Abstract. As a justification for the geoelectric characterization of the hydraulic conductivity field, this paper shows theoretically and empirically that electrical and hydraulic (eh) conductivities of aquifers can be correlated. The correlation, demonstrated at the microscale by a published network model of eh transport, arises from the fact that both eh conductivities are a function of connected pore volumes and connected pore surface areas. By considering skewed pore size distributions the microscale equations of eh conductivity scale up to power laws of porosity and specific surface area similar to Archie's law and the Kozeny equation. Also, a third, apparently unreported Archie-type power law relating electrical conductivity to specific surface area and the cation exchange phenomenon is predicted theoretically and confirmed experimentally. These equations imply a simple log-log linear correlation between eh conductivities that is either positive or negative. The positive correlation corresponds to a pore-volume-dominated electrical flow environment and the negative correlation corresponds to a pore-surface-dominated electrical flow environment. These relationships are supported by many published laboratory and field investigations cited in the paper.
Abstract. This paper describes how to begin with extensive geoelectric measurements of an aquifer along with a few hydraulic measurements and end with an estimate of the aquifer's hydraulic conductivity field and spectrum at variable scales. It is based on a preponderance of theoretical and empirical evidence indicating that electrical and hydraulic (eh) conductivities of aquifers are linearly correlated on a bilogarithmic scale. The steps required for a geoelectric characterization are scaling up, calibration, and spectrum estimation. Scaling up estimates electrical conductivity at variable scales from the apparent resistivity measurement. Calibration equilibrates coincident, equal-scale eh conductivities using the theoretical eh conductivity correlation. Combined, scaling up and calibration provide a variable-scale expression for the hydraulic conductivity field in terms of a geoelectric measurement. From this expression the hydraulic conductivity field spectrum is calculated. These steps are applied to borehole data collected at the Department of Energy Central Nevada Testing Area and the U.S. Geological Survey Cape Cod site. In each case a statistically significant eh conductivity correlation is observed. The paper ends by conjecturing that a horizontal exploitation of the eh conductivity correlation offers for the first time an inexpensive means of characterizing the hydraulic conductivity field at a high resolution and over a large area.
Abstract. This technical note argues the importance of incorporating nonlocal dispersion effects when modeling contaminant travel times. Using the transport theory of Di Federico and Neuman [1998], expressions for nonlocal contaminant travel times and breakthrough are developed. They show that nonlocal travel times are significantly faster than their local (Fickian) counterpart and that nonlocal breakthrough occurs significantly earlier than
All= C1F(1 + 2H) sin (•rH) F(-2H) I + 2H (•t)•+2H'where the right-hand side of (6) where a is local dispersivity (m). One sees from (6) and (7) [1995].) It follows then that normalized concentration breakthrough C(x, t)/Co at distance y -In (x) and at time t is described by 2915
This paper argues how the spectral characteristics of two borehole apparent resistivity traces further corroborate two statistically significant electrical‐hydraulic (eh) conductivity correlations previously reported in Nevada's fractured welded tuffs. Even though the eh conductivity correlation is positive in one borehole and negative in the other, as explained by low pore water electrical conductivity and the absence or presence of alteration minerals, both apparent resistivity amplitude spectra are identically power‐law structured. This is interpreted to mean that eh flow is occurring along rock fractures of a common regional fractal dimension. Furthermore, both apparent resistivity phase spectra are strikingly linear, as mandated by the condition of incompressible fluids. Linear phase implies a groundwater flow that is geostatistically nonstationary in the wide sense, a complication normally not considered by hydrogeologists.
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