利用点源函数建立低渗油藏直井试井解释模型

摘要

For homogeneous reservoir model can not reflect the low permeability reservoir the underground condition problem, must establish the low permeability reservoir pressure gradi- ent effects enabled the mathematical model for well test interpretation.Based on percolation theory to build a mathematical model of seepage flow in low permeability well, and using Lord Kelvin point source solution, Bessel＇s function integral and Poisson superposition for- mula method based on the seepage flow equation along the shaft direction integral solution. And obtained by calculating the dimensionless pressure and pressure derivative of logarith- mic theoretical chart, and on the basis of analysis considering the top and bottom boundary effects of low permeability well percolation characteristics and its influence factors, for the development of low permeability oil reservoir has a certain guiding significance.%针对均质油藏模型不能真实反映出低渗透油藏的井下状况的问题，必须建立低渗油藏启用压力梯度影响的数学模型进行试井解释。本文从渗流理论出发建立了低渗透直井渗流数学模型，并采用Lord Kelvin点源解、贝塞尔函数积分和泊松叠加公式等方法通过对渗流方程沿井筒方向进行积分求解。并通过计算得到无因次压力和压力导数双对数理论图版，并在其基础上分析考虑顶底边界影响的低渗透直井渗流特征及其影响因素，对于低渗透油藏的开发具有一定指导意义。