Numerical Investigation Of The Two-phase Displacement In The Hele-Shaw Cell And Porous Media

The two-phase displacement is present in many applications, such as oil recovery, thin-film coating, gas-assisted manufacture of plastic moulds and lung dynamics. The two-phase displacement often involves interfacial instabilities. Sometimes, the interfa-cial instabilities is adverse, for example, the viscous fingering during water flooding will reduce the oil recovery. So, the problem of two-phase displacement has long attracted the researchers and been studied intensively. In this thesis, the viscous fingering in Hele-Shaw cell and polymer flooding in heavy oil reservoir in porous media are numerically investigated. The main research work and innovation points include:(1) For the viscous fingering of the two Newtonian fluids displacement in the Hele-Shaw with laterally periodic variation of depth, it is found that the wavenumber n of the periodic variation of depth has substantial influence on the the finger patterns. For n=1, the depth variation causes the steady single finger to be a little narrower than that of the conventional Hele-Shaw cell. For n=2, four different finger patterns are captured, which are similar to the available experimental observations in a modified Hele-Shaw cell containing a partially centered step-like occlusion:the symmetric’double-tipped’ finger pattern, the asymmetric finger with one-side oscillation pattern, the asymmetric finger pattern and the localized finger pattern. It is found that new finger patterns appear as n further increases, among which two patterns with spatial oscillation along both sides of the finger are interesting, one is a symmetric oscillatory finger for n=3and the other is an asymmetric one for n=4. Further research shows that the oscillations on the sides of the finger is resulted from the sideways motion of the displaced fluid caused by the decrease of the transverse curvature when the interface is extending backward from the fingertip. The effect of amplitude A of depth variation, the width W of the cell and Ca number on the finger patterns and finger width are also investigated. Then, the effect of the periodic variation of depth along flow direction is studied. It shows that variation of depth along flow direction depth could suppress or accelerate the onset of viscous fingering.(2) For the non-Newtonian fluid as the displacing fluid in the Hele-Shaw cell, the linear stability analysis shows that when the shear rate of the flow in not too small, the introduction of the shear-thinning character to the displacing fluid increases the perturbation growth rate, the most unstable wavenumber and the cutoff wavenumber. For the fingers in the nonlinear stage, the numerical investigation shows that the fingers are more unstable and easily behave the tip-splitting, the pinch-off and the merging which makes the interface irregular. Further studies show that for shear-thinning fluid as the the displacing fluid, wider fingers are found and this is caused by the flow consistency index other than the flow behavior index. The shear-thinning fluid in the Hele-Shaw with laterally periodic variation of depth makes the fingering more intricate. As the displaced fluid, the shear-thinning character suppresses the oscillation on the side of fingers; as the displacing fluid, the finger patterns represent both the effect of the shear-thinning character and the variation of depth.(3) The numerical investigation of the polymer flooding in the heavy oil recovery in porous media shows that there exist an optimal concentration and an optimal slug size of the polymer solutions. The ’optimal’ here means, when the concentration or slug size is below the optimal value, the oil recovery increase rapidly with increasing concentration or slug size, however when the concentration or slug size is above the optimal value, the increasing concentration or slug size only induces little increases of oil recovery and using the higher concentration or bigger slug size is uneconomical. Further study shows that the optimal concentration and slug size increase with increasing oil viscosity; the optimal concentration and slug size increase with increasing permeability variation coefficient; the earlier to start polymer flooding, the lower the optimal concentration and the smaller the slug size; in the range we studied, the injection rate shows no effect on the optimal concentration and slug size.