Abstract: At present, to solve the function of complex potentials in cross-sealed boundaries with an analytic method requires the condition that the boundary angle of the dip equals π/n (where n is a positive integer). To extend the application of n to any real number, performing conformal transformation followed by mirror imaging is proposed. Specifically, the idea is to mirror a sealed boundary of any angle of the tip in the original plane onto a target plane by performing conformal transformation, thereby enabling the angle of the tip of the sealed boundary after mirroring to satisfy the condition that n is a positive integer. According to the property that the values of the complex potential and current of the point source (convergence) of a point in the original plane remain unchanged after conformal transformation, the complex-potential function of the corresponding point in the target plane of the point in the original plane is solved, and the resulting value is the value of the complex-potential function of the point in the original plane. An equation for computing the flow velocity of any point in flow fields was also derived. The streamline distribution in flow fields was rendered graphically by employing the contours method. In addition, the shortage of flow fields computed with the analytic method was reviewed and, correspondingly, improvements were proposed. The field application results show that an area closer to the vertex of the boundary angle of the tip has a higher streamline density, lower flow velocity, and higher degree of oil saturation.

Key words: sealed boundary, cross fault, conformal transformation, mirror imaging, streamline