考虑垂向摩阻的裂缝拟三维延伸模型

裂缝拟三维延伸模型具有极快的收敛速度、令人满意的计算精度和较强的适应性,但该类模型中没有考虑垂向摩阻,计算得到的裂缝高度偏大,不能模拟存在缝高失控的裂缝三维延伸过程。推导存在垂向摩阻的裂缝宽度解析表达式,考察裂缝张开位移判据的精度,认为对于常规水力裂缝没有必要进行小范围屈服修正。在此基础上,考虑双线性流动模式和压裂液的初滤失,建立改进的裂缝拟三维延伸模型。实例模拟分析表明:改进模型精度更高;当隔层应力差较大时,下缝高的延伸极其缓慢,有利于底水油藏压裂;当隔层应力差极小时,裂缝高度与长度近似相等,但由于重力差作用,上、下缝高仍有明显差异。

A pseudo 3D fracture propagation model with consideration of vertical flow resistance

Pseudo 3D fracture propagation models can be used to simulate the process of hydraulic fracturing treatment, which have rapid convergence speed, satisfactory computing accuracy and flexible adaptation. However, these models neglected the effect vertical flow resistance, so they are unable to simulate fracture propagations in the formation lack of stress difference between the upper/lower layers, and the predicted fracture heights are larger than the real ones in most cases. In deriving a fracture width expression with vertical flow resistance and analyzing the accuracy of crack opening displacement (COD) criterion, it has realized that the correction with a small scale yielding is unnecessary for hydraulic fracturing. Therefore, an improved pseudo 3D fracture propagation model with vertical flow resistance was established considering a dual linear flow pattern and the loss of fracture fluid. The calculation results of a case study show that the new model is more accurate. In addition, the propagation of lower fracture height is very slow at the condition of a higher stress difference, which is good for fracturing in bottom water reservoirs. While at the condition of an extremely low stress difference, the fracture height is nearly equal to the fracture length, but there are still significant difference between upper and lower fracture heights due to the gravity effect.