应力敏感页岩气藏水力压裂直井试井分析

应力敏感效应普遍存在于天然裂缝发育的页岩气藏中。本文根据页岩气渗流理论及吸附气解吸特征,引入Langmuir等温吸附公式和渗透率模数,建立了应力敏感双孔单渗页岩气藏水力压裂直井的不稳定渗流数学模型。并用变换式和摄动技术线性化处理非线性偏微分方程,同时应用Lord Kelvin点源基本解、Poisson求和公式、修正Bessel函数积分等方法求解出应力敏感页岩气藏水力压裂直井在Laplace空间中的无因次井底压力响应函数。通过Duhamel叠加定理和Stehfest数值反演算法得到实空间的数值解,并绘制无因次压力和压力导数双对数变化曲线,进一步分析渗流特征及Langmuir体积、Langmuir压力、无因次渗透率模数、储容比、窜流系数等对无因次压力和压力导数动态特征的影响。

Pressure Transient Analysis of Hydraulic Fractured Vertical Well in Stress-Sensitive Shale Gas Reservoirs

Stress-sensitive effects are common in naturally fractured shale gas reservoirs. In this paper, according to shale gas seepage theory, gas adsorption and desorption characteristics, and by introducing Langmuir isothermal adsorption principle and the permeability module, the transient flow mathematical model-hydraulic fractured vertical well in stress-sensitive dual-porosity shale gas reservoir-is established. Through transforming and perturbation technique, nonlinear partial differential equations are linearized. And by applying the Lord Kelvin point-source solution, Poisson superimpose formula and the integral of the modified Bessel function, we obtain the dimensionless pressure response function in Laplace space. Based on the Duhamel principle and Stehfest numerical inversion algorithms, the numerical solution in real space is obtained. In the meanwhile, the log-log type plots of dimensionless pressure and pressure derivative are drawn to further analyze the characteristic, and influence factors: Langmuir volume, Langmuir pressure, elastic storativity ratio, interporosity flow coefficient and permeability module.