均质油藏非线性球向渗流问题解的相似结构  

Similar Structure of Flow Effective Well Radius Model through Homogeneous Reservoir Solutions

作　　者：许丽[1] 李顺初[1] 盛翠翠[1] 

机构地区：[1]西华大学数学与计算机学院应用数学研究所,成都610039

出　　处：《重庆师范大学学报（自然科学版）》2011年第4期32-34,共3页Journal of Chongqing Normal University:Natural Science

基　　金：西华大学应用数学重点学科资助(No.ZX00910-09-1);西华大学创新基金(No.YCJJ200916)

摘　　要：针对均质油藏球向渗流问题,在考虑井筒储集、井底定流量生产、3种外边界(无穷大、定压、封闭)情形下,建立了考虑二次梯度影响的不稳定渗流的试井分析模型;先对此模型作线性化处理,把求解非线性的模型变为求解该线性的偏微分方程的定解问题,对定解问题关于时间tD作Laplace变换得到线性的常微分的定解问题,求解此定解问题得到了线性化后的无因次储层压力和井底压力分布在Laplace空间中的精确解;经全面和深入分析,发现了此模型在3种外边界条件下解式之间的相同的结构式y(rD,z)=-α1/z CDz+1+α+1/Φ(1,z)1/Φ(1,z)Φ(rD,z),只是对应不同边界条件的相似核函数Φ(rD,z)不同。使得不同边界条件下对解的表达式之间的关系更加清晰,极大方便了相应的试井分析应用软件的编制,对油气藏渗流规律的理论研究也具有深远的意义。This article suggests a spherical seepage problem in the homogeneous reservoir, considering well bore storage, bottom hole fixed flow and the three types of outer boundary （ infinite, constant pressure and closed） cases, an instability seepage model was established in well testing analysis with consideration of the quadratic gradient. First, model was linearized, obtained linear partial boundary value of second-order differential equation. Further by using Laplace to transform to the time tD to get the ordinary differential equation boundary value problem. The linearized model obtained the exact solutions of the dimensionless reservoir and dimensionless bottom-hole pressure in Laplace space ; the similar structure of the solution＇ s form in three kinds of outer boundary conditions is achieved through a comprehensive and in-deep analysis of its characteristics. Can be expressed in the following general formula ^-y（rD,z）=-a/z1/CDz＋1＋a＋/1Ф（1,z）1/Ф（1,z）Ф（rD,z）,There are only different kernel functions Ф（ rD ,z） behind different boundary conditions. That made the relationship between the expressions of the solution more clearly. The research is convenient to design the corresponding appli- cation software for well test analysis, and also has a profound significance in the percolation theory of oil and gas law.

关 键 词：相似结构 均质油藏 二次梯度项 不稳定 球向流 

分 类 号：O29[理学—应用数学] O357.3[理学—数学]