分形均质球向流油藏的解的相似结构  

Similar structure of solutions for spherical flow homogeneous fractal oil pool

作　　者：盛翠翠[1] 李顺初[1] 郭丽洁[1] 

机构地区：[1]西华大学应用数学研究所,四川成都610039

出　　处：《兰州理工大学学报》2011年第6期136-139,共4页Journal of Lanzhou University of Technology

基　　金：国家科技重大专项项目(2008ZX50443-14)

摘　　要：针对考虑二次梯度项影响的分形均质球向流油藏,建立以井底定产量生产、考虑井筒储集和三种外边界(无穷大、定压、封闭)条件下的不稳定渗流的试井分析模型;对该模型先进行线性化,再利用Laplace变换,在Laplace空间中得到线性化后的模型的精确解;经全面和深入的分析,发现在三种外边界条件下的精确解之间具有相似结构,并作了进一步的讨论.这项研究,不仅扩展微分方程解的相似结构理论在油藏领域的运用,而且极大地方便试井分析软件的编制,对油藏渗流规律的理论研究也具有深远的意义.Aimed at the spherical flow homogeneous fractal oil pool with a quadratic gradient term, a well test analysis model was established for unsteady seepage flow in the condition of wellbottom fixed yield, existence of wellbore storage, and three kinds of outer boundary conditions （infinite boundary, constant pressure and closed boundary）. First this model was linearized and then the Laplace transform was used to get the accurate solution of the linearized model in Laplace space. It was found by complihensive and deep analysis that a similar structure existed among the exact solutions with the three kinds of outer boundary conditions. And a further discussion was conducted. In this research work not only the use of similar structure theory of differential equations was extended to the oil pool area but the preparation of well test analysis software was also greatly facilitated and the investigation of seepage theory of oil pool also ob- tained far-reaching significance.

关 键 词：分形均质油藏 球向流 二次梯度项 井筒储集 相似结构 核函数 

分 类 号：O29[理学—应用数学] TE3[理学—数学]