低渗透油藏压裂井井底压裂动态

Bottom Hole Pressure of Fracturing Well in Low Permeability Reservoir

根据低渗油藏渗流规律,建立了考虑启动压力梯度的封闭或定压外边界低渗油藏无限导流垂直裂缝井线性流渗流数学模型及无限大低渗油藏有限导流垂直裂缝井双线性流渗流数学模型。对模型做拉氏变换,利用叠加原理、镜像反映原理和格林第二公式求解模型,得到拉氏空间中的井底压力计算公式。利用改进的Stehfest算法,计算得到实空间中的井底压力解。在MATLAB上编写程序并绘制了井底压力及压力导数理论曲线。对启动压力梯度、裂缝导流能力、外边界等影响因素进行分析,区分启动压力梯度与外边界对井底压力的影响。

According to the percolation law for low permeability reservoir,the linear flow mathematical model of the infinite conductivity vertical fracture for low permeability reservoir wells and the bilinear mathematical model of infinite conductivity vertical fractured wells are built,considering the closed starting pressure gradient or the constant pressure outer boundary.Laplace transform of the model is done,and by using the superposition principle,the mirror reflected principle and the second Green formula to solve the model,formula for bottom hole pressure in the Laplace space is obtained.Using the improved Stehfest algorithm,the solution of bottom hole pressure in the real space is calculated.Program is compiled in MATLAB and the bottom hole pressure and the theoretical curve of pressure derivative is mapped.The influenced factors of pressure gradient,fracture conductivity,and outside boundaries are analyzed,which distinguishes the influence on the bottom hole pressure between the starting pressure gradient and outer boundary pressure.