Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media
Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media
复制标题
地下多孔介质中不可压缩三相流模拟的改进 IMPES 方案
DOI：
10.3390/en14102757
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发表时间：
2021-05
期刊：
影响因子：
3.2
通讯作者：
Xingyu Zhu
中科院分区：
文献类型：
--
作者：
Runhong Liang;Xiaolin Fan;Xianbing Luo;Shuyu Sun;Xingyu Zhu
在这项工作中，提出了一种改进的隐式压力和显式饱和（IMPES）方案来求解耦合偏微分方程，以模拟地下多孔介质中的三相流。该方案是第一个针对三相流问题的 IMPES 算法，该算法对所有相都是局部质量保守的。该新颖方案的关键技术依赖于离散压力方程的新公式。与常规方案不同的是，本文的离散压力方程是通过将各相离散守恒方程相加得到的，从而保证了压力方程与三个饱和方程在离散层面的一致性。这种一致性很重要，但不幸的是在传统的 IMPES 方案中并不能满足这一点。在本文中，我们解决并修复了传统 IMPES 中这种不一致所带来的不良且众所周知的后果，即计算出的饱和度仅对于三相流中的两相是保守的，而不是对于所有三相。与标准IMPES方案相比，改进的IMPES方案具有以下优点：首先，局部和全局均保持了各相的质量守恒；其次，它对所有相位都是无偏的，即不需要选择参考相位；第三，迎风方案适用于所有相的饱和，而不是仅参考相的饱和；第四，由于分相守恒和无偏处理，数值稳定性大大提高。还进行了数值实验来证明改进的 IMPES 方案的强度。
In this work, an improved IMplicit Pressure and Explicit Saturation (IMPES) scheme is proposed to solve the coupled partial differential equations to simulate the three-phase flows in subsurface porous media. This scheme is the first IMPES algorithm for the three-phase flow problem that is locally mass conservative for all phases. The key technique of this novel scheme relies on a new formulation of the discrete pressure equation. Different from the conventional scheme, the discrete pressure equation in this work is obtained by adding together the discrete conservation equations of all phases, thus ensuring the consistency of the pressure equation with the three saturation equations at the discrete level. This consistency is important, but unfortunately it is not satisfied in the conventional IMPES schemes. In this paper, we address and fix an undesired and well-known consequence of this inconsistency in the conventional IMPES in that the computed saturations are conservative only for two phases in three-phase flows, but not for all three phases. Compared with the standard IMPES scheme, the improved IMPES scheme has the following advantages: firstly, the mass conservation of all the phases is preserved both locally and globally; secondly, it is unbiased toward all phases, i.e., no reference phases need to be chosen; thirdly, the upwind scheme is applied to the saturation of all phases instead of only the referenced phases; fourthly, numerical stability is greatly improved because of phase-wise conservation and unbiased treatment. Numerical experiments are also carried out to demonstrate the strength of the improved IMPES scheme.
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DOI：
10.1016/c2018-0-04535-1
发表时间：
1979
期刊：
--
影响因子：
--
作者：
K. Aziz;A. Settari
通讯作者：
K. Aziz;A. Settari
影响因子：
5.4
作者：
M. Starnoni;I. Berre;E. Keilegavlen;J. Nordbotten
通讯作者：
M. Starnoni;I. Berre;E. Keilegavlen;J. Nordbotten
DOI：
10.2118/978-g
发表时间：
1959-12
期刊：
Transactions of the AIME
影响因子：
--
作者：
J. Sheldon;W. T. Cardwell
通讯作者：
J. Sheldon;W. T. Cardwell
DOI：
10.2118/2116-pa
发表时间：
1970-02
期刊：
Journal of Petroleum Technology
影响因子：
--
作者：
H. L. Stone
通讯作者：
H. L. Stone
影响因子：
2.7
作者：
J. Lux;Y. Anguy
通讯作者：
J. Lux;Y. Anguy