分形油藏径向渗流问题解的相似结构

Similar structure of solutions for radial flow of fractal reservoir

针对均质分形油藏,考察了井筒储集并引入有效井径,在井底定产量生产的条件下,建立了均质分形油藏考虑二次梯度影响的不稳定渗流数学模型。先对此模型作线性化处理,再作Laplace变换,得到了线性化后模型的Laplace空间精确解;并找出3种外边界(无穷大、定压、封闭)条件下解的相似结构,与数和图形的相似性统一起来,使得不同边界条件下解的表达式之间的关系更加清晰,找出了解式与渗流模型各参数之间的密切联系,为编制相应的试井分析应用软件提供了一个更便利的途径。

To the homogeneous fractal reservoir, the wellbore storage is examined and the effective well radius is introduced. An instability flow mathematical model is established in the case of the fixed production at well bottom. The model considers the impact of the quadratic gradient in hnmugeneous fractal reservoir. The model is processed linearly, further for Laplace transform, obtaining the exact solutions of linearized model in Laplace space. The similar structure of the solutions in the three kinds of outer boundary conditions （infinite boundary, constant pressure outer boundary, and closed boundary） is found out, making the relalionship between the expressions of the solution clearer. The close relationships between the solutions and model parameters are also found out, which can provide a more convenient way for programming the application software for well lest analysis.