Quantifying the Impacts of Stern and Diffuse Layer Polarization onMulti-Frequency Dielectric Permittivity and Electrical Conductivity ofRock-Fluid Systems

摘要

A thorough understanding of the interplay between polarization mechanisms is crucial for interpretation ofelectrical measurements because sub-MHz electrical measurements in sedimentary rocks are dominated byinterfacial polarization mechanisms.However,rock-physics models oversimplify pore-network geometryand the interaction of electric double layers(EDL)pertaining to adjacent grains.The impact of thesesimplifications on the assessment of petrophysical properties,such as hydrocarbon reserves,is difficult toquantify and often unknown.Numerical algorithms present the ideal framework to characterize the electricalresponse of sedimentary rocks,circumventing the limitations intrinsic to rock-physics models.Our recentlydeveloped algorithm simulates the interactions of electric fields with the ions in solution.However,amodel for the polarization mechanism associated with the Stern layer has not been developed.The sub-kHz permittivity enhancement in sedimentary rocks is dominated by Stern layer polarization.Therefore,theobjective of this paper is to develop a numerical simulation framework capable of quantifying the influenceof Stern-and diffuse-layer polarization,temperature,ion concentration,and pore-network geometry onmulti-frequency complex electrical measurements.We developed a numerical simulator to compute time-dependent behavior of electric field,ionconcentration,and interfacial polarization mechanisms in sedimentary rocks.The algorithm numericallysolves the Poisson-Nernst-Planck(PNP)equations in the time domain conjointly with a mineral-dependentelectrochemical adsorption/desorption equilibrium model.Then,we use the numerical simulator to performa sensitivity analysis to quantify the influence of electrolyte and interfacial properties on the permittivityof pore-scale samples at different frequencies.Results demonstrated that the joint effect of Stern layerion concentration and corresponding mobility dominates sub-MHz dielectric response of rocks.The low-frequency permittivity enhancement due to the EDL can sweep several orders of magnitude.The Stern layerpolarization acts as a macroscopic(i.e.,at the grain scale)dipole created by counterions wading around thesurface of the grains due to an externally applied electric field.Therefore,the grain shape and correspondingorientation relative to the electric field significantly affect the behavior of macroscopic Stern layer dipoles.Reliable interpretation of multi-frequency electrical measurements can provide insights in mineralogy,fluid typing,grain size,and interfacial properties.Time-domain numerical modeling of complex permittivitydispersion can greatly enhance interpretation of multi-frequency dielectric measurements.