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A boundary integral technique for modelling two-phase flow in porous media.

机译：一种边界积分技术，用于模拟多孔介质中的两相流。

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In this dissertation, particular attention is directed towards the development of a computationally tractable numerical technique applicable to the initial invasion of a denser than water phase into an initially pristine aquifer. This work applies a novel boundary integral formulation to the flow of two incompressible fluids in a porous medium. The usual boundary element assumption of piston-like flow is relaxed to include the effects of variable saturation on saturation-dependent phase properties, such as relative permeabilities and capillary pressures. The proposed technique may be considered a multiple-front formulation; unlike previous multiple-front formulations, however, capillary pressure effects are accommodated. The formulation straightforwardly accommodates problems where dispersive effects are small or negligible; such problems cause traditional methods great difficulty.; The proposed boundary integral technique places the computational mesh on selected saturation contours. As capillary pressure is considered a function of saturation, capillary pressure gradients can be considered a function of the saturation gradients; the gradient of saturation is determined by a separate boundary integral interpolation step, where the region between each pair of saturation contours is considered separately. Once the saturation field (and thus capillary pressure field) is calculated, the pressure distribution is determined using a multiple zone boundary integral formulation of the total flow equation, in which an effective saturation is used between each pair of contours to determine the saturation-dependent properties. Finally, time-stepping is performed by updating the location of the contours, based on the fluxes calculated from the pressure distribution, using a locally one-dimensional front-moving algorithm.; As the method requires that the contours change position over time, various mesh maintenance and mesh movement algorithms are evaluated. Specific attention is directed to the mesh movement algorithms in the important special case of a piston-like flow. With these results in hand, the formulation is compared against various two-phase analytic solutions, and a finite element simulator. Based on these examples, it is concluded that the method provides a viable new approach to simulating the invasion of a separate fluid phase into an aquifer.
机译：在本文中，特别关注的是开发一种适用于计算的易于处理的数值技术，该技术可用于将比水相更密的水相初始入侵到原始的含水层中。这项工作将新颖的边界积分公式应用于两种不可压缩流体在多孔介质中的流动。放宽了活塞状流动的通常边界元素假设，以包括可变饱和度对饱和度相关的相属性（例如相对磁导率和毛细管压力）的影响。所提出的技术可以被认为是一种多方面的表述。但是，与以前的多前沿配方不同，可以承受毛细管压力的影响。该公式直接解决了分散效应很小或可忽略不计的问题。这些问题给传统方法带来很大困难。提出的边界积分技术将计算网格放置在选定的饱和轮廓上。由于毛细管压力被认为是饱和度的函数，因此毛细管压力梯度可以被认为是饱和度梯度的函数。饱和度的梯度由单独的边界积分插值步骤确定，其中分别考虑每对饱和度轮廓之间的区域。一旦计算出饱和度场（从而计算出毛细管压力场），就可以使用总流量方程的多区域边界积分公式确定压力分布，其中在每对轮廓之间使用有效饱和度来确定与饱和度有关的属性。最后，使用局部一维前移算法，根据从压力分布计算出的通量，通过更新轮廓的位置来执行时间步进。由于该方法要求轮廓随时间变化，因此需要评估各种网格维护和网格移动算法。在活塞状流的重要特殊情况下，应特别注意网格运动算法。有了这些结果，就可以将配方与各种两相分析解决方案和一个有限元模拟器进行比较。根据这些示例，可以得出结论，该方法提供了一种可行的新方法，可以模拟单独的流体相侵入含水层中。

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