Theory Of Porous Media Research Articles

A mixed least‐squares finite element method for a geometrically nonlinear TPM formulation

AbstractIn the present work, a mixed least‐squares finite element method (LSFEM) is used, which is applied on the partial differential equations arising from the Theory of Porous Media (TPM), see for example [1, 2, 3]. Since the LSFEM is not limited to the LBB condition, the method has some theoretical advantages over the well‐known (mixed) Galerkin method, see [4]. In particular, the LSFEM leads to positive definite and symmetric system matrices, even for differential equations with non‐self‐adjoint operators. In detail, we study an incompressible binary model with solid and liquid phases. The modeling of saturated porous structures serves as the basis for the presented approach. The resulting finite element is a four‐field formulation in terms of solid displacements, fluid pressure, mixture stresses, and a new variable associated with the pressure gradient. Vector‐valued Raviart‐Thomas and conventional Lagrangian functions are used to achieve a conforming discretization of the unknowns in the spaces H(div) and H1. The applicability of the LSFEM approach is demonstrated with numerical examples for fluid‐saturated porous structures, which consider incompressible, geometrically nonlinear elastic material behavior.

Thermodynamically consistent variational theory of porous media with a breaking component

Thermodynamically consistent variational theory of porous media with a breaking component

Multiphasic model of early stage hydration in concrete using the theory of porous media

AbstractThe aim of this paper is to model the behavior of concrete during the initial stage of maturing. Most models consider only thermo‐mechanical phenomena assuming the hygral phenomena of less importance due to high liquid saturation. In order to grasp those effects, the proposed model is an extension of Gawin's model (D. Gawin, F. Pesavento, and B. A. Schrefler, Int J Numer Methods Eng 67(3), 299–331, 2006). The fresh concrete, modeled as porous material, is described within the well‐founded framework of the Theory of Porous Media. The multiphase material consists of a solid phase representing, for example, cement, gravel, etc., and a fluid and gas phase representing the pores filled with water and dry air. Compared to Gawin's model, here, beside the effect of hydration‐dehydration, the effect of evaporation‐condensation will be taken into account. A new formulation for the evaporation process in the fresh concrete is proposed and validated by an experimental study. The presented model is implemented in the research code PANDAS. The proposed model investigates and proves the assumption of Gawin's model to have a linear connection between porosity and hydration degree.

Study on diffusion mechanism of viscosity time-varying slurry in unsaturated soil based on displacement effect

Taking Bingham slurry as the research object, an infiltration diffusion model of Bingham slurry in unsaturated soil is established based on the seepage theory of unsaturated porous media, which takes into account the displacement effect and the viscosity time-varying characteristics of slurry. Combined with the seepage motion equation, relevant boundary conditions and interface conditions, the Bingham slurry diffusion equation considers grouting parameters and mechanical parameters is obtained. The research results are degraded to the saturated state and compared with the existing theoretical results. Numerical examples are used to study the influence of the above parameters on grouting pressure and slurry diffusion radius, then the diffusion mechanism of Bingham slurry is verified and analysed by model test. The above analysis and test results confirm the effectiveness and applicability of the research results, which can provide reliable theoretical support and technical reference for the design and construction of grouting engineering in unsaturated soil areas.

Affine transformations accelerate the training of physics-informed neural networks of a one-dimensional consolidation problem

Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks (AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the {mathscr {L}}_2 relative error by 64.84% after 25,000 epochs for a one-dimensional consolidation problem based on Biot’s theory, and an average improvement by 58.80% with a transfer approach to the theory of porous media.

A coupled finite element formulation for the modeling of freezing processes within the Theory of Porous Media using a discontinuous approximation for the volume fraction ice

AbstractThis work presents a multi‐phase approach to model freezing processes within a coupled finite element formulation using the Theory of Porous Media (TPM), see also [1]. The focus of the study is to enhance the numerical stability for the volume fraction ice as is it highly sensitive to phase discontinuities. To address this issue, a discontinuous approximation is employed for the volume fraction ice while the remaining degrees of freedom are still continuously approximated. As a result, the corresponding degrees of freedom are independently solved for each element, as the element nodes are not interconnected with other elements. Academic examples are provided within a standard Galerkin procedure to highlight the optimization effect, comparing the results obtained with a continuous and discontinuous approximation for the volume fraction ice. Additionally, the implementation of the discontinuous approximation allows for the application of static condensation, resulting in reduced computation time.

Numerical simulation on diffusion–reaction behavior of concrete under sulfate–chloride coupled attack

The transport of sulfate–chloride salts in concrete is the main cause of its structural deterioration. Traditional numerical simulation assumes that the diffusion coefficients of sulfate ions and chloride ions are both constant leading to large deviations in the predicted results. Based on the mass conservation law, Fick’s second law, and the theory of porous media, a variable coefficient transport model of sulfate–chloride salts in concrete is established in this paper. The model fully reflects the adsorption and desorption of chloride ions in the transport process, the reaction-filling process of sulfate ions and hydration products, as well as the most important porosity and tortuosity affecting ion transport. Results show that the prediction results of the two-dimensional variable coefficient model are consistent with experimental and literature results, with maximum error of 23.49%. The analysis of influencing factors shows that the interaction between sulfate ions and chloride ions does not change the transport law of ions in concrete, but delays the rate of ion corrosion within about 700 days. The ability of chloride ions to be adsorbed decreases by about 20% when sulfate ions are present, and the desorption rate is about 40% to 60%. The tortuosity decreases with the increase of water-binder ratio, and increasing the initial porosity from 5% to 12% leads to an early appearance of cracks by about 1400 days.

A historical review on porous‐media research

AbstractAt the end of the 18th century, serious problems in dyke constructions in Northern Germany and the need to understand coupled solid‐water problems initiated first attempts to describe porous media. Many attempts followed until a sound Theory of Porous Media (TPM) was born on the basis of continuum mechanics of multi‐component materials with multi‐physical properties. The present article roughly describes the development of the TPM from its origins to contemporary applications, thus presenting a short historical review of porous‐media research.

Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress. Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

Hydrodynamic analysis of the combined structure of offshore monopile wind turbine foundation and aquaculture cage

Reliable prediction in hydrodynamics is crucial for the design of marine structures, especially for columnar structures such as offshore wind turbine foundations. A combined structure of fixed monopile wind turbine foundation and bottom-seated circular aquaculture cage is proposed for efficiently utilizing the offshore space and reducing the wave forces on the monopile wind turbine foundation. A further developed volume-averaged numerical model is adopted to simulate the pressure drop due to clean and fouled cages by introducing the porous media theory, in which the coefficients of source terms are determined by the least square method based on hydrodynamic force on cage from existing experimental data. The Stokes fifth-order wave theory is considered reliable in simulating the nonlinear waves on slopes and corresponding inline wave force by comparing with multiple existing experimental data. Then the effects of incident wave steepness, seabed bottom slopes and cage diameters on simulation results are analyzed. Results reveal the fouled cage can effectively reduce inline wave forces relative to the clean cage of the combined structure, accompanying a significant resonance effect of wave motion inside the cage.

Finite discrete element modeling of desiccation fracturing in partially saturated porous medium

In this study, a numerical framework is presented for the analysis of desiccation fracturing in variably saturated porous media. The solid phase deformation and fracturing are obtained based on the 2D finite-discrete element method (FDEM), while the fluid flow is characterized by nonlinear Richards’ equation and solved by finite volume discretization. The coupling between phases is realized by Biot’s porous media theory. The capabilities of the model in capturing the unsaturated porous medium flow and coupled hydro-mechanical effects are put to the test against benchmark solutions available in the literature. Furthermore, mechanisms of desiccation cracking in the soil are thoroughly investigated through various numerical test cases. In line with experimental observations, results indicate that the type of mechanical constraints and saturation gradients are two main factors contributing to the generation of cracks in desiccation processes.

Numerical simulation of miscible multiphase flow and fluid–fluid interaction in deformable porous media

AbstractThe focus of the underlying research work is on the macroscopic modeling of unstable multiphase fluid flow in deformable porous media, where a lower‐viscous fluid is displaced by a more viscous fluid. This process leads to the formation of channel‐like networks, called viscous fingering. The instability effect is involved in a wide range of different fields in engineering. Some of the most common applications include carbon sequestration to store carbon dioxide (CO2) in underground reservoirs, contaminant transport in geostructures, in industrial processes, such as filtration, catalytic reactions, and in the operation of polymer electrolyte membrane fuel cells with multiphase flow in the gas diffusion layers. In this work, ideal miscible water–glycerin fluids are considered. It is assumed that the interacting fluids in the deformable porous media are incompressible. In addition, a dispersion–diffusion law is applied to capture the fluid–fluid interactions. The presence of a deformable porous material adds additional effects to the problem of the multiphase flow in porous media. The stresses in the porous solid matrix lead to changes in the porosity and influence the flow velocity of the fluids. To couple the deformable porous media with the multiphase flow, a macroscopic approach is used that relies on the theory of porous media. For the porous solid matrix, a linear elastic material model within small strains assumption is applied. The influence of the deformation‐dependent porosity on the instability is studied for 2D simulations, such as a multilayered geometry with different elastic parameters. The presented coupled nonlinear system of differential equations is simulated with the finite element method. Furthermore, a stabilization technique based on the quasi‐compressibility method is used.

Mass transport in an excavation using a ternary Theory of Porous Media model

AbstractThis paper tries to simulate a hydraulic failure by using a ternary, saturated, quasi‐static Theory of Porous Media (TPM) model. The concept of a hydraulic failure is shortly explained and the derivation of the TPM setup including the limitation of the volume fractions is depicted. A schematic excavation with a sheet piling is used to test the created model and prove the general feasibility of the idea.

Surface Motion for P-Wave Scattering by an Arbitrary-Shaped Canyon in Saturated Half-Space

This paper obtained a semianalytical solution for the P-wave scattering problem by an arbitrary-shaped canyon in a saturated half-space by using Biot’s theory, the wave function expansion method, and the moments method. Firstly, based on the Biot fluid-saturated porous media theory and the wave function expansion method, the wave potentials which automatically satisfy the zero-stress boundary condition on the surface of the half-space are obtained. Then, the boundary value problem is transformed into an algebraic problem by the method of moments according to the boundary conditions, and then solved numerically by truncation. By adjusting the parameters, the saturated medium in the original model approximately degenerates into a single-phase elastic medium, and the correctness of the proposed method is verified by comparing it with published results. Finally, the effects of the canyon shape, the porosity of the soil, and the incidence angle and frequency of the incident wave on the amplitude of ground surface motion are investigated. The results show that the incidence angle has a significant effect on the ground surface motion, while the porosity of the soil has little influence on the amplitude of surface motion. The influence of canyon shape on surface motion is mainly reflected in the shielding effect on the incident wave. Although P-wave scattering by a canyon is a traditional problem, most of the analytical solutions are limited to solving the scattering of seismic waves in geometric regular canyons. However, the actual shape of the canyon is not regular, which limits the application of closed analytical solutions in practical engineering. In this paper, the scattering of P-waves in arbitrary-shaped canyons is successfully solved by using a semianalytical method combined with a numerical method-moments method, which provides a possibility for engineering application.

Modelling growth and formation of thrombi: a multiphasic approach based on the theory of porous media

AbstractAortic dissection (AD) has a high mortality rate. About 40% of the people with type B AD do not live for more than a month. The prognosis of AD is quite challenging. Hence, we present a triphasic model for the formation and growth of thrombi using the theory of porous media (TPM). The whole aggregate is divided into solid, liquid and nutrient constituents. The constituents are assumed to be materially incompressible and isothermal, and the whole aggregate is assumed to be fully saturated. Darcy’s law describes the flow of fluid in the porous media. The regions with thrombi formation are determined using the solid volume fraction. The velocity- and nutrient concentration-induced mass exchange is defined between the nutrient and solid phases. We introduce the set of equations and a numerical example for thrombosis in type B AD. Here we study the effects of different material parameters and boundary conditions. We choose the values that give meaningful results and present the model’s features in agreement with the Virchow triad. The simulations show that the thrombus grows in the low-velocity regions of the blood. We use a realistic 2-d geometry of the false lumen and present the model’s usefulness in actual cases. The proposed model provides a reasonable approach for the numerical simulation of thrombosis.

Establishing a transient model of double-layer porous media interfacial evaporation system to reveal the relationship between porous media parameters and evaporation performance

The solar interfacial evaporation system can generate steam efficiently by localizing solar thermal energy to heat air–water interface, which has great application potential in seawater desalination, sewage treatment, and other fields. At present, the solar absorption layer and substrate of the interfacial evaporation system are mainly made of carbon materials, sponges, foams, and other porous media materials. However, the transient interfacial evaporation heat and mass transfer model and the influence of the physical parameters of porous media on evaporation performance have rarely been investigated. Based on heat and mass transfer theory of porous media, a transient theoretical model of porous media interfacial evaporation system is established in this paper. Moreover, the effects of physical parameters such as the porosity and thermal conductivity of porous media on evaporation performance are analyzed, and the accuracy of the model is verified through outdoor experiments. Based on the model calculation, as the porosity of the substrate increases, the evaporation rate and efficiency of the evaporator first increase and then decrease. The lower the thermal conductivity of the substrate and the higher the porosity and thermal conductivity of the solar absorption layer are, the better the evaporation performance is, but the growth rate gradually decreases. Therefore, the relationship between the improvement of evaporation performance and the increased cost caused by the improvement of material properties needs to be considered. The model and related theoretical analysis results can provide a theoretical basis for system structure optimization, material selection and other aspects of future research on double-layer porous media interfacial evaporation system.

Diffraction of plane P waves by a circular-arc canyon in an unsaturated poroelastic half-space

Based on the theory of unsaturated porous elastic medium, the diffraction around the circular-arc canyon in unsaturated half-space under the incidence of plane P wave is studied by using the Fourier-Bessel series expansion method of wave function. Through numerical examples, the influence of parameters such as incident wave frequency, incident angle, arc depth-width ratio and saturation on the surface displacement amplitude in unsaturated half-space circular-arc canyon is analyzed. The results show that the saturation has a significant effect on the variation of surface displacement amplitude, and the influence law of saturated and unsaturated site soils on the variation of surface displacement amplitude is very different under different depth-to-width ratio and incident frequency. In the case of different depth-width ratios of unsaturated half-space circular-arc canyon, the displacement amplitude change of semi-circular canyon (h/a = 1) is more sensitive to the change of saturation than that of shallow circular canyon (h/a = 0.5). When the incident frequency is low, the maximum displacement amplitude of the half-space circular-arc-canyon in both saturated and unsaturated cases increases with the increase of the incident angle. It is worth noting that when the saturation Sr = 0.99, i.e., when the soil is close to saturation, the maximum surface displacement amplitude caused by unsaturated depressed terrain (Sr = 0.8) is greater than that caused by the saturated soil case as the incidence angle increases.

Understanding unsaturated sulfate saline soil in cold regions: A comprehensive hydraulic–thermal–air–salt–mechanical model with experimental research

The destruction of infrastructure built on saline soil in cold regions is closely related to water and salt migration, and soil deformation in foundations. Consequently, it is imperative to understand the mechanisms of heat and mass transfer, along with deformation in saline soil. Based on the unsaturated soil mechanics and porous media theory, a hydraulic–thermal–air–salt–mechanical (HTASM) coupled mathematical model for frozen unsaturated sulfate saline soil is proposed. The model incorporates the impact of ice-water phase change, sodium sulfate crystallization, and vapor flow on heat and mass transfer during the freezing process. Two parameters—salt crystallization pressure, and ice pressure—are introduced into the mechanical control equation to capture the effects of phase change on deformation. In addition, the relationship between the density of soil particles, water, ice and gas, and temperature and pressure is considered to reflect the dynamic change of density during freezing. Finally, the numerical simulation using the HTASM model is conducted and its efficacy is validated by comparing the numerical results with those obtained from indoor unidirectional freezing tests. The coupling effect of the HTASM model is revealed by analyzing the dynamic changes of temperature, water content, salt content, vapor flux and crystallization pressure in the soil column during freezing. The results show that the proposed HTASM model can well simulate the heat and mass transfer behavior in freezing unsaturated sulfate saline soil.

A non-isothermal phase-field hydraulic fracture modeling in saturated porous media with convection-dominated heat transport

This research aims to extend the isothermal continuum mechanical modeling framework of hydraulic fracturing in porous materials to account for the non-isothermal processes. Whereas the theory of porous media is used for the macroscopic material description, the phase-field method is utilized for modeling the crack initiation and propagation. We proceed in this study from a two-phase porous material consisting of thermomechanically interacting pore fluid and solid matrix. The heat exchange between the fluid in the crack and the surrounding porous environment through the diffusive fracture edges is carefully studied, and new formulations here are proposed. Besides, temperature-dependent solid and fluid material parameters are taken into account, which is of particular importance in connection with fluid viscosity and its effect on post-cracking pressure behavior. This continuum mechanical treatment results in strongly coupled partial differential equations of the mass, the momentum, and the energy balance of the thermally non-equilibrated constituents. Using the finite element method, two-dimensional initial-boundary-value problems are presented to show, on the one hand, the stability and robustness of the applied numerical algorithm in solving the emerged strongly coupled problem in the convection-dominated heat transport state. On the other hand, they show the capability of the modeling scheme in predicting important instances related to hydraulic fracturing and the role of the temperature field in this process. Additionally, they show the importance of using stabilization techniques, such as adding an artificial thermo-diffusivity term, to mitigate temperature fluctuations at high flow velocity.

Modelling the Influence of Erosive Fluidization on the Morphology of Fluid Flow and Escape Structures

Focused fluid flow through sub-seafloor pipes and chimneys, and their seafloor manifestations as pockmarks, are ubiquitous. However, the dynamics of flow localization and evolution of fluid escape structures remain poorly understood. Models based on geomechanical mechanisms like hydro-fracturing and porosity wave propagation offer some useful insights into fluid flow and escape dynamics, but face limitations in capturing features like mobilized granular matter, especially in the upper sediment layers where the link between fracture and pockmark is not always clear. Here, we propose a mathematical model based on the multiphase theory of porous media, where changes in subsurface and seafloor morphology are resolved through seepage-induced erosion, fluidization, transport, and re-deposition of granular material. Through simulation of an idealized scenario of gas escape from overpressured shallow gas reservoir, we demonstrate that our model can capture flow localization and formation of pipes, chimneys, and pockmarks. Our simulations show (1) formation of conical focused-flow conduits with a brecciated core and annular gas channels; (2) pockmarks of W and ring shapes; and (3) pulsed release of gas. Sediment erodibility and flow anisotropy control the morphology of focused fluid flow and escape structures, while permeability shows negligible impact. While the geological setting for this study is theoretical, we show that our results have real-world analogs.