46341-AC9
Direct Numerical Simulation of Microscale Rheology and Multiphase Flow in Porous Media
Multiphase fluid flows are encountered in a wide array of industrial operations in the petrochemical industry. Depending upon the process, the multiphase mixture may be a concentrated oil-water suspension, a liquid-liquid foam or even a three phase mixture of oil, gas and water. Multiphase fluid mixtures are also utilized in many manufacturing operations involving flow through pipelines, capillaries, packed beds and porous media. The macroscopic properties of multiphase fluid mixtures of greatest interest include the relative permeabilities (or transport rates) of the individual phases for flow through porous media and the effective rheological properties of the mixture for processing operations. On a macroscopic level, emulsions and foams exhibit a range of non- Newtonian rheological behavior including shear dependent viscosity, normal stresses, viscoelasticity and yield stresses. Theoretical predictions for these properties require analysis on the microscale viscous multiphase flows governed by the Stokes equations.
In this research program, we seek to execute large scale three dimensional hydrodynamic simulations with up to 500-1000 droplets to study highly concentrated emulsions and foams. A new computational approach is being implemented combining a spectral boundary integral method with the PME (particle mesh Ewald) approach. The research focuses on two distinct thrusts: (1) to characterize the rheology and phase behavior of the suspensions in linear shear flows and (2) to analyze the multiphase transport through three dimensional model porous media. For the rheology studies, the phenomena include (i) shear thinning/shear thickening behavior,(ii) disorder-order phase transitions, (iii) phase segregation in bidisperse suspensions,(iv) non-uniform shear fields leading to shear bands and wall slip. For the transport in porous media, attention will focus on the relative transport of the two phases and the effect of pore-constriction geometries on transport properties. Special efforts will focus on the effects of random disordered microstructures on phenomena such as pore blocking, and preferential flow behavior for individual phases.
In the past year, our efforts have focused on two complementary activities. The first has been to develop an asymptotic model based on suspensions of elastic spheres which may be used to characterize the behavior of emulsions with strong surface tension yielding low capillary numbers. Large scale simulations with this simplified model will allow rapid exploration of the phase transitions occurring in concentrated emulsions and provide comparisons for the more complex spectral boundary integral simulations. The comparison of these distinct simulations adds physical insight and computational validation. The primary challenge in this effort has been the development of an accurate low order discretization of the elastohydrodynamic interactions in the near contact region. The resolution of these contact interactions in the droplet approach stage proved straightforward, however the dynamics in the droplet withdrawal stage proved quite a bit more complex. In particular, a variety of distinct scenarios may arise (dimpling, puckering or smooth deformation) depending on the relative importance of the film drainage and surface deformation processes. Accurate resolution of the transitions among these different modes was quickly achieved using a fine resolution computational grid, but achieving similar accuracy with a coarse, low order model required significant effort.
The second focus of our efforts in the past year has been the refinement of the spectral discretization techniques and numerical quadrature approaches for surfaces in the presence of near contact. Robust computation in these extreme interactions lies at the heart of a successful resolution of droplet interactions in the limit of high volume fraction disperse phases. Significant progress has been made in this area, but the final optimum approach for near contact interactions is still being refined.
The support provided by the Petroleum Research Fund will assist in the successful implementation and dissemination of these new, innovative computational algorithms. This will provide a computational toolbox of great utility for both academic and industrial researchers. The support is of significant benefit to the principal investigator as it provides critical early support for a novel computational approach without which the final application to industrial problems could not be achieved. The support for the graduate research assistant is of significant educational benefit as it allows him to develop skills in the complementary areas of asymptotic analysis, large scale computation, physical modeling and statistical analysis of disordered systems.
