基于Schwarz Christoffel变换的曲流河地质建模方法

为了解决曲流河物性参数沿着河道方向多变问题，通过封闭多边形区域到矩形区域的Schwarz Christoffel变换基本原理，建立不规则带状封闭曲流河边界映射到规则矩形区域边界的数学模型。采用高斯雅克比积分方法和牛顿迭代法，完成了从曲流河边界到矩形区域边界映射数学模型的数值计算。根据映射边界参数，采用二维粒子群方法完成了平面井位映射数值计算。在地质模型的建立过程中，考虑了映射规则和缩放比例问题。最后以X砂岩油藏为例，选择了该区域中38口井，建立的映射前后的地质模型，并对物性参数进行了分析。通过分析对比，采用Schwarz Christoffel映射后建立的地质模型及分析的物性参数更加符合地质规律。

Study on Geological Modeling Method of Meandering River Based on Schwarz Christoffel Transformation

In order to solve the problem that the physical parameters of meandering river vary along the river direction. According to the basic principle of Schwarz Christoffel transformation from closed polygonal region to rectangular region, a mathematical model for mapping the boundary of irregular banded closed meandering river to the boundary of regular rectangular region is established. The Gauss Jacobian integral method and Newton iterative method are used to complete the numerical calculation of the mathematical model of mapping from meandering river boundary to rectangular region boundary. According to the mapping boundary parameters, the two-dimensional particle swarm optimization method is used to complete the numerical calculation of well location mapping. In the process of establishing the geological model, the mapping rules and scaling are considered. Finally, taking x sandstone reservoir as an example, 38 wells in this area are selected, the geological model before and after mapping is established, and the property parameters are analyzed. Through analysis and comparison, the geological model established by Schwarz Christoffel mapping and the analyzed property parameters are more in line with the geological rule.