Apolar behavior of hydrated calcite (1014¯ ) surface assists in naphthenic acid adsorption

, , Arjun Valiya Parambathu,† Le Wang,† ‡ D. Asthagiri,† and Walter G. Chapman∗ †

Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., † Houston, Texas 77005, USA Current address: Dow Chemical Company, Freeport, TX ‡

E-mail: [email protected]

1 Abstract

Water molecules bind strongly to the polar calcite surface and form a surface ad- sorbed layer that has properties akin to an apolar surface. This has important impli- cations for understanding the thermodynamic driving forces underlying the adsorption of acid groups from crude oil, in particular naphthenic acid, onto calcite. Free energy calculations show that naphthenic acid binds favorably to the water mono-layer ad- sorbed on the calcite surface. But to bond directly to the calcite, a free energy barrier has to be overcome to expel the intervening layer of water. Further, naphthenic acids with longer alkyl chains bind with lower free energy to the calcite surface than those with shorter alkyl chains, and, for the same chain length, branching also enhances adsorption. To better understand this behavior, for a specified alkyl chain length we study adsorption at different temperatures. Consistent with experiments, we find that adsorption is enhanced at higher temperatures. Examining the enthalpic and entropic contributions to adsorption shows that adsorption of naphthenic acid is entropically favored.

2 Introduction

Carbonate reservoirs constitute over 50% of the world’s discovered oil reserves1 and are the dominant form in Middle-East petroleum fields. The wettability properties of the reservoir rock is of central importance in determining the efficiency of a water-flooding oil recovery process. An oil-wet rock matrix will prevent water from being spontaneously imbibed2 in the porous carbonate. In this case, the injected water must overcome the barrier introduced by capillarity to displace the original oil in place, making oil recovery from oil-wet reservoirs poor.3 If the wettability of the reservoir rock is altered from oil-wet to water-wet, the injected water can spontaneously invade the rock matrix due to favorable capillary forces and thereby displace oil4 and enhance recovery. The unmodified carbonate surface is expected to be hydrophilic or water-wet, because

2+ 2− of the presence of Ca and CO3 ions comprising the calcite crystal. Quite surprisingly, 80% of carbonate reservoirs are preferentially oil-wet under reservoir conditions,5,6 making water flooding less effective. The favorable adsorption of fatty acids on to the calcite sur- face7–9 is a likely reason why calcite mineral in carbonate reservoirs is oil-wet or mixed-wet. It is reasonable to expect that the adsorption of acid on to calcite is driven by electrostat- ics, and this is asserted by enhanced carboxylic acid desorption with temperature.7,10 This also appears to guide some of the wettability alteration approaches, like potential determin- ing anions displacing the carboxylate,11 or cationic surfactants forming a complex with the acid.12 However, experiments by Young et al.13 show that the adsorption of oleic acids on to calcite surface increases with temperature at low carboxylic acid concentrations. This be- havior is not expected when electrostatic interactions dominate association, but it is instead reminiscent of the temperature dependence of association between non-polar molecules in water. This puzzle motivates a need for a molecular-level understanding of the adsorption of carboxylic acids on carbonate surface and is the subject of this paper. To investigate the adsorption of carboxylic acids on carbonate surface, we calculate the free energy of adsorption of naphthenic acids on calcite (1014)¯ surface using molecular dy-

3 namics simulation. We study the effect of chain length, branching, and temperature. We find that the adsorption free energy is affected by the non-polar chain of the acids: longer tail naphthenic acids adsorb more strongly. The free energy of adsorption is also a function of temperature: an increase in temperature enhances the free energy of adsorption, a behavior commonly associated for interaction between non-polar groups in water. Analysis of entropic and enthalpic contributions to adsorption shows that the favorable adsorption results from a favorable change in entropy upon association, but it is opposed by the enthalpy-change in association. Analysis of the adsorption in the presence of the potential determining ion carbonate shows that it is energetically favorable for the carbonate ion to displace short-tail naphthenic acids from the (1014)¯ surface. However, we find that the displacement is less favorable when the acid bears a bulky tail.

Model and Methods

We study the (1014)¯ surface of calcite, as it is the most abundant calcite surface and also the most stable as determined both theoretically and experimentally.14,15 To model the wetting behavior, we use the geometric information of the calcite unit cell from Stockelmann et al.16 to build the crystal. The calcite crystal comprises 6 6 6 unit cells (i.e. 432 CaCO3 × × groups) in x y z directions. We use the forcefield developed by Raiteri et al.17 to − − model the calcite. In this forcefield, the carbonate group is treated as a rigid entity and the interactions between calcium and carbonate and between carbonate and water follow a Buckingham potential form. This slab of mineral is sandwiched by two bulk water layers at a density of 1 g/cc. Water is modeled using the TIP4P/2005 potential model.18 The thickness of the mineral slab is approximately 2 nm and that of each water slab is around 4 nm. The water slab is terminated with a vapor layer that is 2 nm thick. The final dimension of the simulation cell is 4.8576, 2.9940, and 14.0000 in x, y, and z directions, respectively (Fig. 1).

4 z

Figure 1: Schematic showing the acid head group at a distance z from the plane of surface Ca2+ atoms of calcite. For clarity, only half the simulation cell is shown. The simulation system comprises a calcite crystal (Ca in green, C in black and O in red) sandwiched by two water layers (red dots) terminated by a vapor layer (blank space).

− The molecular structure of the naphthenic acid (C5 C9 CO ) was derived based on − − 2 the average molecular weight (248 g/mol) of the experimentally accessible naphthenic acids. To study the effects of tail length on the free energy of adsorption, we also study an acid with

− − the shorter tail length (C5 C2 CO ) and a hypothetical molecule with no tail (O CO ). − − 2 − 2 Branching effects were studied using naphthenic acid of the same molecular weight with a

− branched structure ((C5 C )2C CO ). The GROMACS-compatible molecular topology − − − 2 of all the acids were generated using the PRODRG server.19 The schematics of the molecular structure of the acids are given in Figure 2. The GROMOS 54A7 force field20 is used to describe the acid molecule. Molecular dynamics simulations were performed in GROMACS/4.6.5 simulation pack- age21 in the (NVT ) ensemble. The temperature was controlled by a modified Berendsen thermostat22 that ensures canonical sampling. We use the leap-frog algorithm23 with a 2 fs time step to integrate the equations of motion. The SETTLE algorithm24 is applied to water molecule and other bonds in the system are constrained by the LINCS algorithm.25 Periodic boundary conditions were applied in all directions and the particle mesh Ewald technique was used for the electrostatic interactions. A cut-off distance of 1.4 nm was used for the real-space electrostatics and van der Waals interaction. The system was equilibrated for

5 − Figure 2: Naphthenic acids used in this study. Clockwise from top left: (a) O CO2 , (b) − − − − C5 C2 CO , (c) (C5 C)2 C2 CO (d) C5 C9 CO . − − 2 − − − 2 − − 2

1 ns. The free energy of adsorption was computed using umbrella sampling26,27 with the verti- cal (z) distance between the surface (or outermost) layer of calcite and the carboxyl group of the acid as the reaction coordinate. (The origin of the coordinate is chosen to be the average position of calcium atoms in the outermost layer of calcite (1014)¯ surface.) The naphthenic acid is initially placed 2 nm away from the surface, and we pull the acid group towards the surface. We constructed a series of simulation systems with different z-separations using steered molecular dynamics simulations. The z-separations were of 0.02 nm, with shorter separations near high energy configurations. At each z, we use a harmonic potential, with a force constant of 250 kJ/mol/A˚2, to restrain the z coordinate. From the overlapping umbrel- las and the weighted histogram analysis method (WHAM),28 we construct the free energy profile of adsorption, the potential of mean force (PMF), along the reaction coordinate. At each z, we equilibrated the system for 50 ps and the production lasted at least 5 ns.

6 Results and Discussion

Water structure at calcite/water interface

The structure of the liquid water on calcite surface has been studied both computation- ally17,29–31 and experimentally.32 At the calcite/water interface, water molecules are highly structured due to electrostatic interaction between water oxygen atoms and the Ca2+ atoms of calcite. This leads to a well-defined peak in the density distribution of water oxygen atoms next to the calcite surface (Figure 3). As found before by Raiteri et al.17 using a different water model, the next layer of water molecules fills the interstitial spaces among water molecules that bind Ca2+ (cf. Fig. 7 in Ref. 17). Water molecules in this layer donate

2− a proton to the CO3 groups of calcite. It is for this reason that the peaks in the oxygen density distributions (Fig. 3) occur within an Angstr¨om,unlike˚ what is found in oxygen- oxygen distributions in bulk water.33 Overall, the structure of TIP4P2005 water close to a calcite surface obtained from this study is consistent with what has been shown by Kerisit et al.30 and Raiteri et al.17 using other water models.

Figure 3: (Left) Number density distribution of calcium atoms in calcite and oxygen atoms in the TIP4P2005 water model. (Right) Charge density distribution of calcite and water molecules.

The structuring of water molecules at the surface will also tend to screen the electric field

7 due to the bare calcite surface. The distribution of charge density (Figure 3, Right) shows that two opposing dipole distributions form at the interface, one contributed by the calcite and the screening contribution from the adsorbed water molecules. Thus the hydrated calcite surface is expected to be less polar than the bare mineral. As discussed below, this feature has implications for the adsorption of the acid on to calcite.

Free energy of adsorption of naphthenic acids on the surface

We investigated the adsorption of two isomers of naphthenic acid, one with a straight chain tail and another with a branched (Fig. 4). We observe that the adsorption of acids is energetically favorable, consistent with experimental observations.7–9 Observe that the acid head group can either be in direct contact with the calcite surface forming an inner sphere complex or separated by a water layer forming an outer sphere complex. These two states are separated by a pronounced barrier. Comparing the linear chain and branched chain isomers of the acid, we find that branching enhances the strength of the contact minimum.

12 12 O

O

8 O 8

O

) 4 ) 4 z z ( ( F F

∆ 0 ∆ 0 β β 4 4 − Solvent separated minimum − 8 8 − Contact minimum − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm) z (nm)

Figure 4: Potential of mean force, β∆F (z) for the adsorption of different naphthenic acid ions at 300 K. β = 1/kBT , where T is the temperature and kB the Boltzmann constant. z is defined by the position of the head group from the average position of the first layer of calcium ions of the mineral. Inset shows the adsorbing acid.

To further probe the importance of the tail on adsorption (Fig. 4), we investigated the free energy of adsorption an acid with no tail and one with a shorter tail than the one considered

8 in Fig. 4 (left panel). The one with no tail is a hypothetical monovalent carbonate ion. The free energy profiles are shown in Figure 5. We observe that the adsorption free energy is affected by the length of the naphthenic acid tails. The acid with no tail cannot form an inner sphere complex, i.e. the free energy to expel the water molecule is significantly high.

For the shorter C2 C5 tail, the solvent-separated state is stable, but again the acid is unable − to form an inner-sphere complex.

O 12 12 O

O 8 8 O O

) 4 ) 4 z z ( ( F F

∆ 0 ∆ 0 β β 4 4 − − 8 8 − − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm) z (nm)

− − Figure 5: As in Figure 4. Left: O CO ; Right: C5 C2 CO . − 2 − − 2

Collectively, the results in Figs. 4 and 5 show that the longer the hydrocarbon tail the more favorable is the adsorption on to the surface. Likewise, increased branching of the hydrocarbon tail, for the same number of carbon atoms, also enhances adsorption.

Orientation of the acid molecule

To better understand the physical reason why increasing tail length and/or branching favors adsorption, we studied the orientation of the acid on the surface. With the carboxylate head forming an inner-sphere complex with the calcite, we obtained the PMF for the tail group to rotate and lie on the surface. Our results show that the tail prefers to lie on the water layer formed on the hydrated calcite surface, as opposed to extending into the aqueous phase (Fig. 6).

9 12

O 8 O

) 4 z (

F 0 ∆ β 4 − 8 − 12 − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm)

− Figure 6: PMF for the position of the tail of C5 C9 CO2 , when the head is adsorbed on the surface at 300 K. z is defined by the position− of the− center of the tail group from the average position of the first layer of calcium ions of the mineral.

These observations noted above strongly suggest that the interaction between the acid and the hydrated calcite (1014)¯ surface is akin to the interaction between non-polar groups in water. To confirm this, we study the temperature dependence of adsorption.

Effect of temperature on adsorption at low acid concentration

The interaction between non-polar groups in water is enhanced with increase in temperature. Experimentally, it is observed that the adsorption of an oleic acid on calcite increases with temperature13 at low acid concentration. To this end, we investigated the adsorption at a higher temperature of 343 K (Fig. 7). Similar to the potential of mean force at 300 K (Fig. 4), there are two energy wells at the same positions. It can be seen that the depth of the first energy well (inner sphere complex) changes from around 5 kBT at 300 K to around 7.5 kBT at 343 K while that of the second energy well (outer sphere complex) remains relatively unchanged. Thus at the elevated temperature the inner sphere complexation is greatly favored. Our results show that, consistent with experiments,13 increasing temperature indeed enhances the adsorption at low carboxylic acid concentration. We next consider this observation in greater detail.

10 12 O

8 O

) 4 z ( F

∆ 0 β 4 − 8 − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm)

Figure 7: PMF of adsorption between the C5 C9 acid and calcite at 343 K. Comparing with Figure 4 shows that the inner-shell complexation− − is favored at the higher temperature.

Adsorption driving force

Young et al.13 attribute the observed endothermic adsorption phenomenon to chemisorption and it was speculated that this “chemisorption” is related to the entropy of the system. But no direct evidence was provided by them. To test this hypothesis, we decoupled the free energy into its entropic and enthalpic contributions. To this end, we approximate the entropy by the following two point formula,34

∆F (z, T + ∆T ) ∆F (z, T ) S(z) = − , (1) − ∆T

where S is the entropy, F is the Helmholtz free energy obtained from umbrella sampling, and T is absolute temperature. In the present calculation, T is chosen to be 300 K and ∆T is 10 K. The enthalpic contribution to the PMF, ∆H(z), is then given by

∆H(z) = ∆F (z) + T ∆S(z) . (2)

We find that the enthalpic contribution to adsorption is positive, disfavoring adsorption (Fig. 8). However, the entropic contribution to adsorption is negative, favoring adsorption.

11 Thus, adsorption is indeed entropically driven, consistent with the observations on the oleic acid system.13

100 75 ∆H 50 25 0 25 (kcal/mol) − 50 − T ∆S 75 − − 100 − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm)

Figure 8: Entropic ( T ∆S) and enthalpic (∆H) contributions to the free energy of adsorp- tion (∆F ) at 298 K.−

Free energy of adsorption of carbonate ion

Carbonate ions are potential determining ions for calcite,35 and have been used to desorb carboxylic acids by altering their concentration.11,36 To this end, it proves interesting to

2− compare the free energy of adsorption between CO2 and naphthenic acids. Figure 9 shows the potential of mean force for the adsorption of carbonate to calcite. The contact minimum occurs at 5 kBT and the solvent-separated minimum at 7.3 kBT , emphasizing that the − − adsorption of carbonate ion is energetically more favorable than all the acids considered here, except the branched naphthenic acid. This suggests that carbonate ions may not be effective in displacing naphthenic acids with heavier tails or asphaltene molecules from the calcite surface.

12 12 O

O 8 O

) 4 z ( F

∆ 0 β 4 − 8 − 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 z (nm)

2− Figure 9: PMF of adsorption between the carbonate ion CO2 and calcite at 300 K.

Discussions

It is clear that the structured water layer on calcite impacts the wettability of the surface. Across the different naphthenic acid structures that we studied, we find that all the naph- thenic acids are capable of adsorbing on to calcite in the solvent-separate configuration. But a longer or bulkier hydrocarbon tail is necessary to form an inner-sphere, contact configu- ration. In these cases, we find that the tail lies on the adsorbed water-layer on the calcite surface. In effect, the favorable adsorption of the tail compensates for the need to overcome the energy barrier required to expel water to form an inner-sphere, contact configuration. It is also observed that the solvent separated energy minimum is relatively unchanged for all structures, but deeper in the case of carbonate ion. This reflects the importance of elec- trostatics in the solvent separated adsorption. Interestingly, the tail does not prefer any particular orientation in this state. This further cements our observation of tail adsorption stabilizing the calcite-acid interactions at contact. While our simulations are for a dilute acid, we can consider its implications for the case with high concentrations of acids as well. For the dilute case, the effects are electrostatic in- teraction between the carboxylate head and mineral surface and the preference for the tail to adsorb onto the apolar water-layer. For higher concentrations, we expect tail-tail interactions

13 to become favorable. Indeed, this has been exploited to create polymerized organic films on calcite.9 In this situation, we expect the driving force for adsorption to be enthalpic, rather than entropic. In such as case, adsorption should decrease with increasing temperature. This has indeed been found in experiments with high concentrations of acids.7,10,13 The observations made in this work can impact the design of injection fluid for reservoirs. A dominant idea in smart water design is that a higher valence ion has the capability to replace a lower valence ion from the surface. As the adsorption minima of carbonate ion indicates, this is indeed true, given the dominant mechanism is governed by electrostatics. We believe that happens only when there is a higher concentration of the acid, or low molecular weight of the acid. But, at dilute limits, and heavier molecules with acidic groups, we suspect displacing lower valence ions using higher valence ions may not work.

Conclusions

For the adsorption of naphthenic acids on calcite (1014)¯ surface, a problem of significant interest in understanding the wettability of carbonate reservoirs, we find that the adsorp- tion is affected by the size of the acid tails and by temperature. Longer tail acids adsorb more strongly onto the calcite surface. Additionally, in the dilute limit, consistent with ex- periments, increasing the temperature increases adsorption. This adsorption process is also entropically driven. These findings lead to the surprising finding that the interaction between hydrated calcite and a fatty-acid is akin to that between two non-polar groups in liquid wa- ter. We believe this is due to favorable interactions between the structured water layer and the tail of the carboxylic acid molecule, and this can explain experimental observations of acid adsorption at low concentrations and potentially at high concentrations.

14 Acknowledgement

We gratefully acknowledge Robert A. Welch Foundation (grant C-1241) and Abu Dhabi National Oil Company (ADNOC) for financial support.

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