Dynamics Of Porous Media Research Articles

Groundwater control and curtain grouting for tunnel construction in completely weathered granite

During tunnel construction, groundwater inrush from completely weathered granite strata is a significant challenge to geotechnical engineers. Up to the present, prevention of water inrushing hazards is almost exclusively based on the experience of engineers. This paper presents a coupled seepage–erosion water inrush model to investigate the characteristics of seepage–erosion properties. The proposed model is based on classical theories of solute transport and fluid dynamics in porous media. In the model, changes of porosity link permeability with the accumulation of particle loss in the seepage–erosion process. The coupled seepage–erosion model was applied to examine the influence of curtain grouting thickness on the seepage–erosion process. The results showed that the seepage–erosion process was attenuated as thickness increased. The results also showed that the porosity and permeability visibly changed and the water inflow clearly exceeded the acceptable engineering criterion when the thickness was less than 6 m. However, with a further increase in thickness, the seepage–erosion process was suppressed and little changes of the relative parameters were showed. The numerical results demonstrated that a curtain grouting thickness of 6 m was suitable for curtain grouting in completely weathered granite. Field investigation of Cenxi tunnel verified the effectiveness of the thickness determined by the proposed model.

Mathematical model of one-dimensional penetration stability failure for gaseous coal

Based on the theory of fluid dynamics in porous media, combined with the gas state equation, Darcy's law and the discriminant equation of one-dimensional seepage instability, a mathematical model of one-dimensional penetration stability failure is established to study the seepage damage law of coal seam. Assuming that the background pressure of the coal wall is attenuated according to the exponential law, the mathematical equation is solved by using the finite difference method. Furthermore, the process of coal bed instability which is supposed as a form of a 'sublayer' pushing forward was analysed. That is, the coal bed loses its stability layer by layer. The calculation results showed that the thickness of the failure sublayer decreases with the reduction of coal permeability and the acceleration of dissipation rate of the background pressure. The model provides a method which can analyse the outburst process and its intensity quantitatively.

Prediction of coal mine goaf self-heating with fluid dynamics in porous media

Coal mine goaf self-heating due to exothermic coal oxidation has been recognized as a major threat to coal mine safety. To evaluate the risk of the coal mine goaf self-heating hazard, both gas distribution characteristics in goaf and heat transfer mechanisms in porous media must be studied. However, due to the difficulty of determining goaf permeability and the complexity of the overlaying strata caving characteristics, it is a considerable challenge to determine the thermal-fluid field coupling. Based on the volumetric average method in porous media, this work develops three numerical models for solving fluid dynamics and heat transfer in both longwall face and goaf. The Brinkman-Forchheimer-extended Darcy model is introduced to describe inertia and frictional forces in fluid phase exerted by solid phase. Temperature profile is highly dependent on and affects coal oxidation rate; therefore, governing equations for energy and oxygen mass equilibrium must be coupled. A two-dimensional goaf permeability distribution model is established based on different caving conditions in goafs. Three scenarios are simulated and validated by field and experimental data, and it is observed that these models are capable of predicting gas flow pattern and temperature distribution.

Evaporation Limited Radial Capillary Penetration in Porous Media.

The capillary penetration of fluids in thin porous layers is of fundamental interest in nature and various industrial applications. When capillary flows occur in porous media, the extent of penetration is known to increase with the square root of time following the Lucas-Washburn law. In practice, volatile liquid evaporates at the surface of porous media, which restricts penetration to a limited region. In this work, on the basis of Darcy's law and mass conservation, a general theoretical model is developed for the evaporation-limited radial capillary penetration in porous media. The presented model predicts that evaporation decreases the rate of fluid penetration and limits it to a critical radius. Furthermore, we construct a unified phase diagram that describes the limited penetration in an annular porous medium, in which the boundaries of outward and inward liquid are predicted quantitatively. It is expected that the proposed theoretical model will advance the understanding of penetration dynamics in porous media and facilitate the design of engineered porous architectures.

Influence of Parameterization of Soil Processes on Meteorological Forecasts of Vertical Profiles

Abstract Soil and atmosphere boundary layer (ABL) interact with each other and influence physical processes in soil and atmosphere. Quality of numerical weather forecast depends on good mapping of complex soil process (microphysics processes in soil, fluid dynamics in porous media, soil dynamics, water cycle in soil and soil-plant-water relation, thermal processes in the soil etc.) in parameterization soil schemes. Current parameterizations of soil physical processes in TERRA_ML (multilayer soil module of the COSMO meteorological model) were prepared 30 years ago for numerical model with poor resolution. Nowadays operationally numerical models work with much better resolution. So, previous parameterization must have been improved or prepared from the beginning if it is expected improvement quality of numerical weather forecast. The influence of changing parameterization of water flux through the soil for “bare soil” case on vertical meteorological profiles is presented in this paper. This influence can be seen not only in weather forecasts, but also in any areas where the results of meteorological model(s) are used, like decision support systems in emergency situations or modeling of dispersion of air pollutants.

Fluid dynamics in porous media with Sailfish

In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through them in order to calculate their permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualise these concepts, we analyse the applicability of the Kozeny–Carman equation, which is a well-known permeability–porosity relation, to our artificial samples.

A Fractional Generalised Finite Difference Method to Linear Porous Media Dynamics

The generalised finite difference method (GFDM) is a mesh-free method for solving partial differential equations (PDEs) in non-structured grids. Due to its strong theoretical background and simplicity, hence efficiency, it has been introduced to handle interesting and sophisticate engineering problems. However, the GFDM has not been applied to problems associated to dynamics of porous media yet. In these problems, the strong coupling between solid displacements and liquid pressures may cause large numerical oscillations if equal order interpolation functions are used for both variables. Nevertheless, some fractional steps techniques can be introduced in order to minimise these problems. In this contribution, a fractional steps scheme is developed and applied to the GFDM in order to model fully saturated porous media dynamics. Simulations of 1D and 2D wave propagation are performed in order to reveal the advantages, drawbacks and capabilities of the proposed method.

Non-splat singularity for the one-phase Muskat problem

For the water wave equations, the existence of splat singularities has been shown, i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media.

FDM and FEM solutions to linear dynamics of porous media: stabilised, monolithic and fractional schemes

SummaryA number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf‐sup (Ladyženskaja‐Babuška‐Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so‐called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes. Copyright © 2016 John Wiley & Sons, Ltd.

Modelling of chemical grout column permeated by water in transparent soil

The process of injecting chemical grout into cohesionless soil and its permeation by water are simulated by using a transparent soil model and a finite element model (FEM). The urea-formaldehyde resin is used as the grouting material in the transparent soil modelling. Two black and white charge-coupled device cameras are mounted in an orthogonal position to provide a three dimensional view of the groundwater-grout interface. The groundwater-grout interface is primarily influenced by the advection of the flowing water with increasing distance from the injection point owing to the reduction in the grouting pressure. An equation based on fluid dynamics in porous media and Darcy's law is then proposed to predict the displacement of the groundwater-grout interface in flowing water. A numerical model based on the FEM is also developed to simulate this process. The numerical simulation results are found to match the physical modelling well.

Combining effective media and multi-phase methods of Lattice Boltzmann modelling for the characterisation of liquid-vapour dynamics in multi-length scale heterogeneous structural materials

The combination of the lattice Boltzmann Shan-Chen pseudo-potential method for multiphase fluids (Shan and Chen 1993 Phys. Rev. E 47 1815) and a grey or partial bounce back lattice Boltzmann algorithm for effective media (Walsh et al 2009 Comput. Geosci. 35 1186), is demonstrated for application to liquid-vapour fluid dynamics in porous media with porosity spanning a very wide range of length scales. Liquid / vapour distributions in cellular like structures with cell walls of reduced permeability are seen to follow expectation.

Modified Description of Soil Processes vs. Quality of Numerical Weather Forecasts - “Bare Soil” Case

Abstract Soil and atmosphere boundary layer (ABL) interact with each other and influence on physical processes in soil and atmosphere. Current parameterization of soil physical processes in TERRA_ML (multilayer soil module of COSMO meteorological model) was prepared more than 40 years ago and did not give satisfactory forecast results. New parameterizations should involve physical processes in the soil (microphysics processes in soil, fluid dynamics in porous media, soil dynamics, etc.), water cycle in soil and soil-plant-water relation. The aim of this project was to improve current soil parameterization in the COSMO model, called “TERRA_ML”. The results of the work, related to the parameterization of physical processes of bare soil evaporation, vertical and horizontal water transport in soil and a runoff from soil layers, are presented in this paper. In order to eliminate underestimation of evaporation from soil in the afternoon and overestimation evaporation from soil in the morning a correction time-depending factor was also introduced. In this way, theoretical description of vertical water transport in soil is improved with temperature dependency of hydraulic diffusivity for different sort of soil.

Experimental analysis of spatial correlation effects on capillary trapping of supercritical CO2 at the intermediate laboratory scale in heterogeneous porous media

AbstractSeveral numerical studies have demonstrated that the heterogeneous nature of typical sedimentary formations can favorably dampen the accumulation of mobile CO2 phase underneath the caprock. Core flooding experiments have also shown that contrasts in capillary entry pressure can lead to buildup of nonwetting fluid phase (NWP) at interfaces between facies. Explicit representation of geological heterogeneity at the intermediate (cm‐to‐m) scale is a powerful approach to identify the key mechanisms that control multiphase flow dynamics in porous media. The ability to carefully control flow regime and permeability contrast at a scale that is relevant to CO2 plume dynamics in saline formations offers valuable information to understand immiscible displacement processes and provides a benchmark for mathematical models. To provide insight into the impact of capillary heterogeneity on flow dynamics and trapping efficiency of supercritical CO2 under successive drainage and imbibition conditions, we present an experimental investigation conducted in a synthetic sand reservoir. By mimicking the interplay of governing forces at reservoir conditions via application of surrogate fluids, we performed three immiscible displacement experiments to observe the entrapment of NWP in heterogeneous porous media. Capillary trapping performance is evaluated for each scenario through spatial and temporal variations of NWP saturation; for this reason we adopted X‐ray attenuation to precisely measure phase saturation throughout the flow domain and apply spatial moment analysis. The sweeping performance of two different permeability fields with comparable variance but distinct spatial correlation was compared against a homogeneous base case with equivalent mean permeability by means of spatial moment analysis.

Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition

We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion–reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes–Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation.

Testing a simple model of gas bubble dynamics in porous media

AbstractBubble dynamics in porous media are of great importance in industrial and natural systems. Of particular significance is the impact that bubble‐related emissions (ebullition) of greenhouse gases from porous media could have on global climate (e.g., wetland methane emissions). Thus, predictions of future changes in bubble storage, movement, and ebullition from porous media are needed. Methods exist to predict ebullition using numerical models, but all existing models are limited in scale (spatial and temporal) by high computational demands or represent porous media simplistically. A suitable model is needed to simulate ebullition at scales beyond individual pores or relatively small collections (<10−4 m3) of connected pores. Here we present a cellular automaton model of bubbles in porous media that addresses this need. The model is computationally efficient, and could be applied over large spatial and temporal extent without sacrificing fine‐scale detail. We test this cellular automaton model against a physical model and find a good correspondence in bubble storage, bubble size, and ebullition between both models. It was found that porous media heterogeneity alone can have a strong effect on ebullition. Furthermore, results from both models suggest that the frequency distributions of number of ebullition events per time and the magnitude of bubble loss are strongly right skewed, which partly explains the difficulty in interpreting ebullition events from natural systems.

Imaging methane hydrates growth dynamics in porous media using synchrotron X‐ray computed microtomography

AbstractCommercial‐scale methane (CH4) extraction from natural hydrate deposits remains a challenge due to, among other factors, a poor understanding of hydrate‐host sediment interactions under low‐temperature and high‐pressure conditions that are conducive to their existence. We report the use of synchrotron X‐ray computed microtomography (CMT) to image, for the first time, time‐resolved pore‐scale methane CH4 hydrate growth from an aqueous solution containing 5 wt % barium chloride (BaCl2) and pressurized CH4 hosted in glass beads, all contained in an aluminum cell with an effective volume of 3.5 mL. Multiple two‐dimensional (2‐D) cross‐sectional images show CH4 hydrates, with 7.5 µm resolution, distributed in patches throughout the system without dependence on distance from the cell walls. The time‐resolved three‐dimensional (3‐D) images, constructed from the 2‐D slices, exhibited pore‐filling hydrate formation from dissolved CH4 gas, similar to natural CH4 hydrates (sI) in the marine environment. Furthermore, the 3‐D images show that the aqueous phase was the wetting phase of the glass beads, i.e., the host and the formed hydrate were separated by an aqueous layer. These results provide some fundamental understanding of the nucleation phenomenon of gas hydrate formation at the pore scale. Pore‐filling CH4 hydrate growth is likely to result in a reduced bulk modulus, and thus, could affect seafloor stability during the reverse phenomenon, i.e., dissociation of natural hydrate deposits.

A comparison of a fractional derivative model with an empirical model for non-linear shock waves in swelling shales

Abstract The control of drilling parameters, such as fluid pressure, mud weight, salt concentration, etc., is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, which is fundamental for deep oil drilling and hydraulic fracturing for gas extraction (“fracking”), a non-linear model of mechanical and chemo-poroelastic interactions among fluids, solutes and the solid matrix is discussed here. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid-saturated porous rock. If the non-linear term in these equations is larger than the diffusive term the solutions are quick, non-linear Burgers solitary waves, which are potentially destructive for deep operations. In our study the role of diffusion in presence of these solitary waves has been also analyzed. Then, following Civan (1998) , both diffusive and shock waves are applied to fine particle filtration and their effects on the adjacent rocks. Finally, the resulting time-delayed evolution is discussed. Because time delays in simple porous media dynamics have recently been analysed using a fractional derivative approach, we insert fractional time derivatives, i.e., a type of time-average of the fluid-rock interactions, to make a tentative comparison of these two deeply different methods in our model. The delaying effects of fine particle filtration a la Civan (1998) are then compared with the time delay of the fractional derivative model; thus, the fractional derivative order for this filtration is realistically estimated. Such a comparison can be seen as a heuristic determination of “natural” time averages for fine particle related phenomena in this model.

A consistent u‐p formulation for porous media with hysteresis

SummaryThis paper presents a continuum formulation based on the theory of porous media for the mechanics of liquid unsaturated porous media. The hysteresis of the liquid retention model is carefully modelled, including the derivation of the corresponding consistent tangent moduli. The quadratic convergence of Newton's method for solving the highly nonlinear system with an implicit finite element code is demonstrated. A u‐p formulation is proposed where the time discretisation is carried out prior to the space discretisation. In this way, the derivation of all consistent moduli is fairly straightforward. Time integration is approximated with the Theta and Newmark's methods, and hence the fully coupled nonlinear dynamics of porous media is considered. It is shown that the liquid retention model requires also the consistent second‐order derivative for quadratic convergence. Some predictive simulations are presented illustrating the capabilities of the formulation, in particular to the modelling of complex porous media behaviour. Copyright © 2014 John Wiley & Sons, Ltd.

Drying by cavitation and poroelastic relaxations in porous media with macroscopic pores connected by nanoscale throats.

We investigate the drying dynamics of porous media with two pore diameters separated by several orders of magnitude. Nanometer-sized pores at the edge of our samples prevent air entry, while drying proceeds by heterogeneous nucleation of vapor bubbles--cavitation--in the liquid in micrometer-sized voids within the sample. We show that the dynamics of cavitation and drying are set by the interplay of the deterministic poroelastic mass transport in the porous medium and the stochastic nucleation process. Spatiotemporal patterns emerge in this unusual reaction-diffusion system, with temporal oscillations in the drying rate and variable roughness of the drying front.

Semianalytical Solution to the Wave-Induced Dynamic Response of Saturated Layered Porous Media

AbstractThis paper proposes a semianalytical solution to the dynamic response of saturated-layered porous media under harmonic waves. The equations governing the dynamics of porous media are written in their fully dynamic form and possible simplifications are introduced based on the presence of inertial terms associated with both solid and fluid phases, called formulations. The semianalytical solutions to the response of multiple layers with various physical properties are presented in terms of normalized pore pressure and shear stress variations considering a set of nondimensional parameters and their respective ratios. The effects of layering and inertial terms on the response are also presented.