316 research outputs found
Mixed finite element projection methods for the unsteady Stokes equations
No full textWe develop H(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is applied, where a predictor problem and a corrector problem are sequentially solved, accounting for the viscous effects and incompressibility, respectively. The predictor problem is based on a stress--velocity mixed formulation, while the corrector projection problem uses a velocity--pressure mixed formulation. The scheme results in pointwise divergence-free velocity computed at the end of each time step. We establish unconditional stability and first order in time accuracy. In the implementation we focus on generally unstructured triangular grids. We employ a second order multipoint flux mixed finite element method based on the next-to-the-lowest order Raviart--Thomas space RT_1 and a suitable quadrature rule. In the predictor problem this approach allows for a local stress elimination, resulting in element-based systems for each velocity component with three degrees of freedom per element. Similarly, in the corrector problem, the velocity is locally eliminated and an element-based system for the pressure is solved. At the end of each time step we obtain a second order accurate H(div)-conforming piecewise linear velocity, which is pointwise divergence free. We present a series of numerical tests to illustrate the performance of the method
Flux-mortar mixed finite element methods with multipoint flux approximation
No full textThe flux-mortar mixed finite element method was recently developed in Boon et al. (2022) for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux approximation as the subdomain discretization. The subdomain problems involve solving positive definite cellcentered pressure systems. The normal flux on the subdomain interfaces is the mortar coupling variable, which plays the role of a Lagrange multiplier to impose weakly continuity of pressure. We present well-posedness and error analysis based on reformulating the method as a mixed finite element method with a quadrature rule. We develop a non-overlapping domain decomposition algorithm for the solution of the resulting algebraic system that reduces it to an interface problem for the flux-mortar, as well as an efficient interface preconditioner. A series of numerical experiments is presented illustrating the performance of the method on general grids, including applications to flow in complex porous media. (c) 2022 Elsevier B.V. All rights reserved
A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction
No full textA new numerical continuum one-domain approach (ODA) solver is presented for the simulation of the transfer processes between a free fluid and a porous medium. The solver is developed in the \textit{mesoscopic} scale framework, where a continuous variation of the physical parameters of the porous medium (e.g., porosity and permeability) is assumed. The Navier--Stokes--Brinkman equations are solved along with the continuity equation, under the hypothesis of incompressible fluid. The porous medium is assumed to be fully saturated and can potentially be anisotropic. The domain is discretized with unstructured meshes allowing local refinements. A fractional time step procedure is applied, where one predictor and two corrector steps are solved within each time iteration. The predictor step is solved in the framework of a marching in space and time procedure, with some important numerical advantages. The two corrector steps require the solution of large linear systems, whose matrices are sparse, symmetric and positive definite, with -matrix property over Delaunay-meshes. A fast and efficient solution is obtained using a preconditioned conjugate gradient method. The discretization adopted for the two corrector steps can be regarded as a Two-Point-Flux-Approximation (TPFA) scheme, which, unlike the standard TPFA schemes, does not require the grid mesh to be K-orthogonal, (with {K the anisotropy tensor). As demonstrated with the provided test cases, the proposed scheme correctly retains the anisotropy effects within the porous medium. Furthermore, it overcomes the restrictions of existing mesoscopic scale one-domain approaches proposed in the literature
Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods
No full textIn this work, we consider 2 kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery, i.e., in an artery that is located far away from the heart. For our simulations, we place the stenosis in one of the tibial arteries belonging to the right lower leg (right posterior tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore, it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model
A novel One Domain Approach for free fluid-porous medium transport simulation. Preliminary results
No full textWe present a new numerical solver for free-fluid flowing over and inside a porous medium. It is based over a macroscopic approach and one fictitious medium is assumed inside the domain, according to the One Domain Approach. Preliminary results are shown and compared with the ones provided by the well-known DuMux solver which applies a two Domain Approach
Fronts in two-phase porous media flow problems:The effects of hysteresis and dynamic capillarity
No full textIn this work, we study the behavior of saturation fronts for two-phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses traveling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include nonmonotone profiles, multiple shocks, and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we discuss the implication of our findings in the context of available experimental results.Deutsche Forschungsgemeinschaft, Grant/AwardNumber: 327154368; Technische-Universitat Dortmund; Universiteit Hasselt, Grant/AwardNumber: BOF17BL04; Fonds Wetenschappelijk Onderzoek, Grant/Award Numbers: G051418N, G0G1316N; Darcy Center, Eindhoven University ofTechnology and Utrecht University; Cluster of Excellence in Simulation Technology, Grant/AwardNumber: (EXC310/2); Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Grant/Award Number: 14CSER016Mitra, K (reprint author), Tech Univ Dortmund, Fac Math, Vogelpothsweg 87, D-44227 Dortmund, Germany.
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Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models
No full textThe development of reliable mathematical models and numerical discretization methods is important for the understanding of salt precipitation in porous media, which is relevant for environmental problems like soil salinization. Models on the pore scale are necessary to represent local heterogeneities in precipitation and to include the influence of solution-air-solid interfaces. A pore-network model for saturated flow, which includes the precipitation reaction of salt, is presented. It is implemented in the open-source simulator DuMuX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. In this paper, we restrict ourselves to one-phase flow as a first step. Since the throat transmissibilities determine the flow behaviour in the pore network, different concepts for the decreasing throat transmissibility due to precipitation are investigated. We consider four concepts for the amount of precipitation in the throats. Three concepts use information from the adjacent pore bodies, and one employs a pore-throat model obtained by averaging the resolved pore-scale model in a thin-tube. They lead to different permeability developments, which are caused by the different distribution of the precipitate between the pore bodies and throats. We additionally apply two different concepts for the calculation of the transmissibility. One obtains the precipitate distribution from analytical assumptions, the other from a geometric minimization principle using a phase-field evolution equation. The two concepts do not show substantial differences for the permeability development as long as simple pore-throat geometries are used. Finally, advantages and disadvantages of the concepts are discussed in the context of the considered physical problem and a reasonable effort for the implementation and computational costs. Presentation of a pore-network model for single-phase flow with salt precipitation including pore-space alterationsDifferent concepts to calculate the amount of precipitation in throats and the throat transmissibility are presentedBetween the concepts large differences in the permeability and precipitation distribution are observed in the networkFunding
Open Access funding enabled and organized by Projekt DEAL. This work was fnancially supported by the German Research Foundation (DFG), within the Collaborative Research Center on InterfaceDriven Multi-Field Processes in Porous Media (SFB 1313, Project Number 327154368).
Acknowledgements
This work was fnancially supported by the German Research Foundation (DFG), within the Collaborative Research Center on Interface-Driven Multi-Field Processes in Porous Media (SFB 1313, Project Number 327154368). This study was supported by the Special Research Fund (BOF) of Hasselt University, Project BOF22KV03
Estimation of Capillary‐Associated NAPL‐Water Interfacial Areas for Unconsolidated Porous Media by Kinetic Interface Sensitive (KIS) Tracer Method
No full textAbstract
By employing kinetic interface sensitive (KIS) tracers, we investigate three different types of glass‐bead materials and three natural porous media systems to quantitatively characterize the influence of the porous‐medium grain‐, pore‐size and texture on the specific capillary‐associated interfacial area (FIFA) between an organic liquid and water. By interpreting the breakthrough curves (BTCs) of the reaction product of the KIS tracer hydrolysis, we obtain a relation for the specific IFA and wetting phase saturation. The immiscible displacement process coupled with the reactive tracer transport across the fluid–fluid interface is simulated with a Darcy‐scale numerical model. Linear relations between the specific capillary‐associated FIFA and the inverse mean grain diameter can be established for measurements with glass beads and natural soils. We find that the grain size has minimal effect on the capillary‐associated FIFA for unconsolidated porous media formed by glass beads. Conversely, for unconsolidated porous media formed by natural soils, the capillary‐associated FIFA linearly increases with the inverse mean grain diameter, and it is much larger than that from glass beads. This indicates that the surface roughness and the irregular shape of the grains can cause the capillary‐associated FIFA to increase. The results are also compared with the data collected from literature, measured with high resolution microtomography and partitioning tracer methods. Our study considerably expands the applicability range of the KIS tracers and enhances the confidence in the robustness of the method.Key Points
The capillary‐associated interfacial area is measured with the kinetic interface sensitive tracer method in six unconsolidated porous media
It is found the maximum specific capillary‐associated interfacial area is linearly correlated to the inverse mean grain diameters
The higher capillary‐associated interfacial area is found in natural porous media due to surface roughness and irregular grain shapesAbstract
By employing kinetic interface sensitive (KIS) tracers, we investigate three different types of glass‐bead materials and three natural porous media systems to quantitatively characterize the influence of the porous‐medium grain‐, pore‐size and texture on the specific capillary‐associated interfacial area (FIFA) between an organic liquid and water. By interpreting the breakthrough curves (BTCs) of the reaction product of the KIS tracer hydrolysis, we obtain a relation for the specific IFA and wetting phase saturation. The immiscible displacement process coupled with the reactive tracer transport across the fluid–fluid interface is simulated with a Darcy‐scale numerical model. Linear relations between the specific capillary‐associated FIFA and the inverse mean grain diameter can be established for measurements with glass beads and natural soils. We find that the grain size has minimal effect on the capillary‐associated FIFA for unconsolidated porous media formed by glass beads. Conversely, for unconsolidated porous media formed by natural soils, the capillary‐associated FIFA linearly increases with the inverse mean grain diameter, and it is much larger than that from glass beads. This indicates that the surface roughness and the irregular shape of the grains can cause the capillary‐associated FIFA to increase. The results are also compared with the data collected from literature, measured with high resolution microtomography and partitioning tracer methods. Our study considerably expands the applicability range of the KIS tracers and enhances the confidence in the robustness of the method.Key Points
The capillary‐associated interfacial area is measured with the kinetic interface sensitive tracer method in six unconsolidated porous media
It is found the maximum specific capillary‐associated interfacial area is linearly correlated to the inverse mean grain diameters
The higher capillary‐associated interfacial area is found in natural porous media due to surface roughness and irregular grain shapesDeutsche Forschungsgemeinschaft https://doi.org/10.13039/50110000165
Hydraulic fracturing in unconventional gas reservoirs: risks in the geological system part 1
No full textHydraulic fracturing of unconventional gas reservoirs rapidly developed especially in the USA to an industrial scale during the last decade. Potential adverse effects such as the deterioration of the quality of exploitable groundwater resources, areal footprints, or even the climate impact were not assessed. Because hydraulic fracturing has already been practised for a long time also in conventional reservoirs, the expansion into the unconventional domain was considered to be just a minor but not a technological step, with potential environmental risks. Thus, safety and environmental protection regulations were not critically developed or refined. Consequently, virtually no baseline conditions were documented before on-site applications as proof of evidence for the net effect of environmental impacts. Not only growing concerns in the general public, but also in the administrations in Germany promoted the commissioning of several expert opinions, evaluating safety, potential risks, and footprints of the technology in focus. The first two publications of the workgroup "Risks in the Geological System" of the independent "Information and Dialogue process on hydraulic fracturing" (commissioned by ExxonMobil Production Deutschland GmbH) comprises the strategy and approaches to identify and assess the potential risks of groundwater contamination of the exploitable groundwater system in the context of hydraulic fracturing operations in the Munsterland cretaceous basin and the Lower Saxony Basin, Germany. While being specific with respect to local geology and the estimation of effective hydraulic parameters, generalized concepts for the contamination risk assessment were developed. The work focuses on barrier effectiveness of different units of the overburden with respect to the migration of fracking fluids and methane, and considers fault zones as potential fluid pathway structures
Hydraulic fracturing in unconventional gas reservoirs : risks in the geological system, part 2
No full textHydraulic fracturing is a method used for the production of unconventional gas resources. Huge amounts of so-called fracturing fluid (10,000-20,000 m(3)) are injected into a gas reservoir to create fractures in solid rock formations, upon which mobilised methane fills the pore space and the fracturing fluid is withdrawn. Hydraulic fracturing may pose a threat to groundwater resources if fracturing fluid or brine can migrate through fault zones into shallow aquifers. Diffuse methane emissions from the gas reservoir may not only contaminate shallow groundwater aquifers, but also escape into the atmosphere where methane acts as a greenhouse gas. The working group "Risks in the Geological System" as part of ExxonMobil's hydrofracking dialogue and information dissemination processes was tasked with the assessment of possible hazards posed by migrating fluids as a result of hydraulic fracturing activities. In this work, several flow paths for fracturing fluid, brine and methane are identified and scenarios are set up to qualitatively estimate under what circumstances these fluids would leak into shallower layers. The parametrisation for potential hydraulic fracturing sites in North Rhine-Westphalia and Lower Saxony (both in Germany) is derived from literature using upper and lower bounds of hydraulic parameters. The results show that a significant fluid migration is only possible if a combination of several conservative assumptions is met by a scenario
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