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Geomechanics-Based Stochastic Analysis of Injection- Induced Seismicity

The production of geothermal energy from dry and low permeability reservoirs is achieved by water circulation in natural and/or man-made fractures, and is referred to as enhanced or engineered geothermal systems (EGS). Often, the permeable zones have to be created by stimulation, a process which involves fracture initiation and/or activation of discontinuities such as faults and joints due to pore pressure and the in-situ stress perturbations. The stimulation of a rock mass is often accompanied by multiple microseismic events. Micro-seismic events associated with rock failure in shear, and shear slip on new or pre-existing fracture planes and possibly their propagations. The microseismic signals contain information about the sources of energy that can be used for understanding the hydraulic fracturing process and the created reservoir properties. Detection and interpretation of microseismic events is useful for estimating the stimulated zone, created reservoir permeability and fracture growth, and geometry of the geological structures and the in-situ stress state. The process commonly is referred to as seismicity-based reservoir characterization (SBRC). Although, progress has been made by scientific & geothermal communities for quantitative and qualitative analysis of reservoir stimulation using SBRC several key questions remain unresolved in the analysis of micro-seismicity namely, variation of seismic activity with injection rate, delayed micro-seismicity, and the relation of stimulated zone to the injected volume and its rate, and the resulting reservoir permeability. In addition, the current approach to SBRC does not consider the full range of relevant poroelastic and thermoelastic phenomena and neglects the uncertainty in rock properties and in-situ stress in the data inversion process. The objective of this research and technology developments was to develop a 3D SBRC model that addresses these shortcomings by taking into account hydro-thermo-poro-mechanical mechanisms associated with injection and utilizing a state-of-the-art stochastic inversion procedure. The approach proposed herein is innovative and significantly improves the existing SBCR technology (e.g., Shapiro et al. 2003) for geothermal reservoirs in several ways. First, the current scope of the SBRC is limited with respect to the physical processes considered and the rock properties used. Usually, the geomechanics analyses within SBRC is limited to the pore pressure diffusion in the rock mass, which is modeled using a time-dependent parabolic equation and solved using a finite element algorithm with either a line or a point source. However, water injection induces both poroelastic and thermoelastic stresses in the rock mass which affect the stress state. In fact, it has been suggested that thermoelastic stresses can play a dominant role in reservoir seismicity (Ghassemi et al., 2007). We include these important effects by using a fully-coupled poro-thermoelastic constitutive equations for the rock mass which will be solved using a 3D finite element model with more realistic injection geometries such as multiple injection/extraction sources (and in fractures), uncertainty in the material parameters and the in-situ stress distribution to better reflect the pore pressure and stress distributions. In addition, we developed a 3D stochastic fracture network model to study MEQ generation in fracture rocks. The model was verified using laboratory experiments, and calibrated and applied to Newberry EGS stimulation. In previous SBRC approaches, the triggering of micro-seismicity is modeled base on the assumption that the prior stochastic criticality model of the rock mass is a valid and adequate description. However, this assumption often does not hold in the field. Thus, we improved upon the current SBRC approach by using the micro-seismic responses to estimate the hydraulic diffusivity as well as the criticality distribution itself within the field. In this way, instead of relying on our a priori knowledge of criticality distribution, we combine an initial probabilistic description of criticality with the information contained in microseismic measurements to arrive at criticality solutions that are conditioned on both field data and our prior knowledge. Previous SBRC have relied upon a deterministic inversion approach to estimate the permeability, and the extent of the stimulated zone, whereas a stochastic inversion algorithm that recognizes and quantifies the uncertainties in the prior model, the time evolution of pore pressure distributions (modeling errors), and the observed seismic events is developed and used herein to realistically assess the quality of the solution. Finally, we developed a technique for processing discrete MEQ data to estimate fracture network properties such as dip and dip directions. The approach was successfully applied to the Fenton Hill HRD experiment and the Newberry EGS with results in good agreement with field observations.

15 GEOTHERMAL ENERGY↗

Thermal barrier coating life prediction model

This is the second annual report of the first 3-year phase of a 2-phase, 5-year program. The objectives of the first phase are to determine the predominant modes of degradation of a plasma sprayed thermal barrier coating system and to develop and verify life prediction models accounting for these degradation modes. The primary TBC system consists of an air plasma sprayed ZrO-Y2O3 top coat, a low pressure plasma sprayed NiCrAlY bond coat, and a Rene' 80 substrate. Task I was to evaluate TBC failure mechanisms. Both bond coat oxidation and bond coat creep have been identified as contributors to TBC failure. Key property determinations have also been made for the bond coat and the top coat, including tensile strength, Poisson's ratio, dynamic modulus, and coefficient of thermal expansion. Task II is to develop TBC life prediction models for the predominant failure modes. These models will be developed based on the results of thermmechanical experiments and finite element analysis. The thermomechanical experiments have been defined and testing initiated. Finite element models have also been developed to handle TBCs and are being utilized to evaluate different TBC failure regimes.

Hillery, R. V.↗

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Lee, Jeh Won↗

Probabilistic system identification in the time domain

The objective of system identification is to determine reliable dynamical models of a structure by systematically using its measured excitation and response. It brings together in an integrated fashion, experimental, analytical, and computational techniques in structural dynamics. Areas of application for system identification include the following: (1) Model Evaluation--assessing assumptions (linearity and equivalent viscous damping) and techniques (finite-element modeling) used to construct theoretical models of a structure; (2) Model Improvement--updating of a theoretical model to enable more accurate response predictions for possible future loads on the structure, or for control of the structure; (3) Empirical Modelling--developing empirical relationships (nonlinear models) or empirical parameter values (modal damping) because the present state of the art does not provide theoretical results; and (4) Damage Detection and Assessment--continual or episodic updating of a structural model through vibration monitoring to detect and locate any structural damage. It can be argued that since the construction or modification of models using test data is subject to inherent uncertainties, the above problems should be properly treated within a Bayesian probabilistic framework. Such a methodology is presented which allows the precision of the estimates of the model parameters to be computed. It also leads to a guiding principle in applications. Namely, when selecting a single model from a given class of models, one should take the most probable model in the class based on the experimental data. Practical applications of this principle are given which are based on the utilization of measured seismic motions in large civil structures. Examples include the application of a computer program MODE-ID to identify modal properties directly from seismic excitation and response time histories from a nine-story steel-frame building at JPL and from a freeway overpass bridge.

Beck, James L.↗

Modeling of a Non-Dilute Alloy Solidification Under Terrestrial and Microgravity Conditions

A general finite element model of non-dilute alloy solidification was used to simulate growth of HgCdTe from the melt. 2-D and 3-D models with and without Oberbeck-Boussinesq (O-B) approximation were used. Verification of the 3-D model was based on experimental data. The location and the shape of the interface were determined using melting temperatures obtained from the HgCdTe liquidus curve. Double-diffusive convection in the melt is caused by radial temperature gradients and by rejection at the solid-melt interface of the heavier HgTe-rich solute. Because of these complicating factors, dimensional rather than non-dimensional modeling was performed. Models based on complete set of Navier-Stokes equations for compressible media are superior to the O-B approximation in microgravity, because they provide more accurate estimation of convection.

Bune, Andris V.↗

Response of the Alliance 1 Proof-of-Concept Airplane Under Gust Loads

This report presents the work performed by Lockheed Martin's Langley Program Office in support of NASA's Environmental Research Aircraft and Sensor Technology (ERAST) program. The primary purpose of this work was to develop and demonstrate a gust analysis method which accounts for the span-wise variation of gust velocity. This is important because these unmanned aircraft having high aspect ratios and low wing loading are very flexible, and fly at low speeds. The main focus of the work was therefore to perform a two-dimensional Power Spectrum Density (PSD) analysis of the Alliance 1 Proof-of-Concept Unmanned Aircraft, As of this writing, none of the aircraft described in this report have been constructed. They are concepts represented by analytical models. The process first involved the development of suitable structural and aeroelastic Finite Element Models (FEM). This was followed by development of a one-dimensional PSD gust analysis, and then the two-dimensional (PSD) analysis of the Alliance 1. For further validation and comparison, two additional analyses were performed. A two-dimensional PSD gust analysis was performed on a simplet MSC/NASTRAN example problem. Finally a one-dimensional discrete gust analysis was performed on Alliance 1. This report describes this process, shows the relevant comparisons between analytical methods, and discusses the physical meanings of the results.

Naser, A. S.↗

Synthesis, Microstructure and Properties of Nickel Aluminide Foams

Two Ph.D. students were involved in the project: Mr. Christopher Schuh (part-time, graduated in Spring 2001) and Ms. Andrea Hodge (full-time, graduated Summer 2002). One post-doctoral fellow, Dr. Heeman Choe, worked full-time on the project from July to December 2002. A new process to aluminize and chromize nickel foams was created. A kinetic aluminization model was developed. Creep testing was conducted on the foams. A finite-element model and a simplified analytical model for foam creep were produced. Four articles were written: one is published, two are accepted for publication, and one is in preparation. Ms. Hodge spent four months at NASA Glenn Research Center (9-12/2001 and 2-3/2002) under the supervision of Dr. Nathal. She conducted research on NiAl foam fabrication, mechanical testing and numerical modeling. She gave a talk at the ASM annual conference in November 2001 and presented her results at NASA in December 2001.

Dunand, David C.↗

Structural Dynamics Modeling of HIRENASD in Support of the Aeroelastic Prediction Workshop

An Aeroelastic Prediction Workshop (AePW) was held in April 2012 using three aeroelasticity case study wind tunnel tests for assessing the capabilities of various codes in making aeroelasticity predictions. One of these case studies was known as the HIRENASD model that was tested in the European Transonic Wind Tunnel (ETW). This paper summarizes the development of a standardized enhanced analytical HIRENASD structural model for use in the AePW effort. The modifications to the HIRENASD finite element model were validated by comparing modal frequencies, evaluating modal assurance criteria, comparing leading edge, trailing edge and twist of the wing with experiment and by performing steady and unsteady CFD analyses for one of the test conditions on the same grid, and identical processing of results.

Wieseman, Carol↗

Lumped Parameter Models of the Central Nervous System for VIIP Research

INTRODUCTION: Current long-duration missions to the International Space Station and future exploration-class missions beyond low-Earth orbit, such as to Mars and asteroids, expose astronauts to increased risk of Visual Impairment and Intracranial Pressure (VIIP) syndrome [1]. It has been hypothesized that the headward shift of cerebral spinal fluid (CSF) and blood in microgravity may cause significant elevation of intracranial pressure (ICP), which in turn induces VIIP syndrome through biomechanical pathways [1, 2]. However, there is insufficient evidence to confirm this hypothesis. In this light, we are developing lumped-parameter models of fluid transport in the central nervous system (CNS) as a means to simulate the influence of microgravity on ICP. The CNS models will also be used in concert with the lumped parameter and finite element models of the eye described in the realted IWS abstracts submitted by Nelson et al., Feola et al. and Ethier et al. METHODS: We have developed a nine compartment CNS model (Figure 1) capable of both time-dependent and steady state fluid transport simulations, based on the works of Stevens et al. [3]. The breakdown of compartments within the model includes: vascular (3), CSF (2), brain (1) and extracranial (3). The boundary pressure in the Central Arteries [A] node is prescribed using an oscillating pressure function PA(t) simulating the carotid pulsatile pressure wave as developed by Linninger et al. [4]. For each time step, pressures are integrated through time using an adaptive-timestep 4th and 5th order Runga-Kutta solver. Once pressures are found, constitutive equations are used to solve for flowrates (Q) between each compartment. In addition to fluid flow between the different compartments, compliance (C) interactions between neighboring compartments are represented. We are also developing a second CNS model based on the works of Linninger et al. [4] which takes a more granular approach to represent the interactions of the intracranial and spinal compartments with the inclusion of arteries, arterioles, capillaries, venules, veins, venous sinus, and ventricles. The flow through the arteries, veins and CSF compartments are governed by continuity, momentum and distensibility balance equations. Furthermore, unlike the Stevens et al. approach, the Monro-Kellie doctrine of constant cranial volume and the bi-phasic nature of the brain parenchyma are implemented. These features appear to be more consistent with the physiologic and anatomical behavior of the CNS, and follow a modeling philosophy similar to the lumped parameter eye model that is intended to be integrated with the CNS model. However, Linninger’s approach has never been implemented to include hydrostatic gradient and microgravity simulation capabilities. Therefore, we aim at implement this modeling approach for spaceflight simulations and assess its overall applicability to VIIP research. OBJECTIVES: We will present verification and validation test results for both models, as well as head-to-head comparison to explore their strengths and limitations with respect to mathematical implementation and physiological significance for VIIP research. In doing so, we hope to provide some guidance to the HRP research community on how to appropriately leverage lumped parameter models for space biomedical research.

Vera, J.↗

VIIP: Central Nervous System (CNS) Modeling

Current long-duration missions to the International Space Station and future exploration-class missions beyond low-Earth orbit expose astronauts to increased risk of Visual Impairment and Intracranial Pressure (VIIP) syndrome. It has been hypothesized that the headward shift of cerebrospinal fluid (CSF) and blood in microgravity may cause significant elevation of intracranial pressure (ICP), which in turn may then induce VIIP syndrome through interaction with various biomechanical pathways. However, there is insufficient evidence to confirm this hypothesis. In this light, we are developing lumped-parameter models of fluid transport in the central nervous system (CNS) as a means to simulate the influence of microgravity on ICP. The CNS models will also be used in concert with the lumped parameter and finite element models of the eye described in the related IWS works submitted by Nelson et al., Feola et al. and Ethier et al.

intraocular pressure↗

Influence of Population Variation of Physiological Parameters in Computational Models of Space Physiology

The earliest manifestations of Visual Impairment and Intracranial Pressure (VIIP) syndrome become evident after months of spaceflight and include a variety of ophthalmic changes, including posterior globe flattening and distension of the optic nerve sheath. Prevailing evidence links the occurrence of VIIP to the cephalic fluid shift induced by microgravity and the subsequent pressure changes around the optic nerve and eye. Deducing the etiology of VIIP is challenging due to the wide range of physiological parameters that may be influenced by spaceflight and are required to address a realistic spectrum of physiological responses. Here, we report on the application of an efficient approach to interrogating physiological parameter space through computational modeling. Specifically, we assess the influence of uncertainty in input parameters for two models of VIIP syndrome: a lumped-parameter model (LPM) of the cardiovascular and central nervous systems, and a finite-element model (FEM) of the posterior eye, optic nerve head (ONH) and optic nerve sheath. Methods: To investigate the parameter space in each model, we employed Latin hypercube sampling partial rank correlation coefficient (LHSPRCC) strategies. LHS techniques outperform Monte Carlo approaches by enforcing efficient sampling across the entire range of all parameters. The PRCC method estimates the sensitivity of model outputs to these parameters while adjusting for the linear effects of all other inputs. The LPM analysis addressed uncertainties in 42 physiological parameters, such as initial compartmental volume and nominal compartment percentage of total cardiac output in the supine state, while the FEM evaluated the effects on biomechanical strain from uncertainties in 23 material and pressure parameters for the ocular anatomy. Results and Conclusion: The LPM analysis identified several key factors including high sensitivity to the initial fluid distribution. The FEM study found that intraocular pressure and intracranial pressure had dominant impact on the peak strains in the ONH and retro-laminar optic nerve, respectively; optic nerve and lamina cribrosa stiffness were also important. This investigation illustrates the ability of LHSPRCC to identify the most influential physiological parameters, which must therefore be well-characterized to produce the most accurate numerical results.

biomechanics↗

Comparison of AGR-3/4 Fission Product Transport Model to Measurements and Extraction of Diffusivities via Analytical Fits

A one-dimensional finite-element model based on the MOOSE framework has been constructed, and overall transport estimates are predicted based on available diffusivities and sorption isotherms in the extant literature. The predicted transport profiles are compared to experimental results, where such results are available, including total inventory analysis of gamma emitters, liquid scintillation results for Sr-90 concentrations, radial deconsolidation leach-burn-leach within compacts, tomographic reconstructions based on detailed gamma scanning and destructive physical sampling of several rings. The magnitude of expected transport to the sink ring is generally predicted by the model for silver and cesium, however, modeled detailed concentration profiles are not consistent with experimental results. Strontium and europium transport is not well characterized by model results.

07 ISOTOPE AND RADIATION SOURCES↗

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Gherlone, Marco↗

Second order tensor finite element

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

Oden, J. Tinsley↗

Applications of Displacement Transfer Functions to Deformed Shape Predictions of the G-III Swept-Wing Structure

In support of the Adaptive Compliant Trailing Edge [ACTE] project at the NASA Armstrong Flight Research Center, displacement transfer functions were applied to the swept wing of a Gulfstream G-III airplane (Gulfstream Aerospace Corporation, Savannah, Georgia) to obtain deformed shape predictions. Four strainsensing lines (two on the lower surface, two on the upper surface) were used to calculate the deformed shape of the G III wing under bending and torsion. There being an insufficient number of surface strain sensors, the existing G III wing box finite element model was used to generate simulated surface strains for input to the displacement transfer functions. The resulting predicted deflections have good correlation with the finite-element generated deflections as well as the measured deflections from the ground load calibration test. The convergence study showed that the displacement prediction error at the G III wing tip can be reduced by increasing the number of strain stations (for each strain-sensing line) down to a minimum error of l.6 percent at 17 strain stations; using more than 17 strain stations yielded no benefit because the error slightly increased to 1.9% when 32 strain stations were used.

displacement theory↗

THERMAL STRESS ANALYSIS OF A SPENT NUCLEAR FUEL CANISTER

The potential for chloride induced stress corrosion cracking (CISCC) in spent nuclear fuel dry storage canisters is a current topic of research by the US Department of Energy Spent Fuel and Waste Science and Technology program. One of the important prerequisites for CISCC is a tensile residual stress state. This study utilizes computational models to provide an initial analysis of thermal stresses in a generic spent nuclear fuel canister. A STAR-CCM+ thermal fluid model provides a temperature profile analysis of the canister based on four different ambient temperature conditions. An ANSYS APDL finite element model incorporates the temperature profiles to analyze the thermal stresses in the canister. The calculated thermal stress magnitudes are in the range of 10 MPa to 80 MPa, which could be significant for crack propagation through the canister wall. The maximum thermal stress is not a concern for the structural failure of the canister, but it is high enough that it is a significant contribution to the total stress state of the canister wall, which also includes residual stress from fabrication, internal pressure from helium cover gas, and potential transient mechanical loads, such as earthquakes. This paper describes the initial finite element thermal stress analysis that was completed in 2020, reports the initial findings, and identifies areas where model refinement is still needed to complete this work in the future.

Jensen, Ben J.↗

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE↗