Desorption of hydrocarbon chains by association with ionic and nonionic surfactants under flow as a mechanism for enhanced oil recovery

The need to extract oil from wells where it is embedded on the surfaces of rocks has led to the development of new and improved enhanced oil recovery techniques. One of those is the injection of surfactants with water vapor, which promotes desorption of oil that can then be extracted using pumps, as the surfactants encapsulate the oil in foams. However, the mechanisms that lead to the optimal desorption of oil and the best type of surfactants to carry out desorption are not well known yet, which warrants the need to carry out basic research on this topic. In this work, we report non equilibrium dissipative particle dynamics simulations of model surfactants and oil molecules adsorbed on surfaces, with the purpose of studying the efficiency of the surfactants to desorb hydrocarbon chains, that are found adsorbed over flat surfaces. The model surfactants studied correspond to nonionic and cationic surfactants, and the hydrocarbon desorption is studied as a function of surfactant concentration under increasing Poiseuille flow. We obtain various hydrocarbon desorption isotherms for every model of surfactant proposed, under flow. Nonionic surfactants are found to be the most effective to desorb oil and the mechanisms that lead to this phenomenon are presented and discussed.

random force ( ), and dissipative force ( ); however, given the nature of this study, an additional force was introduced, namely, an effective wall force ( ): The conservative force between the ith particle and the jth particle determines the thermodynamics of the DPD system and is defined by a soft repulsion: where is the parameter expressing the maximum repulsion between ith and the jth beads, and rij = ri − rj, rij = |rij |, ̂i j = rij/rij is the unit vector denoting the direction from bead i to j.
rc is a cut-off radius, and it gives the extent of the interaction range between a pair of beads.
The other two forces in Eq. (S2) are the random force ( ), which is given as follows: = ( )̂ (S4) and the dissipative force ( ): In Eq. (S4), σ is the amplitude of the noise. is a random number between 0 and 1 and is subject to a uniform distribution for simplicity; it is statistically independent from the pair of beads. In Eq. (S5), vij = vi − vj is the difference between the velocity of the ith bead and the jth bead, is the friction coefficient. The and are weight functions; the combination of the dissipative and random forces leads to a thermostat that conserves the total momentum of the system. The magnitude of the dissipative and stochastic forces are related through the fluctuation-dissipation theorem [S1]: where rc is a cut-off distance. At interparticle distances larger than rc, all forces are equal to zero. This simple distance dependence of the forces, which is a good approximation to the one obtained by spatially averaging a van der Waals-type interaction, allows one to use relatively large integration time steps. The strengths of the dissipative and random forces are related in a way that keeps the temperature internally fixed, = 2 2 ; being Boltzmann's constant. The natural probability distribution function of the DPD model is that of the canonical ensemble, where N (the total particle number), V, and T are kept constant.
Surfactant molecules are modeled as linear chains composed of a hydrophilic head group and hydrophobic tail groups, while that hydrocarbon molecules are modeled by a neutral chain of the same type of beads. These groups are connected by a harmonic spring as follows The spring constant is set as = 100 and the equilibrium distance at 0 = 0.7 [S4]. For simplicity, we denote water bead (W), hydrocarbon bead (HC), head group (H), and tail group (T) of the surfactant with the shorthand notations W, HC, H and T, respectively.
Conservative interaction parameters for each one components are listed in Table S1. The interaction parameters have been obtained using the group contribution method (see, for Within the context of DPD there are now some works that have explored the properties of fluids confined by flat surfaces. One us (AGG) proposed an effective wall potential that acts on particles close to the ends of the simulation box through a linearly decaying force [S5], in the spirit of the other DPD forces, namely Equation (S8) represents the force that acts on the ith-particle in the ẑ direction (perpendicular to the plane where the surfaces are placed), , is the interaction strength of such force, and is a cutoff distance, beyond which the force becomes identically zero. A more sophisticated expression for the wall force is available (Solvation force induced by short range, exact dissipative particle dynamics effective surfaces on a simple fluid and on polymer brushes", A. Gama Goicochea and F. Alarcón, J. Chem. Phys. 134, 014703 (2011). DOI: 10.1063/1.3517869), but since it raises the computational time required to reach equilibrium without adding additional insight, it was not used here.
Since in this work ionic surfactants are studied, the electrostatic interactions within the framework of DPD must be considered. For this purpose a Slater-type charge density distribution with the form of is adopted, in which is the decay length of charge q [S6]. The integration of Eq. (S9) over the entire space yields the total charge q. Charged beads interact with other charged beads through the electrostatic interaction, properly adapted for distributions of charge, such as that shown in Eq. (S9). However, they also interact with each other and with neutral beads according to their DPD interactions. Ionic surfactants are also constructed using the beadspring model [S7], with the same parameters as those used for the nonionic surfactants.
The efficiency of the surfactants to desorb hydrocarbons was quantified by the desorption isotherm (Г), which represents the amount of hydrocarbon molecules adsorbed on the surface as a function of concentration of surfactant, whether it is ionic or nonionic. Such adsorption is obtained through the following expression.
where and ( ) are the length of the cell simulation and density profile in direction z respectively, and is bulk density, that is, the density of the unconfined system. parameters for butane, heptane, decane and dodecane are in the range of 13.9 (J/cm 3 ) 1/2 to 15.5 (J/cm 3 ) 1/2 [S5], which yield interaction parameters = 105.2, 103.8, 103.0, 102.8, respectively using the standard method [S2]. Therefore we opted for using an averaged value for all of those parameters, i. e. = 104, as seen in Table S1.
Three values of the external force constant necessary to create Poiseuille flow, Eq. (S11), were used, namely, = 0.0000, 0.0075 and 0.0150. For ionic surfactants all non-electrostatic parameters are kept equal to those of the nonionic surfactants; the difference is that the hydrophilic groups of the ionic surfactants are assigned a charge ( ℎ = 0.5 ). To keep the electroneutrality of the system, a corresponding number of counterions for every concentration of surfactant is added and the charge assigned to these counterions is = −1.0 . We employ Ewald sums to compute the electrostatic interactions, with the appropriate adaptations for confined systems using distributions of charge [S8]. The parameters of the Ewald sums are: the cutoff radius in the real space = 3. 5 using a = 0.9695, on the other hand in the reciprocal space we use the maximum vector = (5,5,5), and take = 0.929 for part of charge distributions. The long surfactants (ionic and nonionic) contain 5 beads more their shortchain counterparts.
Finally, the last case of study consists of a 50:50 mixture of nonionic and ionic long chain surfactants, for every one of concentrations of surfactant .
In all cases the simulations were run for 50 blocks of 10 5 time steps each, of which the first 10 blocks are used to reach equilibrium and the rest for the production phase; this is equivalent to a total simulation time of 24 s. The total number of particles in every simulation is 50000 DPD particles with a total density of the system = 3.0. All calculations reported in this work have been performed using the SIMES code, which is designed to study complex systems at the mesoscopic scale using graphics processors technology (GPUs) [S9]. Table S1. Conservative nonbonded, nonelectrostatic DPD interaction parameters in units of . Here W, HC, H, T represent water, hydrocarbon, the head and tail of the surfactant, respectively.