基于三次B样条模型的油水相对渗透率曲线数值反演方法  

A Method to Implicitly Estimate Water-oil Relative Permeability Curve Using Cubic B-spline Model

作　　者：王代刚[1] 张环环 侯健[2] 孙静静 罗福全[3] 王伟[3] 

机构地区：[1]中国石油勘探开发研究院,北京100083 [2]中国石油大学(华东)石油工程学院,山东青岛266580 [3]中国石油冀东油田分公司,河北唐山063000

出　　处：《西安石油大学学报（自然科学版）》2016年第1期85-89,95,共6页Journal of Xi’an Shiyou University（Natural Science Edition）

基　　金：国家科技重大专项(编号:2011ZX05011);新世纪优秀人才支持计划(编号:NCET-11-0734)

摘　　要：引入三次B样条相渗表征模型,通过半迭代集合卡尔曼滤波(En KF)算法对见水前、后的生产动态数据进行自动历史拟合,提出了一种新的油水相对渗透率曲线数值反演方法。以某径向流数值岩心模型为例,对比分析了三次B样条模型与幂律模型的优劣。结果表明,相比于传统的幂律模型,三次B样条模型可对油水相对渗透率曲线进行局部逼近,灵活性更强,反演精度更高。通过对径向流岩心驱替实验数据进行自动历史拟合,反演估算了油水相对渗透率曲线。对驱替压差、累产油及累产水等观测数据拟合效果好,相对误差均小于5%,说明本文方法可靠性强,计算结果能够满足工程实际的需要。With regard to the problems existing in the current water-oil relative permeability curve calculation methods, the cubic B-spline model is intro-duced to represent the water-oil relative permeability curve, and the optimization of production performance before and after water breakthrough is per-formed using an iterative ensemble Kalman filter （EnKF）algorithm. Finally, a novel estimation method for water-oil relative permeability curve is estab-lished. A test based on the basic data of a radial numerical core experiment is performed to verify the effectness of the proposed method. The results showthat, compared with the conventional power law model, the cubic B-spline model is higher flexiblity and inversion accuracy, and it has the advantage of lo-cal approximation. In addition, the proposed method is utilized for the history matching of the dynamic data of the radial core displacement experiment toestimate the water-oil relative permeability curve. It is indicated that, the fitting effect of the dynamic data including injection pressure, cumulative oil pro-duction and cumulative water production is well, all the relative error is less than 5.0%, which shows that the proposed method is reliable and can meet theengineering requirement.

关 键 词：三次B样条模型 油水相对渗透率 数值反演 EN KF算法 

分 类 号：TE311[石油与天然气工程—油气田开发工程]