利用岭回归模型分析法判断油藏注采关联性

Application of ridge regression analysis in the research of reservoir  injection-production connectivity

王硕亮, 姜汉桥 ,张 媛, 陈民锋

Wang Shuoliang  Jiang Hanqiao  Zhang Yuan  Chen Minfeng

中国石油大学石油与天然气工程学院，北京 102249

College of Petroleum and Gas Engineering, China University of Petroleum, Beijing 102249, China

目前利用油水井动态数据判断油水井间关联性的数据方法多采用多元线性回归。在实际应用过程中，经常遇到回归系数小于0的情况，这给数据解释带来很大困难。对实际数据的计算过程进行分析，指出回归系数小于0是由于动态生产数据存在多重复共线性的现象。利用岭估计方法，在自变量信息矩阵的主对角线元素上人为地加入一个非负因子k，使回归系数的估计稍有偏差，牺牲了矩阵的无偏性，可以换取方差部分的大幅度减少，最终降低其均方误差，很好地解决了因为生产数据的多重共线性而产生的系数小于0的问题。选取生产测试数据较全面的一个区块，对该方法的可靠性进行验证，发现采用最小二乘方法解释出的油水井相关系数小于零的井组，利用岭回归方法解释出的油水井相关系数全部大于零；并且，将岭回归的解释结果与示踪剂解释结果相比较发现，2种方法的判断计算结果基本一致，说明岭回归方法具有一定的可靠性。此方法简洁易懂，非常适合实际应用。

Multiple linear regressions are adopted to infer the connectivity of oil-water wells through the use of performance data of oil-water wells. But the situation of which the regression coefficients are less than zero can be often encountered during practical application. That brings on great difficulty for data explanation. That the regression coefficients are less than zero is because of the existence of multicollinearity in dynamic production data based on the analysis of calculating process of practical data. A non-negative factor, k, is added artificially in principal diagonal element of argument matrix to deviate lightly from the assessment of regression coefficient and give up the unbiasedness in order to decrease the variance and the mean square errors, which resolves the problem of coefficient below zero created from the multicollinearity of performance data. The reliability of this method is verified by a selected block with relatively complete production data. The result shows that the correlation coefficient interpreted by ridge regression method is all greater than zero for the well group interpreted by the least square method, in which the correlation coefficient of oil-water wells is less than zero. Compared the explained result of ridge regression with the result of tracer material, it is found that the calculation result of these two methods is corresponding essentially, which indicates that the method proposed in the paper has a certain reliability. The method is simple and suitable for practical application.