本文選題：體面積分方程 + 矩量法��； 參考：《電子科技大學(xué)》2015年碩士論文

【摘要】：地球物理測(cè)井中,大斜度井、水平井占據(jù)的比重越來(lái)越大,儀器響應(yīng)在這些測(cè)井環(huán)境中不同于直井環(huán)境,傳統(tǒng)的基于直井的測(cè)井解釋和數(shù)值模擬方法變得不再適用。因此,進(jìn)行電法測(cè)井的正演數(shù)值模擬研究,用于解釋和分析測(cè)井儀器在這些測(cè)井環(huán)境中響應(yīng)和異常現(xiàn)象,這對(duì)于儀器的研發(fā)和工程實(shí)際應(yīng)用具有重要意義。基于以上原因,本文對(duì)體面積分方程矩量法進(jìn)行了研究,并用于電法測(cè)井的數(shù)值模擬。傳統(tǒng)的基于SWG基函數(shù)的體積分方程,需要處理邊界面電荷,幾何建模要共形剖分。而本文采用的基于分片常數(shù)基的非共形體積分方程,不需處理邊界面電荷;采用非共形網(wǎng)格剖分使幾何建模更為靈活;只是需要處理雙梯度Green函數(shù)的超強(qiáng)奇異性積分,本文采用了高階奇異值提取法很好地處理了該積分奇異性問題。本文主要內(nèi)容如下:1.詳細(xì)推導(dǎo)了體積分、面積分、體面積分方程的矩量法求解過(guò)程,采用高階奇異值提取法解決了三類積分方程中涉及的奇異性及近奇異性積分;建立了基于分片常數(shù)基的體積分方程,并結(jié)合面積分方程建立了的體面積分方程,用該方程精確計(jì)算了金屬介質(zhì)組合目標(biāo)的近場(chǎng)以及介質(zhì)內(nèi)部的場(chǎng),實(shí)現(xiàn)了很好的精度;2.采用點(diǎn)匹配法測(cè)試非共形體積分方程,實(shí)現(xiàn)了阻抗矩陣的快速填充并達(dá)到了很好的精度,并且將點(diǎn)匹配法的體積分方程與迦遼金法匹配的面積分方程組合實(shí)現(xiàn)了混合兩種測(cè)試方法的體面積分方程,并在算例中驗(yàn)證了其精度;3.用基于球函數(shù)展開的解析方法求解了環(huán)形線圈的近場(chǎng);4.對(duì)比了水平線圈和傾斜線圈在各向異性地層中的響應(yīng)差異;對(duì)各向同性地層中,不同的傾斜線圈系的測(cè)井響應(yīng)進(jìn)行了數(shù)值仿真,發(fā)現(xiàn)幅度比和相位差變化復(fù)雜,出現(xiàn)兩者變化趨勢(shì)不一致的情況;實(shí)現(xiàn)了對(duì)地層傾斜、井斜的三維測(cè)井問題的計(jì)算;5.對(duì)井眼和鉆鋌作縱向截?cái)?其網(wǎng)格相對(duì)于井眼邊界地層非共形剖分,采用井眼內(nèi)網(wǎng)格隨測(cè)量點(diǎn)移動(dòng)的計(jì)算模式來(lái)數(shù)值模擬儀器在井眼中移動(dòng)測(cè)量的過(guò)程,實(shí)現(xiàn)一套網(wǎng)格的多次使用。
[Abstract]:In geophysical logging, the proportion of high deviated wells and horizontal wells is increasing, and the tool response is different from that of vertical wells in these logging environments. The traditional logging interpretation and numerical simulation methods based on vertical wells are no longer applicable. Therefore, the forward numerical simulation of electrical logging is used to interpret and analyze the response and abnormal phenomena of logging tools in these logging environments, which is of great significance for the research and development of tools and the practical application in engineering. Based on the above reasons, the method of moment of the decent integral equation is studied and applied to the numerical simulation of electric logging. The traditional volume fractional equation based on SWG basis function needs to deal with the boundary surface charge, and the geometric modeling needs conformal dissection. The non-conformal integral equation based on piecewise constant basis does not need to deal with the boundary surface charge, the geometric modeling is more flexible by using non-conformal mesh generation, and the super-singularity integral of the bigradient Green function only needs to be dealt with. In this paper, the high order singular value extraction method is used to deal with the singularity of the integral. The main contents of this paper are as follows: 1. The method of moment for solving volume integral, area fraction and decent integral equation is derived in detail. The singularity and near singularity integral of three kinds of integral equations are solved by the method of high order singular value extraction. The volume fraction equation based on the piecewise constant basis is established, and the decent integral equation based on the area integral equation is established. The near field and the internal field of the combined target in the metal medium are accurately calculated by this equation, and the good precision is achieved. The point matching method is used to test the integral equations of non-conformal bodies. The impedance matrix is filled quickly and the precision is very good. The volume fraction equation of point matching method and the area integral equation of Galerkin method are combined to realize the decent integral equation of mixed two test methods, and its accuracy is verified by an example. An analytical method based on spherical function expansion is used to solve the near field of annular coil. The responses of horizontal coils and tilting coils in anisotropic formations are compared, and the logging responses of different tilting coils in isotropic formations are simulated. It is found that the amplitude ratio and phase difference change are complex. The result shows that the variation trend of the two is not consistent, and the 3-D logging problem of formation inclination and well inclination is realized. The borehole and drill collar are truncated longitudinally, and the meshes are not conformal in relation to the borehole boundary formation. The calculation model of the movement of the borehole meshes with the measured points is adopted to numerically simulate the process of the instrument moving and measuring in the borehole. To achieve a set of grid multiple use.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P631.811

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 肖加奇，，張庚驥;水平井和大斜度井中的感應(yīng)測(cè)井響應(yīng)計(jì)算[J];地球物理學(xué)報(bào);1995年03期

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