石油学报 ›› 2013, Vol. 34 ›› Issue (1): 184-187.DOI: 10.7623/syxb201301024

• 石油工程 • 上一篇    下一篇

卡森模式流变参数非线性估计的改进算法

闫吉曾 罗 懿 邓红琳   

  1. 中国石化华北分公司工程技术研究院 河南郑州 450006
  • 收稿日期:2012-06-17 修回日期:2012-08-04 出版日期:2013-01-25 发布日期:2013-04-09
  • 通讯作者: 闫吉曾
  • 作者简介:闫吉曾,男,1975年6月生,2007年获中国石油大学(北京)工学硕士学位,现为中国石化华北分公司工程技术研究院工程师,主要从事钻完井工程设计、油气井流体力学与钻井液流变学等研究工作。
  • 基金资助:

    国家重大科技专项(2011ZX05045-03)资助。

An improved algorithm of nonlinear estimation for the Casson model rheological parameter

YAN Jizeng LUO Yi DENG Honglin   

  • Received:2012-06-17 Revised:2012-08-04 Online:2013-01-25 Published:2013-04-09

摘要:

通常对卡森模式流变参数进行非线性估计的求解过程相当复杂,针对这一问题,提出了一种基于非线性回归的改进算法。该算法不仅将流变参数估计转化为求一元函数的最小值问题,而且还给出了目标函数搜索区间上界和下界的确定方法。通过大量实测数据对一元目标函数进行计算的结果显示,其为搜索区间上的单峰函数,可采用二分法、黄金分割法及Fibonacci法等一维搜索法求解。改进算法计算稳定,无须设初始值,收敛速度快,且易于计算机编程。经实例计算验证,该算法所得的流变参数是基于最小二乘意义下的最优估计。

关键词: 卡森模式, 流变参数, Fibonacci法, 非线性估计, 最小二乘法

Abstract:

The nonlinear estimation of Casson model rheological parameters is usually a complex process. To solve this problem, an improved algorithm which is based on nonlinear regression is proposed. Then rheological parameters estimation algorithm is turned into seeking the minimization of one variable function and a method for determining the upper and lower bounds of the search interval is given. The test results based on a large amount of practical data showed that the object function is a unimodal function in the search interval, which can be solved with one-dimensional search method such as dichotomy, the golden section and Fibonacci method. This algorithm has such advantages as calculation stability, no need to set initial values, fast convergence and easy for computer programming. Through example tests, the proposed rheological parameter estimation was proved to be the optimal estimation based on the least squares method.

Key words: Casson model, rheological parameter, Fibonacci method, nonlinear estimation, least squares method