任意各向异性电阻率三维非结构有限单元数值模拟及其影响研究
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摘要
以各向同性介质为基础的电法勘探理论在很大程度上取得了成功,广泛应用于金属矿、油气资源勘探,水文、工程、环境等浅层探测以及地壳、上地幔探测。然而地下介质的电性各向异性是客观存在的,其产生的地电场与各向同性介质产生的地电场存在着不可忽视的差异,导致观测数据解释的很大偏差甚至难于解释。各向同性电阻率用一个标量描述,而各向异性电阻率随方向变化,通常用一个张量表示。各向同性电阻率是各向异性电阻率的一种特殊情况；对于具有水平层理结构的岩石(多见于沉积岩)或裂隙水平发育的区域,其电阻率是横向同性(VTI)的,需要用两个量来表达；对于具有倾斜层理的岩层或裂隙区,其电阻率是对称轴倾斜的横向同性(TTI),需要用三个量来描述；任意各向异性电阻率则具有六个独立分量。在油气勘探及储层评价中,薄交互储层和裂缝性储层的电阻率各向异性将极大地影响含油气饱和度的评价精度；在地震电磁监测中,电阻率各向异性可反映地壳岩石的应力和微破裂分布,对地震监测预报也有着举足轻重的作用。由于电阻率各向异性理论的复杂性,迄今为止,国内外电法勘探数据的处理解释还主要基于各向同性介质模型,电阻率各向异性的研究仍处于初始阶段,主要是针对各向异性均匀半空间和一维介质的解析解及其应用研究,而实际地下一般为三维复杂介质,因此远远不能满足实际应用的需要。
各向异性电阻率三维问题基本没有解析解,必须利用有限元等方法进行数值计算,而计算区域的网格剖分非常重要,直接影响到三维有限元数值模拟计算的工作量及结果的准确度。本文首先系统地研究了六面体网格、不对称四面体网格、对称四面体网格等规则三维网格剖分对电阻率三维有限元模拟的影响,发现不对称网格剖分的计算结果存在固有的非对称性,即导致虚假的各向异性现象,对真实的电阻率各向异性特征分析带来极为不利的后果。针对这一问题,论文第一次实现了任意各向异性电阻率三维非结构有限单元数值模拟,计算结果精确高,解决了虚假各向异性问题。同时,非结构化网格还具有单元质量可控、允许局部加密、能够模拟复杂几何模型等优点,使得三维非结构有限单元求解效率大幅提高,在精度几乎一致的情况下,非结构化网格相对于规则网格,计算时间和存储量均可下降约一个数量级。
各向异性电阻率三维非结构有限元数值模拟结果揭示了TTI介质各向异性在地面上两个正交方向观测结果畸变的规律,指出了在各向同性介质中成功运用的P2不变量在复杂三维介质中依然有效,但在表征复杂介质电阻率各向异性特征时,其有效性有限,相关问题的探索才刚刚开始。另外,热干岩地热开发合成模型的数值模拟表明,电阻率各向异性可以很好地反映水力压裂系统中岩石的破裂方向,结果对资源、能源勘探开发有重要实际意义。
目前的电阻率反演解释均是基于各向同性介质模型,二维反演已普遍应用于实际勘探,电阻率三维反演也渐渐成熟。然而,各向异性电阻率反演,尤其是多维(二、三维)各向异性电阻率反演由于相关的正演计算一直没有很好解决而鲜有报道。基于任意各向异性电阻率三维非结构有限单元数值模拟,我们可以对二、三维各向异性电阻率模型的响应数据进行各向同性介质反演,结果表明,介质的各向异性对现阶段在用的二、三维反演解释结果有可能造成很大的偏差。
Electrical prospecting basing on isotropic theory generally achieves great success. It is widely applied in exploration of ore and hydrocarbon. It is also popular in near surface detection in hydrology, engineering, environment and crust, upper mantle detection. However, the underground anisotropy really exists and large errors will be produced if anisotropic structure is considered as isotropic. Isotropic resistivity is expressed as a scalar while anisotropic resistivity depends on directions and it is expressed as a tensor. Actually, isotropic resistivity is a special case of anisotropic resistivity. Two quantities should be used to express resistivity in transverse isotropic (VTI) media, just as laminating materials (e.g. sedimentary rock) and areas with horizontal fractures. In dipping laminated rocks and fracture areas, the resistivity is tilted transverse isotropic (TTI), whose resistivity should be expressed as three quantities. There are six independent quantities for arbitrary anisotropic resistivity. In hydrocarbon exploration and reservoir evaluation, the electrical anisotropy of superposed layers and fractured areas greatly influences the accuracy of evaluation of saturation. Besides, electrical anisotropy is especially important for earthquake monitoring and forecast because the anisotropy of resistivity reflects the stress of crust rocks and micro-fractures distribution in geo-electromagnetic monitoring. Owing to the complication of anisotropic theory, the interpretation of geo-electrical data is mainly focused on isotropic models at home and abroad. The research of anisotropic resistivity is just in preliminary step, which is mainly concerning the analytical solution and application of anisotropic half-space and1D model. However, these are far from actual applications because the real underground is generally3D and much more complex.
There is almost no analytical solution in3D anisotropic resistivity media. It's necessary to simulate anisotropic resistivity using numerical methods such as finite element (FE) method. Subsequently, mesh generation is very important which directly influences the efficiency and accuracy of3D FE modeling. We systematically discuss the influence of regular hexahedral grid, asymmetric tetrahedral grid (TS grid) and symmetric tetrahedral grid (TF grid) on3D FE modeling in this paper. It is found that artificial anisotropy exists when using TS grid which confuses us when analyzing anisotropic characteristics. We finish the3D arbitrary anisotropic resistivity modeling using unstructured finite element methods in the first time. Numerical code shows high accuracy and avoids artificial anisotropy. Besides, the unstructured grid also allows element quality controlling, local refinement and complex geometry simulation, which greatly improve the efficiency of3D FE modeling. For almost the same accuracy, both memory requirement and calculation time of3D unstructured FE modeling nearly reduce by one order in comparison to the modeling on regular grid.
3D unstructured finite element simulations for typical TTI media reveal the serious distortion of results in two orthogonal directions. The excellent parameter of P2invariant used in isotropic media is found to be really efficient for3D complicated model, however, it shows limited accuracy while used in3D anisotropic media. Our3D FE simulation for a synthetic anisotropic model of energy exploration in hot-dry-rock area illustrates that the anisotropy of resistivity is able to reflect the fracture system by hydraulic pressure, showing significant potential in resource and energy explorations and exploitations.
The resistivity imagings mainly focus on isotropic media at present. Two dimensional resistivity inversion has already been applied in real exploration and three dimensional resistivity inversion becomes fruitful as well. However, anisotropic resistivity inversion, especially two and three dimensional inversion is hardly seen because the forward modeling is not well solved so far. Basing on3D arbitrary anisotropic resistivity FE modeling, we can use the2D or3D isotropic inversion method to data set from2D or3D anisotropic model in order to measure the effect of anisotropy. Our results show the anisotropy may lead to great deviation in inverted model while the state-of-art2D and3D inversion methods faced on isotropic media are employed.
各向异性电阻率三维问题基本没有解析解,必须利用有限元等方法进行数值计算,而计算区域的网格剖分非常重要,直接影响到三维有限元数值模拟计算的工作量及结果的准确度。本文首先系统地研究了六面体网格、不对称四面体网格、对称四面体网格等规则三维网格剖分对电阻率三维有限元模拟的影响,发现不对称网格剖分的计算结果存在固有的非对称性,即导致虚假的各向异性现象,对真实的电阻率各向异性特征分析带来极为不利的后果。针对这一问题,论文第一次实现了任意各向异性电阻率三维非结构有限单元数值模拟,计算结果精确高,解决了虚假各向异性问题。同时,非结构化网格还具有单元质量可控、允许局部加密、能够模拟复杂几何模型等优点,使得三维非结构有限单元求解效率大幅提高,在精度几乎一致的情况下,非结构化网格相对于规则网格,计算时间和存储量均可下降约一个数量级。
各向异性电阻率三维非结构有限元数值模拟结果揭示了TTI介质各向异性在地面上两个正交方向观测结果畸变的规律,指出了在各向同性介质中成功运用的P2不变量在复杂三维介质中依然有效,但在表征复杂介质电阻率各向异性特征时,其有效性有限,相关问题的探索才刚刚开始。另外,热干岩地热开发合成模型的数值模拟表明,电阻率各向异性可以很好地反映水力压裂系统中岩石的破裂方向,结果对资源、能源勘探开发有重要实际意义。
目前的电阻率反演解释均是基于各向同性介质模型,二维反演已普遍应用于实际勘探,电阻率三维反演也渐渐成熟。然而,各向异性电阻率反演,尤其是多维(二、三维)各向异性电阻率反演由于相关的正演计算一直没有很好解决而鲜有报道。基于任意各向异性电阻率三维非结构有限单元数值模拟,我们可以对二、三维各向异性电阻率模型的响应数据进行各向同性介质反演,结果表明,介质的各向异性对现阶段在用的二、三维反演解释结果有可能造成很大的偏差。
Electrical prospecting basing on isotropic theory generally achieves great success. It is widely applied in exploration of ore and hydrocarbon. It is also popular in near surface detection in hydrology, engineering, environment and crust, upper mantle detection. However, the underground anisotropy really exists and large errors will be produced if anisotropic structure is considered as isotropic. Isotropic resistivity is expressed as a scalar while anisotropic resistivity depends on directions and it is expressed as a tensor. Actually, isotropic resistivity is a special case of anisotropic resistivity. Two quantities should be used to express resistivity in transverse isotropic (VTI) media, just as laminating materials (e.g. sedimentary rock) and areas with horizontal fractures. In dipping laminated rocks and fracture areas, the resistivity is tilted transverse isotropic (TTI), whose resistivity should be expressed as three quantities. There are six independent quantities for arbitrary anisotropic resistivity. In hydrocarbon exploration and reservoir evaluation, the electrical anisotropy of superposed layers and fractured areas greatly influences the accuracy of evaluation of saturation. Besides, electrical anisotropy is especially important for earthquake monitoring and forecast because the anisotropy of resistivity reflects the stress of crust rocks and micro-fractures distribution in geo-electromagnetic monitoring. Owing to the complication of anisotropic theory, the interpretation of geo-electrical data is mainly focused on isotropic models at home and abroad. The research of anisotropic resistivity is just in preliminary step, which is mainly concerning the analytical solution and application of anisotropic half-space and1D model. However, these are far from actual applications because the real underground is generally3D and much more complex.
There is almost no analytical solution in3D anisotropic resistivity media. It's necessary to simulate anisotropic resistivity using numerical methods such as finite element (FE) method. Subsequently, mesh generation is very important which directly influences the efficiency and accuracy of3D FE modeling. We systematically discuss the influence of regular hexahedral grid, asymmetric tetrahedral grid (TS grid) and symmetric tetrahedral grid (TF grid) on3D FE modeling in this paper. It is found that artificial anisotropy exists when using TS grid which confuses us when analyzing anisotropic characteristics. We finish the3D arbitrary anisotropic resistivity modeling using unstructured finite element methods in the first time. Numerical code shows high accuracy and avoids artificial anisotropy. Besides, the unstructured grid also allows element quality controlling, local refinement and complex geometry simulation, which greatly improve the efficiency of3D FE modeling. For almost the same accuracy, both memory requirement and calculation time of3D unstructured FE modeling nearly reduce by one order in comparison to the modeling on regular grid.
3D unstructured finite element simulations for typical TTI media reveal the serious distortion of results in two orthogonal directions. The excellent parameter of P2invariant used in isotropic media is found to be really efficient for3D complicated model, however, it shows limited accuracy while used in3D anisotropic media. Our3D FE simulation for a synthetic anisotropic model of energy exploration in hot-dry-rock area illustrates that the anisotropy of resistivity is able to reflect the fracture system by hydraulic pressure, showing significant potential in resource and energy explorations and exploitations.
The resistivity imagings mainly focus on isotropic media at present. Two dimensional resistivity inversion has already been applied in real exploration and three dimensional resistivity inversion becomes fruitful as well. However, anisotropic resistivity inversion, especially two and three dimensional inversion is hardly seen because the forward modeling is not well solved so far. Basing on3D arbitrary anisotropic resistivity FE modeling, we can use the2D or3D isotropic inversion method to data set from2D or3D anisotropic model in order to measure the effect of anisotropy. Our results show the anisotropy may lead to great deviation in inverted model while the state-of-art2D and3D inversion methods faced on isotropic media are employed.
引文
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