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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

Abstract Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Yang, Hyung Jun↗
DOE OSTI2021

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid–fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. Here, we discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

wormhole formation↗
DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗
DOE OSTI2023

Latest developments in the MOOSE fluid properties module

The fluid properties module in MOOSE serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, SAM~\cite{sam}, the MOOSE thermal hydraulics module, RELAP-7~\cite{relap7} and subchannel~\cite{subchannel}. It is used for coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled simulations~\cite{anl_sam_pgh}. The module offers a consistent set of interfaces to implement to create a new fluid property. There are numerous fluid properties of interest in the entirety of all fields of fluid flow simulations, and this is exacerbated by the use of different variable sets depending on the compressibility of the fluid. For single-phase fluids, the following variable sets may be used to compute fluid properties: (pressure, temperature) and (specific volume, specific internal energy). Some properties may also be computed using the (pressure, density) or the (specific volume, specific enthalpy) variable sets. In order to reduce the challenge of adding a new fluid property, properties may be implemented partially.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Lunar soil properties and soil mechanics. Flow in porous media under rarefied gas conditions. Research phase: Fluid conductivity of lunar surface materials

Theoretical and experimental research on fluid conductivity of lunar surface materials is summarized. Theoretical methods were developed for the analysis of transitional and free-molecular flows, and for analysis of lunar permeability probe data in general. Experimental studies of rarefied flows under conditions of a large pressure gradient show flows in the continuum regime to be responsible for the largest portion of the pressure drop between source and sink for one dimensional flow, provided the entrance Knudsen number is sufficiently small. The concept of local similarity leading to a universal nondimensional function of Knudsen number was shown to have approximate validity; flows in all regimes may be described in terms of an area fraction and a single length parameter. Synthetic porous media prepared from glass beads exhibited flow behavior similar in many regards to that of a natural sandstone; studies using artificial stones with known pore configurations may lead to new insight concerning the structure of natural materials. The experimental method involving the use of segmented specimens of large permeability is shown to be fruitful.

Hurlbut, F. C.↗
DOE OSTI2025

Comparison Study of Conventional and Adaptive Mesh Refinement in Organic Material Decomposition Models

This study compares conventional mesh refinement techniques, specifically Uniform Mesh Refinement (UMR), with a new Adaptive Mesh Refinement (AMR) method, applied to Organic Material Decomposition (OMD) models. The proposed benefit of AMR is that only areas that require refinement, based on minimizing a specific field gradient, are refined thus decreasing model wall time compared to conventional UMR methods. This work specifically focuses on comparing UMR and AMR methods on decomposing (both No-Flow and Porous-Flow material models) Polymeric Methylene Diisocyanate (PMDI) polyurethane foam. Throughout the work, the geometry increased in complexity to assess the refinement methods performance at varying levels geometric intricacy. While AMR has been shown to work well in a variety of applications, the UMR approach proved to be computationally faster, for many of the geometries and foam decomposition models, than AMR. However, it was observed that at higher levels of refinement, greater than 3 UMR, AMR begins to be computationally better. Additionally, the settings used to perform AMR greatly impact its performance, and lessons learned, in terms of OMD models, are shared. Due to physics involved in material decomposition, specifically the evolution of state variables, these problems don’t fully benefit from the advantages of AMR.

36 MATERIALS SCIENCE↗
NASA NTRS1978

Magma production and migration within the moon

Partial melting is likely to have occurred throughout much of the moon due to heating during accretion and the volumetric heating of radioactive isotopes. Important problems that have received relatively little attention concern the migration of the resulting magmas to form surface or near surface volcanic rock. In the paper the basic mechanism for the migration of the magma through the lunar asthenosphere is considered. A porous flow model is proposed. The magma behaves like a liquid flowing through a porous matrix. The volume fraction of liquid present determines the saturated porosity. The differential buoyancy of the magma drives it upwards. It is shown that the per cent partial melt in the lunar interior will only slightly exceed that required to provide interconnecting porosity. Assuming that the radioactive isotopes are preferentially segregated into the magma, the time dependence of the partial melting of the lunar interior is found. It is shown that the total degree of partial melting of the deep lunar interior is likely to be between five and ten per cent.

Turcotte, D. L.↗
NASA NTRS2020

Gas-Liquid Flows Through Porous Media in Microgravity: The International Space Station Packed Bed Reactor Experiment

Experimental results on pressure drop and flow patterns for gas-liquid flow through packed beds obtained in the International Space Station with two types of packing are presented and analyzed. It is found that the pressure drop depends on the packing wettability in the viscous-capillary (V-C) regime and this dependence is compared with previously published results developed using short duration low-gravity aircraft tests. Within the V-C regime, the capillary contribution is the dominant force contributing to the pressure drop for the wetting case (glass) versus the viscous contribution dominating for the non-wetting case (Teflon). Outside of the V-C regime, it is also found that hysteresis effects that are often strong in normal gravity gas-liquid flows are greatly diminished in microgravity and pressure drop is nearly independent of packing wettability. A flow pattern transition map from bubble to pulse flow is also compared with the earlier aircraft data.

Viscous-capiliary regime↗
NASA NTRS2022

Gas-Liquid Flows Through Porous Media in Microgravity: Packed Bed Reactor Experiment-2

Modifications were made to the Packed Bed Reactor Experiment (PBRE) and flown on the ISS as PBRE-2 to eliminate external pressure oscillations at higher liquid flow rates and the packing diameter was reduced to increase the pressure gradient for lower flows. It is found that gas hold-up is a function of bed history at low liquid and gas flow rates whereas higher gas hold-up and pressure gradients are observed for the test conditions following a liquid only pre-flow compared to the test conditions following a gas only pre-flow period. Over the range of flow rates tested, the capillary force is the dominant contributor to the pressure gradient, which is found to be linear with the superficial liquid velocity but is a much weaker function of the superficial gas velocity, and varying inversely with the particle diameter.

Mahsa Taghavi↗
NASA NTRS2004

Liquid flow and distribution in unsaturated porous media

Flow and transport in permeable or porous media and microchannels occurs in a variety of situations in micro- and reduced-gravity environments, many of them associated with environmental control and life support systems. While the role of gravity is limited, due to the typically small size scales associated permeable media, gravity, at the very least, affects the overall disposition of fluid in a macroscopic system. This presentation will discuss examples where the absence of gravity affects flow and phase distribution in selected examples of unsaturated flow and transport of heat and mass in porous media and microchannels that are pertinent to spacecraft systems.

Alexander, J. Iwan↗
NASA NTRS2004

Metal-Silicate Segregation in Deforming Dunitic Rocks: Applications to Core Formation in Europa and Ganymede

Core formation is an important event in the evolution of a planetary body, affecting both the geochemical and geophysical properties of the body. Metal-silicate segregation could have proceeded either by settling of liquid metal through a magma ocean or by percolation of liquid metal through a solid silicate mantle. Percolation of metallic melt had previously been excluded as a viable segregation mechanism because metallic melts do not form an interconnected network under hydrostatic conditions, except at high melt fraction (>5 vol%), due to the high dihedral angle between metals and silicates (>60 ). Without an interconnected network, porous flow of metallic melt is impossible, leaving the magma ocean scenario as the only mechanism to form the core. Moment-of-inertia measurements of Europa and Ganymede from the Galileo probe indicate that they are differentiated. This evidence suggests that a method for segregating metals and silicates at temperatures low enough to retain volatile compounds must exist. We have investigated the effect of deformation on the distribution of metallic melts in silicates. We have deformed samples of olivine + 5-9 vol% Fe-S to strains of 2.5 in simple shear and find that the metallic melt segregates into melt-rich planes oriented at 20 to the shear plane. These metallic melt-rich bands are similar in structure to the silicate melt-rich bands reported by Holtzman, indicating that deformation can interconnect isolated metallic melt pockets and allow porous flow of non-wetting melts. Such a core formation process could have occurred in the jovian satellites.

Hustoft, J. W.↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Multi-stage preconditioners for thermal–compositional–reactive flow in porous media

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe conver-gence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Péclet number) to diffusion dominated (low Péclet number). The number of linear iterations is reduced by 40–85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.

42 ENGINEERING↗