基于电震耦合理论研究电极法储层岩石复电阻率频散特性

复电阻率测井在识别油水层的能力上优于常规电阻率测井,然而储层岩石复电阻率特性的微观机理还没有统一完整的解释和数学模拟方法,致使复电阻率测井技术的开发缺乏足够的理论基础.本文基于孔隙介质Pride电震耦合理论,结合谐变信号激励下渗流场与电流场的耦合理论,推导出一级近似条件下的Pride电震耦合理论.采用格林函数方法建立了一维电震波场的波动方程及其解.构造了双电极法测量储层岩石复电阻率的物理模型和数学模型,从理论上阐明了岩石复电阻率频散特性的微观机制与电震效应的关系,定量分析了储层岩石复电阻率频散特性的影响因素.数学模拟结果表明:储层岩石复电阻率的频散现象是在电震快纵波和电震慢纵波的共同作用下,由孔隙介质中的电渗流机制形成的;储层岩石的复电阻率随孔隙度的增大而减小,随渗透率的增大而增大,地层水矿化度的增加或阳离子交换量的增大使得同频率的复电阻率减小.慢纵波界面极化频率受孔隙度、渗透率和地层弹性模量的影响较大,而快纵波界面极化频率受地层弹性模量的影响较大.

Study on the frequency dispersion of the complex resistivity in reservoir rocks based on electroseismic coupling

Complex resistivity logging has a better ability to distinguish oil and water layers than normal resistivity logging. In recent years, research on this issue focused on experimental studies of factors influencing complex resistivity, while little has been done on the mechanism model and mathematical simulating method for describing complex resistivity, which makes it difficult to reveal the process of frequency dispersion from a microscopic point of view. The development of complex resistivity logging technology is impeded due to insufficient theoretical basis. In this work, mathematical models and analogy methods are developed, and the microscopic mechanism of dispersion characteristics of complex resistivity in reservoir rock is investigated.#br#The electro-osmotic flow process and the electroseismic coupling effect are taken into account to interpret and evaluate the frequency dispersion of complex resistivity in reservoirs. The first thing is to derive a first-order approximation to the Pride electroseismic coupling theory, combining the seepage field and the current field. Next, the Green's function method is applied to build a one-dimensional wave equation and its solution. By the resulting solution, the propagating features of the electroseismic waves are analyzed. And then, according to the theory of two-electrode method measuring complex resistivity, we analyze the propagating characteristics of the current field which is influenced by the electroseismic coupling effect, and on this basis we construct physical and mathematical models of complex resistivity measured by the two-electrode method. Lastly, we clarify the influence factors on the dispersion characteristics by quantitatively analyzing the influence of porosity, permeability, salinity, cation exchange capacity, elastic modulus and core length.#br#Simulation results show that the curve of the complex resistivity exhibits obvious frequency dispersion. The real part of the complex resistivity descends roughly in a ladder-like fashion, i.e. when the frequency is small, the real part experiences a rapid decline, then slows down. With the increasing of frequency, rapid decline happens again, and finally the curve reduces to zero. The imaginary part of W-shape shows two clear peaks. All these characteristics are formed under the combination of the electroseismic fast P-waves and electroseismic slow P-waves. When the porosity is raised, the complex resistivity value and the interfacial polarization frequency of slow-P-wave both decrease, while that of the fast P wave remains fairly constant. When the permeability is raised, the complex resistivity value and the interfacial polarization frequency of slow-P-wave both increase. Enhancing salinity contributes to the decrease of the complex resistivity value, while makes no contribution to the change of the two interfacial polarization frequencies. So does the cation exchange capacity. Changing of the elastic modulus has no effect on the complex resistivity value, while the two interfacial polarization frequencies vary with it evidently. Change of the core length has little influence on the complex resistivity value, while the two interfacial polarization frequencies both reduce with the increasing core length.#br#Frequency dispersion is generated as a result of electroosmotic flow in porous media influenced by the combination of electroseismic fast P-waves and electroseismic slow P-wave. Correctness and reliability of this view are verified using the computing instances. It provides a new idea for the development of complex resistivity logging. Both the real part and the imaginary parts of complex resistivity curves show evident frequency dispersion. The abundant reservoir information contained in the dispersion characteristics can benefit the research of rock structure and fluid property. The value of the complex resistivity increases along with the decreasing of porosity, and the increasing of the permeability, the salinity, and the cation exchange capacity. The interfacial polarization frequencies are dominated by electroseismic wave velocity. The interfacial polarization frequency of slow P waves is found to enhance with the reducing of the porosity, and the raising of the permeability. The interfacial polarization frequency of fast-P-wave is found to vary with the elastic modulus. Both of the two interfacial polarization frequencies change little with the variation of salinity and cation exchange capacity.