Stable hyperbolic singularities for three-phase flow models in oil reservoir simulation
Stable hyperbolic singularities for three-phase flow models in oil reservoir simulation
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油藏模拟中三相流模型的稳定双曲奇点
DOI：
10.1007/bf00047553
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Heloisa Bauzer Mederios
中科院分区：
文献类型：
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作者：
Heloisa Bauzer Mederios
本文研究了考虑重力作用的多孔介质中三相流的两个守恒律方程组的特征速度，在特征速度取复值的开放区域（椭圆区域），双曲性一般失效。这些区域的存在造成的困难，如多个解决方案，这表明一个建模问题，根据一些作者。我们研究的模型的双曲性取决于相对渗透率函数。在石油工程研究中，通常假定水和气体的渗透率仅取决于它们各自的饱和度，而油的相对渗透率则随气体和水的饱和度而变化。这样一个假设的石油相对渗透率一般导致椭圆区域。我们定义了一组三个曲线，围绕任何模型的椭圆区域。通过研究这些曲线，我们指出了一个程序来定位的奇异性，并证明，对于任何选择的重力和粘度参数等区域收缩的特征速度是真实的和平等的点，只要它是假设每个相对渗透率取决于其各自的饱和度。我们的结果，连同Trangenstein的一篇论文，导致的结论是，为了确保真实的波速，这样的假设是必要的和充分的引力效应时，考虑在三相模型。
We study the characteristic speeds of systems of two conservation laws representing three-phase flow in a porous medium with gravity taken into account.Generically hyperbolicity fails on open regions (elliptic regions) where the characteristic speeds assume complex values. The presence of such regions creates difficulties such as multiple solutions which indicate a modeling problem, according to some authors.The hyperbolicity of the models we study depends on the relative permeability functions. It is customary in oil engineering studies to suppose that the water and gas permeabilities depend only on their respective saturation, while the oil relative permeability changes with the gas and water saturations. Such a hypothesis on the oil relative permeability generically leads to elliptic regions.We define a set of three curves that surround elliptic regions of any model. By studying these curves, we indicate a procedure to locate the singularities and prove that for any choice of gravitational and viscosity parameters such regions shrinks to points where the characteristic speeds are real and equal, provided it is assumed that each relative permeability depends on its respective saturation only. Our results, together with a paper of Trangenstein, lead to the conclusion that in order to insure real wave speeds, such an assumption is necessary and sufficient when gravitational effects are considered in three-phase models.