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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Processing-Dependent Structure and Poroelasticity of Nafion in Liquid Water

Ionomers act as the solid polymer electrolyte membrane in many modern electrochemical devices, yet the role of their nanostructure in modulating the poroelastic response remains poorly understood, especially in liquid water, where few techniques can measure simultaneous transport-mechanical properties. Poroelastic Relaxation Indentation (PRI) is uniquely suited for measuring time-dependent transport-mechanical properties of porous solids, specifically hydraulic diffusivity, elastic modulus, Poisson’s ratio, and intrinsic permeability, for porous solids. While ionomers such as Nafion are not porous in the typical sense, Nafion has a nanophase-segregated structure that, when fully swollen in liquid water, behaves as a poroelastic solid with a coupled mechanical-transport response. Using a poroelastic framework, we investigate how casting and pretreatment of Nafion membranes alter their poroelastic response in liquid environments. We characterize both extruded and dispersion-cast Nafion membranes pretreated in water at 25 or 100 °C and relate the mechanical-transport properties to the ionomer structure via hydrophilic and intercrystalline domain spacing measured using Small-Angle X-ray Scattering (SAXS). At 25 °C, dispersion-cast membranes exhibit distinctly lower hydraulic diffusivity and intrinsic permeability than extruded membranes but with comparable mechanical properties. Pretreatment at 100 °C increases hydrophilic domain spacing, improving transport but at the expense of mechanical stiffness. Dispersion-cast membranes respond more strongly to pretreatment than extruded membranes. Using the Carman-Kozeny pore network model and the hydrophilic domain-spacing, we estimate the pore radius and tortuosity to show how pretreatment reduces structure-related tortuosity differences between dispersion-cast and extruded membranes. Here, in this work, we show that nanophase-segregated materials such as Nafion can be rigorously characterized using poroelasticity, resulting in physically meaningful transport-mechanical properties. Coupling PRI with SAXS provides insights into the nanostructural features that govern the coupled mechanical-transport response. By establishing PRI for a nanophase-segregated material, this approach opens avenues for this technique’s application in other hydrated polymeric materials not typically considered to be poroelastic.

Shen, Margaret [University of California, Berkeley↗
DOE OSTI2023

Pressure Transient Analyses and Poroelastic Modeling of Hydraulic Fracture Dilation for Multiple Injections at the Devine Fracture Pilot Site

Our team has conducted electromagnetic (EM) surveys for the past six years to monitor hydraulic-fracture behavior at the Devine Fracture Pilot Site (DFPS). The sub-horizontal orientation of a shallow hydraulic fracture at the DFPS provides uniform access to the fracture area for interrogation and data collection. Ahmadian et al. (2023) suggested a possible correlation between spatiotemporal changes in the flow rate, bottomhole pressure (BHP), and the observed surface recorded electric field at the DFPS. In this paper, we present the development of poroelastic forward models and pressure transient analyses (PTAs) to support the development of a multiphysics inverse model for these EM surveys. First, we conducted PTAs of the shut-in periods after six injections out of 10 to determine the fracture closure pressure (FCP) or the overburden pressure used in a poroelastic fracture reopening model. Second, we developed a finite-element poroelastic model throughout five injection cycles to include the effect of the cumulative injected volumes due to the previous injections on current fracture dilation in the presence of highly permeable unpropped and propped zones adjacent to the cohesive layer that models fracture reopening. Fracture reopening in this poroelastic model is based on a calibrated traction-separation response using the bottomhole pressure collected in two injection campaigns in 2020 and 2022. We used the outcomes of a previous simulation study of the primary hydraulic-fracturing stimulation to define the dimension of an unpropped fracture zone ahead of the propped fracture area. The PTAs led to FCPs consistent with those obtained using the injection data collected at the DFPS in 2020. Further, these analyses showed that at later injections, the fracture closure occurred at a later time with respect to the shut-in time, inferring the effect of cumulative injected volumes in previous injections. The simulation results show that considering the propped and unpropped fracture zones improves our poroelastic model in predicting the injection-well BHP. The numerical simulation results demonstrate a significant excess pore pressure near the fracture because of the preceding formation loadings by the previous injections. The obtained fracture dilation area and fluid pressure distribution provide a basis to improve the development of a multiphysics inverse model. Furthermore, in an iteratively coupled scheme, this pressure distribution can be introduced into EM models to render a holistic view of the causative mechanisms for the surface signal anomalies.

02 PETROLEUM↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2021

Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. 2. Quantifying the Uncertainty

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. We develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)-based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one-dimensional problem and demonstrate it numerically for a three-dimensional aquifer model. Here we design a generalized preconditioned Crank-Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low-rank-based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two-dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media

Recently, the accurate modeling of flow–structure interactions has gained more attention and importance for both petroleum and environmental engineering applications. Of particular interest is the coupling between subsurface flow and reservoir geomechanics. Different single rate and multirate iterative and explicit coupling schemes have been proposed and analyzed in the past. In addition, Banach fixed point contraction results were obtained for iterative coupling schemes, and conditionally stable results were obtained for explicit coupling schemes. In this work, we will consider the mathematical analysis of the single rate and multirate fixed stress split iterative coupling schemes for spatially heterogeneous poroelastic media. We will re–establish the contractivity for both schemes in the localized case, and we will show that heterogeneities come at the expense of imposing more restricted conditions on the number of fine flow time steps that can be taken within one coarse mechanics time step in the multirate case. Our mathematical analysis is supplemented by numerical simulations validating our derived upper bounds. Finally, to the best of our knowledge, this is the first rigorous mathematical analysis of the multirate fixed–stress split iterative coupling scheme in heterogeneous poroelastic media.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach (Kadeethum et al., 2021d) of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn & Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in poroelastic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

In this work, we present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure–displacement system on simplicial and quadrilateral grids. A mixed stress–displacement–rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity–pressure Darcy formulation. The spatial discretization is based on combining the multipoint stress mixed finite element (MSMFE) method for elasticity and the multipoint flux mixed finite element (MFMFE) method for Darcy flow. It uses the lowest order Brezzi–Douglas–Marini mixed finite element spaces for the poroelastic stress and Darcy velocity, piecewise constant displacement and pressure, and continuous piecewise linear or bilinear rotation. A vertex quadrature rule is applied to the velocity, stress, and stress–rotation bilinear forms, which block-diagonalizes the corresponding matrices and allows for local velocity, stress, and rotation elimination. This leads to a cell-centered positive-definite system for pressure and displacement at each time step. We perform error analysis for the semidiscrete and fully discrete formulations, establishing first order convergence for all variables in their natural norms. The numerical tests confirm the theoretical convergence rates and illustrate the locking-free property of the method.

42 ENGINEERING↗
DOE OSTI2022

Evaluation of accuracy and convergence of numerical coupling approaches for poroelasticity benchmark problems

Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. Furthermore, this work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.

58 GEOSCIENCES↗
DOE OSTI2022

Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [C. Rodrigo et al., Comput. Methods App. Mech. Engrg, 341 (2018), pp. 467--484]; we show here why this is a difficult task and, as a result, we modify the discretization in [Rodrigo et al.] through the use of a reduced-quadrature approximation, yielding a more “solver-friendly” discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess--Sarazin relaxation. Further, numerical results are presented to validate the local Fourier analysis predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The Effect of Hydrothermal Alteration and Microcracks on Hydraulic Properties and Poroelastic Deformation: A Case Study of the Blue Mountain Geothermal Field

Abstract Geothermal energy plays a vital role in decarbonizing electricity and heat supply. Effective utilization of geothermal resources hinges on identifying or generating permeable reservoir zones and understanding how effective pressure variations affect fluid circulation and reservoir properties by poroelastic deformation. Hydrothermal alteration can modify the petrophysical properties of geothermal reservoir rocks, which may increase or decrease its productivity. Understanding these alteration effects is essential to predict and optimize long‐term sustainable geothermal operations. Here, we investigate the impact of hydrothermal alteration on poroelastic and hydraulic properties of diverse lithologies in a series of deformation tests performed at several confining (0–80 MPa) and pore pressure (10–30 MPa) levels. Experimental results of hydrothermally altered dikes and phyllites obtained from the Blue Mountain geothermal field (Nevada, USA) are compared to thermally cracked La Peyratte granite (France) and correlated with petrophysical properties, mineral composition, and microstructures. Argillic alteration of dikes increases porosity and storage capacity but lowers thermal conductivity and increases pore compressibility. Conversely, silicate precipitation in phyllites increases stiffness and thermal conductivity but also reduces porosity and permeability. Experimentally determined effective pressure coefficients range from 0.1 to 0.9, differ for permeability and volumetric strain and decrease with increasing effective pressure. The presence of compliant microcracks and crack‐like pores significantly increases the stress sensitivity of La Peyratte granite and silicified phyllites. This study demonstrates how thermal and chemical alteration impacts poromechanical and petrophysical characteristics of geothermal targets, which ultimately govern reservoir stability and subsidence, induced seismicity as well as fluid and heat extraction efficiency during geothermal operations.

Schuster, Valerian [Helmholtz Centre Potsdam GFZ G↗
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↗
NASA NTRS1995

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Salamon, N. J.↗
NASA NTRSDate not supplied

Elastic-Poroelastic Simulation of Locally Resonant Ultrasound for Aging Li-Metal Batteries

An elastic-poroelastic simulation of ultrasound inspection for lithium-metal batteries is presented and compared to empirical reflection spectra measured during battery cycling. Simulated reflection spectra were obtained using a two-dimensional (2D) plane strain model, comprised of dozens of individual microns-thick layers within a Li-metal pouch cell. The simulated reflection spectra were then compared to ultrasonic reflection spectra measurements taken intermittently during cell cycling. A sensitivity analysis and parameter calibration were performed for the pristine pouch cell simulation prior to cycling, providing a baseline to account for difficult to measure poroelastic material parameters. Then, the reduction in solid Li anode thickness and corresponding growth into a mossy lithium layer was modeled to represent aging conditions. Results from both simulations and empirical inspections show similar trends in through-thickness resonance frequencies due to cell aging.

Battery↗
DOE OSTI2024

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Mechanical and poroelastic behavior of porous tuff under drained and undrained conditions

A series of drained and undrained water-saturated constant mean-stress tests were performed to investigate the strength, elasticity, and poroelastic response of a water-saturated high porosity nonwelded tuff. Drained strengths are found to increase with increasing effective confining pressures. Elastic moduli increase with increasing mean stress. Undrained strengths are small due to development of high pore pressures that generate low effective confining pressures. Skempton’s values are pressure dependent and appear to reflect the onset of inelastic deformation. Permeabilities decrease after deformation from ~ 10 –14 to ~ 10 –16 m 2 and are a function of the applied confining pressure. Deformation is dominated by pore collapse, compaction, and intense microfracturing, with the undrained tests favoring microfracture-dominant deformation and the drained tests favoring compaction-dominant deformation. These property determinations and observations are used to develop/parameterize physics-based models for underground explosives testing.

58 GEOSCIENCES↗
DOE OSTI2023

Characterization of Aquifer Poroelastic Response to Impulse and Oscillatory Well Pressure Using Distributed Acoustic Sensing

Abstract The storage of fluids in the subsurface is critical for a broad spectrum of applications including managed aquifer recharge, storage of liquefied carbon dioxide and hydrogen, geothermal heat extraction and exploitation of hydrocarbon. It is surprising then, that there has been relatively little measurement of the vertical distribution of poroelastic storage in geologic formations as compared with permeability. We present experiments in which fluid was injected into an important regional aquifer and the depth‐dependent strain response measured using fiber optic distributed acoustic sensing. The formation expansion and contraction in response to fluid injection were several 100 nanostrain. Strain, and the implied storage distribution, was highly localized in specific strata and demonstrated complex, hydromechanical behavior. This new window into fluid‐geomechanical coupling undermines some typically use models and observations currently in practice, but provides potential for complete representation and prediction of fluid storage in the subsurface.

58 GEOSCIENCES↗
DOE OSTI2021

Rapid custom prototyping of soft poroelastic biosensor for simultaneous epicardial recording and imaging

Abstract The growing need for the implementation of stretchable biosensors in the body has driven rapid prototyping schemes through the direct ink writing of multidimensional functional architectures. Recent approaches employ biocompatible inks that are dispensable through an automated nozzle injection system. However, their application in medical practices remains challenged in reliable recording due to their viscoelastic nature that yields mechanical and electrical hysteresis under periodic large strains. Herein, we report sponge-like poroelastic silicone composites adaptable for high-precision direct writing of custom-designed stretchable biosensors, which are soft and insensitive to strains. Their unique structural properties yield a robust coupling to living tissues, enabling high-fidelity recording of spatiotemporal electrophysiological activity and real-time ultrasound imaging for visual feedback. In vivo evaluations of custom-fit biosensors in a murine acute myocardial infarction model demonstrate a potential clinical utility in the simultaneous intraoperative recording and imaging on the epicardium, which may guide definitive surgical treatments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Physics-informed neural networks for heterogeneous poroelastic media

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural networks predict displacement and pressure variables for each material. While sharing identical activation functions, these networks are independently trained for all other parameters. To address challenges posed by heterogeneous material interfaces, the CoNN is integrated with the Interface-PINNs (I-PINNs) framework (Sarma et al., Comput. Methods Appl. Mech. Eng. 429: 117135, 2024), allowing different activation functions across material interfaces. Further, this ensures accurate approximation of discontinuous solution fields and gradients. Performance and accuracy of this combined architecture were evaluated against the conventional PINNs approach, a single neural network (SNN) architecture, and the eXtended PINNs (XPINNs) framework through two one-dimensional benchmark examples with discontinuous material properties. The results show that the proposed CoNN with I-PINNs architecture achieves an RMSE that is two orders of magnitude better than the conventional PINNs approach and is at least 40 times faster than the SNN framework. Compared to XPINNs, the proposed method achieves an RMSE at least one order of magnitude better and is 40% faster.

42 ENGINEERING↗