﻿ 基于Akima插值的随钻测井数据实时处理方法

A Real-Time LWD Data Processing Method Based on Akima Interpolation
Ma Hai, Xiao Hongbing, Yang Jinzhou, Li Yonghua
Drilling Technology Research Institute,Sinopec Shengli Oilfield Service Corporation,Dongying,Shandong,257017,China
Abstract:A real-time LWD data processing method was proposed to address the "black spots" and "pull straight" problems caused by nonuniform sampling of real-time LWD data. Firstly,singular points of real-time LWD data were detected and eliminated utilizing the thin-layer threshold method together with peak-peak or valley-valley ratio method,and the "glitch" phenomenon caused by high-frequency oscillation of LWD was eliminated to improve the signal-to noise-ratio of real-time LWD data.Secondly,the gridding analysis was performed to the real-time LWD data that was obtained.The data gridding and equal interval resampling were accomplished through the establishment of the resampling model of real-time LWD data.The proposed method was applied in the actual LWD data processing.The comparison of processed real-time LWD data with the memory data showed that the maximum relative error and average relative error were 10.92 percent and 8.73 percent respectively,6.06 percent and 3.46 percent less than conventional method;the correlation coefficient was 0.980 8,0.040 2 more than conventional method.The results showed that the combined method of the thin-layer threshold method and the peak-peak or valley-valley ratio method together with Akima method could successfully address the "black spots" and "pull straight" problems.
Key words: Akima interpolation    logging while drilling (LWD)    data processing    gridding    resample

1 Akima插值算法基本原理

Akima插值算法即用Akima分段三次多项式计算。该算法是在每2个数据点间建立1条由三次多项式拟合而成的曲线，整条曲线保证一阶导数连续[9, 10, 11]

2 基于Akima插值的随钻测井数据实时处理方法

2.1 随钻测井实时数据奇异点检测与剔除

1) 根据仪器的垂直分辨率确定地层的薄层阈值σ

2) 根据所研究区块随钻测井地层响应特征，确定峰峰/谷谷比值范围[pmin,pmax]。

3) 利用导数极值法对获取的随钻测井实时数据求取极大值、极小值，确定随钻测井实时数据的波峰点和波谷点。

4) 逐次判断2个相邻波峰或波谷之间的距离Δs，并与地层薄层阈值进行比较：如果Δsσ且该点为波峰，则计算该波峰与相邻波峰对应随钻测井数据的比值，如果该比值在区间[pmin,pmax]内，则继续下一个骤，否则该峰峰之间的数据点判为奇异点；如果Δsσ且该点为波谷，则计算该波谷与相邻波谷对应随钻测井数据的比值，如果该比值在区间[pmin,pmax]内，则继续下一个步骤，否则该谷谷之间的数据点判为奇异点；如果Δsσ，则继续下一个步骤。

5) 重复步骤4)，直至判断完毕所有的波峰/波谷点。

6) 将上述步骤中判为奇异点的值剔除，该点的值采用五点汉明函数平滑法进行求取。

2.2 随钻测井实时数据等间距处理

1) 选取深度数据间隔δ，邻域半径为δ/2。

2) 对时间间隔Δt内的随钻测井数据进行网格化处理，分成n个均匀的网格区间。

3) 将深度值落在网格区域(i－1)δ±δ/2(i=1,2,3,…,n)内的数据点作为第i个网格的数据集合。

4) 判断第i个采样区间数据集合的大小，如果数据集合不为空则将该数据集合内的所有数据点的深度值及随钻测井数据分别进行算术平均，将深度算术平均值作为该采样区间的随钻测井数据采样点深度值dj(j=1,2,3,…,n1)，将随钻测井数据的算术平均值作为该采样区间的采样点值xj(j=1,2,3,…,n1)。其中，n1为采样点个数。

5) 根据预设的等间距采样间隔σ对时间间隔Δt内的随钻测井深度进行数据重采样rk(k=1,2,3,…，n2)，设各深度值对应的随钻测井数据为yk(k=1,2,3,…,n2)。其中，n2为重采样后的深度点总个数。

6) 利用重采样模型对每个重采样点进行随钻测井数据重构：首先，利用对半插入排序法确定重采样点的深度值rk(k=1,2,3,…，n2)落在采样区间哪2个采样点深度dj(j=1,2,3,…,n1)之间；然后,根据建立的重采样模型结合采样点值xj(j=1,2,3,…,n1)求取每个重采样点对应的随钻测井数值yk(k=1,2,3,…,n2)。

Akima插值方法与常规方法的具体实现过程如图1所示。

 图1 Akima插值方法及常规方法随钻测井实时数据等间距处理过程 Fig.1 Real-time LWD data equal interval processing with the Akima interpolation method and the conventional method

3 应用实例

 图2 随钻测井实时数据间隔分布直方图 Fig.2 Interval histogram of real-time LWD data

 图3 随钻测井实时数据奇异值检测与剔除结果 Fig.3 Real-time LWD data singular value detection and elimination results

 图4 Akima插值方法、常规方法处理结果与随钻测井原始数据对比 Fig.4 Comparison chart of LWD raw data points between the conventional method results and the Akima interpolation method

 图5 常规方法、Akima插值方法处理结果与随钻测井原始数据、内存数据对比1 Fig.5 Results comparison chart 1 of the detail of LWD real-time data points,memory data points,the conventional method and the Akima interpolation method

 图6 常规方法、Akima插值方法处理结果与随钻测井实时数据、内存数据对比2 Fig.6 Results comparison chart 2 of the detail of LWD real-time data points,memory data points,the conventional method and the Akima interpolation method

4 结 论

1) 采用薄层阈值法结合峰峰/谷谷比值法对数据奇异点进行检测与剔除，并采用数据网格化分析及Akima插值方法对数据进行重采样，解决了随钻测井实时数据采样密度不均匀造成的“黑点”及“拉直线”问题。

2) 将Akima插值方法应用于随钻测井实时数据处理，比较处理后的随钻实时数据与内存数据，发现该方法与常规方法相比，最大误差及平均误差小，相关系数大，说明应用该方法处理后的随钻测井实时数据与内存数据具有更好的相似性和一致性。

3) Akima插值方法能够满足不同随钻测井曲线之间、随钻测井实时曲线与内存随钻测井曲线之间、随钻测井实时曲线与电缆测井曲线之间相关的对比需求。

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#### 文章信息

Ma Hai, Xiao Hongbing, Yang Jinzhou, Li Yonghua

A Real-Time LWD Data Processing Method Based on Akima Interpolation

Petroleum Drilling Techniques, 2015, 43(03): 82-86.
http://dx.doi.org/10.11911/syztjs.201503016