# 非轴对称套管井声场并行计算及声波固井质量评价理论与方法研究

Parallel Computation of Acoustic Field in Non-axisymmetric Cased Holes & Theory and Method Studies of Acoustic Cementing Quality Evaluation

作者： 宋若龙 专业：声学 导师：韩炜 年度:2008 学位：博士

##### 关键词

声波测井 固井质量检测 有限差分 并行计算 单界面波 时频分析##### Keywords

acoustic logging, cementing quality detection, finite difference, parallel computation, single interface wave, time-frequency analysis

本文针对目前声波固井质量检测中存在的若干实际问题,进行了理论、方法研究和有限差分并行数值模拟研究。提出了一种可以计算套管井窜槽时各界面单独响应的方法,详细研究了套管井各种水泥胶结状况下各界面广义反射波对井孔声场的贡献,为CBL-VDL测井II界面评价提供了理论依据,并提出解决方法。针对快速地层下地层波早于套管波到达对测井结果造成的多解性这一问题,通过对快速地层套管井I界面不同胶结状况井内声场的分析得出:用主频40kHz或80kHz的声源测井可以避免快速地层的影响;从常规CBL-VDL测井5ft波形的时频分布可以评价快速地层I界面固井质量。基于信息传递接口(MPI)并行程序设计方案,在计算机集群上,用三维柱坐标系下应力-速度有限差分(SVFD)方法和非裂化完全匹配层(NPML)吸收边界条件,实现了扇区发射接收的非轴对称套管井高频(100kHz)三维瞬态声场模拟的并行计算。系统的考察了不同水泥缺失扇区大小、不同缺失方位角下SBT测井仪8对换能器的波形和首波特征,并进行了对比分析和反演方法的研究,完善了SBT解释方法。本文的并行算法也为同类其它大规模数值计算提供了高效的、经济的手段。

Acoustic logging is one of the main well-log methods, has a wide range of applications in many fields such as oilfield exploration and exploitation, engineering geophysical prospecting. The important part is detecting the cement bond condition in casing holes, also called acoustic cementing quality detection. Well cementing means fixing casing string using cement to seal and isolate oil, water and gas layers, it’s the very important aspect in protecting water and gas layers and ensuring the production life of oil and gas wells. As the constraints environment and the complexity of the underground, cementing jobs often show some quality problems, there is interlayer channeling fluid between casing/cement (first interface) and cement/formation (second interface), so called channeling. Detecting and remedying the quality problems regularly, are essential jobs to ensure the normal production of oil and gas wells. So cementing quality detection is very important in both well completion and production process, and detection technology has been continually developed. Where the acoustic detection technologies are the most successful methods, and are developed to a series of acoustic cementing quality detection technology, become the primary cementing quality evaluation methods. Such as CBL-VDL (Cement Bond Log and Variable Density Log) give the average results of cementing by acoustic amplitude in 3ft, and qualitatively evaluate of the situation second interface by VDL in 5ft. CBL-VDL have a wider application, but they only give the average results of cementing, and are susceptible to kinds of underground environment, their log results have multiple solutions. To solve this problem, in the 1980s and 1990s, ultrasonic echo logging (such as CET, PET, CAST and USI) and segmented bond tool (SBT, Western Atlas, and SBT, Compler) have also been introduced at abroad. They can detect small cement channel. However, these cementing quality detection technologies in development, so far there are still many unresolved issues in theoretical reorganization and evaluation method. The main ones are:①The propagating mechanism of acoustic waves in cased hole with second interface channeling (channel II for short) is not clear, the traditional method that evaluating the second interface bond condition using the intensity of formation arrivals in VDL, usually gives wrong results.②In fast formation (velocity of compressional wave greater than that of tube wave), the formation waves arrival earlier than casing waves, the logging results of CBL-VDL have multiplicity of solutions. With the discovery and exploitation of deep oil and gas field, such as Puguang gas field, Qingshen gas field in China, the cementing quality evaluation in fast formation becomes an urgent problem.③Due to the theoretical study of 100kHz acoustic field transmitted and received by sector transmitters in non-axisymmetric cased holes with sector cement deletion, is not in-depth, the interpretation method for SBT (Compler) logging is very imperfect. So there are lots of mechanisms and evaluation methods yet to be resolved. This dissertation concentrates on the above three problems, by proposing new method, using signal processing technology, numerically simulating 3D transient high-frequency acoustic field using the parallel finite difference algorithm, respectively, carried out systematic studies.For investigating the propagation mechanism of acoustic waves in cased hole with channel II, we proposed a new method to calculating the single interface wave (SIW for short) of cylindrically multilayered media including liquid interlayer. This method bases on the modified generalized reflection and transmission (R/T) matrices (Chen, et. al., 1996), overcomes difficulty of singular transfer matrix, obtains the iterative expressions of generalized R/T matrices, which are used to determine the SIW of each interface and the full waveforms. The use of normalization factors and normalized Lamécoefficients makes the algorithm stable numerically. The validity of SIW method has been confirmed by comparing our result with that of Tubman (1984) and Schmitt (1985). Using the method we investigate the acoustic field in cased hole with good bond, first interface channeling, and second interface channeling, study the contribution of SIWs to full-wave by analyzing the multi-wavetrain in time domain and the spectral energy densities in frequency axial-wavenumber domain. When the second interface is channeling, the first arrival of full waveform is contributed by coupled extensional mode of the casing and cement. Its velocity increase from 4000m/s to 5257m/s, as the thickness of cement annulus decreasing from 29mm to 5mm (the velocity of pipe wave is about 5546m/s), its amplitude increases also. It has strong frequency dispersion when the cement annulus is thick. Because it is the mode wave of coupled waveguides of casing and cement, it doesn’t affected by velocities of formation, and show straight line in VDL. Then according to the characteristics of its travel time and amplitude, the second interface channeling can be identified from good bond and first interface channeling. A field example is given to validate our statements. Aiming at the multiplicity of solutions of CBL-VDL results in fast formations, we investigated the acoustic field in cased hole with different bond condition of first interface, and by analyzing the acoustic field in space frequency domain, we obtained that logging with central frequency 40kHz, the fast formation can be identified by the frequency spectra of waveform received at 5ft, and can avoid the impact of micro-annulus; logging with central frequency 80kHz, both the waveform in time domain and spectra in frequency domain can evaluate the bond condition of first interface accurately, but can not avoid the impact of micro-annulus. The time-frequency analysis of 5ft waveform of normal CBL-VDL (central frequency 20kHz) using smoothed pseudo Wigner-Ville distribution (SPWVD) shows that time-frequency distribution can identify the fast formation. The first arrival energy peaks of SPWVD of first interface channeling and good bond have different characteristics, their arrival time are 0.45ms and 0.7ms, the angles between time axis are 90 degrees and 60-80 degrees, central frequencies are 20-22kHz and 23-24kHz, respectively.For improving the interpretation methods of SBT (Compler Com.), on the cluster created by gigabit switch and 5 computers, using the Message Passing Interface (MPI) to realize data communications between processors, using the second order accuracy stress velocity finite difference (SVFD) in 3D cylindrical coordinate system, and nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC), we implemented the parallel numerical computation of acoustic field in non-axisymmetric cased hole with sector cement deletion. The parallel algorithm makes that 3D SVFD simulation of high frequency acoustic field can be realized on general computers. We also analyzed and investigated the implementation of difference equations in cylindrical coordinate system, mesh-size settings, treatment of interfaces, NPML ABC, MPI parallel programming, the relationship between parallel algorithm performances with the number of processors. We compared the results of parallel algorithm and those of discrete wave-number (DW) method under axisymmetric borehole, good bond cased hole, and free pipe cased hole, with central frequencies 20 kHz and 100 kHz. The comparisons show that the SVFD parallel algorithm are convergent and stable, haven’t grid frequency dispersion phenomenon. The NPML ABC does a perfect job, and there are no reflected waves. The whole waveform including Stoneley waves are excellent agreement with those of DW method. The correctness and accuracy are validated.According to the work principle of SBT logging, 8 transmitting and 8 receiving using 100 kHz source, we simulated the borehole acoustic field in cased hole under various situations of cement sector deletion using parallel algorithm, and quantitatively analyzed the arrival time, amplitude of first minus apex, integral of absolute amplitude and integral of square of amplitude of tube waves. We found that the amplitude was the best choice of inversion of the deletion sector size and azimuth, so only the characteristics of amplitude are given out in this abstract. With the deletion sector increasing in size from 0o to 360o, the average of 8 transmitters’amplitude approximately monotonically linearly increases. The numerical simulation and analysis of 45o deletion sector show that the deletion sector azimuth (azimuth for short) has little impact on the average, the ratio of minimum and maximum average is 93.3%. Therefore, the deletion sector size (size for short) can be obtained directly by the average of 8 transmitters’amplitude. For different size, the characteristics of tube waves with the changes of angle between transmitters and azimuth (angle for short) are very different. When the size is 45o, with the increasing of angle, the amplitude approximately linearly decreases between angle 0o and 80o, every increase of 10o decreases 2 dB, after angle bigger than 80o, the change rate is very small. The azimuth can be obtained by 2 or 3 bigger amplitudes. With the size gradually increasing, the maximal amplitude no longer appears in the minimum angle, the relationship between amplitude and angle is non-monotonic. For inversion of azimuth, the fitting function between amplitude and angle must be obtained first by numerical simulations. Then scan the azimuth from 0o to 360o, for each azimuth, compute sum of square of differential value between the amplitudes of 8 transmitters obtained by the fitting function and obtained by logging. The minimum sum of square corresponds to the real azimuth. Therefore, inversion of size is relatively easy, but inversion of azimuth needs the fitting function of each size obtained by numerical simulations. The more situations are simulated, the more accurate of inversion. The parallel algorithm proposed in this dissertation, can complete the job which needs 4 years using general computer, in 3 months using 5 nodes, and has good expansibility, the more computing nodes, the higher efficiency. Parallel algorithm resolves the need of computing resources satisfactorily, and has an economic advantage.To sum up, the SIW method we proposed is helpful to understand the characteristics and mechanism of acoustic field in cased hole, thereby helpful to get more information from acoustic logging data, provides a theoretical basis and interpretation of second interface evaluation, improves the efficiency of exploration. We provided several schemes for cementing quality evaluation in fast formation use space frequency and time-frequency analysis. We proposed 3D SVFD parallel algorithm, which greatly improved the computing efficiency, perfected the theoretical study of non-axisymmetric cased hole acoustic field and interpretation method of SBT. The parallel algorithm provides a powerful and economic method, and is easy to approach.The works in this dissertation are needed to be carried out in-depth, and process and interpret logging data in field, make the methods playing a role in the production practice. Moreover, cementing quality evaluation under the situations with the micro-annulus, and eccentricity of tool, eccentricity of casing, inclined stratum, cuttings bed in inclined or horizontal well, is also the problems need to be studied in acoustic cementing quality detection technology.

非轴对称套管井声场并行计算及声波固井质量评价理论与方法研究

提要 | 5-8 |

第一章 绪论 | 8-24 |

1.1 声波测井概述 | 8-10 |

1.2 固井、固井质量概述 | 10-11 |

1.3 声波固井质量评价及其中存在的问题 | 11-18 |

1.4 复杂情况下井孔声场的有限差分数值模拟 | 18-21 |

1.5 并行计算与并行程序设计 | 21-22 |

1.6 信号处理技术在声波固井质量检测中的应用 | 22-23 |

1.7 本文的研究内容及方法 | 23-24 |

第二章 单界面波计算及其在固井质量评价中的应用 | 24-50 |

2.1 单界面波方法及正确性验证 | 25-34 |

2.2 水泥胶结好时单界面波分析 | 34-36 |

2.3 I界面窜槽时单界面波分析 | 36-42 |

2.4 II界面窜槽时单界面波分析 | 42-48 |

2.5 小结 | 48-50 |

第三章 快速地层固井质量评价 | 50-68 |

3.1 快速地层固井质量评价方法现状 | 50-53 |

3.2 柱源模型套管井声场的计算 | 53-54 |

3.3 空间－频率域谱分析 | 54-59 |

3.4 时频分析方法 | 59-63 |

3.5 时频分析在声波水泥胶结测井中的应用 | 63-67 |

3.6 小结 | 67-68 |

第四章 非轴对称套管井三维有限差分并行程序设计 | 68-104 |

4.1 柱坐标系下应力－速度有限差分的实现 | 69-77 |

4.2 非裂化完全匹配层（NPML）吸收边界条件 | 77-83 |

4.3 MPI并行程序设计 | 83-89 |

4.4 三维有限差分并行程序MPI+Fortra1190 实现 | 89-95 |

4.5 三维有限差分并行程序正确性验证 | 95-101 |

4.6 并行程序与串行程序计算效率比较 | 101-103 |

4.7 小结 | 103-104 |

第五章 非轴对称套管井声场有限差分模拟 | 104-123 |

5.1 声源、模型、网格参数和水泥缺失扇区位置的表示 | 104-106 |

5.2 套管井不同方位角扇区缺失声场模拟 | 106-113 |

5.3 套管井不同大小扇区缺失声场模拟 | 113-118 |

5.4 缺失扇区大小以及缺失方位的反演方法讨论 | 118-120 |

5.5 小结 | 120-123 |

第六章 总结 | 123-128 |

1. 单界面波计算及其在 II 界面评价中的应用 | 123-124 |

2. 用信号处理方法进行快速地层固井质量评价 | 124-125 |

3. 非轴对称套管井三维有限差分并行程序设计 | 125-126 |

4. 扇区水泥缺失时套管井声场有限差分模拟及反演方法研究 | 126-127 |

5. 相关工作的研究展望 | 127-128 |

附录 | 128-133 |

参考文献 | 133-145 |

攻读博士学位期间发表的学术论文及主要科研成果 | 145-146 |

致谢 | 146-147 |

摘要 | 147-152 |

ABSTRACT | 152-158 |

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