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王志凯, 程林松, 曹仁义, 王进, 贾品, 王选茹. 三维压裂缝网不稳定压力半解析求解方法. 力学学报, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183
引用本文: 王志凯, 程林松, 曹仁义, 王进, 贾品, 王选茹. 三维压裂缝网不稳定压力半解析求解方法. 力学学报, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183
Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183
Citation: Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2246-2256. DOI: 10.6052/0459-1879-21-183

三维压裂缝网不稳定压力半解析求解方法

SEMI-ANALYTICAL METHOD FOR UNSTABLE PRESSURE OF 3D FRACTURE NETWORK

  • 摘要: 受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.

     

    Abstract: Due to the influence of in-situ stress and fracturing technology, the distribution of hydraulic fracture network in highly deviated wells is complex with different inclined directions, different distribution forms and different penetration degrees. In this paper, the fracture surface is discretized into several rectangular micro elements to realize the effective characterization of fracture morphology. The seepage process is divided into two stages: matrix flow to fracture and fracture flow to wellbore. The numerical solution of unsteady seepage in discrete fracture surface is constructed by using finite difference method, and the analytical solution of unsteady seepage in matrix is constructed by combining closed boundary source function and superposition principle. The solution of the unstable pressure of the 3D fracture network is obtained by coupling the numerical solution of flow in fracture and the analytical solution of flow in matrix. Based on the integral mean value theorem, a solution method of point source and special line source instead of surface source is proposed to solve the seepage in matrix. The feasibility and applicable conditions of this method are analyzed, which can ensure the accuracy of the model and improve the calculation efficiency. The research shows that the point source function area fraction method can accurately solve the bottom hole pressure dynamic of 3D pressure fracture network in the matrix, but the calculation is quite inefficient. The point source and special line source approximate surface source method based on the integral mean value theorem can greatly improve the calculation efficiency, and can achieve higher accuracy when the fracture micro element division is more precise (the dimensionless side length of micro element is less than 0.15). Based on this model, the flow regimes and related sensitivity analysis are analyzed. The results show that the fracture conductivity, fracture dip angle, fracture height and fracture interval have great influence on the typical well test curves of highly deviated wells. Fracture dip angle and fracture interval mainly affect the pressure and pressure derivative curve from linear flow to early radial flow, especially when the fracture height is small, the pressure derivative has backflow phenomenon.

     

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