations, the momentum Pi can be defined as follow, P i ¼ mi vi

ð9Þ

So, Total energy (E) of the atomic system can be displayed in the formation of Hamilton as below equation, Hðr, P Þ ¼ Fig. 2. Schematic of rock substrate and water /sand mixture, which provided with Packmol package at a) Front, b) Top, and c) Perspective views.

ε (kcal/mol)

σ (Å)

Oxygen Silicon Aluminum Iron Calcium Sodium Potassium Magnesium

0.060 0.402 0.505 0.013 0.238 0.030 0.035 0.111

3.500 4.295 4.499 2.912 3.399 2.983 3.812 3.021

ð10Þ

Furthermore, in MD simulations, Gaussian distribution is used for calculating the temperature of particles that are shown in the following formula:

Table 1 The length scale and energy parameters for LJ interaction in simulated structures [40].

Atom

1 ∑P 2 þ V ðr 1 þ r 2 þ . . . þ r n Þ ¼ E 2m i i

3 1 N 1 kB T ¼ ∑ mv2i 2 Natom i¼1 2

ð11Þ

The instantaneous temperature fluctuates obtained from the below equation, N

T ðt Þ ¼ ∑ i

3

mi v2i ðt Þ kB Nsf

ð12Þ

A. Mosavi, M. Hekmatifar, D. Toghraie et al.

Journal of Molecular Liquids 323 (2021) 114610 -3 0 0

Where Nsf is the degree of freedom of the atomic structures. Finally, we can say that MD simulations of this work carried out in these two steps: Step A: rock substrate with water/sand mixture and graphene nanoparticles were simulated at T = 300 K with 1 fs time step. The simulation package in our molecular dynamics calculations has 100*50*75 Å3 length in x, y, and z directions, respectively. In the temperature equilibration process, we use the NVT ensemble for 2.5 ns [46,47].

Step B: In the second step of our MD simulation, the atomic interaction between substrate and defined atomic mixtures was carried out for 2.5 ns later. For analyzing the interaction between these structures, physical parameters such as mutual atomic force and the number of departed atoms from rock substrate were reported.

Potential Energy (eV)

-4 0 0

-5 0 0

-6 0 0

-7 0 0

3. Discussion and results

3

improve the water /sand mixture mechanical properties. By this improvement, we predict that the hydraulic fracturing process done effectively by adding graphene nanoparticles to water/sand mixture.

3.2. Dynamical evolution of simulated structures After initial molecular dynamics equilibration and simulations process of simulated structure, the NVE ensemble implemented for 2.5 ns later (see Fig. 5). Then, the joint force of two groups of atomic structures (group A: water molecules and sand particles - group B: rock substrate) calculated. Fig. 6 shows that the mutual force between these structures varies from 10.11 eV/ Å to 13.57 eV/ Å by MD simulation time passing.

Physically, the non-zero rate of the joint force rate of these structures shows that the water/sand mixture and atomic substrate distance is lesser than the cut off the radius of them at 300 K, and these structures interacted with each other. By adding graphene nanosheets by a 1% atomic rate, the mutual force of these structures rises. Numerically, by adding armchair and zig-zag graphene nanosheets, the mutual force of initial structures increases from 13.57 eV/ Å to 14.41 eV/ Å and 16.45 eV/ Å, respectively (Table 2). This atomic behaviour displays that, by adding graphene nanoparticles to initial structure, the hydraulic fracturing process can occur effectively, and so nanoparticles are the positive parameter in this mechanical procedure. Furthermore, we can say that using armchair graphene nanosheets has more atomic effects on the substrate, and by using this nanostructure, the hydraulic fracturing process done more effectively.

The number of separated atoms from a simulated rock substrate is proportional to its stability. Our MD simulations show that by MD simulation time passing, the number of these atoms increases (see Fig. 7).

Numerically, after 2.5 ns, the number of departed atoms increases to 57 rates. By adding 1% graphene nanosheets to water/sand mixture, the departing atoms from substrate increases. By adding armchair and zig-zag graphene nanosheet to the original mix, the departed atoms rate after 2.5 ns increases to 63 and 74 rates, respectively (Table 3).

From these calculations, we can say that adding graphene nanosheets to initial water/sand mixture cause improve this atomic structure mechanical strength. Furthermore, nanoparticles adding to atomic structures cause an increase in the atomic interaction between two groups of atoms. So, the more number of atomic substrate interacts with water/sand mixture, and more number of rock substrate atoms departed of them.

The atomic rate of graphene nanosheets, which added to our simulated structures, has an essential effect on the atomic manner of

350

Temperature (K)

2

Fig. 4. Potential energy variation of simulated structures with/without graphene nanosheets as a function of molecular dynamics simulation time.

In the first step of this molecular dynamics simulations, the atomic structure of base fluid (consist of water molecules and sand particles) was studied at T = 300 K. Fig. 2 shows the atomic arrangement of atomic structures in the simulation box. Our MD results in the equilibrium process showed that the initial position of atoms in the hydraulic fracturing process is adopted with UFF and Tersoff force-fields. Numerically, structures atomic stability described by reporting temperature and potential energy of them. Total temperature variation of the simulated structure depicted in Fig. 3. From this Fig, we can say that all structures equilibrated after 2.5 ns. Fig. 4 displays the potential energy of atomic structures as a function of MD simulation time. According to this Fig, we can say that the potential energy of structures converged after 2.5 ns, too. Numerically, the potential energy of simulated structure reaches to −416 eV after 2.5 ns. From our MD result, we can say that simulated structures mean distance increases after the equilibration process and reach to atomic stability after 2.5 ns. By adding graphene nanosheets to base structures by a 1% atomic rate, the simulated structures don't disrupt, and so, the equilibration process can be detected after 2.5 ns. From Fig. 3, we can express that the temperature of atomic structures in the presence of armchair and zig-zag nanosheets converged to 300 K. furthermore, atomic stability of simulated structures after adding graphene nanostructures rises. Numerically, by adding armchair and zig-zag graphene nanosheets to water molecules and sand particles, the potential energy of these structures increases to −599 eV and − 559 eV from −416 eV. By potential energy increases, the atomic stability of structures rises, and so these nanostructures

300

250

W ith o u t G ra p he ne W ith G ra p h e n e -A rm c h a ir W ith G ra p h e n e -Z ig z a g

0

1

T im e (n s )

3.1. Atomic equilibration of simulated structures

200

0

1

2

3

T im e(ns ) Fig. 3. Temperature variation of simulated structures with/without graphene nanosheets as a function of molecular dynamics simulation time.

4

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Journal of Molecular Liquids 323 (2021) 114610 15

Mutual Force (eV/Angstrom)

water/sand and substrate. In this section of our computational study, we describe this subject by reporting departed atoms rate from the substrate as a function of the graphene nanosheet atomic rate. In this section, we add armchair graphene nanosheets by 1%, 2.5%, 5%, and 10% atomic rates to water/sand mixture and calculate the departed atoms from rock substrate (Fig. 8). From Table 3 and Fig. 9, we can conclude

12

9

W ithout G raphene W ith G raphene-A rm chair W ith G raphene-Z igzag

6 0

1

2

3

Tim e (ns) Fig. 6. Mutual force variation of water/sand mixture and rock substrate with/without graphene nanosheets as a function of MD simulation time.

Table 2 Mutual force variation of water /sand mixture and rock substrate with/without graphene nanosheets after 2.5 ns.

Atomic sample

Mutual force (eV/ Ă&#x2026;)

Without Graphene With Armchair Graphene With Zigzag Graphene

13.57 14.41 16.45

that, by 5% graphene nanosheet adding to water/sand mixture, the maximum number of departed rock atoms detectable. Numerically, by adding graphene nanostructures to water /sand mixture by 1%, 2.5%, 5%, and 10%, the number of departed rock atoms from atomic substrate

80

Number of Atoms

60

40

20

0

W ith o u t G r a p h e n e W ith G r a p h e n e - A r m c h a ir W ith G r a p h e n e - Z ig z a g

0

1

2

3

T im e ( n s ) Fig. 7. The number of departed atoms from rock substrate with/without graphene nanosheets as a function of MD simulation time.

Table 3 The number of departed atoms from rock substrate with/without graphene nanosheets after 2.5 ns.

Fig. 5. Time evolution of rock substrate after a) 0, b) 1 ns and c) 2.5 ns.

5

Atomic sample

Number of lost atoms

Without Graphene With Armchair Graphene With Zigzag Graphene

57 63 74

A. Mosavi, M. Hekmatifar, D. Toghraie et al.

Journal of Molecular Liquids 323 (2021) 114610

Fig. 8. Water /sand mixture with a) 1%, b) 2.5%, c) 5%, and d) 10% graphene nanosheets.

Table 4 The number of departed atoms from rock substrate as a function of armchair graphene nanosheet atomic rate after 2.5 ns.

reaches 74, 89, 101, and 91 rates, respectively. So, we can say that the hydraulic fracturing process reaches to maximum efficiency by 5% nanostructure adding to the initial atomic arrangement. Practically, by using the reported results from this section of our MD calculations, one can optimize the hydraulic fracturing process in actual cases (Table 4).

The size of graphene nanosheets is another important parameter on the dynamical manner of water /sand mixture and atomic substrate. In the last section of this molecular dynamics simulations, we estimate this atomic parameter effect by calculating the number of departed particles from the substrate as a function of the graphene nanosheet size. For doing this procedure, we add armchair graphene nanosheets by 20 Å, 30 Å, 40 Å, and 50 Å size in x and y directions to water /sand mixture.

From Table 5 and Fig. 10, we can say by graphene nanosheet with 40 Å length adding to simulated structure, the maximum number of departed particles detectable. Numerically, by adding graphene

Nanoparticle rate (%)

Number of lost atoms

1 2.5 5 10

74 89 101 91

Table 5 The number of departed atoms from rock substrate as a function of graphene nanosheet size.

Nanoparticle size (Å)

Number of lost atoms

20 30 40 50

74 82 93 86

120 100

90

Number of Atoms

Number of Atoms

90

60

A r m c h a ir - 1 % A r m c h a ir - 2 .5 % A r m c h a ir - 5 % A r m c h a ir - 1 0 %

30

0

0

1

2

80

70

60

50 20

3

T im e s ( n s )

30

40

50

60

G r a p h e n e L e n g th ( Å )

Fig. 9. The number of departed atoms from rock substrate as a function of armchair graphene nanosheet atomic rate.

Fig. 10. The number of departed atoms from rock substrate as a function of graphene nanosheet size.

6

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nanostructures with various sizes (20 Å, 30 Å, 40 Å, and 50 Å) to simulated sand /water mixture by 1%, atomic rate, the number of departed particles from rock substance reaches to 74, 82, 93, and 86 particles, respectively.

4. Conclusion The present study investigates the atomic interaction between rock substrate and water /sand mixture with/without graphene nanostructures via molecular dynamics simulations. In our molecular dynamics simulations, rock substrate is modelled by a coarse-graining method.

Also, to simulate of interatomic force, Universal Force Field and Tersoff potential have been implemented to various atomic structures. The result of our simulations shows that graphene nanostructures have a measurable effect on optimizing the hydraulic fracturing process, which can be used for petroleum applications. Generally, our computational outcomes from molecular dynamics simulations are as following: • Universal Force Field and Tersoff potentials are the appropriate interatomic potential for molecular dynamics simulation of defined structures. Numerically, the potential energy of our simulated structures converged to −416 eV and − 599 eV after 2.5 ns at 300 K with and without graphene nanosheets, respectively.

• The mutual force between rock substrate and H2O/sand mixture increases by graphene nanosheets adding to the MD simulation box.

Numerically, the defined joint force in our simulated structures reached to 13.57 eV/ Å and 16.45 eV/ Å after 2.5 ns with and without graphene nanosheets, respectively.

• The departed atoms from rock substrate increase by graphene nanosheet, adding to H2O/sand mixture. Numerically, the number of departed atoms in the hydraulic fracturing process increased to 74 atoms from 57 atoms with a 1% graphene nanosheet presence.

• Graphene nanosheets with an armchair edge have more impact on the hydraulic fracturing process rather than zig-zag edge one.

• By adding graphene nanosheet with a 5% atomic ratio to water /sand mixture, the hydraulic fracturing process optimized and the number of departed atoms from rock substrate reach to the maximum rate.

• The maximum rate of departed atoms from rock substrate (93 particles) occurs by adding graphene nanoparticles with 40 Å length.

CRediT authorship contribution statement Amirhosein Mosavi: Writing - review & editing, Writing - original draft, Investigation. Maboud Hekmatifar: Methodology, Software, Validation, Writing - original draft. Davood Toghraie: Methodology, Software, Validation, Writing - original draft, Investigation. Roozbeh Sabetvand: Methodology, Software, Validation, Writing - original draft. As’ad Alizadeh: Writing - review & editing. Zahra Sadeghi: Writing - review & editing, Writing - original draft. Aliakbar Karimipour: Writing - review & editing, Writing - original draft, Investigation.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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