Roko Andricevic

On the electrical‐hydraulic conductivity correlation in aquifers

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 Archies 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.

Solute flux approach to transport through spatially nonstationary flow in porous media

A theoretical framework for solute flux through spatially nonstationary flows in porous media is presented. The flow nonstationarity may stem from medium nonstationarity (e.g., the presence of distinct geological layers, zones, or facies), finite domain boundaries, and/or fluid pumping and injecting. This work provides an approach for studying solute transport in multiscale media, where random heterogeneities exist at some small scale while deterministic geological structures and patterns can be prescribed at some larger scale. In such a flow field the solute flux depends on solute travel time and transverse displacement at a fixed control plane. The solute flux statistics (mean and variance) are derived using the Lagrangian framework and are expressed in terms of the probability density functions (PDFs) of the particle travel time and transverse displacement. These PDFs are given with the statistical moments derived based on nonstationary Eulerian velocity moments. The general approach is illustrated with some examples of conservative and reactive solute transport in stationary and nonstationary flow fields. It is found based on these examples that medium nonstationarities (or multiscale structures and heterogeneities) have a strong impact on predicting solute flux across a control plane and on the corresponding prediction uncertainty. In particular, the behavior of solute flux moments strongly depends on the configuration of nonstationary medium features and the source dimension and location. The developed nonstationary approach may result in non-Gaussian (multiple modal) yet realistic behaviors for solute flux moments in the presence of flow nonstationarities, while these non-Gaussian behaviors may not be reproduced with a traditional stationary approach.

Modeling kinetic non-equilibrium using the first two moments of the residence time distribution

A method for simulating field scale transport of kinetically adsorbing solutes is described. The non-equilibrium adsorption is modeled as a birth and death process and is coupled with the particle tracking approach using the first two moments of the distribution of the particle residence time, i.e., the time that a solute particle stays in the liquid phase. A single residence time distribution, regardless of the initial and final phase, is demonstrated to yield an accurate description of chemical kinetics in the vast majority of field scale problems. The first two moments of the residence time distribution are derived as a function of chemical reaction rates and the transport time interval Δt. It is shown that the first moment of the residence time represents a measure of the speed of the chemical reaction relative to the transport time scale Δt which is chosen depending on the velocity field. The second moment of the residence time reflects the relative importance of the chemical kinetics versus local equilibrium conditions for the given transport time step Δt. The simulated spatial moments of the contaminant plume are compared in the one-dimensional case with available analytical solutions to demonstrate the accuracy of the proposed technique. A two-dimensional case for stratified formations is presented to study the transport behavior for heterogeneous velocity fields and variable distribution coefficient, hypothesized as being negatively correlated with hydraulic conductivity. The results show that the enhanced plume spreading and the statistics of the arrival time distribution appear to be more sensitive to the spatially variable distribution coefficient than to the kinetics alone. In fact, the second spatial moment was almost doubled in the case of spatially variable distribution coefficient.

Geoelectric characterization of the hydraulic conductivity field and its spatial structure at variable scales

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 aquifers 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.

Cost-effective network design for groundwater flow monitoring

The extensive use of groundwater resources has increased the need for developing cost-effective monitoring networks to provide an indication of the degree to which the subsurface environment has been affected by human activities. This study presents a cost-effective approach to the design of groundwater flow monitoring networks. The groundwater network design is formulated with two problem formats: maximizing the statistical monitoring power for specified budget constraint and minimizing monitoring cost for statistical power requirement. The statistical monitoring power constraint is introduced with an information reliability threshold value. A branch and bound technique is employed to select the optimal solution from a discrete set of possible network alternatives. The method is tested to the design of groundwater flow monitoring problem in the Pomona County, California.

COUPLED WITHDRAWAL AND SAMPLING DESIGNS FOR GROUNDWATER SUPPLY MODELS

A coupled formulation of withdrawal and sampling designs for ground water supply models is presented. The withdrawal design is described as a discrete time optimal control problem and solved using a closed loop stochastic control (CLSC) method. Two main features of the CLSC method are the anticipation of the future observation program and decomposition of the objective function into the deterministic and stochastic part. The former characteristic indicates the necessity for coupling the withdrawal and sampling designs, while the later feature allows a decision maker to estimate the uncertainty in the objective function if certain withdrawal rates are applied. The sampling network is sequentially developed, with the design criterion defined as a sensitivity of the objective function stochastic part to the uncertainty in the hydraulic head distribution multiplied with the variance of the hydraulic head. The concept of minimizing the stochastic part of the objective function with respect to the hydraulic head uncertainty provides a convenient way to couple the withdrawal design objectives with the monitoring network development weighted with the magnitude of the prediction error in the hydraulic head distribution. The Bayesian concept of measurement conditioning is employed to sequentially adjust the withdrawal rates and sampling network development by accounting for the information conveyed in field observations. Between the sampling sessions the uncertainty in the hydraulic head prediction is evaluated using the first- and second-moment analysis applied to the discretized ground water flow model. The uncertainty in the hydraulic head prediction is assumed to come from the natural uncertainty in the hydraulic conductivity and uncertainty in the boundary condition values and other external fluxes (e.g., leakages and recharge). A hypothetical example is included to demonstrate the application procedure and to illustrate the main features of the proposed coupled formulation.

A Transfer Function Approach to Sampling Network Design for Groundwater Contamination

This study presents a new methodology for designing and analyzing three-dimensional sampling networks for groundwater quality monitoring. Sampling design is represented in the frequency domain as a transfer function acting on the concentration spectrum to provide the sampling error variance, which is used as a measure of sampling performance. The presented methodology does not require numerical solution of either flow or transport equations; it operates directly on the statistics of the concentration field evaluated using a spectral representation. It also separates sampling design issues from the statistics of the aquifer properties, allowing better understanding of the influence of the subsurface characteristics on sampling error and therefore on sampling network design. The results show that sampling of groundwater quality should be viewed as a three-dimensional activity with two major design parameters: spatial spacing between wells (Δli, i = 1, 2, 3) and total number of wells. In the horizontal plane there is a clear need for anisotropy in spacing between wells with larger spacing needed in the direction of the mean flow than in the perpendicular direction. The sampling anisotropy ratio Δl1/Δl2 is found to be a function of the correlation structure of the hydraulic conductivity field and number of wells. The presented example demonstrates how sampling network design guidelines can be developed as functions of the statistical structure of the hydraulic conductivity field and other transport parameters.