局部极值搜索的曲率算法及其在泸州地区页岩气裂缝预测中的应用

Local-extremum-searching curvature algorithm and its application to fracture prediction in Luzhou

天然裂缝是页岩气有利区优选、开发政策制定、钻井轨迹优化、压裂方案设计的重要参考因素.物理模拟实验、露头和岩心观测表明,在页岩的褶皱核部,裂缝往往更发育,且以构造缝、高角度缝为主,指示了形变特征预测裂缝的有效性,因此曲率属性广泛应用在川南页岩气裂缝预测中,但面临横向分辨率不够、小尺度裂缝敏感性较低等问题,影响工程实施.基于此,本文提出一种局部极值搜索的曲率算法,利用高斯函数和最大曲率属性建立Hessian矩阵,计算特征值和特征向量,在此基础上构建检测函数提取局部极大值和极小值,得到锐化后的曲率体.正演结果表明,局部极值搜索曲率算法预测的裂缝位置更精准,同时对微幅度构造的伴生裂缝有更高灵敏度.将该算法应用于泸州某页岩气工区,同时表征最大正、负曲率极值的位置,其结果与地质导向断层、压窜、套管变形位置、微地震事件点等具备更好的匹配性,对钻井和压裂设计具有指导意义.

Natural fractures are important factor for optimization of favorable shale gas area,formulation of developing policies,adjustment of drilling trajectories and design of fracturing schemes.Proved by physical model,geological outcrop and drilling core,fractures are often more developed in core area of the fold structure,mostly structural fracture and high-angle fracture.It reveals the feasibility of predicting fracture from deformation characteristic.Therefore curvature attribute is widely used in fracture prediction of shale gas in southern Sichuan.But it faces problems such as insufficient lateral resolution and low sensitivity of small-scale fractures,which affect engineering implementation.To this end,this paper proposes a local-extremum-searching curvature algorithm,which uses the Gaussian function and the maximum curvature attribute to establish the Hessian matrix,calculate the eigenvalues and eigenvectors,therefore construct a detection function to extract the local maximum and minimum,and obtain the sharpened curvature body.The forward modeling shows that the local-extremum-searching algorithm can predict the fracture position more accurately,and has higher sensitivity to the associated fractures of microstructures.The algorithm was tested in Luzhou developing area and it characterizes the position of the maximum positive and maximum negative curvature extremums at the same time.Prediction results are in good correspondence with geological guidance,channeling,casing deforming position and micro-seismic events,etc,which presents the algorithm has significant meaning for drilling and fracturing design.