基于分形孔隙模型的含天然气水合物沉积物电阻率数值模拟

Numerical simulation on the resistivity of hydrate-bearing sediment based on the fractal pore model

电阻率法是确定天然气水合物(以下简称水合物)饱和度的重要方法,通过数值模拟可以有效研究含水合物沉积物的电阻率特性,但过去构建的孔隙模型由于约束条件较少,而与实际的孔隙结构存在着较大的差异。为此,基于自然界沉积物具有自相似特征,选定地毯总边长为3和颗粒边长为1的谢尔宾斯基地毯作为沉积物的分形孔隙模型,根据等效电阻网络模式建立了含水合物沉积物的电导模型,并利用上述模型分析了孔隙度、孔隙水电导率、沉积物骨架电导率等因素对含水合物沉积物电阻率与水合物饱和度关系的影响。研究结果表明:(1)含水合物沉积物的电阻率可以表示为孔隙度、面积比、微观结构尺寸、孔隙水电导度、沉积物骨架电导率及经验参数的函数;(2)孔隙水电导率和孔隙度的减小都会导致沉积物电阻率的增大;(3)含水合物沉积物的电阻率随水合物饱和度的增大而增大;(4)在高水合物饱和度范围内,含水合物沉积物的电阻率随沉积物颗粒骨架电导率的增大而明显减小。结论认为:在一定的水合物饱和度范围内,该分形孔隙模型计算结果与实验数据和测井数据都能较好地吻合,准确度较高。

Resistivity method is an important method to determine the saturation of natural gas hydrate （hereinafter “hydrate” for short）, and numerical simulation is effective to research the resistivity characteristics of hydrate bearing sediments. The pore models established in the past cannot reflect the actual pore structure because there are fewer constraint conditions. Based on the self-similar characteristic of natural sediments, we selected the Sierpinski Carpet with its total side length of 3 and particle＇s side length of 1 as the fractal pore model of sediment, and according to the equivalent resistance network, we established an electrical conductivity model of hydrate bearing sedi-ments. In this paper, the effects of porosity, interstitial water conductivity and sediment skeleton conductivity on the relationship between the resistivity of hydrate-bearing sediment and the hydrate saturation were analyzed using this model. And following research results were obtained. First, the resistivity of hydrate-bearing sediment can be expressed as the function of porosity, area ratio, microstructure size, interstitial water conductivity, sediment skeleton conductivity and empiric parameter. Second, sediment resistivity increases with the decrease of interstitial water conductivity and porosity. Third, the resistivity of hydrate-bearing sediment increases with the increase of hydrate saturation. Fourth, when the hydrate saturation is high, the resistivity of hydrate-bearing sediment decreases significantly with the increase of sediment skeleton conductivity. In conclusion, when the hydrate saturation is in a certain range, the calculation result of this fractal pore model is in line with the experimental data and logging data with a higher accuracy.