基于连通导电理论和HB方程的骨架导电纯岩石电阻率模型

Matrix-conducting resistivity model for clean sands based on connectivity conductance theory and HB equation

针对现有导电模型很难描述骨架含导电矿物黄铁矿的岩石导电规律的难题,利用骨架完全由导电颗粒组成的人造岩样以及骨架部分由导电颗粒组成的天然和人造岩样的岩电实验数据,研究水电阻率和导电颗粒体积分数变化对岩石导电规律的影响,得出骨架导电纯岩石的地层因素与孔隙度及电阻增大系数与含水饱和度在双对数坐标上为非线性关系,随水电导率减小或导电颗粒体积分数增大,地层因素和电阻增大系数值降低。根据骨架导电纯岩石的组成,结合连通导电理论特点,将骨架导电纯岩石分为不导电骨架相、导电骨架相和自由流体相。基于连通导电方程只能描述单一导电相的两相混合介质导电规律而HB方程能描述两相均导电的混合介质导电规律的特点,基于连通导电理和HB方程建立骨架导电纯岩石电阻率模型。结果表明,骨架导电纯岩石电阻率模型预测的地层因素与孔隙度以及电阻增大系数与含水饱和度的理论关系与实验规律相符且模型满足物理约束,该模型能够描述骨架完全和部分由导电矿物组成的纯岩石的导电规律,可用于定量评价骨架导电低阻油层的饱和度。

Most of the commonly used resistivity models are unable to give a precise description of conductive laws of sands whose rock matrix contains a certain amount of pyrite,therefore it is necessary to study the conductive laws and to propose a matrix-conducting resistivity model. The effects of water resistivity and conductive matrix grain content in matrix-conducting clean sands are first analyzed by using laboratory resistivity measurements of artificial and field samples,in which the rock matrix is composed partially or entirely of conductive grains. The results shown in a log-log graph suggest nonlinear relationships between formation resistivity factor and porosity,and between formation resistivity index and water saturation,respectively.Values of the formation resistivity factor and the index decrease with decreasing water conductivity,or increasing conductive matrix grain content. Second,based on the compositions of matrix-conducting clean sands and the characteristics of connectivity conductance theory,matrix-conducting clean sands are divided into non-conducting matrix phase,conductive matrix phase and free fluid phase. Since the connectivity conductance equation applies to only one conducting composition and one non-conducting composition,while the HB equation can describe systems of two conducting compositions,a new matrix-conducting resistivity model for clean sands is proposed combining the connectivity conductance theory and the HB equation. The results show that the theoretical relationships between formation resistivity factor and porosity,and between formation resistivity index and water saturation predicted by the proposed model are consistent with the experimental values,and the proposed model is in compliance with meaningful physical bounds. The matrix-conducting resistivity model for clean sands can describe the conductive law of matrix-conducting clean sands,in which rock matrix is composed entirely or partially of conductive grains. The proposed model can be applied to quantitatively calculate saturation in matrix-conducting low resistivity reservoirs.