分形球向流有效井径模型及其解的相似结构

Effective Wellhole Radius Model for Fractal Reservoir with Spherical Flow and Its Similar Structure of Solution

针对分形球向渗流油藏,将有效井径引入到内边界条件中,建立了以井底定产量生产、考虑二次梯度项的影响和三种外边界(无穷大、定压、封闭)条件下的新数学模型.对该模型先进行线性化,再利用Laplace变换,在Laplace空间中得到了线性化后模型的精确解.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.这项研究不仅完善了渗流规律,而且扩大了微分方程解的相似结构理在分形油藏领域中的应用,对试井分析软件的编制也具有重要意义.

In this paper, in order to solve the problems of fractal reservoir with spherical seepage flow, the ef- fective well radius is introduced into inner boundary condition of the reservoir model to build a new mathematics model, which takes three factors into account, including constant production, the influence of quadratic gradient term and three outer boundary conditions （infinite, constant pressure and closed）. This model first is linearized and then transformed by Laplace. After that the exact solutions of the linear model can be got in Laplace space. It is found that the exact solutions under three outer boundary conditions possess similar structures. The authors will make a further discussion in this thesis. This research not only perfects the seepage rule, but also expands the ap- plication of similar structure theory of differential equation＇ s solution in fractal reservoir, and also has a profound significance for developing well test analysis program.