频率域复电阻率数学模型研究

On Mathematic Model of Complex Resistivity in Frequency Domain.

应用电阻和电容网络模型来模拟电极发射法交变电场岩石阻抗。根据电化学理论 ,给出每个电子元件的数学表达式 ,使网络模型与地层参数 (孔隙度、地层水矿化度、阳离子交换量和含水饱和度 )联系起来 ,从而使网络模型转换成用地层参数描述的数学模型。然后 ,进行数学模型计算结果与岩样实验数据拟合 ,确定了数学模型中的待定系数。再应用阿尔奇公式求出复电阻率。这样 。

The rock impedance with two electrode arrangement in alternating current field is simulated by a new resistance and capacitance network model. From the electrochemistry theory, the mathematic expressions of electric elements are derived, through which the network model and formation parameters(e.g. porosity,formation water salinity, CEC,water saturation) are correlated with each other .So the network model is changed to mathematic model expressed formation parameters. Then undetermined parameters in mathematic model are confirmed by fitting mathematic model results to rock experiment data.Finally complex resistivity is calculated by Archie equation. The mathematic model can describe the response characteristic of rock complex resistivity.