基于Schwarz-Christoffel变换的曲流河井位映射计算

张光生; 王玉风; 姬安召; 刘雪芬; 陈占军

doi:10.21656/1000-0887.400315

基于Schwarz-Christoffel变换的曲流河井位映射计算

doi: 10.21656/1000-0887.400315

陇东学院能源工程学院, 甘肃庆阳 745100

基金项目: 甘肃省高等学校科研项目（2017B-61）；甘肃省工业和信息化厅绿色低碳转型升级课题(GGLD-2019-060)

详细信息

作者简介:
张光生（1981—），男，讲师，硕士（通讯作者. E-mail: 24066932@qq.com）.

中图分类号: TE312
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出版历程
- 收稿日期: 2019-10-15
- 修回日期: 2019-11-07
- 刊出日期: 2020-07-01

Mapping Calculation of Meandering River Well Locations Based on the Schwarz-Christoffel Transform

School of Energy Engineering, Longdong University, Qingyang, Gansu 745100, P.R.China

摘要

摘要: 曲流河改道、改向使得沉积储层物性沿着河道延伸方向进行分布，常规地质统计学方法在储层参数预测时，依赖于变差函数的变程和方向.根据Schwarz-Christoffel变换基本原理，建立了多边形区域映射到矩形区域保形映射的数学模型，提出了映射数学模型的数值计算方法.在整个映射过程中，需要借助带状过渡区域.从多边形区域到带状过渡区域映射的计算过程中，采用二维粒子群优化（PSO）算法的基本原理，得到带状过渡区域的初始化点位.根据映射数学模型及边界映射结果，以带状过渡区域中的初始化点位为积分终点，以初始化点位距带状过渡区域边界的最近点为积分起点.采用Gauss-Jacobi积分方法得到多边形区域中的计算点位.以实际与计算点位的误差平方和作为目标函数，采用PSO算法得到带状过渡区域中的计算点位.在带状过渡区域映射到矩形区域过程中，根据带状过渡区域到矩形区域映射变换尺度的对应规则，提出了矩形区域中点位的初始化方法.采用Newton法对Jacobi椭圆函数进行求解得到矩形区域的映射点位.为了验证模型的可靠性，以鄂尔多斯盆地曲流河沉积的X砂岩油藏为例，选择了研究区域的38口直井进行分析，得出映射前后的井位保持了一定的几何相似性.因此通过Schwarz-Christoffel映射变换，可以将曲流河沿着河道方向映射到矩形的一个方向，从而为复杂曲流河沉积储层的地质建模变换到矩形区域进行研究提供了一定的理论基础.
- 曲流河 /
- SchwarzChristoffel变换 /
- 矩形区域 /
- 粒子群算法
Abstract: The diversion of a meandering river made the properties of sedimentary reservoir distribute along the direction of channel extension. The conventional geostatistics method depends on the range and direction of the variogram in the prediction of reservoir parameters. According to the basic principle of the Schwarz-Christoffel transform, the mathematical model for a polygon region boundary-to-rectangle region conformal mapping was established, and the numerical calculation method for the mapping mathematical model was proposed. In the whole mapping process, the strip transition region was needed. In the process of calculating the mapping from a polygonal region to a strip transition region, the 2D particle swarm optimization (PSO) algorithm was used to get the initialization points of the transition region. According to the mapping mathematical model and boundary mapping results, the initial points in the strip transition region were taken as the end points of integration, and the nearest points between the initial points and the boundary of the strip transition region were taken as the starting points of integration. The Gauss-Jacobi integration method was used to get the calculated points in the polygonal region. The square sum of errors between actual and calculated points was adopted as the objective function, and the optimized PSO algorithm was applied to obtain the calculated points in the strip transition region. With the corresponding rules of transformation scales from the strip transition region to the rectangular region, the initialization method for point positions in the rectangular area was proposed. With Newton’s method, the Jacobi elliptic function was solved for the mapping point positions in the rectangular area. To verify the model reliability, 38 wells of the depositional X sandstone reservoir along an Ordos Basin meandering river was taken as the example. The results show that, the well positions keep in a certain geometric similarity before and after the mapping. Therefore, through the Schwarz-Christoffel mapping transform, the meandering river can be mapped to a rectangular direction along the river direction, which provides a theoretical basis for the transformation of geological modeling of complex meandering river sedimentary reservoirs to rectangular regions.
- meandering river /
- Schwarz-Christoffel transform /
- rectangular region /
- particle swarm optimization

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