Mike Trefry

Numerical simulations of preasymptotic transport in heterogeneous porous media: Departures from the Gaussian limit

[1]xa0The objective of this work is to determine whether conventional solute macrodispersion theories adequately predict the behavior of individual subsurface plumes over time and length scales relevant to practical risk assessment and remediation activities. This issue is studied with a set of high-resolution numerical simulations of conservative tracers moving through saturated two-dimensional heterogeneous conductivity fields. The simulation experiments are designed to mimic long-term field studies. Spatially correlated statistically stationary lognormal conductivity realizations are generated with a Fourier transform procedure. Steady state velocity solutions are calculated for these fields using an accurate Darcian solver. Velocity contour plots reveal the presence of disconnected networks of preferential pathways over a range of correlation lengths. Reverse flow cells are rare. The velocity probability density functions have exponential tails and strong longitudinal asymmetries. Solute concentrations are derived from the simulated velocity fields with an accurate taut-spline transport code that minimizes numerical dispersion. The resulting plumes are tracked for travel distances of over one hundred spatial correlation lengths, corresponding to scales of practical interest. First moments and macrodispersivities, which measure the location and extent of the plume, are reasonably well approximated by conventional Fickian theories but continue to vary after long travel distances. This temporal variability highlights the slow convergence of the plume moments to Gaussian limits. Calculations of the relative dilution index, which is a measure of the plume mixing state, indicate strongly non-Gaussian behavior. Other measures of plume structure suggested by anomalous dispersion theories also reveal the persistence of non-Gaussian behavior after long travel distances. These measures appear to be more sensitive to non-Gaussian behavior than the spatial moments. Taken together, the simulation results suggest that conservative solute plumes moving through statistically stationary random media may not converge to Gaussian limits even after traveling hundreds of log conductivity correlation scales.

Structural characterization of an island aquifer via tidal methods

[1]xa0A set of water level time series collected along a transect through a sedimentary island aquifer was used to test the utility of various simple models of ocean tidal propagation in bounded one-dimensional aquifers. Fourier spectra were calculated for the ocean tidal modes and compared with spectra measured in wells along the island transect. Other sources of fluctuation could be neglected. An observed spatial bias in the well responses (attenuations and lags) could not be modeled by a homogeneous aquifer theory. A theory involving composite heterogeneity accounted well for the spatial bias, yielding estimates of aquifer transmissivities and storage coefficients indicating a fivefold difference in hydraulic diffusivity along the transect. A lack of well locations toward one end of the transect reduced the statistical significance of this result, with correlations between regression parameters evident. At the same time, a second bias was seen involving the ratio of signal amplitude and lag with penetration distance into the aquifer, as observed in prior tidal studies. A brief set of numerical experiments showed that horizontal layering in aquifer properties was the most probable cause of this propagation bias. Application of these results to the island data set supported a conceptual stratigraphic model of a highly conductive, sloping stratum underlying a less conductive, superficial sand layer. This model is inconsistent with well logs along the island transect but is supported by additional off-transect well logs. It was concluded that one-dimensional tidal propagation models may be useful in inverse characterization of aquifers with macroscale hydrogeological structures, and that the analysis of measured propagation bias has the potential to yield extra information on aquifer properties in the vertical direction.

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31, 469–485 (doi:10.1063/1.866828)) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

Heat and mass transport during a groundwater replenishment trial in a highly heterogeneous aquifer

Changes in subsurface temperature distribution resulting from the injection of fluids into aquifers may impact physiochemical and microbial processes as well as basin resource management strategies. We have completed a 2 year field trial in a hydrogeologically and geochemically heterogeneous aquifer below Perth, Western Australia in which highly treated wastewater was injected for large-scale groundwater replenishment. During the trial, chloride and temperature data were collected from conventional monitoring wells and by time-lapse temperature logging. We used a joint inversion of these solute tracer and temperature data to parameterize a numerical flow and multispecies transport model and to analyze the solute and heat propagation characteristics that prevailed during the trial. The simulation results illustrate that while solute transport is largely confined to the most permeable lithological units, heat transport was also affected by heat exchange with lithological units that have a much lower hydraulic conductivity. Heat transfer by heat conduction was found to significantly influence the complex temporal and spatial temperature distribution, especially with growing radial distance and in aquifer sequences with a heterogeneous hydraulic conductivity distribution. We attempted to estimate spatially varying thermal transport parameters during the data inversion to illustrate the anticipated correlations of these parameters with lithological heterogeneities, but estimates could not be uniquely determined on the basis of the collected data.

A partially open porous media flow with chaotic advection: towards a model of coupled fields

In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele–Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.

Transport in a partially open porous media flow

In nature dissipative fluxes of fluid, heat, and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flow and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring.

A note on Hantush's integral M(u, β)

[1]xa0New analytical results are presented pertaining to M. S. Hantushs integral M(u, β). This integral is often employed in studies of unsteady flow near partially penetrating wells and is usually evaluated via numerical quadrature. It is demonstrated here that Maclaurin and asymptotic series may be truncated to provide a choice of accurate algebraic approximations to M(u, β) over the relevant parameter space. The Maclaurin series lead to formally convergent solutions, although practical evaluation of these series is difficult for some ranges of parameter values. In these cases, the asymptotic expansions provide efficient estimates. Numerical implementation of the new results is straightforward, and guidelines for selection of series truncation limits are provided.

Deep geothermal: The ‘Moon Landing’ mission in the unconventional energy and minerals space

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Entropic Bounds for Multi-Scale and Multi-Physics Coupling in Earth Sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer

We consider two sources of geology-related uncertainty in making predictions of the steady-state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.