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: 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

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

doi: 10.21656/1000-0887.400315
  • Received Date: 2019-10-15
  • Rev Recd Date: 2019-11-07
  • Publish Date: 2020-07-01
  • 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.
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