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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↗

Effects of compressibility on design of subsonic fuselages for natural laminar flow

Compressible linear boundary-layer stability analyses of two representative axisymmetric fuselage geometries indicate that a favorable effect will be exerted on the characteristics of a fuselage's axisymmetric boundary layer by compressibility. A freestream Mach number increase from 0.6 to 0.8 significantly reduces TS wave growth rates in the laminar boundary layer of the fuselages analyzed. The generally destabilizing effect of increasing length Re number on boundary layer stability can be overpowered by the favorable effects of compressibility on the fluid.

Vijgen, P. M. H. W.↗

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharamonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. D.↗

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

Dulikravich, D. S.↗

Automatic commanding of the Mars Observer Camera

Mars Observer, launched in September 1992, was intended to be a 'survey-type' mission that acquired global coverage of Mars from a low, circular, near-polar orbit during an entire Martian year. As such, most of its instruments had fixed data rates, wide fields of view, and relatively low resolution, with fairly limited requirements for commanding. An exception is the Mars Observer Camera, or MOC. The MOC consists of a two-color Wide Angle (WA) system that can acquire both global images at low resolution (7.5 km/pixel) and regional images at commandable resolutions up to 250 m/pixel. Complementing the WA is the Narrow Angle (NA) system, that can acquire images at 8 resolutions from 12 m/pixel to 1.5 m/pixel, with a maximum crosstrack dimension of 3 km. The MOC also provides various forms of data compression (both lossless and lossy), and is designed to work at data rates from 700 bits per second (bps) to over 80k bps. Because of this flexibility, developing MOC command sequences is much more difficult than the routine mode-changing that characterizes other instrument operations. Although the MOC cannot be pointed (the spacecraft is fixed nadir-pointing and has no scan platform), the timing, downlink stream allocation, compression type and parameters, and image dimensions of each image must be commanded from the ground, subject to the constraints inherent in the MOC and the spacecraft. To minimize the need for a large operations staff, the entire command generation process has been automated within the MOC Ground Data System. Following the loss of the Mars Observer spacecraft in August 1993, NASA intends to launch a new spacecraft, Mars Global Surveyor (MGS), in late 1996. This spacecraft will carry the MOC flight spare (MOC 2). The MOC 2 operations plan will be largely identical to that developed for MOC, and all of the algorithms described here are applicable to it.

Caplinger, Michael↗

Critical fluid light scattering

The objective is to measure the decay rates of critical density fluctuations in a simple fluid (xenon) very near its liquid-vapor critical point using laser light scattering and photon correlation spectroscopy. Such experiments were severely limited on Earth by the presence of gravity which causes large density gradients in the sample when the compressibility diverges approaching the critical point. The goal is to measure fluctuation decay rates at least two decades closer to the critical point than is possible on earth, with a resolution of 3 microK. This will require loading the sample to 0.1 percent of the critical density and taking data as close as 100 microK to the critical temperature. The minimum mission time of 100 hours will allow a complete range of temperature points to be covered, limited by the thermal response of the sample. Other technical problems have to be addressed such as multiple scattering and the effect of wetting layers. The experiment entails measurement of the scattering intensity fluctuation decay rate at two angles for each temperature and simultaneously recording the scattering intensities and sample turbidity (from the transmission). The analyzed intensity and turbidity data gives the correlation length at each temperature and locates the critical temperature. The fluctuation decay rate data from these measurements will provide a severe test of the generalized hydrodynamic theories of transport coefficients in the critical regions. When compared to equivalent data from binary liquid critical mixtures they will test the universality of critical dynamics.

Gammon, Robert W.↗

Burst-Compression And -Expansion For TDMA Communication

Burst-compression and -expansion technique enables interconnection of users transmitting and receiving data at rates asynchronous with respect to clocks within ground terminals of satellite-switched, time-division-multiple-access (TDMA) communication network. Matrix switch aboard satellite routes bursts of data from source users received on uplink antennas to downlink antennas illuminating ground areas containing destination users. TDMA ground terminal compresses streams of data from source users into rapid bursts for transmission and reexpands bursts of received data into slower streams of data for delivery to destination users. Greater flexibility in interconnecting widely dispersed users achieved by use of hopping beams.

Budinger, James M.↗

Some Design Considerations for Two-Dimensional, Mixed-Compression Inlets for Mach 2.5 to 3.5.

A computational design study was performed to explore design factors for two-dimensional, mixed-compression inlets designed for cruise conditions at Mach 2.5, 2.75, 3.0, 3.25, and 3.5 and their influence on the aerodynamic performance of the inlets. The design factors included the split of external and internal compression, capture aspect ratio, throat section and subsonic diffuser geometry, and location and rates of porous bleed regions. The performance of the inlet was measured by the total pressure recovery, cowl wave drag, bleed flow rates, and total pressure distortion at the engine face. The results provide useful information for the design of inlets for future supersonic aircraft.

Supersonic Inlet↗

SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors

Today's scientific simulations require a significant reduction of data volume because of extremely large amounts of data they produce and the limited I/O bandwidth and storage space. Here, error-bounded lossy compression has been considered one of the most effective solutions to the above problem. In practice, however, the best-fit compression method often needs to be customized or optimized in particular because of diverse characteristics in different datasets and various user requirements on the compression quality and performance. In this paper, we address this issue with a novel modular, composable compression framework named SZ3. Our contributions are four-folds. (1) We develop SZ3 which features an innovative modular abstraction for the prediction-based compression framework, such that compression modules can be plugged in easily to create new compressors based on characteristics of data and user requirements. (2) We create a new compression pipeline by SZ3 for GAMESS data, which significantly improves the compression ratios over state-of-the-art compressors. (3) We develop an adaptive compression pipeline by SZ3 for APS data with minimal efforts, which leads to the best rate-distortion among all existing error-bounded lossy compressors for any bit-rate. (4) We compare the sustainability of SZ3 with leading error-bounded prediction-based compressors, and then demonstrate the necessity of diverse pipelines by integrating and evaluating several compression pipelines on diverse scientific datasets from multiple disciplines. Experiments show that SZ3 incurs very limited overhead in compressor integration and our customized compression pipelines lead to up to 20% improvement in compression ratios under the same data distortion, when compared with the best existing approach.

97 MATHEMATICS AND COMPUTING↗

Determination of solid-propellant transient regression rates using a microwave Doppler shift technique

A microwave Doppler shift system, with increased resolution over earlier microwave techniques, was developed for the purpose of measuring the regression rates of solid propellants during rapid pressure transients. A continuous microwave beam is transmitted to the base of a burning propellant sample cast in a metal waveguide tube. A portion of the wave is reflected from the regressing propellant-flame zone interface. The phase angle difference between the incident and reflected signals and its time differential are continuously measured using a high resolution microwave network analyzer and related instrumentation. The apparent propellant regression rate is directly proportional to this latter differential measurement. Experiments were conducted to verify the (1) spatial and time resolution of the system, (2) effect of propellant surface irregularities and compressibility on the measurements, and (3) accuracy of the system for quasi-steady-state regression rate measurements. The microwave system was also used in two different transient combustion experiments: in a rapid depressurization bomb, and in the high-frequency acoustic pressure environment of a T-burner.

Strand, L. D.↗

Proceedings of the Scientific Data Compression Workshop

Continuing advances in space and Earth science requires increasing amounts of data to be gathered from spaceborne sensors. NASA expects to launch sensors during the next two decades which will be capable of producing an aggregate of 1500 Megabits per second if operated simultaneously. Such high data rates cause stresses in all aspects of end-to-end data systems. Technologies and techniques are needed to relieve such stresses. Potential solutions to the massive data rate problems are: data editing, greater transmission bandwidths, higher density and faster media, and data compression. Through four subpanels on Science Payload Operations, Multispectral Imaging, Microwave Remote Sensing and Science Data Management, recommendations were made for research in data compression and scientific data applications to space platforms.

Ramapriyan, H. K.↗

Ductility evaluation of nitrided Zircaloy-4 cladding by ring compression testing

Here, this study evaluated the embrittlement of Zircaloy-4 cladding by dry air and dry nitrogen environments as a function of process temperature and duration of exposure. A Netzsch thermogravimetric analyzer was used to measure the mass gain of cladding sections over time with specified temperature and gas flow programs. Oxidation of Zircaloy in dry air produced a brittle ZrO 2 layer with ductile unreacted metal. In contrast, nitridation of Zircaloy had a slower reaction rate but produced a brittle cladding that was more easily breached during ring compression tests. The ring compression tests demonstrated that ductility of Zircaloy cladding decreases as nitrogen pickup increases; a ductile-to-brittle transition occurs near a mass gain of 2.1 wt %. Nitridation showed minimal temperature dependency in ductility degradation, whereas oxidation showed significant temperature dependency in ductility degradation, with severe embrittlement occurring at 1200 °C. Optical micrographs confirmed the formation of uniform ZrN layers (approximately 12 µm thick) on the cladding surface, indicating that cladding embrittlement is primarily the result of nitrogen diffusion rather than metal layer thinning.

36 MATERIALS SCIENCE↗

Computer program determines gas flow rates in piping systems

Computer program calculates the steady state flow characteristics of an ideal compressible gas in a complex piping system. The program calculates the stagnation and total temperature, static and total pressure, loss factor, and forces on each element in the piping system.

Franke, R.↗

Voyager image data compression and block encoding

Telemetry enhancement techniques used by Voyager-2 to reduce telemetry transmission rates by over 50 percent compared to those used at Saturn, with negligible loss in information return, are described. The use of the Reed-Solomon encoder is discussed, and the principles and implementation of an Image Data Compressor algorithm for noiseless coding techniques are addressed. Parallel operation of the redundant Flight Data Subsystem processors is discussed.

Urban, Michael G.↗

Material Modeling of Space Shuttle Leading Edge and External Tank Materials For Use in the Columbia Accident Investigation

Upon the commencement of the analytical effort to characterize the impact dynamics and damage of the Space Shuttle Columbia leading edge due to External Tank insulating foam, the necessity of creating analytical descriptions of these materials became evident. To that end, material models were developed of the leading edge thermal protection system, Reinforced Carbon Carbon (RCC), and a low density polyurethane foam, BX-250. Challenges in modeling the RCC include its extreme brittleness, the differing behavior in compression and tension, and the anisotropic fabric layup. These effects were successfully included in LS-DYNA Material Model 58, *MAT_LAMINATED_ COMPOSITE_ FABRIC. The differing compression and tension behavior was modeled using the available damage parameters. Each fabric layer was given an integration point in the shell element, and was allowed to fail independently. Comparisons were made to static test data and coupon ballistic impact tests before being utilized in the full scale analysis. The foam's properties were typical of elastic automotive foams; and LS-DYNA Material Model 83, *MAT_FU_CHANG_FOAM, was successfully used to model its behavior. Material parameters defined included strain rate dependent stress-strain curves for both loading and un-loading, and for both compression and tension. This model was formulated with static test data and strain rate dependent test data, and was compared to ballistic impact tests on load-cell instrumented aluminum plates. These models were subsequently utilized in analysis of the Shuttle leading edge full scale ballistic impact tests, and are currently being used in the Return to Flight Space Shuttle re-certification effort.

Carney, Kelly↗

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↗

Thermal Charging Rate of Composite Wax-Expanded Graphite Phase Change Materials

Phase change materials (PCMs) are valuable for their ability to store heat nearly isothermally around their phase transition temperature. PCMs are at the core of latent heat thermal energy storage (LHTES) systems, which provide the ability to buffer high thermal loads or decouple the time when heating or cooling is needed from when it is produced. Thermal charging and discharging of LHTES systems often employ a constant temperature source, and the rate at which heat can be exchanged is dependent on the thermophysical properties of the PCM. For graphite composite PCMs, the high thermal conductivity of the graphite enables an increased heat transfer rate through the material, but its presence displaces PCM which reduces the effective volumetric latent heat of the composite relative to the pure PCM. This results in a tradeoff between thermal power and volumetric energy storage capacity. The thermal charging rate is the average thermal energy stored in the material for some elapsed time. In this study, composite PCMs of compressed expanded natural graphite (CENG) and n-Octadecane are studied. Samples with varying CENG mass fractions were synthesized and the thermal charging rate was measured under a constant temperature boundary condition. For evaluation of the expanded graphite-PCM composite, one boundary of the material was exposed to a 50°C constant temperature plate, above the 27.5°C melting temperature of the PCM. The melting front progression [mm-s-1] and the thermal charging rate [W-cm-2] of the PCM were determined, and the results were compared with analytical predictions for the 1-D semi-infinite phase change. For CENG addition up to 5.75% mass fraction, a 450% thermal conductivity increase was observed with a 5% decrease in volumetric energy density as compared to pure octadecane. The average thermal charging rate was increased by over 430% for the melt to penetrate a depth of 22 mm. The experimental results matched analytical predictions, indicating that higher CENG fractions can be evaluated using analytical approaches.

Hirschey, Jason↗