A NUMERICAL SIMULATION APPROACH FOR EMBEDDED DISCRETE FRACTURE MODEL COUPLED GREEN ELEMENT METHOD BASED ON TWO SETS OF NODES
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摘要: 对于原始嵌入式离散裂缝模型(EDFM), 在计算包含裂缝单元的基质网格内的压力分布时采用了线性分布假设, 这导致了油藏开发早期对非稳态窜流量的计算精度不足. 因此, 本文提出了一种两套节点格林元法的EDFM数值模拟方法. 两套节点格林元法的核心思想是将压力节点与流量节点区分开, 一套压力节点设置在单元顶点, 另一套流量节点设置在网格边的中点, 满足局部物质守恒、具有二阶精度的同时, 可适用于任意网格类型. 本文将两套节点格林元法与EDFM耦合, 采用了非稳态渗流控制方程的边界积分形式推导了基质网格与裂缝网格之间传质量的新格式, 代替了线性分布假设以提高模拟精度; 此外, 修正后的EDFM能适应任意形态的基质网格剖分, 拓展了原始EDFM仅适用于矩形基质网格、难以考虑复杂油藏边界的局限性. 研究表明: 通过对比商业模拟软件tNavigator® LGR模块与原始EDFM, 验证了本文模型具有较高的早期计算精度; 以复杂油藏边界−缝网−SRV分区模型为例, 通过对比SFEM-COMSOL商业模拟软件, 验证了本文模型处理复杂问题的适应性. 本文研究可用于裂缝性油藏开发动态的精确模拟.Abstract: For the original embedded discrete fracture model (EDFM), the linear-distribution assumption is adopted in calculating the pressure distribution in matrix grids containing fracture elements, which leads to the lack of accuracy in solving unsteady interflux in the early stage of oil reservoir development. Therefore, this paper proposes a numerical simulation approach for EDFM coupled Green element method based on two sets of nodes. The main idea of the Green element method with two sets of nodes is to distinguish pressure nodes from flux nodes, in which one set of pressure nodes is set at the vertex of grids and another set of flux nodes is set at the edge-midpoint of grids. It not only meets the local material conservation and has second-order accuracy, but also can be applied to any grid type. In this paper, the Green element method based on two sets of nodes is coupled with EDFM, and a new scheme of mass transfer between matrix cell and fracture elements is derived by adopting the boundary integral form of the unsteady flow control equation, which replaces the linear distribution assumption to improve the simulation accuracy. In addition, the modified EDFM adapts to any form of matrix mesh generation, which extends the limitations of the original EDFM which is only suitable for rectangular matrix mesh and difficult to consider complex reservoir boundaries. The research shows that the proposed model has high accuracy in the early stage and it is verified by the LGR module of commercial software tNavigator® and the original EDFM. Taking the SRV-zoning model considering fracture networks and complex reservoir boundaries as an example, the flexibility of the proposed model for solving complicated problems is demonstrated by comparing the business simulation software named SFEM-COMSOL. This study can be used for the accurate simulation of dynamic production performance in fractured oil reservoirs.
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图 1 压力和流量两套节点三角形单元示意图
Figure 1. Sketch of pressure and flux two sets of nodes in triangle cell
图 3 两套节点格林元方法中相邻单元方程组耦合示意图
Figure 3. Sketch of coupling adjacent element equations in two sets of nodes-based GEM
图 4 裂缝交汇的星三角变换原理图
Figure 4. Schematics of star-delta transformation for fracture segments intersecting
图 6 三种不同模型压力分布对比图(1000 d)
Figure 6. Comparison of pressure distribution maps for three various simulators (1000 d)
6 三种不同模型压力分布对比图(1000 d)(续)
6. Comparison of pressure distribution maps for three various simulators (1000 d) (continued)
图 7 三种不同模型产油速度的对比图(1000 d)
Figure 7. Comparison of oil rate for three various simulators (1000 d)
图 8 三种不同模型压力分布对比图(10 d)
Figure 8. Comparison of pressure distribution maps for three various simulators (10 d)
图 10 原始EDFM和修正EDFM之间的误差比较
Figure 10. Error comparison between the original EDFM and the modified EDFM
图 12 不同模型的网格剖分对比图
Figure 12. Comparison diagram of mesh division for different simulators
12 不同模型的网格剖分对比图(续)
12. Comparison diagram of mesh division for different simulators (continued)
图 13 修正EDFM与COMSOL产油速度的对比图(1000 d)
Figure 13. Comparison of oil rate between modified EDFM and COMSOL (1000 d)
图 15 不同SRV分区模型的压力分布对比(100 d)
Figure 15. Comparison of pressure distribution of different SRV zoning models (100 d)
图 16 不同SRV对应的产量动态特征对比
Figure 16. Comparison of dynamic production characteristics corresponding to different SRV
表 1 数值算例的输入参数
Table 1. Input parameters of numerical case
Properties Value Properties Value reservoir thickness/m 10 initial reservoir pressure/MPa 20 matrix porosity 0.15 matrix permeability/mD 1 rock compressibility coefficient/MPa−1 1.08 × 10−4 fracture aperture/m 0.005 fracture porosity 0.45 fracture permeability/mD 70000 oil viscosity/(mPa·s) 2 oil compressibility coefficient/MPa−1 3 × 10−3 
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