气体羽流注入曲轴对称多孔通道的演变
The evolution of a gas current injected into a curved axisymmetric porous channel
AI总结：
研究气体注入轴对称的高斯和抛物线形多孔通道中的水饱和通道，分析不同几何形状下气体/液体界面的演变机制，揭示浮力影响的动态过程及多孔通道中气体注入与浮力的时空竞争。
摘要：
我们研究了气体注入到具有高斯和抛物线形轴对称中心线的水饱和多孔通道中的问题，这些通道被理想化为穹形构造中的地下气体储存。利用通道的细长性，我们推导出气体/液体界面的演变方程，使用复合渐近近似方法，该方法能适应大通道坡度，并在小坡度情况下简化为描述弱弯曲通道扩散的方程。在高气体渗透率极限下，与平面通道不同，每种几何形状中浮力通过不同的机制影响动态。对于稳态注入的高斯通道，由于轴对称性导致的气体速度衰减，浮力可以持续影响流动。在抛物线形通道中，增加的通道坡度确保浮力最终影响流动，其时间尺度取决于注入速率和流体性质。抛物线形通道流动的渐近分析揭示出五个时间阶段，每个阶段有多个空间区域和不同的扩散速率，反映了注入和浮力的时空竞争。最初，气体薄层沿上边界扩散；通道坡度和薄膜的延伸生成静水压力梯度，该梯度增强直到浮力阻止上接触线并增厚薄膜。在薄膜下方，液体排水直到在浮力作用下界面变平。减少阶模型的解析解捕捉了每个阶段的界面演变和接触线运动，并通过全数值模拟验证。这些结果对地下氢气和二氧化碳储存有启示，其中水平界面垂直推进增强了安全性和储存效率。
英文摘要：
We investigate gas injection into axisymmetric water-saturated porous channels with Gaussian and parabolic profiles, as idealized models of underground gas storage in dome-shaped anticlines. Exploiting the slenderness of each channel, we derive an evolution equation for the gas/liquid interface using a composite asymptotic approximation that accommodates large channel slopes and has a simplified small-slope form describing spreading in weakly curved channels. In the high gas-mobility limit, in contrast with flat planar channels, buoyancy influences the dynamics through different mechanisms in each geometry. For gas injected steadily into a Gaussian channel, buoyancy can continually affect the flow due to the attenuation of the gas velocity caused by axisymmetry. In parabolic channels, the increasing channel slope ensures that buoyancy eventually influences the flow, at a timescale depending on injection rate and fluid properties. Asymptotic analysis of the parabolic-channel flow reveals five temporal regimes, each with multiple spatial regions and a distinct spreading rate, reflecting the evolving spatiotemporal competition between injection and buoyancy. Initially, a thin film of gas spreads along the upper boundary; the channel slope and elongation of the film then generate a hydrostatic pressure gradient, which strengthens until buoyancy arrests the upper contact line and thickens the film. Beneath the film, liquid then drains until the interface flattens under buoyancy. Analytical solutions of reduced-order models capture interface evolution and contact-line motion through each regime and are validated against full numerical simulations. These results have implications for subsurface hydrogen and CO$_2$ storage, where a horizontal interface that advances vertically enhances both safety and storage efficiency.
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