Publications

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Fractured media models comprise discontinuities of multiple lengths (e.g. fracture lengths and apertures, wellbore area) that fall into the relatively insignificant length scales spanning millimeter-scale fractures to centimeter-scale wellbores in comparison to the extensions of the field of interest, and challenge the conventional discretization methods imposing highly-fine meshing and formidably large numerical cost. By utilizing the recent developments in the finite element analysis of electromagnetics that allow to represent material properties on a hierarchical geometry, this project develops computational capabilities to model fluid flow, heat conduction, transport and induced polarization in large-scale geologic environments that possess geometrically-complex fractures and man-made infrastructures without explosive computational cost. The computational efficiency and robustness of this multi-physics modeling tool are demonstrated by considering various highly-realistic complex geologic environments that are common in many energy and national security related engineering problems.

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The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2022 accomplishments by the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2022, the PFLOTRAN development team made several advancements to our software infrastructure, code performance, and process modeling capabilities.

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Electromagnetic (EM) methods are among the original techniques for subsurface characterization in exploration geophysics because of their particular sensitivity to the earth electrical conductivity, a physical property of rocks distinct yet complementary to density, magnetization, and strength. However, this unique ability also makes them sensitive to metallic artifacts - infrastructure such as pipes, cables, and other forms of cultural clutter - the EM footprint of which often far exceeds their diminutive stature when compared to that of bulk rock itself. In the hunt for buried treasure or unexploded ordnance, this is an advantage; in the long-term monitoring of mature oil fields after decades of production, it is quite troublesome indeed. Here we consider the latter through the lens of an evolving energy industry landscape in which the traditional methods of EM characterization for the exploration geophysicist are applied toward emergent problems in well-casing integrity, carbon capture and storage, and overall situational awareness in the oil field. We introduce case studies from these exemplars, showing how signals from metallic artifacts can dominate those from the target itself and impose significant burdens on the requisite simulation complexity. We also show how recent advances in numerical methods mitigate the computational explosivity of infrastructure modeling, providing feasible and real-time analysis tools for the desktop geophysicist. Lastly, we demonstrate through comparison of field data and simulation results that incorporation of infrastructure into the analysis of such geophysical data is, in a growing number of cases, a requisite but now manageable step.

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Well integrity is one of the major concerns in long-term geologic storage sites due to its potential risk for well leakage and groundwater contamination. Evaluating changes in electrical responses due to energized steel-cased wells has the potential to quantify and predict possible wellbore failures, as any kind of breakage or corrosion along highly-conductive well casings will have an impact on the distribution of subsurface electrical potential. However, realistic wellbore-geoelectrical models that can fully capture fine scale details of well completion design and the state of well damage at the field scale require extensive computational e.ort, or can even be intractable to simulate. To overcome this computational burden while still keeping the model realistic, we use the hierarchical finite element method which represents electrical conductivity at each dimensional component (1-D edges, 2-D planes and 3-D cells) of a tetrahedra mesh. This allows well completion designs with real-life geometric scales and well systems with realistic, detailed, progressive corrosion and damage in our models. Here, we present a comparison of possible discretization approaches of a multi-casing completion design in the finite-element model. The e.ects of the surface casing length and the coupling between concentric well casings, as well as the e.ects of the degree and the location of well damage on the electrical responses are also examined. Finally, we analyze real surface electric field data to detect wellbore integrity failure associated with damage.

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Electrical responses in the vicinity of energized steel-cased well sources offer significant potential for monitoring induced fractures. However, the high complexity of well-fracture-host models spanning multiple length scales compels analysts to simplify their numerical models due to enormous computational costs. This consequently limits our understanding regarding monitoring capabilities and the limitations of electrical measurements on realistic hydraulically fracturing systems. In this paper, we use the hierarchical finite element approach to construct geoelectric models in which geometrically complex fractures and steel-cased wells are discretely represented in 3D conducting media without sacrificing the model realism and computation efficiency. We have discovered systematic numerical analyses of the electrical responses to evaluate the influences of borehole material conductivity and the source type as well as the effects of well geometry, conductivity contrast, source location, fracture growth, and fracture propagation. Furthermore, the numerical results indicate that the borehole material property has a strong control on the electrical potentials along the production and monitoring wells. The monopole source located at a steel-cased well results in a current density distribution that decays away from the source location throughout the well length, whereas the dipole source produces a current density that dominates mainly along the dipole length. Moreover, the conductivity contrast between the fractures and host does not change the overall pattern of the electrical potentials but varies its amplitude. The fracture models near different well systems indicate that the well geometry controls the entire distribution of potentials, while the characteristics of the voltage difference profiles along the wells before and after fracturing are insensitive to the well geometry and the well in which the source is located. Further, the hydraulic-fracturing models indicate that the voltage differences along the production well before and after fracturing have strong sensitivity to fracture growth and fracture set propagation.

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Motivated by the need for improved forward modeling and inversion capabilities of geophysical response in geologic settings whose fine--scale features demand accountability, this project describes two novel approaches which advance the current state of the art. First is a hierarchical material properties representation for finite element analysis whereby material properties can be prescribed on volumetric elements, in addition to their facets and edges. Hence, thin or fine--scaled features can be economically represented by small numbers of connected edges or facets, rather than 10's of millions of very small volumetric elements. Examples of this approach are drawn from oilfield and near--surface geophysics where, for example, electrostatic response of metallic infastructure or fracture swarms is easily calculable on a laptop computer with an estimated reduction in resource allocation by 4 orders of magnitude over traditional methods. Second is a first-ever solution method for the space--fractional Helmholtz equation in geophysical electromagnetics, accompanied by newly--found magnetotelluric evidence supporting a fractional calculus representation of multi-scale geomaterials. Whereas these two achievements are significant in themselves, a clear understanding the intermediate length scale where these two endmember viewpoints must converge remains unresolved and is a natural direction for future research. Additionally, an explicit mapping from a known multi-scale geomaterial model to its equivalent fractional calculus representation proved beyond the scope of the present research and, similarly, remains fertile ground for future exploration.

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Fractures are an interest of many engineering problems. They present complex spatial distributions and hydraulic properties that vary over a wide range of length scales. The multi-length-scale nature as well as the volumetric insignificance of fractures at the filed scale demand an explosive computational effort to account of fractures in standard DC resistivity modeling. Here, we use the hierarchical finite element method (Hi-FEM) to model complex fracture networks in 3D conducting media. The HiFEM method is based on the hierarchy in the electrical properties of 3D geologic media that drastically reduces the computational cost, such that thin conductive fractures can easily be represented by a set of connected 2D facet elements or linear conductive features can be approximated by connected 1D edge elements. Here, we present a demonstrative numerical study of the 3D DC resistivity responses of a complex fractured network consisting of a large number of randomly-oriented fractures. We also simulate the time lapse response of an evolving fracture network as a demonstration of real-time 4D monitoring. Our results indicate that the amplitude and the distribution of DC electric potentials are substantially controlled by fracture properties; moreover, the DC resistivity measurements over a growing fracture network reflect the spatial and the temporal state of the network connectivity.

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Here, the determination of the geometrical properties of fractures plays a critical role in many engineering problems to assess the current hydrological and mechanical states of geological media and to predict their future states. However, numerical modeling of geoelectrical responses in realistic fractured media has been challenging due to the explosive computational cost imposed by the explicit discretizations of fractures at multiple length scales, which often brings about a tradeoff between computational efficiency and geologic realism. Here, we use the hierarchical finite element method to model electrostatic response of realistically complex 3D conductive fracture networks with minimal computational cost.

After the 23 August 2011 Mineral, Virginia, earthquake, a temporary dense array (Aftershock Imaging with Dense Arrays (AIDA)) consisting of ~200 stations was deployed at 200-400 m spacing near the epicenter for 12 days. Backprojection of the data was used to automatically detect and locate aftershocks. The co-deployment of a traditional aftershock network of 36 stations at ~2-10 km spacing enables a quantitative comparison. The AIDA backprojection aftershock catalog is complete to magnitude -1.0 and includes events as small as M-1.8. For comparison, the traditional network was complete to M-0.3 for the same time period. The AIDA backprojection catalog observes the same major patterns of seismicity in the epicentral region, but additional details are illuminated. The primary zone of seismicity is not a single fault but is a tabular zone of multiple small faults, this zone has a subtle concave shape along strike and with depth, and a broader zone of new events is observed at shallow depth. In addition, a new separate, shallow cluster was detected and located to the east of the main aftershock zone. The addition of smaller events to the catalog did not change the b-value or the temporal decay constant, but illuminated spatial and temporal patterns. Both the b-value and temporal decay constant are different for 12 days than for 4 months and are different at < 3km depth than at greater depth. Very low b-value, especially at greater depth, is consistent with observed very high stress drops. Conclusively, the results indicate the benefits of dense arrays and auto-detection by backprojection for aftershock studies. And finally, the reduced detection threshold and higher spatial resolution enabled the study of earthquake mechanisms and strain transfer at an unprecedented small scale.

Backprojection imaging has recently become a practical method for local earthquake detection and location due to the deployment of densely sampled, continuously recorded, local seismograph arrays. While backprojection sometimes utilizes the full seismic waveform, the waveforms are often pre-processed and simplified to overcome imaging challenges. Real data issues include aliased station spacing, inadequate array aperture, inaccurate velocity model, low signal-to-noise ratio, large noise bursts and varying waveform polarity. We compare the performance of backprojection with four previously used data pre-processing methods: raw waveform, envelope, short-termaveraging/long-termaveraging and kurtosis. Our primary goal is to detect and locate events smaller than noise by stacking prior to detection to improve the signal-to-noise ratio. The objective is to identify an optimized strategy for automated imaging that is robust in the presence of real-data issues, has the lowest signal-to-noise thresholds for detection and for location, has the best spatial resolution of the source images, preserves magnitude, and considers computational cost. Imaging method performance is assessed using a real aftershock data set recorded by the dense AIDA array following the 2011 Virginia earthquake. Our comparisons show that raw-waveform backprojection provides the best spatial resolution, preserves magnitude and boosts signal to detect events smaller than noise, but is most sensitive to velocity error, polarity error and noise bursts. On the other hand, the other methods avoid polarity error and reduce sensitivity to velocity error, but sacrifice spatial resolution and cannot effectively reduce noise by stacking. Of these, only kurtosis is insensitive to large noise bursts while being as efficient as the raw-waveformmethod to lower the detection threshold; however, it does not preserve the magnitude information. For automatic detection and location of events in a large data set, we therefore recommend backprojecting kurtosis waveforms, followed by a second pass on the detected events using noise-filtered raw waveforms to achieve the best of all criteria.

Methods for the efficient representation of fracture response in geoelectric models impact an impressively broad range of problems in applied geophysics. We adopt the recently-developed hierarchical material property representation in finite element analysis (Weiss, 2017) to model the electrostatic response of a discrete set of vertical fractures in the near surface and compare these results to those from anisotropic continuum models. We also examine the power law behavior of these results and compare to continuum theory. We find that in measurement profiles from a single point source in directions both parallel and perpendicular to the fracture set, the fracture signature persists over all distances. Furthermore, the homogenization limit (distance at which the individual fracture anomalies are too small to be either measured or of interest) is not strictly a function of the geometric distribution of the fractures, but also their conductivity relative to the background. Hence, we show that the definition of “representative elementary volume”, that distance over which the statistics of the underlying heterogeneities is stationary, is incomplete as it pertains to the applicability of an equivalent continuum model. We also show that detailed interrogation of such intrinsically heterogeneous models may reveal power law behavior that appears anomalous, thus suggesting a possible mechanism to reconcile emerging theories in fractional calculus with classical electromagnetic theory.