التفاصيل البيبلوغرافية
| العنوان: |
An Electrical Parameter Characterizing Solute Heterogeneity: The Mixing Factor M. |
| المؤلفون: |
Fernandez Visentini, Alejandro, Linde, Niklas |
| المصدر: |
Water Resources Research; Jun2024, Vol. 60 Issue 6, p1-24, 24p |
| مصطلحات موضوعية: |
SURFACE conductivity, ELECTRIC conductivity, HETEROGENEITY, PECLET number, POROUS materials, WATER salinization |
| مستخلص: |
Quantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks. Plain Language Summary: Electrical and electromagnetic geophysical methods provide information about the spatio‐temporal distribution of average electrical conductivity of porous media. This property is affected by the transport of electrically conductive solutes, which unfolds over a wide range of spatial scales. However, when translating electrical data into solute concentration, almost all studies to date have ignored solute heterogeneity below the averaging volume inherent to geophysical measurements or modeling, leading to unphysical results. We introduce the mixing factor M, an electrical parameter that links small‐scale solute heterogeneity and average electrical conductivity, via a closed‐form expression depending on the small‐scale features of electric and solute concentration fields. We show that observation of the M‐tensor allows recovering the variance and anisotropy of the solute field in a time‐static setting. For diffusion‐limited transport, the time‐series of M help distinguishing the initial length scales of the fields, whereas for advective‐diffusive transport, these data help distinguishing the Peclet number. The presented framework helps to decode information about solute heterogeneity that is contained in geoelectrical measurements, while also avoid making biased hydrological estimates. Future venues of research will investigate how to incorporate M in available (hydro)geophysical modeling workflows. Key Points: Petrophysical parameter generalizing the high‐salinity limit of electrical conduction for heterogeneous fluid conductivity in porous mediaFormal expression for M provides framework to interpret impact of small‐scale fluid conductivity heterogeneity on electrical measurementsThe mixing factor M depends on geostatistical properties of solute concentration fields and thus on transport characteristics [ABSTRACT FROM AUTHOR] |
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