Molecular Dynamics Study on Mechanism of Preformed Particle Gel

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Molecular Dynamics Study on Mechanism of Preformed Particle Gel Transporting through Nanopores: Deformation and Dehydration Ying Ma, Heng Zhang, Qingquan Hao, Gang Liu, Hua Wang, and Shiling Yuan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04832 • Publication Date (Web): 15 Aug 2016 Downloaded from http://pubs.acs.org on August 20, 2016

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The Journal of Physical Chemistry

Molecular Dynamics Study on Mechanism of Preformed Particle Gel Transporting Through Nanopores: Deformation and Dehydration

Ying Ma†, Heng Zhang*†, Qingquan Hao‡, Gang Liu†, Hua Wang§, Shiling Yuan*† † Key Lab of Colloid and Interface Chemistry, Shandong University, Jinan 250199, P. R. China ‡ School of Chemical Engineering, University of Petroleum (Beijing), Beijing 102200, P. R. China § National Engineering Technology Research Center for Colloidal Materials, Shandong University, Jinan, 250199, P. R. China

Abstract: Understanding the translocation mechanism of preformed particle gel (PPG) through nanoporous medium is crucial for the gel treatment during enhanced oil recovery. On the basis of non-equilibrium molecular dynamics simulation, the translocation process of PPG in silica nanopores consisting of two different diameters was investigated. During the simulation, an external pulling force was applied to PPG representing the injection pressure. The simulation results suggest that a synergetic deformation and dehydration of PPG occurs during the translocation from the wide side into the narrow side. The energy barrier of the translocation process mainly result from the conformational energy change of PPG (mainly from the angle bend and dihedral torsion) and the dissociation energy barrier between PPG’s hydrophilic groups and water. Furthermore, the nanopore size has a crucial impact on the translocation mechanism of PPG, not only the degree of the deformation and dehydration near the entrance, but also the translocation mechanism after they entered the nanopore. For nanopore with large diameter, PPG can reabsorb water to induce a complete hydration layer around it after entered. While for the nanopore with small size, the compression from pore restrict PPG’s rehydration ability. Without the screen and lubrication of the hydration layer, the pulling force needed to drive PPG increased rapidly which means larger injection pressure in macroscopic view. The findings are helpful for understanding the translocation process of PPG in porous media on molecular level, and also, will facilitate technology developments for enhancement of * Corresponding Author, E-mail: [email protected] * Corresponding Author, E-mail: [email protected] 1

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recovery efficiency of petroleum. 1. Introduction In petroleum industry, reservoir heterogeneity is one of the main reasons causing the low sweep efficiency of water flooding. Controlling conformance during water injection, PPG (performed particle gel) treatment has attracted great attention among other enhanced oil recovery technologies recently[1]. PPG is a particled super-absorbent crosslinking polymer. When injected into a target formation, it can swell up to hundreds of times of its original size. The flow capacity of the fractures was then reduced, and following fluid was diverted into unswept oil zones[2, 3]. A good candidate of PPG for water shutoff and profile control should be easily injected into the porous media without any plugging.[4, 5] Hence, the translocation behavior of PPG confined in nanopores is of great interest from both the technological and fundamental point of view[6]. On the other hand, understanding the translocation process through nanopores is necessary in many contexts besides petroleum and gas reservoir engineering, such as many biological processes[7, 8]. Recently, Lyon’s group[9] reported the translocation of hydrated microgel particles through cylindrical nanopores with openings ten times smaller than microgel’s diameter. The pressure differentials they used were similar to renal filtration. They demonstrated the deformability of microgels during translocating through a nanoporous membrane. White’s group[10, 11] investigated the single microgel particle translocation events using resistive-pulse sensing technique. Their results showed that microgel has to deform and compress itself to translocate through the nanopore. The synergetic process will then result in extrusion of interior solution and change of conductivity.

Bai et al.[1, 12] investigated the translocation mechanism of PPG through multi-porous media by conducting coreflooding experiments, and different translocation patterns were proposed at micro and macro scales. A fully understanding of gel particle’s translocation mechanism within nanopore is critical to the development of PPG applications. To obtain detailed information on molecular level, a series of molecular dynamics simulation studies were conducted by our group[13, 14]. In a previous work[14], the translocation of PPG in a silica nanopore 2


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with uniform diameter was investigated. The molecular dynamic simulation results suggested that the hydration layer induced by surface silanol groups of the nanopore may play a key role during PPG’s translocation. It served as a natural physical barrier, and induced an energy barrier to keep PPG away. The hydration layer’s screening and lubrication effect will reduce the fluid resistance largely during PPG’s translocation. At macroscopic level, it will reduce PPG’s injection pressure. In this continuing work, the dynamics of PPG translocating inside three different silica nanopores consisting of two different diameters were investigated using nonequilibrium molecular dynamics simulations. During the simulation, effect of silica nanopore size on translocation process was compared. The conformation and hydration shell change of PPG was investigated. The analysis of the conformational energy change and desolvation energy barrier between PPG’s hydrophilic groups and water were conducted. The research will provide molecular level insights into the translocation behavior of PPG in silica nanopores.

2. Models and Simulation Details 2.1. Models In the simulation, PPG and water molecules were confined within silica nanopores. Here silica was selected as a proxy for rock pore surfaces as it is an abundant mineral in earth and a major component of rock minerals in many geological environments[15]. The structure of the silica nanopore consists of two cylindrical nanopores of different diameters joined with junctions (see Figure 1). The left block was about 6.5 nm long with diameter 5 nm, the central block, i.e. the junction region was about 0.5 nm, and the length of right block was about 20 nm. Considering there are abundant micro-meso pores ranging from 3 to 8 nm in the underground geological environment[16, 17], hence three different silica nanopores were generated and used in the MD simulation. They are d50-d40, d50-d30, and d50-d20 silica nanopores. Taken d50-d30 silica nanopore as an example, the procedure to derive the model were divided into three steps. First, a cylindrical hole with diameter = 3 nm, length = 27 nm was carved from an α-quartz block. All atoms within the 3



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diameter were removed. Then a larger cylindrical hole of diameter = 5 nm length = 6.5 nm was carved from the left end. The junction region connecting two cylindrical holes was smoothed by removing irregular atoms. To reflect the realistic surface chemistry of silica nanopores under complex underground situations, the bare Si atoms were saturate with silanol groups, resulting in a fully hydroxylated inner surface. The hydrophilic surface consist of germinal and isolated silanol groups, i.e., Si-(OH)2 (Q2 type) and Si-OH groups (Q3 type)[18], see Figure 1a. The derived –OH density is ~ 7.2 per nm2, which is consistent with previous works[19, 20 21]. The

PPG

consisting

of

four

HPAM

segments

(-[CH2CHCONH2]3a-

[CH2CHCOO-]a-, partially hydrolyzed polyacrylamide, with degree of polymerization 100 and degree of hydrolysis 25%) and cross linked with -COO(CH2)2NCH3CH2- was initially enclosed at left end of the silica nanopore after equilibrated in vacuum. The structure of PPG is sketched in Scheme 1. Water and sodium ions were then added in the silica nanopores to solvate PPG and keep the system electronically neutral. The simulation box has a size of 8.35×8.35 ×30 nm3. The schematic representation of the simulation system are illustrated in Figure 1.

Scheme 1. Chemical structure of PPG. 4


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Figure 1. Simulation of PPG driven through silica nanopores. (a) Top view of the silica nanopore (Si, yellow; O, red; H, white). The pore was carved from an α-quartz block with hydrophilic surface (terminated with mixed Q2, Q3 type silanols). The bulk SiO2 was constrained during all simulations (colored with gray molecular surface). (b) View from the side and cross-section of the simulation system. PPG was initially settled at the end of the pore (5nm diameter), and then pulled to the other end (3nm diameter).

2.2. Force Fields. The interaction between silica nanopore and PPG was described by GROMOS force field (43a2) [22]. The potential energy includes bond and non-bond terms. The bond term consist of bond stretching, angle bending and dihedral torsions. While the non-bond term was represented by Lennard-Jones potential (LJ 6-12) and coulombic potential. The parameters of LJ potential used for unlike atoms used a geometric combination rule. To get a good prediction of the hydration layers near silica nanopore surface, Hoffmann and Berendsen’s model

[23]

of the surface charge

distribution was adopted. Water molecules were described with SPC (simple point charge) model

[24]

. All parameters used in this study are collected in Tables S1 in the

Supporting Information. 2.3. Equilibrium Molecular Dynamics Simulation (EMD). 5



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All the simulations were performed in GROMACS 4.5.4.

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[25]

During the

simulation, energy minimization was conducted using steepest descent method before equilibrium MD run. After that, a 20ns molecular dynamic simulation was carried out under NVT ensemble. During all simulations, the silica nanopore were kept frozen except for the inner surface, see Figure 1a. The periodic boundary conditions was applied in all three dimensions. The velocity rescale thermostat [26] was used to keep temperature around 298K. LINCS algorithm [27] was used to constrain bond length. The vdw interaction was cut off at 1.4nm and columbic interactions was calculated using PME method[28]. The MD integration step is 2.0 fs, with trajectories stored every 10 ps for further analysis. The visualization of the trajectory used VMD 1.92[29]. During the 20 ns NVT ensemble calculation of each model, the energy and structural properties were monitored and they both rapidly converged. Hence, it can be concluded that the simulation time is long enough for each system to reach its equilibrium structure. 2.4. Nonequilibrium Molecular Dynamics Simulation (NEMD). To mimic the driven force from injection pressure, steered molecular dynamics simulations[30] were then performed. The equilibrium structure from the previous molecular dynamics simulation was selected as the initial configuration of the NEMD. As illustrated in Figure 1a, a pulling force along z-axis with spring constant 1000 kJ·mol-1·nm-2 and pull rate of 0.01 nm·ps-1 was exerted on the COM of PPG. The initial distance between COM of PPG and the pulling reference (a point in the central of the cylindrical pore which kept fixed during simulations) was about 3 nm. The simulations were performed for 2 ns for all three systems. Other detailed simulation method used the same as that discussed in 2.3 part.

3. Results and Discussion 3.1 Translocation process The diameter of the silica nanopore influences the dynamics of the translocation process of the pore fluids due to the complex interface structure. Using NEMD simulations, we investigated the dynamics of the translocation of PPG confined in different silica nanopores. 6


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By analyzing the translocation process of PPG in d50-d30 silica nanopore (see the movie in Supporting Information), we found that PPG passed into the right block of the nanopore with diameter 3 nm in 3ns though it was blocked in the junction region for a while. Four typical snapshots during PPG’s translocation were shown in Figure 2, in which Figure 2(a) shows the initial configuration before pulling at time 0 ps, Figure 2(b) shows PPG compressed and trapped in the juncture of d50-d30 nanopore at time 1500 ps, Figure 2(c) shows the PPG passing through the junction region under larger external pulling force at time 2500 ps, and Figure 2(d) shows the PPG totally inserted into the d30 nanopore at time 2900 ps.

Figure 2. Snapshots of PPG translocation through the d50-d30 silica nanopore under external force at (a) time=0ps, (b) time=1500ps, (c) time=2500ps, (d) time=2900ps.

To quantitatively evaluate PPG’s translocation, the variations of pulling force and COM (center-of-mass) position of PPG with time during the translocation process in d50-d30 silica nanopore is shown in Figure 3 (the corresponding figure for PPG in d50-d40 and d50-d20 silica nanopore were shown in Figure S1, S2). The axial and radial component of the PPG position were also distinguished. It can be seen that under the pulling force exerted on PPG, it moves from the start position at about z = 3 7



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nm to about z = 15 nm in 3 ns. From the radial COM position of PPG, we can conclude that PPG is always in the pore center during the simulation. The force rapidly increased during the first 0.4 ns, while the axial COM position of PPG didn’t change much. The value of the force at 0.4 ns (~3.5×103 kJ·mol-1·nm-1) were interpreted as static friction force Fs, which coincides with previous work[14]. The resistance force mainly arise from the interaction between PPG and nanopore, and the perturbation of hydrogen bond networks around.

Figure 3. Translocation of the PPG through d50-d30 silica nanopore. The variations of the COM positions of PPG in z direction and pulling forces exerted on PPG.

When the pulling force exceed friction force Fs, PPG start to move along the nanopore slowly. As shown in Figure 3, force in the spring and axial COM of position of PPG increases linearly in this period. From 0.4 ns to 1.5 ns (axial COM position < 6 nm), PPG stayed in the d50 nanopore due to the narrower channel of the d30 nanopore. The radius of gyration of PPG along the axial decreased as shown in Figure 4, which means PPG was compressed. This shows that PPG is unable to pass through the d50-d30 nanopore under the strength of the applied pulling force. After 1.5 ns, when the pulling force exceed 12×103 kJ·mol-1·nm-1, it start to insert into the d30 part. The radius of gyration along axial increased rapidly, which means PPG was stretched to move into the narrow nanopore. Similar variation of radius of gyration of PPG was 8


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also found in the d50-d20 system. While for the d50-d40 system, the radius of gyration of PPG didn’t decrease significantly as the other two, cause the quite larger diameter of d40 nanopore. When it came to 2.4 ns, most of the PPG inserted into the d30 nanopore, and the increase of pulling force began to slow down. After 2.75 ns, all of the PPG inserted into d30 nanopore, the pulling force dramatically decreased.

Figure 4. Variations of radius of gyration of PPG along axile direction during translocation.

3.2 Deformation As seen in Figure 2, during PPG’s translocation, it interacts with nanopore surface and produces severe deformation. This can also be reflected by the RMSD (root mean square deviation) of PPG, which was usually used to estimate the structural similarity between equivalent atoms, computed after optimal superposition of the two structures that are compared. Figure 5 illustrated the RMSD of PPG during the transport. The PPG was deformed to transport through the silica nanopore in all three systems. Obviously, the narrower the nanopore, the larger PPG deformed.

9



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Figure 5. Variations of RMSD of PPG in different silica nanopore during translocation.

To explore the intrinsic mechanism of PPG’s deformation during transport, conformational energy was calculated to quantify the conformational change. In this simulation, PPG’s conformational potential energy was composed of bond stretch energy, angle bend energy, and dihedral torsion energy, i.e. the bond terms. Figure 6a illustrated the calculated PPG conformational energy variations during its translocation. It’s clear that the conformational energy didn’t change much until 1.5 ns. When PPG start to insert into the d30 block after 1.5 ns, the conformational energy increased rapidly to a higher level. The decomposed bond, angle and dihedral energy terms of the PPG conformational energy was illustrated respectively in Figure 7. It’s obvious that most of the conformational change of PPG raised from its angle’s bend and dihedral’ torsion. The variations of axial COM position and conformational energy of PPG in d50-d40 and d50-d20 system were also illustrated in Figure 6b, 6c. The narrower the silica nanopore is, the higher the conformational energy change, meaning that PPG is severely deformed.

10


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Figure 6. Translocation of PPG through silica nanopores under external force: the variations of the COM positions of PPG and conformational energy with time. (a)PPG in d50-d30 nanopore, (b) PPG in d50-d40 nanopore, (c) PPG in d50-d20 nanopore.

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Figure 7. Conformational energy change of PPG in d50-d30 silica nanopore and the decomposed bond, angle and dihedral energy terms.

3.3 Dehydration Besides the conformational change of PPG during its translocation in the silica nanopore, dehydration may also be required which depend on the PPG and pore size, PPG’s physical properties, etc. To gain a further insight into the mechanism by which PPG translocate through a nanopore, the variation of hydration number of PPG during the translocation process was examined. Water molecules within 0.4 nm distance with PPG was considered as hydration layer water.

12


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Figure 8. Variations of hydration number of PPG during translocation in different silica nanopore.

As illustrated in Figure 8, at the beginning of the pull simulation, the hydration number of PPG increased for all three systems. This resulted from the perturbation of the pulling force which increased the solvent access probability of PPG. As approaching to the junction region, the PPG was compressed under the pulling force. A portion of water molecules is forced out from the hydration layer, which resulted in the loss of hydration number. While translocate in d50-d40 silica nanopore which is slightly smaller than PPG, it requires minimal dehydration. As to small nanopores (e.g. d50-d20 silica nanopore), the dehydration must be significant in order to pass through. As part of PPG passed through the junction region and into the right block of the silica nanopore, it reabsorbed water, then resulting in an increase of PPG hydration number. An obvious difference between d50-d20 silica nanopore and d50-d40 or d50-d30 silica nanopore is that after PPG entering the narrow side, the change of PPG’s hydration number didn’t show a similar trend. The hydration number of PPG in d50-d20 silica nanopore kept a constant at about 800. That was because the compression from the d50-d20 silica nanopore restricted the reabsorb ability of PPG. While for PPG in d50-d40 and d50-d30 silica nanopore, the space is enough to induce a new hydration layer. It can also be deduced from Figure S2 that without the screen and lubrication of the hydration layer between silica nanopore and PPG, the pulling 13



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force needed to drive PPG increased rapidly which coincides with previous work[14]. The results we derived here is also in consistent with Holden’s experiments which investigated the translocation of poly(N-isopropylacrylamide-co-acrylic acid) microgels with a radius of 570 nm translocating through a single conical nanopore with different radii. The hydrophilic groups of PPG induced a typically strong hydration shell, as demonstrated in our previous work[13]. The dehydration process of PPG has to overcome the energy barriers of the surface hydration layers, which is associated with PPG’s surface chemistry. Here potential of mean force (PMF) was used to quantify the interactions between PPG’s hydrophilic groups and surface hydration layer. In this work, PMF profiles were transformed from the RDF (radial distribution function) of the certain atom of PPG’s hydrophilic group and water molecules through the equation E(r)=-kBTlng(r), where kB is Boltzmann’s constant, T is the simulation temperature, and g(r) is the radial distribution function. The PMF profiles were illustrated in Figure 9a. Taking the energy profile of O (COO-)-OW for example, we can deduce that 1) the first minimum at 0.27 nm is the contact minimum (CM), which is the direct contact distance between COO- group and water; 2) the second minimum at 0.33 nm is the solvent separation minimum (SSM), which is the separation distance between COOgroup and water; 3) the maximum at 0.29 nm between the CM and SSM is the desolvation barrier (BS), which have to be overcome if transform between two minima. At infinity, the PMF increased to zero.

14


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Figure 9. Potential of mean force between hydrophilic group of PPG and water. (a) PMF profile; (b) simplified profile with only CM, BS, SSM illustrated.

The binding energy barrier between hydrophilic groups and surface hydration shell molecules is associated with BS and SSM, i.e., ∆E+ = EBS - ESSM. As for dissociation energy barrier between hydrophilic groups and surface hydration shell molecules, it is associated with BS and CM, i.e., ∆E— = EBS - ECM. The calculated energies of certain atom of hydrophilic groups and water are listed in Table 1. Combining Figure 9b and Table 1 we can conclude that: i) O (COO-) formed an energetic stable hydration layer with energy -1.13 kJ/mol, which is more stable than O (CONH2) and N (CONH2); ii) the binding energy barrier between O (COO-) and water molecules ∆E+ (0.13 kJ/mol) is also small than ∆E+ of O (CONH2) and N (CONH2) with water (0.74 and 1.07 kJ/mol). This means it’s easier for water molecules to combine with O (COO-); iii) while the dissociation energy barrier between O (COO-) and water ∆E- 1.91 kJ/mol is higher than ∆E- of O (CONH2) and N (CONH2) with water (1.40 and 1.32 kJ/mol). This means it’s quite difficult for water molecules to dissociate while combined. Table 1. Binding and dissociation energies between certain atoms of PPG’s hydrophilic groups and water molecules.

Certain atom of PPG’s hydrophilic group

∆E+

∆E—

（kJ/mol）

（kJ/mol）

0.13 0.74 1.07

1.91 1.40 1.32

-

O (COO ) O (CONH2) N (CONH2) 15



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4. Conclusions The translocation mechanism of preformed particle gel (PPG) through nanoporous medium is crucial for the gel treatment during enhanced oil recovery. In this work, molecular dynamics simulation method were used to investigate the translocation process of PPG in silica nanopores that consisting of two different diameters under external driving force.

The simulation results suggest that during translocation a synergetic deformation and dehydration of PPG occurs by analyzing from the radius of gyration, RMSD, and hydration number of PPG which is in consistent with experiments[10]. To understand the intrinsic mechanisms underlying these observations quantitatively, the conformational energy change of PPG and potential of mean force between hydrophilic groups of PPG and water was investigated. The energy barrier for PPG translocation into a smaller nanopore mainly results from the conformational energy change of PPG (mainly from the angle bend and dihedral torsion) and the dissociation energy barrier for PPG’s hydrophilic groups and water. Furthermore the nanopore size has a crucial impact on the translocation mechanism of PPG, not only the degree of the deformation and dehydration near the entrance, but also the translocation mechanism after they entered the nanopore. Figure 10 illustrated two different mechanisms of PPG transporting in the silica nanopore with different size. For nanopore with large diameter, PPG can reabsorb water to induce a complete hydration layer around it after entered (e.g. PPG in d50-d40 and d50-d30 silica nanopore). As discussed in our previous work [14], this hydration layer is a natural physical barrier that screened the direct interaction between PPG and the silica nanopore. It will facilitate PPG’s translocation within nanopore. In macroscopic view, it reduced the injection pressure. While for the silica nanopore with small pore size, the compression from pore restrict the rehydration ability. (e.g. PPG in d50-d20 silica nanopore). Without the screen and lubrication, the pulling force needed to drive PPG increased rapidly.

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Figure 10. Illustration of the translocation mechanism of PPG in different silica nanopores. The PPG was represented with a red ball. Silica nanopores were sketched as cylinders. The hydration layers around silica nanopore and PPG were illustrated as green and blue films.

These findings above are helpful for understanding the translocation process of PPG in porous media, and also, will facilitate technology developments for enhancement of recovery efficiency of petroleum. The ability of PPG to transport through silica nanopores with small openings under driving force presents the significance of considering the gel particle’s chain flexibility, dehydration and rehydration ability in optimizing PPG design. Our future efforts will focus on the impact of atomic-scale geometry and chemical inhomogeneity of silica nanopore or intensity of cross-linking of PPG on the translocation mechanism.

Acknowledgement. We acknowledge the National Science Foundation of China for the financial support (No. 21573130).

Supporting Information: Force field parameters for PPG and SiO2; Movie of PPG’s translocation through silica nanopore; Variations of PPG’s COM position along z-axis and pulling forces exerted on PPG in d50-d40 and d50-d20 silica nanopore.

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Table of Contents graphic:

The translocation mechanism of PPG in silica nanopores. The nanopore size has a crucial impact on its translocation, not only the degree of the deformation and dehydration near the entrance, but also the translocation mechanism after they entered the nanopore: the rehydration ability.

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Molecular Dynamics Study on Mechanism of Preformed Particle Gel

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