面向复杂井型模拟的变栅格法六面体网格自动生成

Multi-branch horizontal well and multi-fractured horizontal well are the most important technology in the oil and gas mining. The hexahedral mesh generation for such three-dimensional reservoir with complex well type, which has great applying value, is the bottleneck in the field of numerical reservoir simulation. The application is intend to combine the vector filed technique and grid-based hexahedral mesh generation algorithm, a variable grid-based hexahedral mesh generation algorithm is proposed for complex well simulation. Firstly, a three-dimensional vector field which is consistent to the boundary of reservoir, cracks and trajectory of well is established by harmonic functions. With the guidance of such vector field, an as-rigid-as-possible mesh deformation method based on linear elastic finite element energy is used to advance the hexahedral mesh from inside to outside layer-by-layer, which can generate variable core grid with high similarity to the shape of reservoir model. Then, a harmonic mesh size field is established according to the trans-scale mesh size constraints, and a set of 8-refinement based density control templates is built for gradual transition between adjacent elements with variable size requirements. A least-square surface fitting and the center of the maximum inscribed circle of convex polygon are used to optimize the direction and position of the projection, which can obtain smoothing surface filled mesh. Finally, a hexahedral mesh optimization algorithm is studied based on the local/global methodology, which can greatly improve the hexahedral mesh quality, and hexahedral mesh generation software is developed on the basis of the above algorithms.

多分支水平井及水平井多段压裂是油气开采中的最重要技术。对这类包含复杂井型的三维油藏空间生成高质量的六面体网格，是当前油藏数值模拟领域的瓶颈，具有极大应用价值。本申请拟将向量场技术及基于栅格法六面体网格生成算法相结合，提出面向复杂井型模拟的变栅格法六面体网格自动生成算法。首先利用调和函数建立与油藏边界、裂缝及井筒轨迹相一致的空间向量场，以该空间向量场为引导场，采用基于线弹性有限元能量的网格保刚性变形方法将六面体网格由内向外逐层推进，生成形状逼近油藏模型的可变核心栅格；然后根据跨尺度网格尺寸约束建立调和网格尺寸标量场，构建8分法六面体网格加密模板，实现不同尺寸需求下相邻网格的协调过渡；采用最小二乘曲面拟合及凸多边形最大内切圆圆心对投影方向和位置进行优化，得到光顺的表面填充网格；采用由局部到整体的策略，研究六面体网格质量优化算法，整体提高网格质量，并在此基础上开发相应的六面体网格生成软件。

有限元网格是数值模拟技术的重要组成部分，高质量的实体网格可以提高数值计算的精度，并提高计算效率。目前，实体模型的六面体网格生成与优化技术依然面临很多挑战，是有限元模拟领域亟待解决的难题。本项目针对六面体网格自动生成、曲面网格质量优化及六面体网格质量优化等关键技术，进行了深入细致的研究，开发了三维有限元网格生成软件。主要研究成果包括：1）提出了向量场引导的变栅格法六面体网格生成方法。首先建立三维模型的空间向量场，基于此向量场，逐层生成方向及大小可控的内部栅格，通过填充栅格和实体模型间隙得到最终的六面体网格；2）提出基于中轴线的曲面网格质量优化算法，由几何特征保持和节点光顺操作组成。采用法向张量投票理论对网格节点进行分类，保证了原始网格的几何特征。节点光顺操作通过不断的调整节点位置来提升网格质量，直到网格质量的变化量小于给定的阈值。针对光滑节点，采用二分法求解领域多边形中轴上的最优中心点，并将该最优中心点投影回三维网格上，折痕点的最优位置则通过二次多项式插值法求得；3）提出了一种局部到整体的六面体网格质量优化算法。针对每个六面体单元采用双八面体几何变换进行局部规则化操作，得到高质量的规则六面体网格。在此基础上，通过迭代优化一个二次能量函数，对规则化后的网格进行整体拼接和优化，该能量函数由节点内力和表面几何约束组成，节点内力保证了规则化后六面体单元的连接性，表面几何约束保持了原始模型的几何形状。在对上述方法深入研究的基础上，借助Open CASCADE几何造型平台，自主开发了三维有限元网格生成软件。该软件具有标准的几何和有限元数据输入输出接口、六面体网格自动生成以及网格质量检查等功能。应用实例表明该软件网格生成效率较高，网格质量满足了三维有限元数值模拟的要求。