Density-Functional Theory Investigation of Barite Scale Inhibition Using Phosphonate and Carboxyl-Based Inhibitors.

Scale deposition is a critical issue in oil and gas exploration and production processes, causing significant blocking in tubing and consequently flow assurance and economic losses. Most studies addressing the scale formation have been limited on the experimental impact of different variables on scale formation. In this work, the inhibition of barite scale deposition was investigated by employing molecular simulations for three different scale inhibitors, namely, polyaspartic acid (PASP), nitrilotrimethylenephosphonate (NTMP), and dimethylenetriaminepenta(methylene-phosphonic acid) (DETPMP). Geometrical analyses were used to explore the performances of the inhibitors and visualize the outcomes. quantitative structure activity relationship parameters were also used to predict the activity of the inhibitors in the system. The order of the inhibitors is in agreement with the experiments with the following values for binding energies: -1.06, -0.17, and -2.33 eV for PASP, NTMP, and DETPMP, respectively. The results of this study indicated that the inhibition strength of the three inhibitors on barite scale formation can be sequenced as DETPMP > PASP > NTMP. Moreover, the ecological toxicity (eco-tox) properties were predicted, and the environmental impact of the different inhibitors was assessed. All inhibitors showed comparable eco-tox properties and predicted to be soluble in water. Molecular simulations proved to be an effective tool in the prediction of the performance and toxicity of barite scale inhibitors.

Introduction

Many challenges can have an impact on oil and gas exploration and production wells including scale formation. A scale is produced by the accumulation of different minerals at the subsurface (i.e., near the surface but not exposed) of the wells and tubes that may lead to clogging in the wellbore, production tubing, and downhole tubulars. Scale formation leads to financial losses, which prompts great interest from the oil and gas industry and the research community to address its causes and associated impacts.

The understanding of scale formation mechanisms and the identification of the different scale formation are pivotal for the control of such occurrence.[1] It is reported that scales can deposit in many forms and in different locations in the well; for example, iron sulfide can deposit near the wellbore region, downhole, and topside tubes of the well, in addition to the sides of the reservoir.[2] Different wells may have scales that are different in composition, severity, and depth. For example, at around 2 km on the downhole tubing, the scale starts to be noticeable, and the severity increases with the depth.[3] The main factors that affect scale formation are temperature, pH, operating pressure, flow velocity, permeation rate, salt content, and the presence of other metal ions in the system.[4] From a thermodynamic point of view, precipitation becomes feasible when the solution is supersaturated; that is, ion concentration in solution is higher than its saturation limit. The severity of scale is impacted by the kinetics of precipitation.[5] Many studies were conducted to evaluate scale types in the oil and gas industry.[6,7] In general, scales are composed of sulfate, phosphates, carbonates, and other salt forms, such as alumina silicates.[8] Other common scale types include different forms of iron sulfides (pyrite, greigite, and marcasite) and ferric compounds depending on reservoir conditions.[3] However, the most common types detected are barite, calcite CaCO3, gypsum CaSO4·2H2O, and dolomite CaMg(CO3)2. Different groups of researchers have studied the iron sulfide scale formation using both theoretical and experimental techniques. Our research group has earlier investigated iron sulfide scale removal by using different molecular simulation techniques.[9−12]

The source of barite in oil and gas wells is typically related to the drilling fluids, and barite scales are one of the toughest scale types to be handled.[13] A study to explain the effect of pH on the dissolution of iron sulfide scales by using tetrakis(hydroxymethyl)phosphonium sulfate was performed,[9] and the effect of pH on barite scale inhibition is studied.[14,15] Another computational work addressed the effect of pH on acidic and basic chelating agents used in the removal of iron sulfide scales. Changes in pH affect particularly the nucleation and growth rates of barite scale. A nanoscale study employing atomic Force Microscopy shows that barite nucleation and growth rates are encouraged clearly in the range of 9–12 pH at the alkaline region.[15] Moreover, pH is a critical variable for scale inhibition efficiency (IE), and its effect for different scale inhibitors such as dimethylenetriaminepenta(methylene-phosphonic acid) DETPMP was reported.[14] As most reservoirs have their pH conditions between 5 and 6.5, DETMPM is mildly affected by pH; however, its optimum pH is at 6.5.[14] It has been proven that lowering the pH is more significant than increasing the concentration of DETPMP when used as a scale inhibitor.[16] For nitrilotrimethylenephosphonate (NTMP), an optimum pH of 8 would help in barite scale inhibition according to the work of Jones et al.;[17] upon increasing the pH to 12, it led to inhibition loss, while for polyaspartic acid (PASP), an optimum pH of about 5 makes it effective as a barite scale inhibitor.[18] An active formulation for the removal of barite scale by using chelating agents and catalysts is studied,[19] and the optimum concentrations for chelating agents and catalysts to dissolve barite scale are obtained.

Experimental evaluation of the performance of many potential inhibitors is costly and lengthy. Researchers opt to conduct theoretical and modeling studies to help understand the governing mechanisms of such inhibition and help verify the experimental data. In this study, the theoretical tools are employed to predict the ability of three commercial chemicals to inhibit the formation of barite scale under typical field conditions. Herein, we study three compounds, PASP, NTMP, and DETPMP, which are classical inhibitors used to evaluate the performance of scale inhibitors over a wide range of scale types, including barite scales.[20−22] The outcomes of the theoretical calculations on the inhibition performance of the three compounds are tested against the reported experimental data. These molecular simulations are expected to help with the screening and development of new green scale inhibitors.

Results and Discussion

The molecular structure of each inhibitor was built and then optimized; the barite surface was simulated and optimized separately. After that, each optimized inhibitor was introduced into the optimized barite surface to study the interactions between the inhibitor molecules and the scale surface. Figure shows the optimized three-dimensional (3-D) structures for the inhibitors used in this study.

Figure 1

Optimized 3-D structures for the inhibitors: (A) PASP, (B) NTMP, and (C) DETPMP.

Adsorption Energy Calculation

After building and optimizing the system of inhibitors and the barite (BaSO4) scale, the adsorption energy was calculated to evaluate the performance of the barite scale inhibitors’ efficiency. The adsorption energy between the barite surface and the scale inhibitor molecules can be expressed aswhere E(surf+inhib) is the energy of the system with the inhibitor, Esurf is the optimized barite surface energy, which was fixed for all inhibitors because the same surface was used for the different inhibitors, and Einhibitor is the energy of the optimized inhibitor alone. The values for Einhib for each inhibitor was obtained directly from the output data from the VASP simulation.

After optimizing the system (Figure ), eq was used to calculate the interaction energies for the three inhibitors; the results are summarized in Table .

Figure 2

Optimized structures of the barite surface slab with (A) PASP, (B) NTMP, and (C) DETPMP. (D–F) Their corresponding orientations from top view.

Table 1

Interaction Energies between the Three Inhibitors and the Barite Scale Surface

inhibitor	E(surf+inhib) (eV)	Esurf (eV)	Einhib (eV)	ΔEads (eV)
PASP	–2731.367	–2545.382	–184.927	–1.06
NTMP	–2712.668	–2545.382	–167.111	–0.17
DETPMP	–2903.677	–2545.382	–355.964	–2.33

The predicted interaction energies are all negative, indicating the favorable interaction between the barite surface and the scale inhibitor. The performance of the three inhibitors used in this study can be classified as DETPMP > PASP > NTMP. Therefore, molecular simulations predicted DETPMP to be more efficient in attracting the scale molecules compared to the other two inhibitors.

Geometrical Analysis

Because of computational expenses and high number of atoms (438 atoms) on the system, this work utilizes a four-layer slab to conduct the calculation. Analysis of the geometry and 3-D figures of the optimized system can yield results and new findings of the bond types that are formed, number of bonds, and bond length between the surface and the scale inhibitors. Figure shows the optimized calculation of the studied systems. The shortest bond length was found in DETPMP (3.346 Å) among all the three inhibitors. However, this was not able to form a chemical bond, thereby indicating that the mode of adsorption is physisorption and not chemisorption. Nevertheless, it corroborates the adsorption energy and further confirms why DETMPM has the strongest adsorption among the three, which agrees with experimental observations.[23] The top view of the inhibitors on the barite scale indicates that DETPMP covers more surface area on the barite scale compared to the other two inhibitors, thereby contributing to why it has the highest adsorption energy among the three inhibitors.

Figure 3

Charge densities of Barite surface slab with (A) PASP, (B) NTMP, and (C) DETPMP.

Charge Analysis

To gain further insight into the mechanisms of interaction charge analysis was Bader charges[24,25] relative to the valence electrons for each inhibitor (PASP, NTMP, and DETPMP) before and after adsorption was computed. The charge densities of the three inhibitors are shown in Figure . However, the significant information is the charge difference before and after adsorption. For all the three inhibitors, the charge differences (Tables S1–S3) are insignificant, confirming that the mode of adsorption is physisorption. Nevertheless, it was observed that DETPMP had the largest charge difference, which correlates with that having the highest adsorption energy. These charge differences occur mostly on some of the phosphorus and oxygen atoms (Table S3), which suggest that the presence of these atoms in an inhibitor will aid adsorption on barite scale. A similar observation is noticed in the phosphorus atoms in NTMP but on a smaller scale compared to DETPMP as the former has fewer phosphorus atoms than the latter.

Quantitative Structure Activity Relationship Calculations

QSAR corresponds to the quantitative structure–activity relationship. This technique is used to predict the activity and reactivity of molecules on a system based on a set of equations and analyze the resulted behavior. There are theoretical parameters that can be used to indicate the behavior of the inhibitors. Some of these parameters are (A) electron affinity (calculated by A = −ELUMO), (ΔN) amount of electron transfer, (I) ionization potential (I = −EHOMO), (χ) electronegativity (calculated by ), and (η) global hardness (calculated by ).[26,27]EHOMO corresponds to the energies of the highest occupied molecular orbital and ELUMO corresponds to energies of the lowest unoccupied molecular orbital, and these two values can be obtained directly from the computational results. High EHOMO values indicate good electron donation, and ELUMO relates to the binding capability between the surface and the inhibitor employing electron-donating potential. If the difference between the values of EHOMO and EHOMO(ΔEL–H) is small, high adsorption will occur. Moreover, another critical parameter is calculated, which is the total negative charge (TNC); a high value of TNC indicates high adsorption of the inhibitor molecule on the metal surface.[28]Table summarizes the results of the calculated QSAR main parameters of the optimized system.

Table 2

QSAR Parameters of the Studied Inhibitors

compound	HOMO (eV)	LUMO (eV)	ΔEL–H (eV)	I (eV)	A (eV)	η (eV)	χ (eV)	TNC (e)
PASP	–6.995	–0.786	6.210	6.995	0.786	3.105	3.891	–1.857
NTMP	–6.317	–0.091	6.225	6.317	0.091	3.113	3.204	–2.750
DETPMP	–6.100	–0.014	6.086	6.100	0.014	3.043	3.057	–4.599

Moreover, it has to be noted that the lower the ionization potential (I), the higher the reactivity.[28] PASP has the highest ionization potential, while DETPMP has the lowest value, which accounts for the high reactivity of DETPMP and explains its highest binding affinity with barite as a low ionization potential correlates with high reactivity and vice versa. On the other hand, , inhibitors with high electronegativity (χ) have lower reactivity and thus lower IE. Applying the same principle here, compound DETPMP has the lowest electronegativity value and hence it has better IE compared to other inhibitors studied. Moreover, if the energy gap (ΔEL–H) value is small, it suggests high adsorption on the surface. Table highlights that the energy gap is the lowest for inhibitor DETPMP, and thus, it has the best adsorption potential and IE compared to PASP and NTMP on barite surface. In addition, TNC is another critical parameter that can describe the behavior of inhibitors in a system. Inhibitors with high TNC values can be considered having higher donation and adsorption electron properties with the metal surface, and these inhibitors will show better inhibition effects. In this study, inhibitor DETPMP shows the highest TNC, followed by NTMP and PASP. Thus, according to the different QSAR parameters, the order of IE for the studied inhibitors is DETPNP > NTMP > PASP.

Table 4

Properties of Scale Inhibitorsa

inhibitor	chemical name	formula	Mw (Da)	density (g/cm3)
PASP	polyaspartic acid	C8H12N2O7	248.2	1.555 ± 0.06
NTMP	Nitrilotrimethylenephosphonate	C3H12NO9P3	299.1	2.094 ± 0.06
DETPMP	Dimethylenetriaminepenta (methylene-phosphonic acid)	C9H28N3O15P5	573.2	1.945 ± 0.06

The density values are at standard conditions (297.15 K, and 1 atm).

Ecological Toxicity Predictions

To study the interaction of the inhibitors with the environment, the ecological toxicity (eco-tox) properties of the inhibitors were predicted to determine whether the studied inhibitors could be considered as environment-friendly molecules. The results of the predicted eco-tox properties are shown in Table . The three inhibitors show similar eco-tox properties. Moreover, all the inhibitors have been predicted to be safe with regard to Ames mutagenesis, biodegradation, crustacean aquatic toxicity, and fish aquatic toxicity. Looking at the carcinogenicity aspects, PASP is found to be safe, while NTMP and DETPMP are toxic. However, all the inhibitors are reported to be toxic and slightly toxic with respect to eye irritation, acute oral toxicity (class III), and honey bee toxicity. Nevertheless, for acute oral toxicity, all inhibitors are slightly toxic, but it is not a critical parameter because these inhibitors are not expected to be consumed orally. Moreover, for fish aquatic toxicity, all inhibitors were safe, which suggests that they would not raise problems even if they were used for offshore production operations.

Table 3

Predicted Eco-tox Properties of the Studied Inhibitors

		PASP	NTMP	DETPMP
S/N	category	probability (remark)	probability (remark)	probability (remark)
1	carcinogenicity	(safe) 0.76	(toxic) 0.63	(toxic) 0.63
2	eye irritation	(slightly toxic) 0.64	(toxic) 0.96	(toxic) 0.81
3	ames mutagenesis	(safe) 0.61	(safe) 0.76	(safe) 0.68
4	acute oral toxicity (class III)	(slightly toxic) 0.82	(slightly toxic) 0.67	(slightly toxic) 0.74
5	honey bee toxicity	(slightly dangerous) 0.53	(slightly toxic) 0.57	(slightly toxic) 0.57
6	biodegradation	(safe) 0.65	(safe) 0.68	(safe) 0.63
7	crustacean aquatic toxicity	(safe) 0.91	(safe) 0.87	(safe) 0.67
8	fish aquatic toxicity	(safe) 0.56	(safe) 0.92	(safe) 0.84
9	water solubility (log S)	(very soluble) −0.85	(very soluble) −0.20	(highly soluble) −1.01

For solubility in water, the three compounds show similar behavior ranging from very soluble to highly soluble. Moreover, water solubility of the inhibitors can be referred through the presence of hydroxyl OH groups in all the inhibitors, and as the number of OH groups increases, the solubility increases. DETPMP has the highest number of OH (hydroxyl) groups; hence, it has the highest water solubility compared to other inhibitors, and this was confirmed by the eco-tox predications in Table . The simulation predictions for solubility are compared to the reported properties in their product data sheet and they are in agreement that all the three inhibitors are soluble in water.

In addition, both the adsorption energy calculation and geometry analysis support the same conclusions. Furthermore, an experimental study has analyzed the mechanism of barium sulfate deposition inhibition for multiscale inhibitors.[23] This experimental study on barite scale inhibition showed that DETPMP inhibitor has a very high efficiency compared to other classical inhibitors such as phosphinopoly carboxylic acid and sulfonated poly(carboxylic acid), which supports the findings of this theoretical investigation.[23] DETPMP is a classical inhibitor that used a lot for scale inhibition, and it is experimentally proven that it has an excellent performance in inhibiting barite scale.[20,21,29] Moreover, the theoretical studies provide insights into why DETPMP has a superior performance compared to the other two inhibitors, PASP and NTMP. DETPMP has the highest adsorption energy; moreover, the optimized structure of the inhibitors on the barite scale slab shows that DETPMP has covered a large surface area on the scale compared to the other two inhibitors. Furthermore, the QSAR studies show that the structure of DETPMP contributes to its activity of being a good inhibitor with superior performance by having the lowest ionization energy, nucleophilicity, and electronegativity; the smallest band gap; and the highest TNC, all of which correlate with the characteristics of a compound that can serve as a good inhibitor.

Conclusions

Scale formation is a serious issue in oil and gas production wells, and it causes blocking flow, leading to production and economic losses. In this paper, the performance and eco-tox of three different barite scale inhibitors (PASP, NTMP, and DETPMP) have been evaluated using molecular simulation tools.

The binding energy calculations between the barite surface and the scale inhibitors have suggested the following order of inhibitor strength as DETPMP > PASP > NTMP.

Furthermore, the geometrical and charge analysis of the barite slab surface and scale inhibitors supported the same sequence of inhibition strength.

The investigation of QSAR parameters such as electronegativity, band gap, and TNC verified that DETPMP has the highest IE in comparison with other inhibitors. Besides, all inhibitors have shown similar eco-tox properties.

This study reveals the agreement of theoretical and experimental findings and indicates that molecular simulation tools can be used to screen and predict the performance of scale inhibitors.

Computational Details

In this work, scale inhibitors are theoretically studied using density functional theory (DFT) to understand the mechanisms of barite scale inhibition. The structures and properties of the three inhibitors (PASP, NTMP, and DETPMP) are shown in Figure and Table , respectively. The compounds selected for studying the inhibition effect of barite scale are conventional inhibitors that are widely used for barite scale inhibition investigations.[23,30,31] Three different commercial inhibitors were selected for the simulation study to evaluate and compare their performance. Table shows the main properties of the inhibitors used in this study. The density for inhibitors is obtained directly from the Advanced Chemistry Development ACD/Labs Chemsketch software.[32]

Figure 4

Structures of (a) PASP, (b) NTMP, and (c) DETPMP.

The Vienna Ab Initio Simulation Package (VASP) version 5.4.4. code was used for all calculations,[33] while periodic boundary conditions were applied for all the studied systems. The revised generalized gradient approximation of Perdew, Burke, and Ernzerhof was used for exchange–correlation energy for all elements. For the description of the ion–electron interactions, the projected augmented wave pseudopotentials were employed.[34,35] Because of the importance of dispersion forces in describing surfaces and interfaces, the semiempirical correction by Grimme (DFT + D3) was included.[36,37] The structure of barite was obtained from the materials project database[38] and cleaved at the 001 surface. The 001 surface is known to be the most stable barite surface.[31] Both the 001 and 210 surfaces have the lowest surface energies. The 001 surface is the most stable based on growth morphology while the 210 surface is the most stable based on equilibrium morphology[39] the former is the most commonly observed surface and hence used in this work.[31,40]

A supercell of 3 × 3 × 1 was created as the slab that consists of four layers (438 atoms) using a relaxed structure of barite (mp-3164) from the materials project database.[38,41] The choice of this number of layer was to compromise between the computational costs of running a system with a large number of atoms while having a system large enough to represent the bulk. The bottom layer was fixed to mimic the bulk. A vacuum region of 12 Å was placed above the slab. The final configuration of the bulk alongside the vacuum is 16.67 × 21.83 × 31.00 Å3. The surface area was large enough to accommodate the inhibitors studied. The DFT calculations were based on the Gamma-centered k-point because of the large number of atoms in the system while the plane wave cutoff energy was 520 eV. This value was chosen by adding a 30% to 400 eV, which had the highest cutoff energy among the pseudopotentials of the different elements of the system studied. For the adsorption calculations, the inhibitors were placed above the optimized slab surface of barite. The Quantum ATK virtual Nano lab[10,42] was used for building the models and visualization of results.

For the quantum chemical calculations of the optimized structures, which was used in deducing the QSAR, Gaussian 09[43] was employed, and the three inhibitors were calculated at the B3LYP level of theory using the deftzvp basis set. This level of theory and basis set have been used in previous studies and known to give reliable results.[11,44] All calculations were done in implicit solvent using the polarizable continuum model self-consistent reaction field.[45] There were no imaginary frequencies, ensuring that the molecules had reached a true minimum.

ADMETSAR 2.0 program[46,47] was employed to predict the eco-tox parameters of the studied inhibitors. This web tool uses a machine learning model which is based on more than 210,000 experimental data for about 100,000 compounds.