二次压力梯度非线性渗流理论与应用  

THEORY AND ITS APPLICATION FOR NONLINEAR PERCOLATION WITH QUADRATIC PRESSURE GRADIENT

作　　者：聂仁仕[1] 贾永禄[1] 石国新[2] 李小华[3] 聂科[4] 戴荣东[5] 

机构地区：[1]西南石油大学石油工程学院,四川成都610500 [2]新疆油田公司陆梁作业区,新疆克拉玛依834000 [3]新疆油田公司重油开发公司,新疆克拉玛依834000 [4]西南油气田分公司重庆气矿,重庆400021 [5]胜利石油管理局钻井工艺研究院,山东东营257000

出　　处：《大庆石油地质与开发》2010年第5期96-103,共8页Petroleum Geology & Oilfield Development in Daqing

基　　金：中石油总公司重点工程攻关项目（971007110165）资助.

摘　　要：从质量守恒原理出发,详细推导出了二次压力梯度非线性渗流偏微分方程.通过建立考虑井储和表皮效应的不稳定渗流数学模型,并通过变量代换,将渗流方程线性化,求得模型在不同外边界条件下的Laplace空间解析解,利用数值反演得到实空间的解,进而绘制出了不同参数团下的压力和压力导数双对数新型样板曲线,分析了其压力动态特征.通过对某参数团下二次压力梯度非线性项作用的压力误差以及压力导数误差分析,获得理论误差.最后通过实例拟合解释发现：非线性渗流模型与线性模型在实例解释结果上存在一定的差异,解释结果误差与样板曲线理论误差接近,二次压力梯度不应该被忽略 非线性渗流规律代表原油在油藏中的真实流动规律,非线性渗流模型可解释出更为准确的油藏动态参数,应加强非线性渗流理论模型与应用研究.This paper deduces the partial differential equation for the nonlinear flow with the quadratic pressure gradient in detail based on the mass conservation principle. By establishing the mathematical model for the transient percolation considering the effects of wellbore storage and the skin effect, and moreover through variable substitution, the flow equation is linearized, the Laplace space analytic solution is obtained under different external boundary conditions, and then the real space solution is procured with the help of numerical inversion. Finally, the bilogarithmic new type curves of the pressures and the pressure derivatives under different parameter groups have beendrawn up, and the dynamic characteristics of their pressures are also analyzed. The pressure and pressure derivative errors of quadratic pressure gradient effects under a certain parameter group are analyzed, so the theoretical errors can be obtained. In the end, the example match explanation is made. The above explanation shows that there are some differences in the explanation results between the linear and non-linear models, and the errors of the explanation results are very close to the theoretical ones, so the quadratic pressure gradient should not be neglected; the nonlinear percolation laws stand for the actual percolation laws of the oil in reservoir, and the explanation results from the non-linear model can represent more precise reservoir dynamic parameters, so researches on the theoretical model and its application for nonlinear percolation should be strengthened.

关 键 词：二次压力梯度 非线性渗流 模型 LAPLACE变换 有效井径 

分 类 号：TE312[石油与天然气工程—油气田开发工程]