分形合采油藏非线性渗流模型解的相似结构  

SIMILAR STRUCTURE OF THE SOLUTIONS OF MATHEMATICAL MODEL FOR THE NONLINEAR FLOW OF FRACTAL COMMINGLED OIL RESERVOIRS

作　　者：李伟[1] 李晓平[1] 李顺初[2] 李全勇[2] 

机构地区：[1]西南石油大学油气藏地质及开发工程国家重点实验室,四川成都610500 [2]西华大学应用数学研究所,四川成都610039

出　　处：《大庆石油地质与开发》2012年第6期79-83,共5页Petroleum Geology & Oilfield Development in Daqing

基　　金：国家科技重大专项（2008ZX50443-14）;西华大学应用数学重点学科资助（ZX00910-09-1）;西华大学创新基金（YCJJ201110）.

摘　　要：传统的分形油藏模型的非线性偏微分方程中，根据弱可压缩流体的假设，忽略了二次压力梯度项的影响，但这种方法对于混气油藏和低渗透油藏应当是有疑问的。针对分形合采油藏渗流数学模型考虑二次压力梯度项的影响，建立了考虑有效井筒半径和三种外边界（无穷大、定压、封闭）条件下的非线性渗流数学模型；通过利用Laplace变换进行全面和深入的分析研究发现该类油藏在三种外边界条件下的渗流特征的解式之间具有相似结构，即它们的解式具有统一的形式（此式有一种类似于几何图形相似的特征），它们的差异只在于其相似核函数的不同。In the classical nonlinear partial differential equation of fractal oil reservoirs, according to the assump- tion of slightly compressible fluids, the effects of quadratic pressure gradient term is ignored , however this method is questionable for oil-mixed gas reservoirs and low-permeability oil reservoirs. Aiming at the influences of the above term considered in the mathematic model for the flow of fractal commingled oil reservoirs, the nonlinear flow mathe- matical model considering the effective wellbore radius and the conditions of three outer boundaries （ infinite, con- stant pressure and Closed） is established. By using Laplace transform and with the help of comprehensive and deep anaylses and studies, there is the similar structure in the solution＇s form of these flow characteristics in above three cases, and furthermore their differences are only displayed in the contrasts of their similar kernel functions.

关 键 词：分形合采油藏 二次压力梯度 有效井筒半径 LAPLACE变换 相似结构 

分 类 号：TE353[石油与天然气工程—油气田开发工程]