Darcy Fluid Research Articles

Seepage effect on progressive failure of shield tunnel face in granular soils by coupled continuum-discrete method

Seepage induced by the difference of hydraulic head between the ground and the shield’s chamber will adversely affect the stability of tunnel face when tunnels are excavated through water-rich stratum. In order to investigate the influence of seepage on the stability of tunnel face, a 3D continuum-discrete method is proposed to simulate the failure of tunnel face. The large deformation behavior of soil is determined by the discrete element method and the fluid flow in soil phase is described by the Darcy fluid model and continuity equation. A series of simulations are carried out to obtain the failure mechanism and critical support pressure of tunnel face. Then the results under dry, undrained and seepage conditions are analyzed and the seepage effect on the stability of tunnel face with different water depth is investigated. Besides, a comparison between the simulation results and solutions in previous researches is conducted. Additionally, the micro-mechanical analysis under dry and seepage conditions are presented. The results show that the coupled method can well evaluate the stability of tunnel face considering seepage effect and provider useful guidance for practical tunnel designs.

Determination of Three-Dimensional Brinkman—Forchheimer-Extended Darcy Flow

The aim of this study is to determine a 3D incompressible Brinkman–Forchheimer-extended Darcy fluid flow. Based on global well-posedness and regularity of solutions with a periodic boundary condition, the determining modes for weak and regular solutions is achieved via the generalized Grashof number for a 3D non-autonomous Brinkman–Forchheimer-Darcy fluid flow in porous medium. Furthermore, the asymptotic determination of the complete trajectories inside an attractor via Fourier functionals is shown for a 3D autonomous Brinkman–Forchheimer-extended Darcy model.

Study of non-linear flow in coarse granular material through converging boundaries

Over the past century, there has been a continuously growing research interest in fluid seepage through coarse porous material. Experimental data on nonlinear flow behaviour in several coarse granular materials are provided in the current work. The aim of the present work is to investigate, theoretically and experimentally, the seepage patterns arising from non– Darcy fluid flows through coarse granular materials, with a particular reference to the effect of convergence. Along with the above, the effect of variation in size and shape of the media on the seepage patterns is also analyzed. Experiments have been conducted on flow through porous material with converging permeameter and equations relating the different parameters affecting the seepage flow are established. A thorough review of different regimes of seepage flow has been carried out. In order to meet the prime objective, i.e., to propose governing equations for different regimes of radial seepage flow, experiments are conducted in a converging permeameter with crushed rock and small glass balls as solid material and water as fluid media. The analysis of the experimental data is carried out in two phases. In first phase, coefficient of resistance and Reynolds number is computed using ‘volume diameter’ as ‘characteristic length’. Then expressions relating these two parameters are proposed for different regimes of flow. In second phase, hydraulic radius is used as characteristic length while defining the coefficient of resistance and Reynolds number. Then analysis is repeated as done in first phase and the corresponding equations have been proposed relating the coefficient of resistance and Reynolds number.

Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$ , captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$ , the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.

Computational analysis model of intense pulsed sintering of silver nanoparticles

Intense pulsed light sintering uses a high-power pulsed xenon lamp to release large amounts of energy and promote the growth of sintered necks between nanoparticles in additive manufacturing. However, the process results in poor stability of the sintering effect on conductive patterns and easily damages the target materials. An analysis model was developed in this study to investigate the mechanism of intense pulsed sintering. The sintering process was divided into pre-sintering and formal sintering. In pre-sintering, the conductive pattern is described by the porous volatilization model based on Darcy's fluid equation to calculate the solvent phase change volatilization state, whereas a multi-scale analysis model was established for the formal sintering process. First, a molecular dynamics model was used to analyze the sintering state of nano-silver clusters in a variable temperature field to calculate the time-varying parameters. Second, from a finite element model, the intense pulsed sintering temperature field was constructed for different sintering parameters and applied to the two-phase flow model of sintering nano-silver particles to calculate the sintering process state of nano-silver particles. The relationship between the intense pulsed sintering parameters and the sintering state was revealed, thus providing a reliable theoretical basis for the sintering process to improve sintering stability.

Virus spreading and heat spreading

Here we propose a heat transfer framework for how human-to-human interaction spreads everything on the landscape: disease, goods, knowledge, news, technology, science, language and culture. We show that the phenomenon of “human spreading” shares key features with phenomena that are fundamental in physics (heat, electricity, species, Darcy fluid flow), which spread through continua. As example for discussion and illustration, we construct this theoretical framework by using the early phase of the coronavirus outbreak, from before May 2020. The human spreading phenomenon (S curve) is unveiled systematically by using a minimum of measurable parameters: the number of persons with whom one person comes in contact, the radial size of each step in the growth of the swept territory, the radial scale of the inhabited territory, and the directions in which infrastructure (e.g., air routes) are available for long and fast spreading. The resulting configuration of spreading is a multiscale assembly of clusters of fast channels embedded in interstices with slow diffusion. The configuration is dendritic, where each direction of long and fast spreading is covered by a finger of clusters, and each finger generates its own ramifications. The similarities between this configuration and the dendritic architectures for heat and fluid flow through heterogeneous media are discussed.

Structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in [formula omitted

The structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in R2 was studied. We assumed that the viscous fluid was governed by the Boussinesq equations in Ω1, while in Ω2, we supposed that the flow satisfies the Darcy equations. Some interfacing boundary conditions are imposed. The traditional Poincare´ inequalities can’t be used. With the aid of some useful a priori bounds and some new Poincare´ inequalities, we were able to demonstrate the continuous dependence result on the interface coefficient α. The result showed that the structural stability is valid for the interfacing problem.

Structural Stability in Resonant Penetrative Convection in a Brinkman–Forchheimer Fluid Interfacing with a Darcy Fluid

Structural Stability in Resonant Penetrative Convection in a Brinkman–Forchheimer Fluid Interfacing with a Darcy Fluid

THM response of a borehole in naturally fractured media

The response of a circular borehole to a constant fluid flow rate and a temperature step-change in a coupled hydraulic-thermal-mechanical system is formulated and quantified. A new coupled formulation is developed, based on a dual-porosity model to simulate a naturally fractured stratum under non-isothermal and two-phase fluid flow conditions. The semi-analytical closed-form solutions for pore pressure, temperature and stresses including rotational displacement effects are developed by coupling an averaged conductive heat transfer process and extended single-phase Darcy fluid flow in both fracture and matrix systems. Deformations and stress changes can be induced on the bulk skeleton during a temperature change, potentially leading to shear and tensile mechanical yield. Effective stresses on the borehole wall corresponding to either fracture or shear yield initiation are calculated and explained. In a fractured medium, tensile and shear yield may initiate along the natural fractures thus take place earlier than in a continuum, displaced from the immediate borehole wall. A negative pore pressure near the wellbore may be induced during cold fluid injection when the thermally induced back flow volumes may surpass those from the injected fluid. Thus, unexpected higher effective compressive stresses may be induced on the wellbore wall, leading to yield or formation damage for the injection well. This semi-analytical development permits rapid assessment of potential fracturing initiation and shear yield to be analyzed for various cases such as injection and production in a geothermal extraction system, fluid waste disposal including CO2 sequestration, and oil and gas related EOR processes such as an initiation stage of hydraulic fracturing.

Structural stability for the Forchheimer equations interfacing with a Darcy fluid in a bounded region in mathbb{R}^{3}

The structural stability for the Forchheimer fluid interfacing with a Darcy fluid in a bounded region in mathbb{R}^{3} was studied. We assumed that the nonlinear fluid was governed by the Forchheimer equations in Omega _{1}, while in Omega _{2}, we supposed that the flow satisfies the Darcy equations. With the aid of some useful a priori bounds, we were able to demonstrate the continuous dependence results for the Forchheimer coefficient λ.

Simulation of hydraulic fracturing and Darcy fluid flow in a porous medium using a coupled Discrete Element Method with fluid flow

Studying fluid penetration of the rock matrix during fracture propagation is one of the most difficult technical challenges of hydraulic fracture engineering. To deal with this issue, a coupled hydraulic-mechanical model was performed to simulate fracture propagation during hydraulic fracturing. For this purpose, a new discrete elements approach with a force-displacement law was used for simulating the fracturing process in a flow-coupled Discrete Element Method (DEM). A series of cases was simulated to evaluate the effect of different rates of injection and permeability. Good agreement was obtained between the numerical results of this study and the reported experimental results. The results of hydraulic fracture modeling indicated that a low fluid viscosity led to wider fluid penetration and simultaneous occurrence of failure phenomenon and penetration. In the case of high viscosity, the fracture is propagated beyond the fluid penetration zone, and higher fluid pressure for fracture creation was needed than was the case for a low viscosity fluid. The results of the simulations with different permeability and low viscosity of fluid revealed that when the permeability was high, the fluid penetration was faster relative to the case with low permeability. The growth pattern of fracture in low permeability is straight and branching, but in the case of high permeability, the fracture pathway was straight and thick. The pressurization rate affected the number of cracks and the geometry of the fracture in the hydraulic fracturing model. Finally, an increase in pressurization rate resulted in an increase in the number of tensile cracks.

Continuous Dependence on the Forchheimer Coefficient of the Forchheimer Fluid Interfacing with a Darcy Fluid

The continuous dependence of the two fluids which interface with each other in a bounded domain is derived. It is first shown how to establish the a priori results for the solutions for the flow in a bounded domain occupied by a viscous fluid in contact with a porous solid. It is also proved that the solution depends continuously on the Forchheimer coefficient.

Subseafloor Cross‐Hole Tracer Experiment Reveals Hydrologic Properties, Heterogeneities, and Reactions in Slow‐Spreading Oceanic Crust

AbstractThe permeability, connectivity, and reactivity of fluid reservoirs in oceanic crust are poorly constrained, yet these reservoirs are pathways for about a quarter of the Earth's heat loss, and seawater‐rock exchange within them impact ocean chemical cycles. We present results from the second ever cross‐hole tracer experiment within oceanic crust and the first conducted during a single expedition and in slow‐spreading crust west of the Mid‐Atlantic Ridge at North Pond. Here we employed boreholes that were drilled by the Integrated Ocean Drilling Program (Sites U1382 and U1383) that were instrumented and sealed. A cesium salt solution and bottom seawater tracer experiment provided a measure of the minimum Darcy fluid velocity (2 to 41 m/day) within the upper volcanic crust, constraining the minimum permeability of 10−11 to 10−9 m2. We also document chemical heterogeneities in crustal fluid compositions, rebound from drilling disturbances, and nitrification within the basaltic crust, based on systematic differences in borehole fluid compositions over a 5‐year period. These results also show heterogeneous fluid compositions with depth in the borehole, indicating that hydrothermal circulation is not vigorous enough to homogenize the fluid composition in the upper permeable basaltic basement, at least not on the time scale of 5 years. Our work verifies the potential for future manipulative experiments to characterize hydrologic, biogeochemical, and microbial process within the upper basaltic crust.

Modelling fluid flow in complex natural fault zones: Implications for natural and human-induced earthquake nucleation

Pore fluid overpressures in active fault systems can drive fluid flow and cause fault weakening and seismicity. In return, deformation accommodated by different modes of failure (e.g. brittle vs. ductile) also affects fault zone permeability and, hence, fluid flow and pore fluid pressure distribution. Current numerical simulation techniques model how fluid flow controls fault reactivation and associated seismicity. However, the control exerted by pore fluid pressure on the transition from slow aseismic fault sliding to fast seismic sliding, during the earthquake nucleation phase, is still poorly understood. Here, we model overpressured, supercritical CO2 fluid flow in natural faults, where non-linear, complex feedback between fluid flow, fluid pressure and fault deformation controls the length of the nucleation phase of an earthquake and the duration of the interseismic period. The model setup is an analogue for recent seismic source events in the Northern Apennines of Italy (e.g. Mw 6.0 1997-98 Colfiorito and Mw 6.5 2016 Norcia earthquakes). Our modelling results of Darcy fluid flow show that the duration of the nucleation phase can be reduced by orders of magnitude, when realistic models of fault zone architecture and pore pressure- and deformation-dependent permeability are considered. In particular, earthquake nucleation phase duration can drop from more than 10 years to a few days/minutes, while the seismic moment can decrease by a factor of 6. Notably, the moment of aseismic slip (M0=109Nm) obtained during the nucleation phase modelled in our study is of the same order as the detection limit of local strain measurements using strain meters. These findings have significant implications for earthquake early warning systems, as the duration and moment of the nucleation phase will affect the likelihood of timely precursory signal detection. Interestingly, aseismic slip has been measured up to a few months before some recent large earthquakes, although in a different tectonic context than the model developed here, rekindling interest in the nucleation phase of earthquakes. In addition, our results have important implications for short and long term earthquake forecasting, as crustal fluid migration during the interseismic period may control fault strength and earthquake recurrence intervals.

Modelling combined electroosmosis–vacuum–surcharge preloading consolidation considering large-scale deformation

A numerical model, EC3, which was developed to simulate soil consolidation arising from the combined electroosmosis–vacuum–surcharge preloading processes, is presented. The EC3 model improves on its predecessor, model EC2, through incorporating the additional preloading element of vacuum and simulating the consolidation in three-dimensional (3D) space. In EC3, the 3D consolidation was simulated in polar coordinates, which allows for concurrent flows in the radial and vertical directions. The rates of the flows were formulated using the finite difference method. This method enables the model to approximate large-deformation consolidation where the deformation has yielded nonlinear changes in soil properties and nonlinear Darcy fluid flow. The performance of the model was validated against laboratory test results, and the model was applied to example problems in order to optimise the combined consolidation processes. The optimisation results suggested that the combined electroosmosis–vacuum–surcharge preloading process outperforms any two element combination processes with respect to the attained final soil layer settlement when the input parameters remain the same. The presence of a smear zone decreases the consolidation rate but increases the final settlement. The less permeable the smear zone is, the less the attained consolidation rate in the soil layer.

Numerical solutions of a 2D fluid problem coupled to a nonlinear non-local reaction-advection-diffusion problem for cell crawling migration in a discoidal domain

In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and a reaction-advection-diffusion problem. Moreover, the advection velocity depends on boundary values, making the problem nonlinear and non local. For a discoidal domain, numerical solutions can be obtained using the finite volume method on the polar formulation of the model. Simulations show that different migration behaviours can be captured.

Continuous dependence for the Brinkman–Forchheimer fluid interfacing with a Darcy fluid in a bounded domain

This paper studies the continuous dependence of the Forchheimer coefficient λ and the Brinkman coefficient μ in a bounded domain of a viscous fluid interfacing with a porous solid. We assume that the viscous fluid is slow in Ω1, and the governing equations are Brinkman–Forchheimer equations. For the porous medium in Ω2, we suppose that the flow satisfies the Darcy equations. We can get the continuous dependence results of the solutions using the method of differential inequality.

Structural stability for the Brinkman fluid interfacing with a Darcy fluid in an unbounded domain

We study the structural stability for the Brinkman fluid interfacing with a Darcy fluid in an unbounded domain. We show that the solutions depend continuously on the interface coefficient α1 by using the method of a second order differential inequality. We have never seen any paper deal with the structural stability for the interface fluids in an unbounded domain. Our method would be useful in studying the structural stability for other interface fluid equations in porous media in an unbounded domain.

A Thermo-Poro-Viscoelastic Model for the Behavior of Polymeric Porous Separators

Porous separator membranes play an important role in the long-term performance of lithium battery cells. They provide a barrier between two electrodes and enable migration of lithium ions through the pores, where lithium ions migrate through the electrolyte via diffusion-migration and reach the electrode materials. During the discharge process, the intercalation of Li ions into active materials in the electrode leads to swelling of active particles, expansion of the electrode, mechanical stresses, and compression of the separator membrane. Moreover, the extreme thermal condition lessens the performance of the separator by closing the pores through a melting process. To assess the performance of the separator under mechanical and thermal conditions, we present a thermo-poro-viscoelastic model for polymeric porous separators. We study the thermo-mechanical behavior of fully saturated porous separators through the thermo-poromechanics formulations. Two-phase mixture with solid and fluid phases is considered. Governing and balance equations are presented for the solid-fluid mixture, where the displacement of the solid skeleton, temperature and fluid pore pressure are considered as unknowns with a quasi-static loading condition. The stress-strain behavior of the polymeric separator membrane is described by a viscoelastic constitutive law in the form of convolution integral, where the thermal effects are considered through the thermal strain. The flow of the fluid through the porous medium is described by the Darcy’s law. The constitutive equation for the Darcy fluid velocity is described by the permeability of the fluid. To present more realistic physical phenomena, the hydraulic conductivity is described as a function of the porosity in the solid phase. Numerical simulations are performed to study the performance of the separator in a saturated porous medium.

A coupled discrete element model for the simulation of soil and water flow through an orifice

SummarySoil erosion around defective underground pipes can cause ground collapses and sinkholes in urban areas. Most of these soil erosion events are caused by fluidization of the surrounding soil with subsequent washing into defective sewer pipes. In this study, this soil erosion process is simplified as the gradual washout of sand particles mixed with water through an orifice. The discrete element method is used to simulate the large deformation behavior of the sand particles, and the Darcy fluid model is coupled with this approach to simulate fluid flow through porous sand media. A coupled 3D discrete element model is developed and implemented based on this scheme. To simulate previous experiments using this coupled model considering the current computing capacity, we incorporated a ‘supply layer’ to study the continuous erosion process. The coupled model can predict the erosion flow rates of sand and water and the shape of erosion void. Thus, the model can be used as an effective and efficient tool to investigate the soil erosion process around defective pipes. Copyright © 2017 John Wiley & Sons, Ltd.