中文摘要：

自然电位和激发极化电位测井响应所涉及的离子导体激发极化电位的微观机理解释，主要依据双电层形变假说和浓差极化假说，缺少定量描述的数学模型和理论体系.本文利用孔隙介质的微观毛管模型，给出了毛管模型中双电层理论和阳离子交换量与Zeta电位的关系，推导出毛管中离子流量和电流强度表达式.由电荷守恒定律和物质守恒定律，推导出毛管中离子浓度分布的解析表达式，建立了描述含水泥质砂岩激发极化电位和自然电位的数学模型.从而系统地严格证明了含水泥质砂岩激发极化现象是在电流场和浓度梯度场的共同作用下，由孔隙中离子浓度浓差极化电位和双电层形变电位形成的.并且证明了描述泥质砂岩自然电位的数学方程和描述激发极化电位的数学方程及形成机理是一致的.计算结果表明：激发极化极化率随孔隙度和渗透率的增大而减小；极化率随溶液浓度的增加而减小，随阳离子交换量的增加而增加；证明了地层水浓度、阳离子交换量是影响自然电位大小的主要因素.

英文摘要：

The microscopic mechanisms of induced polarization potential involved in the spontaneous potential and the induced polarization potential logging response is mainly from the hypothesis of the electrical double-layer deformation and the concentration difference polarization. There is no mathematical model to describe this up to now. In this paper, we formulated the flux of ion and the electric current from the theory of electrical double-layer and the relationship between the cation exchange capacity and Zeta potential based on the microscopic capillary model of porous media. We derived an analytical expression of ion concentration distribution and the mathematical model of the induced polarization potential and the spontaneous potential for water bearing shaly sandstone from the conservation law of charge and the conservation law of matter. The work rigorously proved that the induced polarization of water bearing shaly sandstone is caused by the ion concentration difference polarization potential and the deformation potential of electrical double-layer under the common influence of the electric current field and the concentration gradient field. And it proved that the mechanism and the equation describing spontaneous potential in shaly sandstone are consistent with that of induced polarization potential. The results show that the induced polarizability decreases with the increase in porosity, permeability and concentration of solution but increases with the increase in the cation exchange capacity. It noted that the concentration of formation water and the cation exchange capacity are the main factors that influence the spontaneous potential.