Energy Fuels 2011, 25, 562–567 Published on Web 12/13/2010
: DOI:10.1021/ef1012038
Dissipative Particle Dynamics (DPD) Study of Crude Oil-Water Emulsions in the Presence of a Functionalized Co-polymer† Fernando Alvarez,*,‡ E. A. Flores,‡ L. V. Castro,§ J. G. Hernandez,‡ A. L opez,‡ and ‡ F. Vazquez ‡
Programa de Ingenierı´a Molecular, Instituto Mexicano del Petr oleo, Eje Central L azaro C ardenas 152, 07730 Mexico City, Distrito Federal (DF), Mexico, and §Escuela Superior de Ingenierı´a Quı´mica e Industrias Extractivas (ESIQIE), Instituto Polit ecnico Nacional, Unidad Profesional Adolfo L opez Mateos Zacatenco Edificio 7, 07738 Mexico City, Distrito Federal (DF), Mexico Received September 6, 2010. Revised Manuscript Received November 23, 2010
This work presents a theoretical study of the effects of different molecular weights of a triblock co-polymer ethylene oxide/propylene oxide/ethylene oxide, bifunctionalized with ethalamine, on the coalescence of water drops imbibed in a crude oil environment. The polymer/crude oil/water (PCW) time evolution of the emulsion was simulated using the framework of the dissipative particle dynamics (DPD) technique. The bead-bead interactions of the molecular components were calculated using the correlation between the solubility parameter, χij, of the Flory-Huggins theory and the conservative force parameter, aij. The solubility parameter was obtained from atomic molecular models of prototype molecules of saturates, aromatics, resins, asphaltenes, and the triblock co-polymer, through the blend methodology. The dynamic evolution of coarse-grain mesomolecules was carried out in cells of 20 20 20 DPD unit length with periodic boundary conditions. The composition of the emulsion was chosen to be similar to a Mexican heavy crude oil: asphaltenes, 11.9%; resins, 11.8%; aromatics, 42.7%; saturates, 29.6%; polymer, 4%; and two water drops of 3 DPD length units in radius. Finally, a drastic change in the coalescence of water molecules is observed for a short co-polymer length with respect to long co-polymer lengths.
acids, fatty amines, glycols, alkylphenol products, and a large variety of polymers.3,4 The chemical demulsifiers most commonly used in the petroleum industry reach values of 20% water removal for low-molecular-weight surfactants.5 In contrast, the use of polymeric surfactants, including polyols, propylene oxide/ethylene oxide (PO/EO) co-polymers, and alkylphenol formaldehyde resins modified with PO/EO removed about 90% water.5 In the petroleum industry, the usual emulsions encountered are water droplets dispersed in the oil phase, although the reverse situation is also possible. The destabilization of water in crude oil emulsion involves a process of flocculation, followed by sedimentation of water droplets because of density differences, and finally coalescence of the individual water droplets. The role played by the demulsifiers is to destabilize emulsions by changing interfacial properties, such as elasticity and thickness of interfacial regions, surface tension, and mechanical strength, promoting the coalescence and flocculation of water droplets.6-10 Water droplets in crude oil
1. Introduction The world’s growing energy demand has boosted the production of more and more heavy and extra-heavy crude oils that, in some cases, are contaminated with water in the form of free water or emulsion during the well production. This wastewater must be broken to separate water from petroleum to prevent additional transportation volume and corrosion in the equipment. The removal of this emulsionated water in oil is first driven by a gravity process; however, the reduction of water content in heavy and extra-heavy crude oils is not a direct process because the stability of water drops with respect to the gravity force in the oil fluid. The treatment of petroleum wastewater is carried out mainly by mechanical, electric, and chemical methods. From these methods, the most common way of water removal is the use of external alternating-current or direct-current fields,1,2 which produce the coalescence of the water drops and the breaking of the water-in-oil emulsion. However, the effectiveness of the electric methods decreases when the viscosity and density of the petroleum are incremented. In the case of chemical demulsifiers, the variety goes from alcohols, fatty
(4) Xinru, X.; Yang, J.; Gao, J. Pet. Sci. Technol. 2006, 24, 673–688. (5) Wu, X. Energy Fuels 2003, 17, 179–190. (6) Zhang, L. Y.; Xu, Z. H.; Masliyah, J. H. Langmuir 2003, 19, 9730– 9741. (7) Sjoblom, J.; Johnsen, E. E.; Westvik, A.; Ese, M. H.; Djuve, J.; Auflem, I. H.; Kallevik, H. In Encyclopedic Handbook of Emulsion Technology; Sjoblom, J., Ed.; Marcel Dekker: New York, 2001; pp 595-619. (8) Urdahl, O.; Movik, A. E.; Sjoblom, J. Colloids Surf., A 1993, 74, 293–302. (9) Singh, B. P. Energy Sources 1994, 16, 377–385. (10) Kumar, K.; Nikolov, A. D.; Wasan, D. T. Ind. Eng. Chem. Res. 2001, 40, 3009–3014.
† Presented at the 11th International Conference on Petroleum Phase Behavior and Fouling. *To whom correspondence should be addressed. E-mail: falvarez@ imp.mx. (1) Bailes, P. J.; Larkai, S. K. L. Trans. Inst. Chem. Eng. 1981, 59, 229–237. (2) Waterman, L. C. Chem. Eng. Prog. 1965, 61, 51–57. (3) Taylor, G. N.; Mgla, R. Method of demulsifying water-in-oil emulsions. U.S. Patent 5,505,878, 1996.
r 2010 American Chemical Society
562
pubs.acs.org/EF
Energy Fuels 2011, 25, 562–567
: DOI:10.1021/ef1012038
Alvarez et al.
emulsions might be up to 100 μm in diameter, which is large compared to the common definition of the upper limit of colloidal size (1 μm),11 but coalescence begins on the nanometer scale, when surfactant molecules on the surfaces of two adjacent droplets come into contact with each other. However, experimental information in the nanometric scale of the coalescence mechanism of water drops in a crude oil environment is not provided in detail. The most accurate method of simulating the dynamics of an atomistic system is to integrate the equation of motion for all atoms in the system; this is the basis of the molecular dynamics (MD) simulation method. However, the MD method is limited to simulating the dynamics of a few thousand molecules over a few nanoseconds, transforming this technique into inadequate for the simulation of physical processes that occur on the microsecond (or longer) time scale. An alternative to the MD methodology is the dissipative particle dynamics (DPD).12,13 The advantage of DPD over conventional molecular MD relies on the fact that DPD is a coarsegrained technique that captures the gross features of mesoscopic portions of fluid. The microscopic details, which are computationally expensive and not even interesting, are averaged out in DPD. In a DPD simulation, the number of particles is significantly lower than a full atomistic representation and each particle represents the center of mass of a cluster of atoms. This technique has been successfully applied in a large variety of systems, including flow in porous media,14 colloidal suspensions,14,15 immiscible binary fluids,16 polymer mixtures,17-19 surfactant monolayers,20,21 lipid bilayers,22-24 micelles,25 vesicles,26 oil-water surfactant,27 and stability of crude oil emulsions.28 In this work, we focus on the interaction between a bifunctionalized EO/PO/EO co-polymer in an oil-water emulsion to discern the dynamical evolution of water drops at the early stages of water drop coalescence immersed in a crude oil environment based on the DPD technique.
2. Methodology 2.1. Equation of Motion in DPD. DPD is a mesoscale modeling method for simulating equilibrium and dynamical properties of fluids subjected to soft potentials and governed by predefined collision rules. In DPD, similar to MD, the motion of particles is calculated by Newton’s equation of motion; however, in DPD, groups of atoms are replaced by mesoscopic “bead” or “droplets” of fluid, named dissipative particles, which represent small regions of fluid material interacting via phenomenological forces.29-31 These dissipative particles interact with dissipative forces that depend upon the relative approaching velocity of the particles and with random forces that satisfy a fluctuationdissipation theorem.32,33 Newton’s third law is satisfied and the total momentum of the system is conserved, although energy is not.34 A more detailed model DPD description can be found elsewhere;35 however, in the Appendix, some general aspects of this technique are presented. 2.2. Course-Grain Description and DPD Parameters. Crude oils are a continuum of tens of thousands of different hydrocarbon molecules, but in a general scheme, crude oils can be separated in four main chemical groups based on polarity and solubility differences. The four fractions are saturates (S), aromatics (A), resins (R), and asphaltenes (A), commonly denoted as SARA fractions.36 Our first step in the polymer/water/crude oil (PWC) simulation is to select the minimum set of molecules to describe the different components and fractions in the PWC emulsion. Therefore, we have selected a set of 11 prototype molecules as the building blocks of the different molecular components in the PWC. The selection criterion of the prototype molecules was based on their chemical and structural characteristics and the ability of these molecules to emulate most of the miscibility characteristics of the larger molecules in the PWC system. Figure 1 shows the set of 11 prototype molecules selected in this work. The asphaltene and resin cores were chosen on the basis of the core models suggested by De Souza et al., which are the result of fitting analytical infrared spectroscopy data.37,38 These asphaltene cores are structurally formed by fusion of polycyclic aromatic and naphthenic units in a pericondensed configuration, whereas the resin core consists of 100% aromatic regions. On the other hand, 3,5-dimethyl-4-ethyloctane, benzo[a]pyrene, diethanolamine, and the monomers of propylene oxide and ethylene oxide were selected as components of the saturated, aromatic, and polymer molecules, respectively. There exists a debate between the island and archipelago molecular architectures of asphaltene.39-41 In the “archipelago” model, individual asphaltene monomers are comprised of polycyclic aromatic and naphthenic ring moieties, some with polar functional groups, connected to each other by aliphatic polymethylene chains that likely contain some sulfide and carbonyl functional groups, while in the “island or continent” model, the
(11) Schramm, L. L. Emulsions: Fundamentals and Applications in the Petroleum Industry; American Chemical Society (ACS): Washington, D.C., 1992. (12) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhys. Lett. 1992, 19, 155–160. (13) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423–4435. (14) Koelman, J. M. V. A.; Hoogerbrugge, P. J. Europhys. Lett. 1993, 21, 369–374. (15) Boek, E. S.; Coveney, P. V.; Lekkerkerker, H. N. W.; van der Schoot, P. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 1997, 55, 3124–3133. (16) (a) Coveney, P. V.; Novik, K. E. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 1996, 54, 5134–5141. (b) Coveney, P. V.; Novik, K. E. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 1997, 55, 4831. (17) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423–4435. (18) Groot, R. D.; Madden, T. J. J. Chem. Phys. 1998, 108, 8713–8724. (19) Wijmans, C. J.; Smit, B.; Groot, R. D. J. Chem. Phys. 2001, 114, 7644–7654. (20) Rekvig, L.; Kranenburg, M.; Vreede, J.; Hafskjold, B.; Smit, B. Langmuir 2003, 19, 8195–8205. (21) Rekvig, L.; Hafskjold, B.; Smit, B. J. Chem. Phys. 2004, 120, 4897–4905. (22) Groot, R. D.; Rabone, K. Biophys. J. 2001, 81, 725–736. (23) Shillcock, J. C.; Lipowsky, R. J. Phys. Chem. 2002, 117, 5048– 5061. (24) Kranenburg, M.; Venturoli, M.; Smit, B. J. Phys. Chem. B 2003, 107, 11491–11501. (25) Pool, R.; Bolhuis, P. G. Phys. Chem. Chem. Phys. 2006, 8, 941–948. (26) Laradji, M.; Sunil Kumar, P. B. Phys. Rev. Lett. 2004, 93, No. 198105. (27) Rekvig, L.; Frenkel, D. J. Chem. Phys. 2007, 127, 134701-1– 134701-11. (28) Zhang, S. F.; Sun, L. L.; Xu, J. B.; Wu, H.; Wen, H. Energy Fuels 2010, 24, 4312–4326.
(29) Espa~ nol, P.; Warren, P. Europhys. Lett. 1995, 30, 191–196. (30) Groot, R. D.; Warren, P. B. J. Chem. Phys. 1997, 107, 4423–4435. (31) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Europhys. Lett. 1992, 19, 155–160. (32) Coveney, P. V.; Espa~ nol, P. J. Phys. A 1997, 30, 779–784. (33) Marsh, C. A.; Yeomans, J. M. Europhys. Lett. 1997, 37, 511–516. (34) Marsh, C.; Backx, G.; Ernst, M. H. Europhys. Lett. 1997, 38, 411–415. (35) Moeendarbary, E.; Ng, T. Y.; Zangeneh, M. Int. J. Appl. Mech. Eng. 2009, 1, 737–763. (36) Speight, J. G. The Chemistry and Technology of Petroleum; Marcel Dekker: New York, 1999. (37) De Souza, W. F.; Kondo, T.; Sato, S.; Matsumura, A.; Saito, I. Proceedings of the 3rd International Symposium on Colloid Chemistry in Oil Production Asphaltene and Wax Deposition (ISCOP ’99); Huatulco, Mexico, Nov 14-17, 1999. (38) Carauta, A. N. M.; Seidl, P. R.; Chrisman, E. C. A. N.; Correia, J. C. G.; Menechini, P. O.; Silva, D. M.; Leal, K. Z.; Menezes, S. M. C.; de Souza, W. F.; Teixeira, M. A. G. Energy Fuels 2005, 19, 1245–1251. (39) Merdrignac, I.; Espinat, D. Oil Gas Sci. Technol. 2007, 62, 7–32. (40) Murgich, J. Mol. Simul. 2003, 29, 451–461. (41) Spiecker, P. M.; Gawrys, K. L.; Trail, C. B.; Kilpatrick, P. K. Colloids Surf., A 2003, 220, 9–27.
563
Energy Fuels 2011, 25, 562–567
: DOI:10.1021/ef1012038
Alvarez et al.
Figure 1. Molecular species used in the bead emulsion of the PWC emulsion.
asphaltene molecules are composed of aromatic and naphthenic cores with alkyl chains branching out.42-46 In our case, we follow the architecture proposed by De Souza et al. that corresponds to archipelago architecture;37 however, both architectures can be developed with this methodology. The aliphatic and core regions stand out over the rest of the asphaltene features; therefore, when this distribution is taken into account, we have proposed an asphaltene mesomolecule formed by beads through harmonic springs.47 Our bead asphaltene mesomolecule simplifies the core and aliphatic regions to only one bead for each core region and one bead for each aliphatic chain (Figure 2a). The H/C ratio of the molecular model associated with the asphaltene bead has a value of 1.05 that is in the range of experimental H/C ratios of Mayan crude oil reported in the literature: 1.69,48 0.85, 1.04, 0.8, 0.95,49 1.003, 1.000, 0.999,50 and 1.17.51 In a similar representation to the asphaltene mesoscale, our simulation of the resin mesomolecule was carried out by one mesomolecule particle with the solubility properties of the resin core interconnected with three aliphatic-like mesoparticles interconnected by harmonic
Figure 2. Coarse-grain representation of (a) asphaltene, (b) resin, (c) aromatic, and (d) saturated prototype molecules. The chemical qualities of the functional groups in the oil fractions were selected as criteria in the mesomolecule representation.
springs (Figure 2b). In the case of co-polymer, we chose a triblock model, whose structures follow the sequence ðFÞðEOÞN ðPOÞ2N ðEOÞN ðFÞ
ð5Þ
where PO, EO, and F are propylene oxide, ethylene oxide, and diethanolamine, respectively, and N = 5, 10, 20, and 40. The polymer mesoscale representation was carried out by a linear Gauss chain of EO-, PO-, and F-like mesoparticles interconnected with harmonic springs and following the sequence of eq 5. Oil components, such as aromatic molecules, were emulated by an aromatic core linked to a single aliphatic chain (Figure2c), whereas the saturated and water molecular fractions were directly represented by a single bead that emulates the whole molecular solubility properties (Figure 2d). Recently, Zhang et al. have developed DPD studies extending the bead representation of the core asphaltene region to a set of hexaparticle rings, keeping the rigidity of these aromatic rings to preserve a little bit more aspects of the core region.28 Because, in our case, we have simplified the asphaltene and resin core regions to a single bead, we cannot impose rigidity to this region. On the other hand, the bound connection rigidity between the asphaltene and resin core beads and their aliphatic connected beads was considered similar to the rigidity of the interconnection of the polymer beads. Therefore, the rigidity parameter c, associated with the strength of the string interaction between beads i and j, was kept constant, with a value of 4 for the string constant (in reduced units, kBT/rc2) in all of the connected beads in the system. Since the coarse bead model has been developed, the pair repulsion parameters, aij, between each pair were calculated. For this purpose, we use the link established by Groot and Warren between the aij DPD parameter and Flory-Huggins χij parameter for polymer solutions. According to this link, the
(42) Murgich, J. Mol. Simul. 2003, 29, 451–461. (43) Zhang, L. Q.; Greenfield, M. L. J. Chem. Phys. 2007, 127, No. 194502. (44) Mullins, O. C.; Betancourt, S. S.; Cribbs, M. E.; Dubost, F. X.; Creek, J. L.; Andrews, A. B.; Venkataramanan, L. Energy Fuels 2007, 21, 2785–2794. (45) Hortal, A. R.; Hurtado, P.; Martinez-Haya, B.; Mullins, O. C. Energy Fuels 2007, 21, 2863–2868. (46) Schneider, M. H.; Andrews, A. B.; Mitra-Kirtley, S.; Mullins, O. C. Energy Fuels 2007, 21, 2875–2882. (47) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: New York, 1998. (48) Ancheyta, J.; Betancourt, G.; Marroquı´ n, G.; Centeno, G.; Casta~ neda, L. C.; Alonso, F.; Mu~ noz, J. A.; G omez, Ma. T.; Rayo, P. Appl. Catal., A 2002, 233, 159–170. (49) Trejo, F.; Ancheyta, J. Ind. Eng. Chem. Res. 2007, 46, 7571–7579. (50) Trejo, F.; Ancheyta, J.; Centeno, G.; Marroquı´ n, G. Catal. Today 2005, 109, 178–184. (51) Rahmani, S.; McCaffrey, W. C.; Dettman, H. D.; Gray, M. R. Energy Fuels 2003, 17, 1048–1056.
564
Energy Fuels 2011, 25, 562–567
: DOI:10.1021/ef1012038
Alvarez et al.
Table 1. Bead Notation and Repulsion Strength Parameters Used in the DPD Simulations repulsion strength parameter, aij (kBT/rc) molecular prototype
bead name
A
B
C
D
E
N1
N2
N3
R1
PO
OE
aliphatic aromatic saturated diethanolamine water asphalene core 1 asphalene core 2 asphalene core 3 resin core 1 propylene oxide ethylene oxide
A B C D E N1 N2 N3 R1 PO EO
25 75 27 40 66 149 122 104 93 27 26
75 25 70 24 107 28 25 35 26 96 103
27 70 25 39 75 104 115 89 89 32 30
40 24 39 25 25 72 47 34 56 33 34
66 107 75 25 25 188 167 154 135 45 48
149 28 104 72 188 25 45 46 43 195 146
122 25 115 47 167 45 25 43 45 172 158
104 35 89 34 154 46 43 25 30 140 124
93 26 89 56 135 43 45 30 25 124 128
27 96 32 33 45 195 172 140 124 25 25
26 103 30 34 48 146 158 124 128 25 25
repulsion parameters between beads of the same type are calculated according to eq 6 for all of the bead types.17 aij ¼
75 kB T kB T ¼ 25 F rc rc
ð6Þ
In our case, the compressibility of fluid was chosen as F = 3rc-3, which is close to that of water; thus, aij = 25kBT. Additionally, we have chosen kBT = 1 in the same way as Hoogerbrugge and Koelman.31 The repulsion parameters, aij, between different bead types were obtained by the Goot et al.17 approximation given in eq 7 aij aii þ 3:27χij ð7Þ where the χij is the Flory-Huggins parameter, which was obtained in this work by the blends method52-55 calculated at 298 K. Table 1 shows the bead notation and the corresponding repulsion strength parameters aij for the different beads used in the construction of the mesomolecules. The symmetric character of this array is noted, and aii = 25 (in reduced units, kBT/rc) for all of the self-repulsion interactions. Finally, the interaction parameter scheme was completed, choosing the noise strength σij = 3 and the dissipation strength γij = 4.5, both in reduced units, kBT/rc. 2.3. PWC DPD Simulation. The effects of the polymer chain length in the emulsification PWC stability was simulated using periodic boundary condition cells of 20 20 20 DPD length units divided into two regions that correspond to the polymer/crude oil matrix (PCM), noted here as region I, and two water drops, noted here as region II. The polymer/crude oil section practically fills the entire cell with the exception of the two water drops, whose centers were located in the (0.33, 0.33, and 0.33) and (0.66, 0.66, and 0.66) fractional coordinates, with drop radii of 3 DPD length units (Figure 3a). The PCM emulsion fraction was chosen on the basis of SARA analysis of Mayan crude oil56 and minimal polymer concentration used in the demulsification process with the following composition for the crude oil: asphaltene, 11.9%; resin, 11.8%; aromatic, 42.7%; saturate, 29.6%; and polymer, 4%. This composition gives saturate/aromatic = 0.693 and asphaltene/resin = 1.008. Therefore, on the basis of the emulsion stability curves of ref 28, our formulation is in the limit between the stable and unstable emulsions. Four cells were built to analyze the co-polymer length effects in the emulsification, keeping the polymer/SARA/ water composition and changing the number of beads in the polymeric chain (F)(EO)N(PO)2N(EO)N(F), with N = 5, 10, 20, and 40. The initial configuration of the cells was constructed with a random distribution of the PCM mesomolecules in region I, whereas region II was completely filled with water-like beads. To relax the initial configuration, first DPD simulations were (52) (53) (54) 1027. (55) (56) 4437.
Figure 3. (a) Definition of cell regions I and II. Region I corresponds to the oil/polymer volume, whereas region II is linked to the water drops. (b) View of the initial and final configurations of the crude oil, polymer, and water for the co-polymer (F)(EO)40(PO)80(EO)40(F). (c) Polymer water configuration view of the initial and final configurations shown in panel b.
carried out, allowing for the free movement of beads in region I and keeping the water beads fixed in region II. Finally, the results of region I relaxations were used as input configuration in a second DPD simulation, allowing in this case for the movement of the whole system. In both region I relaxation and whole system dynamics, the simulations were carried out considering a NVT ensemble at 104, with Δt = 0.05 DPD time units.
3. Results and Discusion Figure 3b displays the initial and final configurations of the dynamic process for the case of (F)(EO)40(PO)80(EO)40(F). The first aspect to stand out is the localization of co-polymer in the oil/water after the relaxation of region I. The agglomeration of the co-polymer in the oil/water interface is independent of the co-polymer length; however, the way in which the co-polymer covers the water drop surface has polymer length dependence, observing the tendency of the larger the co-polymer length, the larger the agglomeration of the co-polymer water drop surface. An example of this agglomeration phenomenon is displayed in Figure 3b, where the first DPD relaxation, keeping the water drops fixed, gives the agglomeration of the polymeric mesomolecules in the region between the water drops. The second DPD simulation, where the whole system is allowed to move, shows similar agglomeration results but with a lower water drop
Tiller, A.; Gorrella, B. Polymer 1994, 35, 3251–3259. Sun, H. Macromolecules 1995, 28, 701–712. Kamide, K.; Matsuda, S.; Saito, M. Polym. J. 1985, 17, 1013– Blanco, M. J. Comput. Chem. 1991, 12, 237–247. Zhao, B.; Becerra, M.; Shaw, J. M. Energy Fuels 2009, 23, 4431–
565
Energy Fuels 2011, 25, 562–567
: DOI:10.1021/ef1012038
Alvarez et al.
Figure 4. View of the spatial final distribution of the different emulsion components on the simulation cell after the second DPD simulation, where the whole system was allowed to relax for (F)(EO)10(PO)20(EO)10(F): (a) total, (b) aromatic, (c) asphaltene, (d) co-polymer, (e) resin, and (f) saturate. In all of the cases, black balls denotes the final water drop.
covering (final configuration in Figure 3b). Similar results for the rest of the co-polymer lengths are displayed in Figure S1 of the Supporting Information. The spatial localization of the different oil fractions in the cell shows a homogeneous distribution with the presence of small asphaltene and resin agglomerations, which could be a sign of asphaltene aggregation (panels c and e of Figure 4). To quantify the asphaltene and resin clusters, we have carried out partial radial distribution functions (PRDFs) of asphaltene/X and resin/X, with X = asphaltene, resin, saturate, aromatic, polymer, and water (see Figure S2 of the Supporting Information). In all of the cases, the largest contributions comes from the asphatene/asphaltene and resin/resin for the asphaltene and resin cases, respectively. Therefore, the asphaltene beads are mainly surrounded by asphaltene beads, and resins are mainly surrounded resins. Both results imply the formation of small clusters of asphaltenes and resins. On the other hand, the saturated and aromatic fractions have a similar spatial homogeneous distribution, stabilizing the emulsion (panels b and d of Figure 4). This spatial distribution is
common to all of the co-polymer lengths and is practically invariant along the DPD simulation (see Figures S3-S5 of the Supporting Information). The limited presence of asphaltene stacking could be the result of the crude oil fraction composition or our simplified representation of the asphaltene cores; however, we are more interested in the water drop coalescence than in the oil stability being the topic out of the limits of this work. The more drastic change in the different DPD simulations is the coalescence of the water drop phenomenon, which is directly affected by the presence of the co-polymer in the emulsion. Figure 5 shows the coalescence state of water drops as a function of the polymer length and DPD unit times, observing large changes in the coalescence varying from polymer-stabilized water drop states for small polymeric chains to completely favorable states for large polymer chains. In particular, for the case of (F)(EO)5(PO)10(EO)5(F), a total stabilization of water drops completely inhibiting the coalescence process is observed (Figure 5b). The (F)(EO)10(PO)20(EO)10(F) co-polymer produces a delay on the coalescence 566
Energy Fuels 2011, 25, 562–567
: DOI:10.1021/ef1012038
Alvarez et al.
where fi is the force on bead i as a result of the interaction with the other beads. The force, fi, includes stochastic and nonstochastic pairwise bead interaction terms, generally denoted D R as conservative, FC ij , dissipative, Fij , random Fij , and spring FSij, forces. The conservative force uses a simple linear weight function, which describes a soft repulsion ( aij ð1 - rij Þ^rij if ðjrij j < 1Þ C ð2Þ Fij ¼ 0 if ðjrij j g1Þ where |rij| is the relative distance between the beads i and j, whereas the interbead unit vector is defined as ^rij = (ri - rj)/|rij|. Within the DPD approach, reduced units are usually adopted as being all of the properties expressed from rc, m, and kBT, where t is the time, m is the mass, rc is the bead size, k is Boltzmann’s constant, and T is the temperature. Therefore, in reduced units, 2 R 1/2 1/2 rij = rR ij /rc, t = t/(mrc /kBT) , vij = vij /(kBT/m) , and aij = R aij kBT/rc, where R denotes the real values. In what follows in this work, all of the units are going to be expressed in reduced form. The repulsion nature of the FC ij interaction is imposed through the conservative force parameter condition, aij = aji > 0. In this case, the cutoff radius of the interbead interaction was chosen as the reduced unit of length, i.e., at rc = 1, the bead-bead interactions vanish. The dissipative FD and random FR forces act between pairs of beads. In particular, FD is proportional to the velocity with which two beads approach each other.
Figure 5. Coalescence state of water drops as a function of the copolymer length and DPD time.
time with respect to the non-polymer system, acting as a water drop stabilizer (Figure 5c). In contrast, (F)(EO)20(PO)40(EO)20(F) and (F)(EO)40(PO)80(EO)40(F) co-polymers drastically decrease the coalescence time mainly because, in both cases, the polymeric chains are large enough to interconnect the water drops and work as a path for the water bead flux (panels d and e of Figure 5).
( FD ij
¼
4. Conclusion
(
Using a 3D DPD simulation method, we are able to address the coalescence of water drops in a crude oil/ polymer environment as a function of co-polymer chains. The PWC components were simulated using a coarsegrain description of each molecular species. The bead interaction parameters were obtained from saturated, asphaltene, resin, aromatic and co-polymer atomic molecular models by the blend technique. The four propylene oxide-ethylene-oxide-diethanolamine (PO-EO-F) triblock coarse-grain models, (F)(EO)N(PO)2N(EO)N(F), with N = 5, 10, 20, and 40, display a drastic change effect in the coalescence of water drops in the simulated crude oil environment. For N = 5, the coalescence is completely stopped by the presence of the polymer forming a film around the water doplets. For N = 10, the coalescence time is delayed with respect to the non-polymer system. In contrast, for N = 20 and 40, the co-polymer drastically speeds up the coalescence. Finally, if the polymeric chain is large enough to interconnect the water drops, then the polymer works as a route for the water bead migration between droplets.
FR ij
Let us consider a fluid, such as a set of interacting beads with uniform mass m, where the position and velocity of the ith bead are denoted by ri and vi, respectively, then the evolution of ri and vi over time are given by the classical equation of motion fi ¼ m
n X dvi D R S ¼ ðFC ij þ Fij þ Fij þ Fij Þ dt i6¼j
if ðjrij j < 1Þ
0
if ðjrij j g1Þ
- σij ωR ðrij Þζij Δt- 1=2^rij
if ðjrij j < 1Þ
0
if ðjrij j g1Þ
ð3Þ
ð4Þ
In eqs 3 and 4, γij and σij are symmetric and positive parameters; i.e., γij = γij > 0 and σij = σij > 0, both being terms associated with the friction and noise strength, respectively (both γij and σij are expressed in reduced units, kBT/rc). vij = vi - vj is the velocity difference between beads i and j. The weight expressions ωD and ωR are a function of the relative bead distance dependence, rij, and have a similar algebraic form to the conservative term, ωD(r) = (1 - rij/rc)2 for r < rc and ωR(r) = 1 - rij/rc. In the random force expression, the noise term ζij is a random number with zero mean and unit variance; i.e., Æζijæ = 0, Æζij2æ = 1, and Δt is the time step of the discretized Newtonian equations of motion (eq 1). Finally, if a mesomolecule contains more than one bead, there are additional bonded interactions essentially described by Hooke’s law, elastic strings, with the general form FSij = -c(rs - rij)^rij. In this expression, the parameter c is associated with the strength of the string interaction and is expressed in reduced units, kBT/rc2, and rs is the reduced equilibrium distance between beads i and j.
Appendix
dri ¼ vi dt
¼
- γij ωD ðrij Þð^rij vij Þ^rij
Supporting Information Available: Initial and final configurations of the polymer/water/crude oil emulsion for the copolymers (Figure S1), asphaltene radial distribution functions (ARDFs) and resin radial distribution functions (RRDFs) for the co-polymers (Figure S2), and view of spatial final distribution of the different emulsion components on the simulation cell after the second for (F)(EO)5(PO)10(EO)5(F) (Figure S3) and (F)(EO)20(PO)40(EO)20(F) (Figures S4 and S5). This material is available free of charge via the Internet at http://pubs.acs.org.
ð1Þ 567
