Two-phase gravity currents resulting from the release of a fixed volume of fluid in a porous medium
Two-phase gravity currents resulting from the release of a fixed volume of fluid in a porous medium
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多孔介质中释放固定体积的流体而产生的两相重力流
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
J. Neufeld
中科院分区：
文献类型：
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作者：
M. J. Golding;H. Huppert;J. Neufeld
我们考虑在充满不同密度的第二种不混溶流体的多孔介质中瞬时释放有限体积的流体。由于电流消退时流体的残留捕获以及电流前进和后退区域之间表面张力的不同影响，由此产生的两相重力流表现出丰富的行为。我们为这种电流的演化开发了一个框架，特别关注残余捕获和初始饱和之间本构关系形式的大规模影响。电流内的孔隙尺度滞后由与毛细管压力和相对渗透率与饱和度相关的扫描曲线族来表示。在生成的垂直集成模型中，所有毛细管效应都包含在针对每个区域专门定义的饱和度和通量函数中。在长时间限制下，当电流高度及其饱和度较低时，饱和度和磁通函数可以通过数学上方便的幂律来近似。如果捕获模型在低饱和度下近似线性，则方程允许晚期重力流的传播速率和高度剖面的相似解。我们还对非线性 Land 俘获模型的控制偏微分方程进行数值求解，该模型常用于两相流研究。我们的研究表明，对于俘获关系，俘获与初始流体饱和度的比例随着初始饱和度的降低而增加并趋于一致（这两者都是兰德模型的属性），重力流减慢并最终停止。这种捕集行为具有重要的应用，例如污染物或储存的二氧化碳可能在地下移动的最终距离。
We consider the instantaneous release of a finite volume of fluid in a porous medium saturated with a second, immiscible fluid of different density. The resulting two-phase gravity current exhibits a rich array of behaviours due to both the residual trapping of fluid as the current recedes and the differing effects of surface tension between advancing and receding regions of the current. We develop a framework for the evolution of such a current with particular focus on the large-scale implications of the form of the constitutive relation between residual trapping and initial saturation. Pore-scale hysteresis within the current is represented by families of scanning curves relating capillary pressure and relative permeability to saturation. In the resulting vertically integrated model, all capillary effects are incorporated within specially defined saturation and flux functions specific to each region. In the long-time limit, when the height of the current and the saturations within it are low, the saturation and flux functions can be approximated by mathematically convenient power laws. If the trapping model is approximately linear at low saturations, the equations admit a similarity solution for the propagation rate and height profile of the late-time gravity current. We also solve the governing partial differential equation numerically for the nonlinear Land’s trapping model, which is commonly used in studies of two-phase flows. Our investigation suggests that for trapping relations for which the proportion of trapped to initial fluid saturation increases and tends to unity as the initial saturation decreases, both of which are properties of Land’s model, a gravity current slows and eventually stops. This trapping behaviour has important applications, for example to the ultimate distance contaminants or stored carbon dioxide may travel in the subsurface.