基于二阶B样条的ILK流量反褶积算法改进及应用

doi:10.7623/syxb201803008

石油学报 ›› 2018, Vol. 39 ›› Issue (3): 327-334.DOI: 10.7623/syxb201803008

基于二阶B样条的ILK流量反褶积算法改进及应用

刘文超^1,2, 刘曰武², 朱维耀¹, 孙贺东³

1. 北京科技大学土木与资源工程学院北京 100083;
2. 中国科学院力学研究所北京 100190;
3. 中国石油勘探开发研究院气田开发研究所河北廊坊 065007

收稿日期:2017-06-02 修回日期:2017-12-20 出版日期:2018-03-25 发布日期:2018-04-10
通讯作者: 刘文超,男,1984年8月生,2007年获中国石油大学(华东)学士学位,2013年获中国石油大学(华东)博士学位,现为北京科技大学土木与资源工程学院讲师,主要从事渗流力学及工程应用方面的教学及研究工作。Email:wcliu_2008@126.com
作者简介:刘文超,男,1984年8月生,2007年获中国石油大学(华东)学士学位,2013年获中国石油大学(华东)博士学位,现为北京科技大学土木与资源工程学院讲师,主要从事渗流力学及工程应用方面的教学及研究工作。Email:wcliu_2008@126.com
基金资助:
国家重大科技专项（2011ZX05038-003，2011ZX05046-03）、国家自然科学基金项目（No.51404232）和中央高校基本科研业务费专项基金项目（FRF-TP-17-023A1）资助。

Improvement and application of ILK flow-rate deconvolution algorithm based on the second-order B-splines

Liu Wenchao^1,2, Liu Yuewu², Zhu Weiyao¹, Sun Hedong³

1. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
3. Department of Gas Field Development, PetroChina Research Institute of Petroleum Exploration & Development, Hebei Langfang 065007, China

Received:2017-06-02 Revised:2017-12-20 Online:2018-03-25 Published:2018-04-10

摘要/Abstract

摘要：

受ILK压力反褶积算法压力计算精度高的启发，基于一个等价的褶积积分方程，改用流量数据代替原算法所采用的累积流量数据进行反褶积计算，并给出了反褶积算法的快速求解方法：利用褶积积分的数学性质，采用按照压力降落段进行分段积分的方法，快速地解析求解反褶积计算过程中的敏感性矩阵；同时利用二分法快速查找每组流量数据点所属的压力降落段，进一步提高了计算效率。通过理论算例和实际算例的测试分析表明，改进后的ILK流量反褶积算法具有更高的计算精度，尤其使初始和后期阶段的流量数据精度有了较大提高，实际算例的计算结果更加符合单位井底压力降下的流量递减变化规律。与原算法相比，改进算法在产量递减分析时可以获得更长的表征拟稳态流的特征直线段，显著提高了数据的拟合效果，也具备较高的计算速度、稳定性及实用性。因此，将该反褶积算法应用于产量递减分析不仅可以有效降低数据误差影响的敏感性，还可以获得更多的数据信息量，提高数据的拟合效果，降低解释结果的不确定性。

关键词: 反褶积, 产量递减分析, 二阶B样条, 最小二乘法, 生产数据

Abstract:

Inspired by the high-accuracy pressure calculation of ILK production-pressure deconvolution algorithm and based on an equivalent convolution integral equation, the intrinsic accumulative flow data were replaced by flow rate data to carry out the deconvolution calculation. Meanwhile, the fast solution method of deconvolution algorithm was also presented. Using the mathematical property of deconvolution integral, a method of subsection integral was adopted according to the pressure decline segments, so as to quickly analytically solve the sensitivity matrix in deconvolution calculation. Simultaneously, the dichotomy was also applied to quickly search for the pressure decline segment at the data point of each flow rate set, further improving the calculation efficiency. In-depth analyses on theoretical and actual case tests indicate that the improved ILK flow-rate deconvolution algorithm has higher calculation accuracy; especially in the initial and the later periods, the accuracy of flow rate data has been largely improved; the calculation results for actual cases are more consistent with the production rate decline laws corresponding to the unit wellbore pressure drop. In contrast with the original algorithm, the longer characteristic line segments for representing quasi-steady state flow can be gained when analyzing the production decline, obviously improving the data fitting effect. The improved algorithm also exhibits very high calculation speed, good stability and practicability. Therefore, the application of this deconvolution algorithm to production decline analysis can not only effectively reduce the sensibility influenced by data errors, but also acquire more data information, improving data fitting effects and reducing the uncertainty of interpretation results.

Key words: deconvolution, production decline analysis, second-order B-splines, the least square method, production data

中图分类号:

TE319

刘文超, 刘曰武, 朱维耀, 孙贺东. 基于二阶B样条的ILK流量反褶积算法改进及应用[J]. 石油学报, 2018, 39(3): 327-334.

Liu Wenchao, Liu Yuewu, Zhu Weiyao, Sun Hedong. Improvement and application of ILK flow-rate deconvolution algorithm based on the second-order B-splines[J]. Acta Petrolei Sinica, 2018, 39(3): 327-334.

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基于二阶B样条的ILK流量反褶积算法改进及应用

Improvement and application of ILK flow-rate deconvolution algorithm based on the second-order B-splines

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