A combination of the Hashin-Shtrikman bounds aimed at modelling electrical conductivity and permittivity of variably saturated porous media

Brovelli, Alessandro; Cassiani, Giorgio

doi:10.1111/j.1365-246x.2009.04415.x

Cited by 36 publications

(39 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The petrophysical constitutive model of Brovelli and Cassiani [2010b] was developed by combining variational bounds for the transport properties of granular composites [ Hashin and Shtrikman , 1962; Milton , 1981] and Archie 's [1942] law, a constitutive model commonly used to parameterize electrical conductivity of variably saturated porous media. The model was consistently developed for two‐ and three‐phase materials on the basis of the same basic assumptions.…”

Section: Petrophysical Modelmentioning

confidence: 99%

“…On the contrary, electrical conductivity is often influenced by the conductance arising from the excess of charge in the vicinity of the negatively charged solid surfaces of silica, clays, and organic matter [ Brovelli et al , 2005; Revil and Glover , 1997; Revil et al , 1998]. The additional contribution of the charged interface is often converted into an equivalent grain (volumetric) conductivity [ Bussian , 1983; De Lima and Sharma , 1990], and therefore analogous boundary value problems can describe both bulk permittivity and electrical conductivity [ Brovelli and Cassiani , 2010b; Brovelli et al , 2005; Linde et al , 2006]. Although developed using different approaches, including empirical or semiempirical considerations [ Archie , 1942; Clavier et al , 1984; Waxman and Smits , 1968], effective medium theories [ Bussian , 1983; Miller , 1969; Sen et al , 1981], and volume‐averaging algorithms [ Linde et al , 2006; Pride , 1994], most of the petrophysical equations suited to model both DC electrical conductivity and high‐frequency permittivity utilize a parameterization that is compatible with that introduced by Archie [1942].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Combined estimation of effective electrical conductivity and permittivity for soil monitoring

Brovelli

Cassiani

2011

Water Resources Research

Self Cite

View full text Add to dashboard Cite

[1] The mapping of moisture content, composition, and texture of soils is attracting a growing interest, in particular with the goal of evaluating threats to soil quality, such as soil salinization. Fast noninvasive geophysical surveys are often used in this context. The aim of this work was to study constitutive models that can be used to parameterize electrical conductivity and permittivity starting from a unifying conceptual approach, and to evaluate whether the information carried by one measurement type can be used to identify soil parameters that are then used to predict the other geophysical quantity. To this end, a recently developed constitutive model was extended and modified to consider the grain surface conductivity, a critical component in most natural situations. The extended model was successfully tested against laboratory measurements. In addition, the new model was compared against five other equations that use similar soil parameterizations. It was concluded that only three out of the five selected models yield similar predictions, while the remaining two predict a different geophysical response for the same soil texture. Following this analysis, a methodology was developed to estimate soil salinity starting from the simultaneous measurements of bulk electrical conductivity and permittivity and validating this methodology against laboratory experiments. The method is valid in situations where the conductivity of the pore water remains approximately constant during the measurement period. Key features of the approach proposed to map soil salinization are (1) simplicity, (2) absence of fitting parameters, and (3) the fact that moisture content does not need to be measured or estimated independently. The methodology was tested on a large number of soil samples and proved robust and accurate.Citation: Brovelli, A., and G. Cassiani (2011), Combined estimation of effective electrical conductivity and permittivity for soil monitoring, Water Resour. Res., 47, W08510,

show abstract

Section: Petrophysical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Combined estimation of effective electrical conductivity and permittivity for soil monitoring

Brovelli

Cassiani

2011

Water Resources Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…In other words, identification of many parameters using relatively little, somewhat noisy information that is collected only at the domain boundary clearly represents a difficult challenge [e.g., Menke , 1984]. In addition, suitable constitutive models linking geophysical and hydrological parameters are needed [e.g., Brovelli and Cassiani , 2010, 2011], often to be calibrated on a site‐by‐site basis. These limitations can make geophysical methods more of a qualitative tool, unless information concerning the relevant hydrological processes involved are properly taken into account.…”

Section: Introductionmentioning

confidence: 99%

Assessment of local hydraulic properties from electrical resistivity tomography monitoring of a three‐dimensional synthetic tracer test experiment

Camporese¹,

Cassiani²,

Deiana³

et al. 2011

Water Resources Research

Self Cite

View full text Add to dashboard Cite

[1] In recent years geophysical methods have become increasingly popular for hydrological applications. Time-lapse electrical resistivity tomography (ERT) represents a potentially powerful tool for subsurface solute transport characterization since a full picture of the spatiotemporal evolution of the process can be obtained. However, the quantitative interpretation of tracer tests is difficult because of the uncertainty related to the geoelectrical inversion, the constitutive models linking geophysical and hydrological quantities, and the a priori unknown heterogeneous properties of natural formations. Here an approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) data assimilation technique is applied to assess the spatial distribution of hydraulic conductivity K by incorporating time-lapse cross-hole ERT data. Electrical data consist of threedimensional cross-hole ERT images generated for a synthetic tracer test in a heterogeneous aquifer. Under the assumption that the solute spreads as a passive tracer, for high Peclet numbers the spatial moments of the evolving plume are dominated by the spatial distribution of the hydraulic conductivity. The assimilation of the electrical conductivity 4D images allows updating of the hydrological state as well as the spatial distribution of K. Thus, delineation of the tracer plume and estimation of the local aquifer heterogeneity can be achieved at the same time by means of this interpretation of time-lapse electrical images from tracer tests. We assess the impact on the performance of the hydrological inversion of (i) the uncertainty inherently affecting ERT inversions in terms of tracer concentration and (ii) the choice of the prior statistics of K. Our findings show that realistic ERT images can be integrated into a hydrological model even within an uncoupled inverse modeling framework. The reconstruction of the hydraulic conductivity spatial distribution is satisfactory in the portion of the domain directly covered by the passage of the tracer. Aside from the issues commonly affecting inverse models, the proposed approach is subject to the problem of the filter inbreeding and the retrieval performance is sensitive to the choice of K prior geostatistical parameters.Citation: Camporese, M., G. Cassiani, R. Deiana, and P. Salandin (2011), Assessment of local hydraulic properties from electrical resistivity tomography monitoring of a three-dimensional synthetic tracer test experiment, Water Resour.

show abstract

“…A key step in all interpretations is to know what field-scale petrophysical relationships should be used to transform the models into geologic or hydrogeologic properties. It is helpful to use petrophysical relationships that share similar parameterizations and assumptions about the pore structure for all model types, as done here for the HS lower bounds, using a weighted average of the HS bounds (Brovelli and Cassiani, 2010) or volume averaging . Even if the joint inversion improves resolution, similar resolution-dependent petrophysical relationships, as for individual inversions, remain.…”

Section: Discussionmentioning

confidence: 99%

“…The lower and upper bounds for dielectric permittivity in saturated media are (e.g., Hashin and Shtrikman, 1962;Brovelli and Cassiani, 2010) …”

Section: Seismic and Radar Wave-speed Cross-property Relationsmentioning

confidence: 99%

1. Joint Inversion of Crosshole GPR and Seismic Traveltime Data

Linde¹,

Doetsch²

2010

Advances in Near-Surface Seismology and Ground-Penetrating Radar

View full text Add to dashboard Cite

Joint inversion of crosshole ground-penetrating radar and seismic data can improve model resolution and fidelity of the resultant individual models. Model coupling obtained by minimizing or penalizing some measure of structural dissimilarity between models appears to be the most versatile approach because only weak assumptions about petrophysical relationships are required. Nevertheless, experimental results and petrophysical arguments suggest that when porosity variations are weak in saturated unconsolidated environments, then radar wave speed is approximately linearly related to seismic wave speed. Under such circumstances, model coupling also can be achieved by incorporating cross-covariances in the model regularization. In two case studies, structural similarity is imposed by penalizing models for which the model cross-gradients are nonzero. A first case study demonstrates improvements in model resolution by comparing the resulting models with borehole information, whereas a second case study uses point-spread functions. Although radar seismic wavespeed crossplots are very similar for the two case studies, the models plot in different portions of the graph, suggesting variances in porosity. Both examples display a close, quasilinear relationship between radar seismic wave speed in unconsolidated environments that is described rather well by the corresponding lower Hashin-Shtrikman (HS) bounds. Combining crossplots of the joint inversion models with HS bounds can constrain porosity and pore structure better than individual inversion results can.

show abstract

A combination of the Hashin-Shtrikman bounds aimed at modelling electrical conductivity and permittivity of variably saturated porous media

Cited by 36 publications

References 59 publications

Combined estimation of effective electrical conductivity and permittivity for soil monitoring

Combined estimation of effective electrical conductivity and permittivity for soil monitoring

Assessment of local hydraulic properties from electrical resistivity tomography monitoring of a three‐dimensional synthetic tracer test experiment

1. Joint Inversion of Crosshole GPR and Seismic Traveltime Data

Contact Info

Product

Resources

About