关于油水两相渗流顺序求解格式稳定性的研究

Study on Stability of Sequential Scheme for Oil-water Two-phase Simulation in Porous Media

对不可压缩油水两相渗流模型的一种顺序求解格式数值振荡的原因进行了探究。针对不同物理量选取不同的显隐式处理对应着不同的顺序求解格式,而不同的顺序求解格式体现出差异性较大的稳定性表现。A.G.Spillette,J.W.Watts[1-2]等人提出在顺序求解格式饱和度的求解中使用固定的总渗流速,而非直接计算单相流速,能够允许采用更大的时间步长进行数值计算。尽管直接使用达西定律计算单相流速进行隐式求解的方式更为直观,然而其却在时间步长较大时,数值结果出现振荡。针对以上现象,相关研究并未进行深入的探究。通过理论和数值分析,对直接使用达西定律计算单相流速的顺序求解格式的稳定性进行了分析,指出其在计算过程中不满足通量守恒条件,从而导致了大时间步长下的求解失败,数值结果呈现振荡现象。基于此,对直接使用达西定律计算单相流速的顺序求解格式中饱和度的求解方式进行了一定的修正,数值验证表明修正后的格式在大时间步长下不再出现数值振荡。

The factors which account for the stability of sequential scheme used in incompressible two-phase model simulation are studied.Different choices of explicit and implicit schemes of different physical quantities result in various sequential schemes;and the stability of corresponding schemes vary greatly.A.G.Spillette,J.W.Watts proposed the way that using a fixed total velocity to calculate single-phase velocity instead of directly calculating it through Darcy’s law could allow a much larger time step for numerical simulation.Although it is more intuitive to use Darcy’s law to calculate single-phase velocity directly,we can get oscillations when the time step is large.However,there is no in-depth study on the cause of this phenomenon.Based on the theoretical and numerical experimental results,this paper compares the stability of two sequential schemes for incompressible oil-water two-phase model,and explores the reason for the oscillation of one of the methods under large time step.In addition,the method above is modified and numerical result shows that the modified scheme overcomes oscillations under large time step.