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

ZHANG Guangsheng; WANG Yufeng; JI Anzhao; LIU Xuefen; CHEN Zhanjun

doi:10.21656/1000-0887.400315

Volume 41 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(7): 771-785

ZHANG Guangsheng, WANG Yufeng, JI Anzhao, LIU Xuefen, CHEN Zhanjun. Mapping Calculation of Meandering River Well Locations Based on the Schwarz-Christoffel Transform[J]. Applied Mathematics and Mechanics, 2020, 41(7): 771-785. doi: 10.21656/1000-0887.400315

Citation:

PDF( 1581 KB)

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

doi: 10.21656/1000-0887.400315

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

Received Date: 2019-10-15
Rev Recd Date: 2019-11-07
Publish Date: 2020-07-01

Abstract

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

FullText(HTML)

References(18)

References

[1]	单敬福, 张吉, 赵忠军, 等. 地下曲流河点坝砂体沉积演化过程分析: 以吉林油田杨大城子油层第23小层为例[J]. 石油学报, 2015,36(7): 809-819.(SHAN Jingfu, ZHANG Ji, ZHAO Zhongjun, et al. Analysis of sedimentary and evolution process for underground meandering river point bar: a case study from number 23 thin layer of Yangdachengzi oil reservoir in Jilin oilfield[J]. Acta Petrolei Sinica,2015,36(7): 809-819.(in Chinese))
[2]	范峥, 吴胜和, 岳大力, 等. 曲流河点坝内部构型的嵌入式建模方法研究[J]. 中国石油大学学报(自然科学版), 2012,36(3): 1-6.(FAN Zheng, WU Shenghe, YUE Dali, et al. Embedding modeling method for internal architecture of point bar sand body in meandering river reservoir[J]. Journal of China University of Petroleum(Edition of Natural Science),2012,36(3): 1-6.(in Chinese))
[3]	刘可可, 侯加根, 刘钰铭, 等. 多点地质统计学在点坝内部构型三维建模中的应用[J]. 石油与天然气地质, 2016,37(4): 577-583.(LIU Keke, HOU Jiagen, LIU Yuming, et al. Application of multiple-point geostatistics in 3D internal architecture modeling of point bar[J]. Oil and Gas Geology,2016,37(4): 577-583.(in Chinese))
[4]	白振强, 王清华, 杜庆龙, 等. 曲流河砂体三维构型地质建模及数值模拟研究[J]. 石油学报, 2009,30(6): 898-902, 907.(BAI Zhenqiang, WANG Qinghua, DU Qinglong, et al. Study on 3D architecture geology modeling and digital simulation in meandering reservoir[J]. Acta Petrolei Sinica,2009,30(6): 898-902, 907.(in Chinese))
[5]	邹拓, 吴淑艳, 陈晓智, 等. 曲流河点坝内部超精细建模研究: 以港东油田一区一断块为例[J]. 天然气地球科学, 2012,23(6): 1163-1169.(ZOU Tuo, WU Shuyan, CHEN Xiaozhi, et al. Super-fine modeling of the inner point bar of meandering river: a case study on the fault one of area Ⅰ in eastern Dagang oilfield[J]. Natural Gas Geoscience,2012,23(6): 1163-1169.(in Chinese))
[6]	COSTAMAGNA E, FANNI A. Analysis of rectangular coaxial structures by numerical inversion of the Schwarz-Christoffel transformation[J]. IEEE Transactions on Magnetics,1992,28(2): 1454-1457.
[7]	COSTAMAGNA E. A new approach to standard Schwarz-Christoffel formula calculations[J]. Microwave and Optical Technology Letters,2002,32(3): 196-199.
[8]	HOWELL L H, TREFETHEN L N. A modified Schwarz-Christoffel transformation for elongated regions[J]. SIAM Journal on Scientific and Statistical Computing,1990,11(5): 928-949.
[9]	DRISCOLL T A. Algorithm 843: improvements to the Schwarz-Christoffel toolbox for MATALAB[J]. ACM Transactions on Mathematical Software,2005,31(2): 239-251.
[10]	NATARAJAN S, BORDAS S, MAHAPATRA D R. Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping[J]. International Journal for Numerical Methods in Engineering,2009,80(1): 103-134.
[11]	CROWDY D. The Schwarz-Christoffel mapping to bounded multiply connected polygonal domains[J]. Proceedings of the Royal Society,2005,146(2061): 2653-2678.
[12]	王玉风, 姬安召, 崔建斌. 矩形到任意多边形区域的Schwarz-Christoffel变换数值解法[J]. 应用数学和力学, 2019,40(1): 75-88.(WANG Yufeng, JI Anzhao, CUI Jianbin. Numerical solution of Schwarz-Christoffel transformation from rectangles to arbitrary polygonal domains[J]. Applied Mathematics and Mechanics,2019,40(1): 75-88.(in Chinese))
[13]	崔建斌, 姬安召, 王玉风, 等. 单位圆到任意多边形区域的Schwarz Christoffel变换数值解法[J]. 浙江大学学报(理学版), 2017,44(2): 161-167.(CUI Jianbin, JI Anzhao, WANG Yufeng, et al. Numerical solution method for Schwarz Christoffel transformation from unit circle to arbitrary polygon area[J]. Journal of Zhejiang University(Science Edition),2017,44(2): 161-167.(in Chinese))
[14]	陈汉武, 朱建锋, 阮越, 等. 带交叉算子的量子粒子群优化算法[J]. 东南大学学报(自然科学版), 2016,46(1): 23-29.(CHEN Hanwu, ZHU Jianfeng, RUAN Yue, et al. Quantum particle swarm optimization algorithm with crossover operator[J]. Journal of Southeast University(Natural Science Edition),2016,46(1): 23-29.(in Chinese))
[15]	田瑾. 高维多峰函数的量子行为粒子群优化算法改进研究[J]. 控制与决策, 2016,31(11): 1967-1972.(TIAN Jin. Improvement of quantum-behaved particle swarm optimization algorithm for high-dimensional and multi-modal functions[J]. Control and Decision,2016,31(11): 1967-1972.(in Chinese))
[16]	程林辉, 钟洛. 求解多峰函数优化问题的并行免疫遗传算法[J]. 微电子学与计算机, 2015,32(5): 117-121.(CHENG Linhui, ZHONG Luo. A parallel immune genetic algorithm for multimodal function optimization problem[J]. Microelectronics and Computer,2015,32(5): 117-121.(in Chinese))
[17]	高岳林, 余雅萍. 基于混合量子粒子群优化的投资组合模型及实证分析[J]. 工程数学学报, 2017,34(1): 21-30.(GAO Yuelin, YU Yaping. Portfolio model based on hybrid quantum particle swarm optimization with empirical research[J]. Chinese Journal of Engineering Mathematics,2017,34(1): 21-30.(in Chinese))
[18]	ABRAMOWITZ M, STEGUNＩA. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables [M]. Washington DC: Dover Publications, 1996.