三参数非线性方程自动拟合方法的研究及应用  

Study and Application of Automatic Matching Method for Non-linear Function with Three Parameters

作　　者：邹存友[1] 常毓文[1] 唐玮[1] 王东辉[1] 胡丹丹[1] 

机构地区：[1]中国石油勘探开发研究院,北京100083

出　　处：《石油天然气学报》2009年第2期111-115,共5页Journal of Oil and Gas Technology

摘　　要：针对油藏工程中广泛存在的三参数非线性方程的求解问题,提出了一种简单有效的自动拟合方法。其基本思路是:首先,将三参数非线性方程进行归一化处理,并确定待定参数的初始分布区间;其次,以待定参数最优解使非线性方程的线性化程度最高为准则,在待定参数分布区间内,通过等步长进行迭代、对比以不断缩小参数分布范围,在计算精度的控制下,最终获得最优解。将上述算法开发成计算机分析软件,并应用软件对我国和世界范围内的大量油田资料进行了分析。经实际验证,该算法及应用软件具有计算速度快、精度高、易操作的优点,而且不存在收敛问题。据初步统计,将待定参数分布区间分成100等份,迭代2～7次即可完全满足精度要求。最后,通过三个油田实例说明了这种方法的应用效果。In consideration of the solutions of non-linear function with three parameters witch was widely used in reservoir engineering, a simple and efficient automatic matching method was proposed. The basic thoughts are: first the non-linear function was normalized and the distribution area of the unknown parameter was ensured; second, the correlation coefficient maximization was used as the standard to seek the best solution of the unknown parameter in distribution area through iteration with equal step and comparison to reduce the range of the solution gradually. Finally, under the control of computation accuracy, the best solution was found. The method was developed into a software and used in interpretation and prediction of field data in our country and the world. It is indicated that the method motioned has the advantages of fast computation, high precision and easy operation. Moreover, there is no problem of convergence. According to the statistics, the iteration times between 2 to 7 can meet the demand of the accuracy while dividing the distribution area to 100 equal areas. The application results are presented through three field example.

关 键 词：三参数 非线性方程 分布区间 迭代 自动拟合 

分 类 号：TE328[石油与天然气工程—油气田开发工程]