NUMERICAL SIMULATION OF MULTI-SCALE FRACTURED RESERVOIR BASED ON CONNECTION ELEMENT METHOD
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摘要: 针对油藏不同尺度复杂几何特征描述和动态连通性识别等难题, 近年来发展了一种基于非欧物理连通网络具有无网格特征的油藏数值模拟连接元方法. 文章将连接元法推广到裂缝性油藏, 从流体流动的角度, 利用连接单元将油藏离散为物理连通网络; 根据节点物性参数、影响域半径和加权最小二乘法给出了压力扩散项的广义差分近似; 结合物质守恒方程计算节点控制体积、基质节点间传导率、裂缝节点间传导率以及基质节点与裂缝节点间传导率; 从而构建渗流控制方程组的全隐式离散格式, 求解压力、饱和度以及含水率等生产动态参数; 引入图论深度优先搜索算法, 基于每个时间步求解的节点间压力梯度, 计算各时间步注入井的劈分系数, 定量表征井节点间的流动关系和连通性. 算例验证表明, 相较基于网格体系的传统方法, 该方法能够自由灵活地刻画包括裂缝复杂分布、不规则油藏边界在内的复杂油藏几何, 在粗化模型情况下能够保留更丰富的流动拓扑结构, 实现计算精度和计算效率的更优平衡, 能更好满足实际大规模裂缝性油藏的生产动态模拟预测需求, 同时为具有多尺度几何特征的裂缝性油藏及复杂边界油藏的数值模拟提供了新思路.Abstract: In order to solve the complex geometric characteristics description and dynamic connectivity identification problems of reservoir at different scales, a new method of reservoir numerical simulation, connection element method (CEM), based on non-European physical connectivity network with meshless characteristics has been developed in recent years. In this paper, CEM is extended to fractured reservoirs. From the perspective of fluid flow, the reservoir is discretized into physical connected network by the connection element. The generalized difference approximation of the pressure diffusion term is given according to the physical parameters of the node, the radius of the influence domain and the weighted least square method. Meanwhile, the control volume of nodes, the transmissibility between matrix nodes, the transmissibility between fracture nodes, and the transmissibility between matrix nodes and fracture nodes were calculated based on the material conservation equation. Thus, a fully implicit discrete scheme of seepage control equations is constructed to solve dynamic production parameters such as pressure, saturation and water cut. Based on the pressure gradient between nodes solved by each time step, the allocation factors of injection wells at each time step were calculated by the depth-first search algorithm of graph theory to quantitatively characterize the flow relationship and connectivity between well nodes. The algorithm validation shows that the method can freely and flexibly portray complex reservoir geometry including distribution of complex fractures networks and irregular reservoir boundaries. Compared with the traditional grid-based method, this method can retain more abundant flow topologies under the condition of coarser model, so as to achieve a better balance between computational accuracy and computational efficiency. As a result, CEM can better meet the demand of production dynamic simulation and prediction of actual large-scale fractured reservoirs, and provides a new idea for numerical simulation of fractured reservoirs with multi-scale geometric characteristics and complex boundary reservoirs.
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图 7 不同影响域半径压力计算误差
Figure 7. Calculation error of pressure with different radius of influence
图 8 不同间距布点CEM计算压力
Figure 8. The pressure is calculated by CEM at different collocation intervals
图 9 不同间距布点CEM压力计算误差
Figure 9. Calculation error of CEM pressure at different collocation intervals
表 1 油藏物性参数
Table 1. Physical parameters
Parameter Value Parameter Value initial porosity 0.2 rock compressibility/MPa−1 6.5 × 10−5 initial pressure/MPa 25 irreducible water saturation 0.2 oil viscosity/mPa·s 2 fluid compressibility/Pa−1 5 × 10−4 water viscosity/Pa·s 1 fluid volume coefficient 1 fracture aperture/m 0.01 reservoir thickness/m 10 fracture permeability/mD 20000 
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