部分射开压裂直井渗流压力动态分析

建立符合非均质油藏部分射开地层实际的物理模型和三维各向异性矩形油藏的不稳定渗流数学模型,考虑不渗透顶、底边界和定压顶、底边界等边界条件的组合,通过无因次量纲变换、拉普拉斯变换、傅里叶余弦变换和分离变量等方法,得到拉普拉斯域的解析解,利用斯蒂芬森数值反演方法,得出实数域的压力数值解.绘制压力动态曲线,并进行敏感性分析.计算结果与数值模拟基本吻合,证实方法的可靠性.敏感性分析表明:压力动态曲线可分为早期线性流、中期径向流、晚期球形流、边界控制流四个流动期.裂缝长度主要影响早期线性流,渗透率各向异性主要影响中期径向流,储层射开程度和裂缝方位主要影响晚期球形流,边界条件和油藏宽度主要影响边界控制流.该方法可以确定最优射开程度、垂向渗透率等参数,为油藏工程分析和压裂工艺设计提供指导.

Pressure Dynamic Analysis of Vertical Well Flow with Partial Penetration Fractures

An actual physical model which shows partial penetration of heterogeneous reservoir formations was built and a three-dimensional mathematical model for instability of anisotropic rectangular reservoirs was built. The mathematical model takes impermeable top, combination of boundary conditions of constant pressure and top border and bottom border into consideration. By using dimensionless transformation, Laplace transformation, Fourier cosine transformation and variable separation methods analytical solution of Laplace domain was obtained. By using Stephenson numerical methods numerical solution pressure of real domain was obtained.Dynamic pressures were plotted and sensitivity analysis was carried out.Pressures obtained are basically consistent with numerical simulation, which shows reliability of the method. Sensitivity analysis shows that:Dynamic pressure curve can be divided into early linear flow, mid-radial flow, late spherical flow and boundary control flow.Fracture length mainly affects early linear flow. Permeability anisotropy mainly affects mid-radial flow.Degree of penetration in reservoir and fracture orientation mainly affect late spherical flow.Boundary conditions and reservoir border width mainly affect boundary control flow.Optimal degree of open shot, vertical permeability and other parameters can be obtained easily.It provides theoretical guidance for reservoir engineering analysis and fracturing process design.