An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
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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.
Dilatancy-controlled gas flow in preferential pathways plays a key role in the safety analysis of radioactive waste repositories. This is particularly the case for bentonite, an often-preferred barrier material. Gas flow in preferential pathways is characterized by localization and spontaneous behavior, which is challenging to simulate in numerical models due to strong hydro-mechanical coupling. To analyze a laboratory experiment in the framework of the DECOVALEX-2023 project, this study introduced a new approach of combining continuous modelling methods with spatial material properties derived from material heterogeneities and experimental observations. The proposed model utilized hydro-mechanical spatial distributions, namely Young's modulus and gas entry pressure, and elastoplasticity combined with a linear swelling model. A conceptual strain-dependent permeability approach simulated dilatancy-controlled gas flow based on hydro-mechanical coupling. To test the effectiveness of the presented approach, a gas injection test in a compacted, saturated bentonite sample was simulated using the open-source code OpenGeoSys 5.8 and compared with experimental observations. The presented methodology is capable of simulating localized gas flow in preferential pathways. The spatial distributions of Young's modulus and gas entry pressure affect the swelling pressure, relative permeability and, in combination with the strain-dependent permeability model, also the intrinsic permeability.
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This study utilizes synchrotron X-ray micro-tomography and pore scale modeling to investigate the process of gas exsolution and how it affects non-wetting phase relative permeability. Exsolved gas distributions are measured on Domengine and Boise sandstone samples using synchrotron X-ray micro-tomography. Observed gas phase distributions are compared to a new model that simulates the growth and distribution of exsolved gas phase at the pore-scale. Water relative permeability curves are calculated using a Stokes flow simulator with modeled and observed gas distributions, under various conditions, such as rock geometry, and pressure depletion rates. By comparing the actual bubble distributions with modeled distributions, we conclude that exsolved gas is more likely to form and accumulate at locations with higher water velocities. This suggests that convective delivery of CO2 to the gas bubble is a primary mechanism for bubble growth, as compared to diffusive transport through the aqueous phase. For carbonated brine flowing up a fault at half a meter per day, with 5% exsolved gas, the water relative permeability is estimated to be 0.6~0.8 for various sandstones. The reduction of water mobility reduces upward brine migration when even a small amount of exsolution occurs.
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An intermediate-scale beadpack drainage experiment was conducted to investigate how simple layered lamination heterogeneity affects CO 2 flow. Two simple layers of capillary barriers are manually packed in the tank and slow drainage was carried out using analog fluids to mimic the capillary- and gravity-dominated CO 2 upward migration process in deep saline aquifers. Nonwetting phase saturation time series clustering analysis and frequency analysis have been conducted on the experimental data. Additionally, modified invasion percolation numerical simulations were done on a digital model of the beadpack to compare to experimental results. Results show that capillary barriers can lead to strong pulsation behavior, which in turn can cause unexpected early breaching through other barriers. The inlet pressure is found to be able to respond to saturation changes in far regions of the domain, indicating that the wetting phase can transmit pressure changes from the other phase. Although static simulations were not able to capture all the dynamic behavior observed in the experiment, Monte Carlo composite simulation results combining many different realizations can better illustrate how the nonwetting phase will behave in the heterogeneous domain. Furthermore, our results suggest the need for CO 2 storage site selection with preference given to aquifers with more capillary barriers with finer grain sizes to avoid flow pulsation and to retard plume upward migration.
Detecting radionuclide gas seepage from clandestine underground nuclear tests is central to nonproliferation explosion monitoring research. Yet, early-time (<6 day) gas transport driven by the explosive pressure wave remains poorly constrained due to scarcity of field data. We simulate multi-phase gas transport in the vadose zone using pre-shot data from a recent chemical explosion in P-Tunnel at the Nevada National Security Site, USA. Despite using a simplified 2D-radial model, predictions of tracer arrival matched observations within one order-of-magnitude. Our results show how transient blast forcing rapidly mobilizes gases from the cavity into surrounding rock – critical for optimizing sensor placement and test planning. This unique integration of field data and modeling represents a significant improvement in our ability to predict gas migration from underground explosions. More broadly, it offers insights into the coupled dynamics of pressure waves and contaminant transport in the vadose zone, with implications for monitoring and hazard assessment.
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An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term “dispersed phase” represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.
This study proposes a method for approximating the fully resolved flow through a monodisperse array of spherical particles using only the locations of the particles and the volume-averaged Reynolds number, both of which are available in Euler-Lagrange (EL) simulations. To achieve this, we first determine a superposable wake (SW) which best captures the behavior of direct numerical simulations (DNS). By adding the SW for all the particles, the pseudo-turbulence caused by the perturbed flow around a distribution of particles in an EL simulation can be approximated. Finally, a Reynolds stress model is then developed for use in an Euler-Lagrange framework. The range of Reynolds numbers and particle volume fractions considered in this study are 0.3 ≤ Re ≤ 173 and 0.11 ≤ Φ ≤ 0.45 accordingly.
Presented by NETL at AJK Fluids 07/19
Presented by NETL at AJK Fluids 07/19