可互溶流體於Hele-Shaw Cell 下界面不穩定現象─注入及拉升流場

Abstract

Viscous fingering is an interfacial fluid flow instability that occurs when less viscous fluid displaces another more viscous one in a Hele-Shaw cell or porous media, leading to the formation of finger-like pattern at the interface of both fluids. The interfacial evolution of multiphase flows will severely impact on the quality of production and efficiency in a variety of practical application of industrial process. Most frequent example of this instability is that of oil recovery for which viscous fingering takes place when an aqueous solution displaces more viscous oil in underground reservoirs, leading to the formation of nontrivial fingerlike structure and reduce the efficiency of the displacement process. Another particularly interesting variation of the classic radial flow is the investigation of fingering instabilities in Hele-Shaw cells presenting variable gap spacing. This is also a very important issue in many industrial areas including adhesion, lubrication, and colloidal hydrodynamics. In this dissertation, we carried out the highly accurate simulation to investigate the interfacial evolution in two scenarios－radial injection-driven miscible flow and lifting radial Hele-Shaw flow, both with the monotonic and nonmonotonic viscosity profile. So, the thesis consists of two parts: Part 1 focus on radial injection-driven miscible flow in a Hele-Shaw cell and covers three major topics. To begin with, we perform numerical experiments in a wide range to study the dispersion relation on both the Peclet number and the parameters of the viscosity profile. A monotonic viscosity-concentration relation of exponential type (concave) by other scholars is assumed, and a linear and reverse (convex) monotonic viscosity profiles and nonmonotonic one are also discussed. Results of this study show that as the overall viscosity contrast held constant, nonmonotonic viscosity profile lead to a more stable flow than that of monotonic one, and there are no significant differences in different viscosity profiles. However, if the nonmonotonic viscosity profile crosses the convex monotonic viscosity profile, the nonmonotonic feature enhances the prominence of interfacial instability. Then, a great variety of morphological behaviors is systematically introduced. In general, the nonmonotonic feature enhances the prominence of interfacial instability. Formation of dual vortex pairs and “reverse fingering”, where the fingers spread farther in the backward than in the forward direction are observed, which are not present in monotonic viscosity profile. Finally, we have carried out a parameter study to understand the effects of nonmonotonicity on the stability of the injection flow. In part 2, discussions start with the investigation of the influence of lifting scenario and the perturbation set. Contrast to the injection-driven miscible flow in radial Hele-Shaw cells which leads to the formation of morphing flow phenomenon of finger tip-splitting and side-branch events are plentiful if the injection rate is constant with time. More complicated flow are present for time-dependent gap flow which results in different kinds of patterns, and leads to intricate morphologies if the cell’s gap width grows exponentially with time. Recent studies show that the growing of intricate patterns due to lifting can be ntrolled by properly adjusting the time-dependent gap width. Moreover, we found the exponential lifting case will cause the flow more unstable than the variant lifting situation. We also deduce higher Peclet number and viscous contrast (A in monotonic viscosity profile and μm in nonmonotonic one) demonstrate more vigorous fingering. The sensitivity of the system to changes in the initial conditions and perturbation set is also discussed. Next, the effects of four viscosity profiles as stated in part 1 have been investigated. Unlike injection flow,the stability of three monotonic viscosity profiles are always in the series of concave, linear and convex. However, as injection flow, if the nonmonotonic viscosity profile crosses the convex curve will enhances the prominence of interfacial instability. Finally, we have carried out a parameter study to understand the effects of nonmonotonicity viscosity profile on the stability of the lifting flow.