Accurate and efficient flow models for hydrocarbons are important in the development of enhanced geotechnical engineering for energy source recovery and carbon capture & storage in low-porosity, low-permeability rock formations. This work reports an atomistically-validated, mesoscopic model for heptane based on a many-body dissipative particle dynamics (mDPD) method. In this model, each heptane molecule is coarse-grained in one mDPD bead and the mDPD model parameters are calibrated with a rigorous approach using reference data, including experimental measurements and/or molecular dynamics (MD) simulations. Results show that this mDPD model accurately predicts the bulk pressure-density relation of heptane and surface tension. Notice that our approach can be used to calibrate the mDPD model for other hydrocarbons as well, though heptane is chosen as a representative source fluid for its abundance in source rocks. Further, our timing test indicates that the mDPD model is three orders of magnitude faster than its MD counterpart for simulations of bulk heptane in equivalent volumes. Overall, this work serves as a key prerequisite for the development of accurate and efficient mesoscale models for the flow of hydrocarbons confined in mesoporous rock formations.
A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.
Waterflooding is one of the geotechniques used to recover fuel sources from nanoporous geological formations. The scientific understanding of the process that involves the multiphase flow of nanoconfined fluids, however, has lagged, mainly due to the complex nanopore geometries and chemical compositions. To enable the benchmarked flow of nanoconfined fluids, architected geomaterials, such as synthesized mesoporous silica with tunable pore shapes and surface chemical properties, are used for designing and conducting experiments and simulations. This work uses a modified many-body dissipative particle dynamics (mDPD) model with accurately calibrated parameters to perform parametric flow simulations for studying the influences of waterflooding-driven power, pore shape, surface roughness, and surface wettability on the multiphase flow in heptane-saturated silica nanochannels. Remarkably, up to an 80% reduction in the effective permeability is found for water-driven heptane flow in a baseline 4.5-nm-wide slit channel when compared with the Hagen-Poiseuille equation. In the 4.5-nm-wide channels with architected surface roughness, the flow rate is found to be either higher or lower than the baseline case, depending on the shape and size of cross sections. High wettability of the solid surface by water is essential for achieving a high recovery of heptane, regardless of surface roughness. When the solid surface is less wetting or nonwetting to water, the existence of an optimal waterflooding-driven power is found to allow for the highest possible recovery. A detailed analysis of the evolution of the transient water-heptane interface in those nanochannels is presented to elucidate the underlying mechanisms that impact or dictate the multiphase flow behaviors.
An implicit method for a reconstructed discontinuous Galerkin (RDG) method is presented to solve compressible flow problems on tetrahedron grids. The idea is to combine the accuracy of the RDG method and the efficiency of implicit methods to obtain a better numerical algorithm in computational fluid dynamics. A least-squares reconstruction method is presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via an in-cell reconstruction process. The devised in-cell reconstruction is able to augment the accuracy of the DG method by increasing the order of the underlying polynomial solution. A matrix-free GMRES (generalized minimum residual) algorithm with an LU-SGS (lower-upper symmetric Gauss- Seidel) preconditioner is presented to solve an approximate system of linear equations arising from the Newton linearization. The implicit method is used to compute a variety of three-dimensional problems on tetrahedron grids to assess its accuracy and robustness. The numerical experiments demonstrate that the implicit reconstructed discontinuous Galerkin method can obtain an overall speedup of more than two orders of magnitude for all test cases compared with multi-stage Runge-Kutta reconstructed DG methods. The numerical results also indicate that this implicit RDG(P1P2) method can deliver the desired third-order accuracy, while maintaining advantage in cost over the implicit DG(P2) method.
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