The electrical resistivity-porosity relationship of porous media is critical for reliable formation evaluation. Archie's equation is empirical, and uses only porosity as pore-space property, neglecting the spatial variability of the pore space; its fitting parameters may have unclear physical meaning and be nonconstant over a wider porosity range or in spatially complex rocks. We use microfluidics augmented with pore-network modeling to investigate the effects of pore-space properties and their evolution processes on electrical resistivity-porosity relationships. Both a flow-pattern parameter and a measure of porosity efficiency are implemented to quantify the spatial variability of the flow field and the conduction efficiency of porous media. Results indicate that both pore-size distribution and pore-space evolution impact the electrical behavior considerably. In cases of unimodal pore-size distributions, a larger pore-size variation or a higher porosity reduction in small pores results in higher values of Archie's porosity exponent, m; the flow pattern becomes more heterogeneous, and the efficiency of porosity to conduct electricity decreases. For cases of bimodal pore-size distributions, the formation factor-porosity relationship is nonlinear in log–log plots; the flow behavior is primarily affected by the fraction and connectivity of large pores. Results suggest that using porosity alone as pore-space characteristic is inadequate to describe the electrical behavior of complex porous media. Petrophysical classification based on flow patterns and porosity efficiency is an effective alternative to differentiate the results. We introduce the electrical quality index as an effective parameter for petrophysical classification, which is verified with core data for both Fontainebleau sandstones and carbonates.

中文翻译：

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饱和多孔介质电阻率的孔尺度研究：流动模式和孔隙率

多孔介质的电阻率-孔隙度关系对于可靠的地层评估至关重要。Archie 方程是经验式的，仅使用孔隙度作为孔隙空间属性，忽略孔隙空间的空间变异性；它的拟合参数可能具有不明确的物理意义，并且在更宽的孔隙度范围内或在空间复杂的岩石中是非恒定的。我们使用通过孔隙网络建模增强的微流体来研究孔隙空间特性及其演化过程对电阻率-孔隙率关系的影响。实施流动模式参数和孔隙率效率的测量来量化流场的空间可变性和多孔介质的传导效率。结果表明，孔径分布和孔隙空间演化都会显着影响电学行为。在单峰孔径分布的情况下，较大的孔径变化或小孔中更高的孔隙率降低会导致 Archie 孔隙率指数的值更高，米；流动模式变得更加不均匀，孔隙率导电效率降低。对于双峰孔径分布的情况，地层因子-孔隙度关系在对数-对数图中是非线性的；流动行为主要受大孔隙的分数和连通性影响。结果表明，单独使用孔隙度作为孔隙空间特征不足以描述复杂多孔介质的电学行为。基于流动模式和孔隙度效率的岩石物理分类是区分结果的有效替代方法。我们引入了电气质量指数作为岩石物理分类的有效参数，并通过枫丹白露砂岩和碳酸盐岩的岩心数据进行了验证。