Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “strain tensor inversion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

16 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. Furthermore, this workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

42 ENGINEERING↗
DOE OSTI2022

Proxy-Based Bayesian Inversion Of Poroelastic Simulations To Interpret Strain Tensor Data Measured During Well Testing

The long runtimes of 3D poroelastic numerical simulators makes it impractical to interpret deformation datasets using many inversion schemes. Recent advances in instrumentation have made it possible to measure the strain tensor during well testing, but the lack of robust inversion methods is limiting the ability to interpret these data. We have developed an inversion workflow that reduces the number of computations required to complete a Bayesian inversion using DREAMzs. The workflow trains a KNN model using output from the poroelastic simulator, and then uses the KNN model as a proxy for the simulator during inversion. The workflow also includes a strategy for ensuring the results from the proxy model converge to the results from the simulator, ensuring the accuracy of the final results. An idealized example configured to represent a well test in a deep aquifer is used to verify that the workflow correctly identifies parameters and characterizes noise. Field data measured using strainmeters during an injection test at an oil reservoir in Oklahoma are used to evaluate performance with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), and the results are used to characterize posterior parameter distribution and evaluate the prediction uncertainty. This approach makes it feasible to invert strain data measured during well testing and this has the potential to improve the characterization of aquifers and reservoirs.

Roudini, Soheil↗
DOE OSTI2024

Utah FORGE 3-2514: Strain Sensing Array for Deformation Characterization - 2024 Annual Workshop Presentation

This is a presentation on the Strain Sensing Array to characterize deformation at the FORGE site project by Clemson University, presented by Lawrence Murdoch. The project's objective was to evaluate the feasibility of measuring and interpreting tensor strain data to improve the performance of EGS. This presentation was featured in the Utah FORGE R&D Annual Workshop on August 23, 2024.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring. We have deployed strainmeters and then conducted injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters (30 to 40m depth) was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 n/d over a few days. The signal at two strainmeters at shallow depth were consistent, although the magnitude of the horizontal strains were different reflecting the different radial directions from the well. The signal at a deep strainmeter deployed at reservoir depth was much different, with tensile vertical strains and compressive horizontal strains. These data can be interpreted by inverting poroelastic forward models developed using numerical and analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. This model is fast and can be inverted to estimate reservoir stiffness and geometry. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. The proxy model is periodically updated and refined using the finite element model to ensure accuracy. This approach significantly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. We have shown that the strain tensor in the caprock is sensitive to pressure in the reservoir, boundaries in the reservoir, and pressure in the caprock caused by leaks. These results indicate that coupling strain tensor data with inversion has the potential to help evaluate reservoirs during initial characterization, and to monitor them during the CO2 injection and storage process.

Murdoch, Larry↗
DOE OSTI2023

Toward Global Regional Seismic Moment Tensor Inversion with Three-Dimensional Earth Models for Nuclear Explosion Monitoring with Sparse Networks: Demonstration of Reciprocity for Strain Greens Tensor Database Simulation with Salvus

Seismic source characterization is an essential function of global nuclear explosion monitoring (NEM). While large events (roughly with moment magnitude, M w , greater than 5.0) can often be easily detected, located and identified with high signal-to-noise ratios at teleseismic distances (> 20°), trends in NEM research require confident source characterization at much lower magnitudes (say down to 3.0) and exploitation of sparse observations (from only a few stations) at regional distance (< 20°). Regional distance waveform inversion to characterize sources is now widely used and effective (e.g. Ford et al., 2009; Alvizuri and Tape, 2018; Alvizuri et al., 2018; Chiang et al., 2018; Ford et al., 2022). These methods obtain the magnitude, depth and seismic moment tensor, which represents the forces that excited the observed seismic waves (slip on an earthquake fault, explosion, collapse or a combination of various forces). Common to many problems in seismology, the isolation of the source 2 properties requires removal of path propagation effects that waves experience while traveling through the three-dimensional (3D) Earth (the structure exists due to different rock types, material properties, temperature and tectonic processes).

58 GEOSCIENCES↗
DOE OSTI2022

Evolution of tensile and shear cracking in crystalline rocks under compression

Here we performed laboratory-scale unconfined compression experiments on Barre granite specimen with a single pre-existing flaw to study the evolution of tensile and shear cracking that occurs during different stress levels. Moment tensor inversion of acoustic emission (AE) events in combination with the nonelastic strain component obtained through the 2D digital image correlation (DIC) technique are used to track the changes in the source mechanisms of the stress-induced cracks. The mode of deformation computed from the image based strain profiles, enables visual comparison of the nucleation, growth and interaction of the tensile and shear cracks with the microseismic source mechanism observed by moment tensor inversion of the AE events. Comparing the results obtained from the two techniques on the same dataset demonstrates a quantitative correlation between the acoustic and visual observations in terms of the cracking mechanisms obtained at different stages of cracking from crack initiation at the flaw tips to the failure of the rock specimen.

58 GEOSCIENCES↗
DOE OSTI2026

Uncovering hidden bias in neutron diffraction residual strain measurements

When calculating residual strain via neutron or X-ray diffraction, uncertainties propagated from the peak fit are often inadequate to describe the true scatter of measurements about a singular strain state, such as one that should describe a macroscopic continuum. Because diffraction is inherently a selective process, orientation-dependent scatter arises from the sub-sampling of strong microstructure and strain gradients. This paper investigates the appropriateness of propagated uncertainties with reference to their original intention, i.e. noise about a mean value. Thirty-six unique orientations of strain measurements are taken at multiple locations within an additive friction-stir deposition component with fine-scale gradients (∼200 µm) of plastic strain, texture and residual elastic strain. Multiple strain and stress calculation pathways are compared: direct substitution of three measurements into Hooke's law, direct inversion of any six unique orientations into the strain state tensor and thirty-six measurement least-squares estimation. For the last two cases, the appropriateness of the uncertainty interval is statistically evaluated on the basis of a physical constraint: common agreement under the strain transformation law. For this sample, the direct inversion of six measurements retains a conservative estimate of the uncertainty. However, propagated uncertainties in the least-squares solution greatly underestimate the true experimental scatter. A simple pathway to estimate appropriate uncertainty intervals is suggested. These results demonstrate that the interpretation of uncertainty in residual strain is strongly dependent on intrinsic sample-dependent effects, and that oversampling orientations and statistical analysis can give more accurate results with realistic uncertainties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Robust In-Situ Strain Measurements to Monitor CO 2 Storage

The goal of this project was to develop and demonstrate robust instrumentation to monitor the in-situ strain tensor in order to improve the reliability and security of CO 2 storage in geologic formations. We met the original goals of the project and the major overarching accomplishment is the advancement of strain tensor monitoring from an intriguing concept to a commercially available technology with a solid foundation of novel instruments supported by theoretical analyses and validation experiments. The main accomplishments of the project are summarized below. We designed, built and evaluated nine new optical fiber strainmeters and tiltmeters using Michelson interferometers to measure deformation with ultra-high resolution at both shallow and deep point locations in the subsurface. These are the robust strainmeters that motivated the title of the project. We designed, built and evaluated a novel method of measuring distributed strain in optical fibers with nanostrain resolution, and cm-scale location, and sampling into the seismic band. The new method is called Coherence-length-gated Microwave Photonics Interfereometry (CMPI). CMPI technology has advantages over existing commercial DAS and DSS methods. We developed and demonstrated capabilities to deploy instruments in the field and used them to measure strain caused by ambient signals like barometric pressure and tides, as well as induced signals like surface loading and pore pressure changes from pumping tests. We deployed a working strainmeter at 1,700 ft depth, slightly above an active reservoir. This is to our knowledge the greatest depth a strainmeter has been deployed and the techniques we used can readily be extended to greater depths. Optical fiber borehole tensor strainmeter techology was advanced from a TRL 4 at the start, to a TRL of 7 at the conclusion of the project. The project included advances in simulations and theoretical analyses. We developed and demonstrated a computational workflow that uses machine learning to reduce the computational requirements and make it practical to use Bayesian inversion to solve large numerical poroelastic analyses needed to interpret strain tensor field data. We evaluated the strain tensor fields and time series that would be caused by leaks of CO 2 or other fluids from reservoirs. These simulations demonstrated that signals from leaks could be measured with instruments developed for the project, opening a potentially new method for ensuring storage security. We showed that strains in caprock can be used to estimate pressure in a reservoir. This avoids the need to drill monitoring wells into the reservoir, and it expands the capabilities of monitoring in the caprock. The project includes a derivation and application of a novel analytical solution to the strains in the vicinity of a pressurized poroelastic inclusion. This solution explains field data measured during injeciton tests at the North Avant Field, and it will simplify future interpretation of strain tensor data. The project included a broad range of experiments, and of the most significant is the characterization of the strain tensor at an array three strainmeters during six injection tests at the North Avant Field, Oklahoma. This demonstrated repeatability of the strain signal measured by the new instruments developed for the project, and it showed similarities between the strain signal at shallow depths and pressure in the underlying reservoir. We also demonstrated that useful strain data can be measured at reservoir depths. This confirms that strain tensor data can be measured throughout the caprock over a reservoir. The project demonstrated the feasibility of using the strain tensor and distributed strain measured in caprock during a variety of different well tests where the pumping rate was constant, sinusoidal and positive, or a periodic square wave with zero net rate. This further strengthens the validity of using strain data to characterize reservoirs and aquifers. We also demonstrated that strain caused be fluctuations of air pressure and water pressure in the vadose zone can be measured and interpreted, suggesting that high resolution distributed strain measurements hold promise for monitoring the vadose zone. The project partially supported nine graduate students in the Environmental Engineering, Hydrogeology, Electrical Engineering programs at Clemson University. The research was described in nine journal papers, 23 talks and conference abstracts. Additional journal papers are in preparation. A new company called Tensora was started to provide strainmeter technology for commercial applications.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Utah FORGE 3-2514: A Strain Sensing Array to Characterize Deformation at the FORGE Site - Workshop Presentation

This is a presentation on the Strain Sensing Array to Characterize Deformation at the FORGE Site project by Clemson University, presented by Lawrence Murdoch. The project's objective was to evaluate the feasibility of measuring and interpreting tensor strain data to improve the performance of EGS. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 8, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

CCUS 2024, Interpreting the strain tensor Larry Murdoch Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Murdoch, Larry↗
DOE OSTI2021

Overview of Hydraulic Fracturing Test Site 2 in the Permian Delaware Basin (HFTS-2)

Here, the Hydraulic Fracturing Test Site 2 (HFTS-2) is a large collaborative field-based R&D program in the Permian Delaware Basin, funded by the US Department of Energy through the National Energy Technology Laboratory (NETL) and the E&P industry, with support from academia. The projects' main objective is to improve the understating of the hydraulic fracturing process through utilization of advanced diagnostics and collection of through-fracture cores to provide undisputable evidence and attributes of the created hydraulic fractures. At the HFTS-2, in excess of $30 million was used to perform hydraulic fracturing research focusing on the Wolfcamp formation at a field site hosted and operated by Occidental. In addition to the research data collected by the project, Occidental provided a significant amount of background data for about a dozen existing wells in the test area as well as access to previously collected core. Additional technical and laboratory support was provided by the program members. Building on learnings and unanswered questions from HFTS-1 in the Permian Midland basin, the HFTS-2 used eight new producing wells and two existing (parent) wells to perform hydraulic fracturing research. Multiple science wells were drilled to sample and characterize the subsurface, including the collection of 540 feet of core in a vertical pilot hole and 948 feet of high-angle through-fracture core. The project installed permanent fiber optic cables in 3 wells to monitor near wellbore signals during fracturing and to collect cross-well strain measurements. Additional advanced diagnostics included a significant formation evaluation program on the vertical whole core, multi array moment tensor inversion capable microseismic survey, multi-well time-lapse geochemistry analysis, analysis of proppant distribution in producing child and slant core well, and others. We will provide an overview of the HFTS-2 project, including list of the consortium members, details of the test site, experiments performed, and technologies tested.

58 GEOSCIENCES↗
DOE OSTI2023

Using the Shallow Strain Tensor to Characterize Deep Geologic Reservoirs

Abstract Storing and recovering water, carbon, and heat from geologic reservoirs is central to managing resources in a changing climate. We tested the hypothesis that the strain tensor caused by injecting or producing fluids can be measured at shallow depths and interpreted to advance understanding of underlying deep aquifers or reservoirs. Geodetic‐grade strainmeters were deployed at 30 m depth overlying the Bartlesville Formation, a 500‐m‐deep sandstone near Tulsa, OK. The strainmeters are 220 m east of injection well 9A completed in a permeable lens at the base of the Bartlesville Formation. Water was injected into well 9A at approximately 1.0 L/s during four tests that ranged in duration from a few hours to a few weeks. The horizontal strain increased (tension) and the circumferential strain was a few times larger than the radial strain. The vertical strain decreased (compression) during injection. Strain rates were approximately 100 nε/day during the first few hours, but the rates decreased and were approximately 10 nε/day during most of the tests. Four independent methods of poroelastic simulation and inversion predict reservoir properties and geometries that are similar to each other and consistent with independent information about the reservoir. All strain interpretations predict that a boundary to the permeable lens occurs beneath the vicinity of the strainmeters, which is consistent with core data from the site. The boundary of the permeable lens is located by matching the vertical, radial and circumferential strains, which demonstrates the value of measuring the strain tensor.

Murdoch, Lawrence C.↗
DOE OSTI2026

The 10 September 2025 M w 4.1 Earthquake in Northeastern Utah, United States: An Archetypal Continental Mantle Event

The 10 September 2025 M w 4.1 earthquake in northeastern Utah, United States, had a focal depth 68 km beneath sea level, which is ∼20–25 km greater than estimates of local crustal thickness, making it a rare example of a continental mantle earthquake (CME). The focal depth is well resolved from arrival-time inversion (nearest station ∼13 km away) and moment tensor inversion of regional waveforms. Similar to other CMEs in the Intermountain West, there were no obvious aftershocks or foreshocks, and the waveforms were enriched in high-frequency energy. Spectral modeling gives a stress drop of ∼80 MPa and a radiation efficiency of ∼0.08, albeit with large uncertainties. The high stress drop and low radiation efficiency are consistent with a dissipative source process such as thermal runaway. Also similar to previous Intermountain West CMEs, the event occurred along the boundary of the Archean Wyoming craton, where pressure–temperature conditions favor ductile deformation. We hypothesize that edge-driven or regional-scale mantle convection produces increased strain rates near the craton boundary that make either conventional brittle failure or thermal runaway feasible at relatively high pressure–temperature conditions. High conductivity inferred around the edge of the craton may suggest that fluids also contribute to CME occurrence.

Koper, Keith D. [Univ. of Utah, Salt Lake City, UT↗
DOE OSTI2021

Structural, Electrical, and Electromechanical Properties of Inverse Hybrid Perovskites from First-Principles: The Case of (CH 3 NH 3 ) 3 OI

Inverse-hybrid perovskites (IHPs) with large polarization have recently been predicted from first-principles computations. Here, we use one representative from the IHP class of materials, (CH 3 NH 3 ) 3 OI (MA3OI), to propose a route to the first-principles prediction of structural and electrical properties, such as polarization, polarization reversibility, and the associated coercive field for hybrid organic–inorganic perovskites. The route relies on the construction of the polarization reversal path that models experimental measurements. Such a path was found to play an important role in the ground-state search as well as in the identification of competing structural variations. The latter is believed to be the origin of the structural disorder that is characteristic of hybrid organic–inorganic perovskites. The application of such an approach to MA3OI leads to the prediction of several structural variations that are expected to result in a structurally disordered phase above 766 K and of the polar ground state with a polarization of 25.3 μC/cm 2 that is reversible with the application of an electric field. The upper estimate for the coercive field associated with homogeneous polarization reversal is 6.9 GV/m. The piezoelectric constants of MA3OI are predicted to be an order of magnitude smaller in comparison with a prototypical inorganic ferroelectric PbTiO 3 ; however, the low symmetry of the MA3OI structure yields finite values for all components of the piezoelectric tensor. The polarization in MA3OI is tunable by the epitaxial strain (11.5% change under 5% epitaxial strain), although less so as compared with PbTiO 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Recent Developments in Hydrogeologic Applications for Strain Tensor Analyses

Changes in fluid pressure deform porous media and this effect occurs in a variety of hydrogeologic processes, from the change in storage during pumping or injection to fluctuations in water levels caused by barometric pressure. We have developed instruments for measuring small strains in porous media, and we have used the resulting strain data to evaluate well testing, hydraulic fracturing, manual loading at the ground surface, and ambient hydrologic processes, like rainfall and evaporation. A particularly important application is the use of strain tensor data measured at shallow depths to analyze well tests or hydraulic fractures conducted at much greater depths. An early demonstration of this technique was conducted at the North Avant Field north of Tulsa, Oklahoma, where Pennsylvanian sandstone creates a confined aquifer and oil reservoir at a depth of 530m. We have showed that the strains caused by injecting into the aquifer could be measured at a depth of 30m and used to evaluate the properties of the aquifer. We recently expanded the array of strainmeters at the North Avant Field by deploying three more instruments at shallow depth (30m) along with a deep instrument at 520m depth in the winter, 2021. The deep instrument is deployed in shale caprock slightly above the aquifer. To our knowledge, the deep strainmeter at the North Avant Field is the deepest strainmeter ever deployed and this required refining methods originally developed for shallow deployments. The instrument was lowered to depth on oil field tubing and cemented in place using techniques and materials developed for use in oil wells. Optical fiber used to communicate with the instrument was cemented in the annulus on the outside of tubing. This is significant because the techniques we used could readily be extended to greater depth, suggesting that strainmeters can be deployed over a wide range of depths for monitoring critical subsurface processes. For example, it suggests that strainmeters could be deployed through the caprock to monitor for leaks from underlying CO2 storage reservoirs. The strainmeter array at the North Avant Field has been used to characterize deformation during a series of injection tests in the spring and summer, 2021. All the new strainmeters respond to pumping, and the strainmeters we installed earlier also responded. To our knowledge, this is the first application of well testing in a deep aquifer that was monitored by an array of strainmeters—our earlier work used strainmeters at a single location. We are currently analyzing the strain data using an analytical solution, a proxy-based Bayesian inversion algorithm, and other methods. Strainmeter data has also been used to characterize periodic pumping tests by us and Riley Blais. A periodically varying pumping rate causes both hydraulic head and strain signals that vary with the same period as the pumping. The peaks and troughs of the head in monitoring wells lag behind the peaks and troughs of the head in the pumping well, and this lag time increases with distance from the pumping well. The lag time of the pressure and the distance to the monitoring well can be used in a simple analysis to estimate the hydraulic diffusivity of the aquifer. The lag time determined from strain data can be used to estimate aquifer properties using the same analysis that works for the pressure only for strain data measured at particular locations. That is because the strain field in a confining unit advances upward, laterally and then downward even though the pressure in the underlying aquifer only advances laterally, according to our recent simulations. We have field data showing that a small periodic signal superimposed on an injection rate at the North Avant Field will create a periodic strain signal at shallow strainmeters. The field data and the recent simulations suggest that including a periodic component to injection or pumping and then monitoring the resulting strain signal could be a way to monitor the subsurface.

Murdoch, Larry↗
DOE OSTI2023

Recent Developments in Hydrogeologic Applications for Strain Tensor Analyses

Changes in fluid pressure deform porous media and this effect occurs in a variety of hydrogeologic processes, from the change in storage during pumping or injection to fluctuations in water levels caused by barometric pressure. We have developed instruments for measuring small strains in porous media, and we have used the resulting strain data to evaluate well testing, hydraulic fracturing, manual loading at the ground surface, and ambient hydrologic processes, like rainfall and evaporation. A particularly important application is the use of strain tensor data measured at shallow depths to analyze well tests or hydraulic fractures conducted at much greater depths. An early demonstration of this technique was conducted at the North Avant Field north of Tulsa, Oklahoma, where Pennsylvanian sandstone creates a confined aquifer and oil reservoir at a depth of 530m. We have showed that the strains caused by injecting into the aquifer could be measured at a depth of 30m and used to evaluate the properties of the aquifer. We recently expanded the array of strainmeters at the North Avant Field by deploying three more instruments at shallow depth (30m) along with a deep instrument at 520m depth in the winter, 2021. The deep instrument is deployed in shale caprock slightly above the aquifer. To our knowledge, the deep strainmeter at the North Avant Field is the deepest strainmeter ever deployed and this required refining methods originally developed for shallow deployments. The instrument was lowered to depth on oil field tubing and cemented in place using techniques and materials developed for use in oil wells. Optical fiber used to communicate with the instrument was cemented in the annulus on the outside of tubing. This is significant because the techniques we used could readily be extended to greater depth, suggesting that strainmeters can be deployed over a wide range of depths for monitoring critical subsurface processes. For example, it suggests that strainmeters could be deployed through the caprock to monitor for leaks from underlying CO2 storage reservoirs. The strainmeter array at the North Avant Field has been used to characterize deformation during a series of injection tests in the spring and summer, 2021. All the new strainmeters respond to pumping, and the strainmeters we installed earlier also responded. To our knowledge, this is the first application of well testing in a deep aquifer that was monitored by an array of strainmeters—our earlier work used strainmeters at a single location. We are currently analyzing the strain data using an analytical solution, a proxy-based Bayesian inversion algorithm, and other methods. Strainmeter data has also been used to characterize periodic pumping tests by us and Riley Blais. A periodically varying pumping rate causes both hydraulic head and strain signals that vary with the same period as the pumping. The peaks and troughs of the head in monitoring wells lag behind the peaks and troughs of the head in the pumping well, and this lag time increases with distance from the pumping well. The lag time of the pressure and the distance to the monitoring well can be used in a simple analysis to estimate the hydraulic diffusivity of the aquifer. The lag time determined from strain data can be used to estimate aquifer properties using the same analysis that works for the pressure only for strain data measured at particular locations. That is because the strain field in a confining unit advances upward, laterally and then downward even though the pressure in the underlying aquifer only advances laterally, according to our recent simulations. We have field data showing that a small periodic signal superimposed on an injection rate at the North Avant Field will create a periodic strain signal at shallow strainmeters. The field data and the recent simulations suggest that including a periodic component to injection or pumping and then monitoring the resulting strain signal could be a way to monitor the subsurface.

Murdoch, Larry↗