Article pubs.acs.org/jced
Density Functional Theoretical Study of the Interaction of Geminal Zwitterionic Liquids with Limestone, Regarding the Behavior of the Wettability Parameter Paper presented at the 18th Symposium on Thermophysical Properties, Boulder, CO, June 24 to 29, 2012. Ernesto López-Chávez,*,† Alberto García-Quiroz,† Rodrigo Muñoz-Vega,† Jorge I. Benítez-Puebla,† Luis S. Zamudio-Rivera,‡ José-Manuel Martínez-Magadán,§ Eduardo Buenrostro-González,‡ and Raúl Hernández-Altamirano‡ †
Universidad Autónoma de la Ciudad de México, CCyT, Av. Fray Servando Teresa de Mier #92, C.P. 06080, Col. Centro, México D.F., México Grupo de Química Aplicada a la Industria Petrolera, ‡Programa de Ingeniería Molecular and §Programa de Recuperación de Hidrocarburos, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, San Bartolo Atepehuacán, CP 07730, México D.F., México ABSTRACT: Zwitterionic liquids have a wide variety of applications in enhanced oil recovery (EOR). In particular, geminal zwitterionic substances have been used as wettability modifiers of limestone, dolomites, and sandstones at high temperatures and pressures. The understanding of the interaction mechanisms of such molecules with the limestone surface is an important step toward the comprehension of the modification in wettability. In the study here presented, the interaction energies of limestone with geminal zwitterionic liquids of the type bis-N-alkyl polyether were calculated within the framework of the density functional theory (DFT). With the use of the DMOL3 library of the Material Studio Software (a DFT-based computational code), we calculated the interaction energies of the bis-N-alkyl polyether liquids, asphaltene with the limestone rocks.
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injected fluids are used to modify the wettability of the reservoir rock.2,3 Zwitterionic liquid (ZL) molecules are considered among the surfactant molecular species used in EOR. The surface activity of asphaltenes (ASP) is crucial for establishing reservoir rock wettability, which impacts the EOR process. The key to a successful EOR formulation is to carefully select the components that provide ultralow interfacial tension (IFT) under reservoir conditions. Achieving ultralow IFT greatly reduces capillary forces that trap oil. The objective of this work is the theoretical study of the influence of a class of geminal zwitterionic liquid on interfacial tension or changes on wettability of the rock under reservoir conditions. The ZL molecule used in this study was designed by Zamudio-Rivera,4 while the asphaltene model was originally proposed by Buenrostro-González et al.5,6 Ab initio methods based on density functional theory (DFT) were used to calculate interaction energies of a rock-ASP-ZL system. The interaction energies explain the mechanism of oil production and change of rock wettability.
INTRODUCTION
Most production and hydrocarbon reserves in Mexico come from areas dominated by deposits of carbonate rocks. Naturally fractured reservoirs (NFR) are those showing lower recovery factors (RF) of hydrocarbons, because they exhibit low porosity, presence of fractures, solution cavities, and oil-wetting or intermediate-wetting (a condition when a solid does not have a marked preference for one fluid over the other). The application of enhanced oil recovery (EOR) methods will help to recover 10% to 20% more oil from the original place, which could seem small, but it is incredibly high for the actual oil industry in accordance with the current rates of recovery and current production.1 After exhausting the primary and secondary processes for the extraction of oil, EOR should be applied. There are several methods for EOR: for example, the use of chemical products such as polymers and surfactants, thermal (steam stimulation and combustion on site) methods, miscible (oil solvents) methods, microbial methods, electrical methods, vibrational methods, and horizontal drilling, among others. In NFR, oil recovery depends on the spontaneous imbibition of water to expel oil from the matrix into the fracture system, provided that the matrix blocks are water-wet. To enhance the spontaneous imbibition process in NFR, low concentrations of surfactants in © 2012 American Chemical Society
Received: June 29, 2012 Accepted: September 19, 2012 Published: November 9, 2012 3538
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Figure 1. Molecular structure of (a) limestone rock, (b) an asphaltene molecule, and (c) geminal zwitterionic liquid in a cell simulation.
Figure 2. Interaction between asphaltene with the ZL13, i.e., the formation of an ion−dipole pair, which has an energy of ΔEpair = −1066.5 kJ·mol−1.
Figure 3. Ion−dipole pair capture of another molecule of oil; this process has an energy of ΔEpair+oil = −342.3 kJ·mol−1.
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COMPUTATIONAL DETAILS
exchange and correlation energies; the local density approximation (LDA) assumes that the exchange and correlation energies are a function of the electron density at the point of evaluation only. LDA is good for studying systems with a slowly varying charge density and for most geometries; therefore LDA is appropriate for calculating the interaction energies of the ASP-ZL-limestone system. The DFT package utilized for this study was Dmol3 used through the MS Modeling Suite,9 and the functional is using a double numerical plus polarization basis set. All electrons were included in the calculations with a basis set cutoff of 0.4 nm. The calculations were realized using effective core potentials for core treatment, multipolar expansion hexadecapole, smearing 13 kJ·mol−1, and direct inversion in an iterative (DIIS) subspace which was used to speed up SCF convergence (DIIS size = 10). Preliminary, molecular structures of ASP, ZL and limestone were built, and optimization of geometries was applied using the DFT method before quantum calculations.
Ab initio calculations using the DFT approach with functional LDA-VWN and DN basis sets7 were performed on the ASP, ZL, and limestone rock structures. When choosing a basis set, we considered two aspects: they should have a behavior that agrees with the physics of the problem, and the chosen functions should make it easy to calculate all of the required integrals. The DN (double numerical) basis set is a minimal basis (MIN) plus a second set of valence atomic orbitals (AOs). For the case of ASP, ZL, limestone, and different interactions, where anions are present, the electronic density is more spread out over the molecules and solid, so that the linear combination of atomic orbitals is a good approximation to model this correctly. DFT has a relatively low computational cost, compared with other quantum mechanical approaches, which makes it an ideal method for calculating the interaction energies of many-atom systems such as ASP-ZL-limestone. However, the exchange and correlation energy functions are not known explicitly.8 Many approximations have been put forward to calculate the 3539
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Figure 4. Oil production, which involves the capture of a molecule of oil by the supramolecular complex formed in the second step and the subsequent release of a dimer of oil. This process involves a change in production energy ΔEproduction = −541.4 kJ·mol−1.
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RESULTS AND DISCUSSION The model used was constructed using models of asphaltene by Buenrostro-González et al.5,6 for oil from the Gulf Area in Mexico and the ZL model by Zamudio-Rivera.4 These were obtained using experimental data. The surface model of limestone is built considering physicochemical information reported in the literature.10 It is noteworthy that, in this work, we use an arbitrary pattern, since, with the experimental information obtained, we could have built other configurations consistent with experimental data, and even we could have built a smaller molecular model. In this work, we propose a first approach to model the system, which could explain, at the molecular level, some of the experimental results of enhanced recovery processes. In relation to geometry optimization and solvent effects, the effect of solvation was simulated using the dielectric constant of water and no water molecules themselves. However, this approach was adjusted so that, in our calculations, we have consistency with reality and not work with the system in a vacuum. Figures 1 through 4 were obtained and generated as part of the DFT optimization process of the model, and although several configurations are obtained, we choose one that corresponds to the first minimum of energy on the potential energy surface. The final total energy allowed us to calculate the different energies of interaction. Each atom in Figure 1 is identified using the color code following: red, oxygen; gray, carbon; white, hydrogen; blue, nitrogen; yellow, sulfur; violet, sodium; pale green, chlorine; green, calcium. Figure 1 shows the molecular structures used to model the system rock-ZL-ASP. This study was realized using limestone as rock; Figure 1a displays the supercell of molecular model of limestone. The rock surface that interacts with the asphaltene and zwitterionic molecules is (104), which is the most commonly exposed surface. As is known, limestone has a crystal structure of calcite (CaCO3) type, with a R-3C underlying space group.10 A primitive cell contains 10 atoms (two units of CaCO3) and consists of planes (111) alternating Ca atoms and groups carbonates. Calcium atoms are located at 0 and 1/2, along the direction (111), while carbonate groups lay at 1/4 and 3/4, along the said vector. Each group carbonate form an equilateral triangle on the plane (111) and carbonate groups of adjacent layers of carbonates are rotated π/3 radians apart. The supercell limestone parameters have lengths: a = 3.1 nm, b = 2.4 nm, c = 2.8 nm; and angles α = π/2 rad, β = π/2 rad, γ = π/2 rad. The study was realized creating a surface supercell from rhombohedral crystal structure of calcite. A surface supercell is obtained if, instead of defining the unit cell as the smallest possible repeat unit in the surface, a larger repeat unit is used. The range of supercell is defined in unit cells of
calcite. In this study, the supercell is formed by surface (104), three adjacent layers of CaCO3, and a vacuum slab. The region of vacuum is used for introducing asphaltene and/or ZL molecules in the cell. Then interaction between surface of calcite, ASP, and ZL molecules is possible. The size of supercell is dependent on the size of ASP and ZL molecules. The asphaltene model is based on studies realized by Buenrostro-González et al.5 from Mexican Petroleum Institute (MPI),5,6 and it is presented in Figure 1b. As seen therein, the asphaltene molecular model consists of structures of pyridine, thiophene, 2-methylphenol, benzene, cyclohexane, and 3methylnonane. The molecular structure of zwitterionic liquid is constituted by two hydrocarbon chains, a bridge and two polar groups of zwitterionic type. Zwitterionic liquids are compounds contained a cation and an anion in different atoms of the same molecule, making them electrically neutral and gives them the opportunity to behave as acids or bases (donor or acceptor) according to the characteristics of the environment in which they are found. That is, they behave as smart molecules that can be designed such that respond efficiently depending on the characteristics of one or more specific environments. Figure 1c shows the molecular structure of the zwitterionic liquid proposed by Zamudio-Rivera4 from the MPI, which was evaluated in this work. The mechanism by which the chemical product enhances oil recovery was investigated in first instance using a ZL with alkyl chains of 13 carbon atoms (ZL13) as a chemical model; some properties and applications of zwitterionic microgels have been given by Das et al.11 with the surface (104) of calcite as the contact surface of the rock with the oil and the chemical. The energetic results were obtained within of a medium solvated by water (see Table 1). The mechanism can be divided into two parts: the production of oil and changing the rock wettability. Oil production consists of three steps: the first step is the Table 1. Energy Valuesa Required for Each Process, obtained with Dmol3 of Material Studio 6.0, during Enhanced Oil Recovery and Calcite Wettability Change with Proposed Germinal Zwitterionic Liquid LZ13 energy/kJ·mol−1a ion−dipole pair (asphaltene plus a zwitterionic liquid) pair + oil (ion−dipole pair plus asphaltene) production (pair + oil plus asphaltene) adsorption (ion−dipole) desorption (asphaltene detachment of the rock) a
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−1066.5 −342.3 −541.4 −26 160.9 −27 227.4
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Figure 5. Wettability of the rock changes. Phenomenon 1: the chemical (ZL13) must be transported to the rock.
Figure 6. Detachment of the asphaltene from the chemical. The latter ZL13 is adhered to the calcite surface, so that, due the polar characteristics of the chemical product, the wettability of the rock will be now water-wet rather than oil-wet.
allowed evaluating ZL molecule as a chemical agent for EOR methods. In this study, the mechanism of EOR was simulated by means of two processes: the production of oil and changing the rock wettability. The oil production consists of three exothermic processes: interaction between asphaltene with the ZL, that is, the formation of an ion−dipole pair, where the system releases heat with a energy variation equal to ΔEpair = −1066.5 kJ·mol−1; the capture of another molecule of oil by ion−dipole pair, which has an energy variation of ΔEpair+oil = −342.3 kJ·mol−1; and the production of oil, which involves the capture of a molecule of oil by the oil-ZL-oil system and the subsequent release of a dimer of oil, with a change in energy production ΔEproduction = −541.4 kJ·mol−1. The process of changing of calcite wettability is carried out by two phenomena: oil-ZL is adheres to calcite rock, and then oil-ZL-rock is formed, which requires that system releases −26 160.9 kJ·mol−1 of energy; finally, oil is released from the oil-ZL-calcite system, so that −27 227.4 kJ·mol−1 is released in the process. These results confirm that, theoretically, ZL is a good chemical product for EOR.
interaction between asphaltene with the ZL13, that is, the formation of an ion−dipole pair, which has a formation energy of ΔEpair = −1066.5 kJ·mol−1 (Figure 2). The second step is the capture of another molecule of oil by ion−dipole pair; this process requires an energy of ΔEpair+oil = −342.3 kJ·mol−1 (Figure 3). The third step is the production of oil; it involves the capture of a molecule of oil by the supramolecular complex formed in the second step and the subsequent release of a dimer of oil,12 and this process involves a change in energy production ΔEproduction = −541.4 kJ·mol−1 (Figure 4). In the second part of the mechanism, that is, change in wettability of the rock,13 the chemical must be transported to the rock (first step, Figure 5), which is achieved through adhering asphaltene to ZL13 in the ion−dipole pair; then asphaltene helps ZL13 to pass through the oil phase that separates from the surface of the rock. The ion−dipole pair is adsorbed on the surface of calcite with an interaction energy of adsorption of the pair ΔEads.ion‑dipole = −26 160.9 kJ·mol−1. The second step is the detachment of the asphaltene from the chemical; the latter ZL13 is adhered to the calcite surface, so that, due the polar characteristics of the chemical product, the rock will be now water-wet rather than oil-wet (Figure 6). The detachment of asphaltene requires an energy ΔEdesorption = −27 227.4 kJ·mol−1. The interaction energies obtained are of the order than ones reported by Rezaei et al.;13 this ensures, in a sense, our results. In this work, water was used as solvent to simulate physical conditions of reservoir.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
This work was partially supported by CONACYT-SENERHIDROCARBROS under project 146735. We also acknowledge Sistema Nacional de Investigadores del Consejo Nacional de Ciencia y Tecnologiá (SNI-CONACYT), Instituto de Ciencia y Tecnologiá del Distrito Federal (ICyT-DF), under project PIUTE 10-32, and Instituto Mexicano del Petroleo (IMP), all located in Mexico City.
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CONCLUSIONS DFT calculations have been realized to obtain the energies of interaction of the system oil-ZL-calcite. These studies have 3541
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Notes
The authors declare no competing financial interest.
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REFERENCES
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