Abstract: The wells with finite conductivity vertical fractures would be formed after fracture treatment in the low-permeability double-porosity reservoirs.Based on the Warren-Root model,the mathematical models for wells with finite conductivity vertical fractures in low-permeability reservoirs were developed using the mass conservation law and elliptical flow method,considering the influences of threshold pressure gradient.The equations for bottom pressure of vertical fractured wells could be achieved using the Laplace transformation.The analysis on the affecting factors of dynamic pressure indicated that the threshold pressure gradient had a remarkable influence on the typical curves of the low-permeability wells with vertical fractures.The curves of dimensionless pressure and pressure derivation climb up at the later stage.The curves get up earlier with the more increase of the threshold pressure gradient.A real build-up testing explanation example of a fractured well in low-permeability reservoir was given.

Key words: threshold pressure gradient, low-permeability reservoir, vertical fracture, mass conservation law, elliptical flow, method mathematical model

摘要： 低渗透双重介质地层压裂后会形成有限导流垂直裂缝井。结合沃伦-鲁特模型,利用质量守恒定律和椭圆流法,建立了低渗透双重介质油藏椭圆流数学模型,求得了在拉普拉斯空间井底压力表达式,并对影响井底压力动态的主要因素进行了分析。结果表明:启动压力梯度对低渗透垂直裂缝井试井曲线影响显著,无因次压力及其导数曲线后期呈上升趋势。且随启动压力梯度的增大,压力及其导数曲线抬升越高,上升得也越早。并对一口低渗透油藏垂直裂缝井进行了实例解释。

关键词: 启动压力梯度, 低渗透油藏, 垂直裂缝, 质量守恒定律, 椭圆流法, 数学模型