基于阿尔奇公式的三维直流电阻率有限元正演

Three-Dimensional DC Finite Element Orthogonal Simulations Based on the Archie Formulation

关键词:  直流电阻率  阿尔奇公式  有限单元法  数值模拟

Key words:  Archie Formula  DC Resistivity Method  Finite Element Method  Numerical Simulation

摘要:

水文地质模型中介质电阻率往往受孔隙度、含水饱和度等参数共同影响，当前有关直流电阻率方法在水文地质勘探中的研究，尚未深入分析相关参数对正演响应的影响。因此，本文基于阿尔奇公式研究了适用于渗流条件的三维直流电阻率有限元正演。采用非结构四面体网格进行区域离散,以准确刻画地质模型；通过阿尔奇公式建立孔隙度、含水饱和度等参数与岩石电阻率的内在联系,构建渗流场的多参数模型；以典型砂岩型模型与砂岩型油水模型为例开展了一系列的数值模拟,分析了不同阿尔奇参数条件下的正演视电阻率响应规律。数值模拟结果表明,孔隙度、含水饱和度、胶结指数以及溶液电阻率对三维直流电正演响应的影响不容忽视；基于阿尔奇公式相关参数与视电阻率影响规律分析,为深入研究渗流场提供参考。

Abstract:

In hydrogeological models, the resistivity of the medium is often jointly affected by parameters such as porosity and water saturation.However,current research on the application of direct current(DC) resistivity methods in hydrogeological exploration has not delved deeply into the impact of relevant parameters on forward modeling response. Therefore, this paper presents a study on 3D DC resistivity forward modeling using finite element method based on Archie's formula, which is applicable to seepage condition.An unstructured tetrahedral mesh is used for regional discretization to accurately depict the geological mpdel; Archie's formula establishes the intrinsic relationship between parameters such as porosity,water saturation.and rock resistivity ,constructing a multiparameter model of the seepage field. A series of numerical simulations are conducted using typical sandstone models and sandstone oil-water models as examples,analyzing the charac- teristic of apparent resistivity response under different Archie parameter conditions. The synthetic example show that porosity,water saturation, cementation index,and solution resistivity significanly affect the re- sponse from forward modeling; the analysis of the relationship between Archie's formula-related parameters and apparent resistivity provides a reference for further research on seepage fields.