椭圆形井筒破裂压力预测模型

A model predicting breakdown pressure of elliptical wellbore

水力压裂是油气藏增产的一项重要技术手段,准确预测破裂压力是水力压裂成功的关键。目前的破裂压力预测模型假设井筒为圆形,但测井数据表明井筒为椭圆形。因此,运用复变函数理论和弹性力学理论,推导出椭圆形井筒井周应力场计算解析表达式,建立椭圆形井筒破裂压力预测模型,通过公式蜕化和数值计算检验证明本文模型的正确性。分析椭圆长短轴比和地应力差对破裂压力的影响,研究表明:(1)以我国西部地区某井为例,本文模型计算的破裂压力与现场实际的误差在4%以内;受井筒形状的影响,最小水平地应力方向有应力集中效应,裂缝沿着该方向起裂。(2)当长短轴比较大时,裂缝在最小水平地应力方向起裂,将会发生近井筒裂缝弯曲现象;当长短轴比较小时,小范围的井壁坍塌会引起破裂压力有较大提升。(3)平衡曲线有y(28)ax(10)1的表达形式,当参数点落在区域I内时,破裂压力受地应力差影响大,井筒沿着最大水平地应力方向起裂;当参数点落在区域II内时,破裂压力受井筒形状影响大,井筒沿着最小水平地应力方向起裂;当参数点落在平衡线及其附近区域时,井筒各个方向的破裂压力相近,井筒内多裂缝同时起裂。

Hydraulic fracturing is an important technique to increase the production of oil and gas reservoirs. The prediction of breakdown pressure accurately is the key to the success of hydraulic fracturing. The current prediction model of breakdown pressure assumes that the wellbore is circular,but the wellbore is actually elliptical according to the log data. The complex function theory and the theory of elasticity are therefore used to derive the analytical stress field around the elliptical wellbore and a prediction model for the breakdown pressure of an elliptical wellbore is established. The correctness of the model is verified through formula deduction and numerical calculation. The influence of the ratio of major axis to minor axis and the difference of in-situ stress on the breakdown pressure are analyzed. A well in western China was studied as an example. The error of breakdown pressure calculated with this model is within 4%. The stress concentration due to the influence of wellbore shape occurs in the direction of minimum horizontal stress and fractures initiate along this direction. When the ratio of major axis to minor axis is large,fractures initiate along the direction of minimum horizontal stress and fracture bending occur near the wellbore. When the ratio is small,the collapse of small area of well wall leads to drastic increasing in breakdown pressure. The equilibrium curve has an expression of y（28）ax（10）1. When the point of the parameter falls in zone I,the breakdown pressure is greatly influenced by the difference of in-situ stress,and the wellbore fractures initiate along the direction of maximum horizontal stress. When it falls in zone II,the breakdown pressure is greatly influenced by the shape of the wellbore,and the wellbore fractures initiate along the direction of minimum horizontal stress. When it falls on the balance line and its adjacent area,the breakdown pressure is close in different directions of the wellbore,and the multiple fractures initiate in the wellbore at the same time.