考虑二次梯度影响的渗流模型与试井样版曲线

从质量守恒原理出发，结合达西定律，考虑恒压缩系数的弹性多孔介质和单相微可压缩液体的等温渗流过程，推导出了考虑二次压力梯度影响的渗流方程。建立了考虑井储影响的无穷地层定产量生产试井模型，并通过变量代换，将渗流方程线性化，求得Laplace空间解析解，利用数值反演得到实空间的解，进而绘制了压力和压力导数双对数样版曲线。从物理渗流机理上对曲线形态特征进行了分析，得出了无因次二次压力梯度项系数α对渗流和试井曲线的影响结果。特别对低渗稠油油藏，二次压力梯度项的影响不应被忽略，所获得的结果可用于研究低渗油藏和稠油油藏的渗流规律和试井分析。

THE FLOW MODEL CONSIDERING THE QUADRATIC PRESSURE GRADIENT AND THE WELL TEST TYPE CURVES

Embarking from the mass conservation principle and the Darcy′s law, the flow equation of the elastic porous medium and the slightly compressible single phase fluid are deduced with the quadratic pressure gradient for constant compressibility and isothermal flow. Considering the well bore storage effects, the well test model has been established for the infinite reservoir with the onephase constant voluemetric sandface rate production. Through variable substitution and linearizing the flow equation, the Laplace space analytic solution and procuring the real space solution is obtained by use of the numerical inversion. In the end, the pressure and the pressure derivative bilogarithmic type curves are drawn up. From the physical seepaging mechanism, the analysis to the curve shape characteristics is carried on, then the influence result of the dimensionless quadratic pressure gradient coefficient alpha to the transfusion and the well test curve is obtained. Specially on low permeable reservoir and the heavy oil reservoir, the influence of the quadratic pressure gradient term should not be neglected, the result can be used in the study of the flow rule and the well test analysis of heavy oil reservoir.