# 臺灣博碩士論文加值系統

(44.192.254.59) 您好！臺灣時間：2023/01/27 19:30

:::

### 詳目顯示

:

• 被引用:0
• 點閱:163
• 評分:
• 下載:18
• 書目收藏:0
 石油油井在鑽井、探勘、植入鋼套管、固井過程中，油井形成圓柱多層結構。傳統油井超聲波探勘技術，會將測井儀器置於圓柱多層結構內，超聲波轉能器 (ultrasonic transducer) 發射訊號產生彈性波於地質結構中傳遞，同時其亦可接收反射訊號，藉此了解地層結構的狀態並確認固井水泥層的完善。本論文的目的是協助完成與美國Halliburton 新加坡子公司的建教合作計畫中關於圓柱多層結構中的彈性波 (elastic waves) 場型的基礎分析，進而幫助Halliburton公司在石油探勘、固井方面所需的彈性波模擬技術有所提升。吾人首先回顧彈性力學中的基本物理量，包含應力 (stress)、應變 (strain)、及剛度張量 (stiffness tensor)。藉由描述連續介質的廣義虎克定律 (Hooke''s law) 與牛頓第二運動定律 (Newton''s second law of motion)，吾人可獲得於連續介質中傳遞的彈性波的控制方程式：速度-應力耦合一階偏微分方程式 (velocity-stress coupled first-order PDE)。此控制方程式可進一步推導出彈性波所滿足之向量波動方程式，其解包含兩種擾動模態：P波與S波。接著吾人將採用時域有限差分法 (FDTD, finite-difference time-domain method) 將控制方程式離散化以在 MATLAB 平台上進行數值模擬。各個未知物理量的安排採用標準的錯置網格 (staggered layout)。FDTD的模擬將在標準矩形網格與圓柱形網格上實現。藉著將圓柱形網格的計算結果內插至矩形網格的取樣位置上，吾人可更嚴謹地交錯驗證這兩種網格下模擬結果的正確性。在選取適當的模擬參數下，矩形網格與圓柱形網格的模擬結果近乎一致，並對模擬結果所得的應力場 (stress field) 與速度場 (velocity field) 的場型作圖，藉此了解彈性波在圓柱多層結構中的場型分佈。
 In oil field exploration, various logging devices are put into the borehole structure during and after the drilling process and also after the well cementation job to check for the hydraulic isolation between different fluid layers. Ultrasonic transducers transmit acoustic signals and produce elastic waves in the geological structure. The reflected and scattered signals are then received and processed at the same time. By the sonic and ultrasonic measuring techniques, we may understand the compositions and orientations of the geological structure and confirm the isolation quality of the cementing layer. This work is part of the four-year cooperative education research program “Modeling of borehole ultrasonic measurement” between National Sun Yat-sen University and Halliburton Far East Pte Ltd.We begin with the review of the basic physics of elasticity, including definitions of stress, strain, and stiffness tensors. For continuous media, we may apply the Hooke''s law to linearly relate the strain and the stress tensors. This is followed by Newton''s second law of motion to obtain, VS-PDEs, the first-order (in time and space), velocity-stress coupled partial differential equations for elastic wave propagation in the continuum. These control equations can be shown to be equivalent to the standard second-order vector wave equations for elastic waves and the solutions are well known to include both compressional (P) waves and shear (S) waves.We use the FDTD method to discretize the first-order VS PDEs and perform numerical simulations on the MATLAB platform. The arrangement of unknown quantities is based on the standard staggered grid (in both space and time) layout. Simulations in FDTD will be implemented on standard rectangular grid in both the Cartesian and polar coordinate systems. The calculations in the cylindrical mesh are then mapped into a rectangular grid for cross verification with the calculations done in the Cartesian mesh. By selecting the appropriate simulation parameters, simulation results in rectangular grid and in cylindrical grid are nearly identical. We plot, from these simulation results, for both types of the stress and velocity components. From these results we are able to gain clear physical pictures regarding the distribution, propagation and scattering of the elastic waves in a cylindrical multilayer structure.
 論文審定書 .................................................................................................... i誌謝 ............................................................................................................... ii中文摘要 ...................................................................................................... iii英文摘要 ...................................................................................................... iv目錄 ............................................................................................................... v圖次 ............................................................................................................ viii表次 ............................................................................................................... x第一章 緒論 ............................................................................................... 11.1 研究動機 ........................................................................................................... 11.2 研究方法與架構 ............................................................................................... 1第二章 彈性波波動方程式推導 ............................................................... 42.1 彈性力學物理概念 ........................................................................................... 42.1.1 應力與應變之定義 ................................................................................. 42.1.2 廣義虎克定律 ....................................................................................... 102.1.3 連續介質中的牛頓第二運動定律 ....................................................... 122.2 速度-應力耦合一階偏微分方程式推導 ....................................................... 152.2.1 二維直角坐標系下的形式 ................................................................... 152.2.2 二維圓柱座標系下的形式 ................................................................... 172.3 彈性波波動方程式推導 ................................................................................. 20第三章 時域有限差分法 (FDTD) 簡介與實現 ................................... 233.1 時域有限差分法之概述 ................................................................................. 233.2 時域有限差分法之實現說明 ......................................................................... 263.2.1 FDTD的布局與離散化 ...................................................................... 263.2.2 不連續界面的處理方法 ....................................................................... 283.2.3 時間步與空間步的參數最佳化 ........................................................... 293.2.4 計算邊界的處理方法 ........................................................................... 32第四章 均勻介質中的彈性波場型計算 ................................................. 334.1 二維矩形網格FDTD的模擬 ........................................................................ 344.1.1 矩形網格的布局與方程式離散化 ...................................................... 344.1.2 矩形網格的模擬結果 .......................................................................... 394.2 二維圓柱形網格FDTD的模擬 .................................................................... 424.2.1 圓柱形網格的布局與方程式離散化 .................................................. 424.2.2 圓柱形網格的模擬結果 ...................................................................... 474.3 等間距柱形網格轉換為等間距矩形網格 ..................................................... 504.3.1 二維內差法說明 ................................................................................... 504.3.2 圓柱形網格與矩形網格的交互驗證 ................................................... 50第五章 圓柱多層二維結構中的彈性波場型計算................................. 535.1 圓柱多層結構與FDTD模擬 ........................................................................ 535.1.1 圓柱多層結構 ....................................................................................... 535.1.2 FDTD 模擬 ........................................................................................... 545.2 圓柱形網格FDTD的彈性波場型模擬結果與討論 .................................... 575.2.1 圓柱多層結構—水泥層無裂縫 ........................................................... 575.2.2 圓柱多層結構—水泥層中存有裂縫 ................................................... 635.2.3 圓柱多層結構—軌跡比較圖 ............................................................... 68第六章 結論 ............................................................................................. 72參考文獻 ..................................................................................................... 74
 [1] H.-W. Chang and C. J. Randall, “Finite-difference time-domain modeling ofelastic wave propagation in the cylindrical coordinate system,” IEEE UltrasonicsSymposium, 1988.[2] K. S. YEE, “Numerical solution of Initial Boundary Value Problems Involving Maxwell''s Equations in Isotropic Media,” IEEE Transactions on Antennas and Propagation, 1966.[3] Hamid R.Hamidzadeh and Reza N. Jazar, Vibrations of Thick Cylindrical Structures, New York: Springer.[4] Hung Loui, “1D-FDTD using MATLAB,” Student Member IEEE[5] Salam Alnabulsi, (2012). Introduction to elastic wave equation, Retrieved June 9, 2015, from University of Calgary,from http://people.ucalgary.ca/~maelena/AMAT621/AlNabulsi_lect5.pdf[6] Strains in Cylindrical Coordinates, Retrieved June 22, 2015, from Iowa State University, from http://www.public.iastate.edu/~e_m.424/Strain-Cylindrical.pdf[7] Chapter 5 The equations of linear elasticity, Retrieved May 30, 2015, form , University of Manchester http://www.maths.manchester.ac.uk/~ahazel/MATH35021/elasticity_summary.pdf[8] C.T. Schroeder and W. R. Scott, Jr. ” Finite-difference time-domain model for elastic waves in the ground,” School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA[9] Akira Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice Hall, Englewood Cliffs, New Jersey, 1991.[10] Allen Taflove and Susan C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition, Artech House, Norwood, MA, 2005.[11] H.-W. Chang and S.-Y. Mu, “Semi-analytical solutions of the 2-D Homogeneous Helmholtz equation by the method of connected local fields,” Progress In Electromagnetics Research, Vol. 109, 399-424, 2010.[12] S.-Y. Mu and H.-W. Chang, “Theoretical foundation for the method of connected local fields,” Progress In Electromagnetics Research, Vol. 114, 67-88, 2011.[13] Laurent Anne and Quang Huy Tran, “Dispersion and cost analysis of some finite difference schemes in one-parameter acoustic wave modeling,” Computational Geosciences, Vol. 1, 1-33, 1997.[14] Kishore Rama Rao, John Nehrbass, and Robert Lee, “Discretization errors in finite methods: issues and possible solutions,” Comput. Methods Appl. Mech. Engrg. ,Vol. 169, 219-236, 1999.[15] E. L. Lindman, ““Free-space” boundary conditions for the time dependent wave equation,” Journal of Computational Physics, Vol. 18, 66-78, 1975.[16] Bjorn Engquist and Andrew Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Applied Mathematical Science, Vol. 74, 1765-1766, 1977.[17] Robert Clayton and Bjorn Engquist, “Absorbing boundary conditions for acoustic and elastic wave equations,” Bulletin of the Seismological Society of America, Vol. 67, 1529-1540, 1977.[18] Mur, G., “Absorbing boundary conditions for the finite difference approximation of the time domain electromagnetic field equation,” IEEE Trans. Electromagnetic Compat., EMC-23, Vol. 4, 377-382, November 1981.[19] J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, Vol. 114, 185-200, 1994.[20] Daniel S. Katz, Eric T. Thiele, and Allen Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave and Guided Wave Letters, Vol. 4, 268-270, 1994.[21] Stephen D. Gedney, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagat., Vol. 44, 1630–1639, 1996.
 電子全文
 國圖紙本論文
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 1 壓力與犯罪行為之縱貫性研究 2 發光二極體之薄膜應力與光電特性的關係 3 三維有限元素分析補綴物連結與否對植體旁骨內應力及應變的影響 4 越南北部紅河剪切帶自中生代以來應變史之探討 5 中尺度孔洞(Si/MCM-41&Pt/Si/MCM-41)薄膜及(GeSi/Ge)介面奈米結構研究:同步輻射實驗 6 Si(100)/Ta/Co/AlOx/Co/IrMn/Ta系統之穿隧磁阻及外加應力對該磁阻之影響 7 從大客車車身結構剖析客車應有的安全設計之研究 8 胸腰椎骨之表面應變量測與分析 9 覆晶封裝中底膠材料之最佳化材料參數研究 10 台灣地區BATS地震矩張量震源解的品質評估及其在地震地體構造上的應用 11 各種板件在受邊界應力下之潛變及潛變損壞分析 12 高強度混凝土軸壓下之力學行為 13 拉伸老化對聚酯彈性體物性之影響 14 平面震波通過橈性與剛性斜面之研究 15 大客車車體結構之安全性分析與研究

 無相關期刊

 1 陣列式鏡頭影像品質提升之探討 2 以分子動力學模擬二硫化鉬奈米線機械性質與熱穩定性質 3 數位影像相關法於Cr薄膜殘留應力的量測 4 新穎有機光電材料分子排列與載子傳輸特性之研究 5 嵌入式電極光纖之製作與對光纖折射率之影響 6 動態驅動三穩態膽固醇液晶之研究 7 含isoindigo與bodipy之施體材料於光伏元件之表現 8 雙芴環聚芳香醚之合成及其應用於高分子發光二極體 9 調控液晶微環形共振腔之研究 10 Facebook上的利益與風險之拉鋸：人氣需求與隱私顧慮對於Facebook隱私管理之影響 11 搭載能量收割及噴泉碼機制之感知無線電網路中最佳資源分配 12 雙向式中繼點網路中考慮通道估測誤差下中繼點選擇之效能分析 13 臺灣綠黨支持者投票考量與特性之初探 14 實廠含重金屬有機廢水活性污泥法改善及化學反應平衡應用之效能預測 15 應用火法再製銀合金線之可行性評估

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室