RESUMEN
Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.
RESUMEN
We discuss the application of Helfrich's surface torque density concept to microemulsion design and analysis from three different angles: (i) from the point of view of coarse-grained molecular simulations, using Dissipative Particle Dynamics, including charge interactions and added salt, (ii) using an approximate double-film model for the surface, and (iii) comparison with formulation approaches. The simulations use that the surface torque can be calculated unambiguously from the stress profile, provided the surface is tensionless. Very good agreement is found on predicting optimal salinity (or the absence of that) for a range of surfactants: dioctyl sodium sulfosuccinate, various twin-tailed sulfonates and sodium dodecyl sulfate. The simulations are very fast, on par with times for experiments, thus they could lead to a practical tool for discovery of more efficient surfactants, although much remains to be done with respect to other important variables: oil composition, surfactant mixtures, aggregation in solution, and so on. The microscopic model (second approach) is highly approximate: it is essentially based on two opposing swelling tendencies, that are both of osmotic nature. In accordance with the model, the tails are swollen by the oil and the charged head groups are confined in a salty layer in Donnan equilibrium with the salt solution. In this way, the surface interactions are purely entropic. The comparison of the film model with existing formulation approaches (third approach) covers the interfacial tension minimum, Winsor R theory, quantitative structure property relations (QSPR), hydrophilic-lipophilic deviation (HLD), HLD-net average curvature, and temperature coefficients. Using the surface torque analysis, we succeed in deriving in an ab initio way QSPR empirical coefficients that have been known for decades, but until now, have been obscure in origin.
